Co-ordinated Control of Microgrids

Department of Electrical & Electronic

Engineering

NE 4020: Final Year Project Report

"Co-ordinated Control of Microgrids"

Student Name: Mark Roche .

Student Number: 109479961 .

Student Name: John Collins .

Student Number: 109607081 .

Project Supervisor: Dr. Gordon Lightbody .

Date: 27/03/2013 .

Final Year Project Report Mark Roche "Co-ordinated Control of Microgrids" John Collins

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Declaration I confirm that this report is entirely the work of my project partner and I. All sources used have been

appended in the Bibliography section, and while writing this document extreme caution was used to

avoid plagiarism as defined by UCC regulations.

Signature: ___________________

Date: ___________________

Signature: ___________________

Date: ___________________


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Acknowledgements The students would like to thank Dr. Gordon Lightbody, who supervised the project and was always very patient when explaining challenging material relating to the subject matter at hand. Also, the students appreciate the assistance which was provided by Dr. Michael Egan, who was also

consulted on issues relating to the project material, such as the Park and Clarke Transformations as

well as the quantification of the time lag associated with the buck converter in the wind energy

conversion system.


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Contents Declaration ________________________________________________________________________________ i

Acknowledgements __________________________________________________________________________ ii

List of Figures ______________________________________________________________________________ vi

List of Tables ______________________________________________________________________________ ix

Nomenclature ______________________________________________________________________________ x

Wind Energy Conversion System (WECS) ______________________________________________________ x

Solar Array ______________________________________________________________________________xiv

DC Battery Bank _________________________________________________________________________xvi

Complete Microgrid _____________________________________________________________________ xvii

1 Executive Summary _____________________________________________________________________ 1

2 Introduction ___________________________________________________________________________ 2

3 Wind Energy Conversion System ___________________________________________________________ 7

3.1 Wind Turbine ______________________________________________________________________ 7

3.2 Operational Parameters _____________________________________________________________ 8

3.3 Operation _________________________________________________________________________ 9

3.4 Power Regulation _________________________________________________________________ 11

3.5 Permanent Magnet Synchronous Generator ____________________________________________ 13

3.5.1 Choice of Electrical Generator ___________________________________________________ 13

3.5.2 Physical Construction __________________________________________________________ 15

3.6 Six Pulse Diode Rectifier and DC/DC Buck Converter _____________________________________ 24

3.6.1 Six -Pulse Rectifier ____________________________________________________________ 24

3.6.2 DC/DC Buck Converter _________________________________________________________ 25

3.7 Full Set of Modelling Equations ______________________________________________________ 27

3.8 Simulation of WECS ________________________________________________________________ 28

3.8.1 Open Loop Non Linear Model of WECS ____________________________________________ 28

3.8.2 Potential System Operating Points _______________________________________________ 29

3.8.3 Analysis of Operating Point Characteristics _________________________________________ 33

3.8.4 Linearization _________________________________________________________________ 36

3.8.5 Comparison of Linear & Non-Linear Model _________________________________________ 37

3.8.6 Nyquist Stability & Inversion of Linear Process ______________________________________ 39

3.8.7 Current Controller Design ______________________________________________________ 41

3.8.8 Maximum Power Point Tracking Controller ________________________________________ 49

4 Solar Array ___________________________________________________________________________ 52

4.1 Physical Construction ______________________________________________________________ 52

4.2 Operational Procedure _____________________________________________________________ 53

4.3 Full Set of Modelling Equations ______________________________________________________ 54


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4.4 Parameterization __________________________________________________________________ 55

4.5 Implementation of Newton-Raphson Algorithm _________________________________________ 56

4.6 Solar Panel Performance ____________________________________________________________ 57

4.6.1 Selection of Diode Ideality Factor ________________________________________________ 57

4.7 Solar Array Model _________________________________________________________________ 62

4.8 Maximum Power Point Tracking Controller _____________________________________________ 65

4.8.1 Perturb & Observe (P&O) _______________________________________________________ 65

4.8.2 Incremental Conductance Algorithm ______________________________________________ 67

5 Battery Model_________________________________________________________________________ 73

5.1 Introduction ______________________________________________________________________ 73

5.2 Battery Cell Model _________________________________________________________________ 74

5.3 Layout of Battery Bank _____________________________________________________________ 77

5.4 Operation of the Battery Bank _______________________________________________________ 80

6 Complete Microgrid ____________________________________________________________________ 81

6.1 Compilation of Models _____________________________________________________________ 81

6.2 Modelling of Loads ________________________________________________________________ 82

6.2.1 Critical and Non-Critical Loads ___________________________________________________ 82

6.3 Grid Imports/Exports ______________________________________________________________ 83

6.4 Supervisor Control _________________________________________________________________ 84

6.5 Scenario Analysis __________________________________________________________________ 86

6.5.1 Introduction to Scenarios _______________________________________________________ 86

6.5.2 Scenario 1 ___________________________________________________________________ 86

6.5.3 Scenario 2 ___________________________________________________________________ 88

7 Potential Project Improvements __________________________________________________________ 91

8 Bibliography __________________________________________________________________________ 93

9 Appendices __________________________________________________________________________ 104

9.1 Appendix A: Derivation of Modelling Equations for WECS ________________________________ 104

9.1.1 Derivation of Available Wind Power [110] ________________________________________ 104

9.1.2 Derivation of Extractable Wind Power [111] _______________________________________ 105

9.1.3 Derivation of Clarke and Park Transformations ____________________________________ 108

9.1.4 Amplitude Invariance _________________________________________________________ 115

9.1.5 Derivation of Inverse Park Transformation ________________________________________ 116

9.1.6 Modelling the Permanent Magnet Synchronous Generator __________________________ 120

9.1.7 Derivation of Electromechanical Power Equation __________________________________ 125

9.1.8 Electromechanical Torque Equation _____________________________________________ 126

9.1.9 General Torque Expression ____________________________________________________ 127

9.1.10 Derivation of Rectifier Output Voltage and the Phase Voltage ________________________ 128


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9.1.11 Derivation of Current Injected onto DC Busbar ____________________________________ 129

9.2 Appendix B – Calculation of the Optimum Operating Conditions ___________________________ 132

9.3 Appendix C - Calculation of the Initial Conditions for WECS Model _________________________ 133

9.4 Appendix D – Linearization of WECS _________________________________________________ 134

9.5 Appendix E- Subsystems of the WECS ________________________________________________ 137

9.6 Appendix F- WECS Current Controller Test Configuration _________________________________ 139

9.7 Appendix G- Code for WECS Current Controller Design __________________________________ 140

9.8 Appendix H: Modelling of Solar Array ________________________________________________ 141

9.8.1 Shockley Diode Equation ______________________________________________________ 141

9.8.2 Current Flow within the Equivalent Circuit ________________________________________ 144

9.8.3 Series Resistance ____________________________________________________________ 146

9.9 Appendix I- Shell SP70 Solar Panel Datasheet __________________________________________ 147

9.10 Appendix J- Solar Array Subsystems __________________________________________________ 148

9.11 Appendix K – M-File Example for the Complete Microgrid ________________________________ 151

9.12 Appendix L – Indexes for Supervisory Switches _________________________________________ 154

9.13 Appendix M – Supervisor Control Blocks of Complete Microgrid ___________________________ 156


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List of Figures Figure 2-1: CO2 Levels in Earth's Atmosphere versus Time [6] ________________________________________ 2

Figure 2-2: Percentage Electricity Generation by Source (2010) [7] ____________________________________ 2

Figure 2-3: Schematic of a Community/Utility Microgrid [28] _________________________________________ 5

Figure 2-4: Schematic of Hybrid Microgrid System [34]______________________________________________ 6

Figure 3-1: Power Coefficient versus Tip Speed Ratio _______________________________________________ 8

Figure 3-2: Optimal Power Extraction Curve ______________________________________________________ 9

Figure 3-3: Power Extraction of a Variable Speed Fixed Pitch Wind Turbine [46]_________________________ 11

Figure 3-4: Difference between Control Using Passive Stall and Pitch Regulation [140] ___________________ 11

Figure 3-5: 3 Main Modes of Grid Connection for Modern Wind Turbines [49] __________________________ 13

Figure 3-6: Direct Drive PMSG Wind Turbine Generator [54] ________________________________________ 14

Figure 3-7: Cylindrical Rotor Design for High Speed Applications [67] _________________________________ 15

Figure 3-8: Sinusoidally Distributed Phase Windings on a Synchronous Machine [66] ____________________ 16

Figure 3-9: Typical Lamination of PMSG Stator [67] _______________________________________________ 16

Figure 3-10: Positioning of Direct and Quadrature Axes in a Four Pole Machine _________________________ 17

Figure 3-11: Equivalent Stator Winding Circuits [74] _______________________________________________ 19

Figure 3-12: Magnetically Salient Rotor Design (Ld>Lq) ____________________________________________ 22

Figure 3-13: Magnetic Saliency Characteristics of SPM & IPM [81] ___________________________________ 23

Figure 3-14: Circuit Configuration of Six Pulse Diode Rectifier & DC/DC Converter _______________________ 24

Figure 3-15: Balanced 3 Phase Line-to-Line Voltage Input to Rectifier _________________________________ 24

Figure 3-16: Output Voltage of Six-Pulse Rectifier _________________________________________________ 25

Figure 3-17: Simulink Diagram of the Open Loop Non Linear WECS ___________________________________ 28

Figure 3-18: Design Parameters for WECS _______________________________________________________ 29

Figure 3-19: Operating Values ________________________________________________________________ 29

Figure 3-20: Two Alternate Operating Points _____________________________________________________ 29

Figure 3-21: Power Output at Operating Point Corresponding to Id=3.666A,u=6.46 ______________________ 30

