Thesis Report - Murdoch University · Thesis Report Voltage and Frequency Droop Control of a Microgrid in Islanded Modes Zhaoyi Liu 1/13/2016 Supervisor: Dr. Gregory Crebbin . Droop

MURDOCH UNIVERSITY

Thesis Report Voltage and Frequency Droop Control of a

Microgrid in Islanded Modes

Zhaoyi Liu

1/13/2016

Supervisor: Dr. Gregory Crebbin

Droop Control of Micrigrid

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Abstract

Nowadays, there are increased amount of distributed generation and renewable resources

(including geothermal, ocean tides, solar and wind) used in the microgrid systems, which are

connected via the power inverters. Microgrid is a concept that the systems include at least one

distributed generation resources and local loads can switch to islanded power distributed

systems, [1]. Duo to the small scale of microgrid, the voltage and frequency of system will

carry more severe fluctuations then the larger grids, which will be able to stable these

fluctuations via the wider systems, [9]. The inverters can provide the stability and redundancy

to the power systems. For the normally working of the high current electronic devices, it is

deviation that several inverters operate in parallel in the systems, [3]. The inverter control

methods which should be able to bring the reliable and efficient electricity to microgrid

system have attracted much attention in recent years. Various droop control methods are

regarded as the effective solving technique in conventional generation system.

The droop control strategy is associated with using local power to detect the load changes of

complex powers in the system and adjusting the outputs, automatically, [2]. The advantage of

droop control method is to allow the distributed generators in the system can operate without

external mechanism communications, [3]. No mechanical communication means the system

can adjust and share the loads among distributed generators (connected via inverters)

automatically when the loads change happen. This is based on the calculation of droop

control characteristics. The droop control uses the real power to adjust the frequency of

loads, and vary the reactive power to vary the voltage of loads. However, droop control

scheme are different when the impact of complex impedance is considered. The experimental

simulation results will be presented to illustrate how the droop control scheme impacts the

power distributions of parallel-connected inverters.


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Disclaimer

I declare all the information and knowledge has been developed are all my works except the

parts had been referenced.

Signature:

January 2016


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Acknowledgements

It is a great self-study opportunity that finishing a thesis research project to gain the

knowledge before finishing my bachelor degree of engineering at Murdoch University. It will

be beneficial to my engineer career and any type of futures learning.

I would first like to thank my supervisor Dr. Greg Crebbin for not only provide the chance to

study under his guidance but also the patience and academic knowledge that provided over

the course of thesis. He donates a big amount of time to recommend me and support

questions to run my thesis smoothly and correctly.

I would also acknowledge all my friends from the School of Engineering and Information

Technology at Murdoch University, for providing direct and indirect helps towards the

completion of this thesis period.

Lastly, I would like to thank my family that supporting me on getting an overseas bachelor

degree. They spend much of the patience to guide me to be beneficial to the society.


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Contents

Abstract ...................................................................................................................................... 1

Acknowledgements .................................................................................................................... 3

Contents of table ........................................................................................................................ 6

1.0 Introduction .......................................................................................................................... 8

1.1 Introduction ...................................................................................................................... 8

1.2 Aims description .............................................................................................................. 9

1.3 Thesis Structure ................................................................................................................ 9

2.0 Background ........................................................................................................................ 11

2.1 Microgrid Concept ......................................................................................................... 11

2.2 Microgrid Technologies ................................................................................................. 12

2.3 Distributed Generation ................................................................................................... 13

2.4 Distributed Storage ......................................................................................................... 14

2.5 Interconnection Switch ................................................................................................... 15

2.6 Filters Selection .............................................................................................................. 15

3.0 Droop Control .................................................................................................................... 23

3.1The reasonable justification of the droop control approach ............................................ 23

3.2 Theoretical background .................................................................................................. 24

3.3 Droop controller among inverters .................................................................................. 27

4.0 Modelling and Simulation.................................................................................................. 30

4.1 Theoretical concept of droop controller construction .................................................... 30


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4.2 Average Active Power ................................................................................................... 33

4.3 Average Reactive Power ................................................................................................ 34

4.4 Software Introduction ..................................................................................................... 35

5.0 Implementation .................................................................................................................. 36

5.1 Design of a Single Controller to Achieve Resistive Output impedance. ....................... 36

5.2 Design of a Double Controller with Resistive Output impedance to achieve 2:1 power

sharing. ................................................................................................................................. 39

5.3 Single Inverter Controller Simulations of inductive Output Impedance........................ 40

5.4 Double Inverters Controller Simulations of inductive Output Impedance .................... 42

6.0 Simulation Results ............................................................................................................. 44

6.1 Single Inverter Controller Simulations of Resistive Output Impedance ........................ 44

6.2 Two Inverters Controller Simulations of Resistive Output Impedance ......................... 46

6.3 Single Inverter Controller Simulations of inductive Output Impedance........................ 48

6.4 Two Inverters Controller Simulations of inductive Output Impedance ......................... 50

7.0 Conclusions and Future Works .......................................................................................... 52

7.1 Conclusion ...................................................................................................................... 52

7.2 Future Works .................................................................................................................. 53

Bibliography ............................................................................................................................ 54

Appendix A SPICE Netlist for Signal Inverter Resistive Case ............................................... 56

Appendix B SPICE Netlist for Double Inverters resistive Case .............................................. 59

Appendix C SPICE Netlist for single Inverters inductive Case .............................................. 63

Appendix D SPICE Netlist for Double Inverters resistive Case.............................................. 66


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Contents of table

Figure 1 Simple RC Circuit Figure.1 Simple RC Circuit ........................................................ 16

Figure 2 Bode plots of the second order low-pass filter .......................................................... 18

Figure 3 Simple LC low pass filter circuit ............................................................................... 19

Figure 4 Simple LC low pass filter circuit .............................................................................. 20

Figure 5 Second Order Low Pass Filter Block Input Setting................................................... 21

Figure 6 Bode plots of Second Order Low-pass Filter ............................................................ 21

Figure 7 Power Flowing through a Line .................................................................................. 24

Figure 8 Classic droop control characteristic plots .................................................................. 27

Figure 9 Inverters with same droop characteristics ................................................................. 28

Figure 10 Inverters with different droop characteristics .......................................................... 29

Figure 11 Two parallel-connect inverters with resistive output impedances .......................... 30

Figure 12 Droop control characteristic Line Graph ................................................................. 32

Figure 13 Droop control Block Diagram (Resistive Case) ...................................................... 32

Figure 14 Single phase inverter controller scheme .................................................................. 37

Figure 15 Single Phase Inverter Controller Equivalent Circuit ............................................... 38

Figure 16 Single Phase Two Inverters Controller Scheme (Resistive Case) ........................... 39

Figure 17 Droop control Block Diagram (Inductive Case) ..................................................... 40

Figure 18 Single Phase One Inverter Controller Component (Inductive Case) ....................... 41

Figure 19 Single Phase Two Inverters Controller Scheme (inductive Case) ........................... 42

Figure 20 RMS value of load voltage for single inverter (resistive case) ............................... 44

Figure 21 Single Inverter Controller Frequency Variation (Resistive Case) ........................... 45

Figure 22 Single Inverter Controller Amplitude Variation (Resistive Case) .......................... 45


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Figure 23 Load voltages for Two Inverters (Resistive Case) .................................................. 47

Figure 24 Two Inverters Controller Amplitude Variation (Resistive case) ............................. 47

Figure 25 Two Inverters Controller Frequency Variation (Resistive case) ............................. 47

Figure 26 Single Inverter Controller Output Variation (Inductive Case) ................................ 49

Figure 27 Load voltages for Two Inverters (Inductive Case) .................................................. 50

Figure 28 Two Inverters Controller Amplitude Variation (Resistive case) ............................. 50

Figure 29 Two Inverters Controller Frequency Variation (Resistive case) ............................. 50


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1.0 Introduction

1.1 Introduction

Nowadays, the distributed generations and renewable energy resources (solar panels, variable

speed wind turbines, and ocean tidal power plants) have been more and more prevalent in the

modern electrical power generations. With the development of this, the power inverters

technology has been applied in terms of connecting the energy resources to the main power

grids. However, it is inevitable that several inverters connected in parallel. Therefore, how to

control these parallel-connected inverters to has become a significant problem. The control

method can make the system can detect the outages and finish the maintaining work

automatically.

There is another problem is that how to share the power among these inverters, [3]. It will

happen when the load demand change. A conventional technology named droop control is

used widely to achieve the power sharing goal. There is no external mechanical

communication requirement needed to achieve sharing power automatically, [3]. In addition,

the microgrid system is regarded as a useful way to provide the advantages to the reliability

and stability of the systems, which is discussed in paper, [1]. The microgrid can operate in

both grid-connected and autonomous (islanded) modes, [11] [12].

Islanding mode is one system disconnected to main power grid and can operates

independently, [11]. The independent system can satisfy the local load requirement.

Disconnecting from the main grid is used to protect the components when the fault occurs,

[11]. This thesis project will investigate the microgrid technology and the performance of

droop control approach. These control approach are used to achieve the proportional power

sharing among the inverters without external mechanical communications. In the thesis, a

simplified microgrid circuit in standalone mode will be researched. The simplification


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process will use the voltage sources represent the complicated elements such as the

renewable resources or distributed generators. The simplified circuit will be easier to evaluate

the response duo to the load changes. In addition, the relevant information includes filter

selection and mathematical block diagrams calculations will be investigated in future

research progress.

