MODELING, STABILITY ANALYSIS AND CONTROL OF …eprints.qut.edu.au/37670/1/Ritwik_Majumder_Thesis.pdf · MODELING, STABILITY ANALYSIS ... interconnection of the DG to the utility/grid

MODELING, STABILITY ANALYSIS AND CONTROL OF MICROGRID.

A Thesis submitted in Partial Fulfilment of the Requirement for the

Degree of

Doctor of Philosophy

Ritwik Majumder

M.Sc (Engg), B.E (Electrical engineering)

Faulty of Build and Environment Engineering

School of Engineering Systems

Queensland University of Technology

Queensland, Australia

February 2010

KEYWORDS

Microgrid Distributed Generators Islanding Resynchronization Voltage Source Converter Converter Structure and Control Voltage Control State Feedback Control Power Sharing Droop Control Frequency Droop Angle Droop Power Quality Back to Back Converters Stability Rural Distributed Generation Modified Droop Control Web Based Communication

ABSTRACT

With the increase in the level of global warming, renewable energy based

distributed generators (DGs) will increasingly play a dominant role in electricity

production. Distributed generation based on solar energy (photovoltaic and solar

thermal), wind, biomass, mini-hydro along with use of fuel cells and micro turbines

will gain considerable momentum in the near future. A microgrid consists of clusters

of load and distributed generators that operate as a single controllable system. The

interconnection of the DG to the utility/grid through power electronic converters has

raised concern about safe operation and protection of the equipments.

Many innovative control techniques have been used for enhancing the

stability of microgrid as for proper load sharing. The most common method is the use

of droop characteristics for decentralized load sharing. Parallel converters have been

controlled to deliver desired real power (and reactive power) to the system. Local

signals are used as feedback to control converters, since in a real system, the distance

between the converters may make the inter-communication impractical. The real and

reactive power sharing can be achieved by controlling two independent quantities,

frequency and fundamental voltage magnitude.

In this thesis, an angle droop controller is proposed to share power amongst

converter interfaced DGs in a microgrid. As the angle of the output voltage can be

changed instantaneously in a voltage source converter (VSC), controlling the angle

to control the real power is always beneficial for quick attainment of steady state.

Thus in converter based DGs, load sharing can be performed by drooping the

converter output voltage magnitude and its angle instead of frequency. The angle

control results in much lesser frequency variation compared to that with frequency

droop.

An enhanced frequency droop controller is proposed for better dynamic

response and smooth transition between grid connected and islanded modes of

operation. A modular controller structure with modified control loop is proposed for

better load sharing between the parallel connected converters in a distributed

generation system. Moreover, a method for smooth transition between grid

connected and islanded modes is proposed.

Power quality enhanced operation of a microgrid in presence of unbalanced

and non-linear loads is also addressed in which the DGs act as compensators. The

compensator can perform load balancing, harmonic compensation and reactive

power control while supplying real power to the grid

A frequency and voltage isolation technique between microgrid and utility is

proposed by using a back-to-back converter. As utility and microgrid are totally

isolated, the voltage or frequency fluctuations in the utility side do not affect the

microgrid loads and vice versa. Another advantage of this scheme is that a

bidirectional regulated power flow can be achieved by the back-to-back converter

structure.

For accurate load sharing, the droop gains have to be high, which has the

potential of making the system unstable. Therefore the choice of droop gains is often

a tradeoff between power sharing and stability. To improve this situation, a

supplementary droop controller is proposed. A small signal model of the system is

developed, based on which the parameters of the supplementary controller are

designed.

Two methods are proposed for load sharing in an autonomous microgrid in

rural network with high R/X ratio lines. The first method proposes power sharing

without any communication between the DGs. The feedback quantities and the gain

matrixes are transformed with a transformation matrix based on the line R/X ratio.

The second method involves minimal communication among the DGs. The converter

output voltage angle reference is modified based on the active and reactive power

flow in the line connected at point of common coupling (PCC). It is shown that a

more economical and proper power sharing solution is possible with the web based

communication of the power flow quantities.

All the proposed methods are verified through PSCAD simulations. The

converters are modeled with IGBT switches and anti parallel diodes with associated

snubber circuits. All the rotating machines are modeled in detail including their

dynamics.

CONTENTS

List of Figures xv

List of Tables xix

List of Principle Symbols xxi

1 Introduction 1 1.1 Power Sharing In Distributed Generation 2

1.2 Microgrid And Its Autonomous Control 2

1.2.1 Controls for Grid and Island Operation 4

1.3 Power Quality And Reliability 4

1.4 System Stability 6

1.5 Power Sharing In Rural Network 7

1.6 Objectives of the Thesis and Specific Contributions 8

1.6.1 Objectives of the Thesis 8

1.6.2 Specific Contributions of the Thesis 9

1.7 Thesis Organization 10

2 Power Sharing with Converter Interfaced Sources 13 2.1 Control Of Parallel Converters For Load Sharing With

Frequency Droop 13

2.1.1 Frequency Control 14

2.1.2 Modular Control Structure 14

2.1.3 Converter Voltage Angle Calculation 15

2.1.4 Reference Generation 15

2.2 Angle Droop Control 17

2.2.1 Angle Droop Control And Power Sharing 18

2.3 Angle Droop And Frequency Droop Controller 20

2.4 Simulation Studies 22 2.4.1 Frequency Droop Controller 22

2.4.2 Angle Droop Controller 23 2.4.3 Comparison Of Frequency Droop And Angle Droop 23 2.4.4 Angle Droop In Multi DG System 25

2.5 Conclusions 27

3 Load Frequency Control in Microgrid 28 3.1 Seamless Transfer between Grid Connected and Islanded Modes 28 3.2 Proposed Control 29

3.3 Simulation Studies 30

x

3.3.1 Islanded Mode 30

3.3.2 Grid Connected Mode 32

3.3.3 Seamless Transfer Between Grid Connected

and Islanded Modes 33

3.4 Microgrid with Inertial and Non Inertial DGs 37

3.4.1 System Structure 38

3.4.2 Micro Source Model 38

3.4.2.1 Fuel Cell 38

3.4.2.2 Photo Voltaic Cell (PV) 39

3.4.2.3 Battery 39

3.4.3 Simulation Studies 40

3.4.3.1 Case 1: Grid Connected and Autonomous Operating Modes 40

3.4.3.2 Case 2: Power Sharing In Autonomous Mode 40

3.4.3.3 Case 3: Source Inertia And System Damping 41

3.5 Conclusions 42

4 Power Quality Enhanced Operation of a Microgrid 44 4.1 System Structure 45

4.2 Reference Generation And Compensator Control 46

4.2.1 Compensator Reference Generation in Grid

Connected Mode 46

4.2.2 Compensator Control 50

4.2.3 Compensator Reference Generation in Islanded Mode 51

4.2.4 DG Coordination for Sharing the Common Load 52


4.3.1 Sharing the Local Load with Utility 54

4.3.2 Sharing the Common Load by The DGs 56

4.3.3 Sharing a Common Induction Motor Load 57

4.3.4 DG-1 Supplying the Entire Common Load during Islanding 58

4.4 Discussions 59

4.5 Conclusions 60

5 Power Flow Control with Back-to Back Converters in a Utility Connected Microgrid 65 5.1 System Structure and Operation 65

5.2 Converter Structure And Control 68

5.3 Back-To-Back Converter Reference Generation 68

5.3.1 VSC-1 Reference Generation 68

xi

5.3.2 VSC-2 Reference Generation in Mode-1 69

5.3.3 VSC-2 Reference Generation in Mode-2 69

5.4 Reference Generation for DG Sources 70

5.4.1 Mode-1 70

5.4.2 Mode-2 71

5.5 Relay and Circuit Breaker Coordination during Islanding and Resynchronization 72


5.6.1 Case-1: Load Sharing of the DGs with Utility 74

5.6.2 Case-2: Change in Power Supply from Utility 76

5.6.3 Case-3: Power Supply from Microgrid to Utility 77

5.6.4 Case-4: Load Sharing with Motor Load 78

5.6.5 Case-5: Change in Utility Voltage and Frequency 79

5.6.6 Case-6: Islanding and Resynchronization 81

5.6.7 Case-7: Variable Power Supply from Utility 81

5.6.8 Case-8: DC Voltage Fluctuation and Loss of A DG 83

5.7 Microgrid Containing Multiple DGs 84

5.8 Conclusions 85

6 Stability Analysis of Multiple Converter Based Autonomous Microgrid 87 6.1 Converter Structure and Control 87

6.2 Droop Control and DG Reference Generation 88

6.2.1 Droop Control 88

6.2.2 DG Reference Generation 88

6.3 State Space Model of Autonomous Microgrid 89

6.3.1 Converter Model 90

6.3.2 Droop Controller 93

6.3.3 Combined Converter-Droop Control Model 94

6.3.4 Transformation to Common Reference Frame 95

6.3.5 Network and Load Modeling 97

6.3.6 Complete Microgrid Model 98

6.4 System Structure and Model of Autonomous Microgrid Example 99

6.5 Eigenvalue Analysis of Microgrid 101


6.6.1 Case 1: Full System of Fig. 6.2 (3 DG And 3 Loads) 105

6.6.2 Case 2: The Effect of System Reduction 105

6.7 Improvement in Stability with Supplementary Droop Control 107

6.7.1 Test System 110

6.7.2 Simulation Studies with Supplementary Droop Controller 110

xii

6.7.2.1 Case 1: Full System Of Fig. 6 With Lower Droop Gains 110

6.7.2.2 Case 2: Reduced System with Lower Droop Gains 111

6.7.2.3 Case 3: System Stability with High Droop Gain 112

6.7.2.4 Case 4: Power Sharing with The Proposed Supplementary Controller 113

6.7.2.5 Case 5: Power Sharing with the Proposed Controller in Reduced System 113

6.8 Conclusions 115

7 Droop Control of Converter Interfaced Micro Sources in Rural Distributed Generation 117 7.1 Power Sharing with Angle Droop and Proposed Droop Control 117

7.1.1 Proposed Controller-1 without Communication 119

7.1.2 Proposed Controller-2 with Minimum Communication 121

7.1.3 Multiple DG System 122

7.1.4 Web Based Communication 124

7.2 Converter Structure and Control 125

7.2.1 Converter Control 125

7.2.2 DG Reference Generation 126


7.3.1 Case 1: Load_3 and Load_4 Connected to Microgrid 128

7.3.2 Case 2: DG-1 and DG-3 Supply Load_1 and Load_2 130

7.3.3 Case 3: Induction Motor Loads 131

7.3.4 Case 4: Load Sharing with Advanced Communication System 132

7.3.5 Case 5: Load Sharing with Conventional Droop Controller 133

7.3.6 Case 6: Load Sharing With Conventional Droop Controller 134

7.4 Conclusions 134

8 Conclusions 137 8.1 General Conclusions 137

8.2 Scope for Future Work 138

Appendix-A: Converter Structure and Control 139 A.1 Converter Structure 139

A.2 Converter Control 139

A.3 Output Feedback Voltage Controller 140

A.4 State Feedback Controller 142

Appendix-B: List of Publication 145

xiii

References 149

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xv

LIST OF FIGURES

2.1. Microgrid system under consideration

2.2. The modular control structure

2.3. Voltage angle control loop

2.4. Converter structure

2.5. Equivalent circuit of one phase of the converter

2.6. Source angle extraction from rotating angle

2.7 DG connection to microgrid

2.8 System stability as function of frequency droop gain

2.9 System stability as function of angle droop gain

2.10 DG power output with frequency droop control

2.11 DG power output with angle droop control

2.12 Frequency variation with frequency droop control

2.13 Frequency variation with angle droop control

2.14 Angle variation with angle droop control

2.15 Microgrid Structure with multiple DGs

2.16 Real Power Sharing of the DGs

2.17 Real Power Sharing of the DG-1 and DG-4

3.1 Microgrid system under consideration

3.2 System response with impedance load in islanded mode

3.3 System response with motor load in islanded mode

3.4 System response with impedance load in grid connected mode

3.5 System response with induction motor load in grid connected mode

3.6 System response with synchronous motor load in grid connected mode

3.7 System response during islanding and resynchronization with impedance load

3.8 PCC voltage during islanding and resynchronization with impedance load

3.9 System response during islanding and resynchronization with motor load

3.10 PCC voltage during islanding and resynchronization with motor load

3.11 DG connection to microgrid

3.12 Microgrid system

3.13 Single-phase equivalent circuit of VSC

3.14 System stability as function of frequency droop gain

3.5 System stability as function of angle droop gain

3.6 DG power output with angle droop control

3.7 Frequency variation with angle droop control

3.8 DG power output with frequency droop control

3.9 Frequency variation with frequency droop control

3.10. Microgrid structure under consideration

3.11 Fuel cell modeled equivalent circuit

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3.12 Equivalent circuit of PV and boost chopper based on MPPT

3.13 MPPT control flowchart for PV

3.14 Islanding and resynchronization

3.15 Real power sharing of the DGs

3.16 Current output of the micro sources



4.1 The microgrid and utility system under consideration

4.2 Equivalent circuit of one phase of the converter

4.3 Real and reactive power sharing in DG-1and DG-2

4.4 Voltages at the PCC1 and PCC2

4.5 Power sharing and DG-1current and PCC1 voltages

4.6 Real power sharing by DG-1 and DG-2

4.7 Common load sharing between DG-1 and DG-2

4.8 Real power sharing of the DGs and voltages at PCC1 and PCC2

4.9 Microgrid structure with large number of DGs and loads

5.1 The microgrid and utility system under consideration

5.2 Angle controller for VSC-1

5.3 Schematic diagram of VSC-2 connection to microgrid

5.4 Power flow from DG-1 to microgrid

5.5 Logic for breaker operation and converter blocking

5.6 Breakers and converter blocking timing diagram

5.7 Real and reactive power sharing for Case-1

5.8 Voltage tracking of DG-1 Case-1.

5.9 Capacitor voltage and angle controller output for Case-1

5.10 Real and reactive power sharing for Case-2

5.11 Three phase PCC voltage and injected current for Case-2

5.12 Real and reactive power sharing during power reversal (Case-3)

5.13 PCC voltage and injected current for Case-3

5.14 Real and reactive power sharing with motor load (Case-4)

5.15 Real and reactive power during frequency fluctuation (Case-5)

5.16 Real and reactive power during voltage sag (Case-5)

5.17 DC capacitor voltage and angle controller output during voltage sag

5.18 Location of the single line to ground fault

5.19 DC capacitor voltage and angle controller output during islanding and resynchronization (Case-6)

5.20 Real and reactive power during islanding and resynchronization (Case-6)

5.21 Real power sharing during power limit and mode change (Case-7)

5.22 DC voltage fluctuation in DG-1 and its tripping (Case-8)

5.23 Microgrid structure with large number of DGs and loads

xvii

5.24 Real power sharing with four DGs

6.1 Interconnection diagram of the complete microgrid system


6.3 Eigenvalues for nominal operating condition

6.4 Eigenvalue locus with real power droop gain change

6.5 Eigenvalue locus with reactive power droop gain change

6.6 Eigenvalue locus without DG-3

6.7. Real and reactive power during a change in load 1

6.8 Unstable operation with m = 8.18×10−5 rad/W

6.9 Marginally stable operation with n = 2.5×10−3 V/VAr

6.10 System response 3 and 2 DGs for m = 6.18×10−5 rad/W

6.11 System response for different system configuration

6.12 . Supplementary Droop Controller Configuration

6.13 Supplementary controller structure


6.15 Real and reactive power during a change in load 1

6.16 Power sharing with reduced system

6.17 System stability with high droop gain

6.18 Power sharing with proposed controller

6.19 Droop controller and supplementary controller output

6.20 System response for different system configuration

6.21 Power sharing in reduced system

7.1 Power sharing with angle droop

7.2 Power sharing in resistive-inductive line

7.3 Multiple DG connected to microgrid

7.4 (a) Web based PQ monitoring scheme and (b) web based communication for DG-1

7.5 Power sharing with conventional controller (Case 1)

7.6 Power sharing with Controller-1 (Case 1)

7.7 Power sharing with Cntroller-2 (Case 1)







7.14 Power sharing with high bandwidth communication (Case 4)

7.15 Error in power sharing with different control techniques

7.16 Frequency droop and angle droop

7.17. Power sharing with frequency droop Case 1

7.18. Frequency dependent load

xviii

xix

LIST OF TABLES

2.1 System and Controller Parameters

2.2 Microgrid System and Controller Parameters

3.1 System Parameters

4.1 System Parameters

4.2 Numerical Results

5.1 System and controller parameters

6.1 Nominal System Parameters

6.2 Mode participation factors

6.3 Parameters of the supplementary droop control loop



7.2 Simulation Results

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LIST OF PRINCIPLE SYMBOLS vsa, vsb, vsc Source voltages of phases a, b, and c respectively

isa, isb, isc Source current of phases a, b, and c respectively

vPCCa, vPCCb, vPCCC PCC voltages of phases a, b, and c respectively

i1a, i1b, isc Converter current of phases a, b, and c respectively

Rs, Ls Feeder resistance and inductance respectively in utility

XD Line reactance

RD Line resistance

Cf Filter capacitance

L1, L2, L3 Filter inductance

Lf Transformer leakage reactance

Rf Transformer and VSC losses

VDC1, VDC2, VDC3 DC voltage source of the Distributed Generators

u Converter switching function

ωs Synchronous frequency

V Magnitude of converter output voltage

Angle of converter output voltage

VP Magnitude of PCC voltage

P Angle of PCC voltage

vcf Voltage across filter Capacitor

icf Current through filter Capacitor

ω Operating frequency

ωS Cut off frequency of low pass filter

P1, P2 Real power injected by DGs to microgrid

Q1, Q2 Reactive power injected by DGs to microgrid

Prated, Qrated Real and reactive power rating of the DG

Pg Real power injected by utility to microgrid

Qg Reactive power injected by utility to microgrid

PL, QL Real and reactive load power

PLC, QLC Real and reactive power of common load

1P, 1Q Real and reactive power sharing ratio with utility

m, n Droop coefficients

K State feedback controller gain

S, R Polynomials in pole shift controller

Pole shift factor

Z-1 Delay operator

h Hysteresis band

KP, KI Proportional and integral gain constant

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STATEMENT OF ORIGINAL AUTHORSHIP

The work contained in this thesis has not been previously submitted to meet requirements for an award at this or any other higher education institution. To the best of my knowledge and belief, the thesis contains no material previously published or written except where due reference is made.

Signature ___ ______________________________ Date________________06.06.2010_______________

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ACKNOWLEDGEMENT

First and foremost I offer my gratitude to my supervisors, Prof. Arindam Ghosh, Prof. Gerard Ledwich and A/Prof. Firuz Zare, who have supported me throughout my doctoral research. It was a great honor for me to pursue my research under their supervision.

I would like to thank Australia for giving me the opportunity of doctoral research here. I thank Queensland University of Technology and Australia Research Council (ARC) for the financial support.

I thank Saikat da, Rajat, Sachin, Ali, Arash, Jaffar, Manjula and all for the technical and much needed non technical discussions. Rajat gave me a warm welcome to Australia and without his presence, this Ph.d in QUT would not have started.

With many other staff in QUT, I would like to thank our research office (Diane and her team), theme coordinator (Christine), School Office (Noelene) for all the support and help.

Life has been always bigger than science. I thank Kie for showing me the power of simplicity and honesty in life. I thank my parents for their support and unconditional love.

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1

CHAPTER 1

The concern for climate change is driving major changes in electricity generation and

consumption patterns. Various countries have set a target of 20 % greenhouse gas reduction by the

year 2020.

Large scale changes in both transmission and distribution levels are expected to occur in the

near future. Transmission systems will be bolstered to transmit power generated from large windfarm,

geothermal and solar thermal generations.

In distribution levels, many smaller renewable generators (e.g. photovoltaic, fuel cells, micro

hydro etc.) will be connected to the networks. These are called distributed generators (DGs) or

distributed energy resources (DERS). Their integration into distributions systems disturbs the radial

nature of power flow through distribution feeders.

The interconnection of DG to the utility/grid through power electronic converters has raised

concern about safety and protection. IEEE P1547 standard [1] provides the technical requirement for

the interconnection of the distributed resources (DR) units to the electric power system. The current

IEEE recommended industry practice is to isolate all distributed energy resources (DERs, e.g., PV and

wind) from the grid in the event of a fault in the grid. This approach is adequate when the total

capacity of the DERs is not significant and they can be removed without major impact on the system.

However it is expected that the penetration level of grid-connected DERs will increase substantially

over the next few decades. In addition, the number of Plug-in Hybrid Electric Vehicles (PHEVs) will

increase in the near future and microgrids will become popular in rural communities and commercial

buildings. The cumulative effect of these innovations will be a change in the power flow patterns in

power distribution systems.

1.1 MICROGRID AND DISTRIBUTED GENERATION

A microgrid is a cluster of loads and microsources operating as a single controllable system that

provides power to its local area. To the utility, the microgrid can be thought of as a single controllable

load that can respond in seconds to meet the needs of the transmission system. To the customer, the

microgrid can meet their special needs; such as, enhancing local reliability, reducing feeder losses,

2

supporting local voltages, providing increased efficiency through the use of waste heat, voltage sag

correction or providing uninterruptible power supply functions to name a few [2]. In ref [3], the focus

is on systems of distributed resources that can switch from grid connection to island operation without

causing problems for critical loads. Different microgrid control strategy and power management

techniques are discussed in [4-8] Premium power is a concept based on the use of power electronic

equipment (such as custom power devices and active filters), multi utility feeders and uninterruptible

power supplies to provide power to users having sensitive loads. This power must have a higher level

of reliability and power quality than normally supplied by the utility. These technologies require

power electronics to interface with the power network and its loads. In many of the cases, there is a dc

voltage source (e.g. PV), which must be converted to an ac voltage at the required frequency,

magnitude and phase angle. In these cases, the conversion will be performed using a voltage source

converter, using a possible pulse width modulation to provide fast control of voltage magnitude. The

reliability, economic operations and planning of microgrid are investigated in [9-11]. Some of the

basic issues that need to be addressed are:

• Control: A major issue in distributed generation is the technical difficulties related to control

of a significant number of microsources.

• Operation and investment: The economy of scale favors larger DG units over microsources.

For a micro source, the cost of the interconnection protection can add as much as 50% to the

cost of the system [6]. DG units with a rating of three to five times that of a microsource have

a connection cost much less per kW since the protection cost remains essentially fixed. The

microgrid concept allows for the same cost advantage of large DG units by placing many

microsources to a single dc bus with single voltage source converter interface.

• Power quality/Power Management/Reliability: DG has the potential to increase system

reliability and power quality due to the decentralization of supply. Increase in reliability

levels can be obtained if DG is allowed to operate autonomously in transient conditions [6].

1.2 POWER SHARING IN DISTRIBUTED GENERATION

Parallel converters have been controlled so as to deliver desired power (and reactive power) to the

system. Local signals are used as feedback to control converters, since in a real system, the distance

3

between the converters may make the communication impractical. A common approach for real and

reactive power sharing is droop control of two independent quantities – the frequency and the

fundamental voltage magnitude [12-22]. In this, the real power controls the system frequency, while

the reactive power controls the voltage magnitude. In [12] real and reactive power management

strategies of electronically interfaced distributed generation (DG) units in the context of a multiple-

DG microgrid system are addressed, where emphasis is primarily on electronically interfaced DG (EI-

DG) units. Robust voltage regulation with harmonic elimination under island and decoupled active

and reactive power flow control under grid-connected mode is proposed in [13]. The impact of

distributed generation technology and the penetration level on the dynamics of a test system is

investigated in [15]. The pre-planned switching events and the fault events that lead to islanding of a

microgrid are explored in [17] with the desired power sharing. The slow and oscillating nature of the

load sharing with a conventional droop control is overcome by introducing power derivative integral

terms [23], where a better controllability of the system is obtained and improvement in transient

performance is achieved. A transient droop characteristic [23] achieves a steady state invariant

frequency and good current balance. Sometimes an additional faster loop is added to program the

output impedance. Both inductive and resistive output has been investigated. In the resistive output,

the active power is controlled by terminal voltage where the reactive power is controlled by the source

angle. Karimi et al [24] developed a dynamic model and a control system for autonomous operation of

a stand-alone DG, which includes an electronically interfaced distributed resource and a local load.

The DG is represented by a DC voltage source in series with a three phase voltage-sourced converter

and an RL filter. The local load is modeled by a parallel RLC network. A state-space dynamic model is

developed for the DR (distributed resources) including the RLC network. A controller is designed to

maintain stability and control voltage and frequency of the stand-alone DG based on dynamic model

of the DG.

It is always desired in a microgrid that all the DGs respond to any load change in a similar rate to

avoid the overloading of a lagging or leading DG. In the presence of both inertial and non inertial

DGs, the response time for each DG to any change in load power demand will be different. A

converter interfaced DG can control its output voltage instantaneously and so the change in the power

demand can be picked up quickly, while in an inertial DG, the rate of change in power output is

4

limited by the machine inertia. To ensure that a load change is picked up by all the DGs in same rate,

the rate of change in converter interfaced DGs is to be limited.

1.2.1 CONTROLS FOR GRID AND ISLAND OPERATION

Power electronic interfaces introduce new control issues and possibilities. It is necessary to create

a power electronic interface, which allows large clusters of micro generators to operate in both an

island mode and as a satellite to the power grid while providing a high quality of power at a minimum

equipment cost. Basic requirements of the power electronic interface are:

• To provide fixed power and local voltage regulation

• To facilitate DG fast load tracking using storage

• To incorporate “frequency droop” methods to insure load sharing between micro-sources in

islanded operation without communications

Keyhani et all [25] propose the use of a low-bandwidth data communication system along with

locally measurable feedback signal for each DG. This is achieved by combining two control methods:

droop control method and average power control. The average power method with a slow update rate

is used in order to overcome sensitivity voltage and current measurement errors. In addition, a

harmonic droop scheme for sharing harmonic content of the load currents is also proposed. But the

communication between DGs may not be always possible in reality due to the physical distance

between them. The application of adaptive control or robust control in distributed generation is shown

in [26-27]. A strategic analysis and optimal voltage control technique for distributed generation are

proposed in [28 and 29].