Figure 3-22: Power Output at Operating Point Corresponding to Id=77.095A,u=0.4562 ___________________ 30

Figure 3-23: Response to a Step in u of 0.5 at 300 seconds - Operating Point: (Id=3.666A,u=6.46) __________ 31

Figure 3-24: Response to a Step in u of 0.5 at 300 seconds - Operating Point: (Id=77.095A,u=0.4562) _______ 32

Figure 3-25: Variation of Electrical Frequency Operating Point with Desired Power ______________________ 33

Figure 3-26: Variation of Velocity Operating Point with Desired Power ________________________________ 33

Figure 3-27: Variation of Iq Operating Point with Desired Power _____________________________________ 34

Figure 3-28: Variation of u Operating Point with Desired Power (Root 2) ______________________________ 34

Figure 3-29: Variation of Id Operating Point with Desired Power (Root 2) ______________________________ 35

Figure 3-30: Variation of u Operating Point with Desired Power (Root 1) ______________________________ 35

Figure 3-31: Variation of Id Operating Point with Desired Power (Root 1) ______________________________ 35

Figure 3-32: Bode Magnitude and Phase Plots for WECS Linear Model ________________________________ 36

Figure 3-33: Response of Linear and Non-Linear Systems to a Train of Steps ___________________________ 37

Figure 3-34: Simulink Diagram of Test Configuration ______________________________________________ 38

Figure 3-35: Close Up View of Transient Step Response (Linear & Non-Linear) __________________________ 38

Figure 3-36: Initial Nyquist Plot for Inverted Linear Model __________________________________________ 39

Figure 3-37: Nyquist Plot of Inverted Linear Model Incorporating Time Lag ____________________________ 39

Figure 3-38: Nyquist Plot Corresponding to Marginal Stability _______________________________________ 40

Figure 3-39: Marginally Stable Response Achieved ________________________________________________ 40

Figure 3-40: Zeigler Nichols Tuning Parameters [85] _______________________________________________ 41

Figure 3-41: Step Response of Linear & Non-Linear System Using Zeigler Nichols PI Controller _____________ 41

Figure 3-42: Bode Magnitude & Phase Plots of Inverted Linear System incorporating Time Lag ____________ 43

Figure 3-43: Bode Magnitude & Phase Plots of Inverted Linear System ________________________________ 43

Figure 3-44: Step Responses Using PI Controller (Desired Phase Margin 30 Degrees) _____________________ 45

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Figure 3-49: Step Responses Using Tweaked PI Controller __________________________________________ 47

Figure 3-50: Quadrature Current of Non-Linear Model Diverging from Setpoint as Machine Speed Drops ____ 47

Figure 3-51: Turbine Torque and Electrical Frequency for a Current Setpoint of 20A _____________________ 48

Figure 3-52: Complete Wind Energy Conversion System ____________________________________________ 49

Figure 3-53: Optimal Turbine Rotor Power & Actual Turbine Rotor Output _____________________________ 50

Figure 3-54: Wind Speed & Mechanical Speed ____________________________________________________ 50

Figure 3-55: Tip Speed Ratio & Quadrature Current versus Time _____________________________________ 51

Figure 3-56: Actual and Optimal Electrical Power to DC Busbar ______________________________________ 51

Figure 4-1: Physical Construction of a PV Cell [87] _________________________________________________ 52

Figure 4-2: Principle of Operation of a PV Cell [89] ________________________________________________ 53

Figure 4-3: Solution of the Implicit Current Equation via Using the Newton Raphson Method ______________ 56

Figure 4-4: Solar Cell Model __________________________________________________________________ 57

Figure 4-5: Power- Voltage Characteristic of Solar Panel ___________________________________________ 58

Figure 4-6: Maximum Power point (1000W/m2) __________________________________________________ 58

Figure 4-7: I-V Curve of Solar Panel for Different Levels of Irradiance _________________________________ 59

Figure 4-8: Shell SP70 I-V Curves for Different Levels of Irradiance (From Datasheet) [94] _________________ 60

Figure 4-9: P-V Curves for Shell SP70 Solar Panel For Different Levels of Irradiance ______________________ 60

Figure 4-10: Increase in Device Temperature Results in Increased Short Circuit Current ___________________ 61

Figure 4-11: Scaled Voltage Output Achieved by Adding Multiple Panels in Series _______________________ 62

Figure 4-12: Scaled Current Output Achieved by Adding Multiple Panels in Parallel ______________________ 62

Figure 4-13: Solar Array Arrangement Consisting of 5 Rows of 6 Panels _______________________________ 63

Figure 4-14: Power Curves of Complete Solar Array For Different Levels of Irradiance ____________________ 64

Figure 4-15: P&O Control Logic [96] ____________________________________________________________ 65

Figure 4-16: Incremental Conductance Algorithm Control Logic [95] __________________________________ 67

Figure 4-17: Rate of Change of Voltage with Respect to Voltage For a Typical Solar Array [98] _____________ 68

Figure 4-18: Control Logic of Incremental Conductance Controller ____________________________________ 69

Figure 4-19: Implementation of Incremental Conductance Controller _________________________________ 70

Figure 4-20: Second Branch Subsystem _________________________________________________________ 70

Figure 4-21: Performance Achieved Using Incremental Conductance Algorithm _________________________ 71

Figure 4-22: Convergence of Operating Point to Maximum Power Point _______________________________ 72

Figure 5-1: Battery Cell Equivalent Circuit _______________________________________________________ 75

Figure 5-2: Battery Cell Model ________________________________________________________________ 76

Figure 5-3: VOC Variation with SOC _____________________________________________________________ 77

Figure 5-4: Battery Bank Configuration _________________________________________________________ 78

Figure 5-5: Battery Bank Complete Discharge at 4.8kW ____________________________________________ 79

Figure 6-1: Complete Microgrid Model on Simulink ________________________________________________ 81

Figure 6-2: Example of Multi-port Switch in Simulink ______________________________________________ 85

Figure 6-3: Scenario 1 – Power Flows ___________________________________________________________ 87

Figure 6-4: Scenario 1 - SOC Variation __________________________________________________________ 87

Figure 6-5: Scenario 2 - Power Flows ___________________________________________________________ 89

Figure 6-6: Scenario 2 - SOC Variation __________________________________________________________ 89

Figure 9-1: Cylindrical Volume of Wind ________________________________________________________ 104

Figure 9-2: Control Volume for Derivation of Extractable Wind Power ________________________________ 105

Figure 9-3: Positive Sequence Network ________________________________________________________ 108

Figure 9-4: Negative Sequence Network _______________________________________________________ 108















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Figure 9-5: Orientation of Alpha and Beta Axes with Respect to abc Axes _____________________________ 109

Figure 9-6: Projection of abc Phase Components for Clarke Transformation ___________________________ 110

Figure 9-7: Orientation of d and q Axes ________________________________________________________ 111

Figure 9-8: Development of Park Transformation ________________________________________________ 112

Figure 9-9: Alternative Reference Frame Used in [116] ____________________________________________ 114

Figure 9-10: Choices of Scaling Factor and Resulting Transformation Properties [117] ___________________ 115

Figure 9-11: Amplitude Invariant Park Transformation for 3 Phase Balanced Sine Waves ________________ 115

Figure 9-12: Amplitude Invariant Park Transformation for 3 Phase Exponentially Damped Sine Waves _____ 115

Figure 9-13: Equivilent Stator Circuit of a Synchronous Generator [76] _______________________________ 120

Figure 9-14: Direct Axis and Quadrature Axis Circuits for PMSG _____________________________________ 124

Figure 9-15: Per-Phase Equivalent Circuit and Phasor Diagram for PMSG [18] _________________________ 129

Figure 9-16: Scaling Procedure Required for Derivation ___________________________________________ 130

Figure 9-17: Inside the "Find Tt" Subsystem _____________________________________________________ 137

Figure 9-18: Inside the "Find Cp" Subsystem ____________________________________________________ 137

Figure 9-19: Inside the "Find ωe" Subsystem ____________________________________________________ 137

Figure 9-20: Inside the "Find ωm and tipspeed" Subsystem ________________________________________ 137

Figure 9-21: Inside the "Find Iq" Subsystem _____________________________________________________ 138

Figure 9-22: Inside the "Find Id" Subsystem _____________________________________________________ 138

Figure 9-23: Inside the "Find K" Subsystem _____________________________________________________ 138

Figure 9-24: Inside the "Find Iw" Subsystem ____________________________________________________ 138

Figure 9-25: Linear and Non-Linear System under Zeigler Nichols PI Controller _________________________ 139

Figure 9-26: Concentration of Holes and Electrons within a Solar Cell [123] ___________________________ 141

Figure 9-27: Ideal Solar Cell Model ____________________________________________________________ 142

Figure 9-28: Equivalent Circuit of Solar Cell Analysed (Single Diode & Series Resistance Only) [127] ________ 143

Figure 9-29: Shell SP70 Datasheet [93] ________________________________________________________ 147

Figure 9-31: Inside the "Ioact" Subsystem ______________________________________________________ 148

Figure 9-30: Inside the "Iphact" Subsystem _____________________________________________________ 148

Figure 9-32: Inside the "Rseries (Fixed Based on Reference Values)" Subsystem ________________________ 148

Figure 9-33: Inside the "f(x)" Subsystem ________________________________________________________ 149

Figure 9-34: Inside the "f(x)’" Subsystem _______________________________________________________ 149

Figure 9-35: Inside the "6 Panels in Series" Subsystems ___________________________________________ 150

Figure 9-36: Inside the "First Branch" Subsystem ________________________________________________ 150

Figure 9-37: Inside the "Second Branch" Subsystem ______________________________________________ 150