1.2 Aims description

The aims of the thesis project are to get familiar with the principle of frequency droop control

method operating in the purely inductive and purely resistive network. In additon, the project

is developed to simulation a simple two parallel-connected inverters circuit. What is more,

the reason for the droop control method is used widely to control the distributed generation

resources will be explained.

The project is to evaluate the various frequency and voltage controller options with the

objective of minimize the energy losses and matching the proportional load sharing

throughout the microgrid power system. In addition, to investigate the control and

management of mircogrid, the strategy of frequency and voltage droop control which will

impact frequency and amplitude of output voltage in the islanded mode will be simulated.

In addition, to evaluate the performance of the droop control method, several simple test

electrical circuits will be constructed for SPICE simulations. Therefore, the test system

components which include various elements will be demonstrated by the suitable method in

order to get the final results.

1.3 Thesis Structure

This thesis will evaluate the performance of simple droop control scheme in the case of

purely inductive and purely resistive. The report is divided into 7 chapters. The first chapter


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is going to introduce the whole thesis work, the second chapter reviews the significant

background information, which includes the microgrid concept and its technologies that keep

the system running regularly. In addition, the filter selection will be discussed in the chapter 2.

Chapter 3 illustrates the reasonable justification and theoretical calculations of the traditional

droop control method. In this chapter, the basic information about the droop control works

process will be explained. Throughout chapter 4, the droop control schemes’ mathematical

block diagram will be developed with the aid of data and information provided in Zhang’s

example technical article, [3]. In this chapter, the descriptions are using the mathematical

model that is easier to understand to represent the physical technique. The computer software

introducing is also covered in this part. Chapter 5 is going to show the several conditional

experiments’ implementation in the SPICE. Chapter 6 provides all the results of the projects,

including the case of two inverters systems that are simple microgrids. Chapter 6 concludes

the project and propose the improvements to the conventional droop control. The Appendices

list all of the Netlist used in Icap 4 SPICE.


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2.0 Background

2.1 Microgrid Concept

It has been claimed that the microgrid technology can provide the advantages of reliability

and stability of the systems. A microgrid is defined as “a subsystem of distributed energy

sources and their associated loads”, [1]. The microgrid grid concept is described as resources

which include the distributed generation and renewable energy resources connected to the

local electric power networks via the power inverters. [4] The usage of microgrids has

increased to a large extent due to its largest advantage which is to provide higher reliability

electric energy and higher quality to the system load, [1]. To achieve the objectives, a mini

robust system using the distributed generations which utilize the local information to

maintain system operations will be constructed, [2]. This approach can be a stand-alone

system or connected to the main intelligent power grids, which correspond to the islanding

mode and grid-connected mode, respectively. In addition, most microgrid system

implementations associate loads and from the intentional islanding, the available waste heat

of system is trying to be used, [5]. These concepts are all depending on the complex

communications among system components and various control methods, [5]. Microgrid

concept is to create generator-base controls which can run in “plug- and-play” mode without

mechanical communications, [5].

The microgrid can provide the three main benefits over the traditional centralised distributed

generations [2]:

Opportunities to increase efficiency of the total energy supply system

Practical optimum utilizing of the waste thermal recovery technologies

Improvement of system stability and power quality


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According to [5], the overall fuel-to-electricity efficiency of current power plants which

includes the distributed and central type can be only kept in the range of 28%-32%. This

means that the approximately 70% of energy. To increase system efficiency, both fuel-to-

electricity efficiency and waste heat recovery technologies are utilized in practical. By using

the combined power cycles technology, the entire system efficiency can attain as 60%, [5]. In

addition, based on [5], the waste heats which carry low total fuel-to-useful efficiency (28%-

32%) as mentioned above can be enhanced to greater than 80% by use the “heat exchangers”,

“absorption chiller” and “desiccant dehumidification”. [5] To the biggest extent, the fuel-to-

use energy frequency can get higher than 80% currently by use 60 kW microturbines to warm

the water, [5].

Combined heat and power (CHP) and co-generation technologies are utilized to finish the

waste heat recovery and electricity delivery from the energy resources. [5] Generally, heat is

in the form of steam or hot water in the generation systems, which is hard and not economical

to transmit over the long distance, [5]. Therefore, the heat generation locations should be

constructed near the location of heat requirement load rather than the electricity requirement

load. According to [5], the heat recovery efficiencies are 20% to 80% in a typical combine

heat and power (CHP) system which is near the heat load. This advanced generation

technology should be placed near the heat loads. Lasseter mentioned that the fuel cells are

placed in the each floors of a hospital. The fuel cells can satisfy the requirements of

electricity load and heat water, [5].

2.2 Microgrid Technologies

The microgrids normally are the loacalized grids which are able to disconnect from the main

power gird. [9] In recent years, the mcirogrid technology has been developed and could be


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able to finish the combiniation of clean generations (wind source, solar source or tidal energy

etc.) and traditional generations (diesel and natural gas sources).[9] In addition, the system

can deliver electric and heat at the same time to solve the problem of low efficiency.

Microgrid architecture consists of several technologies to achieve the objective of operating.

Microgrid systems, as a kind of Distributed energy resources (DER) must include distributed

generation (DG) and distributed storage (DS), which can play a role on manage current of

systems, [5]. In addition, microgrids consist of interconnection switches and control systems,

[1] As mentioned in the [5], the biggest challenge is associated with usage and design of low-

cost technology when operate a microgrid system.

2.3 Distributed Generation

Distributed energy resources which include the distributed generation and distributed storage

have amount of advantages such as system reliability improvement when distributed energy

resources can operate properly in the electrical power systems. [6] The distributed energy

resources is defined as “are source of energy located hear local loads and can provide a

variety of benefits including improved reliability if they are properly operated in the electrical

distributed system”, [1]. Distributed generation source are typically include photovoltaic (PV),

wind turbines, traditional resources such as fuel cells, [1]. Either of fossil and renewable

resources can supply the regular operation of the power system. As mentioned above, some

kinds of distributed generation of microgrid have the function of heat recovery by recover the

wasted heat. This technique can increase the efficiency of heat and electric combination

system. It is necessary for most of the distributed generation technologies that a power

electronic used to converter the energy to main grid, [1]. The power electronics required both

rectifier and inverters or just inverter, [1]. The converter can harmonize the voltage and

frequency of components of systems. In addition, the necessary output filter is also demanded


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between the inverter and girds. The protection will also be provided by the power electronics

to the distributed generations and the local electric systems, [1].

2.4 Distributed Storage

It is deviation that the generation and local loads cannot harmonize exactly in some

conditions. To handle this technical problem, the distributed storage devices will be applied

in microgrid, [1]. Normally, the capacity applications which can categorize in terms of energy

density requirement or in term of power density requirement can play a positive role on

system performance in the 3 terms [1]:

1 It can stabilize the fluctuation of the distributed generation to run at a constant output.

2 It offered the necessary capability which is used to keep stable when the variation of load

occurs.

3 It benefit the operation of distributed generation as the seamlessly delivery unit in the

systems.

In addition to the benefit of distributed storage, it can solve the short-time power disturbances

and provide the energy reservation for the future demand. [1] Several types of the storage

applications can be utilized in the microgrid. Basically, the batteries, capacities and flywheels

are used widely. Batteries can store the electrical energy in forms of the chemical energy.

Batteries require a power converter to transfer DC power to the AC power used in the

intelligent girds, [1]. Suppercapacitors which are named ultracapacitors in some reference can

storage the electrics and enhance the density of power and high cycling capacity, [1].

Moreover, due to its quick respond compared to traditional electrical storage, the flywheels

systems came back to the public vision and play an effective role in terms of supply the

critical load demand when the system interruptions occurs, [1].


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2.5 Interconnection Switch

The interconnection switch is used to connect and disconnect the mirogrid and the rest of

distributed generation systems. Advanced technologies can combine the consolidates the

powers and switch functions which include the protection relays, metering, switching and

communications functions provided by the traditional relays and other electronic interfaces.

Specifically, the design plan of interconnection switches should match the requirements of

gird design standard. [1]

2.6 Filters Selection

According to the Zhong’s literature article [3], the low pass filter is appeared as significant

component in the simulation model. It plays an important role in terms of cutting high

frequency and passing low frequency. Therefore, the suitable value of low pass filter should

be demonstrated in the process of constructing simulation models.

2.6.1 Theoretical background

In a linear electrical system, sinusoidal input signals, can be represented used to evaluate the

frequency response in the system. This evaluation can be divided into the following steps:

1. Convert the sinusoidal input source to use phasor equivalent:

𝑥𝑖𝑛(𝑡) = 𝑋𝑖𝑛 cos(𝑤𝑡 + 𝜃𝑖𝑛) → 𝑋𝑖𝑛 = 𝑋𝑖𝑛𝑒𝑗𝜃𝑖𝑛

2. Convert all inductors and capacitors to their impedance:

𝑍𝑙 = 𝑗𝜔𝐿

𝑍𝐶 =1

𝑗𝜔𝐶= −𝑗(

1

𝜔𝐶)


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3. Calculate the voltages and currents of unknown phasors by using KVL and KCL

equations.