1.3 POWER QUALITY AND RELIABILITY

A microgrid may contain non linear unbalanced loads. Moreover the voltage source converter

(VSC) connecting the DGs are themselves sources of harmonic generation. Therefore, it is important

to ensure a compensator configuration that is suitable for supplying electrical power to the microgrid,

while at the same time compensating for the non linearity/unbalance.

5

Power quality is always been a major concern and different filtering techniques are proposed in [30,

31, 32]. Determination of allowable penetration levels of distributed generation resources based on

harmonic limit consideration has been addressed in [33]. Many optimization methods are also been

proposed for planning and energy loss reduction [34, 35 and 36].

The authors of [37] propose a single-phase high-frequency ac (HFAC) microgrid as a solution

towards integrating renewable energy sources in a distributed generation system. For a better

performance of the DGs and more efficient power management system, it is important to achieve

control over the power flow between the grid and the microgrid. With a bidirectional control on the

power flow, it is possible not only to specify the exact amount of power supplied by the utility but

also the fed back power from microgrid to utility during lesser power demand in the microgrid.

Reliability is also a major issue in microgrid operation. Frequent load change, DG location and

change in DG power output always challenge the power management system and system reliability.

From the reliability point of view, frequency isolation between a microgrid and utility may be

desirable.

With number of DGs and loads connected over a wide span of the microgrid, isolation between the

grid and the microgrid will ensure a safe operation, in most cases.. Any voltage or frequency

fluctuation in the utility side has direct impact on the load voltage and power oscillation in the

microgrid side. For a safe operation of any sensitive load, it is not desirable to have any sudden

change in the system voltage and frequency. The isolation between the grid and microgrid not only

ensures safe operation of the microgrid load, it also prevents direct impact of microgrid load change or

change in DG output voltage on the utility side.

Protection of the devices both in utility and microgrid sides during any fault is always a major

concern [38-42]. Of the many schemes that have been proposed, [38] explores the effect of high DG

penetration on protective device coordination and suggests an adaptive protection scheme as a

solution to the problems. In [39], a method has been proposed for determining the coordination of the

rate of change of frequency (ROCOF) and under/over-frequency relays for distributed generation

protection considering islanding detection and frequency-tripping requirements. The method is based

on the concept of application region, which defines a region in the trigger time versus active power

imbalance space where frequency-based relays can be adjusted to satisfy the anti-islanding and

frequency-tripping requirements simultaneously.

6

1.4 SYSTEM STABILITY

The system stability during load sharing has been explored by many researchers [13, 15, and 43].

The Transient stability of the power system with high penetration level of power electronics interfaced

(converter connected) distributed generation is explored in [13]. But the study is based on presence of

an infinite bus. The other important issue, with isolated operation of the power system network has

been overlooked in the study. A scheme for controlling parallel connected converter in a standalone ac

system is presented in [44]. A modular structure of the controller is presented. The structure can be

modified to meet the control requirement for any other ac system. The scheme proposed a P-I

regulator to determine the set points for generator angle and flux. The dynamic performance of the

system can be substantially improved by using other advanced control technique. Similar to the small-

signal stability of conventional power system, [45] establishes how the control scheme gives rise to

the oscillatory modes with poor damping. To identify the possible feedback signals for controllers, a

sensitivity analysis is carried out. The low frequency stability problem with change in power demand

is investigated in [46]. It is shown that with the change in power demand, the movement of the low

frequency oscillations to new location affects the relative stability of the system. The decentralized

control strategies for parallel converters are shown in [47 and 48].

The robust stability of a voltage and current control solution for a stand-alone distributed generation

(DG) unit is analyzed in [49] using structured singular values. This results in a discrete-time sliding

mode current controller. In [50], small-signal stability analysis of the combined droop and average

power method for load sharing control of multiple distributed generation systems in a stand-alone ac

supply mode is discussed. A small-signal model is developed and its accuracy is verified from

simulations of the original nonlinear model.

Modeling and analysis of autonomous operation of converter-based microgrid is presented in [20,

51], in which the converters are controlled based on voltage and frequency droop. Each sub-module of

the system is modeled in state-space form and all the modules are then combined together on a

common reference frame. The model captures the detail of the control loops of the converter but not

the switching action. Normal PI controllers are used for voltage and current control.

7

1.5 POWER SHARING IN RURAL NETWORK

Rural electrification should ensure the availability of electricity irrespective of the technologies,

sources and forms of generation, but many cannot afford it due to a shortage of resources. Distributed

generation is one of the best available solutions for rural microgrids. However the locations of the

micro sources are very important. The success or failure of the rural electrification activities in a

developing country invariably depends on the extent to which the relevant issues have been

systematically analyzed and addressed. Power electronic converter solution is introduced that is

capable of providing rural electrification at a fraction of the current electrification cost. For weaker

networks, this inevitably leads to poor voltage regulation.

A highly resistive line, typical of low or medium voltage rural networks, challenges the power

sharing controller efficacy. The strong coupling of real and reactive power in the network leads to an

inaccurate load frequency control. High values of droop gains are required to ensure proper load

sharing, especially under weak system conditions. However, high droop gains have a negative impact

on the overall stability of the system. Moreover, proper load sharing cannot be ensured even with a

high gain if the lines are highly resistive. In such cases, the main assumption of the droop control that

active and reactive powers are decoupled is violated and the conventional droop control [43] is not

able to provide an acceptable power sharing among the DGs.

The decoupling of the real and reactive power is achieved in [52] for a high R/X line with

frequency droop control. It is shown that a modification of the droop equation can accommodate the

effect of line impedance. However, the choice of droop gains for rating based sharing of power has

not been addressed in [52].

As discussed previously, in the case of voltage source converter (VSC) based DGs, the output

angle can be changed instantaneously and so drooping the angle is a better way to share load [53].

Frequency regulation constraint limits the allowable range of frequency droop gain, which in turn,

may lead to chattering during frequent load changes in a microgrid. In [54], it is assumed the lines are

mainly resistive and conventional droop can work with real power controlled by voltage and reactive

8

power by angle. But in a rural network a high R/X ratio is common. With a strong coupling of real

and reactive power, they cannot be controlled independently with either frequency or voltage and so

the droop equations need to be modified. The real power droop coefficients can be chosen depending

on the load sharing ratio.

It is often difficult to install extensive distribution network, especially since the customer density in

the rural areas can be sparse. Distributed generation is one of the best available solutions for such a

predicament. Planning of a typical medium-voltage rural distribution system in different loading

conditions is discussed in [55-57]. The bottom up approach through an evaluation of autonomous or

non-autonomous modified microgrid concept to provide electricity to local residents is proposed in

[56].

The policy and prospective planning achievements for rural electrification are hindered in many

countries are described in [58-69]. Electrification in Africa, Uganda, Nepal or India has their own site

specific requirements [63, 65, 66 and 68]. The general rural electrification is described in [61].

Planned islanding in rural distribution system is demonstrated in [69].

The off grid renewable connection at Anangu Solar Station of South Australia [70], where 220 kW

power is distributed covering 10,000 square km among number of communities up to 500 people or

minigrid connection at Hermannsburg in central Australia [70], where three communities each with

several hundred households with 720 kW total power consumption are the examples of the scenario

where the converter interfaced micro sources and loads are geographically far from each other in a

low voltage network.

1.6 OBJECTIVES OF THE THESIS AND SPECIFIC CONTRIBUTIONS

The objectives of the thesis and the specific contributions are discussed in this section.

1.6.1 OBJECTIVES OF THE THESIS

Based on gaps in the literature, the objectives of the research are set as,

• To improve power sharing techniques in a microgrid with converter interfaced sources.

9

• To facilitate load frequency control of the microgrid and a smooth transition between grid

connected and islanded mode.

• To enhance power quality in a microgrid which may contain unbalanced and non linear loads.

• To improve power management system and reliability of the microgrid:

• To perform stability analysis and enhancement in stability with supplementary controller

• To achieve superior power sharing in rural network with high R/X lines.

1.6.2 SPECIFIC CONTRIBUTIONS OF THE THESIS

Based on the above objectives, the specific contributions of this thesis are

1. An angle droop controller is proposed to share power amongst converter interfaced DGs in a

microgrid. As the angle of output voltage can be changed instantaneously in a voltage source

converter (VSC), controlling the angle to control the real power is beneficial for quick

attainment of steady state. Thus converter based DGs, load sharing can be done by drooping

the converter output voltage magnitude and its angle instead of system frequency. The angle

control results in much lesser frequency variation compared to the frequency variation with

frequency droop.

2. An enhanced frequency droop controller is proposed for better dynamic response and smooth

transition between grid connected and islanded mode of operation. A modular controller

structure with modified control loop is proposed for better load sharing between the parallel

connected converters in a distributed generation system. The integral control in the voltage

angle loop helps to influence the close loop dynamics without affecting the steady state

frequency regulation. Moreover, a smooth transition between grid connected mode and

islanded mode is very important to ensure a superior system performance.

3. Power quality enhanced operation of a microgrid with unbalanced and non linear loads is

addressed. The proposed controllers are capable of compensating the local unbalanced and

non linear loads. The local loads can be shared with utility in any desired ratio. The common

loads which are normally supplied by the utility in grid connected mode, shared among the

DGs proportional to their rating in the islanded mode.

4. An isolation technique between microgrid and utility, for better reliability, is proposed by

using a back-to-back converter. As utility and microgrid are totally isolated, the voltage or

10

frequency fluctuations in the utility side do not affect the microgrid loads. Proper switching

of the breaker and other power electronics switches has been proposed during islanding and

resynchronization process. With a bidirectional power flow, it is possible to control the

power flow to and from the utility and microgrid.

5. A linearized state space model of an autonomous microgrid supplied by all converter based

DGs and connected to number of passive loads is formed. The proposed generalized model is

valid even when the network is complex containing any number of DGs and loads. The

model is utilized for eigenvalue analysis around a nominal operating point. A supplementary

loop is proposed around the primary droop control loop of each DG converter to stabilize the

system despite having high gains that are required for better load sharing. The control loops

are based on local power measurement that modulates of the d-axis voltage reference of each

converter. The coordinated design of supplementary control loops for each DG is formulated

as a parameter optimization problem and is solved using an evolutionary technique.

6. Two methods are proposed for load sharing in an autonomous microgrid in rural network

with high R/X ratio lines. The first method proposes power sharing without any

communication between the DGs. The feedback quantities and the gain matrices are

transformed with a transformation matrix based on the line resistance-reactance ratio. The

second method is with minimal communication based output feedback controller. The

converter output voltage angle reference is modified based on the active and reactive power

flow in the line connected at PCC. It is shown that a more economical and proper power

sharing solution is possible with the web based communication of the power flow quantities.

Publications covering the contribution of this thesis are given in Appendix B.

1.7 THESIS ORGANIZATION

The thesis has been organized in seven chapters. This chapter presents the relevant literature

survey and sets the motivation for the research work carried out in this thesis.

11

Chapter 2 compares the performance of angle and frequency droops in an autonomous microgrid

that only contains voltage source converter (VSC) interfaced distributed generators. As a VSC can

instantaneously change output voltage waveform, power sharing in a microgrid is possible by

controlling the output voltage angle of the DGs through droop. The angle droop is able to provide

proper load sharing among the DGs without a significant steady state frequency drop in the system. It

is shown that the frequency variation with the frequency droop controller is significantly higher than

that with the angle droop controller.

In Chapter 3, the control methods for proper load sharing between parallel converters connected

to microgrid supplied by distributed generators is described. A control strategy is proposed to improve

the system performance through seamless transfer between islanded and grid connected modes. The

smooth transition between the grid connected and off grid mode is achieved by changing the control

mode from voltage control in islanded mode to state feedback control in grid connected mode. Its

efficacy has been validated through simulation for various operating conditions.

A control strategy is proposed in Chapter 4 to improve power quality and proper load sharing in

both islanded and grid connected modes. It is assumed that each of the DGs has a local load connected

to it, which can be unbalanced and/or nonlinear. The DGs compensate the effects of imbalance and

nonlinearity of the local loads. Common loads are also connected to the microgrid, which are supplied

by the utility grid under normal conditions. However during islanding, each of the DGs supplies its

local load and shares the common load through droop characteristics.

Chapter 5 proposes a method for power flow control between utility and microgrid through

back-to-back converters, which facilitates isolation and desired controlled real and reactive power

flow between utility and microgrid. In the proposed control strategy, the system can run in two

different modes depending on the power requirement in the microgrid. In mode-1, specified amounts

of real and reactive power are shared between the utility and microgrid through the back-to-back

converters. Mode-2 is invoked when the power that can be supplied by the DGs in the microgrid

reaches its maximum limit. In such a case, the rest of the power demand of the microgrid has to be

supplied by the utility.

The problem of appropriate load sharing in an autonomous microgrid is investigated in chapter 6.

High gain angle droop control ensures proper load sharing, especially under weak system conditions.

However it has a negative impact on the overall stability. Frequency domain modeling, eigenvalue

12

analysis and time domain simulations are used to demonstrate this conflict. A supplementary loop is

proposed around the conventional droop control of each DG converter to stabilize the system while

using high angle droop gains. The control loops are based on local power measurement that

modulation of the d-axis voltage reference of each converter.

Chapter 7 proposes new droop control methods for load sharing in a rural area with distributed

generation. To overcome the conflict between higher feedback gain for better power sharing and

system stability in angle droop, two control methods have been proposed. The first method considers

no communication among the distributed generators (DGs) and regulates the converter output voltage

and angle ensuring proper sharing of load in a system having strong coupling between real and

reactive power due to high line resistance. The second method, based on a smattering of

communication, modifies the reference output voltage angle of the DGs depending on the active and

reactive power flow in the lines connected to point of common coupling (PCC).

The general conclusions and scope for future works are given in Chapter 8. Appendix A

discussed the converter structure and control methods used in the thesis.

13

CHAPTER 2

POWER SHARING WITH CONVERTER INTERFACED SOURCES

With the growth of distributed generation and its operation in tandem with utility power supply,

the interconnection of distributed generators (DGs) to the utility grid through power electronic

converters has raised concern about system control and power sharing among the DGs. Control of the

DG system is important and system regulation such as frequency deviation and voltage drop becomes

very crucial during the decentralized power sharing through droop control.

This chapter presents, the power sharing in microgrid with converter interfaced sources. The

conventional frequency droop control is first demonstrated. As the sources are converter interfaced, it

is possible to control the output voltage angles instantaneously. The proposed angle droop control is

derived from load flow analysis and demonstrated in a similar system to compare the performance of

both the droop controllers.

2.1 CONTROL OF PARALLEL CONVERTERS FOR LOAD SHARING WITH

FREQUENCY DROOP

The basic power system model with two DG sources connected to the load at the point of common

coupling (PCC) is shown in Fig. 2.1. The load can be a constant impedance load or a motor load. The

converter output voltages are denoted by V1∠δ1 and V2∠δ2 and are connected to the microgrid with

output filter of inductance L1.and L2. . P1, P2 and Q1, Q2 represent the real and reactive power supplied

by the DGs while PL and QL are respectively the real and reactive power demand of the load. The line

resistances are denoted by R1 and R2 while Lline1 and Lline2 represent the line inductances.

14

Fig. 2.1. Microgrid system under consideration.

2.1.1 FREQUENCY CONTROL

The conventional droop control method is given by [43]

nQVV

mPs

−=

−=∗

ωω (2.1)

where m and n are the droop coefficients, ωs is the synchronous frequency, V is the magnitude of the

converter output voltage and ω is its frequency, while P and Q respectively denote the active and

reactive power supplied by the converter. Thus the frequency and the voltage are being controlled by

the active and reactive power output of the DG sources.

2.1.2 MODULAR CONTROL STRUCTURE

A modification to the conventional droop controller is proposed here. This is shown in Fig. 2.2

for DG-1 only. A similar structure is also used for DG-2. The output voltage V1∠δ1 and output current

I1 of the converter are used for calculating the real power (P1) and reactive power (Q1) injected by

DG-1. These are then used in (2.1) to calculate ωs and V1*. The quantity ωs and the angle of the PCC

voltage δPCC are then used to calculate the reference angle δ1*. This is described in Section 2.1.3. The

reference magnitude V1* and its angle δ1

* are then used to generate the instantaneous reference

voltages of the three phases which are then compared with the measured instantaneous phase voltages

of V1. The resultant error is used in the feedback control to generate the firing pulses (u) of VSC-1.

The feedback control and converter structure are discussed in Appendix-A. In islanded mode state

feedback control (A.4) is used while voltage control (A.3) is employed in the grid connected

operation.

15

Fig. 2.2. The modular control structure

2.1.3 CONVERTER VOLTAGE ANGLE CALCULATION

The converter voltage angle control loop is shown in Fig. 2.3. The frequency ω1 is calculated from

the droop given in (2.1) and is then compared with the frequency (ωPCC) of the PCC voltage. The error

is passed through an integrator with a gain of KI and is then added with the integral of ωPCC to obtain

φ1*. The angle φ1

* rotates at the synchronous speed ωs making an angle δ1* with the reference.

Changing the value of KI, we can influence the close loop dynamics without affecting the steady state

frequency regulation.

Fig. 2.3. Voltage angle control loop.

2.1.4 REFERENCE GENERATION

With respect to Fig. A.3 in Appendix A, a state vector is defined as

[ ]1iivx cfcfT = (2.2)

The reference for vcf is v1*, as mentioned in the previous sub-section. Given V1

* and φ1*, the phasor

current through the capacitor Cf is given by

16

( )°+∠= ∗∗∗ 9011 δω VCI fcf (2.3)

The reference icf* is obtained from the instantaneous value of Icf

*.

The reference for i1 is derived through its phasor quantity I1*. Fig. 2.1 identifies that if the

references are strictly followed

*1

*1

*111 )( IVjQP ×−∠=− δ (2.4)

It is to be noted that in this section * denote reference quantities and not conjugate functions.

Let us define I1* = I1p

* + j I1q*. Then from 2.4,

[ ][ ]∗∗

∗∗

∗∗∗

∗

−=

+=

11111

1

11111

1

cossin1

sincos1

δδ

δδ

QPV

I

QPV

I

q

p

(2.5)

Therefore the phasor reference is given by

+= ∗

∗−∗∗∗

p

qqp

I

IIII

1

11111 tan (2.6)

The voltage angle controller of Fig. 2.3 generates a rotating angle φ1*, which is equal to ωst + δ1

*.

The angle φ1* is reset after every 2π. Fig. 2.6 shows the variation along with the reference ωst. From

this figure, we can write

∗+== 110 2 δωπω tt ss

Therefore

( )011 tts −=∗ ωδ (2.7)

Fig. 2.6. Source angle extraction from rotating angle.

17

Once the references for the state vector are obtained, the control law is computed as shown in

Appendix-A with the state feedback controller (A.4).

2.2 ANGLE DROOP CONTROL

The DGs have the potential to deliver reliable power when their locations are strategically planned.

However, for large scale application of DGs, the commercial and regulatory challenges have to be

considered before their benefits can be realized [71]. One of the most significant aspects is the change

in system frequency. As discussed in [12-14], DG real power output is controlled by dropping the

system frequency. Depending on the stiffness of the power-frequency curve, the steady state

frequency will change with the changes in system loads.

It is not desirable to operate the system in a much lower frequency and a complimentary frequency

restoration strategy is proposed in [43]. The reference powers of the DGs are modified to restore the

frequency which is equivalent to shifting the power-frequency curve vertically. The process can be

controlled in a slow, coordinated manner by a master controller, using a slow communication channel

between the converters [43]. In conversational frequency droop, the frequency deviation signal is used

to set the power output of the converter. The limitations of the use of frequency deviation alone have

been established for many years [72]. Nevertheless, the conventional droop method has several

drawbacks that limit its application, such as: slow transient response, frequency and amplitude

deviations, imbalanced harmonic current sharing, and high dependency on converter output-

impedance [73]. High frequency signals are injected to overcome the imbalance reactive power flow.

Since the power balance and the system stability rely on these signals, the application of such signal

increases system complexity and reduces reliability.

It is possible for a VSC to instantaneously change its output voltage waveform and power sharing

in a microgrid by controlling the output voltage angle of the DGs through droop. Let us consider same

microgrid system as shown in Fig. 2.1 is considered. First, the load sharing with angle droop is

derived using the DC load flow method. It is possible to share power among the DGs proportional to

their rating by dropping the output voltage angles.

The angle droop control strategy is applied to all the DGs in the system. It is assumed that the total

power demand in the microgrid can be supplied by the DGs such that no load shedding is required.

18

The output voltages of the converters are controlled to share the load proportional to the rating of the

DGs. As an output inductance is connected to each of the VSCs, the real and reactive power injection

from the DG source to the microgrid can be controlled by changing voltage magnitude and its angle

[12-14]. Fig. 2.7 shows the power flow from a DG to the microgrid where the RMS values of the

voltages and current are shown and the output impedance is denoted by jXf. It is to be noted that real

and reactive power (P and Q) shown in the figure are average values.

Fig. 2.7. DG connection to microgrid.

2.2.1. ANGLE DROOP CONTROL AND POWER SHARING

The average real power is denoted by P and the reactive power by Q. These powers, from the DG to

the microgrid, can then be calculated as

( )

( )f

tt

f

tt

X

VVVQ

XVV

P

δδ

δδ

−×−=

−×=

cos

sin

2 (2.8)

These instantaneous powers are passed through a low pass filter to obtain the average real and

reactive power P and Q. It is to be noted that the VSC does not have any direct control over the

microgrid voltage at the bus Vt∠δt (see Fig. 2.7). Therefore from (2.8), it is obvious that if the angle

difference ( − t) is small, real power can be controlled by controlling , while the reactive power can

be controlled by controlling voltage magnitude. Thus the power requirement can be distributed among

the DGs, similar to a conventional droop by dropping the voltage magnitude and angle as

( )( )ratedrated

ratedrated

QQnVV

PPm

−×−=−×−= δδ

(2.9)

19

where Vrated and rated are the rated voltage magnitude and angle respectively of the DG, when it is

supplying the load to its rated power levels of Prated and Qrated. The coefficients m and n respectively

indicate the voltage angle drop vis-à-vis the real power output and the voltage magnitude drop vis-à-

vis the reactive power output. These values are chosen to meet the voltage regulation requirement in

the microgrid.

To derive power sharing with angle droop, a simple system of Fig. 2.1 with two machines and a

load is considered. Applying DC load flow with all the necessary assumptions we get,

2222

1111

)(

)(

PXX

PXX

L

L

+=−

+=−

δδδδ

(2.10)

where X1 = L1/(V1V) , XL1 = LLine1/(V1V), X2 = L2/(V2V) and XL2 = LLine2/(V2V).

From (2.9), the angle droop equations of the two DGs are given by

( )( )ratedrated

ratedrated

PPm

PPm

22222

11111

−×−=−×−=

δδδδ

(2.11)

The offsets in the angle droop are such that when DG output power is zero, the DG source angle is

zero. Therefore the rated droop angles are taken as 1rated = m1P1rated and 2rated = m2P2rated. Then from

(2.11) we get

221121 PmPm −=−δδ (2.12)

Similarly from (2.10) we get

22211121 )()( PXXPXX LL +−+=−δδ (2.13)

Assuming the system to be lossless (as normally used in DC load flow), we get,

LLL

L

LLLL

PmXXmXX

mXXP

PPmPmPPXXPXX

111222

2221

1211122111 )())(()(

+++++++=

−−=−+−+ (2.14)

Similarly P2 can be calculated as

LLL

L PmXXmXX

mXXP

111222

1112 +++++

++= (2.15)

From (2.14) and (2.15), the ratio of the output power is calculated as,

20

111

222

2

1

mXXmXX

PP

L

L

++++= (2.16)

It is to be noted that the value of X1 and X2 are very small compared to the value of m1 and m2.

Moreover if the microgrid line is considered to be mainly resistive with low line inductance and the

DG output inductance is much larger, we can write

222111 and LL XXmXXm >>>>>>>>

Therefore from (2.16), it is evident that the droop coefficients play the dominant role in the power

sharing. Since the droop coefficients are taken as inversely proportional to the DG rating, from (2.16)

we can write

rated

rated

PP

mm

PP

2

1

1

2

2

1 =≈ (2.17)

The above approximation can incorporate little error in power sharing ratios depending on the

droop gain and inductances values. The error is further reduced by taking the output inductance (L1

and L2) of the DGs inversely proportional to power rating of the DGs. If the microgrid line is

inductive in nature and of high value, then knowledge about the network is needed.

2.3 ANGLE DROOP AND FREQUENCY DROOP CONTROLLER

The converter structure is given in Appendix A (A.1). Both the angle and frequency droop

controllers are modeled separately from their droop equations (2.9) and (2.1) respectively. The droop

controller model is then combined with the converter model. All the combined converter and

controller models are converted to a common reference frame and then connected to the network to

derive the entire microgrid model as shown in [51]. The microgrid model is used to select the

parameters of the droop controllers through eigenvalue analysis. The detail converter model with

droop equation is given in Chapter 6.

The droop controllers are designed based on the composite model discussed above. The system

parameters considered for the study are given in Table-2.1. The eigenvalue trajectory is plotted by

varying either the angle droop or frequency droop gain. The voltage droop gain is held constant. Fig.

2.8 shows one of the dominant complex conjugate eigenvalue trajectories with the angle droop

21

controller. It can be seen that, the complex pole crosses the imaginary axis, for a droop controller gain

of 0.00045 rad/kW. Similarly Fig. 2.9 shows the corresponding eigenvalue trajectory as function of

frequency droop controller gain.