Figure 9-38: Display of Top and Bottom Supervisor Blocks in the Microgrid Model ______________________ 156

Figure 9-39: Top Supervisor Block _____________________________________________________________ 157

Figure 9-40: Bottom Supervisor Block__________________________________________________________ 157

























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List of Tables Table 3-1: Tuning Parameters for PI Controllers (Various Levels of Damping) ___________________________ 44

Table 4-1: Maximum Power Point Tracking- Results _______________________________________________ 72

Table 5-1: Battery Cell Parameters _____________________________________________________________ 74

Table 6-1: Supervisory Control - Price Levels _____________________________________________________ 84

Table 6-2: Index Example for Supervisor Control __________________________________________________ 85

Table 6-3: Scenario 1 Initial Conditions _________________________________________________________ 87

Table 6-4: Changes made throughout Scenario 1 _________________________________________________ 87

Table 6-5: Scenario 2 Initial Conditions _________________________________________________________ 88

Table 6-6: Changes made throughout Scenario 2 _________________________________________________ 88

Table 9-1; Indexing for PL > PWS _______________________________________________________________ 154

Table 9-2: Indexing for PWS > PL _______________________________________________________________ 155


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Nomenclature

Wind Energy Conversion System (WECS)


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Solar Array

(

=


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DC Battery Bank


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Complete Microgrid


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1 Executive Summary The goal of this project was to complete the modelling of a grid-connected DC microgrid consisting

of generation sources, an energy storage device and loads. The generating sources modelled include

a Wind Energy Conversion System (WECS) and a solar array. Energy storage is being provided in the

form of a 9.6kWh battery bank.

The WECS consists of a small 5kW variable speed wind turbine and a Permanent Magnet

Synchronous Generator (PMSG) which provides alternating current to a downstream uncontrolled

rectifier. The rectifier is connected to a DC/DC buck converter through a DC link capacitor. The

power generated in the wind turbine flows through these components and onto a DC busbar, the

voltage of which is maintained at a constant value determined by the DC battery bank. In order to

achieve Maximum Power Point Tracking (MPPT), an inner loop PI current controller and an outer

loop speed controller were designed for the system. Control is achieved through varying the duty

cycle in the DC/DC converter in order to vary the voltage on the terminals of the generator.

The solar array which was modelled consists of five rows of six multi-crystalline panels resulting in a

rated power output of 2.1kW. Similarly to the WECS, MPPT is realised by varying the duty cycle of

the downstream DC/DC converter. In order to achieve this performance, a control scheme known as

the “Incremental Conductance Algorithm” is implemented. Unlike the WECS, there is no

requirement for a rectifier as the power being generated is inherently DC.

A key element for the microgrid was the modelling of the DC battery bank. This storage element

helps to minimise the intermittency characteristics of the renewables sources, which improves the

prospects for further integration of these “green” technologies. The presence of such a storage

element is imperative to the operation of the microgrid as it enhances the security of power supply

to local consumers. A lithium ion battery cell was modelled in Simulink and subsequently a battery

bank consisting of five parallel branches, each containing fifteen cells in series, was designed.

Each of the models above was culminated to form a complete microgrid in Simulink. The concepts of

loads and grid-connection were introduced to the model in a very simplistic manner. Loads were

subdivided into critical and non-critical loads. The microgrid has the ability to import/export power

from/to the grid when required. Price levels were used in the simulations to make the scenarios

more dynamic. A supervisory control was created to make the decisions on the power flows in the

microgrid and ensure supply to the loads, based on information provided such as the State of Charge

(SOC) of the battery, prices of importing power etc. The decisions are made in the interest of

reliability of supply to the consumers, maximising the use of the renewables and the minimising the

operating costs. The final section in the report tests the complete model in order to illustrate how

the microgrid operates under different conditions.


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2 Introduction

“There is strong evidence that the warming of the Earth over the last half-century has been caused

largely by human activity, such as the burning of fossil fuels and changes in land use, including

agriculture and deforestation.” [1] – The Royal Society 2010

“It has been demonstrated beyond reasonable doubt that the climate is changing due to man-made

greenhouse gases. “ [2] – Met Office Hadley Centre 2007.

One of the major challenges confronting our generation is our over-reliance on fossil fuels. This

dependence stems from advances in generating technologies, which occurred throughout the

nineteenth and twentieth centuries. This facilitated the exploitation of the high level of energy

density available from these fossil fuels, which is one of the key reasons for their popularity. [3]

Aside from this, the relatively low cost, widespread availability and resulting consumer convenience

have also contributed to their dominance within the energy market. [4] As shown in Figure 2-1, it is

clear that corresponding to this surge in fossil fuel usage, there has been colossal increase in the

level of CO2 measured within the earth's atmosphere. Resulting from this quandary are several other

pressing predicaments such as rising sea levels, melting ice sheets, rising global temperature and

glacial retreat, which together can be defined as climate change. [5] , [6] Evidently, these issues are a

danger for humankind and nature alike, and hence must be counteracted.

Figure 2-1: CO2 Levels in Earth's Atmosphere versus Time [6]

Figure 2-2: Percentage Electricity Generation by Source (2010) [7]


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Despite this global realisation which is occurring, worldwide electricity generation is still dominated

by fossil fuels. As shown in Figure 2-2, a sizeable portion (67.4%) of electricity generation was

accounted for by fossil fuels in 2010. [7] Consequently, the power system currently being used

consists of large conventional generating plants (coal, gas turbine etc.) which generate electrical

energy via steam/gas turbine coupled to an electrical generator. [8] These conversion processes are

quite inefficient: a conventional coal plant having an upper limit Carnot Efficiency of 63.6%. [3]

Voltage produced by these machines is stepped up to a high level for transmission (up to 400kV [9]),

which typically occurs over long distances to the end-user. [8] Due to the exponential trend that is

evident relating to global energy consumption [9], it is clear that if the current means of electrical

transmission and distribution are maintained, that a vast expansion of global electrical power grids is

inevitable. [10]

Expansion of the present power system however presents some challenges. For instance, the

extension of a power grid inherently implies an increased necessity for long-distance transmission.

Hence, this entails the need for installation of more High Voltage Direct Current (HVDC) lines which

diminish transmission losses over long distances by 30-50% compared to AC transmission. [10] This

may appear to be an adequate solution; however the high expense which is associated with

installing rectifiers and inverters at either end of the line is an issue. [11] Coupled with this is the

predicament of power system blackouts which can occur in large power systems. Large, centralized

power systems can be prone to suffering from severe power outages such as that which occurred on

August 14, 2003 in the United States which left 50 million customers without electricity. [4]

Therefore, apart from the large issue of Green House Gas (GHG) emissions associated with

conventional fossil fuels, attempting to meet a constantly rising energy demand could potentially

prove problematic within such a large interconnected system. As well as this, it is important to note

that by definition fossil fuels are non-renewable and will deplete over time. This fact coupled with

increasing energy demand will inevitably result in increasing fossil fuel prices over time, as by using

common sense one could conclude that if supply drops then price will increase. This can already be

seen by the increasing trend in coal and gas over the last 20 years. [12]

"Renewable energy technologies provide many benefits that go well beyond energy alone. More and

more, renewable energies are contributing to the three pillars of sustainable development – the

economy, the environment and social well-being – not only in IEA countries, but globally." [13]-

International Energy Agency 2002

Hence, one might conclude that a better alternative to using fossil fuels as an energy source would

be to integrate more renewable energy sources (wind, solar etc.) onto the power grid. The

advantages of using renewable energy are numerous. For instance, aside from having a great

potential for counteracting global climate change, utilising sources of energy such as wind, solar,

tidal and wave also helps to reduce negative health problems associated with high levels of carbon

in the atmosphere. Other benefits consist of increasing the security of energy supply and enhancing

economic development. [14] The downside to utilising Renewable Energy Sources (RES), is that due

to their intermittent nature, a constant power output is difficult to obtain, which is an issue for

practical usage within the power grid. [15] The difficulty caused by this power fluctuation can be

reduced by using programmable support systems in tandem with controlled microgrids. [16] The

aforementioned dilemma of power variability is mitigated by integrating an energy storage device

into the system such as a DC battery bank. [15], [17] The use of such energy storage devices allows


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for continuous power to be supplied to loads, despite the variable nature of the source. [18] Another

method of dealing with this changeability in power output is to install a dump load within the system

in order to dissipate unwanted intermittent power. [19] Compared to other means of coping with

this problem, this is undesirable due to the fact that power being generated is effectively being

intentionally wasted. In comparison to using a dump load, a more economical solution would be to

utilise a fuel cell coupled with an aqua electrolyzer. In such a system, hydrogen is produced using the

unwanted power. The hydrogen can then be stored and subsequently used to power a fuel cell. [19]

Due to these technologies, and the ease with which they facilitate the effective implementation of

RES, microgrids are becoming a more attractive option within future power systems.

"Microgrids are systems that have at least one distributed energy resource and associated loads and

can form intentional islands in the electrical distribution system" [20]

Energy sources located close to the position of the load are termed Distributed Energy Resources

(DER) and can be separated into Distributed Generation (DG) and Distributed Storage (DS). [20] A DG

unit is the boundary between the microgrid and an energy source, which generates electrical power

which is subsequently delivered to the microgrid. [21] A practical example of a DG unit is a

Permanent Magnet Synchronous Generator (PMSG) connected to a Variable Speed Wind Turbine

(VS-FP). DS components on the other hand assist in achieving the power requirements of the system

loads. Throughout fluctuations in both the source and load, the DS system allows DG units to

operate at constant output. Hence, a prime example of a DS unit is a D.C. battery bank/ fuel cell as

mentioned previously, although flywheels and super-capacitors can equally play this role on such a

system. [20] This combination of DG and DS units coupled with loads represents a microgrid.