4. Transfer the output phasor back to sinusoids:

𝑋𝑜𝑢𝑡 = 𝑋𝑜𝑢𝑡𝑒𝑗𝜃𝑜𝑢𝑡 → 𝑥𝑜𝑢𝑡(𝑡) = 𝑋𝑜𝑢𝑡 cos(𝑤𝑡 + 𝜃𝑜𝑢𝑡)

It also should be noted that, there should be a phasor that is selected as the reference phasor.

Normally, the input phasor will be selected but the specified phasor should lead a simpler

calculation. In addition, the phasors can be represented by the either polar (magnitude, angles)

or rectangular forms (real, imaginary numbers). The phasor analysis suit the situation where

there are multiple same-frequency input sources.

The phase analysis is very effective in terms of understanding amplitudes and phase shifts

relevant to the input signals and determining the expressions for amplitude and phase changes

as function of frequency.

A simple example will be developed to determine the transfer functions:

Figure 1 Simple RC Circuit Figure.1 Simple RC Circuit

The capacitors in the simple RC circuit can be converted to 1/j𝜔C, and following equation

was gained by the impedance divider rules:


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𝑉𝑜 =

1𝑗𝜔𝐶

𝑅 +1

𝑗𝜔𝐶𝑅

𝑉𝑖𝑛

𝑉𝑜

𝑉𝑖𝑛=

1

1 + 𝑗𝜔𝐶𝑅

The ratio of output phasor and input phasor is called transfer function. The transfer function

can be represented in polar form:

H(ω) =𝑉𝑜

𝑉𝑖𝑛

=1

1 + 𝑗𝜔𝐶𝑅

=1

√1 + (𝜔𝐶𝑅)2 < 𝑡𝑎𝑛−1(𝑤𝐶𝑅)

= H(ω) < 𝜃𝐻(𝜔)

The output voltage will be giving by

𝑣𝑖𝑛(𝑡) = 𝐻(𝜔𝑜)𝑉𝑠𝑖𝑛(𝜔𝑜𝑡 + 𝜃𝐻(𝜔𝑜))

The transfer function can play a significant role in terms of evaluating the amplitude and

phase deviation between input and output. The plots of the amplitude and phase shown in

figures are called Bode plots. In addition, the Bode plot in this case is for a second order low

pass filter.


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Figure 2 Bode plots of the second order low-pass filter

As seen in Figure.2, the amplitude decrease from low frequency level as frequency increase.

In figure, the circuit passes low frequency but blocks high frequency sinusoids. Therefore, the

circuit play a role as a low-pass filter. In this plot, the frequency area where the signal was

passed and broken to a very small extent is named as passband region. The area where

attenuations occur to a very big extant is called stopband region. The main objective of the

low pass filter is to cut the unwanted high frequency, automatically. The critical region that

lies between the stopband and passband is named as transition region. The low pass filter is

regarded as key equipment in the convention of analog to digital.

2.6.2 Filter selecting

An LC low pass filter has components of shunt capacitor and a series inductor as shown in

fugure 3. At low frequency, the inductor and capacitor acts like short circuit and open circuit,

respectively.


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Figure 3 Simple LC low pass filter circuit

The transfer function at low frequency is given by:

H(0) =𝑉𝑜

𝑉𝑖𝑛

(0) =𝑅𝐿

𝑅𝑠 + 𝑅𝐿

At high frequencies, the inductor and capacitor act as the open circuit and short circuit,

respectively. Both of the two elements have the function of blocking the high frequency.

The first-order low pass filter given in figure 1 has a transfer function which is defined as

H(ω) =𝐴

1 + 𝑗𝜔𝜔𝑐

H(ω) =𝐴

√1 + (𝜔𝜔𝑐

)2

In this equation, A =1 and𝜔𝑐 =1

𝑅𝐶. In addition, the transfer function of second order low pass

Butterworth filter is given:

H(ω) =𝑉𝑜

𝑉𝑖𝑛(ω)

=𝑅

√(2𝑅 − 𝜔2𝐶𝐿𝑅 + 𝜔2(𝐶𝑅2 + 𝐿)2


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=1/2

√1 + (𝜔

𝜔𝐶)4

WhereR = √𝐿

𝐶 , 𝜔𝐶

4 =4

𝐶2𝐿2 and 𝜔𝑐 = √2

𝐿𝐶

Converting the gain to decibel the second-order response: at high frequencies

H(ω) = −6.02 − 10 log10(1 + (𝜔

𝜔𝐶)4)

In this equation, the slope is -40 dB/decade. The objective of the calculation is to get suitable

value of inductor, resister and capacitor which suit the situation of filter low frequency and

block high frequency. The design calculations of low pass filter will be used in the droop

control simulations.

2.6.3 Filters development in SPICE

To evaluate the performance of the filter, a modelling of second order Butterworth low pass

filter, a model can be built and simulated on SPICE, as shown in figure. All the parameters

for the filter are taken from Zhong’s paper, [3].

Figure 4 Simple LC low pass filter circuit


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It should be noted that Resistor R1 is only includes in order to make sure that two elements

are connected to model, is required by SPICE analysis rules. In this SPICE simulation, the

voltage source is set to supply 1 Volt AC voltage, while the load resistance is given as 1 ohm

to illustrate the response of frequency. The input settings of the filter block are shown in

figure 5:

Figure 5 Second Order Low Pass Filter Block Input Setting

Figure 6 Bode plots of Second Order Low-pass Filter


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The bode plots shown in figure 6 shown the result of the second order low pass filter. It can

be noted that the filter works effectively. It cut the high frequency sinusoids above 5 Hz, the

cut off frequency is approximately -5.01 dB.


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3.0 Droop Control

3.1The reasonable justification of the droop control approach

Due to the sharply increased use of the renewable resources, more and more parallel

connected inverters are being used in both utility grids and microgrids, [3]. Even in the

microgrid system, it is inevitable that several generators operate in parallel to supply the local

load. Normally, the distributed generators or renewable resources are connected to the grid

using inverters, [3]. A significant issue with using is how to solve the problem of power

sharing among inverters in parallel-connected inverters system.

An optimum active power P and reactive power Q is need by a steady power system, [7].

The conventional droop control is spending the active power and reactive power to achieve

proportional power sharing among several uninterruptible power supplies (UPS).

The reason why use droop control method is to allow the distributed generators in the system

to operate without external mechanism communications. It is a symbol of zero mechanism

communications system can adjust and share the loads among distributed generators

(connected via inverters) automatically when the loads changes occur is a symbol of zero

mechanism communications, [3]. This is based on the calculation of droop control

characteristics. Specifically, one of challenge problem is frequency control. In islanded mode,

the frequency harmony of system is based on rotating masses in the large grid, which is

significant to enhance the internal stability of systems, [1]. However, microgrid is the system

entirely controlled by converters, which is relevant to rotating mass, [1]. Therefore, the

control of frequency is based on the converters’ management. The converter control systems

must be adjusted to get respond before getting respond from rotating mass.


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In addition, f-P and V-Q control can use droop character to distribute unbalanced load

requirement among the inverters which are connected to the distributed generators or

renewable resources. This simple and reliable method can guarantee the unity of whole

system’s frequency and voltage in standalone model. Droop control of adjusting active power

and reactive power to control frequency and voltage separately.

3.2 Theoretical background

To get familiar with the original approach of droop control, the complex impedance of

transmission lines model is going to be considered below. The most essential assumption

which is used below is that the inductive value is much greater than the resistive value. This

assumption is suitable for high-voltage transmission lines. microgrid may operate in the

situation of low voltage cables which have resistance, so obviously. For these cases resistance

cannot be ignored.

The relationships between power flow and voltages can be derived by considering the power

flow through a transmission line between two buses, as shown in Figure.7 is described [8]

Figure 7 Power Flowing through a Line

The power flow through the line from point A to point B which is shown in the Fig.7 is

described [8]:

P + jQ = 𝑆∗ = 𝑉1𝐼∗ = 𝑈1 (𝑉1−𝑉2

𝑍)*


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= 𝑉1(𝑉1 − 𝑉2𝑒𝑗𝛿

𝑍𝑒−𝑗𝜃)

=𝑉1

2

𝑍𝑒𝑗𝜃 −

𝑉1𝑉2

𝑍𝑒𝑗(𝜃+𝛿)

Therefore, the active power and reactive power flow into lines should be illustrated in the

equation below:

P =𝑉1

2

𝑍𝑐𝑜𝑠𝜃 −

𝑉1𝑉2

𝑍cos (𝜃 + 𝛿)

Q =𝑉1

2

𝑍𝑠𝑖𝑛𝜃 −

𝑉1𝑉2

𝑍sin(𝜃 + 𝛿)

Substituting the equation𝑍𝑒𝑗𝜃 = 𝑅 + 𝑗𝑋, the real power and reactive power of the

transmission line is [8]:

𝑉2𝑠𝑖𝑛𝛿 =𝑋𝑃 − 𝑅𝑄

𝑉1

𝑉1 − 𝑉2𝑐𝑜𝑠𝛿 =𝑅𝑃 + 𝑋𝑄

𝑉1

When it comes to the purely inductive transmission lines, inductive impedance X is much

greater than the resistive impedance R. That means R can be neglected, the equation should

be rewritten:

𝑃 ≈𝑉1𝑉2𝑠𝑖𝑛𝛿

𝑋

𝑄 ≈𝑉1

2 − 𝑉1𝑉2𝑐𝑜𝑠δ

𝑋


26

According to De Brabandere [8], if the power angle δ is small, then the reactive power and

active power are proportional to the Voltage V1 and angle speed δ, respectively. Therefore,

the P-w and Q-u are both feedback loops:

𝛿 ≅𝑋𝑃

𝑉1𝑉2

𝑉1 − 𝑉2 ≅𝑋𝑄

𝑉1

From these two equations that varying active power can be used to control the angle 𝛿 while

vary the reactive power Q to control inverter voltage U1 can be adjusted by the Q. However,

in the droop control method, the frequency is used instead of the power angle δ, [2] [13]. The

reason for not use the power angle or phase angle is to do with unknown initial value of phase

of the other elements in the standalone systems. [2]

Then, we get the basis well-known droop control formulae:

𝑓 − 𝑓0 = −𝑘𝑝(𝑃 − 𝑃0)

𝑉1 − 𝑉0 = −𝑘𝑞(𝑄 − 𝑄0)

The frequency and voltage droop associate with the P and Q increasing figure are shown in

figure 8:


27

Figure 8 Classical droop control characteristic plots

The droop control characteristic plots can be used to explain the conventional droop control

method. The control method can fix the fault frequency to the normal frequency when the

frequency errors occur. [8]

However, the frequency restoration of inverter in practice is not easily to be done. This is

because all formulas are based on the assumption that impedance is purely inductive. In

practice, the transmission lines have both resistive and inductive parts. When increase the

active power, the current will be increased. This is because system voltage is constant.

3.3 Droop controller among inverters

In real situations, there are usually two or more inverters in the system. They share the load

demand together. The inverter droop controls can be divided into two situations below. The

first situation is under the condition that two inverters controllers have same droop

characteristics. In this case, the load changes are shared equaling between two inverters,

which means the droop proportion is 1:1. Figure 9 below indicates the tendencies of the

droop characteristics of two parallel-connected inverters with same load power sharing

proportion. It can be clarified that the trends of 2 curves are same. This is duo to the

proportion of load sharing is designed as the 1:1. In contrast, from the figure 10, it should be

noted that if active power (reactive power) is increased same value, frequencies (voltages)

will decreased to a different extent. This is due to the difference in the inverters


28

characteristics when they are operating in parallel. In addition, the frequency and voltage

deviations will increase when the active power and reactive power increase.

Figure 9 Inverters with same droop characteristics

Therefore, the design procedures should be considered based on the mean load sharing and

deciation extent. The inverters in figure 10 use the different droop characristics. It can be

used when the rated loads of inverters are different. The inverters can share loads according


29

to the unit rated values. By setting the suitble set points and droop characteristics, the

propertions of load sharing can be achieved easily without external or internal mechanical

comunications among the distributed generation. In addtion, it should be noted aht the figure

10 construction are base on the [14].

Figure 10 Inverters with different droop characteristics


30

4.0 Modelling and Simulation

4.1 Theoretical concept of droop controller construction

To simulate the droop control method among parallel-connected inverters, a droop control

scheme model should be created and analysed.

In this chapter, a reactive power-angle speed (Q-𝜔) and active power –voltage (P-V) droop

model will be created according to [3], which is easily to export to the Q-E and P-w. The Q-E

and P-w droop model is described in section 3.0. The purely resistive base circuit of two

generators operating in parallel will be analysed.

Figure 11 Two parallel-connect inverters with resistive output impedances

The Figure 11 is constructed base on [3]. Each impedance includes both of generator

impedance and the impedance of transmission lines which connected the generator and loads.

The active power and reactive power injected to loads will be given in the chapter 3.2:

P =𝑉1

2

𝑍𝑐𝑜𝑠𝜃 −

𝑉1𝑉2

𝑍cos (𝜃 + 𝛿)

Q =𝑉1

2

𝑍𝑠𝑖𝑛𝜃 −

𝑉1𝑉2

𝑍sin(𝜃 + 𝛿)


31

Generally, the inductive inverter output impedance is used a lot in the transmission lines, [3].

However, when the inverter output impedance is resistive which is applied in the low-voltage

conditions, the equation above change to the formulas below [3]:

𝑃𝐿 =𝑉𝐿𝐸1𝑐𝑜𝑠𝛿1 − 𝑈𝐿

2

𝑅1

𝑄𝐿 = −𝑉𝐿𝐸1𝑠𝑖𝑛𝛿1

𝑅1

If the power angle δ is small, the simplified equations become:

𝐸1 ≈ (𝑅1

𝑉𝐿) 𝑃𝐿 + 𝑉𝐿

𝛿1 ≈ −𝑅1

𝑉𝐿𝐸1𝑄𝐿

According to the equation above in order to achieve the demand of changing active power of

loads P, increase active P can lead to increasing of voltage E. Similarly, an inverse response

between reactive power Q and power angle δ can occur, so that increase power angle δ can

finish by decreasing reactive power Q. It should be noticed that in order to keep the feedback

loops of P-E negative, the droop characteristic should be adjusted to negative value.

To achieve the objective of maintaining an optimal operating point, a droop controller should

be designed to oppose the characteristic trend of P-E. For instance, the figure below shows

that the Voltage of droop controller decreases versus active power P.


32

Figure 12 Droop control characteristic Line Graph

The equations for a conventional droop controller in the purely resistive conditions are given

by [3]:

𝐸𝑖 = 𝐸∗ − 𝑛𝑖𝑃𝑖

𝑤𝑖 = 𝑤∗ + 𝑚𝑖𝑄𝑖

, where the E*and w* is rated voltage and frequency, respectively. [3] The droop control

scheme block diagram is shown in figure 13 [3] [4]:

Figure 13 Droop control Block Diagram (Resistive Case) [3]

It should be noticed that the output of this diagram is 𝐸𝑖 ∗ sin (𝜔𝑡 + 𝜑𝑖), which is the voltage

of output impedance.


33

4.2 Average Active Power

The first step of the droop controller is to take the continuous voltage V and current I signals,

and calculated average values of active power and reactive power. The continuous value for

voltage and current and the input to the controller are given by [15]:

𝑣0(𝑡) = 𝑉0sin (2𝜋𝑓0𝑡)

𝑖1(𝑡) = 𝐼1sin (2𝜋𝑓0𝑡 + 𝜑)

The relationship with input power P is described [15]:

p(t) = 𝑣0(𝑡)𝑖1(𝑡)

p(t) = 𝑉0𝐼1sin (2𝜋𝑓0)sin (2𝜋𝑓0𝑡 + 𝜑)

The equation can be simplified to the formula below [15]:

p(t) = 𝑉0𝐼1[cos(−𝜑) − cos(4𝜋𝑓0𝑡 + 𝜑)]

According to this, the waveform includes a DC component and a time vary compound with

frequency that is twice the frequency of the initial voltage and current sinusoidal waveforms.

The averaging operating can be carried out by using a low pass filter (LPF) with a cut of

frequency that is less than 2f0. The area from 0 to 2f0 should be chosen as the band-edge of

filter. This filter shown passes the average (DC) value. However, the birck-wall filter which

can eliminate the AC (sinusoidal) waveform does not exist in real situations. According to

earlier discussion, a simple first-order low past filter has a frequency response is described

[15]:

|H(f)| =1

√1 + (𝑓𝑓𝑐

)2


34

To make the gained at f=100Hz be as small as possible, the smallest cut-off frequency fc

should be used. However, if fc is too low, the filter will respond too slowly when changes in

power demand occur over time. The changes happen when the faults occur or when load

demands change. Therefore, the value of cut-off frequency should trade off these two

requirements. The selection of a higher order level filter means the sharper characteristic of

filter response. The second order Butterworth filter has a magnitude response which can

present by the equation is described [15]:

|H(f)| =1

√1 + (𝑓𝑓𝑐

)4

4.3 Average Reactive Power

The output of the reactive power is given by [15]:

q(t) = 𝑣0(𝑡)𝑖1(𝑡)

q(t) = 𝑉0𝐼1sin (2𝜋𝑓0 + 90°)sin (2𝜋𝑓0𝑡 + 𝜑)

It should be noted that the waveform has been phase shift by 90 degrees from the active

power expression. The equation can be simplified [15]:

q(t) = 𝑉0𝐼1[cos(90° − 𝜑) − cos(4𝜋𝑓0𝑡 + 90° + 𝜑)]

The requirement of voltage phase shift by 90 degrees can easily satisfied by using an all-pass

filter in the SPICE model construction. The transfer function of this strategy is given by [15]:


35

H(f) = −1 − 𝑗(

𝑓𝑓0

)

1 + 𝑗(𝑓𝑓0

)

Substituting frequency f=f0 + 50 Hz the transfer formula becomes [15]:

H(50) = −1 − 𝑗1

1 + 𝑗1

H(50) = (1 180°)√2 − 45°

√2 45°

H(50) = 1 90°

4.4 Software Introduction

ICAP/4 SPICE (Simulation Program with Integrated Circuit Emphasis) circuit analysis

software is developed by Intusoft. It should be noted that SPICE was developed by university

of California Berkeley, [10]. ICAP by latusoft is a commercial vision of SPICE. It is used to

simulate the analog and mixed signal circuits, [10]. The benefit of ICAP is able to simulate

both electrical circuits and systems. In this project, the SPICE is used to combine the droop

controllers which are analog signals and data collecting circuit of droop controller which are

represented at a system level. The SPICE can be used to check and evaluate the transient and

frequency response of the circuit networks over a range of operating conditions.