Fig.2.8. System stability as function of frequency droop gain.

Fig. 2.9. System stability as function of angle droop gain.

To compare the results of the two droop controllers, the nominal values of the controller gain are

chosen at 75% of the gain at which the system becomes unstable. This implies that the gain with the

angle droop controller is m = 0.00034 rad/kW and with the frequency droop controller is mω =

0.000375 rad/s/kW.

22

TABLE-2.1: SYSTEM AND CONTROLLER PARAMETERS

System Quantities Values

Systems frequency 50 Hz

Load ratings

Load

2.8 kW to 3.1 kW

DG ratings (nominal)

DG-1

DG-2

1.0kW

1.33kW

Output inductances

LG1

LG2

75 mH

56.4 mH

DGs and VSCs

DC voltages (Vdc1 to Vdc4)

Transformer rating

VSC losses (Rf)

Filter capacitance (Cf)

Hysteresis constant (h)

0.5kV

0.415kV/0.415 kV, 0.25 MVA, 2.5% Lf

0.1 Ω

50 µF

10-5

Angle Droop Controller

m1 0.000340 rad/kW

m2 0.000255 rad/kW

Frequency Droop Controller

mw1 0.000375 rad/s/kW

mw2 0.000281rad/s/kW

2.4 SIMULATION STUDIES

Simulation studies are conducted with different types of load and operating conditions to check the

system response and controller action. Some of the results are discussed below. The system data used

is given in Table 2.1.

2.4.1 FREQUENCY DROOP CONTROLLER

The frequency droop controller is employed to share power in this case. The output impedances of

the two sources are chosen in a ratio of DG-1: DG-2 = 1:1.33 and the power rating of these DGs are

also chosen in the ratio of 1.33:1. To investigate the power sharing in a constant load changing

situation, the load conductance is chosen as the integral of a Gaussian white noise with zero mean and

a standard deviation of 0.01 Mho. The system parameters and the controller gains are shown in Table-

2.1.The power outputs of the DGs are shown in Fig. 2.10.

23

Fig. 2.10. DG power output with frequency droop control.

2.4.2 ANGLE DROOP CONTROLLER

The same system is used to investigate the angle droop controllers. Fig. 2.11 shows the power

output of the DGs in case of the angle droop controller. It can be seen that the constant deviation in

power output from the DGs are always in the desired ratio and the fluctuation in output power is

almost 10% as per the load change.

Fig. 2.11. DG power output with angle droop control.

24

2.4.3 COMPARISON OF FREQUENCY DROOP AND ANGLE DROOP

To compare the performance of the controllers, the frequency deviation is presented for

both cases. The frequency deviation of the DG sources is shown in Fig. 2.12. It is evident that the

frequency variation with the frequency droop controller is significantly high.

The standard deviation with the frequency droop controller is 0.4081 rad/s and 0.4082 rad/s for the

two DGs. It can also be seen that the mean frequency deviation is large.

Fig. 2.12. Frequency variation with frequency droop control

Fig. 2.13 shows the frequency deviation with the angle droop control. The steady state frequency

deviation is zero-mean and the standard deviation of the frequency deviation is 0.01695 rad/s and

0.01705 rad/s respectively for DG-1 and DG-2. The deviation in the frequency is small and the angle

droop controller is able to share load in the desired ratio despite the random change in the load

demand. This demonstrates that the angle droop controller generates a substantially smaller frequency

variation than the conventional frequency droop controller. Fig. 2.14 shows the angle deviation with

the angle droop. It can be seen that the nature of angle deviation is similar to the frequency deviation

with the frequency droop.

25

Fig. 2.13. Frequency variation with angle droop control.

Fig. 2.14. Angle variation with angle droop control.

2.4.4 ANGLE DROOP IN MULTI DG SYSTEM

To investigate the efficacy of the angle droop controller in a microgrid with multiple DGs and

loads, angle droop controllers are designed for the system shown in Fig. 2.15 with system parameter

shown in Table-2.2. It has four DGs and five loads as shown. It is desired that DG-1 to DG-4 share the

load in 1.0:2.0:1.5:1.5 ratio (to share power proportional to the DG rating). With the system running at

steady state, the loads Ld2 and Ld3 are disconnected at 0.2 s. The power sharing among the DGs is

shown in Fig. 2.16.

26

Fig. 2.15. Microgrid Structure with multiple DGs.

TABLE-2.2: MICROGRID SYSTEM AND CONTROLLER PARAMETERS



Feeder impedance

Z12 = Z23 = Z34 = Z45 = Z45 = Z56 =

Z67 = Z78 = Z89

0.1 + j 0.6 Ω

Load ratings

Ld1

Ld2

Ld3

Ld4

Ld5

1.8 kW and 1.6 kVAr

0.8kW and 0.6 kVAr

0.8 kW and 0.6 kVAr

0.8 kW and 0.6 kVAr

1.8 kW and 1.6 kVAr


DG-1

DG-2

DG-3

DG-4

1.0kW

2.0kW

1.5 kW

1.5 kW

Output inductances

LG1

LG2

LG3

LG4

75 Mh

37.5 mH

50 mH

50mH

DGs and VSCs


Transformer rating

VSC losses (Rf)



0.5kV

0.415kV/0.415 kV, 0.25 MVA,

2.5% Lf

0.1 Ω

50 µF

10-5

Angle Droop Controller

in multi machine

m1 0.1 rad/MW

m2 0.05 rad/MW

m3 0.075 rad/MW

m4 0.075 rad/MW

The efficacy of the angle droop is further verified by sharing power only between DG-1 and DG-4,

when DG-2 and DG-3 are disconnected from the system. Let us assume that the system is running in

the steady state supplying the loads Ld1, Ld2 and Ld4. At 0.2 s, the load Ld4 is disconnected. The

27

system response is shown in Fig. 2.17. This test studies the controller response when the power

generation and load demand is not evenly distributed along the microgrid. It can be seen that after 0.2

s, the sharing is not very accurate. Choosing a higher droop controller gain, we can assure better

sharing in such situations. However, a very high value of droop gain can lead the system to instability

as shown in eigenvalue trajectory of Fig. 2.9. The choice of controller gain is thus a trade off between

system stability and system response.

Fig. 2.16. Real Power Sharing of the DGs.

Fig.2.17. Real Power Sharing of the DG-1 and DG-4.

2.5 CONCLUSIONS

A modular controller structure with modified voltage angle control loop is proposed for better load

sharing between the parallel connected converters in a distributed generation system. The integral

28

control in the voltage angle loop helps to influence the close loop dynamics without effecting the

steady state frequency regulation. The efficacy of angle droop over frequency droop in a voltage

source converter based autonomous microgrid is also demonstrated in this chapter. The power sharing

of the DG sources with angle droop is derived first. A frequency droop controller and an angle droop

controller are designed to ensure the same stability margin in a two DG system. It is shown that the

frequency variation with the frequency droop controller is significantly higher than that with the angle

droop controller. The efficacy of the angle droop controller is further verified in a microgrid with

moderate number of DGs and loads. It is to be noted that, angle droop requires measurement of angle

with respect to a common reference frame and GPS phasor measurement can be used for this purpose.

Frequency droop does not require any GPS measurement. Moreover, with the presence of inertial DGs

(synchronous machine), it is easier to share power with the frequency droop controller. In the next

chapter, the frequency droop controller is discussed for a smooth transfer between grid connected and

islanded operations.

29

CHAPTER 3

LOAD FREQUENCY CONTROL IN MICROGRID

A smooth transfer between the grid connected and standalone modes is essential for a reliable

operation in a microgrid. Control of the DG system is important in both the grid connected and

islanded mode and system stability becomes very crucial during the transfer between grid connected

and islanded mode. A seamless transfer can ensure a smooth operation with proper load sharing and

quick attainment of steady state.

In this chapter a scheme for controlling parallel connected converters in islanded and grid

connected mode are presented. The control techniques for a smooth transfer between these two modes

are also shown. A modular structure of the controller is used as described in Chapter 2. Later the

frequency droop controller strategy is applied to a microgrid containing both inertial and inertia-less

DGs. To investigate the operation of all the micro-sources together, a microgrid is planned at

Queensland University of Technology (QUT) where the main issue is decentralized power sharing and

system stability. As mentioned in Chapter 2, a converter interfaced DG can control its output voltage

instantaneously and so the change in the power demand can be picked up quickly, while in an inertial

DG, the rate of change in power output is limited by the machine inertia. To ensure that a load change

is picked up by all the DGs at the same rate, the rate of change in converter interfaced DGs needs to

be limited. To investigate the system response with the dynamics of the DG units, the sources and all

the power electronic interfaces are modeled in detail.

3.1 SEAMLESS TRANSFER BETWEEN GRID CONNECTED AND ISLANDED

MODES

The basic power system model with two DG sources connected to the load at the point of common

coupling (PCC) is shown in Fig. 3.1. In this, the system runs in islanded mode when the circuit

breaker (CB) is open; otherwise it runs in grid connected mode. The load can be a constant impedance

30

load or a motor load. In Fig. 3.1, the voltage source VS is the utility voltage that is connected to the

PCC with a feeder of impedance RS + jXS. The current drawn from the utility is denoted by Ig, while Pg

and Qg are respectively the real and reactive power supplied by the grid. It is assumed that the DGs are

constant dc voltage sources Vdc1 and Vdc2. The converter output voltages are denoted by V1∠δ1 and

V2∠δ2 and they are connected to the PCC through reactances jX1 and jX2 respectively. P1, P2 and Q1,

Q2 represent the real and reactive power supplied by the DGs.


3.1.1 PROPOSED CONTROL

The frequency droop controller described in Chapter 2 has been employed here. The detail

converter structure is also the same as given in Appendix A (A.1).

1. As discussed in the last chapter the voltage regulation is a problem with frequency droop when

the load changes frequently. In this chapter it is shown that better load sharing and a rapid steady

state attainment are achieved when the voltage control is used in the islanded mode, while the

state feedback ensures better response in the grid connected mode (Detail converter control

techniques are discussed in Appendix A). A seamless transfer between these two modes is

proposed by changing state feedback to voltage control and vice versa. Ordinarily, in the grid

connected mode, the DGs operate under the state feedback control. When an islanding is

detected, the DGs are switched to the voltage control mode. These are switched back to the state

feedback control mode after resynchronization.

31

3.1.2 SIMULATION STUDIES

Simulation studies are carried out with different type loads and operating conditions to check the

system response and controller action. Some of the results are discussed below. The system data used

are given in Table 3.1.

3.1.2.1 ISLANDED MODE

In the islanded mode, the VSCs are operated in voltage control mode through output feedback. In

this mode, the grid is not available and the total power demand of the load is supplied by the DGs.

The frequency is also not fixed and is calculated from the modified droop to meet the active and

reactive power requirements. With any load change, the active and reactive power requirements

change and the VSC reference voltage magnitude and angle must change to meet the new load

requirement. Two types of load are considered here – constant impedance type load and motor load.

Fig. 3.2 shows the response with impedance load, where the values of the load impedances are

doubled at 1 s. The load is changed back to its nominal value at 1.5 s. It can be seen that DG-1 shares

more load than DG-2 in accordance with their droop characteristics, while the grid does not supply

any power.

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7-0.5

0

0.5

1

1.5

Act

ive

pow

er (M

W)

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7-0.2

00.20.40.6

Rea

ctiv

e p

ower

(M

VAR

)

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7-0.1

0

0.1

Time(s)

Cu

rren

t-ph

ase

a (k

A)

DG1DG2Grid

DG1DG2Grid

DG1DG2Grid

Fig.3.2 System response with impedance load in islanded mode.

Fig. 3.3 shows the results when the inductor motor is connected in parallel with the passive load at

2 s and disconnected at 2.75 s. The motor is operated in speed control mode. The change in active

32

power supplied by the DGs and output current of the converters show proper load sharing with a quick

steady state attainment. The zero power and zero current from the grid confirm the islanded condition.

TABLE 3.1. SYSTEM PARAMETERS


Systems Frequency (ωs) 100π rad/s

Source voltage (Vs) 11 kV rms (L-L)

Feeder impedance (Rs + jXs) 3.025 + j12.095

DG-1

DC voltage (Vdc1)

Transformer rating

VSC losses

Source inductance (L1)

Filter Capacitance (Cf)

Frequency droop coefficient (m)

Voltage droop coefficient (n)

3.5 kV

3 kV/11 kV, 0.5 MVA, 2.5%

reactance (Lf)

1.5 Ω

0.0578 H

30 µF

0.005 rad/s/kW

0.2045 kV/kVAr

DG-2

DC voltage (Vdc1)

Transformer rating

VSC losses

Source inductance (L1)


Frequency droop coefficient (m)

Voltage droop coefficient (n)

3.5 kV

3 kV/11 kV, 0.5 MVA, 2.5%

reactance (Lf)

1.5 Ω

0.0722 H

30 µF

0.00625 rad/s/kW

0.2727 kV/kVAr

Passive load The load is varied between

4.84 + j30.25 Ω and

102.85 + j157.3 Ω

Motor load (synchronous)

Rated rms voltage (L-N)

Rated rms line current

Inertia constant

Iron loss resistance

6 kV

5 kA

1 s

300 pu

Motor load (induction)

Rated rms voltage (L-N)

Rated rms line current

Rated power

6 kV

0.11 kA

50 hp

3.1.2.2 GRID CONNECTED MODE

In the grid connected mode, the steady state system frequency is fixed to the utility frequency. It is

assumed that the distributed generators supply their rated power at rated frequency. When the load

requirement is less than the total rated power of the DGs, the excess power flows from DGs go to the

33

grid.For a motor load, even a slight transient in voltage causes large power swing. Therefore the PCC

voltage should not deviate much from its nominal value and the VSCs must supply the change in the

power demand as quickly as possible. To accomplish this, relying only on a voltage control may not

be sufficient. It is desirable that a current controller is added with the voltage controller to ensure

better power tracking. Therefore the control is changed to a state feedback control which uses the

feedback of DG output voltage; output current and the current through the filter capacitor (see

Appendix A).

1.8 2 2.2 2.4 2.6 2.8 3 3.2

0

0.5

1

1.5

2

Act

ive

pow

er (

MW

)

1.8 2 2.2 2.4 2.6 2.8 3 3.2-0.6

-0.4

-0.2

0

0.2

0.4

Time (s)

Cur

rent

-pha

se a

(kA

)

DG1DG2Grid

DG1DG2Grid

Fig .3.3. System response with motor load in islanded mode.

The reference voltage magnitude and angle are calculated from the droop similar to the islanded

mode. However the steady state frequency is fixed to the grid frequency and the power output of the

DGs are equal to their rated power. Thus the active and reactive power requirements for an individual

DG are calculated based on their rating. The output current reference is calculated from the power and

voltage reference. The reference for the filter capacitor current is calculated from the voltage reference

(Appendix A).

Fig. 3.4 shows the system response during change of load in the grid connected mode. In this mode,

any change in load is picked up by the grid as the DGs always provide the rated power (or the

maximum available power). The change in grid current with active power demand ensures a stable

operation.

Fig. 3.5 shows the results when an induction motor gets connected at 2 s and disconnected at 2.75 s

while the passive load remains connected all the time. It is obvious that the additional power required

by the motor is coming from the grid as the DGs supply the rated power.

34

Fig. 3.6 shows the results when a synchronous motor is connected in parallel with impedance load.

With the motor and impedance operating in the steady state, the motor is disconnected at 1.5 s and

reconnected at 3 s. It can be seen that the powers supplied by the DGs remain constant during both the

transients and the oscillations in the grid current die out within 1 s.

1.2 1.4 1.6 1.8 2 2.2 2.4-0.5

0

0.5

1

1.5

Act

ive

pow

er (M

W)

1.2 1.4 1.6 1.8 2 2.2 2.4-0.2

-0.1

0

0.1

0.2

Time(s)

Gri

d C

urr

ent -

pha

se a

(kA

)

DG1DG2Grid

Fig. 3.4. System response with impedance load in grid connected mode.

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.20

1

2

3

Act

ive

pow

er (

MW

)

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2-0.4

-0.2

0

0.2

0.4

Time(s)

Gri

d c

urr

ent -

pha

se-a

(kA

)

DG1DG2Grid

Fig.3.5. System response with induction motor load in grid connected mode.

3.1.2.3 SEAMLESS TRANSFER BETWEEN GRID CONNECTED AND ISLANDED

MODES

The results simulated so far show that a better load sharing and a quick steady state attainment are

achieved with the voltage control in the islanded mode, while the state feedback ensures better

response in the grid connected mode. A seamless transfer between these two modes is proposed by

changing state feedback to voltage control and vice versa. Ordinarily, in the grid connected mode, the

35

DGs operate under the state feedback control. When an islanding is detected, the DGs are switched to

the voltage control mode. These are switched back to the state feedback control mode after

resynchronization. The sequence of control from a grid connected operation to islanded mode and

then again back to grid connected is given in Fig. 3.7.

1 1.5 2 2.5 3 3.5 4 4.5

0

0.5

1

Act

ive

pow

er (

MW

)

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3-0.04

-0.02

0

0.02

0.04G

rid

cur

rent

(kA

)

2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4-0.04

-0.02

0

0.02

0.04

Time (s)

Gri

d cu

rren

t(k

A)

DG1DG2Grid

Fig.3.6. System response with synchronous motor load in grid connected mode.

Figs. 3.8 and 3.9 show the response of the system during islanding and resynchronization with the

impedance load. The islanding occurs at 1.5 s and the resynchronization occurs at 2 s. Fig. 3.8 shows

the power sharing and currents, while the PCC voltages are shown in Fig. 3.9.

An impedance load is an infinite sink as it can absorb any change in instantaneous real and reactive

power with a change in the supply voltage. This however is not true for an inertial load such as motor.

Thus any change in the terminal voltage will result in large oscillation in the real and reactive powers.

So damping becomes a major issue during islanding with inertial load. Since the voltage control is a

slow process, a re-initialization in the reference value is required to force the system to a new steady

state quickly.

For this analysis it is assumed that an online load flow study is always performed in background

with the microgrid load and generation. At the instant of islanding, the values obtained from the load

flow are used to determine the new voltage reference. The new reference ensures minimal change in

the load voltage after islanding and proper sharing of the loads among the DGs. These new values are

assigned as the new reference for the controllers.

36

Fig.3.7. Control sequence from a grid connected operation to islanded mode

Fig. 3.8, System response during islanding and resynchronization with impedance load.

37

Fig. 3.9. PCC voltage during islanding and resynchronization with impedance load

Fig. 3.10 shows the active power sharing during islanding and resynchronization with a motor load.

An induction motor is used here. The active power input to the motor load is also shown in this figure.

It can be seen that this power remains constant during islanding and resynchronization, validating a

seamless transfer between the two modes. Phase-a of the DG output currents along with the grid

currents are shown separately during islanding and resynchronization in Fig. 3.11. It can be seen that

all the currents reach their steady state values with 0.2 s, both during islanding and resynchronization.

0.5 1 1.5 2 2.5 3 3.5

0

0.5

1

1.5

2

2.5

Act

ive

pow

er (M

W)

0.5 1 1.5 2 2.5 3 3.50.5

1

1.5

2

2.5

Time (s)

Act

ive

pow

er o

f M

oto

r L

oad

(MW

)

DG1DG2Grid

Fig. 3.10. System response during islanding and resynchronization with motor load.

3.2 MICROGRID WITH INERTIAL AND NON INERTIAL DGS

A microgrid should appear as a single controllable load that responds to changes

in the distribution system. Different micro-sources can be connected to the

microgrid, such as inertial sources like diesel generators and converter interfaced

sources such as fuel cells or photovoltaics (PV). A diesel generator set (genset)

38

consists of an internal combustion (IC) engine and a synchronous generator mounted

on the same shaft. Such systems are widely used as backup or emergency power in

commercial as well as industrial installations. Diesel gensets are also heavily used in

remote locations where it is impractical or prohibitively expensive to connect to

utility power [73]. Over the last few decades, there has been a growing interest in

fuel cell systems for power generation. These has been identified as a suitable

solution for distributed generation [74].

Fig. 3.11. PCC voltage during islanding and resynchronization with motor load.

Other than fuel cell, the use of new efficient photovoltaic solar cells (PVs) has emerged as an

alternative source of renewable green power, energy conservation and demand side management. [75].

To investigate the operation of all the micro-sources together, a microgrid is planned at QUT where

the main issue is decentralized power sharing and system stability. It is desired that in a microgrid all

the DGs respond to any load change in a similar rate to avoid the overloading of a lagging or leading

DG. In the presence of both inertial and non inertial DGs, the response time for each DG to any

change in load power demand will be different. A converter interfaced DG can control its output

voltage instantaneously and so the change in the power demand can be picked up quickly, while in an

inertial DG, the rate of change in power output is limited by the machine inertia. To ensure that a load

change is picked up by all the DGs in same rate, the rate of change in converter interfaced DGs needs

to be limited.

39

3.2.1 SYSTEM STRUCTURE

The microgrid system under consideration is shown in Fig. 3.12. There are four DGs as shown;

one of them is an inertial DG (diesel generator) while the others are converter interfaced DGs (the PV,

fuel cell and battery). There are five resistive heater loads and six induction motors. The parameters of

the grid, DGs, loads and controllers are given in Appendix A. The microgrid can run both in grid

connected, as well as, autonomous mode of operation.

Fig.3.12 Microgrid structure under consideration

To increase the system damping and to restrict the rate of change in power output in non inertial

DGs, the droop equations are modified as

dtdQ

nQQnVV

dtdP

mPPm

drated

drateds

+−−=

+−−=

∗ )(

)(ωω (3.1)

3.2.2 MODEL OF MICRO SOURCE

As mentioned before there are four DGs in the microgrid. The diesel generator is modeled as [73]

and not shown in this chapter. The other three DG models and associated power electronic controllers

are discussed below.

3.2.2.1. FUEL CELL

Various methods have been introduced for modeling of fuel cells; however a simplified empirical

model, introduced in [74], is used here. The output voltage-current characteristic of the fuel cell is

given in (3.2). An open loop boost chopper is used at fuel cell output for regulating the necessary DC

voltage VC across the capacitor. The schematic diagram of the simulated model with the output

chopper is shown in Fig. 3.13.

40

ieiiiV 025.02242.02195.0)log(38.123.371)( −−−= (3.2)

Fig. 3.13. Fuel cell modelled equivalent circuit

3.2.2.2. PHOTOVOLTAIC CELL (PV)

PV arrays are built with combination of series and parallel PV cells which are usually

represented by a simplified equivalent circuit as shown in Fig. 3.14. PV cell output voltage is a

function of the output current while the current is a function of load current, ambient temperature and

radiation level. The output chopper controls the voltage VC across the capacitor. The reference voltage

of the chopper is set by a Maximum Power Point Tracking (MPPT) method for getting the maximum

power from the PV based on the load or ambient condition changes. The MPPT algorithm used as

shown in Fig. 3.15 [75]. The chopper uses a PI controller in order to achieve the desired reference

voltage set by the MPPT.

Fig. 3.14. Equivalent circuit of PV and boost chopper based on MPPT

3.2.2.3. BATTERY

The battery is modeled as a constant dc source voltage with series internal resistance where the VSC

is connected to its output. The battery has a limitation on the duration of its generated power and

depends on the amount of current supplied by it.

3.2.3. SIMULATION STUDIES

The system is simulated for various operating conditions with different load demand in the

microgrid. The simulation results are discussed below.

41

Fig. 3.15. MPPT control flowchart for PV

3.2.3.1. CASE 1: GRID CONNECTED AND AUTONOMOUS OPERATING MODES

In this case, the microgrid operation has been simulated during grid connected and autonomous

modes. In grid connected mode, each DG will generate its rated power and the extra load demand will

be supplied by the grid. In autonomous mode total power demand is shared among the DGs

proportional to their rating. Fig. 3.16 shows the system response where the grid is disconnected at 0.5

sec. and resynchronized at 1.5 sec. A smooth resynchronization can be achieved as shown in this

figure. It can be seen that the system reaches steady state within 10 cycles in either case.

3.2.3.2. CASE 2: POWER SHARING IN AUTONOMOUS MODE

The response of the power sharing controller in accordance with load changes in autonomous

mode is investigated in this subsection. In this case, it is assumed the system is operating in steady

state while all the micro sources are connected and supplying the three 1.5 kW fan heater load. At 0.5

sec all inductions motors get connected to the microgrid and the system response is shown in Fig.3.17.

It can be seen the system reaches to the steady state condition within 5-6 cycles and the extra power

requirement is picked up by all the DGs. The micro sources output currents are shown in Fig. 3.18.

For converter interfaced DGs, the change in output current are achieved within 1 cycle. The delay in

change of power in the power output is due to the micro source dynamics (fuel cell and PV).

42

Fig. 3.16. Islanding and resynchronization

Fig.3.17 Real power sharing of the DGs

0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62-30

-20

-10

0

10

20

30

40

Time (s)

Cu

rren

t (A

)

Current Output of DG Units

IFC IPV IBat ISynGen

Fig.3.18 Current output of the micro sources

3.2.3.3. CASE 3: SOURCE INERTIA AND SYSTEM DAMPING

In the previous section it is noted that there is a finite difference in the rate of change in output

current and power between the inertial and non inertial sources. As mentioned before it is always

43

desired that all the DGs respond to any load change in a similar rate to avoid the overloading of a

lagging or leading DG. In this case, it is assumed that synchronous generator, battery and fuel cell are

supplying the entire network load while at 0.5 sec. the PV is also connected to the system. The total

power demand is shared by all the DGs. The system response is shown in Fig. 3.19. The inertia of the

diesel generator and dynamics of the PV result in a large overshoot.

To limit the rate of change in power output, the proposed derivative feedback [76] in the power

sharing controller is used. System response with the derivative feedback is shown in Fig. 3.20. It is

apparent that derivative feedback has decreased the overshoot and improved the dynamic response of

the system.