The advantages of microgrid systems are numerous when contrasted with the characteristics of

conventional power grids. The most beneficial characteristic of a microgrid is the higher level of

power quality which is achieved within the system, which is important for sensitive loads such as

digital computers, digital clocks and programmable logic controllers. [22], [23] Aside from this,

microgrids have lower associated feeder losses [24] and because of the lower transmission distance

between energy sources and loads, electrical losses are reduced. By downsizing the system,

transmission and distribution bottlenecks are eliminated. [25] Another major advantage however is

the improved reliability which the system yields. A microgrid consists of numerous small generating

sources- hence, in the event of losing a generator; the impact on the system is minimized. [26]

Reliability is also improved on a local scale, provided that the system can operate in islanded mode.

[27]

The ability to operate in both grid-connected and autonomous (islanded) mode not only improves

reliability of local power supply, but also improves efficiency of operation. [22] There is a diverse

array of applications for microgrid technology ranging from off-grid and island microgrids which have

no connection to the utility grid, to utility microgrids which are constantly connected to the main

grid. Institutional/campus and industrial microgrids can also be designed, which operate in islanded

mode continuously, but are connected to the utility grid for back up purposes. [28] Figure 2-3 shows

a typical configuration for a utility microgrid. As shown, such a system is connected to the main grid

via a Point of Common Coupling (PCC), which consists of an “interconnection switch”, which is

governed by international standards IEEE 1547 and UL 1741. [20] In the case of a fault on the main

grid or a drop in power quality, the purpose of the interconnection or “static” switch is to island the


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microgrid from the utility grid. [25] In order to recognise unsatisfactory conditions within the main

grid, it is necessary to install a Voltage Monitoring Module (VMM). When connected to the main

grid, the burden of balancing power generation and demand from loads is greatly alleviated [16].

However prior to reconnecting to the main grid, it is imperative to adjust the properties of the

voltage, frequency and phase to match that of the main grid. This process is termed synchronization.

[20] Once synchronized, it is typically necessary to maintain these characteristics for a short period

before connecting back to the utility grid. [16]

As stated, alternatives to utility microgrids are island or off-grid microgrids. An off-grid system is for

use in remote areas which cannot be readily connected to the utility grid as in some cases, this may

not exist (i.e. within developing countries). [28] The installation of conventional power plants is

therefore not practical in such regions of the world [29], due to lack of required resources. The range

of applications of these off-grid systems is numerous. In fact it is estimated that 40% of the world’s

population live in remote areas without a connection to the utility grid [30] The high potential that

these third world countries have for DG sources such as wind and solar energy, present a logical path

to the conclusion that the implementation of off-grid microgrids are the solution to the energy

issues plaguing these regions of the world. [31] Similarly, island microgrid systems operate

unconnected to the utility grid and as their name suggests facilitate supply of power on isolated

islands. These systems have a high potential for implementation in Japan which has the largest

amount of isolated island specific power systems in the world. [32]

However it is important to recognise the distinction between AC and DC microgrids. Clearly the

implementation of an AC system has advantages in terms of connection to the utility grid, as there is

no requirement for inverter which is the case when coupling a DC bus based system to the main grid.

[33]Figure 2-4 shows a hybrid system illustrating the means of grid connection for AC and DC buses.

[34] However there are certain issues which make implementation of AC systems challenging such as

harmonics, 3 phase unbalance and the presence of reactive power in the system. [35] As well as this,

due to the low bus voltage in a DC system, the risk of electric shock is reduced, making the concept

of plug-and-play operation more feasible. [36] This phenomenon allows loads, DS or DG units to be

connected/ disconnected at will from the system with ease [37] The ISO-95 standard defines the

laws for implementation of control systems in such microgrid systems. [35]

Figure 2-3: Schematic of a Community/Utility Microgrid [28]


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The microgrid in question within this report is a grid connected system with the capability to buy and

sell electrical energy from the main grid, during times of insufficient or excess generation. The

system contains a Wind Energy Conversion System (WECS) made up of a variable speed wind turbine

connected to a Permanent Magnet Synchronous Generator (PMSG), rectifier and buck converter,

which together facilitate power flow onto the system’s DC bus which is home to a battery bank (DS).

The voltage at the DC bus is dictated by the voltage of the battery bank, and the level of power flow

between the wind turbine and the bus can be altered by varying the duty cycle of the intermediary

buck converter. [18] In addition to the WECS, the microgrid to be analysed also incorporates a solar

array which due to the nature of wind and solar resources act in a complementary manor. [30] The

end goal of the project is to control the DG and DS in unison so that the microgrid load can be met

during normal operation, energy can be sold/bought between the microgrid and the utility, and in

times of high electricity prices and low generation certain noncritical loads can be shed.

Figure 2-4: Schematic of Hybrid Microgrid System [34]


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3 Wind Energy Conversion System

3.1 Wind Turbine As mentioned in the introduction, the microgrid being analysed in this report incorporates a wind

turbine which converts the kinetic energy of the wind into rotary mechanical energy, and is

connected to a PMSG which subsequently converts this rotational energy to electrical energy. This

section will illustrate the design, choice of operational parameters, power extraction process, and

the derivation of modelling equations for the wind turbine. The wind turbine being analysed within

this project is a Small Wind Turbine (SWT), meaning that it has a rated power of equal to or less than

less than 100kW. [38] Dissimilar to large wind turbines, the most common blade design for a SWT is

a fixed pitch configuration [39] (angle is a constant value between 0o and 10o [40]). Such machines

are low in cost and simple in structure compared to larger commercial machines, and hence are

suitable for small scale implementation such as within a microgrid, which is the focus of this report.

[41] The variable speed nature of the wind turbine allows grid connection via a PMSG which is a

gearless “direct drive” system [42]. Typically, upon installing the blades onto the rotor of a fixed

pitch machine, the desired pitch is selected and once the blades have been attached, it is a fixed

value. [39] An advantage of a fixed pitch system over a variable pitch configuration is that the rotor

of such a system generally requires less maintenance compared to an equivalently rated variable

pitch machine [43]. Other benefits include cheaper operational and construction costs, assuming

that the turbine is situated in a suitable location. [40] Key characteristics of the Variable Speed-Fixed

Pitch design are that maximum efficiency (i.e. power coefficient) is attainable at low wind speeds,

and that rated power is only attainable at one wind speed. [44]


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3.2 Operational Parameters The wind turbine analysed in this report is based on that used by Valenciaga and Puleson in [30]. The

turbine has a VS-FP design and the rotor of the machine has 3 blades. The power coefficient of the

machine, expressed as a function of the tip speed ratio is as shown below:

*where , , and other machine parameters are defined in Figure 3-19: Operating Values in Section 3.8.2 of the

report

A plot of the power coefficient of the machine versus tip speed ratio is shown below, which clearly

identifies the optimal tip speed ratio as 7.198 and the maximum attainable power coefficient as

38.13% (0.3813), which as predicted is lower than the Betz Limit.

Figure 3-1: Power Coefficient versus Tip Speed Ratio

This optimum operating point has also been found via differentiation with respect to tip speed ratio,

as shown in Section 9.2.

N.B. It is important to realise that this curve defines the operational characteristics of the wind

turbine and is valid for any wind speed/rotor speed combination. Subsequent plots in sections to

come are done against angular velocity of the rotor, for various wind speeds, and hence are only

valid for one position of the operating point.


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3.3 Operation A typical value for the cut-in wind speed associated with an SWT is 2m/s. [45] Hence, below this

value of wind speed, the wind turbine will generate no electrical output. The machine is to operate

under Maximum Power Point Tracking (MPPT). This operational procedure entails the retention of

optimal performance (maximum power coefficient) beneath the rated rotational speed of the

machine (49.39 rad/s) in the case of a varying wind speed. In order to achieve this, it is necessary to

maintain the tip speed ratio at its optimum value (7.198). To understand how this works on a

physical basis, it is imperative to realise that for a fixed pitch rotor rotating at a constant speed, an

increase or decrease in incident wind speed will result in a variation in the angle of attack between

the wind and the blade aerofoil. In order to maintain a desired performance, it is necessary to vary

the speed of rotation of the wind turbine proportionally to the variation in oncoming wind, hence

maintaining this ratio as a constant value. [39] Hence, as MPPT is only possible below rated wind

speed for a fixed pitch machine, it is intended that the wind turbine will only generate power above

the cut-in wind speed and below the rated value of wind speed (12.629m/s). It is thought that this is

a suitable assumption due to the small scale nature of the turbine, and the intended application

within a microgrid.

The locus of ideal performance of a wind turbine utilising MPPT control is shown in black in Figure

3-2: Optimal Power Extraction Curve. It is important to realise that at each of the wind speeds

shown, the tip speed ratio has a constant value of (approximately) 7.198. (Slight deviations from this

value are a result of rounding errors in the calculation of this value in the previous section).

For instance at a wind speed of 7.5m/s:

and at 10m/s:

Figure 3-2: Optimal Power Extraction Curve


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The black curve shown in the diagram is the ideal locus of the machine operating point below rated

wind speed. Note that as the speed of the wind increases so does that of the turbine rotor and that

rated power (5kW) is achieved at rated speed of the machine. This curve will be used as a reference

later in a report in order to verify the performance of the model.


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3.4 Power Regulation The power curve achieved by a VS-FP turbine in reality is as shown in Figure 3-3: Power Extraction of

a Variable Speed Fixed Pitch Wind Turbine :

Figure 3-3: Power Extraction of a Variable Speed Fixed Pitch Wind Turbine [46]

The dark black line shows the power output of a VS-FP machine over a range of wind speeds. Clearly,

below cut-off wind speed ( , no power is generated. For wind speeds between those

corresponding to the points A and E in the above diagram, MPPT is used to maintain maximum

power extraction. In the diagram, rotor speed is constant at wind speeds above that at point E.