36

5.0 Implementation

The control algorithms have been installed in a SPICE Netlist. In the example given in [3],

two single phase inverter with 42 volts supply voltage, which is controlled by dSPACE kits.

As mentioned in section 3.4, an IGBT bridge controlled by PWM technology was used to

construct the continuous sinewave. The filter values of the inductor and capacitor are 2.35mH

and 22μF, respectively. [3] The switching frequency of PWM circuit is 7.5 kHz, and rated

frequency of system is 50 Hz. The switching frequency of PWM circuit is 7.5 kHz. The rated

voltage is 12V, [3].

5.1 Design of a Single Controller to Achieve Resistive Output

impedance.

Based on the main works of the project, the droop control scheme of resistive output

impedance is installed in the SPICE netlist. To illustrate the accuracy of the droop control

strategy, a single-phase inverter with different load demands system will be tested using

SPICE. This model is based on the assumption that the load impedance is purely resistive.


37

Figure 14 Single phase inverter controller scheme

The Netlist is given in the Appendix. It can be seen from the corresponding schematic

diagram in figure that network can be divided into 2 components: the controller and that

electrical circuit. There are two feedback loops in that controller. The top side feedback loop

adjusts the amplitude of output sinewave signals via controlling the active power P and

system voltage V signals. In contrast, the bottom feedback loop is controls the frequency of

output sinusoid waveform by controlling the reactive power Q and system frequency signal.

As mentioned above in section 4.3, there is an all-pass filter is applied to achieve the phase

shift when calculating the reactive power delivered to the load. There are two feedback loops

designed to achieve the objectives of controlling amplitude and frequency of output sinewave

signals at the same time. In addition, the line current of the controller can be gotten by

measuring value of a dummy voltage source which corresponds to the voltage source Vind1

in the electrical circuit. The load voltage at node 8 is returned to the input of the controller

A

B

K*A*B

8

10

3

MUL

S^2+AS+B K

- 4

X2

POLE2

SUM2

K1

K22

1

X3

SUM2

RE

1

V1

12

9

5

X5

SWITCH

Vswitch

Rload2

9

Rload1

9

C1

22uF

6 7

L1

2.35mHVind1

8

8

K=1

B1

Voltage

1.4142*V(1)*cos(V(16))

H1

1

A

B

K*A*B

11

12

X4

MUL

S+A

S+B

X6

PZ

S^2+AS+B K

- 13

X7

POLE2

16

Rw

1

14

V4

314.295

Vo

SUM2

K1

K2

15

X8

SUM2

K/S

X9

SINT


38

using, the continuation element. The electrical network, with test points for node voltage and

line current, is shown in Figure 15

Figure 15 Single Phase Inverter Controller Equivalent Circuit

All the parameters in the equivalent circuit are provided in the [3]. The circuit is installed in

ICAP SPICE simulation. The switch is used to connect and disconnect an additional load at

specific time. The value of voltage source Vind1 is set to 0 V. Generally, measure the current

value of dummy voltage source is an effective way to identify and adjust the line current

value. The controller generates the amplitude and frequency of the output voltage according

to the equations:

𝐸𝑖 = 𝐸∗ − 𝑛𝑖𝑃𝑖

𝑤𝑖 = 𝑤∗ + 𝑚𝑖𝑄𝑖

, where the E*and w* is rated voltage and frequency, respectively. [3]

It should be noted that the reactive power Qi is proportional to -δi if the power angle is small.

In order to make sure all the feedback loops of this strategy are negative, the signs before

𝑚𝑖𝑄𝑖 has been set to positive, [3]. In the single inverter simulation, either frequency droop

characteristic or voltage droop characteristic is set to 1. The results of this simulation will be

illustrated in the section 6 experiment results.


39

5.2 Design of a Double Controller with Resistive Output impedance to

achieve 2:1 power sharing.

The main objective of this project is to use droop control to achieve proportional power

sharing among inverters. Therefore, the core experiments are designed to research the

performance of multiple inverters. Firstly, the simulation set up for two parallel-connected

inverters was constructed in SPICE; the schematic diagram for this set- up is shown in

figure.17

Figure 16 Single Phase Two Inverters Controller components (Resistive Case)

A

B

K*A*B

8

10

3

MUL

S^2+AS+B K

- 4

X2POLE2

SUM2

K1

K22

1

X3SUM2

RE1

Erated12

9

5

X5SWITCH

Vswitch

Rload29

Rload19

C122uF

6 7

L12.35mH

Vind1

8

8

n1=0.4

B1Voltage

1.4142*V(1)*cos(V(16))

H11

A

B

K*A*B

11

12

X4MUL

S+A

S+B

X6PZ

S^2+AS+B K

- 13

X7POLE2

16

Rw1

14

Vrated314.295

Vo

SUM2

K1

K2

15

X8SUM2

K/S

X9SINT

Line current

C222uF

17

Vind2

18

L22.35mH

B2Voltage

A

B

K*A*B

19

20

-xMUL

n2=0.8

S^2+AS+B K

- 21

X11POLE2

SUM2

K1

K222

23

X12SUM2

REx1

Eratedx12

8

H21

Line current

A

B

K*A*B

24

25

X13MUL

S+A

S+B

X14PZ

S^2+AS+B K

- 26

X15POLE2

27

Rwx1

28

Vratedx314.295

SUM2

K1

K2

29

X16SUM2

K/S

X17SINT

1.4142*V(23)*cos(V(27))

Vo2

m1=0.1

m2=0.2


40

As can be seen clearly, the two inverters are connected in parallel. In this concept, there are

two controllers for each inverter. The droop coefficients of inverters are set to n1= 0.4 and

n2= 0.8; m1= 0.1 and m2= 0.2. It can be confirmed that P1=2 P2, and Q1= 2Q2 which is 1:2

power sharing. In addition, the two inverters share the same output voltage and load

impedance. The test point was also placed to demonstrate the output voltage of the second

inverter. The results of this experiment will be described in the section 6.2.

5.3 Single Inverter Controller Simulations of inductive Output Impedance

Generally, the impedance of power grid with high voltage cables have is inductive. The

traditional droop control method can easily satisfy the conditions of purely inductive. A

modelling of inductive output impedance will be established in SPICE. can be used to

evaluate the frequency and voltage response of a circuit. The mathematical blocks diagram

which rewrite base on the Figure, 13 is given above:

Figure 17 Droop control Block Diagram (Inductive Case)

Hence, the detail circuit component according to the concept of block diagram is shown:


41

Figure 18 Single Phase One Inverter Controller Component (Inductive Case)

To compare with the case of resistive, the droop feedback loops are much different.

According to the theoretical background knowledge of droop control, the active power Pi is

proportional to the δ, while reactive power Q corresponds V. The rest parts of this modelling

follow the same concept as resistive case, which is indicated above. It should be notice that,

the conventional droop controller equation of purely inductive is given:

𝐸𝑖 = 𝐸∗ − 𝑛𝑖𝑄𝑖

𝑤𝑖 = 𝑤∗ − 𝑚𝑖𝑃𝑖

, where the E*and w* is rated voltage and frequency, respectively. In the single inverter

simulation, either frequency droop characteristic or voltage droop characteristic is set to 1.

The results of this simulation will be illustrated in the section 5 experiment results.

A

B

K*A*B

11

10

3

MUL

S^2+AS+B K

- 4

X2

POLE2

SUM2

K1

K22

1

X3

SUM2

RE

1

V1

12

8 9

5

X5

SWITCH

Vswitch

C1

11uF

6 7

L1

1.36mHVind1

8

8

K=1

B1

Voltage

1.4142*V(1)*cos(V(16))

H1

1

A

B

K*A*B12

X4

MUL

S+A

S+B

X6

PZ

S^2+AS+B K

- 13

X7

POLE2

16

Rw

1

14

V4

314.295

Vo

SUM2

K1

K2

15

X8

SUM2

K/S

X9

SINT

L2

8mH

L3

8mH


42

5.4 Double Inverters Controller Simulations of inductive Output Impedance

According to the single controller operation concept, a double inverters controller component

can be easily constructed in the SPICE, which is shown in Figure. 19:

Figure 19 Single Phase Two Inverters Controller components (inductive Case)

In the double inverters of resistive case, the droop characteristics are set as: n1= 0.4 and n2=

0.8; m1= 0.1 and m2= 0.2. The controllers are set to share the power in the proportion of 1:2.