0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

1

2

3

4

5

6

7

8

9

10

Time (s)

Act

ive

Po

wer

(kW

)

Active Power Sharing of DG Units

PBat

PSynGen

PPV PFC


44

3.2.4 CONCLUSIONS

A modular controller structure with modified voltage angle control loop is proposed for

better load sharing between the parallel connected converters in a distributed generation system. The

integral control in the voltage angle loop help to influence the close loop dynamics without affecting

the steady state frequency regulation. By switching the control action of the DGs from state feedback

in grid connected mode to voltage control in islanded mode, a seamless transfer is achieved. A step by

step control method is proposed for a smooth transition during islanding and resynchronization. The

efficacy of the controller is verified with impedance as well with motor loads. The decentralized

control of a microgrid in presence of inertial and non inertial DGs is achieved and the system stability

is enhanced with a derivative feedback. Inclusion of the micro source model ensures proposed power

electronic control can work in tandem with the associated dynamics of micro sources.

45

CHAPTER 4

POWER QUALITY ENHANCED OPERATION OF A MICROGRID

Power quality and proper load sharing between different DGs and the grid is one of most

important issues that need to be investigated in a microgrid. Concerning the interfacing of a microgrid

to the utility system, an important area of study is to investigate the overall system performance with

unbalanced and non linear loads. Such loads are common and distributed through distribution feeders.

A common practice is to isolate the microgrid from the utility grid by an isolator if the voltage is

seriously unbalanced [46]. However when the voltages are not critically unbalanced, the isolator will

remain closed, subjecting the microgrid to sustained unbalanced voltages at the point of common

coupling (PCC), if no compensating action is taken. Unbalance voltages can cause abnormal operation

particularly for sensitive loads and increased losses in motor loads.

Many innovative control techniques have been used for power quality enhanced operation as

well as for load sharing [46]. A microgrid that supplies to a rural area is widely spread and connected

to many loads and distributed generators at different locations. In general, a DG may have local loads

which are very close to it. There may be loads which are not near to any of the DGs and they must be

shared by the DGs and the utility. These are termed as common load in this chapter.

In this chapter a control algorithm for power electronics interfaced microgrid containing

distributed generators is developed. It is assumed that the common load is supplied solely by the

utility in the grid connected mode. However, when an islanding occurs, this load will be shared by the

DGs through traditional droop method. Furthermore, each DG will supply part of its local load in grid

connected mode, while at the same time, compensating for their unbalance and nonlinearities.

However in the islanded mode, each of the DGs supplies its local load and shares the common load

through droop characteristics.

46

4.1 SYSTEM STRUCTURE

A basic power system model with two DGs is shown in Fig. 4.1 in which the real and

reactive power drawn/supplied is denoted by P and Q respectively. The microgrid is connected to the

utility grid at PCC. Both DG-1 and DG-2 are connected directly to the microgrid through circuit

breaker CB-3 and CB-4 respectively. As mentioned, both the DGs have local loads which may be

unbalanced and nonlinear. In addition, the microgrid may also have a common load, which is assumed

to be balanced and linear and further away from any of the DGs. One of the functions of the DGs is to

correct for the unbalance and nonlinearity of its local load. In the grid connected mode, the DGs share

a percentage of its local load with the utility, while the common load is supplied entirely by the utility.

During islanding, each DG supplies its local load and shares common load with the other DG. The

complex powers drawn by the local loads are PL1 + jQL1 and PL2 + jQL2. The common load draws a

current iLC and a complex power of PLC + jQLC. The local loads are connected to the DGs at PCC1 and

PCC2 with voltages of vp1 and vp2 respectively. The real and reactive powers supplied by the DGs are

denoted by P1, Q1 and P2, Q2. It is assumed that the microgrid is mostly resistive, being in the

distribution level, with line impedances of RD1 and RD2. The utility supply is denoted by vs and the

feeder resistance and inductance are denoted respectively by Rs and Ls. The utility supplies PG and QG

to the microgrid and the balance Ps − PG and Qs − QG are supplied to the utility load. The breakers

CB-1 can isolate the microgrid from the utility supply.

The structure of the VSCs connecting DG-1 and DG-2 to the microgrid is similar to as shown

in Appendix A, Fig. A.1. But the output filter is not present. Equivalent one phase of the converter is

shown in Fig. A.2 (b).

4.2 REFERENCE GENERATION AND COMPENSATOR CONTROL

In this chapter, the reference generation for the DG with compensator is presented. The

control strategy for both the compensators is same. Here description is given only for DG-1 and its

compensator.

47

Fig.4.1. The microgrid and utility system under consideration.

4.2.1. COMPENSATOR REFERENCE GENERATION IN GRID CONNECTED

MODE

It is assumed, for the time being, that the common load and DG-2 are not connected (i.e., CB-

2 and CB-4 are open), while DG-1 is supplying part of its local load only. The main aim of the

compensator is to cancel the effects of unbalanced and harmonic components of the local load, while

supplying pre-specified amount of real and reactive powers to the load. If it is successful in its aim,

then current ig1 will be balanced and so will be the voltage vp1 provided that vs is balanced. Let us

denote the three phases by the subscripts a, b and c. Therefore since ig1 is balanced we have

0111 =++ cgbgag iii (4.1)

From Fig. 4.1, the Kirchoff’s current law (KCL) at vp1 gives

cbakiii kLkgk ,,,111 ==+ (4.2)

48

Therefore combining (4.1) and (4.2) by adding the currents of the all the three phases together, we get

cLbLaLcba iiiiii 111111 ++=++ (4.3)

Since ig1 is balanced due to the action of the compensator, the voltage vp1 will also become

balanced. Hence the instantaneous real powers PG1 will be equal to its average component. Therefore

we can write

1111111 Gcgcpbgbpagap Piviviv =++ (4.4)

From the KCL of (4.2), (4.4) can be written as

( ) ( ) ( ) 1111111111 GccLcpbbLbpaaLap Piiviiviiv =−+−+− (4.5)

Similarly the reactive powers QG will be equal to its instantaneous component, i.e.,

( ) ( ) ( ) 1111111111 3 Gcgbpapbgapcpagcpbp Qivvivvivv ×=−+−+− (4.6)

Using the KCL of (4.2), (4.6) can be rewritten as

( )( ) ( )( ) ( )( ) 1111111111111 3 GccLbpapbbLapcpaaLcpbp Qiivviivviivv =−−+−−+−− (4.7)

Equations (4.3), (4.5) and (4.7) form the basis of the algorithm. From these three, the

following can be written

−−+

=

1

1

1

1

1

1

1

1

3

0

G

G

cL

bL

aL

c

b

a

Q

P

i

ii

A

i

ii

A (4.8)

49

where

−−−=

bpapapcpcpbp

cpbpap

vvvvvv

vvvA

111111

111

111

The determinant of the matrix A is given by

( ) ( ) ( )cpapbpcpbpcpapbpapbpcpap vvvvvvvvvvvvA 111111111111 222 −++−++−+= (4.9)

If vp1 is balanced, then the following is true

0111 =++ cpbpap vvv (4.10)

Substituting (4.10) in (4.9), we get |A| = − K, where

( )21

21

213 cpbpap vvvK ++= (4.11)

Then the solution of (4.8) is given as

( )( )( )

−+−+−+

−

=

bpapGcpG

apcpGbpG

cpbpGapG

cL

bL

aL

c

b

a

vvQvP

vvQvP

vvQvP

Ki

ii

i

ii

11111

11111

11111

1

1

1

1

1

1

333333

1 (4.12)

As we have stipulated that DG-1 supplies a fraction of the average real and reactive power

demanded by the local load, we can write

avLQ

avLP

QQ

PP

111

111

×=×=

λλ

(4.13)

50

where PL1av and QL1av are respectively the average real and reactive power demanded by the local load

and λ1P and λ1Q are respectively the real and reactive power fractions supplied by DG-1. It is to be

noted that both the active and reactive powers will have double frequency and distorted components

over the average components [87]. DG-1 will supply the double frequency and distorted component to

cancel out the unbalance and harmonics. Then, as a consequence, the active (PG1) and reactive (QG1)

power supplied by the grid will not contain any double frequency and distortion components.

Additionally DG-1 will also supply a part of the average component.

Therefore the active and reactive power supplied by the grid is given by using the KCL of

(4.2) as

( )( )QavLavLQavLG

PavLavLPavLG

QQQQ

PPPP

111111

111111

1

1

λλλλ−=×−=

−=×−= (4.14)

We can then modify (4.12) as to get the following reference currents for i1

( ) ( )( )( ) ( )( )( ) ( )( )

−−+−−−+−−−+−

−

=

bpapQavLcpPavL

apcpQavLbpPavL

cpbpQavLapPavL

cL

bL

aL

c

b

a

vvQvP

vvQvP

vvQvP

Ki

i

i

i

i

i

1111111

1111111

1111111

1

1

1

1

1

1

1313

1313

13131

λλλλλλ

(4.15)

In a similar way, the current references for DG-2 can be calculated and are given by

( ) ( )( )( ) ( )( )( ) ( )( )

−−+−−−+−−−+−

−

=

bpapQavLcpPavL

apcpQavLbpPavL

cpbpQavLapPavL

cL

bL

aL

c

b

a

vvQvP

vvQvP

vvQvP

Ki

ii

i

ii

2222222

2222222

2222222

2

2

2

2

2

2

1313

1313

13131

λλλλλλ

(4.16)

Equations (4.15) and (4.16) will remain valid so long as DG-1 and DG-2 are supplying a part of their

local loads and neither of the DGs is supplying the common load. When they will be required to

supply the common load during islanding, (4.15) and (4.16) will be suitably modified to accommodate

this. This will be discussed later in Section 4.2.3.

51

4.2.2. COMPENSATOR CONTROL

The equivalent circuit of one phase of the converter is shown in Fig. A. 2 (b). The following

state vector is chosen

[ ]pcccfT viix 1= (4.17)

where the PCC voltage vpcc is the same as the voltage across the filter capacitor vcf, i.e., vcf = vpcc.

The state feedback control shown in appendix (A.4) is used to track the references. In exactly

a similar fashion, DG-2 VSCs are controlled and its reference states are computed.

4.2.3. COMPENSATOR REFERENCE GENERATION IN ISLANDED MODE

In Section 4.2.1, it has been assumed that the DGs are not required to supply the common

load as it will be supplied by the utility. In case of an islanding, however, each of the DGs will have to

supply its local load entirely. In addition, they must also share the real (PLC) and reactive (QLC) power

demand of the common load. Therefore in this mode, λ1P = λ1Q = λ2P = λ2Q = 1. Also PG1, QG1, ig1,

PG2, QG2 and ig2 will be negative with respect to the directions shown in Fig. 4.1. If DG-1 supplies the

local load PL1, QL1 and inject power − PG1, − QG1 to the microgrid to share the common load then the

total real and reactive power generated by the DG-1 are P1 = PL1 − PG1 and Q1 = QL1 −

QG1.respectively. Similarly the total real and reactive power generated by the DG-2 are P2 = PL2 − PG2

and Q2 = QL2 − QG2.respectively.

Note from (4.15) and (4.16) that when λ1P = λ1Q = λ2P = λ2Q = 1, and the DGs also supply the

grid currents, we have

+

=

cg

bg

ag

cL

bL

aL

c

b

a

i

i

i

i

i

i

i

i

i

1

1

1

1

1

1

1

1

1

and

+

=

cg

bg

ag

cL

bL

aL

c

b

a

i

i

i

i

i

i

i

i

i

2

2

2

2

2

2

2

2

2

(4.18)

Following the derivations presented in (4.1) to (4.12) the injected currents are computed as

52

( )( )( )

−+−+−+

−=

bpapGcpG

apcpGbpG

cpbpGapG

cg

bg

ag

vvQvP

vvQvP

vvQvP

Ki

i

i

11111

11111

11111

1

1

1

33

33

331

and

( )( )( )

−+−+−+

−=

bpapGcpG

apcpGbpG

cpbpGapG

cg

bg

ag

vvQvP

vvQvP

vvQvP

Ki

i

i

22122

22122

22222

2

2

2

33

33

331

(4.19)

Therefore combining (4.18) and (4.19) we get the references for the islanded mode as

( )( )( )

−+−+−+

−

=

bpapGcpG

apcpGbpG

cpbpGapG

cL

bL

aL

c

b

a

vvQvP

vvQvP

vvQvP

Ki

ii

i

ii

11111

11111

11111

1

1

1

1

1

1

33

33

331

(4.20)

( )( )( )

−+−+−+

−

=

bpapGcpG

apcpGbpG

cpbpGapG

cL

bL

aL

c

b

a

vvQvP

vvQvP

vvQvP

Ki

i

i

i

i

i

22122

22122

22222

2

2

2

2

2

2

33

33

331

(4.21)

The generalized form for the reference currents of DG-1 can be given from (4.15) and (4.20)

as

( ) ( )( )( ) ( )( )( ) ( )( )

( ) ( )( )( ) ( )( )( ) ( )( )

−−+−−−+−−−+−

−

−−+−−−+−−−+−

−

=

bpapQGGcpPGG

apcpQGGbpPGG

cpbpQGGapPGG

bpapQLavcpPLav

apcpQLavbpPLav

cpbpQLavapPLav

cL

bL

aL

c

b

a

vvQvP

vvQvP

vvQvP

K

vvQvP

vvQvP

vvQvP

Ki

i

i

i

i

i

1111111

111111

1111111

1111111

1111111

1111111

1

1

1

1

1

1

1313

13113

13131

1313

1313

13131

λλλλλλ

λλλλλλ

(4.22)

In the above equation, 1P = 1Q = 1 and 1PG = 1QG = 0 while sharing the common in the islanded

mode, which will result in (4.20). However in the grid connected mode, when the local load is shared

by the DG-1 and the grid, we have 0 < 1P ≤ 1 and 0 < 1Q ≤ 1 and 1PG = 1QG = 1. A similar

expression as (4.22) can also be written for DG-2.

53

4.2.4. DG COORDINATION FOR SHARING THE COMMON LOAD

From Fig. 4.1, it is clear that the total power demand from the common load PLC, QLC is

shared only by the DGs in the islanded mode. The KCL at PCC gives the following expression

21 ggLC iii −−= (4.23)

Assuming that the microgrid is (almost) resistive, the active power balance equation at PCC is given

from Fig. 4.1 by

22

212

121 DgDgGGLC RIRIPPP ++−−= (4.24)

where |Ig1| and |Ig2| are the rms values of ig1 and ig2 respectively. The reactive power balance equation

at PCC is

21 GGLC QQQ −−= (4.25)

With respect to Fig. 4.1, let us define the rms voltage of the PCC as |Vp|∠δp and that of the

PCC1 as |Vp1|∠δp1.The real and reactive power flow from vp1 to vp is then given as

( ) *

1

1111

∠−∠×∠=−−

D

ppppppGG R

VVVjQP

δδδ

From the above equation, the real and reactive power is calculated as

1

111

1

112

1

)sin(

)cos(

D

PPppG

D

pppppG

R

VVQ

R

VVVP

δδ

δδ

−=−

−+−=−

(4.26)

54

When the angle difference δp − δp1 is small (4.26) can be rewritten as

( )

( )111

111

111

12

1

)(PPG

D

PPppG

ppGD

pppG

QR

VVQ

VVPR

VVVP

δδδδ

−∝−−

=−

−∝−+−

=− (4.27)

Equation (4.27) gives us approximate relationships, which clearly indicate that the real and reactive

power can be controlled by controlling the voltage magnitude (|Vp| − |Vp1|) and angle δp1. Therefore the

real and reactive power output to the microgrid from the DG-1 can be controlled using their respective

droop relations with the voltage magnitude and angle respectively. Since the voltage |Vp| is not locally

measurable, these are given by

( )( )∗∗

∗∗

−×−=

−×−=

11111

11111

GGpp

GGpp

PPnVV

QQmδδ (4.28)

where |Vp1|∗, δp1∗, PG1

∗ and QG1∗ respectively are the rated values of the voltage magnitude, angle, real

and reactive power. The coefficients m1 and n1 denote respectively the voltage magnitude and angle

drop with real and reactive power output. These values are chosen to meet the voltage regulation

requirement at point PCC1. In a similar way, the droop characteristics of DG-2 are given by

( )( )∗∗

∗∗

−×−=

−×−=

22222

22222

GGpp

GGpp

PPnVV

QQmδδ (4.29)

In grid connected mode, the droop is inactive. Hence the reference voltage is set from the

positive sequence fundamental component of the PCC1 (or PCC2) voltage. However, when the DGs

are operating in the islanded mode, the magnitude and angle of the reference voltage are derived from

the droop equations (4.28-4.29) given above. These are then used in the state feedback controller.

Hence the positive sequence voltage extraction is unnecessary in this case and the nominal value

before the islanding can be used in the droop equations. Once the voltage magnitude and angle from

55

equations (4.28) and (4.29) are calculated, the current references are obtained from (4.20) and (4.21)

respectively. Noting that each DG will have to supply its local load, the droop coefficients are chosen

based on the ratings of the DGs. Neglecting the resistive drops across the microgrid, these are given

by

( ) ( )( ) ( )max_2_22max_1_11

max_2_22max_1_11

LratedLrated

LratedLrated

QQmQQm

PPnPPn

−×=−×

−×=−× (4.30)


Simulation studies are carried out in PSCAD/EMTDC (version 4.2) in which different

configurations of load and its sharing is considered. The DGs are considered to be ideal dc sources.

The system data are given in Table 4.1. The numerical results of all the simulation studies are

summarized and listed in Table 4.2 for better clarity.

4.3.1. SHARING THE LOCAL LOAD WITH UTILITY

In this section, the sharing of the local load by the DGs with utility is shown. In this case the current

references of the DG compensators are calculated from (4.22) with 1PG = 1QG = 1 and 2PG = 2QG = 1

such that the DGs do not share the common load. It is desired that DG-1 shares 20% of both real and

reactive power of its local load, while DG-2 shares 50% of the real power and 70% of the reactive

power requirement of its own local load. So in this case 1P = 0.2, 1Q = 0.2 and 2P = 0.5, 2Q = 0.7.

The common load is totally supplied by the utility. At 0.5 s, the common load impedance is made half

of its initial value. Fig. 4.2 shows the power sharing of DG-1 and DG-2. The voltages of PCC1, PCC2

are shown in Fig. 4.3. The power sharing in same desired ratio and balanced voltages even after

change in the common load indicate a stable operation.

To investigate the controller response in the islanded mode, with the same value of local and common

loads, system is islanded at 0.4 s and, at the same time, the common load is also disconnected. As the

island is detected, the each DG reference is changed to supply its total local load. A rapid island

56

detecting scheme is introduced. The instantaneous power pG injected by the grid is computed from the

following relation

Fig.4.2. Real and reactive power sharing in DG-1and DG-2

Fig.4.3. Voltages at the PCC1 and PCC2

gcpcgbpbgapaG ivivivp ++= (4.31)

Once this power falls below a threshold value, an islanding signal is generated. This instantaneous

power pG is used to detect the resynchronization when it rises above the threshold value. Fig. 4.4 (a)

and (b) show the real and reactive power sharing of DG-1. Fig. 4.4 (c) and (d) show DG-1 current and

voltages at PCC1. As soon as the islanding is detected at 0.4 s, the compensator current increases to

deliver the total local load demand. A balanced voltage at PCC1 ensures proper functioning of the

controller even after islanding. DG-2 also behaves in a similar fashion and its plots are not shown

here.

57

Fig.4.4. Power sharing and DG-1current and PCC1 voltages

4.3.2. SHARING THE COMMON LOAD BY THE DGs

If the common load exists in the islanded mode, it is shared among the DGs proportional to

their rating. It is desired to supply the real and reactive power from the DGs to their local load as

before (as shown in Fig.4. 2). An islanding occurs at 0.3 s, where the common load remains

connected. It is desired now that the local loads are totally supplied by the individual DGs and they

share the common load as per (4.30). The droop coefficients of the DGs are taken such that they share

the common load in 1:2 ratio in which DG-2 supplies 2/3rd of the load. Fig. 4.5 shows the real power

sharing of DG-1 and DG-2. At the onset of the islanding, both PCC1 and PCC2 voltage drop, causing

a slight drop in PL1 and PL2. However both P1 and P2 increase to supply the common load, as indicated

by negative power flow in PG1 and PG2. At 1.0 s, the utility is reconnected and the power sharing goes

back to the initial values.

4.3.3. SHARING A COMMON INDUCTION MOTOR LOAD

An impedance load can absorb a sudden change in instantaneous real and reactive power like

a infinite sink. However in case of a motor load, a sudden change in the terminal voltage gives large

oscillation in real and reactive power level. To investigate the system response with the motor load,

the common load shown in Fig. 4.1 is now replaced with an induction motor and the power sharing is

58

observed by islanding and resynchronization the utility. Fig. 4.6 shows the results. The islanding and

resynchronization occur at 0.2 s and 0.7 s respectively. During islanding it is desired that the motor

load is shared between DGs in 1:2 ratio. The absolute value of common load supplied by the DGs

along with the total motor load during islanded mode is indicated in Fig. 4.6. The system reaches

steady state within 0.2 s after islanding and 0.3 s after resynchronization.

Fig.4.5. Real power sharing by DG-1 and DG-2.

Fig. 4.6. Common load sharing between DG-1 and DG-2

4.3.4. DG-1 SUPPLYING THE ENTIRE COMMON LOAD DURING ISLANDING

Let us now assume that DG-2 is capable of supplying only its local load. Hence during an

islanding, DG-1 must supply both its local load and the entire requirement of the common load. To

investigate this operation an islanding is created at 0.25 s. Before islanding the following λ’s are

chosen:

59

1P = 0.2, 1Q = 0.2 and 2P = 1.0, 2Q = 1.0

1PG = 1QG = 2PG = 2QG = 1.0

Once the islanding occurs, the following λ’s are chosen:

1P = 1.0, 1Q = 1.0, 2P = 1.0, 2Q = 1.0

1PG = 1QG = 0 and 2PG = 2QG = 1.0

The system response is shown in Fig. 4.7. Once the islanding occurs, there is a slight voltage

drop in both PCC1 and PCC2, causing PL1 and PL2 to drop. DG-1 supplies its local and common load

causing a rise in P1 and negative PG1. However DG-2 supplies only its local load, thereby maintaining

PG2 to nearly zero.

Fig.4.7. Real power sharing of the DGs and voltages at PCC1 and PCC2

4.4 DISCUSSIONS

In the studies presented in this chapter, it has been assumed that only two DGs and a common

load are connected to the microgrid. In general, however, there might be several DGs and loads

connected to the microgrid as shown in Fig. 4.8. In this case a total number of n common loads and m

60

DGs, with the compensators and local load are considered. The one way communication needed to

broadcast the CB_grid status to the DG compensator is shown in Fig. 4.8. The total active and reactive

powers consumed by the common loads are given by

LCnLCLCLC

LCnLCLCLC

QQQQ

PPPP

+++=+++=

21

21 (4.32)

This total power will be supplied by the grid alone. However in islanded mode this power will be

shared among the DGs. The power can be shared depending on the DG rating. Coefficient of the

droop characteristics of the DGs should be chosen by

( ) ( ) ( )( ) ( ) ( )max__max_2_22max_1_11

max__max_2_22max_1_11

LmratedmmLratedLrated

LmratedmmLratedLrated

QQmQQmQQm

PPnPPnPPn

−×=−×=−×

−×=−×=−× (4.33)

However, similar to conventional droop method, the different line impedance between the load

connection points throughout the microgrid will have impact on the load sharing. As the line

impedances are not purely resistive or inductive, control of the active and reactive powers are not

totally decoupled in nature. The detail impact of the line impedance on droop control is discussed in

[77 and 78].

Fig.4.8. Microgrid structure with large number of DGs and loads.

61

4.5 CONCLUSIONS

In this chapter a local load sharing technique is proposed for a distributed microgrid. The controllers

are capable of compensating the local unbalanced and non linear loads. The local loads can be shared

with utility in any desired ratio. The common loads which are normally supplied by the utility in grid

connected mode, shared among the DGs proportional to their rating in the islanded mode. A smooth

transfer between the islanded and grid connected mode assures a stable operation of the system. The

controller efficacy is checked both with impedance and motor loads. The application is mainly aimed

at rural area where unbalanced load is common and wire less communication is always desirable due

to the large network size. Similar to any droop control method, the distance among the load and DG

determine the line impedance between them and that impedance has impact on the load sharing.

However load sharing can be made more accurate by incorporating the line impedance values in the

power reference calculation.

62

TABLE-4.1: SYSTEM PARAMETERS




Feeder impedance Rs = 1.025 Ω, Ls = 57.75 mH

DG-1 Local Unbalanced load RLa = 48.4 Ω, LLa = 192.6 mH

RLb = 24.4 Ω, LLb = 100.0 mH

RLc = 96.4 Ω, LLc = 300.0 mH

DG-1 Local Nonlinear load A three-phase rectifier supplying an

RL load with R = 200 Ω, L = 100 mH

DG-2 Local Unbalanced load RLa = 48.4 Ω, LLa = 192.6 mH

RLb = 24.4 Ω, LLb = 100.0 mH

RLc = 96.4 Ω, LLc = 300.0 mH

DG-2 Local Nonlinear load A three-phase rectifier supplying an

RL load with R = 200 Ω, L = 100 mH

Common Impedance Load RLa = 24.4 Ω, LLa = 100.0 mH

RLb = 24.4 Ω, LLb = 100.0 mH

RLc = 24.4 Ω, LLc = 100.0 mH

Common Motor Load (M) Induction motor rated 40 hp, 11 kV

rms (L-L).