Hence, maximum power extraction is not actually achieved although power output still increases

(with the cube of wind velocity) until point D is reached, and rated power is achieved. The grey line

shown in the diagram is the power curve of a VS-VP wind turbine. This type of machine is capable of

tracking the maximum power point below rated power and maintaining this rated output at higher

speeds by controlling the pitch of the blades (i.e. varying pitch in proportion to wind speed changes).

It is important to note that the method of MPPT control used for the VS-FP machine in this project is

equivalent to that of the VS-VP turbine in the above diagram. This is because the machine designed

will not stall prior to nominal wind speed being achieved. Hence, rated power will be achieved at

nominal wind speed as in the case of the VS-VP wind turbine shown above. As the machine is being

designed for usage in low wind speed areas, it is likely that rated wind speed will not be reached

very often. Hence the assumption that MPPT can be used up to rated speed, without the need for

stalling is a safe assumption. If rated wind speed is exceeded for the turbine being designed, passive

stall can be used to maintain constant rotor speed above this value of wind speed. In reality, the

power curve for such a machine would be equivalent to that of the passive stall machine in Figure

3-4: Difference

between Control Using

Passive Stall and Pitch

Regulation :


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Power output via

MPPT is utilised when wind speeds are lower than the nominal value. [47] As mentioned, this

technique effectively entails maintaining the tip speed ratio at the optimal value for power

generation, between the cut-in and nominal wind speed, by varying the speed of rotation of the

wind turbine rotor in direct proportion with the changing wind speed. In the event of high wind

speeds, a fixed-pitch turbine is not capable of perform power regulation via active pitch control.

Instead it is necessary to use passive stall to limit the power output. [40] [47]. It is important to note

that above the rated speed of the machine, the speed no longer increases with wind speed to

maintain a constant angle of attack. Once rated speed is reached, the speed of the rotor remains at a

constant level, despite increasing wind speed. [48]

Despite this fact, the wind turbine model designed by the students does not take this effect into

account as it is expected that the turbine will predominantly be operating at below rated speed

while operating as part of the microgrid.

Figure 3-4: Difference between Control Using Passive Stall and Pitch Regulation [140]


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3.5 Permanent Magnet Synchronous Generator

3.5.1 Choice of Electrical Generator

In order to achieve an electrical power output from a wind turbine, it is necessary to employ an

electrical generator to convert the rotational energy of the shaft into useable electrical energy.

There are multiple choices of generator possible for wind power applications; however this choice is

usually dictated by such things as the desired performance of the WECS. Figure 3-5: 3 Main Modes of

Grid Connection for Modern Wind Turbines shows the 3 main grid interconnection methods being

used in the world today: [49]

Part (a) of the Figure 3-5: 3 Main Modes of Grid Connection for Modern Wind Turbines shows the

connection of a wind turbine to an asynchronous Squirrel Cage Induction Generator (SCIG) via a

mechanical gearbox. These machines are attractive due to their durability and low cost and

maintenance requirements. [50] It is vital to realise that grid connection via a SCIG in this manner is

a fixed speed design as the speed of such a generator typically varies from the rated value by

approximately 1-2%. [51]. Within a fixed speed system such as this, the nature of the SCIG dictates

that the rotor of the turbine must have a fixed speed, as the generator effectively does. Hence, in

the case of a varying wind speed, it is the torque of the rotor which must vary- not the speed, as a

changing wind speed means a changing power output. [52] This method of interconnection to the

power system is classified as a direct grid connection as there is no need for a power electronic

converter connected to the generator [53].

Figure 3-5: 3 Main Modes of Grid Connection for Modern Wind Turbines [49]


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However when variable speed operation is desired (as in this project), it is classified as an indirect

grid connection (i.e. connection aided by power electronic rectifiers and inverters). [53] The diagram

in Part (b) of Figure 3-5: 3 Main Modes of Grid Connection for Modern Wind Turbines shows an

indirect grid connection via a Double-Fed Induction Generator (DFIG). The implementation of a

power electronic converter (taking power from the grid) on the rotor side of the machine allows for

the production of constant amplitude and frequency voltage and current on the stator side of the

machine. [52] Similar to the squirrel cage generator, the DFIG is also asynchronous and requires a

gearbox between the wind turbine shaft and the generator rotor. The DFIG is a popular choice for

use in large wind turbines, hence for the application illustrated in this report a DFIG would be

considered unsuitable due to the low power rating of the wind turbine being used. [50], [52]

Part (c) of Figure 3-5: 3 Main Modes of Grid Connection for Modern Wind Turbines gives an

illustration of the grid interconnection method followed in this project. A synchronous generator is

used to convert the mechanical energy of the wind turbine rotor to 3 phase electrical power,

without the need to install an intermediary gearbox. The physical construction of a PMSG for wind

energy applications should be a machine with projecting rotor poles having a large stator radius and

short stator length (as shown in Figure 3-6: Direct Drive PMSG Wind Turbine Generator ), which is

suited to low speed applications. Conversely, cylindrical pole machines with a short stator radius and

long stator length are suited to high speed applications (note the clear difference by comparing

Figure 3-6: Direct Drive PMSG Wind Turbine Generator and Figure 3-7). [55] As no gearbox is

needed, the system is an example of a direct drive connection. [56]

Within the arena of wind energy, Permanent Magnet (PM) machines are most commonly used for

low power applications, and hence are a suitable choice for use with a low power SWT (in particular

up to 10kW). [50] [57] Synchronous generators are of two basic designs: those which have a rotor

winding and obtain a rotor field via DC excitation of this winding, and those which obtain a rotor

magnetic field via permanent magnets. The former are dubbed Wound Rotor Synchronous Machines

(WRSM) and the latter are called Permanent Magnet Synchronous Machines (PMSM). When

compared to a WRSM, it is clear that the lack of rotor excitation means a higher associated efficiency

when using a PMSM. [58]

The main disadvantage of using permanent magnets within a generator is the high cost associated

with acquiring the magnetic material (e.g. neodymium iron/samarium cobalt). [50] However, the

main reason for the popularity of this design for low power applications is the reduction in the cost

Figure 3-6: Direct Drive PMSG Wind Turbine Generator [54]


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of the material that is coupled with a reduction in the size of the machine (and hence the magnets).

[59] It is evident that despite the high cost associated with the PMs, both the costs of these

magnetic materials and the power electronics needed for the downstream converter are decreasing

over time, and hence direct drive PMSG systems are likely to increase in popularity in the future.

[58] In comparison to geared systems, this direct drive configuration offers advantages in terms of

elimination of downtime due to gearbox maintenance. [60] Clearly, the lack of a gearbox also implies

a lack of any associated losses/inefficiencies. [61] Another issue to be aware when operating a

PMSM is that if the current (and hence the temperature) within the machine rises excessively high, it

is possible that the magnetic material used in the poles of the machine can become demagnetized.

[62] , [63]

3.5.2 Physical Construction

3.5.2.1 Stator Design

The synchronous generator is capable of producing 3 phase AC current and voltage in its stator

windings which oscillate with an angular frequency proportional to the rotational frequency of the

rotor of the generator (which in this case is direct driven via the rotor of the wind turbine). This

proportionality is dictated by the number of rotor poles : [64]

Hence, for a two pole machine, the electrical frequency of the output voltage and current will equal

that of rotor. Due to the constant relationship between a constructed synchronous machine, such

machines are classified as "constant speed machines" [55]. The relationship shown above is integral

to the understanding of the operation of such machines, however in order to completely understand

the operation a PMSG, it is fundamental to be aware of how the machine is constructed, both on the

stator and rotor side.

The stator configuration of a synchronous machine is exactly the same as that of an induction

machine. [65] The phase windings on the stator of such machines are said to be sinusoidally

distributed , which means that the conductor density of each of the phase windings is a sinusoidal

function as shown below [66], (where a change in sign indicates a change in current direction):

Figure 3-7: Cylindrical Rotor Design for High Speed Applications [67]


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This winding configuration is shown in Figure 3-8: Sinusoidally Distributed Phase Windings on a

Synchronous Machine , for the phase A winding of a machine. It is clear that the number of phase A

conductors wound on the stator peaks at angles of radians and radians, and is a minimum

(0), at 0 radians and radians, hence following a sinusoidal function. All of the conductors shown in

the diagram contribute to a magnetic flux acting along the phase A magnetic axis as shown in the

diagram- this is due to the fact the current flows in opposite directions above ( radians < <

radians) and below ( radians < < radians) the magnetic axis of the phase- this is denoted by

the dots and x's on the conductors shown- respectively implying current out of the machine, and

current into the machine. Therefore, based on the conductor density functions shown above for

phases B and C of the machine, it is logical to conclude that the magnetic axes of these phases are in

the direction of radians and radians respectively. [66]

As an additional point of interest, it is interesting to note the manner in which the phase current

flows through the respective stator winding. As shown above, the current enters the machine at 1,

and exits at 7'. The order in which the current flows through each of the windings shown in the

above diagram is as follows: 1-1'-2-2'-2-2'-3-3'-3-3'-3-3'-4-4'-4-4'-4-4'-4-4'-5-5'-5-5'-5-5'-6-6'-6-6'-7-

7'. [66] Note that in reality, the number of windings on the stator of such a machine is much higher

than the number shown in the diagram, and it is merely representative of the machine construction.

The stator of the machine is constructed from a stack of laminations, an example of which is shown

in Figure 3-9: Typical Lamination of PMSG Stator [67].The slots on the rotor side of the machine

serve the purpose of holding the stator windings. The goal of using stacked laminations is the

minimization of losses due to eddy currents in the material.