In addition, from the output-voltage results of single inverter (inductive case), it has been

A

B

K*A*B

11

10

3

MUL

S^2+AS+B K

- 4

X2POLE2

SUM2

K1

K22

1

X3SUM2

RE1

Erated12

8

C144uF

6 7

L15mH

Vind1

8

8

n1=0.4

B1Voltage

1.4142*V(1)*cos(V(16))

H11

A

B

K*A*B12

X4MUL

S+A

S+B

X6PZ

S^2+AS+B K

- 13

X7POLE2

16

Rw1

14

Vrated314.295

Vo

SUM2

K1

K2

15

X8SUM2

K/S

X9SINT

Line current

9

5

X5SWIT CH

V2

L28mH

L38mH

19

B2Voltage

17

L45mHVind2

C211uF

A

B

K*A*B

18

20

21

-xMUL

n2=0.8

S^2+AS+B K

- 22

X11POLE2

SUM2

K1

K223

24

X12SUM2

REx1

Eratedx12

8

H2Vind2

Line current

A

B

K*A*B25

X13MUL

S+A

S+B

X14PZ

S^2+AS+B K

- 26

X15POLE2

27

Rwx1

28

Vratedx314.295

SUM2

K1

K2

29

X16SUM2

K/S

X17SINT

1.4142*V(24)*cos(V(27))

V8

m2=0.2

m1=0.1


43

demonstrated that the frequency of output voltage is pretty high. That means the low pass

filter dose not works well. This is because the value of inductor and capacitor that is the

components of filter is too small. Therefore, the values of low-pass filter are increased to

5mH and 44uF, respectively to cut the high frequency and pass low frequency. The results of

inductive controllers will be illustrated in chapter 6.


44

6.0 Simulation Results

To prove the accuracy of the droop control strategy among parallel-connected inverters

described in the project, a series of droop control feedback loops were tested using the same

constructing concept of block diagram. The results are detailed as follows. The output

sinusoid waveforms are given firstly, while the frequency variation figures and amplitude

variation figures are given in the second place.

6.1 Single Inverter Controller Simulations of Resistive Output Impedance

The result from the single inverter controller with droop characteristic =1 is indicated in the

figure.20 while the frequency and amplitude results from conventional droop controller is

indicated from figure.21 to figure22. Obviously, there are two steady states. During 0.5

seconds, the load demand is doubled. The system need rework and get the new amplitude and

frequency to achieve the new steady state.

Figure 20 RMS value of load voltage for single inverter (resistive case)


45

Figure 21 Frequency Response of Single Inverter (Resistive Case)

Figure 22 Amplitude Response of Single Inverter (Resistive Case)

1 v(1)

100m 300m 500m 700m 900mtime in seconds

7.50

8.50

9.50

10.5

11.5

v(1

) in

vo

lts

Plo

t1

1


46

In this concept, the amplitude measurement can be done by measure the voltage of node 1 in

controller, while the amplitude performance demonstrated by the measurement of voltage of

node 15. The voltage node 15 corresponds the2πf + φ; (2πf + φ)x t should be calculated by

the integrator and measured by voltage node 16. The proposed block diagram strategy was

able to achieve the goal of varying the RMS value of output voltages. In addition, it should be

noticed that the unit of frequency in Figure 21 are volts. This is the voltage is used as the

controllers signals. Therefore, it can be transferred to the Hz by using the equationω = 2πf.

From the figures above, it can be clarified that both of frequency and voltage dropped at the

beginning and get the first steady state at approximately 0.15 seconds. After that, the load

impedance was doubled. The consequence of that is frequency’s fluctuation again and getting

the steady state at finals. The system frequency value of finally steady state is around 314.06

rad/s. When it comes to the amplitude variation, the tendency as a whole is decreased to a

small extent, which satisfies inverse proportion response. The final value of amplitude

decreased to approximately 5.5 Volts when the load power increased because load impedance

is doubled.

6.2 Two Inverters Controller Simulations of Resistive Output Impedance

There are two sinusoid waveforms in the Figure 23. The line 1 represents the inverter 1 while

line 2 represents the inverter No.2.


47

Figure 23 Load voltages for Two Inverters (Resistive Case)

Figure 24 Amplitude Response of two inverters (Resistive case)

Figure 25 Frequency Response of Two inverters (Resistive case)


48

The results of the two inverters with 2:1 proportions power sharing was indicated above. The

figures include the output voltages, amplitudes and frequency. In detail, the amplitudes

variations of inverter No.1 and inverter No.2 are measured by measuring the Voltages of

node 1 and node 23, respectively. The Figure.23 demonstrates same trends of two controllers.

However, the value of V (1) is dropped to 11.9364V that is the first steady state and decrease

to 11.8751V. The difference between first and final steady state is 0.06. On the contrary, the

value of V (23) changed approximately 0.03 which is from 11.96 to 11.93. Hence, it can be

clarified that the inverter No.1 which corresponds V (1) shared 2 times power as Inverter

No.2 that corresponds V (23). The results satisfied the goals which 2:1 proportional power is

sharing. When it comes to the amplitudes, by measuring the values of voltage node 15 and

voltage node 29, the amplitudes of controller 1 and controller 2’s output sinusoid voltage can

be evaluated, respectively. The first steady state of inverter No.1 occurred in approximately

0.15 second. The RMS value of V (15) can be obtained as 314.2923Vand decrease to the

314.2918V. On the other hand, the RMS values of another inverter’s frequency have changed

0.0002 Voltage. Although the frequencies of inverters ran smoothly and changed to a slight

extent, the power sharing ratio of this system is 2:1, which is satisfied the initial settings.

6.3 Single Inverter Controller Simulations of inductive Output Impedance

The results of single inverter controller strategy are indicated in Figure.26, which include the

performance of output voltage, amplitude and system frequency.


49

Figure 26 Single Inverter Controller Output Variation (Inductive Case)

As can be seen clearly, the system fluctuated a while after started and get the first steady state

at approximately 0.15 second. The value of droop characteristic Ki was chosen as 1 to

intentionally look forward the performance of feedback loops when the load doubled. A

linear load of inductor that is about 8 mH was connected in parallel to the initial circuit at 0.5

second to achieve load increasing. In addition, it can be demonstrated from the figure.26 that

both the amplitude and frequency feedback loops are negative. That means the performance

of specified system works well and satisfied the theoretical background of Figure 8 Classic

droop control characteristic plots. In addition, the losses in the transmission lines are ignored

in this simulation. This is because the impedance of cables in this circuit is much greater than

the output impedance. The attention should be paid to the response of output impedance.


50

6.4 Two Inverters Controller Simulations of inductive Output Impedance

Figure 27 Load voltages for Two Inverters (Inductive Case)

Figure 28 Two Inverters Controller Amplitude response (Resistive case)

Figure 29 Two Inverters Controller Frequency response (Resistive case)

The results of double controller with inductive output impedance are shown above. To

compare with the single controller condition, the filter can provide a better performance in

terms of decrease the frequency. In addition, the results of both amplitude and frequency have


51

the same trends among two inverters. The amplitude dropped to a big extent when the load

demand is doubled. On the contrast, the frequency decreased to a very small extent. When it

comes to the accurate value, the frequency of inverter no.1 dropped from 3.14294 to 3.14282,

while the frequency of no.2 inverter decreased from 3.14294 to 3.14288. In terms of

amplitude scope, the value of inverter 1 decreased from 8.27 to 8.21, while the value of

another inverter dropped from 9.22 to 9.16. The frequency of inverter 1 dropped

approximately 0.00012, while the frequency of inverter 2 dropped approximately 0.00006.

Both of amplitude and frequency response satisfy the 2:1 droop ratio. In terms of amplitude,

the amplitude of inverter1 dropped 0.12, while the amplitude of inverter 2 dropped 0.06. Both

of amplitude and frequency response satisfy the 2:1 droop ratio.


52

7.0 Conclusions and Future Works

7.1 Conclusion

With the rapid growth in size and number of renewable resource generation system connected

to the power grids, the utility and the control approach of parallel-connected inverters become

more significant to develop. This trend leads to an increasing utilize of microgrid technology

due to its main advantages, which are reliability and stability of the systems. In the microgrid

system, it is hard to avoid the need for inverters connected in parallel. Therefore, how to

solve the problem of power sharing among inverters when the load demands changed has

triggered much attention.

The goal of sharing the power in proportional without mechanical communications led to the

droop control approach being researched in this thesis. The algorithm that was developed in

this thesis is based on the DC power flow assumption, which ignored any power losses in the

transmission progress. Based on the assumption, the droop control algorithms for resistive

and inductive case are explained in the thesis. In addition, as necessary components of the

test network, the low pass filter selection is also discussed.

The results indicated in chapter 6 illustrate the response of output voltage, which include the

amplitude and frequency scopes. There are four series of results show the single and double

inverters in parallel and purely resistive and inductive impedance, respectively. The single

inverter experiments are used to test basic control schemes in the SPICE, while the double

inverters cased is to test whether supplies can achieve proportional power sharing. The

proportion of power sharing is set to 2:1 in this project. It is matched to a big extent, which

means the simulations show that the proportional power sharing is achieved by using the

theoretical algorithm of conventional droop control.


53

In summary, the purpose of this thesis report is to evaluate the performance of droop control

in the simple microgrid in standalone mode. The thesis has been completed focusing on the

two inverters circuits with purely inductive and purely resistive loads. The power sharing

satisfies the droop control algorithm and the objective 2:1 proportion.

7.2 Future Works

The control strategy that simulated in the thesis achieved the proportional power sharing

successfully. Therefore, future work could investigate an innovative method of reducing the

losing throughout transmission lines, which increases the accuracy of proportional power

sharing among parallel-connected inverters. According to Zhang’s paper [3], the per-unit

resistive or inductive output impedance and voltage set point (Ei) will impacts the

improvement of accuracy of power sharing.