Microgrid Line Impedance RD1=RD2=0.2 Ω

DGs and Compensators

DC voltage (Vdc1)

Transformer rating

VSC losses


3.5 kV

3 kV/11 kV, 0.5 MVA,

2.5% reactance (Lf)

1.5 Ω

50 µF

Droop Coefficients

m1

m2

n1

n2

- 0.1 rad/MVAr

- 0.05 rad/MVAr

0.12 kV/MW

0.06 kV/MW

63

TABLE-4.2: NUMERICAL RESULTS

Case-I Active

Power

Initial

value

(MW)

Final value

(MW) Reactive Power

Initial

value

(MVAr)

Final value

(MVAr)

Section 4.3.1

Sharing the Local

Load with Utility

Fig.4.2

P1 0.275 0.274 Q1 0.28 0.28

PG1 1.125 1.125 QG1 1.12 1.12

PL1 1.4 1.39 QL1 1.4 1.4

P2 0.71 0.69 Q2 0.42 0.41

PG2 0.69 0.69 QG2 0.18 0.17

PL2 1.4 1.38 QL2 0.6 0.58

Fig.4.3

Voltage drop at PCC1 (%) Voltage drop at PCC2 (%)

3.15% 3.38%

Fig.4.4

Active

Power

Initial

value

(MW)

Final

value

(MW)

Reactive

Power

Initial

value

(MVAr)

Final value

(MVAr)

P1 0.142 0.71 Q1 0.09 0.43

PG1 0.568 0.0 QG1 0.36 0.0

PL1 0.71 0.69 QL1 0.45 0.43

Case-II

Active

Power

Initial

value

(MW)

Intermediate value

(In Islanded Mode)

(MW)

Final value

(After resynchronization)

(MW)

Section 4.3.2

Sharing the

Common Load

by the DGs

Fig.4.5

P1 0.142 0.78 0.142

PG1 0.568 -0.13 0.568

PL1 0.71 0.65 0.71

P2 0.35 0.91 0.35

PG2 0.35 -0.31 0.35

PL2 0.70 0.60 0.70

Case-III

Active

And

Reactive

Power

Initial value

(Active power in

MW and

reactive power

in MVAr)

Intermediate value

(In Islanded Mode)

(Active power in MW and

reactive power in MVAr)

Final value

(After

resynchronization)

(Active power in MW

and reactive power in

MVAr)

Section 4.3.3

Sharing a

Common

Induction Motor

Load

Fig.4.6

PG1 0.95 -.081 0.95

PG2 0.60 -0.157 0.60

PLC 0.238 0.238 0.238

QG1 0.59 -0.039 0.59

QG2 0.21 -0.076 0.21

QLC 0.115 0.115 0.115

Case-IV

Active

Power

Initial value

(MW)

Final value

(In Islanded Mode)

(MW)

Section 4.3.4 Fig.4.7 P1 0.34 1.86

64

DG-1 Supplying

the Entire

Common Load

During Islanding

PG1 1.50 -0.28

PL1 1.83 1.58

P2 1.825 1.625

PG2 0.01 -0.025

PL2 1.835 1.6

Voltage Drop at PCC1 (%) Voltage Drop at PCC2 (%)

4.3% 5.8%

65

CHAPTER 5

POWER FLOW CONTROL WITH BACK-TO BACK CONVERTERS IN A UTILITY

CONNECTED MICROGRID

In general, a microgrid is interfaced to the main power system by a fast semiconductor switching

system called the static switch (SS). It is essential to protect a microgrid in both the grid-connected

and the islanded modes of operation against all faults. Converter fault currents are limited by the

ratings of the silicon devices to around 2 per unit rated current. Fault currents in islanded converter

based microgrids may not have adequate magnitudes to use traditional overcurrent protection

techniques [40]. To overcome this problem, a reliable and fast fault detection method is proposed in

[41].

The aim of this chapter is to set up power electronics interfaced to the microgrid containing

distributed generators, connected to the utility through back-to-back converters. Bidirectional power

flow control between the utility and microgrid is achieved by controlling both the converters. The

back-to-back converters provide the much needed frequency and power quality isolation between the

utility and the microgrid. A proper relay breaker co-ordination is proposed for protection during fault.

The scheme not only ensures a quick and safe islanding at inception of the fault, but also a seamless

resynchronization once the fault is cleared. This application of back-to-back converters in distributed

generation would facilitate:

controlled power flow between microgrid and utility which can be used in case of any contractual

arrangement.

reliable power quality due to the isolation of the microgrid system from utility.

5.1 SYSTEM STRUCTURE AND OPERATION

A simple power system model with back to back converters, one microgrid load and two DG

sources is shown in Fig. 5.1. A more complex case is considered in Section 5.7. In Fig. 5.1, the real

66

and reactive power drawn/supplied are denoted by P and Q respectively. The back to back converters

are connected to the microgrid at the point of common coupling (PCC) and to the utility grid at point

A as shown in Fig. 5.1. Both the converters (VSC-1 and VSC-2) are supplied by a common dc bus

capacitor with voltage of VC. The converters can be blocked with their corresponding signal input

BLK1 and BLK2. DG-1 and DG-2 are connected through voltage source converters to the microgrid.

The output inductances of the DGs are indicated by inductance L1 and L2 respectively. The real and

reactive powers supplied by the DGs are denoted by P1, Q1 and P2, Q2. While the real and reactive

power demand from the load is denoted by PL, QL. It is assumed that the microgrid is in distribution

level with mostly resistive lines, whose resistances are denoted by RD1 and RD2.

The utility supply is denoted by vs and the feeder resistance and inductance are denoted respectively

by Rs and Ls. The utility supplies PG and QG to the back-to-back converters and the balance amounts

Ps − PG and Qs − QG are supplied to the utility load. The breakers CB-1 and CB-2 can isolate the

microgrid from the utility supply. The power supplied from the utility side to microgrid at PCC is

denoted by PT, QT, where the differences PG − PT and QG − QT represent the loss and reactive power

requirement of the back-to-back converter and their dc side capacitor.

The system can run in two different modes depending on the power requirement in the microgrid.

In mode-1, a specified amount of real and reactive power can be supplied from the utility to the

microgrid through the back-to- back converters. Rest of the load demand is supplied by the DGs. The

power requirements are shared proportionally among the DGs based on their ratings. When the total

power generation by the DGs is more than the load requirement, the excess power is fed back to the

utility. This mode provides a smooth operation in a contractual arrangement, where the amount of

power consumed from or delivered to the utility is pre-specified.

67

Fig. 5.1. The microgrid and utility system under consideration.

When the power requirement in the microgrid is more than the combined maximum available

generation capacity of the DGs (e.g. when cloud reduces generation from PV), a pre-specified power

flow from the utility to the microgrid may not be viable. The utility will then supply the remaining

power requirement in the microgrid under mode-2 control, while the DGs are operated at maximum

power mode. Once all the DGs reach their available power limits, the operation of the microgrid is

changed from mode-1 to mode-2. While mode-1 provides a safe contractual agreement with the

utility, mode-2 provides more reliable power supply and can handle large load and generation

uncertainty. The rating requirement of the back to back converters will depend on the maximum

power flowing through them. The maximum power flow will occur when

the load demand in the microgrid is maximum and minimum power is generated by the DGs

(power flow from utility to microgrid)

maximum power is generated by DGs, while the load demand in the microgrid is minimum

(power flow from microgrid to utility).

The rating issue has to be determined a priori. The microgrid cannot supply/absorb more power than

the pre-specified maximum limit.

68

5.2 CONVERTER STRUCTURE AND CONTROL

The converter structure for VSC-3 is shown in appendix-A and converter contains three H-bridges

(with output inductance). They are controlled in output feedback control as shown in Appendix-A.

All the four VSCs are controlled using the same control strategy. Hence, all these controllers

require their instantaneous reference voltages. These are discussed in the next two sections.

5.3 BACK-TO-BACK CONVERTER REFERENCE GENERATION

This section describe the reference generation for the back-to-back VSCs. Both the VSCs are

supplied from a common capacitor of voltage VC as shown in Fig. 5.1. Depending on the power

requirement in the microgrid; there are two modes of operation as discussed previously. However the

reference generation for VSC-1 is common for both these modes. This is discussed next.

5.3.1. VSC-1 REFERENCE GENERATION

Reference angle for VSC-1 is generated as shown in Fig. 5.2. First the measured capacitor voltage

VC is passed through a low pass filter to obtain VCav. This is then compared with the reference

capacitor voltage VCref. The error is fed to a PI controller to generate the reference angle ref. VSC-1

reference voltage magnitude is kept constant, while angle is the output of the PI controller. The

instantaneous voltages of the three phases are derived from them.

Fig. 5.2. Angle controller for VSC-1.

The two modes of VSC-2 reference generation are discussed next.

69

5.3.2. VSC-2 REFERENCE GENERATION IN MODE-1

VSC-2, which is connected with PCC through an output inductance LG, controls the real and

reactive power flow between the utility and the microgrid. Fig. 5.3 shows the schematic diagram of

this part of the circuit, where the voltages and current are shown by their phasor values.

Fig. 5.3. Schematic diagram of VSC-2 connection to microgrid.

Let us assume, that in mode-1 the references for the real and reactive power be PTref and QTref

respectively and the VSC-2 output voltage be denoted by VT∠δT and the PCC voltage by VP∠δP. Then

the reference VSC-2 voltage magnitude and its can be calculated as

( )PTP

GTrefPT V

XQVV

δδ −+

=cos

2

(5.1)

PGTrefP

GTrefT

XQV

XPδδ +

+= −

21tan (5.2)

Depending on the real and reactive power demand, these references are calculated, based on which the

instantaneous reference VSC-2 voltages for the three phases are computed. It is to be noted that, sign

of the active and reactive power references are taken as negative when it is desired to supply the

power from the microgrid to the utility side.

5.3.3 VSC-2 REFERENCE GENERATION IN MODE-2

In mode-2, the utility supplies any deficit in the power requirement through back-to-back

converters while the DGs supply their maximum available power. Let the maximum rating of the

70

back-to-back converters are given by PTmax, QTmax. Then the voltage magnitude and angle reference of

VSC-2 is generated as

( )( )TTTTT

TTTTT

QQnVV

PPm

−×−=−×−=

maxmax

maxmaxδδ (5.3)

where VTmax and Tmax are the voltage magnitude and angle, respectively, when it is supplying the

maximum load. The VSC-2 droop coefficient mT and nT are chosen such that the voltage regulation is

within acceptable limit from maximum to minimum power supply.

5.4 REFERENCE GENERATION FOR DG SOURCES

In this section, the reference generation for the DGs is presented. It is to be noted that the reference

generations of the DGs are different from reference generation of the back-to-back converters. The

control strategy for both the DGs is the same and hence only DG-1 reference generation is discussed

here.

5.4.1. MODE-1

It is assumed that in mode-1 the utility supplies a part of the load demand through the back-to-back

converters and rest of the power demand in the microgrid is supplied and regulated by the DGs. The

output voltages of the converters are controlled to share this load proportional to the rating of the

DGs. As the output impedance of the DG sources is inductive, the real and reactive power injection

from the source to microgrid can be controlled by changing voltage magnitude and its angle [43]. Fig.

5.4 shows the power flow from DG-1 to microgrid where the voltages and current are shown in rms

values and the output impedance is denoted by jX1.

Fig. 5.4. Power flow from DG-1 to microgrid.

71

As mentioned before, the power requirement can be distributed among the DGs, similar to

conventional droop [43] by dropping the voltage magnitude and angle as (2.9) and can be represented

as,

( )( )ratedrated

ratedrated

QQnVV

PPm

11111

11111

−×−=−×−= δδ

(5.4)

where V1rated and 1rated are the rated voltage magnitude and angle respectively of DG-1, when it is

supplying the load to its rated power levels of P1rated and Q1rated.

So DG-1 can supply the desired power if the output voltage of VSC-3 has magnitude and angle as

given in (5.4). From the rms quantities the instantaneous reference voltages of the three phases are

obtained. In a similar way, the instantaneous reference voltages for VSC-4 are also obtained. This

method of load sharing is based only on local measurements and does not need intercommunication

between the DGs. For the determination of the phase angles, a common reference is used.

5.4.2. MODE-2

In mode-2, the DGs supply their maximum available power. The reference generation for the DGs

in mode-2 is similar to the reference generation of VSC-2 of back-to-back converter in mode-1 as

given in (5.1) and (5.2). Let us denote the available active power as P1avail. Then based on this and the

current rating of the DG, the reactive power availability Q1avail of the DG can be determined. Based on

these quantities, the voltage references as shown in Fig. 5.4 is calculated as

( )PPP

availP

VXQV

Vδδ −

+=11

112

11 cos

(5.5)

111

21

1111 tan P

availP

avail

XQV

XP δδ +

+= − (5.6)

The references for the other DGs are generated in a similar way.

72

5.5 RELAY AND CIRCUIT BREAKER COORDINATION DURING ISLANDING

AND RESYNCHRONIZATION

The reference generations described in the previous section for DGs and back-to-back converters

are totally independent of each other. In mode-1, once the desired value of real and reactive power

flow through the back-to-back converters is set, the rest of the required power will automatically be

shared amongst the DGs. In mode-2, the DGs supply their maximum available power while the extra

power requirement from the utility is supplied through the back-to-back converter. When a DG

reaches its maximum available signal, it broadcasts it to VSC-2 control center. The mode change is

initiated when all the DGs their available limits. Note that other than the broadcast signals, no other

communication is needed between the back-to-back converters and the DGs Even during islanding

and resynchronization, no communication is needed. But proper relay breaker coordination, along

with converter blocking, will be required to maintain the voltage of the dc capacitor during islanding

and resynchronization. Fig. 5.5 shows the logic diagram used for this purpose, where Trip_Signal

initiates the tripping of CB-2 (Fig. 5.1) and the signal BLK1 blocks VSC-1. The same logic is also

used for the tripping CB-1 and the blocking of VSC-2. The rate of rise of current ig is monitored by

the protection scheme. When it exceeds a threshold value in response to a fault in the utility grid, the

output of the Protection Scheme (Fig. 5.5) becomes high. This output is used to set all the RS flip

flops. The upper flip flop (F/F-1) generates the trip signal. This flip flop is reset by the Fault_Clear

signal. The lower two flip flops, F/F-2 and F/F-3 generate BLK1 and BLK2 signals respectively. The

blocking deactivation is initiated when the fault is cleared and Fault_Clear signal is set high

manually. The converter VSC-1 is deblocked by resetting F/F-2 when the breaker CB-2 is closed, as

indicated by Br_Status signal. The AND gate insures that no false deblocking occurs till both these

signals are high. VSC-2 is deblocked after VSC-1 is deblocked. This is why Fault_Clear signal is

passed through a time delay circuit to generate the reset signal for F/F-3.

73

Fig. 5.5. Logic for breaker operation and converter blocking.

Fig. 5.6 shows the timing diagram of the breakers and converter blocking during islanding and

resynchronization process. If a breaker is closed, the signal Br_Status is high and it goes low when the

breaker opens. As evident from Fig. 5.5, the output of the Protection Scheme triggers the RS flip

flops, which simultaneously generates both the trip and block signals. The block signals blocks both

VSC-1 and VSC-2 simultaneously. Once the trip signals goes high, the breakers CB-1 and CB-2 open

after a finite time delay (t_op) as indicated in Fig. 5.6. Unless the two VSCs are blocked, the dc

capacitor voltage collapses due to the sudden increase in power requirement on the utility side. Also to

prevent the angle reference δref from diverging during the contingency, the angle controller of Fig. 5.2

is bypassed and the reference is held at the pre-fault value. Note that, once a breaker opens, the

Protection Scheme output goes low causing the set input of the flip flops of Fig. 5.5 to become 0.

During islanding, breakers CB-1 and CB-2 are opened simultaneously. However during

resynchronization, CB-2 is closed and VSC-1 is deblocked first connecting this to the utility. This will

cause the dc capacitor voltage to rise taking a finite time depending on the capacitor voltage drop

during islanding. Once the capacitor voltage settles to its reference value and the angle controller of

Fig. 5.2 settles, CB-1 is closed and VSC-2 is deblocked.

Once the fault is cleared, Fault_Clear signal is set high manually. This signal is the same as

Br_Close signal of CB-2. The Fault_Clear signal also resets Trip_signal, used both by CB-1 and CB-

2. With a finite time delay (t_cl) from the initiation of Br_Close signal, CB-2 closes, making the

Br_Status signal for CB-2 high. This resets F/F-2 and deactivates BLK1 signal causing switching

devices of VSC-1 to start conducting. As mentioned earlier and shown in Fig. 5.5 that Br_Close signal

for CB-1 is generated after a time delay from the Fault_Clear signal. Once this signal is generated,

74

CB-1 closes after a time delay t_cl. This then resets F/F-3 and VSC-2 starts conducting. To even

further safeguard the dc capacitor voltage, the power flow reference for VSC-2 is switched to zero

during islanding and brought back to its previous value after resynchronization. This step by step

process ensures a seamless resynchronization.

Fig. 5.6. Breakers and converter blocking timing diagram.


Different configurations of load and its sharing are considered. The DGs are considered as inertia-

less dc source supplied through a VSC. The system data are given in Table 5.1. The droop coefficients

are chosen such that both active and reactive powers of the load are divided in 1:1.25 ratios between

DG-1 and DG-2.

5.6.1 CASE-1: LOAD SHARING OF THE DGS WITH UTILITY

If the power requirement of the load in microgrid is more than the power generated by the DGs, the

balance power is supplied by the utility through the back-to-back converters. The desired power flow

from the utility to the microgrid is controlled by (5.1) and (5.2), while droop equation (5.4) controls

the sharing of the remaining power. It is desired that 50% of the load is supplied by the utility and rest

of the load is shared by DG-1 and DG-2. The impedance load of Table 5.1 is considered for this case.

Fig. 5.7 shows the real and reactive power sharing between utility and the DGs. Fig. 5.8 (a) shows the

phase-a reference and output voltage, whereas three phase voltage tracking error is shown in Fig. 5.8

(b). It can be seen that the tracking error is less than 0.2%. Fig. 5.9 shows the capacitor voltage and

75

the output of the angle controller. At 0.1 s, the impedance of the load is halved and at 0.35 s, it is

changed back to its nominal value. It can be seen that the system goes through minimal transient and

reaches its steady state within 5 cycles (100 ms) for both the transients.

TABLE 5.1. SYSTEM AND CONTROLLER PARAMETERS




Feeder impedance Rs = 3.025 Ω, Ls = 57.75 mH

Load

Impedance (Balanced)

or

Induction motor

RL = 100.0 Ω, LL = 300.0 mH

Rated 40 hp, 11 kV rms (L-L)

DGs and VSCs

DC voltage (Vdc1, Vdc2)

Transformer rating

VSC losses (Rf)


Inductances (L1, L2)

Inductances (LG)


3.5 kV

3 kV/11 kV, 0.5 MVA, 2.5% reactance (Lf)

1.5 Ω

50 µF

20 mH and 16.0 mH

28.86 mH

10-5

Angle Controller

Proportional gain (Kp)

Integral gain (KI)

− 0.2

− 5.0

Droop Coefficients

Power−−−−angle

m1

m2

Voltage−−−−Q

n1

n2

0.3 rad/MW

0.24 rad/MW

0.15 kV/MVAr

0.12 Kv/MVAr

Fig. 5.7. Real and reactive power sharing for Case-1.

76

Fig. 5.8. Voltage tracking of DG-1 Case-1.

Fig. 5.9. Capacitor voltage and angle controller output for Case-1.

5.6.2 CASE-2: CHANGE IN POWER SUPPLY FROM UTILITY

If the power flow from the utility to the microgrid is changed by changing the power flow

references for VSC-2, the extra power requirement is automatically picked up by the DGs. Fig. 5.10

shows the real and reactive power sharing, where at 0.1 s the power flow from the utility is changed to

20% of the total load from the initial value of 50% as considered in Case-1. It can be seen that the

DGs pick up the balance load demand and share it proportionally as desired. The unchanged real and

reactive load power during the change over proves the efficacy of the controller for smooth transition.

Fig. 5.11 shows the PCC voltage and change in current injection at PCC from utility. It can be seen

that the PCC voltage remained balanced and transient-free, while the injected currents reach steady

state within 4 cycles.

77

Fig. 5.10. Real and reactive power sharing for Case-2.

5.6.3 CASE-3: POWER SUPPLY FROM MICROGRID TO UTILITY

When the power generation of the DGs is more than the power requirement of the load, excess

power can be fed back to the utility through the back-to-back converters. It is desired the utility

supplies 50% of the microgrid load initially. At 0.1 s, however, the same amount of power is fed back

to the utility by changing the sign of the power flow reference for the back-to-back converters. The

DG output increases automatically to supply the total load power and power to the utility, as evident

from Fig. 5.12.

Fig. 5.11. Three phase PCC voltage and injected current for Case-2.

78

Fig. 5.12. Real and reactive power sharing during power reversal (Case-3).

Fig.5.13 (a) shows the phase-a voltage at PCC and phase-a current injected from the utility to the

microgrid, where current is scaled up 30 times. The change in the power flow direction is indicated by

the sudden change in phase of the injected current phase at 0.1 s vis-à-vis that of the voltage. Fig.5.13

(b) shows the three phase current injected by the utility to the microgrid. It reaches steady state within

3 cycles. Apart from the phase reversal, the magnitude of the currents remain the same indicating that

the same amount of power flow is taking place, albeit in opposite direction.

Fig. 5.13. PCC voltage and injected current for Case-3.

5.6.4. CASE-4: LOAD SHARING WITH MOTOR LOAD

In this section, load sharing with the induction motor load, given in Table 5.1, is investigated. An

impedance load is an infinite sink as it can absorb any change in the instantaneous real and reactive

power. However an inertial load such as motor is not capable of that. Thus any sudden big change in

79

the terminal voltage results in large oscillation in the real and reactive power. At the beginning it is

assumed that the utility supplies 0.2 MW of real power and 0.5 MVAr of reactive power to the

microgrid. Then at 0.05 s, the power reference is changed such that the utility supplies 0.3 MVAR of

reactive power and no real power. The power sharing results for this case is shown in Fig. 5.14.

Fig. 5.14. Real and reactive power sharing with motor load (Case-4).

5.6.5 CASE-5: CHANGE IN UTILITY VOLTAGE AND FREQUENCY

One of the major advantages of the back-to-back converter connection is that it can provide

isolation between the utility and the microgrid, both for voltage and frequency fluctuations. Fig. 5.15

shows the system response for frequency fluctuation in the utility side from 0.05 s to 0.25 s. At 0.05 s,

the utility frequency dropped by 0.5%, and at 0.25 s, it comes back to its initial value of 50 Hz. The

real and reactive power injections from utility to VSC-1 are shown as PG and QG respectively. It can

be seen that while PG and QG fluctuate, the load power (PL, QL) and the injected power to the

microgrid (PT, QT) remain constant.

Fig. 5.15. Real and reactive power during frequency fluctuation (Case-5).

80

Fig. 5.16. Real and reactive power during voltage sag (Case-5).

With the system operating in steady state, a 50% balanced sag in the source voltage occurs in 0.1 s.

The sag is removed after 0.5 s. Fig. 5.16 shows the power and the reactive power during this

condition. It can be seen that the load power (PL, QL) and the injected power to the microgrid (PT, QT)

remain almost undisturbed. The real power drawn from the grid (PG), barring transients at the

inception and removal of the sag, is maintained at the steady state level in order to supply power to the

microgrid. The reactive power (QG) however reverses sign as the utility voltage drop causing it to

absorb reactive power. During the sag, the dc capacitor supplies reactive power to the utility. The dc

capacitor voltage and the output of the angle controller are shown in Fig. 5.17. It can be seen that

while the dc capacitor voltage is maintained at its pre-specified value, the angle drops in sympathy

with the source voltage drop to maintain the injected power constant. The angle returns to its pre-sag

value once the sag is removed.

Fig. 5.17. DC capacitor voltage and angle controller output during voltage sag.

81

5.6.6. CASE-6: ISLANDING AND RESYNCHRONIZATION

In this section the system response during a fault in the utility is investigated. Let us assume a

single-line to ground fault occurs at point F, which is half way between the utility source and point A,

as shown in Fig. 5.18. As the fault occurs, the trip signal for the breakers CB-1 and CB-2 are initiated

by the protection scheme which measure the rate of rise of current ig. But breakers need a finite time

to physically open the contact. During this time, the back to back converters start feeding the fault as

shown by PG, QG in Fig. 5.18, which will result in the collapse of the capacitor voltage VC. As

explained in Section 5.5 , the coordination of breaker tripping and VSC blocking is required to avoid

the voltage collapse.

Fig. 5.18. Location of the single line to ground fault.

With the system is operating in steady state, the single-line to ground fault in phase-a occurs at 0.05

s and the fault is cleared at 0.1 s. The resynchronization process starts at 0.25 s when the Br_Close

signal of CB-2 is generated. Subsequently, at 0.35 s, the Br-Close signal of CB-1 is generated. The dc

capacitor voltage and the angle controller output are shown in Fig. 5.19 in which the angle controller

output is kept constant to its pre-fault value between 0.05 s to 0.25 s. Fig. 5.20 shows real and reactive

power sharing, which are in accordance to the desired objective to keep microgrid load power

constant.

5.6.7. CASE-7: VARIABLE POWER SUPPLY FROM UTILITY

In cases presented above, it has been assumed that the system is running in mode-1 where DGs can

supply the balance of the load requirement once the pre-specified amount of power is drawn from the

utility. The following example shows the switch from mode-1 to mode-2 when the maximum

82

available power that can be supplied by the DGs is reached. Initially the microgrid is running in mode

1. At 0.1 s, the input power from DG-1 (P1avail) suddenly reduces to 60 KW. DG-2 then supplies the

shortfall as can be seen in Fig. 5.21. The load power and that supplied by the utility remain

unchanged. Subsequent to this, suddenly the load changes at 0.35 s in which the power demand in the

microgrid increases from 0.53 MW to 0.64 MW. However, the maximum power that can be supplied

by DG-2 is set at 300 kW. This implies that both the DGs together can supply 360 KW. Moreover, the

utility grid was supplying 200 kW before this event. Therefore an additional 80 KW power is required

from the utility grid and hence a mode change is inevitable. This mode change is initiated with VSC-2

droop gains of mT = 0.03 rad/MW and nT = 0.02 kV/MVAr. The results are shown in Fig. 5.21. It can

be seen that there is no appreciable overshoot in the active powers supplied by the DGs. The utility

power (PT) rises sharply in order to supply the load demand. The system settles in 5 cycles.