Figure 3-9: Typical Lamination of PMSG Stator [67]

Figure 3-8: Sinusoidally Distributed Phase Windings on a Synchronous Machine [66]


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It is important to realise that if the magnetic axis of the phase A winding is taken as an angular

reference, the magnetic field and flux resulting from current flowing in the stator windings are

cosinusoidal functions (with respective phase shifts of radians and radians in the case

of the B and C phases). This may have already been apparent as Figure 3-8: Sinusoidally Distributed

Phase Windings on a Synchronous Machine indicates that flux produced by the A phase peaks at 0

radians and is minimized at radians. In order to properly describe how the choice of rotor affects

the performance of the machine, it is first necessary to introduce notation, which is imperative to

understand if the machine is to be properly modelled and ultimately controlled.

3.5.2.2 DQ Theory

As stated the generator has three phase components of current, voltage etc. (i.e. phases , , ). It is

possible to represent these quantities in an alternative way. The Park Transformation can be used to

change from a three phase reference frame (composed of 3 axes , and ), to a two axis reference

frame (composed of axes and ). [68] The reference frame is fixed to the rotor of the machine,

and hence reference frame rotates at the same speed as the machine (electrical rotational speed).

This is dissimilar to the reference frame which is an intermediary step between transforming

between and variables, as the reference frame is considered to be fixed to the stator of

the machine and hence, does not rotate. [69] The reference frame consists of two axes- the

direct ( ) axis and the quadrature ( ) axis, which are also respectively known as the polar and

interpolar axes. [70] By definition, the direct axis lies along the axis of the rotor pole, [71] and the

quadrature axis lies in the direction which corresponds to an electrical angle orthogonal to that of

the direct axis. [72]. In order to explain this concept, it is essential to realise that by integration with

respect to time the following relationship between electrical and mechanical angular displacement

can be found:

Figure 3-10: Positioning of Direct and Quadrature Axes in a Four Pole Machine


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Hence, if the electrical angle between the two axes must be radians at all times, it is clear that

the mechanical angle between the two axes is dependent on the number of rotor poles. For

instance, if a 4 pole rotor is analysed, the mechanical angle between the axes must be radians.

This is demonstrated in Figure 3-10: Positioning of Direct and Quadrature Axes in a Four Pole

Machine. It is also interesting to note that in the case of a two pole rotor, the mechanical angle of

separation between the direct and quadrature axes equals - i.e. it equals the angle of electrical

separation, indicating that in this case, the respective direct and quadrature axes of the electrical

and mechanical system coincide. Note that the image shown in Figure 3-10: Positioning of Direct and

Quadrature Axes in a Four Pole Machine is that of a synchronous machine with rotor windings. The

purpose of this excitation is to produce a rotor magnetic field in the absence of permanent magnets.

Hence, the mode by which magnetic field is generated in this machine is fundamentally different to

the machine being used throughout this project, however for the purpose of demonstrating the

positioning of the direct and quadrature axes in a multi-pole machine, this diagram achieves its goal.

It seems logical to conclude that the quadrature axis is dubbed as the inter-polar axis, as in the

mechanical system, when the quadrature axis is fixed to the rotating multipolar rotor, it will always

point in a direction midway between adjacent rotor poles, as indicated by the diagram.

At this point, it is important to clarify that these axes which are "placed" on the rotating rotor of the

mechanical system are merely representative of the direct and quadrature axes of the electrical

system. Hence, for the purpose of the derivation of the Park Transformation which will be carried

out in a subsequent section, the angle between the direct and quadrature axes will be taken as

radians and the speed of rotation of the axes will be - as for the purposes of this derivation it is

the electrical system being considered. Therefore this transformation which is obtained is applicable

to synchronous machines with an arbitrary number of pole pairs (not just two pole machines- which

would be the case if the derivation of the Park Transformation was utilising the representative direct

and quadrature axes within the mechanical system).

It is important to note that in reality, when three phase ( ) variables are transformed to

notation, the system still effectively has 3 axes. For the purposes of balanced machine analysis,

the direct and quadrature axes are those of interest- however there is also another axis present

when analysing the system using notation. This axis is sometimes called the normal ( ) axis [73],

however quantities pertaining to this axis are more often given the subscript 0. The idea behind

dubbing it the normal axis, is that if the direct and quadrature axes are analysed so that they lie on

the same ( ) plane, the third axis is said point in a direction normal to this plane. [73] The variables

represented by this axis however, are only of interest in the case of unbalanced operation as they

represent the zero-sequence components of system variables (i.e. voltage/current), and hence have

a constant value of 0 in the case of balanced operation. Therefore, for the purpose of modelling the

generator, these components are not of interest. However in order to construct the 3 x 3 invertible

Park Transformation matrix, it is necessary to note that:

Defining as phase vectors and as the corresponding zero sequence component, these

two equations can be further generalized to: [68]


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This conversion from a 3 axis reference frame to an effective 2 axis reference frame (for balanced

operation), means that the way in which the operational procedure of the machine is perceived, can

be changed. As previously stated, the physical construction of the stator consists of 3 sinusoidally

distributed windings, which have three separate magnetic axes. After applying the Park

Transformation, the number of magnetic axes is reduced from 3 to 2. However, it is also apparent

that these magnetic axes are rotating in space, as the rotor of the machine rotates. This means that

the machine can now be analysed as if it had two rotating sinusoidally distributed windings, which

have separate magnetic axes parallel to the direct and quadrature axes respectively. The current

flowing in these imaginary windings is and respectively, and at any instant in time, together

these two rotating windings produce the same flux within the air gap as produced by the windings

fixed to the stator.

It is useful at this stage to acquire a representation for the stator equivalent circuit of the machine.

This can be done prior to analysing the effects of different rotor configurations, and will in fact aid

the process. Figure 3-11: Equivalent Stator Winding Circuits shows the equivalent stator circuits.

There are 3 circuits to represent the three stator phase windings. Each of these windings has an

equivalent ohmic resistance (synchronous resistance, [75]) which results in heating loss in the

winding. The respective back emfs generated due to changing magnetic flux linking the windings is

represented by the letter , with an appropriate subscript. Similarly the terminal voltages of each

Figure 3-11: Equivalent Stator Winding Circuits [74]


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winding are represented by the letter , with an appropriate subscript. The quantity is called the

synchronous reactance however, this term merits further analysis:

The equations which describe the operation of the generator are as follows [76]:

* where is the flux linkage, linking the nth winding.

It is vitally important to understand components that contribute to these flux linkage terms. To do

this, the students analysed [76] and [77]. For instance, the machine analysed by Krause in [76] has

rotor windings, as opposed to permanent magnets. Hence the analysis technique used here will

differ somewhat. Krause (pp215) states:

Where: [68]

At this juncture, it is important to note that the statement in purple effectively states that the flux

linkage across each of the phase windings has a component which is proportional to stator current

and one which is proportional to rotor current. As a permanent magnet machine is being used, there

is no rotor current and hence, the flux linkage due to the permanent magnets will be defined as:

Where:

Hence, it seems logical to conclude that:

- As this is effectively the same statement which was made by Krause above.

However, as defined by Krause:


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Where and are inductance parameters which quantify the extent to which the rotor of the

machine is non-cylindrical. The quantity is the leakage inductance of each of the stator windings.

[76] The direct and quadrature magnetising inductances are also defined as:

It is also evident that as: [76]

It must be true that:

And therefore:

It is important to note that the quantity is included within the above equations in order to

account for the usage of non-cylindrical rotors. For instance, in the case of a cylindrical rotor,

[76], and therefore the inductances associated with the rotating and windings are:

It is well known that if the rotor of a synchronous machine is cylindrical then: [78]

This is due to the constant air gap between the rotor and the stator of the machine. [79] In fact this

is the conclusion which Yamamura draws in [77]. Yamamura also states that the value of is equal

to the inductance of each stator phase winding ( ). Hence, now it is clear that for a synchronous

machine with a cylindrical rotor:

Hence the inductance matrix now becomes:


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3.5.2.3 Choice of Rotor

Despite what was shown in the previous section- the rotor being used within the generator of the

wind turbine is not cylindrical. As previously stated in the report, cylindrical rotors are usually used

for high speed applications. For low speed applications a salient-pole machine is usually preferable.

The term "salient" effectively means that the poles are projecting from the rotor and hence the air

gap between the stator and rotor is not uniform as is the case with a cylindrical rotor. [79] At this

point it is useful to analyse again the equation, used by Krause, in which the term was included to

account for a non-uniform air gap along the and axes. When , the airgap is uniform,

however it is clear that when , - and this is indicative of a salient pole machine. [80]

As previously stated, a salient pole machine has projecting poles- which will of course be located

along the direct axis of the machine. Hence, the air gap along the quadrature axis will be greater

than that along the direct axis. This means that the air gap reluctance will be higher along the

quadrature axis and as inductance is inversely proportional to reluctance, the inductance is logically

greater along the direct axis than along the quadrature axis in this case.

The rotor being used by the students however, has surface mounted permanent magnets on the

rotor which project from the surface of the rotor body. An example of such a configuration is shown

in Figure 3-12 in which SPM denote a Surface Mounted Permanent Magnet Machine and IPM

denotes an Internal Permanent Magnet Machine. [81] It is important to realise that despite the

projecting nature of the magnets, the rotor is considered to be magnetically non-salient. [81], [82]

This is effectively due to the fact that the permeability of the permanent magnets is very close to

that of air- hence the effective air gap is uniform around the machine. [81], [83] This trait means

that, from a magnetic perspective, the rotor can undergo the same analysis as the cylindrical

machine, and hence the expressions for quadrature, direct and synchronous inductance which have

been developed for a cylindrical rotor machine are valid in this case also. Hence:

Figure 3-12: Magnetically Salient Rotor Design (Ld>Lq)


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[83], [81], [75]

Also, as the SPM follows the same theory as the cylindrical rotor machine the inductance matrix can

be defined as:

This matrix is important for the modelling procedure of the PMSG, and is used in Section 9.1.