It also could investigate the multiple output impedance condition. As mentioned in the report,

the inverter output impedance and the transmission lines are inductive. The droop control

algorithm discussed in the section 3.2 is used widely. On the contrary, in low-voltage

applications, another droop algorithm discussed in section 4.1 is applied due to the purely

resistive output impedance. However, there is also the third condition that the components

include both inductive and resistive impedance; the droop control algorithm suit combination

condition should be investigated in the future. What is more, the grid-connected mode of

microgrid should be investigated because the power grid will also impact the performance of

local standalone system. To sum up, much work can be done to understand the control and

maintaining method of microgrids. To finish the future research work will lead the full

potential of droop control in the standalone mode of microgrid concepts.


54

Bibliography

[1] Benjamin Kroposki et al, “Making Microgrid work”. IEEE Power& Energy, May/June

2012, pp. 40-53. [Online] available:

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[2] Andrew Mark Bollman, “An Experimental Study of Frequency Droop Control In a Low-

Inertia Microgrid”, College of the University of Illinois, 2009 [online] Available:

https://www.ideals.illinois.edu/bitstream/handle/2142/14647/Bollman_Andrew.pdf?sequence

=2

[3]Qing-Chang Zhong “Robust Droop Controller for the Accurate Proportional Load

Sharing among Inverters Operated in parallel”, IEEE Trans Ind. Electron., vol.60, No.4,

pp.1281-1290, Apr, 2013

[4] Josep M. Guerrero et al, “Decentralized Control for Parallel Operation of Distributed

Generation Inverters Using Resistive Output Impedance”, IEEE Transactions on Industrial

Electronics, Vol. 54 ,No.2, pp.994-1004, Apr, 2007

[5] R. Lasseter and P. Piagi, “Microgrid: A conceptual solution” in Proceedings of the 35th

IEEE Power Electronics Specialist Conference, Germany, 2004

[6] J. DunCan Glover, Mulukutla S. Sarma, Thomas J. Overbye, “Power System Analysis and

Design” 5th ed. Cengage Learning, pp.32-33, 2012.

[7] Mukul C. Chandorkar, Deepakraj M.Divan and Rambabu Adapa, “Control of Parallel

Connected Inverters in Standalone ac Supply Systems” IEEE Transactions on Industrial

Electronics Applications, Vol. 29, No. 1, Jan1993. pp.136-143, [online]. Avalible: http://0-

ieeexplore.ieee.org.prospero.murdoch.edu.au/xpls/abs_all.jsp?arnumber=195899&tag=1

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[8] Karel De Brabandere, Bruno Bolsens, Jeroen Van den Keybus, Achim Woyte, Johan

Driesen, Ronnie Belmans, “A Voltage and Frequency Droop Control Method for Parallel

Inverters.” IEEE Transactions on Power Electronics, Vol.22, No.4 pp. 1107-1115 July, 2007.

[online]. Available:

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4267747&url=http%3A%2F%2Fieee

xplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4267747 [Accessed Oct. 9, 2015]

[9] Katherine Tweed “ Synchronization Controls Could help Smooth Microgrids” IEEE

Spectrum 21 August 2015. [online] .

Available : http://spectrum.ieee.org/energywise/energy/the-smarter-grid/synchronization-

controls-could-help-smooth-microgrids-

[10] Intusoft, 2015 [Online], Available: http://www.intusoft.com/icap.htm

[11] Travis Wilson. “Control and Management of a Microgrid and the use of Droop

Control”. Murdoch University, June 2015 [online] available:

http://researchrepository.murdoch.edu.au/28266/

[12]Jinwei He et al, “An Islanding Microgrid Power Sharing Approach Using Enhanced

Virtual Impedance Control Scheme.” IEEE Transactions on Power Electronics covers

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[13]Wang Jing et al, “Research on operation control of micro sources within a microgrid”

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56

[14] Anuroop.P.V at el, “Droop Control of Parallel Inverters with LCL Filter and Active

Damping in stand-alone Operation” International Journal of Engineering Research and

Development (IJERD), Vol.7 Issue 11 pp.43-52 July 2013 [online] available:

http://www.slideshare.net/ijerd_editor/international-journal-of-engineering-research-and-

development-ijerd-24675936

[15] Gregory Crebbin “Droop controllers for Power sharing” Murdoch University

November 2016

Appendix A SPICE Netlist for Signal Inverter Resistive Case

.TRAN 1m 1 0 1m UIC

.OPTIONS acct

.PRINT TRAN Vo

X- 8 10 3 MUL { K=1 }

.SUBCKT MUL 1 2 3 {K=???}

B1 3 0 V = V(1) * V(2) * {K}

.ENDS

X2 3 4 POLE2 { K=-0.04 FN=5 Z=0.707 }

.SUBCKT POLE2 1 2 {K=??? FN=??? Z=???}

*PARAMS ARE: DC GAIN = {K}

* FREQ = {FN}

* DAMPING = {Z}

*

*TRANSFER FUNCTION: K*WN^2/(S^2 +2*Z*WN*S + WN^2)

* WHERE WN=2*PI*FN

http://www.slideshare.net/ijerd_editor/international-journal-of-engineering-research-and-development-ijerd-24675936

http://www.slideshare.net/ijerd_editor/international-journal-of-engineering-research-and-development-ijerd-24675936


57

RI 1 0 1E12

E1 3 0 1 0 {K}

R1 3 4 1MEG

E2 5 0 0 4 1E6

C1 4 5 {.159155U/FN} IC=0

RZ 4 5 {.5MEG/Z}

R2 5 7 -1MEG

E3 2 0 0 7 1E6

C2 2 7 {.159155U/FN} IC=0

R3 2 4 1MEG

.ENDS

X3 4 2 1 SUM2 { K1=-1 K2=1 }

.SUBCKT SUM2 1 2 3 {K1=??? K2=???}

B1 3 0 V = {K1}*V(1) + {K2}*V(2)

.ENDS

RE 1 0 1

V1 2 0 DC=12

X9 15 16 SINT { K=1 }

.SUBCKT SINT 1 2 {K=???}

* INTEGRATOR

*PARAMS ARE GAIN={K}

RIN 1 0 1E12

E1 3 0 0 1 {K}

C1 2 4 1U IC=0

R1 3 4 1MEG


58

E2 2 0 0 4 1E6

.ENDS

X5 8 9 5 SWITCH { }

.SUBCKT SWITCH 1 2 3

R1 1 2 1E10

G1 1 2 POLY(2) 1 2 3 0 0 0 0 0 1

.ENDS

L1 6 7 2.35mH

Vswitch 5 0 PULSE 0 100 0.5 1m 1m 10 20

Rload2 9 0 9

Rload1 8 0 9

C1 8 0 22uF IC=6V

Vind1 7 8

B1 6 0 V=1.4142*V(1)*cos(V(16))

H1 10 0 Vind1 1

X4 11 10 12 MUL { K=1 }

X6 8 11 PZ { K=-1 FP=50 FO=-50 }

.SUBCKT PZ 1 2 {K=??? FP=??? FO=???}

*PARAMS ARE DC GAIN = {K}

* POLE FREQ = {FP} HERTZ

* ZERO FREQ = {FO} HERTZ

*

E1 0 3 1 0 {K}

RI 1 0 1E12

R1 3 4 1MEG


59

R2 4 2 1MEG

C1 3 4 {1U/(6.28319*FO)}

C2 2 4 {1U/(6.28319*FP)}

E2 2 0 0 4 1E6

.ENDS

X7 12 13 POLE2 { K=-0.05 FN=5 Z=0.707 }

Rw 16 0 1

V4 14 0 DC=314.295

X8 13 14 15 SUM2 { K1=-1 K2=1 }

.END

Appendix B SPICE Netlist for Double Inverters resistive Case

.TRAN 0.01m 1 0 0.01m UIC

.OPTIONS abstol=10n itl4=200 method=GEAR

.OPTIONS reltol=0.02 vntol=10u vsectol=1.00u

.OPTIONS acct

.OPTIONS Bypass=0

.PRINT TRAN Vo

.PRINT TRAN Vo2

X- 8 10 3 MUL { K=0.4 }


B1 3 0 V = V(1) * V(2) * {K}

.ENDS

X2 3 4 POLE2 { K=-1 FN=5 Z=0.707 }

.SUBCKT POLE2 1 2 {K=??? FN=??? Z=???}


60


* FREQ = {FN}

* DAMPING = {Z}

*


* WHERE WN=2*PI*FN

RI 1 0 1E12

E1 3 0 1 0 {K}

R1 3 4 1MEG

E2 5 0 0 4 1E6

C1 4 5 {.159155U/FN} IC=0

RZ 4 5 {.5MEG/Z}

R2 5 7 -1MEG

E3 2 0 0 7 1E6

C2 2 7 {.159155U/FN} IC=0

R3 2 4 1MEG

.ENDS

X3 4 2 1 SUM2 { K1=-1 K2=1 }

.SUBCKT SUM2 1 2 3 {K1=??? K2=???}

B1 3 0 V = {K1}*V(1) + {K2}*V(2)