Fig. 5.19. DC capacitor voltage and angle controller output during islanding and resynchronization (Case-6).

Fig. 5.20. Real and reactive power during islanding and resynchronization (Case-6).

83

Fig. 5.21. Real power sharing during power limit and mode change (Case-7).

5.6.8 CASE-8: DC VOLTAGE FLUCTUATION AND LOSS OF A DG

Photovoltaic (PV) cells are the most common form of converter interfaced DGs. The power output

from these cells may vary during the day and may also have fluctuations depending on the

atmospheric conditions. However so long at the DC voltage remains above a threshold, the converter

tracks the output voltage reference. If the voltage falls below this threshold, the converter is switched

off and the utility and the other DGs will have to share the microgrid load. To prove this point, a

simulation is carried out in which it is assumed that DG-2 is capable of supplying the excess load

demand, while the utility supplies the pre-specified amount of power in mode-1. If this is not possible,

a switch to mode-2 will be necessary, which is not shown here.

Fig. 5.22. DC voltage fluctuation in DG-1 and its tripping (Case-8).

84

The simulation results for this case are shown in Fig. 5.22. The dc voltage of DG-1 has a sinusoidal

fluctuation of 3% and at 0.05s, it starts ramping down as in Fig. 5.22 (a). The 500 Hz fluctuation is

shown in the inset. At 0.3 s, when the dc voltage falls below 2.25 kV, this DG is isolated from the

system. Since the other DG picks up the load, any appreciable drop in vp1 (Fig. 5.4) does not occur as

evident from Fig. 5.22 (b). Fig 5.22 (c) and (d) show the real and reactive powers respectively. It can

be seen that there is a slight drop in the load power indicating a slight microgrid voltage drop.

However the utility power remains unchanged and that supplied by DG-2 increases.

5.7 MICROGRID CONTAINING MULTIPLE DGS

In the studies presented so far, it has been assumed that only two DGs and a load are connected to

the microgrid. In general, however, there might be several DGs and loads connected to it, as shown in

Fig. 5.23. It is assumed that there are a total number of n loads and m DGs. The total active and

reactive powers consumed by the loads are given by

LnLLL

LnLLL

QQQQ

PPPP

+++=+++=

21

21 (5.7)

The required power will be shared by DGs depending on their rating, given by

mratedmratedrated

mratedmratedrated

QnQnQn

PmPmPm

×==×=××==×=×

2211

2211 (5.8)

However, like any droop method, the different line impedance between the load connection points,

throughout the microgrid will have slight impact on the load sharing. The reference generation for the

DGs will remain the same as before.

To validate a proper load sharing with multiple DGs, two more DGs are connected to the microgrid.

The DG parameters, output impedance, converter structure and controller are the same as those used

for DG-1 and DG-2. The droop coefficients for the four DGs are chosen such that they share both real

and reactive power in the ratio of DG-1: DG-2: DG-3: DG-4 is 1:1.25:1.55:1.72. The load is also

distributed in three different places to achieve a microgrid structure similar as shown in Fig. 5.23 with

m = 4 and n = 3. Fig. 5.24 shows the real power sharing, where the load power demand is doubled at

0.3 s, and brought back to initial value at 0.8s. It is evident from the figure that a proper load sharing

occurs in the desired ratio.

85

Fig. 5.23. Microgrid structure with large number of DGs and loads.

Fig. 5.24. Real power sharing with four DGs.

5.8 CONCLUSIONS

In this chapter, a load sharing and power flow control technique is proposed for a utility

connected microgrid. The utility distribution system is connected to the microgrid through a set of

back-to-back converters. In mode-1, the real and reactive power flow between utility and microgrid

can be controlled by setting the specified reference power flow for back-to-back converters module.

Rest of the power requirement in the microgrid is shared by the DGs proportional to their rating. In

case of high power demand in the microgrid, the DGs supply their maximum power while rest of the

power demand is supplied by utility through back-to-back converters (mode-2). A broadcast signal

can be used by the DGs to indicate their mode change. However only locally measured data are used

by the DGs and no communication is needed for the load sharing. The utility and microgrid are totally

isolated, and hence, the voltage or frequency fluctuations in the utility side do not affect the microgrid

86

loads. Proper switching of the breaker and other power electronics switches has been proposed during

islanding and resynchronization process.

87

CHAPTER 6

STABILITY ANALYSIS OF MULTIPLE CONVERTER BASED AUTONOMOUS

MICROGRID

In an autonomous microgrid, all the DGs are responsible for maintaining the system voltage and

frequency while sharing the power and reactive power.

In this chapter, stability of multiple converter based autonomous microgrid is studied through

the eigenvalue analysis. The VSC of each DG with its state feedback and droop controllers are

modeled in the state space domain. Each DG is referred to a common reference frame. The network

and loads are also modeled separately. As the converters operate in high frequency mode, the network

dynamics are not neglected [79]. Hence the overall system is represented in differential equation form

rather than differential-algebraic form. The models of the DGs, loads and network are connected

together to get complete generalized model of an autonomous microgrid. A detail eigenvalue analysis

is carried out to identify the trajectory of the eigenvalues with respect to the droop control parameters.

Also the effect of droop control parameters on system stability is investigated when system

configuration changes. A sensitivity analysis is also performed to detect the modes participation to

state variables. The eigenvalue analysis results are verified through simulation studies using

PSCAD/EMTDC. It has been shown that the stability predicted by the eigenvalue analysis is fairly

accurate.


All the DGs are assumed to be an ideal dc voltage source supplying a voltage of Vdc to the VSC. The

structure of the VSC is as shown in Appendix A.

The following state vector is chosen

[ ]cfcfT viix 2= (6.1)

where converter output voltage is the same as the voltage across the filter capacitor vcf.

88

The control action results in perfect tracking when the error is within limit [80].

6.2 DROOP CONTROL AND DG REFERENCE GENERATION

The same control strategy, as discussed in this section, is applied to all the DGs. It is assumed total

power demand in the microgrid can be supplied by the DGs and no load shedding is required. The

output voltages of the converters are controlled to share this load proportional to the rating of the

DGs. As an output inductance is connected to each of the VSCs, the real and reactive power injection

from the DG source to the microgrid can be controlled by changing voltage magnitude and its angle

[53]. Fig. 3.1 shows the power flow from a DG to the microgrid where the rms values of the voltages

and current are shown and the output impedance is denoted by jXf. It is to be noted that real and

reactive power (P and Q) shown in the figure are average values.

6.2.1. DROOP CONTROL

The power sharing among the converter interfaced sources is achieved through angle droop

control as discussed in Section 2.2 of Chapter 2.

6.2.2 DG REFERENCE GENERATION

It is evident that the reference for all the elements of the states, given in (6.1), is required for state

feedback. Since V and δ are obtained from the droop equation, the reference for the capacitor voltage

and current are given by

( )δω += tVvcfref cos (6.2)

( )δωω += tCVi fcfref sin (6.3)

The reference for the current i2 can be calculated as

f

tcfref jX

vvi

−=2

89

The above calculation will need a phase shifter for the instantaneous current reference. This may not

be desirable. Hence the measured values of the average real and reactive power output of the VSC can

be used to find the magnitude and phase angle of the reference rms current. From Fig. 3.1, it can be

seen that

( )PQIV

QPI ref

cfref /tanand 1

2

22

2−−=∠

+= δ

Hence the current reference can be given as

( )refrefref ItIi 222 cos ∠+= ω (6.4)

6.3 STATE SPACE MODEL OF AUTONOMOUS MICROGRID

The stability of a microgrid needs to be studied through the analysis of state-space models, and so

suitable models of converters are needed to complement the well-established models of rotating

machines. As machine models include features such as automatic voltage regulators and wash-out

functions, the converter model should also include the internal control loops [51]. In an autonomous

microgrid that contains converter based DGs only, the fast switching action can influence the network

dynamics [51]. Hence the network is modeled by differential equations rather than algebraic equations

for stability investigation. So far we have presented the single-phase control of the converter.

However, for the analysis of the total microgrid system, a common reference frame is chosen and the

system voltages and currents are converted in a DQ reference frame.

Fig. 6.1 shows the block diagram of the complete microgrid system containing Z number of DGs. It

is assumed that the model of each of DGs is same. This includes the VSC with its state feedback

controller, droop controller and the interface block that connects the converter to the network. The

system equations are nonlinear and thus they are linearized to perform eigenvalue analysis. The linear

quantities are denoted by the prefix ∆. The measured real and reactive power output (P, Q) of

converter is fed to the droop controller, while voltage reference (vcfref, ref), set by droop controller,

is fed back to the converter. The DGs are connected to the network through the interface block which

convert the input/output signal from DG reference frame to the common reference frame and vice

versa. Each DG block has, current output to the network, which is converter output current (i2D,

90

i2Q) and network voltage as input (vtD, vtQ). Similarly, the input to the load model is the network

voltage at the connected nodes (vtD, vtQ) and its output is the load current (iLoadDQ). The state space

equations of the DG-VSC, load and network are derived separately in a modular fashion. These are

then combined together depending on the network structure to get the overall microgrid system model.

Fig. 6.1. Interconnection diagram of the complete microgrid system.

6.3.1 CONVERTER MODEL

From equivalent circuit shown in Fig.A.4 of Appendix-A, the following equations are obtained for

each of the phases of the three-phase system

( )T

dccf

T

T

L

Vuvi

LR

dtdi .

11 +−

+−= (6.5)

( )f

cf

Cii

dt

dv 21 −= (6.6)

dtdi

Lvv ftcf2=− (6.7)

Equations (6.5-6.7) are translated into a d-q reference frame of converter output voltages, rotating at

system frequency , where a-b-c to d-q transformation matrix P is given by

91

( )

( )

+−

−−−

+

−

=

21

21

21

32

sin3

2sinsin

32

cos3

2coscos

32 πωπωω

πωπωω

ttt

ttt

P

Defining a state vector as

Tcfqcfdqdqdi vviiiix ][ 2211=

the state equation in the d-q frame is given by

tdqcdqiii vBuBxAx 21 ++= (6.8)

In (6.8), the matrices are

−−

−

−

−−−

−−

=

01

01

0

001

01

10000

01

000

1000

01

00

ω

ω

ω

ω

ω

ω

ff

ff

f

f

TT

T

TT

T

i

CC

CC

L

L

LLR

LLR

A

−

−

=

=

0000

10

01

0000

and0

0000000

0

0

21

f

fT

dc

T

dc

L

LB

LV

LV

B

It is assumed here that the tracking is perfect and hence, in the limit, u can be represented by uc. ucdq

can be expressed as

( ) ( )( )

( )cfrefdqcfrefdq

refdqcfdqdqdq

cfrefdqcfdq

cfrefdqdqdqrefdqdqcdq

vkik

ikvkikkik

vvk

iiikiiku

32

21321212

3

212221

−−

−−−+−=

−−

−−−−−=

(6.9)

92

The above equation can be written in matrix form as

refdqiiiq

d yHxGu

u+=

(6.10)

where,

( )( )

−−−−−−

=3122

3122

000

000

kkkk

kkkkGi

−−−−−−

=321

321

000

000

kkk

kkkH i

Tcfrefqcfrefdcfrefqcfrefdrefqrefdrefdq vviiiiy ][ 22=

Substituting (6.9) into (6.10) we get

( ) tdqrefdqiiii vByHBxGBAx 2111 +++= (6.11)

Since Vdc is assumed to be constant, the linearization of (6.11) will not alter B1. This linearization

results in

tdqrefdqCONViCONVi vByBxAx ∆+∆+∆=∆ 2 (6.12)

where , ACONV = Ai + B1Gi and BCONV = BiHi.

The current references can be expressed in terms of the voltage reference as

∆∆

−=

∆∆

cfrefq

cfrefd

f

f

cfrefq

cfrefd

v

v

C

C

ii

00

ωω

(6.13)

∆∆

−+

∆∆

−=

∆∆

tq

td

f

f

cfrefq

cfrefd

f

f

refq

refd

vv

L

Lvv

L

L

i

i

01

10

01

10

2

2

ω

ω

ω

ω (6.14)

Combining (6.13) and (6.14), the reference vector is given as

tdqcfrefdqrefdq vMvMy ∆+∆= 21 (6.15)

where

93

−

=

−

−

=

00

00

00

00

01

10

and

10

01

0

0

01

10

21f

f

f

f

f

f

L

L

M

C

CL

L

Mω

ω

ωω

ω

ω

Combing (6.12) and (6.15) we get the converter model as

tdqBUScfrefdqTiCONVi vBvBxAx ∆+∆+∆=∆ (6.16)

where BT = BCONVM1 and BBUS = BCONV (M2 + B2).

6.3.2 DROOP CONTROLLER

The droop controller set the references for converter output voltage magnitude and its angle. The

output voltage of the converter is equal to voltage across the capacitor Cf. The measured instantaneous

real and reactive power are passed through two lowpass filters to obtain the average values of P and Q

respectively. These can be expressed as

( )

( )dcfqqcfdC

C

C

C

qcfqdcfdC

C

C

C

ivivs

Qs

Q

ivivs

Ps

P

22

22

ˆ

ˆ

−+

=+

=

++

=+

=

ωω

ωω

ωω

ωω

(6.17)

where c is cut-off frequency of the filter. Linearizing equation (6.17) we get,

∆∆

+

∆∆

−−

=

∆∆

dq

cfdqP

C

C

i

vB

QP

QP

20

0

ωω

(6.18)

where,

−−=

000202

000202

cfdCcfdCdCqC

cfqCcfdCqCdCP VVII

VVIIB

ωωωωωωωω

and 0 indicates the nominal values.

Let us now define the three-phase reference filter capacitor voltages as

94

+

−=

)3

2cos(

)3

2cos(

)cos(

πω

πω

ω

tV

tV

tV

v

v

v

cfref

cfref

cfref

c

b

a

(6.19)

Then using the transformation matrix P we get

−−+−−=

−+++=

)3

42sin()

34

2sin()2sin(3

)3

2(cos)

32

(cos)(cos3

2 222

πωπωω

πωπωω

tttV

v

tttV

v

cfrefcfrefq

cfrefcfrefd

From the above equation we get

0 and == cfrefqcfrefcfrefd vVv (6.20)

It can be seen from Fig. 3.3 that vcf is the converter output voltage. Hence from the droop equation and

(6.20), we can write the voltage droop equation as

( )ratedratedcfrefcfrefd QQnVVv −−== (6.21)

Linearizing and combining the droop equation angle droop (Section 2.2 of Chapter 2) and (6.21) them

we get the droop controller model as

∆∆∆

−−

=

∆∆∆

Q

Pn

m

v

v

cfrefq

cfrefd

ref δδ

00000

00 (6.22)

6.3.3 COMBINED CONVERTER-DROOP CONTROL MODEL

Let us now substitute Vcfrefdq from (6.22) in the converter model of (6.16). This gives

tdqBUSGiCONVi vBQP

BxAx ∆+

∆∆

+∆=∆ (6.23)

where,

−=

000 n

BB TG .

Combining the converter and droop controller state vectors together an extended state vector is

formed as

95

[ ]TcfqcfdqdqdCONV vviiiiQPx 2211=

The combined state equation is then written as

tdqcCONVcCONV vBxAx ∆+∆=∆ (6.24)

where

Ο=

= ×

BUSc

CONVG

ccc B

BAB

AAA 221211 and

where Oi×j represents null matrix of dimension i×j and

−−

=C

CcA

ωω0

011

−−=

020200

02020012 00

00

dCqCcfdCcfqC

qCdCcfqCcfdCc IIVV

IIVVA ωωωω

ωωωω

6.3.4 TRANSFORMATION TO COMMON REFERENCE FRAME

Since all the converters are modeled individually with their own d-q axis reference, they need to be

transformed into common reference D-Q frame. The small signal output current of the converter in D-

Q frame is

δ∆+∆=∆ CdqSDQ TiTi 22 (6.25)

where

−−−

=

−=

020020

020020

00

00

sincoscossin

cossinsincos

δδδδ

δδδδ

qd

qdCS II

IITT

Similarly the input to the converter from the network, the network voltage can be expressed in as,

δ∆+∆=∆ −− 11VtDQStdq TvTV (6.26)

where

−−+−

=−

0000

00001

sincoscossin

δδδδ

QtDt

QtDtV VV

VVT

96

Substituting equation (6.26) in (6.24) we get

δ∆+∆+∆=∆ 1PtDQLCONVcCONV BvBxAx (6.27)

where BL = BC TS−1 and BP1 = BC TV

−1

It is to be noted that in equation (6.27) can be expressed as the droop controller output equation

in terms of P. It is assumed that the change in angle in the converters is instantaneous such that the

converter produces the demanded angle (ref). The state equation (6.27) can be written as

tDQLCONVLCONV vBxAx ∆+∆=∆ (6.28)

where [ ]781 ×Ο−= PcL BmAA .

Similarly (6.25) is expressed as

CONVPDQ XCi ∆=∆ 2 (6.29)

where

−=

00cossin000

00sincos000

0021

0011

δδδδ

C

CCP and

)sincos(

)cossin(

02002021

02002011

δδδδ

qd

qd

IImC

IImC

−−=

+=

Let us assume that the microgrid has Z number of DGs with their state space and output equations

being given by

ZiXCi

vBxAx

CONViPiDQi

tDQiLiCONViLiCONVi ,,1,2

=

∆=∆∆+∆=∆

(6.30)

Then the combined state space equation including all the converters in the system is written as

ZZZ

tZZZZZ

xCi

vBxAx

∆=∆∆+∆=∆

2

(6.31)

where AZ, BZ and CZ are block diagonal matrices, given by

( )( )( )PZPPZ

LZLLZ

LZLLZ

CCCC

BBBB

AAAA

21

21

21

diag

diagdiag

===

The input, output and state vectors of the state space equations are defined as

97

∆

∆∆

=∆

∆

∆∆

=∆

∆

∆∆

=∆

CONVZ

CONV

CONV

Z

DQZ

DQ

DQ

Z

tDQZ

tDQ

tDQ

tZ

x

x

x

x

i

i

i

i

v

v

v

v

2

1

2

22

12

22

1

6.3.5 NETWORK AND LOAD MODELING

The network and the loads are modeled as shown in [51]. We have assumed that there are L number

of loads, N number of network nodes and LN number of lines. The state space equation of the ith load

connected at jth node is given by

tDQiLoadiLoadDQiLoadiLoadDQi vBiAi ∆+∆=∆ (6.32)

where

=

−−

−=

Loadi

LoadiLoadi

Loadi

Loadi

Loadi

Loadi

Loadi

L

LB

LR

LR

A1

0

01

ω

ω

Combining the total of L number of loads together, we get

tLoadLoadLoadLoadLoad vBiAi ∆+∆=∆ (6.33)

where ALoad and BLoad are block diagonal matrices and

∆

∆∆

=∆

∆

∆∆

=∆

tDQL

tDQ

tDQ

tLoad

LoadL

Load

Load

Load

v

v

v

v

i

i

i

i

2

1

2

1

In a similar way the state space equation for the network is written as

tLNLNLNDQLNLN vBiAi ∆+∆=∆ (6.34)

where ALN and BLN are block diagonal matrices containing the

individual state matrices for the ith line connected between jth and kth node. These matrices are given

by

98

LNi

LR

LR

A

Linei

Linei

Linei

Linei

Ni ,,1, =

−−

−=

ω

ω

−

−=

...1

0...1

0...

...01

...01

...

LinekLinej

LinekLinejNi

LL

LLB

It can be seen that the matrix BNi contains elements only pertaining to nodes j and k.

6.3.6. COMPLETE MICROGRID MODEL

Once the converters, network and loads are modeled, they are combined to get the complete model

of the microgrid. Between each network node and ground a virtual resistance (rN) of large magnitude

( 1000 ) is chosen to ensure a well defined node voltage [51]. Suppose node i contains both a

converter and a load. Then the node voltage can be written in terms of the three currents, e.g.,

converter output currents, load currents and line currents in the network as

( )LineDQiLoadDQiDQiNtDQi iiirv ∆+∆−∆=∆ 2 (6.35)

Therefore the node voltage equation for the complete microgrid can be written as

( )LineNETLoadLOADZCONVNtM iMiMiMRv ∆+∆+∆=∆ 2 (6.36)

where, the matrix RN is defined as the 2N×2N matrix with diagonal elements equal to rN. The MCONV is

a 2N×2Z matrix. Let us assume that the ith converter is connected with the jth node. Then the (j,i)

element of the matrix is 1, all other element in the row is 0. Similarly MNET is 2N×2LN matrix, whose

(j,i) element will be + 1 or − 1, depending on whether the current entering or leaving the node, if the

ith line is connected to the jth node. MLOAD is the 2N×2L matrix with an entry of − 1 for the nodes

where the loads are connected.

It is to be noted that in (6.31) the state space equation for DGs, is derived for the network nodes

where the DGs are connected. Similarly the state space equation for load and lines are derived for the

point of load and line connection in the network. To derive a general equation for the DGs taking all

the network nodes into account, (6.31) can be written as

99

ZZZ

tMZZZZ

xCi

vBxAx

∆=∆∆+∆=∆

2

1 (6.37)

where vtM represents the complete network voltage vector, considering all the network nodes. BZ1 can

be derived from BZ where the diagonal terms are zero if no DG is connected to that node and BLi for

the ith node if a DG is connected to that node.

Similarly the load and line equations (6.33) and (6.34) can be represented in terms of all the

network nodes as

tMLoadLoadLoadLoad vBiAi ∆+∆=∆ 1 (6.38)

tMLNLNDQLNLN vBiAi ∆+∆=∆ 1 (6.39)

The total microgrid model is then derived by combining equation (6.36), (6.37), (6.38) and (6.39)

∆∆∆

=

∆∆∆

Load

LN

Z

MG

Load

LN

Z

i

i

x

A

i

i

x

(6.40)

The state matrix of the whole microgrid AMG is given

++

+=

LOADNLOADLOADNETNLOADZCONVNLOAD

LOADNLNNETNLNLNZCONVNLN

LOADNZNETNZZCONVNZZ

MG

MRBAMRBCMRB

MRBMRBACMRB

MRBMRBCMRBA

A

111

111

111

(6.41)

6.4 SYSTEM STRUCTURE AND MODEL OF AUTONOMOUS MICROGRID

EXAMPLE

The structure of the study system is shown in Fig.6.2. The real and reactive powers supplied

by the DGs are denoted by Pi, Qi, i = 1, …, 3. The real and reactive power demand from the loads are

denoted by PLi, QLi, i = 1, …, 3. The load and line impedances are also shown in the figure.

100


For the system shown in Fig. 6.2, Z = 3. Then the matrices defined in the previous section are given

below.

DG:

=

=

=

3

2

1

3

2

1

3

2

1

00

0000

,

00

00

00

,

00

00

00

P

P

P

Z

L

L

L

Z

L

L

L

Z

C

CC

C

B

B

B

B

A

A

A

A

Line:

=

=

2

1

2

1 ,0

0

N

NLN

N

NLN B

BB

A

AA

Load:

=

=

3

2

1

3

2

1

,

00

00

00

Load

Load

Load

Load

Load

Load

Load

Load

B

B

B

B

A

A

A

A

These three M matrixes in (6.43) are calculated for the given example as

6IMCONV =

where I6 is a 6×6 identity matrix and

−−

−−

−−

=

001000

000100100000

010000

000010000001

LOADM

101

−−

−−

=

1000

01001010

0101

00100001

NETM

The matrix AMG is then derived from these matrices for eigenvalue analysis.

6.5 EIGENVALUE ANALYSIS OF MICROGRID

The parameters chosen for the system shown in Fig. 6.2 are listed in Table-6.1. When the system

operates with the parameters given in Table-6.1, it is assumed to be operating in the nominal operating

condition. The eigenvalues of the system for this nominal operating condition are shown in Fig. 6.3. It

can be seen that the eigenvalues, based on their damping (real component), are placed on four

different clusters. It will be shown that the dominant eigenvalues of cluster 1 are sensitive to the

changes in the droop controller parameters. The eigenvalues of clusters 2, 3 and 4 are sensitive to the

other parameters, like filter, state feedback controller, load etc., and their effects are not investigated

here.

TABLE-6.1: NOMINAL SYSTEM PARAMETERS




Line impedance Line-1: RLine1=3.83Ω, LLine1 =0.0053 H (R/X>2)

Line-2: RLine2=5.83Ω, LLine2 =0.0308 H (R/X<1)

Load

RLOAD1 = 420.0 Ω, LLOAD1 = 0.5 mH

RLOAD2 = 333.0 Ω, LLOAD2 = 0.5 mH

RLOAD3 = 420.0 Ω, LLOAD3 = 0.5 mH

DGs and Controller

DC voltage (Vdc1, Vdc2, Vdc3)

Transformer rating

VSC losses (Rf)


Filter Inductances (Lf)

3.5 kV

3 kV/11 kV, 0.5 MVA, 2.5%

1.5 Ω

185 µF

20 mh

State Feedback

Controller (K)

[1.6963 0.3449 1.6959]

Droop Coefficients

m1 = m2 = m3 = m

n1 = n2 = n3 = n

4.18×10−5 rad/W

2.272×10−4 V/Var

Low pass Filter cut-off C 31.4 rad/sec

102

Fig. 6.3. Eigenvalues for nominal operating condition.