Figure 3-13 also shows a rotor structure using imbedded magnets. Without exploring this in excess

detail, it is interesting to note that the consequence of such a rotor design is (as shown in the

diagram)- . This is due to the fact that (as stated previously), the low permeability of the

permanent magnets means that their presence in the configuration can be treated as an effective air

gap. As in the case of an IPM, the magnets are imbedded in the rotor and lie along the direct flux

path, it is apparent that the direct axis reluctance is higher than that of the quadrature axis and

therefore- .

3.5.2.4 Design Parameters

As in the case of the wind turbine, the parameters of the PMSG were chosen based on those used by

Valenciaga and Puleston in [75]. Hence, the number of rotor poles was chosen to equal 28 and the

synchronous resistance and inductance of the machine are equal to and

respectively. The peak rotor flux is equal to .

Figure 3-13: Magnetic Saliency Characteristics of SPM & IPM [81]


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3.6 Six Pulse Diode Rectifier and DC/DC Buck Converter Shown in Figure 3-14 is a six-pulse diode rectifier, DC link capacitor and DC/DC buck converter which

are installed between the PMSG and the DC busbar in order to inject a satisfactory level of DC

current onto the busbar:

Figure 3-14: Circuit Configuration of Six Pulse Diode Rectifier & DC/DC Converter

3.6.1 Six -Pulse Rectifier

The rectifier is fed with a three-phase voltage source. The corresponding line-to-line input voltage

waveforms are shown in Figure 3-15:

Figure 3-15: Balanced 3 Phase Line-to-Line Voltage Input to Rectifier

The rectifier works in such a way that the highest line to line voltage will be the voltage that

conducts the current in the rectifier. This results in each line to line voltage conducting for one –sixth

of the period of oscillation. The resulting output DC voltage from the rectifier is shown in Figure

3-16. [84]:


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Figure 3-16: Output Voltage of Six-Pulse Rectifier

Each line to line voltage has the same amplitude, so the DC output voltage can be found for any

single section of the waveform over a radians phase period. The calculations and derivation of

the DC output voltage amplitude (shown below) is illustrated in Section 9.1.10.

As well as this, an important characteristic of this DC/DC converter is that it only allows active power

to flow.

Hence, the power factor associated with the power flowing from the generator terminals is 1 [64]:

This quality is important for the purpose of derivation of the modelling equations of the WECS.

3.6.2 DC/DC Buck Converter

By design, the voltage is imposed on the terminals of the PMSG by varing the duty cycle of the

DC/DC converter. [75] This is a very important characteristic as it will allow the speed of the wind

turbine rotor to be varied in order to facilitate Maximum Power Point Tracking.

The derivation of this voltage is shown in Section 9.1.10. This equation gives the phase voltage on

the terminals of the WECS which depends on the duty cycle

. The duty cycle can hence be varied

in order to change the magnitude of the voltage on the PMSG. This method for varying the voltages


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on the PMSG by varying the duty cycle is the method used later in Section 3.8.7 to facilitate

Maximum Power Point Tracking and Current Control.


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3.7 Full Set of Modelling Equations The full set of modelling equations for the WECS is:

The complete derivation of these equations can be found in Section 9.1 of this report.


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3.8 Simulation of WECS

3.8.1 Open Loop Non Linear Model of WECS

Using the equations given in the previous section, the following model of the WECS was formed

using Simulink:

The relationships between the inputs and outputs of subsystems within this diagram are contained

within Section 9.5 of the report.

Figure 3-17: Simulink Diagram of the Open Loop Non Linear WECS


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3.8.2 Potential System Operating Points

The design parameters used during this simulation are equivalent to those used in [75], except for

the DC bus voltage. The parameters used are shown below:

Figure 3-18: Design Parameters for WECS

At this point, it is necessary to determine the operating point of the system. To do so, the students calculated the values of system variables for rated power output. For a desired power output of 5kW, the results gathered were as follows:

In order to calculate the operating values for and it was necessary to first calculate the results of

a quadratic in and subsequently calculate the corresponding values of . It was then necessary to

test both pairs of operating values and identify that which resulted in a power output of 5kW, which

was the desired result.

Figure 3-19: Operating Values

Figure 3-20: Two Alternate Operating Points


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The power output of the system at each of the operating points is shown in the below diagrams:

Figure 3-21: Power Output at Operating Point Corresponding to Id=3.666A,u=6.46

Figure 3-22: Power Output at Operating Point Corresponding to Id=77.095A,u=0.4562


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As the power output in both cases is extremely close to the desired value (5000W), one might think

that both of the operating points are equally viable. However this is not the case. The fact that both

scenarios perform almost perfectly in order to output 5kW is to be expected due to the fact that the

each condition ( and ) is a solution for this desired

power, as was calculated by the students.

However one must consider the viability of each of the operating points. For instance, an

understanding for the stability at each condition can be developed by implementing a slight step

from the designed value of u, at some stage during the simulation. The condition which results in the

smallest variation in output power can be considered to be the more viable of the two operating

points, and therefore the most attractive from a control perspective.

Hence, for both cases, the system was simulated at the respective operating point for 10 seconds (

is stepped up by 0.5 from its operating point at 1 second). The results are as shown below:

Figure 3-23: Response to a Step in u of 0.5 at 300 seconds - Operating Point: (Id=3.666A,u=6.46)


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Figure 3-24: Response to a Step in u of 0.5 at 300 seconds - Operating Point: (Id=77.095A,u=0.4562)

Hence, it is clear that using the value and yields a more stable operating point

as a step change of 0.5 in u merely results in a drop in power of 200W. Conversely the impact of this

step on the power output when the system is operated at the alternative operating point

( , ) is much larger, causing the power output to drop to zero. For this

reason, it can be concluded that the desired operating point is , .


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3.8.3 Analysis of Operating Point Characteristics

As previously stated, an operating point has been designed for the system based on a desired power

output of 5kW. However, it is interesting to analyse how this operating point varies for a range of

power requirements. For the purpose of this analysis, the locus of the operating point values for

velocity, electrical angular frequency , and will be examined as the required power varies

from 0 to 10kW. Using this analysis, the locus of both roots of the quadratic and corresponding

values of will be analysed.

Figure 3-26: Variation of Velocity Operating Point with Desired Power

Figure 3-25: Variation of Electrical Frequency Operating Point with Desired Power


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Before plotting the loci of operating points for and , it is important to recognise that Root 1

corresponds to the operating point ( , ) and Root 2 corresponds to the

operating point ( , ), which are the two roots of the equation below:

Figure 3-27: Variation of Iq Operating Point with Desired Power

Figure 3-28: Variation of u Operating Point with Desired Power (Root 2)


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Figure 3-31: Variation of Id Operating Point with Desired Power (Root 1)

Figure 3-30: Variation of u Operating Point with Desired Power (Root 1)

Figure 3-29: Variation of Id Operating Point with Desired Power (Root 2)


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3.8.4 Linearization

Once the non-linear model was found to be accurate, it was necessary to take steps towards

developing an inner loop controller for the system. This controller is to control the current . In

order to do this, the students linearized the non-linear model for

within the WECS. This was

done by hand and was cross checked against the transfer function given by the “ss2tf” function in

Matlab. The linear transfer function obtained by hand was:

Upon comparison, it is clear that it is extremely similar to that achieved using state-space within

Matlab. For all accounts these transfer functions can be assumed to be the same as differences in

the two are only due to rounding errors within the hand calculation.

It is evident that this linearization has been a success as the bode magnitude and phase plots

acquired for this transfer function are identical to those attained using the “linearize block”

command within Simulink for the non-linear

subsystem block. This bode plot is shown below:

Figure 3-32: Bode Magnitude and Phase Plots for WECS Linear Model

Note that the complete mathematical linearization of the non-linear system can be found in Section

9.4.


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3.8.5 Comparison of Linear & Non-Linear Model

Factorizing the linear transfer function for the WECS it can be found that:

Hence, there the linear system has zeros at:

The poles of the linear system are:

The difference in performance between the linear and non-linear model can be demonstrated by

analysing step responses of the two systems. The illustrate this, the value of which initially was set

to the operating value 6.46, was increased in value by 0.05 every 3 seconds.

Figure 3-33: Response of Linear and Non-Linear Systems to a Train of Steps

Once 57 seconds has passed, the value of u has diverged by 1 from its design value of 6.46. This

graph clearly shows the degree of non-linearity which is present in the system. The Simulink

arrangement utilised to achieve these results is shown below:


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Figure 3-34: Simulink Diagram of Test Configuration

The shape of the initial transient is analysed in more detail below:

Figure 3-35: Close Up View of Transient Step Response (Linear & Non-Linear)

In order to obtain a desirable power output from the machine, it is first necessary to design a current

controller which will be capable of meeting a declared setpoint (assuming a roughly constant

mechanical speed of the machine during controller testing). Prior to this however it is important to

note that the complete linear and non-linear models of the system also contain another component

which has gone unmentioned up to this point. This factor is the time delay associated with the buck

DC/DC converter within the WECS. This time lag which was approximated to be 1ms is included in

order to approximate the time lag caused in the WECS due to the delay between changes in system

parameters caused by instantaneous changes in the PWM buck converter duty cycle.