.ENDS

RE 1 0 1

VErated 2 0 DC=12

X9 15 16 SINT { K=1 }



61

* INTEGRATOR


RIN 1 0 1E12

E1 3 0 0 1 {K}

C1 2 4 1U IC=0

R1 3 4 1MEG

E2 2 0 0 4 1E6

.ENDS

C2 8 0 22uF IC=6V

L1 6 7 2.35mH

Vswitch 5 0 PULSE 0 100 0.5 1000m 1m 10 20

Rload2 9 0 9000

Rload1 8 0 9.0

C1 8 0 22uF IC=6V

Vind1 7 8

B1 6 0 V=1.4142*V(1)*cos(V(16))

H1 10 0 Vind1 1

X4 11 10 12 MUL { K=0.1 }

X6 8 11 PZ { K=-1 FP=50 FO=-50 }

.SUBCKT PZ 1 2 {K=??? FP=??? FO=???}




*

E1 0 3 1 0 {K}


62

RI 1 0 1E12

R1 3 4 1MEG

R2 4 2 1MEG

C1 3 4 {1U/(6.28319*FO)}

C2 2 4 {1U/(6.28319*FP)}

E2 2 0 0 4 1E6

.ENDS

X7 12 13 POLE2 { K=-1 FN=5 Z=0.707 }

Vind2 17 8

Rw 16 0 1

Vrated 14 0 DC=314.295

X8 13 14 15 SUM2 { K1=-1 K2=1 }

L2 17 18 2.35mH

B2 18 0 V=1.4142*V(23)*cos(V(27))

X-x 8 19 20 MUL { K=0.8 }

X11 20 21 POLE2 { K=-1 FN=5 Z=0.707 }

X12 21 22 23 SUM2 { K1=-1 K2=1 }

REx 23 0 1

VEratedx 22 0 DC=12

H2 19 0 Vind2 1

X13 24 19 25 MUL { K=0.2 }

X14 8 24 PZ { K=-1 FP=50 FO=-50 }

X15 25 26 POLE2 { K=-1 FN=5 Z=0.707 }

Rwx 27 0 1

Vratedx 28 0 DC=314.295


63

X16 26 28 29 SUM2 { K1=-1 K2=1 }

X17 29 27 SINT { K=1 }

X18 8 9 5 0 SSWITCH { RON=0.1 ROFF=1MEG VON=1 VOFF=0 }

.SUBCKT SSWITCH 1 2 3 4 {RON=1 ROFF=1MEG VON=1 VOFF=0}

*Connections + - NC+ NC-

*Parameters: Ron On Resistance in Ohms, Roff Off Resistance in Ohms

* VON On Current in Amps, VOFF Off Current in Amps

* IF V(3,4) > VON THEN RSwitch=RON, IF V(3,4) < VOFF THEN RSwitch=ROFF, ELSE

* RSwitch will smoothly transistion between the on and off states

A1 1 2 3 4 SMOOTH

.MODEL SMOOTH VSWITCH RON={RON} ROFF={ROFF} VON={VON}

VOFF={VOFF}

.ENDS

.END

Appendix C SPICE Netlist for single Inverters inductive Case

.TRAN 1m 1 0 1m UIC

.OPTIONS acct

.PRINT TRAN Vo

X- 11 10 3 MUL { K=1 }


B1 3 0 V = V(1) * V(2) * {K}

.ENDS

X2 3 4 POLE2 { K=1 FN=5 Z=0.707 }

.SUBCKT POLE2 1 2 {K=??? FN=??? Z=???}


64


* FREQ = {FN}

* DAMPING = {Z}

*


* WHERE WN=2*PI*FN

RI 1 0 1E12

E1 3 0 1 0 {K}

R1 3 4 1MEG

E2 5 0 0 4 1E6

C1 4 5 {.159155U/FN} IC=0

RZ 4 5 {.5MEG/Z}

R2 5 7 -1MEG

E3 2 0 0 7 1E6

C2 2 7 {.159155U/FN} IC=0

R3 2 4 1MEG

.ENDS

X3 4 2 1 SUM2 { K1=-1 K2=1 }

.SUBCKT SUM2 1 2 3 {K1=??? K2=???}

B1 3 0 V = {K1}*V(1) + {K2}*V(2)

.ENDS

RE 1 0 1

VErated 2 0 DC=12

X9 15 16 SINT { K=1 }



65

* INTEGRATOR


RIN 1 0 1E12

E1 3 0 0 1 {K}

C1 2 4 1U IC=0

R1 3 4 1MEG

E2 2 0 0 4 1E6

.ENDS

X5 8 9 5 SWITCH { }


R1 1 2 1E10

G1 1 2 POLY(2) 1 2 3 0 0 0 0 0 1

.ENDS

L2 9 0 8mH

L1 6 7 1.36mH

V2 5 0 PULSE 0 100 0.5 1m 1m 10 20

C1 8 0 11uF IC=6V

Vind1 7 8

B1 6 0 V=1.4142*V(1)*cos(V(16))

L3 8 0 8mH

H1 10 0 Vind1 1

X4 8 10 12 MUL { K=1 }

X6 8 11 PZ { K=-1 FP=50 FO=-50 }

.SUBCKT PZ 1 2 {K=??? FP=??? FO=???}



66



*

E1 0 3 1 0 {K}

RI 1 0 1E12

R1 3 4 1MEG

R2 4 2 1MEG

C1 3 4 {1U/(6.28319*FO)}

C2 2 4 {1U/(6.28319*FP)}

E2 2 0 0 4 1E6

.ENDS

X7 12 13 POLE2 { K=1 FN=5 Z=0.707 }

Rw 16 0 1

Vrated 14 0 DC=314.295

X8 13 14 15 SUM2 { K1=-1 K2=1 }

.END

Appendix D SPICE Netlist for Double Inverters resistive Case

.TRAN 1m 1 0 1m UIC

.OPTIONS acct

.PRINT TRAN Vo

.PRINT TRAN V8

X- 11 10 3 MUL { K=1 }


B1 3 0 V = V(1) * V(2) * {K}


67

.ENDS

X2 3 4 POLE2 { K=0.4 FN=5 Z=0.707 }

.SUBCKT POLE2 1 2 {K=??? FN=??? Z=???}


* FREQ = {FN}

* DAMPING = {Z}

*


* WHERE WN=2*PI*FN

RI 1 0 1E12

E1 3 0 1 0 {K}

R1 3 4 1MEG

E2 5 0 0 4 1E6

C1 4 5 {.159155U/FN} IC=0

RZ 4 5 {.5MEG/Z}

R2 5 7 -1MEG

E3 2 0 0 7 1E6

C2 2 7 {.159155U/FN} IC=0

R3 2 4 1MEG

.ENDS

X3 4 2 1 SUM2 { K1=-1 K2=1 }

.SUBCKT SUM2 1 2 3 {K1=??? K2=???}

B1 3 0 V = {K1}*V(1) + {K2}*V(2)

.ENDS

RE 1 0 1


68

V1 2 0 DC=12

X9 15 16 SINT { K=1 }


* INTEGRATOR


RIN 1 0 1E12

E1 3 0 0 1 {K}

C1 2 4 1U IC=0

R1 3 4 1MEG

E2 2 0 0 4 1E6

.ENDS

L2 0 8 8mH

X5 8 9 5 SWITCH { }


R1 1 2 1E10

G1 1 2 POLY(2) 1 2 3 0 0 0 0 0 1

.ENDS

L3 0 9 8mH

L1 6 7 5mH

Vswitch 5 0 PULSE 0 100 0.5 1m 1m 10 20

X-x 17 18 19 MUL { K=0.8 }

X11 19 20 POLE2 { K=0.4 FN=5 Z=0.707 }

C1 8 0 44uF IC=6V

Vind1 7 8

B1 6 0 V=1.4142*V(1)*cos(V(16))


69

X12 20 21 22 SUM2 { K1=-1 K2=1 }

H1 10 0 Vind1 1

X4 8 10 12 MUL { K=0.1 }

X6 8 11 PZ { K=-1 FP=50 FO=-50 }

.SUBCKT PZ 1 2 {K=??? FP=??? FO=???}




*

E1 0 3 1 0 {K}

RI 1 0 1E12

R1 3 4 1MEG

R2 4 2 1MEG

C1 3 4 {1U/(6.28319*FO)}

C2 2 4 {1U/(6.28319*FP)}

E2 2 0 0 4 1E6

.ENDS

X7 12 13 POLE2 { K=0.5 FN=5 Z=0.707 }

REx 22 0 1

Rw 16 0 1

V4 14 0 DC=314.295

X8 13 14 15 SUM2 { K1=-1 K2=1 }

V3 21 0 DC=12

H2 18 0 Vind2 1

X13 8 18 23 MUL { K=0.2 }


70

X14 8 17 PZ { K=-1 FP=50 FO=-50 }

X15 23 24 POLE2 { K=0.5 FN=5 Z=0.707 }

Rwx 25 0 1

V5 26 0 DC=314.295

X16 24 26 27 SUM2 { K1=-1 K2=1 }

X17 27 25 SINT { K=1 }

B2 28 0 V=1.4142*V(22)*cos(V(25))

L4 29 28 5mH

Vind2 29 8

C2 8 0 44uF

.END

Documents

Thesis Report - Murdoch University · Thesis Report Voltage and Frequency Droop Control of a Microgrid in Islanded Modes Zhaoyi Liu 1/13/2016 Supervisor: Dr. Gregory Crebbin . Droop