Table-6.2 lists the modes of the eigenvalues of cluster 1 and their participation factor on the real

and reactive power state variable of the three DGs. In this table, mode Q-1-2 indicates that this mode

is sensitive to the reactive powers of DG-1 and DG-2. In a similar way, all the other modes are

defined.

TABLE-6.2: MODE PARTICIPATION FACTORS.

Dominant Modes

Mode Q-1-2 Mode Q-1-2-3 Mode PQ-1-2-3

State Participation State Participation State Participation

P1 0.0008 P1 0.0006 P1 0.1689

Q1 0.4600 Q1 0.2216 Q1 0.1600

P2 0.0010 P2 0.0003 P2 0.1683

Q2 0.5385 Q2 0.1366 Q2 0.164

P3 0.0000 P3 0.0000 P3 0.1679

Q3 0.0035 Q3 0.6428 Q3 0.1804

Not Dominant Modes

Mode P-1-2 Mode P-1-3

P1 0.1929 P1 0.1199

Q1 0.0005 Q1 0.0005

P2 0.2357 P3 0.2291

Q2 0.0007 Q3 0.0005

For example, PQ-1-2-3 is sensitive to real and reactive power of all three DGs. This strong real and

reactive coupling is due to highly resistive lines in the network. It can also be seen that the modes P-1-

2 and P-1-3 are not very sensitive. However the DG real powers have some influence on them

103

Fig. 6.4 shows the locus of the eigenvalues of cluster 1 as the droop controller real power coefficient

m changes. It can be seen that for a very high value of m (6.18×10−5), a complex conjugate pair the

eigenvalues almost reaches the imaginary axis indicating a low system stability. For m = 8.18×10−5,

the above pair crosses the imaginary axis and three more eigenvalues reach the imaginary axis,

indicating an unstable operation

Fig. 6.5 shows the locus of the eigenvalues of cluster 1 as the droop controller reactive power

coefficient n changes. It can be seen that this coefficient also has significant effect on system stability.

It can be seen that a complex conjugate pair of eigenvalues of cluster 1 reaches the imaginary axis

Fig. 6.4. Eigenvalue locus with real power droop gain change.

Fig. 6.5. Eigenvalue locus with reactive power droop gain change.

104

Fig. 6.6. Eigenvalue locus without DG-3.

when n = 2.5×10−3. The results of the eigenvalue analysis will be validated through simulation studies

in the next section, where the effect of these droop controller parameters will be clearly shown.

Fig. 6.6 shows the eigenvalue locus as a function of the real power coefficient when DG-3 removed

from the system, with the loads reaming the same. It can be seen that the eigenvalues remain stable

even with m = 8.18×10−5, for which the 3-DG system was unstable (Fig. 6.4). The effect of reduction

of the size of the microgrid is further investigated through simulation studies in the next section.

It is to be mentioned here that the gains of the state feedback controllers have no adverse effects on

the system stability. The controllers are designed using LQR, which is very robust. This has been

observed by changing the cost function in the LQR design and the results are not shown here.


Simulation studies are carried out in PSCAD/EMTDC (version 4.2). Different configurations of load

and its sharing are considered. The DGs are considered as inertia less dc source supplied through a

VSC. The system data used for eigenvalue analysis (Table-6.1) are also used here. It is to be noted

that R/L value of Line-1 in Fig. 6.2 is very high. Hence there is a strong real and reactive power

coupling present in the system. The power sharing accuracy will improve further with inductive line

where the real and reactive power coupling is much weaker. The nominal values of the droop

controller parameter are chosen such that there is 3% voltage drop with the maximum reactive power

output.

105

6.6.1 CASE 1: FULL SYSTEM OF FIG. 6.2 (3 DG AND 3 LOADS)

In this case it is assumed that all the DGs and loads are connected in the system shown in Fig.6.2.

The nominal values of controller parameters, given in Table-6.1, are considered here. With the system

operating in the steady state, load 1 is increased by 0.45 MW at 0.1 s. The results are shown in Fig.

6.7. The system takes around 5-6 cycles to reach steady state.

From Fig. 6.4, it can be seen that the system becomes unstable when m = 8.18×10−5 rad/W. With

the system operating in the steady state with the nominal value of m, which is suddenly changed to

8.18×10−5 at 0.05 s. The unstable system response is shown in Fig. 6.8.

Similarly for n = 2.5×10−3, the dominant eigenvalues are oscillatory. This can be observed from Fig.

6.9, where n is changed to this value from the nominal value at 0.1 s. Figs. 6.8 and 6.9 validate the

eigenvalue study.

6.6.2 CASE 2: THE EFFECT OF SYSTEM REDUCTION

In this section, we shall investigate the effect of the reduction of loads, lines and DGs on the system

stability. From Fig. 6.4, it can be seen that the full system is oscillatory for m = 6.18×10−5. This is also

evident from Fig. 6.10 (a), where a sustained oscillation can be observed following a small (0.15 MW)

change in load 1 at 0.1 s. The response for the same load change is shown in Fig. 6.10 (b), when DG-3

is not operational. From the eigenvalue locus of Fig. 6.6, it can be seen that the system remains stable

for this condition. This is also evident from Fig. 6.10 (b).

With same value of m and load change as above, the system is simulated first with DG-3 and line 2

removed. This implies that DG-1, DG-2 and load-1 and load-3 remain in the system. Fig. 6.11 (a)

shows the real power sharing. Even with high value of m, the system remains stable. In Fig.6.11 (b),

the real power sharing is shown when only DG-1, DG-3 and load 3 remain in the system. Though high

line impedance between the DG-1 and DG-3 makes the load sharing less accurate, the system reaches

much quickly than when 2 DGs and 2 loads are present. (Fig. 6.11 (a)).

106

Fig. 6.7. Real and reactive power during a change in load 1.

Fig. 6.8. Unstable operation with m = 8.18×10−5 rad/W.

Fig. 6.9. Marginally stable operation with n = 2.5×10−3 V/VAr.

107

Fig. 6.10. System response 3 and 2 DGs for m = 6.18×10−5 rad/W.

Fig. 6.11. System response for different system configuration.

6.7 IMPROVEMENT IN STABILITY WITH SUPPLEMENTARY DROOP

CONTROL

The schematic layout of the supplementary loop around the conventional droop control is shown in

Fig. 6.12. The real power output Pi, of the ith converter is fed through a high pass washout circuit (with

0.05 s time constant) to capture the oscillatory behavior, eliminating the dc component, ∆Pi about the

steady-state value Pi. The supplementary control signal, ∆vdrefi, modulates the output of the droop

controller to generate a modified d-axis voltage reference, vdrefi´ for each converter. The droop

equation is then modified for the ith converter as

( )( ) iiratediiratediii

iiratediiratediii

VQQnVVVV

PPm

∆+−×−=∆+=

∆+−×−=∆+=*

* δδδδδ (6.42)

108

where ∆Vi and ∆i are the voltage magnitude and voltage angle correction by the supplementary

controller signal ∆Vdrefi. The resultant voltage reference for the converter is

qrefidrefiii VjVV ∗+=∠ ** δ (6.43)

Fig. 6.12. Supplementary Droop Controller Configuration

When the DGs are supplying rated power, the angle of the converter output voltage is rated. As the

irated = miPirated, the rated angles for all the DGs are 0.1 rad,. It is to be noted that the rated angles are

chosen so that when the output power of the DGs are zero, the reference output voltage angle is zero.

The test system considered for this study has three critical oscillatory modes with frequencies in the

vicinity of 50 Hz which require stability enhancement. To ensure adequate controllability and

observability of these modes, each of the four converters were equipped with a separate

supplementary control loop. The structure of each controller was fixed a priori and is comprised of

three lead-lag blocks and a gain as shown in Fig. 6.13 for the ith converter. The calculation of these

unknown gains, Ki, i=1,2,3,4, and the time constants Tij, i =1,2,3,4; j = 1,2,..,6, are formulated as a

parameter optimization problem with the constraint on stability of the closed-loop over a range of

operating conditions. A lower limit of 0.01 and an upper limit of 100 were imposed on the search

space of the denominator time constants to ensure stable poles and fast enough controller response.

Simultaneous design of the four decentralized controllers eliminates possible interactions and ensures

overall stability due to their combined action.

Fig. 6.13. Supplementary controller structure

It is not straight forward to solve the above parameter optimization problems using analytical

techniques [80, 81], one of the reasons being lack of proper choice of initial guess. Hence, swarm

optimization [82] – one of the standard evolutionary techniques – was employed here. The optimum

gains and time constants obtained are shown in Table 6.3. Parameters of the supplementary controllers

109

are tuned simultaneously to eliminate possible interactions. No constraint on gain of the controller and

lead time constant of each lead-lag compensator block have been imposed during the optimization

stage to allow more search space. This has resulted in one negative gain and a few right half plane

zeros in the compensator. If the phase compensation required is less than zero, it is more effective (in

terms of the number of lead-lag blocks required) to use a negative feedback (180 degrees) and to

compensate for only the difference between 180 degrees and original phase compensation. For the

first channel with negative gain (K1) this turned out to be the case. Also a non minimum phase

feedback controller does not imply a non minimum phase closed loop system. The step responses did

not show any evidence of non minimum phase behavior. Constraining feedback to be minimum phase

for this problem with a wide range of droop gains resulted in no feasible solution. Permitting non

minimum phase feedback enabled a feasible solution to be found. If there were less onerous

requirement on the range of gain then a feasible solution become possible with a minimum phase

constraint. However we placed the major emphasis in accurate sharing and the optimization process

results in right half plane zeros as mentioned above.

A standard lead lag compensation structure, which is most widely adopted and easily

implementable structure of different kind of supplementary controllers in power system application

such as PSS (Power System Stabilizer), is adopted during control design.

Table-6.3: PARAMETERS OF THE SUPPLEMENTARY DROOP CONTROL LOOP

Parameters Conv 1

Conv 2

Conv 3

Conv 4

Ki -13.8409 4.8089 12.3064 12.4806

Ti1 13.1384 -12.805 14.6033 14.8943 Ti2 8.6429 12.4003 13.9471 1.0895 Ti3 15.6881 16.1046 -1.1439 -14.482 Ti4 0.3669 0.01 6.1067 0.01 Ti5 3.8954 5.2054 0.01 0.4818 Ti6 0.2475 0.4223 0.01 5.9059

As high droop gains are needed for proper load sharing, the proposed supplementary controller is

aimed to guarantee the system stability even with high droop gains. Note that the controller gains were

optimized to obtain a good performance over a range of operating conditions despite the requirement

of stabilizing a family of a number of unstable plants with a fixed structure low order compensator.

This has resulted in the change of frequencies of the dominant eigenvalues. However, as the

frequencies did not migrate either up to the switching range or down to the low oscillatory frequency

range, it was not necessary to modify the performance index to avoid the frequency shift.

110

6.7.1 TEST SYSTEM

The structure of the study system is shown in Fig. 6.14. The real and reactive powers supplied by

the DGs are denoted by Pi, Qi, i = 1, …, 4. The real and reactive power demand from the loads are

denoted by PLi, QLi, i = 1, …, 5. The line impedances are denoted by Z12-Z89 in the figure. The system

matrix AT is derived with all the parameter shown in Table-6.4 for eigenvalue analysis.


6.7.2 SIMULATION STUDIES WITH SUPPLEMENTARY DROOP CONTROLLER Different configurations of load and power sharing of the DGs are considered to ensure that the

propose controller provide a stable operation in all the situations . The DGs are considered as inertia

less dc source supplied through a VSC.

6.7.2.1 CASE 1: FULL SYSTEM OF FIG. 6 WITH LOWER DROOP GAINS

In this case, it is assumed that all the DGs and loads are connected to the microgrid as shown in Fig.

6. The lower droop gains values of controller parameters, given in Table-6.4, are considered here.

With the system operating in the steady state, Ld1 changed to 155 kW from 100 kW at 0.25 s. Fig.

6.15 (a) shows the real power sharing while Fig. 6.15 (b) shows the three phase terminal voltages of

DG-1. It can be seen that the controller provides proper load sharing with stable system operation.

6.7.2.2 CASE 2: REDUCED SYSTEM WITH LOWER DROOP GAINS

To investigate the load sharing with reduced system, DG-2 and DG-3 are disconnected at 0.25 s and

the total power is shared by DG-1 and DG-4 as shown in Fig. 6.16. At 1.3 s, Ld2 Ld3, Ld4 and Ld5 are

also disconnected. The two DGs connected to the microgrid supply the 100 kW load, Ld1. It can be

seen that system operation is stable. However due to weak system condition, as the DGs are located

geographically far from each other, they can not share load in the desired ratio of 1:1.33

111

Fig. 6.15. Real and reactive power during a change in load 1.

Fig. 6.16.Power sharing with reduced system

6.7.2.3. CASE 3: SYSTEM STABILITY WITH HIGH DROOP GAIN

As discussed before, the power sharing can be made independent of the system condition and the

converter output reactance by choosing high droop controller gains. The eigenvalue analysis, on the

other hand, predicted system instability for such gains. To investigated the system stability with high

droop gain, the full system (Case-1) is operated first with lower value of droop gain and at 0.2 s, the

droop gains are changed to higher values as mentioned in Table-I. Fig. 6.17 (a) shows the system

response with only droop controller while Fig. 6.17 (b) shows system response with proposed

supplementary droop controller.

112

Fig. 6.17. System stability with high droop gain.

6.7.2.4. CASE 4: POWER SHARING WITH THE PROPOSED SUPPLEMENTARY CONTROLLER

In this section, we shall investigate the load sharing capability with proposed supplementary

controller and the system stability. All the simulations are done with high droop controller gain as

mentioned in Table-6.4. With the system running in steady state and supplying power to all the loads,

Ld5 is disconnected from the microgrid at 0.25 s. Fig. 6.18 shows the system response. The power

output of all the converters reduces proportionally and system attains steady state within 8-10 cycles.

The droop controller converter output voltage reference angle and supplementary controller d-axis

voltage modulation is shown in Fig. 6.19, which clearly shows a damping type controller with 90°

phase shift during transients.

Fig. 6.18. Power sharing with proposed controller.

113

Fig. 6.19.Droop controller and supplementary controller output.

6.7.2.5. CASE 5: POWER SHARING WITH THE PROPOSED CONTROLLER IN REDUCED SYSTEM

The power sharing with the proposed controller in the reduced system is investigated in this section.

DG-1 is disconnected first at 0.25 s when system is running in steady state. Fig. 6.20 shows the

response and it can be seen that the other three DGs supply the extra power requirement. Ld5 is

disconnected at 1.3 s and the DG outputs reduce proportionally. From the system response and

numerical values (Appendix-A) it can be concluded that the DGs share the loads as desired while

ensuring stable operation of the system.

Fig. 6.20. System response for different system configuration.

To validate the performance of the supplementary proposed controller, the microgrid is operated

similar situation as described in Case 2 with reduced system. Fig. 6.21 shows the system response.

114

Fig. 6.21. Power sharing in reduced system.



Systems frequency 50 Hz Feeder impedance

Z12 = Z23 = Z34 = Z45 = Z45 = Z56 = Z67 = Z78 = Z89

1.03 + j 4.71 Ω

Load ratings Ld1 Ld2 Ld3 Ld4 Ld5

100 kW and 90 kVAr 120 kW and 110 kVAr 80 kW and 68 kVAr 80 kW and 68 kVAr 90 kW and 70 kVAr

DG ratings (nominal) DG-1 DG-2 DG-3 DG-4

100 kW 200 kW 150 kW 150 kW

Output inductances L1 L2 L3 L4

75 mH 37.5mH 56.4 mH 56.4Mh


DGs and VSCs DC voltages (Vdc1 to Vdc4) Transformer rating VSC losses (Rf) Filter capacitance (Cf) Hysteresis constant (h)

3.5 kV 3 kV/11 kV, 0.5 MVA, 2.5% Lf 1.5 Ω 50 µF 10-5

Droop Coefficients Power−−−−angle

(Lower Droop Gains) m1 m2 m3 m4

Power−−−−angle (Higher Droop Gains)

m1 m2 m3 m4

Voltage−−−−Q n1 n2 n3 n4

0.1 rad/MW 0.05 rad/MW 0.075 rad/MW 0.075 rad/MW 1.0 rad/MW 0.5 rad/MW 0.75 rad/MW 0.75 rad/MW 0.04 kV/MVAr 0.02 Kv/MVAr 0.03 Kv/MVAr 0.03 Kv/MVAr

115

6.8 CONCLUSIONS

In this chapter, a linearized state space model of an autonomous microgrid supplied by all converter

based DGs and connected to number of passive loads is formed. The proposed generalized model is

valid even when the network is complex containing any number of DGs and loads. The model is

utilized for eigenvalue analysis around a nominal operating point. A sensitivity analysis is carried out

to indicate the eigenvalue participation on the state variables. It has been shown that real power modes

get affected with the real power droop coefficients, while the reactive power modes are sensitive to

reactive power droop coefficients. Extensive simulation studies are carried out to validate the results

of the eigenvalue analysis. It has been shown that both the results agree with each other.

High gain angle droop control ensures proper load sharing, especially under weak system

conditions, but has a negative impact on the overall stability. This is illustrated through frequency

domain modeling, eigenvalue analysis and time domain simulations. A supplementary loop is

proposed around the primary droop control loop of each DG converter to stabilize the system despite

having high gains that are required for better load sharing. The control loops are based on local power

measurement and modulation of the d-axis voltage reference of each converter. The coordinated

design of supplementary control loops for each DG is formulated as a parameter optimization problem

and is solved using an evolutionary technique. The use of the supplementary droop control loop is

shown to stabilize the system for a range of operating conditions while ensuring satisfactory load

sharing.

116

117

CHAPTER 7

DROOP CONTROL OF CONVERTER INTERFACED MICRO SOURCES IN

RURAL DISTRIBUTED GENERATION

Two methods have been proposed in this chapter for power sharing with VSC connected DGs in a

rural distributed generation. In first method, decentralized operation of DGs without any

communication is investigated. A transformation matrix is derived for control parameters and

feedback gains taking into consideration the R-by-X ratios of the lines. In second method, the angle

droop power sharing controller is modified to accommodate the highly resistive line. The reference

angle of each converter output voltage is modified based on the desired active and reactive power flow

and the line impedances. A minimum amount of communication is needed among the DGs for the

change in reference angle of the output voltage. We have assumed a low-cost web-based

communication system [83-85] for this purpose.

The main focus of this chapter is the development of a graduated set of control algorithms to deal

with different levels of communication infrastructure to support the microgrid with particular

emphasis on highly resistive lines. The accuracy of the controllers is shown in different weak system

conditions where the conventional angle droop fails to share the power as desired due to high coupling

between the real and reactive power. Mathematical derivations and time domain simulations are used

to illustrate the methodologies.

7.1 POWER SHARING WITH ANGLE DROOP AND PROPOSED DROOP

CONTROL

The power sharing with angle droop in a system with two DGs and a load as shown in Fig. 7.1 is

shown in Section 2.2 as

118

rated

rated

PP

mm

PP

2

1

1

2

2

1 =≈ (7.1)

It is evident from (7.1) that the droop coefficients should be inversely proportional to the DG rating

and also the droop coefficients play the dominant role in the power sharing. The error is further

reduced by taking the output inductance (Lf1, Lf2) of the DGs inversely proportional to power rating of

the DGs. The comparison between the performance of this angle droop and a conventional frequency

droop [12] is shown in Section 2.3.

The simple system shown in Fig. 7.1 is used to show the power sharing. In a real system with

number of DGs and loads in different location line impedance will have an impact on the load sharing.

But for a microgrid within a small geographical area, the line inductance will never be very high.

Moreover a high droop coefficient will always play a dominant role and share the power as desired

with a very small deviation.

Fig. 7.1. Power sharing with angle droop.

To control power flow explicitly from any of the DGs to the local bus (e.g., DG-1 and the bus with

voltage V11∠δ11), an output inductance (e.g., Lf1) is required. This output inductance enables us to

decouple the real and reactive power injection. We shall use this structure for controlling power flow

with communication (the 2nd proposed method). However, in the 1st proposed method, the output

inductance is assumed to be zero. In this control method, we do not require a decoupling of real and

reactive power as will be explained in the next sub-section. Also this control is based on the R/X ratio

of the line and therefore the inclusion of output inductance will require the knowledge of the line

length. Note that the output inductance can be taken as zero depending on the converter output filter

structure, discussed in Appendix.

119

7.1.1 PROPOSED CONTROLLER-1 WITHOUT COMMUNICATION

As discussed before, in the rural distribution system, at the medium or low voltage level the lines

are mostly resistive and the values of the line impedances are not negligible. In that case (7.1) is not

valid. In this case we have assumed that the DGs do not have any output inductance, in which case,

Fig.7.1 is redrawn as shown in Fig. 7.2. Here the line reactance (ωLD) value is chosen to be the same

as line resistance value RD.

Fig. 7.2. Power sharing in resistive-inductive line.

The power flow from DG-1 for system shown in Fig.7.2 as

( )[ ]( )[ ]δδδδη

δδδδη−−+−−=

−+−−=

111111111

111111111

cos()sin(

)sin(cos(

VVXVRQ

VXVVRP

DD

DD

where ( )12

12

11 DD XRV +=η . From the above equation, multiplying Q1 by RD1 and subtracting the

product from the multiplication of P1 and XD1 we get

)sin( 11111111 δδ −=− VVQRPX DD (7.2)

In a similar way, we also get

)cos( 11112

111111 δδ −−=+ VVVQXPR DD (7.3)

It is to be noted that DG-1 does not have any control over the load voltage magnitude and angle.

Thus the linearization of (7.2) and (7.3) around the nominal values of V110 and δ110 results in

( ) 11110111101111 )()( VVVVQRPX DD ∆+∆−∆=∆−∆ δδδ (7.4)

111101111 )2( VVVQXPR DD ∆−=∆+∆ (7.5)

where ∆ indicates the perturbed value. From (7.4) and (7.5), the output voltage magnitude and angle

of a DG-1 can be written in terms of real and reactive power as,

120

∆∆

=

∆∆

−=

∆∆−∆

1

1

1

1

1

1

1

1

1

1

1

1

11

11 )()(Q

PTVK

Q

P

ZR

ZX

ZR

ZX

VKV DD

DDδδ

(7.6)

where the impedance Z1 and the matrix K(V) are given by

1

110

1101101

21

211 20

)(−

−=+=

VV

VVVZVKXRZ DD

δ

Defining pseudo real and reactive power as

∆∆

=

′∆′∆

1

1

1

1

Q

PT

Q

P

From equation (7.6) the control strategy can be chosen as

( )

′∆′∆

=

∆∆

1

1

11

11 1Q

PK

V

δ (7.7)

The above equation forms the basis of modified droop sharing where the matrix K(V) is approximated

as K(1) with the assumption that bus voltage is constant at 1 per unit, giving an error in the control

gain of less than 5%. This will have no significant effect on the power sharing. The load bus angle δ is

not measurable at the DG end. The chosen control (7.7) will automatically correct for changes in δ,

while retaining the desired decoupling property.

The droop control equation for DG-1 is then written as

( )( )ratedrated

ratedrated

QQnVV

PPm

1111111

1111111

′−′×′−=′−′×′−= δδ

(7.8)

where the rated powers (P′1rated, Q′1rated) are also represented after multiplying the conversion matrix

[T]. Similar transformation is also used for the rated powers of DG-2 as well. The droop gains of the

both the DGs are also transformed by the matrix T and are given by as

=

′′

=

′′

2

2

2

2

1

1

1

1 and n

mT

n

m

n

mT

n

m (7.9)

where the real and reactive power droop coefficients are

121

rated

rated

rated

rated

QQ

nn

andPP

mm

2

1

1

2

2

1

1

2 == (7.10)

Then droop equation (7.8) can be expressed as,

′−′′−′

−

=

rated

rated

rated

rated

QQ

PP

n

mT

VV 11

11

1

1

11

11

11

11 δδ (7.11)

This modified angle droop control not only ensures decoupling of the real and reactive power in a

high R/X line, but also provide a rating based power sharing. The control of the output angle results in

a much lower frequency deviation compared to frequency droop as shown in Section 2.3.

7.1.2 PROPOSED CONTROLLER-2 WITH MINIMAL COMMUNICATION

In this sub-section, a droop control is proposed that requires minimal communication. The system

in Fig. 7.1 is considered here and the DGs are connected to the microgrid with their output

inductances.

For small angle difference between the DGs and their respective local buses shown in Fig. 7.1, the

power flow equations of the DGs are given by

22222

11111

PX

PX

=−=−

δδδδ

(7.12)

Both the active and reactive power flow in a highly resistive line are determined by angle difference in

the terminal voltages. The power flow equations over the line for small angle differences can be

written as

222222

111111

PXQR

PXQR

L

L

+−=−

+−=−

δδδδ

(7.13)

where R1= RD1/(V11V), R2 = RD2/(V22V), XL1 = LD1/(V11V) and XL2 = LD2/(V22V).

From (7.13) and (7.14) we get,

2222222

1111111

PXQRPX

PXQRPX

L

L

+−=−

+−=−

δδδδ

(7.14)

The difference between δ1 and δ2 is derived from (7.14) as

122

22222211111121 PXQRPXPXQRPX LL −+−+−=− δδ (7.15)

Again from (2.11) we get,

( )( )rated

ratedratedrated

PPm

PPm

222

1112121

−×+−×−−=− δδδδ

(7.16)

Since the ratio of the droop gains m2:m1 is chosen as the ratio of the rated power P1rated:P2rated, from the

above equation we get

22112121 PmPmratedrated +−−=− δδδδ (7.17)

Equating (7.15) and (7.17) we get,

221121

222222111111

PmPm

PXQRPXPXQRPX

ratedrated

LL

+−−=++−+−

δδ (7.18)

The rated values of the converter output voltage angles are selected with active and reactive power

output of the converter as

2222222

1111111

PXQRPX

PXQRPX

Lrated

Lrated

+−=+−=

δδ

Substituting these values in (7.), we get

rated

rated

PP

mm

PP

PmPm2

1

1

2

2

12211 === (7.19)

It can be seen that the power sharing of the DGs are proportional to their rating. This control

technique shown with above simple example can be extended to multiple DG system. This is

discussed below.

7.1.3 MULTIPLE DG SYSTEM

Fig. 7.3 shows a multiple DG system where three DGs are connected at different location of the

microgrid. The four loads that are connected to the microgrid are shown as Load_1, Load_2, Load_3

and Load_4. The real and reactive power supply from the DGs are denoted by Pi, Qi, i = 1,…, 3. The

real and reactive power flow for different line sections and load demand are shown in Fig. 7.3. The

123

line impedances are denoted as ZDi (= RDi + jXDi), i = 1,…,6. Each of the DG controllers needs to

measure its local quantities only and hence, the real and reactive power flow measurements into and

out of the DG local bus are required. It is to be noted all the line impedances and loads are assumed to

be lumped.

From the power output of DG-3 we can write,

RLRL PXQRPX 36363343 +−=−δδ (7.20)

where R6= RD6/(V33VL4) and XL6= XD6/(V33VL4). Similarly from the DG-2 power output we can write,

RLRL PXQRPX 24242232 +−=− δδ (7.21)

The angle difference between the loads can be represented as,

RLRLLLLL PXQRPXQR 3636353543 +−+−=− δδ (7.22)

From (7.21) and (7.22) we get,

RLR

LLLRLRL

PXQR

PXQRPXQRPX

3636

353524242242

+−+−+−=− δδ

(7.23)

Similarly the power output of DG-1 can be expressed as,

LLRLLLRLR

LLLRLRL

PXQRPXQRPXQR

PXQRPXQRPX

363635352424

232312121141

+−+−+−

+−+−=−δδ (7.24)

It is to be noted that in (7.23) and (7.24), all the active and reactive power quantities, except the first

term, are not locally measureable. The angle difference shown in (7.22) can be measured by DG-3 and

then communicated to DG-2 and DG-1. As these quantities only modify the reference angle to ensure

better load sharing, updates can be done using longer sample rates and a much slower communication

process can achieve that. Furthermore, the first term in (7.23) and (7.24) indicates the primary output

feedback loop that is based on the locally measurable power output of the DG. This control action is

instantaneous and ensures initial load sharing among the DGs. We can write (7.24) as

131211141 δδδδδδ +++=− pL (7.25)

where

124

LLRLLL

RLRLLL

RLRp

PXQRPXQR

PXQRPXQR

PXQRPX

3636353513

2424232312

121211111 ,

+−+−=

+−+−=

+−==

δ

δ

δδ

(7.26)

Fig. 7.3. Multiple DG connected to microgrid.

The longer updates can be made using a web based communication [84] that is discussed below. It is

to be noted that in this proposed method, there is a requirement of site specific tuning of the

parameters for the reference angle generation. This tuning is required to improve the performance of

the site independent decentralized control of Controller-1.

7.1.4 WEB BASED COMMUNICATION

The web based measurement system is shown in Fig. 7.4. The real and reactive power (P and Q)

measured at each DG unit is communicated to a dedicated website or company intranet with the help

of a modem. Assuming that the PQ measurement units are already installed at each DG location, the

equipment needed for each DG unit are a computer to collect the measurements from local and remote

units, and a modem to transmit the measurements to the dedicated website, or to download remote

measurements from it. Fig. 7.4 (a) shows the web connection of all the DGs, while the communication

in each DG is shown in Fig. 7.4 (b). The power monitoring unit sends the real and reactive power

measurement to the computer to calculate 11 as shown in (7.31). The other angle component 12 and

13 are received by the modem and communicated to the DG control unit through the computer. As

mentioned before the main load sharing term δ1p in (7.30) is based on local measurement and so even

in case of communication failure, a rough load sharing is ensured among the DGs. As the DGs are

125

interfaced through converters, the structure and control of the converters are very important for the

power sharing. They are discussed in the next section.

(a)

(b)

Fig. 7.4 (a) Web based PQ monitoring scheme and (b) web based communication for DG-1.


All the DGs are assumed to be an ideal dc voltage source supplying a voltage of Vdc to the VSC. The

structure of the VSC is same as discussed in Section 2.3 of Chapter 2.

7.2.1 CONVERTER CONTROL

The converters are controlled in state feedback control as described in Appendix A. To facilitate

this, we define set of state vectors as

[ ]cfcT viix 2= (7.27)

126

This control strategy is applied to all the DGs, when operating with the web based communication of

Section 7.1.2. The control law discussed so far is for the system in which the DGs have an output

inductor. This implies the converter output stage has LCL (or T) filter structure. Alternatively, when

the DGs do not have an output inductance, the inductance Lfi is removed and the output filter is a

simple LC filter. The system states are then modified as

[ ]cfcfT vix = (7.28)

However the control law and switching logic remain the same. This control strategy is applied to all

the DGs, when operating without any communication of Section 7.1.1.

It is assumed the total power demand in the microgrid can be supplied by the DGs and no load

shedding is required. The output voltages of the converters are controlled to share this load

proportional to the rating of the DGs as discussed in different droop control methods.

7.2.2. DG REFERENCE GENERATION

It is evident from (7.27) and (7.28) that references for all the elements of the states are required for

state feedback. Since V and δ are obtained from the droop equation, the reference for the capacitor

voltage and current are given by

( )δω += tVvcfref sin (7.29)

( )°++= 90sin δωω tCVi fcfref (7.30)

For the LCL filter, the reference for the current i2 can be calculated as

( )refrefref tIi 222 sin δω += (7.31)

Where,

( )PQV

QPI ref

cfref /tanand 1

2

22

2−−=

+= δδ

127




Feeder impedance

ZD1

ZD2

ZD3

ZD3

ZD3

1.0 + j 1.0 Ω

0.4 + j 0.4 Ω

0.5 + j 0.5 Ω

0.4 + j 0.4 Ω

0.4 + j 0.4 Ω

Load ratings

Load1

Load2

Load3

Load4

13.3 Kw and 7.75 kVAr

11.2 kW and 6.60 kVAr




DG-1

DG-2

DG-3

30 kW

20 kW

20 kW

Output inductances

L1

L2

L3

0.75 mH

1.125mH

1.125mH

DGs and VSCs


Transformer rating

VSC losses (Rf)



0.220 kV

0.220 kV/0.440 kV, 0.5

MVA, 2.5% Lf

1.5 Ω

50 µF

10-5

Droop Coefficients

Power−−−−angle

m1

m2

m3

Voltage−−−−Q

n1

n2

n3

7.5 rad/MW

11.25 rad/MW

11.25 rad/MW

0.001 kV/MVAr

0.0015 Kv/MVAr

0.0015 Kv/MVAr

128

7.3. SIMULATION STUDIES

Simulation studies are carried out in PSCAD/EMTDC (version 4.2). Different configurations of load

and power sharing of the DGs are considered. To consider the web based communication, a delay of 5

ms is incorporated in the control signals which are not locally measureable. As only one measurement

is taken in one main cycle, a 100 byte/s communication is needed, which is a very low speed

communication compared to any of the high bandwidth communication. The system parameters are

shown in Table-7.1. For clarity, the numerical values of power sharing ratios obtained from all the

simulation are given in Table-7.2.

7.3.1 CASE 1: LOAD_3 AND LOAD_4 CONNECTED TO MICROGRID

In this case, all the three DGs are connected to the microgrid and supplying only Load_3 and

Load_4. While the system in steady state, Load_3 is disconnected at 0.5 s. Fig. 7.5 (a) shows the

power output of the DGs and Fig. 7.5 (b) shows the power sharing ratios with conventional angle

controller given by (7.2). In Fig. 7.5 (b), Pratio-ij indicates Pi:Pj. It can be seen that due to high line

impedance, the power sharing of the DGs are not as desired (see Table-7.2). Fig. 7.6 shows the system

response with proposed Controller-1. The error in power sharing is reduced. Fig. 7.7 shows the system

response with proposed Controller-2. The power sharing ratio of the DGs are much closer to the

desired sharing and the system reaches steady state within 4-5 cycles as in the case with the

conventional controller.

The results of this case with a conventional frequency droop controller are discussed in Section

7.3.5.

129

Fig. 7.5. Power sharing with conventional controller (Case 1).

Fig. 7.6. Power sharing with Controller-1 (Case 1).

Fig. 7.7.Power sharing with Controller-2 (Case 1).

130

7.3.2 CASE 2: DG-1 AND DG-3 SUPPLY LOAD_1 AND LOAD_2

It is assumed that only two DG, DG-1 and DG-3 are connected to the microgrid and they are

supplying Load_1 and Load_2. The system response shown in Fig 7.8 is with the conventional

controller (7.2). Load_2 is disconnected at 0.5s and the two DGs, connected at the two ends of the

microgrid supply only Load_1. Figs.7.9 and 7.10 show the response with the proposed controllers. It

can be seen that a closer to desired power sharing is achieved with these controllers. High line

impedance (and high R/X ratio) between the DGs and load makes the power sharing difficult and the

power sharing with conventional controller shown in Fig. 7.8 is not acceptable.



131

Fig.7.10. Power sharing with Controller-2 (Case 2).

7.3.3 CASE 3: INDUCTION MOTOR LOADS

To investigate the system response with induction motors connected to the microgrid, a 30 hp

motor is connected as Load_3, while Load_4 constitutes a 50 hp motor. With the system running in

steady state, DG-2 is disconnected at 0.25s. The simulation results are shown in Figs. 7.11 to 7.13 for

the conventional controller and the two proposed controllers. After DG-2 is disconnected, DG-1 and

DG-3 supply the total power demand and it can be seen that system takes around 0.3 s to reach the

steady state. Due to the high impedance of the line, conventional angle controller fails to share the

power as desired (error is almost 20%). Controller-1 reduces the error to some extent but not able to

share as desired (Fig. 7.12 (b)). However, Controller- 2 is able to share the induction machine load

almost in the desired ratio (error is less than 2%).


132

7.3.4 CASE 4: LOAD SHARING WITH ADVANCED COMMUNICATION SYSTEM

In this section it is assumed that the system has advanced high bandwidth communication among all

the DGs and loads and all the control parameters are measurable without any significant time delay.

With the same induction motor load as in Case 3, the simulations are carried out considering all the

measured variables are accessible to all the DGs. In this case, the droop sharing becomes redundant.

Fig. 7.14 shows the system response. It can be seen that an accurate power sharing is achieved. The

error is less than 0.5%. However the cost involved in a high bandwidth communication is much larger

compared to the proposed no-communication or web based minimum communication control. From

this perspective, either Controller-1 or Controller-2 can provide an acceptable power sharing in a rural

area with potentially a much lower cost.



133

Fig. 7.14. Power sharing with high bandwidth communication (Case 4).

Fig. 7.15 shows the mean percentage error in the different control techniques for the cases

discussed above. The operating cases were chosen for weak system conditions, where the micro

sources and loads are not symmetrically distributed through out the network. These results in high

values of power sharing error but it can be seen that with the proposed control methods, the error can

be reduced significantly. While the first proposed method (Controller-1) can reduce the error below

10%, the web based minimum communication method (Controller-2) has an error around 3.5%.

Though the error in case with an advanced communication system is much lower, the cost involved is

likely to be high.

The decentralized droop sharing control has also been studied when the loads are voltage and

frequency dependent. The results are discussed in Section 7.3.6.

7.3.5 CASE 5: LOAD SHARING WITH CONVENTIONAL DROOP CONTROLLER

The performance of the conventional frequency droop controller for the high R/X system of Case 1

is shown in Fig. 7.16. It can be seen, as is in the case of the conventional angle droop performance

seen in Fig. 7.5, the power sharing with this frequency droop is far from desired.

134

Fig. 7.16. Power sharing with frequency droop Case 1.

7.3.6 CASE 5: LOAD SHARING WITH CONVENTIONAL DROOP CONTROLLER

To investigate the angle control performance with a frequency (F) and voltage (V) dependent load,

a system as shown in Fig. 7.1 is chosen with a continuous load perturbation. The dependent load

characteristic [86] is given by

( )dFKVV

PP PF

NP

+

= 1

00 (7.A.1)

where NP (0.95) and KPF (2.0) are the voltage and frequency dependent coefficients. The system is

initially running with a continuous varying impedance load. Then the dependent load described by

(7.A.1) is connected at 0.4s. The power sharing is shown in Fig. 7.17 (a). The system frequency and

the power demand from the frequency dependent load is shown in Fig. 7.17 (b-c). It can be seen that

the power sharing is as desired. However the droop gains may need to be reduced as the frequency

dependence of the loads can be destabilizing.

7.4 CONCLUSIONS

Load sharing in an autonomous microgrid through angle droop control is investigated in this chapter

with special emphasis on highly resistive lines. Two control methods are proposed. The first method

proposes power sharing without any communication between the DGs. The feedback quantities and

135

the gain matrixes are transformed with a transformation matrix based on the line resistance-reactance

ratio. The second method is with minimal communication based output feedback controller. The

converter output voltage angle reference is modified based on the active and reactive power flow in

the line connected at PCC. It is shown that a more economical and proper power sharing solution is

possible with the web based communication of the power flow quantities. In many scenarios, the

difference in error margin between proposed control schemes and a costly high bandwidth based

communication system does not justify considering the increase in cost. This section proposes and

demonstrates low cost control methods to ensure acceptable power sharing in a weak system condition

and highly resistive network for rural distribution networks.

Fig. 7.17. Frequency dependent load

Percentage Error in Power Sharing

18.24

9.98

3.54

0.5

0

2

4

6

8

10

12

14

16

18

20

1

% e

rror

Conventional

Controller-1

Controller-2

Full_comm

Fig. 7.15. Error in power sharing with different control techniques

136

TABLE-7.2: SIMULATION RESULTS

Ca

se

Controller Power Sharing Ratio

P1 /P2 P1 /P3 P2 /P3

Initia

l

Final Initia

l

Final Initia

l

Final

1 Desired Values 1.5 1.5 1.5 1.5 1.0 1.0

Conventional 1.32 1.3 1.22 1.2 0.62 0.59

Controller-1 1.39 1.41 1.31 1.37 0.71 0.72

Controller-2 1.59 1.6 1.53 1.54 1.02 1.03

2 Desired Values − − 1.5 1.5 − −

Conventional − − 1.60 1.69 − −

Controller-1 − − 1.55 1.58 − −

Controller-2 − − 1.48 1.46 − −

3

&

4

Desired Values − − 1.5 1.5 1.0 0.0

Conventional − − 1.22 1.25 0.97 0.0

Controller-1 − − 1.39 1.42 1.10 0.0

Controller-2 − − 1.52 1.51 1.02 0.0

Full comm − − 1.51 1.51 0.99 0.0

137

CHAPTER 8

CONCLUSIONS

The general conclusions of the thesis and future scope of the work are presented in this chapter.

The conclusions are based on the work carried out and reported in the earlier chapters.

8.1 GENERAL CONCLUSIONS

The summarized conclusions of the thesis are

1. In case of converter interfaced sources, power sharing can be achieved with drooping the

output voltage angles of the converters. Angle droop controllers provide desirable power

sharing with much lower frequency deviations compared to that of frequency droop

controller.

2. The system response can be improved significantly by changing the state feedback

controller in grid connected mode to voltage control in islanded mode of operation. A

change in control algorithm also ensures a smooth transition of a microgrid between the

modes.

3. Power quality of distributed generation can be improved significantly by proper reference

generation for the DGs. In this the compensating DG can perform load balancing,

harmonic filtering and reactive power compensation while supplying real power. This is

not possible by a DSTATCOM.

4. The reliability in a microgrid can be improved with the application of back-to-back

converters for bidirectional power flow and voltage and frequency isolation between the

microgrid and the utility.

5. High droop gains can improve power sharing. However it can also have detrimental effect

on system stability. A supplementary controller, which takes real power as input, can

improve the system stability significantly.

6. In the rural network, with high R/X line, the droop equation has to be modified to

improve decentralized operation. A low band width communication can also improve the

power sharing significantly.

138

8.2 SCOPE FOR FUTURE WORK

Some areas for future work are listed below.

1. The angle droop control scheme can be modified to share power in a microgrid with inertial

and non inertial DG.

2. Protection of back-to-back converters in case of fault in utility or microgrid faults can be

investigated.

3. Improvement in supplementary droop control for enhanced system damping under weak

operating conditions. The improvement can be achieved by selection of more appropriate

input signals or controller gains.

4. A modified droop control can be derived for frequency dependent loads.

5. Improvement and further application of the low bandwidth communication (100 byte/s) can

be performed in distributed generation. Communication can be used to correct the reference

quantities or communicating the load measurements.

139

APPENDIX-A

The converter structure and control used in this thesis from existing publication by other

authors are presented in this appendix. All the inertia less DGs are connected to the microgrid through

interfacing converters. The converter structure and control is described in this appendix. Depending

on the requirement, three phase or single phase converters are used. The converter is connected to

microgrid with an output filter. Either LCL to LC filter has been used based on requirements. The

converter control strategies adopted in this thesis are state feedback control or voltage control based

on application and requirement.

A.1 CONVERTER STRUCTURE

The converter structure is shown in Fig. A.1. This contains three H-bridge converters that are

connected to the DG sources, denoted by Vdc1. The outputs of the H-bridges are connected to three

single-phase transformers that are connected in wye for required isolation and voltage boosting [87].

The resistance Rf represents the switching and transformer losses, while the inductance Lf represents

the leakage reactance of the transformers. The filter capacitor Cf is connected to the output of the

transformers to bypass switching harmonics. The inductance L1 is added to provide the output

impedance of the DG source. The advantage of this structure is that power flow can be controlled

independently in the three phases and the phases are magnetically decoupled from each other.

Fig. A.1. Three Phase converter structure.

140

The above structure is used for all the three phase DGs with LCL type of filter. If the DGs output filter

is LC type, the output inductance L1 shown in Fig. A.1 is not present. For single phase DGs, the

converter structure is shown in Fig. A.2.

A.2 CONVERTER CONTROL

The equivalent circuit of one phase of the converter is shown in Fig. A.3. In this, u⋅Vdc1 represents

the converter output voltage, where u = ± 1. The main aim of the converter control is to generate u.

Fig. A.2 Single phase converter structure

(a) Ouput filter LCL type (b) Output filter LC type

141

Fig. A.3. Equivalent circuit of one phase of the converter.

From Fig. A.3 (a), state space description of the system can be given as

PCCc vBuBAxx 2111 ++= (A.1)

While the state space equation for Fig. A.3 (b) can be given as,

cuBAxx 122 += (A.2)

where uc is the continuous time version of switching function u. Based on this model and a suitable

feedback control law, uc(k) is computed.

The equivalent circuit of one phase of the converter is shown in Fig. A.4. The choice of states

depends on the converter output filter type. In case of LCL filter the state vector is chosen from the

circuit of Fig. A.4, as

[ ]cfT viix 211 = (A.3)

While in case of LC filter, the states are

[ ]cfT vix 12 = (A.4)

Fig. A.4. Single-phase equivalent circuit of VSC (LCL filter).

The switching function u is then generated as

1 then elseif1 then If

−=−<+=>uhu

uhu

c

c (A.5)

where h is a small number. Two types of feedback controllers are used here. They are discussed

below.

142

A.3 OUTPUT FEEDBACK VOLTAGE CONTROLLER

Let the output of the system given in (A.2) be vcf. Let the reference for this voltage is given in terms

of the magnitude of the rms voltage V1* and its rotating angle φ1

*. From this the instantaneous voltage

reference v1* for the three phases are generated. Neglecting the PCC voltage since it is a disturbance

input, the input-output relationship of the system in can be written in discrete form as

( )( )

( )( )1

1

−

−

=zNzM

zu

zv

c

cf (A.6)

The control is computed from

( ) ( )( ) ( ) ( ) zvzvzRzS

u cfc −= ∗−

−

11

1

z (A.7)

Then the closed-loop transfer function of the system is given by

( )( )

( ) ( )( ) ( ) ( ) ( )1111

11

1−−−−

−−

∗ +=

zSzMzRzNzSzM

zv

zvcf (A.8)

The coefficients of the polynomials S and R can be chosen based on a pole placement strategy [88].

Once uc is computed, the switching function u can be generated from (A.5).

A.4 STATE FEEDBACK CONTROLLER

In state feedback controller, the chosen states of the system are compared with their reference

quantities to generate the converter switching. It is easy to generate references for the output voltage

vcf and current i2 from power flow condition. However, the same cannot be said about the reference for

the current i1.

To facilitate this, we define a new set of state vectors as

[ ]cfcT viix 21 = (A.9)

We then have the following state transformation matrix

143

11

100010011

xCxx P=

−= (A.10)

The transformed state space equation is then given by combining (A.9) and (A.10) as

PCCpcppp CvCBuCxACCx ++= −1

11 (A.10)

The control law is given by

( ) ( ) ( )[ ]kxkxKku refc 11 −−= (A.11)

where K is a gain matrix and xref is the reference vector. The gain matrix is obtained using discrete

time linear quadratic regulator (LQR) with a state weighting matrix of Q and a control penalty of r.

The control law discussed so far is for the system in which the DGs have an output inductor.

Alternatively, when the DGs do not have an output inductance, the inductance L1 is removed and the

output filter is a simple LC filter. The system states are then modified as

[ ]cfcfT vix =2 (A.12)

However the state space is similar to (A.10) and the control law (A.11) and switching logic remain the

same.

144

145

APPENDIX-B

LIST OF PUBLICATIONS

The following papers are published (or under publication process) from the work described in this

thesis.

Journal papers:

1. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Load sharing and power quality

enhanced operation of a distributed microgrid,” IET Renewable Power Generation, Vol-2,

No-3, pp 109-119, June, 2009.

2. Ritwik. Majumder, B. Chaudhuri, A. Ghosh, Rajat. Majumder, G. Ledwich and F. Zare,

“Improvement of Stability and Load Sharing in an Autonomous Microgrid Using

Supplementary Droop Control Loop,” Accepted to appear in IEEE Trans. in power system,

September, 2009.

3. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Power Management and Power Flow

Control with Back-to-Back Converters in a Utility Connected Microgrid,” Accepted to

appear in IEEE Trans. in power system, October, 2009.

4. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Load Frequency Control of Rural

Distributed Generation”, accepted in Electric Power Components and Systems, October,

2009.

5. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Enhancing the Stability of an

Autonomous Microgrid using DSTATCOM”, Accepted to appear in International Journal of

Emerging Electric Power Systems.

6. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Enhancing Stability of an Autonomous

Microgrid using a Gain Scheduled Angle Droop Controller with Derivative Feedback”,

Accepted to appear in International Journal of Emerging Electric Power Systems.

7. R. Majumder, G. Ledwich, A. Ghosh, and F. Zare “Droop Control of Converter Interfaced

Micro Sources in Rural Distributed Generation”, IEEE Trans. in power delivery, accepted.

146

8. R. Majumder, M. Dewadasa, G. Ledwich, A. Ghosh, and F. Zare “Control and Protection of

a Microgrid Connected to Utility through Back-to-Back Converters”, IET Generation

Transmission and Distribution, under minor revision.

9. F. Shahnia, R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Operation and Control of a

Hybrid Microgrid Containing Unbalanced and Nonlinear Loads”, EPSR, Accepted.

Conference Papers:

1. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Control of parallel converters for load

sharing with seamless transfer between grid connected and islanded modes”, IEEE Power

and Energy Society General Meeting, Pittsburgh, USA, 20-24 July 2008.

2. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Angle droop versus frequency droop in

a voltage source converter based autonomous microgrid: IEEE Power Engineering Society

General Meeting 2009, 26-30 July 2009, Calgary Telus Conventional Centre, Calgary,

Canada.

3. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Operation and Control of Single Phase

Micro-Sources in a Utility Connected Grid” IEEE Power Engineering Society General

Meeting 2009, 26-30 July 2009, Calgary Telus Conventional Centre, Calgary, Canada.

4. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Power System Stability and Load

Sharing in Distributed Generation” .In Proceedings POWERCON2008 & 2008 IEEE Power

India Conference, New Delhi, India.

5. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Enhancing the Stability of an

Autonomous Microgrid using DSTATCOM”, National Power System Conference (NPSC),

Mumbai, India, 2008

6. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Stability Analysis and Control of

Multiple Converter Based Autonomous Microgrid”, IEEE International Conference in

Control and Automation (ICCA), Christchurch, New Zealand, 2009.

7. A. Ghosh, R. Majumder, G. Ledwich and F. Zare, “Power Quality Enhanced Operation and

Control of a Microgrid based Custom Power Park”, IEEE International Conference in

Control and Automation (ICCA), Christchurch, New Zealand, 2009.

147

8. R. Majumder, Farhad Shahnia, A. Ghosh, G. Ledwich, Michael Wishart and F. Zare,

“Operation and Control of a Microgrid Containing Inertial and Non-Inertial Micro Sources”,

IEEE TENCON, Singapore, 2009.

9. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Power Sharing and Stability

Enhancement of an Autonomous Microgrid with Inertial and Non-inertial DGs with

DSTATCOM”, IEEE International Conference in Power System (ICPS)-2009, Kharagpur,

India.

10. M. Dewadasa, R. Majumder, A. Ghosh, G. Ledwich, “Control and Protection of a

Microgrid with Converter Interfaced Micro Sources”, IEEE International Conference in

Power System (ICPS)-2009, Kharagpur, India.

11. R. Majumder, A. Ghosh, G. Ledwich, S. Chakraborti and F. Zare, “Improved Power

Sharing among Distributed Gen-erators using Web Based Communication”, Accepted to

appear in IEEE PES General Meeting, July 26 - July 29, 2010, Minneapolis, Minnesota,

USA.

148

149

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