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3.8.6 Nyquist Stability & Inversion of Linear Process

As shown previously, the linear transfer function incorporates a negative sign outside of the poles

and zeros. This negative sign must be removed prior to design of a controller for the system (which

“inverts” the model). The Nyquist Plot acquired for the modified linear system (-G(s)) is shown below

in Figure 3-36. However, this plot does not account for the converter time delay. Once this

parameter is incorporated into the system, the resulting Nyquist Plot of the inverted linear system is

as shown in Figure 3-37:

The Nyquist Plot which was acquired whilst ignoring converter time lag clearly shows that regardless

of the choice of proportional gain, the system cannot go unstable. This is due to the fact that the

point -1+0j can never lie within the loop traced by the Nyquist Plot. However, once the time delay is

introduced to the system it is clear that the stability of the closed loop system under proportional

control is dependent on the choice of gain. For instance, for a proportional gain of 1, as shown

above, the system will be unstable. However by decreasing the gain, stability can be achieved. Upon

decreasing the gain of the P controller to 0.21809807, marginal stability was achieved as shown.

Figure 3-36: Initial Nyquist Plot for Inverted Linear Model

Figure 3-37: Nyquist Plot of Inverted Linear Model Incorporating Time Lag


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Using this gain, it was found that the Nyquist Plot of the open loop system cuts the -1 point which

corresponds with a steady state sinusoidal response ( ) from the system for a constant setpoint ( ).

:

Figure 3-38: Nyquist Plot Corresponding to Marginal Stability

Figure 3-39: Marginally Stable Response Achieved


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3.8.7 Current Controller Design

3.8.7.1 Zeigler Nichols Design Route

The ultimate gain is 0.21809807 ( ), as previously stated. The period of oscillation of the resulting

sinusoid is approximately 3.575ms ( ). Hence, following the Zeigler Nichols tuning rule for a PI

controller as given in [85]:

Figure 3-40: Zeigler Nichols Tuning Parameters [85]

Hence for the PI controller:

It is clear that:

By implementing this controller on the linear and non-linear system, for a desired output of 20A, the

following response was obtained:

Figure 3-41: Step Response of Linear & Non-Linear System Using Zeigler Nichols PI Controller


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The Simulink diagram used to achieve this response is given in the Section 9.6. From this diagram, it

can be seen that a gain of -1 is utilised in order to invert the linear model. The controller which is

designed for this inverted linear model, is then itself subsequently inverted when being used to

control the non-linear system- this is the cause of the gain of -1 present in series with the non-linear

system.

It is important to note that the integrator used within the controller of the linear system has an

initial condition of 0. This is because, at 0 seconds the system is assumed to be at its operating point

and hence the change from this operating point (i.e. delta values which are the quantities measured

within the linear system) is 0. It is important to note that unlike the linearized model, the non-linear

system deals with the actual system values, as opposed to the linearized model which quantifies the

difference between the quantity of a variable and its operating value.

However, this should be compared to the manner in which the non-linear system was configured.

The integrator within the controller of the non-linear system was set to equal -6.46/0.0981441315.

This is due to the fact that the variable which passes through the integrator ( ) is yet again

presumed to be at its operating point initially. At the design operating point, has a value of 6.46.

However, it is necessary to incorporate a negative sign due to the inversion which occurs

downstream of the PI controller, and similarly it is necessary to divide by 0.0981441315 due to the

proportional gain of the controller. Doing so guarantees that the value of is initially at the designed

operating point.

Despite the relatively satisfactory response which was obtained using the Zeigler Nichols design

route, this design technique is generally not used in industry. Therefore, the students went about

redesigning the controller based on a method used in class.


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3.8.7.2 Bode Plot Design Route

The bode plot design route for PI controller design first entails plotting the uncompensated bode

plot of the open loop system. The controller design is to be based upon the inverted linear system as

previously mentioned, and the resulting controller will subsequently be inverted for use with the

non-linear system. The only difference between the bode plot of the regular linearized model and

that of the inverted linearized model is that there is a constant phase shift of -180o. This can be seen

by comparing the bode plot previously shown for the uncompensated linear system, to that shown

below for the inverted system:

This plot however, does not include the time lag associated with the buck converter. By

incorporating this time lag, the phase plot is changed significantly:

Figure 3-43: Bode Magnitude & Phase Plots of Inverted Linear System

Figure 3-42: Bode Magnitude & Phase Plots of Inverted Linear System incorporating Time Lag


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The bode plot design route assumes second-order dominance within the system. The following

approximation is used:

*where is the phase margin, and is the level of damping of the response.

By selecting a desired level of damping for the system response, it is possible to calculate a desired

phase margin ( .

This facilitates the location of the desired gain crossover frequency ( . The gain crossover

frequency is the frequency at which the dB gain is equal to 0dB. Hence, the desired gain crossover

frequency is the frequency at which the phase plot of the uncompensated system equals (-180o +

) i.e. -150o in this case.

The desired gain crossover frequency is equal to 1256rad/s. This implies that the integral gain can be

calculated to be:

However, in order to make the dB gain of the system equal to 0dB at the desired gain crossover

frequency, it is necessary to remove 15.92dB of gain. Hence:

If this process is repeated for a number of desired levels of damping, the transient responses can be

analysed and the most suitable chosen. A table of the PI tuning parameters for a number of different

values of desired phase margin (and hence, desired closed loop damping) is shown below:

Table 3-1: Tuning Parameters for PI Controllers (Various Levels of Damping)

Desired Phase Margin (Degrees) Desired Closed Loop Damping

30 0.3 125.6 0.159956

40 0.4 110.6 0.14174

50 0.5 96.97 0.125314

60 0.6 83.5 0.10927

80 0.8 59.72 0.08147


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Figure 3-44: Step Responses Using PI Controller (Desired Phase Margin 30 Degrees)




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Upon comparison of the step responses, the most favourable response was that of the controller

designed for a closed loop damping of 0.5. This is because of the relatively low peak overshoot and

settling time which it achieves. However the parameters of the controller are now tweaked slightly

to get an even more desirable response. The proportional gain of the controller was decreased in

order to reduce the peak overshoot of the response, and the parameter was increased

simultaneously in order to yield a shorter settling time. The response of the tweaked PI controller,

( , ) is shown below:


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Figure 3-49: Step Responses Using Tweaked PI Controller

This response is almost perfect, due to the low level of overshoot. Apart from the mild overshoot, no

oscillation is present and the signal converges rapidly to the setpoint. This PI controller will now be

implemented permanently as the current controller of the WECS.

It is important to note however, that over a large time scale, if the current setpoint is set to 20A and

wind velocity is at it is operating value, the quadrature current is seen to diverge from the setpoint

value and the speed of the rotor of the machine tends towards zero. This is due to the relationship

between the angular speed within the system, and the quadrature current:

Figure 3-50: Quadrature Current of Non-Linear Model Diverging from Setpoint as Machine Speed Drops


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Figure 3-51: Turbine Torque and Electrical Frequency for a Current Setpoint of 20A

It is possible however, to design a current controller for this system by analysing a very short time

period, where the speed of the system is roughly constant (at its operating value). This process has

been carried out above for a time period of approximately 0.02 seconds. However, in order to

implement the current controller usefully within the system, it will be used in conjunction with an

outer loop controller, which will change the current setpoint in such a way that the speed of the

machine is controlled. This outer loop controller is the topic of the next section.


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3.8.8 Maximum Power Point Tracking Controller

As previously stated, regardless of the wind speed maximum power coefficient (and hence

maximum power output) will be achieved if the tip speed ratio is equal to its optimum value (7.198).

Hence, the optimum turbine torque is:

The relationship between the mechanical power of the wind turbine rotor and the

electromechanical output power is defined by the following expression:

Within the model of the wind energy system, the rotor speed will be measured on an instantaneous

basis. Hence, at any instantaneous measurement of rotor speed, the electrical frequency will be a

constant value. Therefore, in order to calculate the current setpoint for a given rotor speed, it is

necessary to let the derivative of electrical frequency with respect to time equal 0, hence equating

the mechanical rotor power and the electromechanical power/torque.

Therefore, by measuring the instantaneous speed of the turbine rotor, it is possible to attain an

instantaneous value for the current in the system required for maximum power point tracking. The

quadrature current is then forced to meet this setpoint by the current controller which has been

designed. The full control scheme is as shown below:

Figure 3-52: Complete Wind Energy Conversion System


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The process was then simulated under a varying wind speed profile. The following graphs illutrate

the performance of the WECS under full control (current control & MPPT). The first graph clearly

illustrates that the maximum power point is being tracked accurately, as for wind speeds of

12.629m/s, 10m/s, 7.5m/s and 5m/s, the powers obtained from the machine correlate with those

given in Figure 3-2 which show the maximum power available at a given windspeed.

Figure 3-53: Optimal Turbine Rotor Power & Actual Turbine Rotor Output

Figure 3-54: Wind Speed & Mechanical Speed


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The following diagram shows the variance of the tip speed ratio of the machine with varying wind

speed. As shown, if a change in wind velocity occurs, the mechanical speed of the rotor will gradually

change which in turn will cause the current setpoint to change. As the mechanical speed of the

machine changes, the tip speed ratio of the machine converges to the optimum value (this may take

some timed depending on the magnitude of the velocity change). Once the optimal tip speed ratio is

reached after a change in wind speed, the machine is once again taking maximum power from the

wind for the given wind speed.

Figure 3-55: Tip Speed Ratio & Quadrature Current versus Time

Figure 3-56: Actual and Optimal Electrical Power to DC Busbar


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4 Solar Array

4.1 Physical Construction Photovoltaic (PV) systems are capable of producing DC voltage and current by absorption of sunlight.

PV systems are divided into cells, modules and arrays. A PV cell is made of semiconductor material

which makes up a p-n junction. [86] Many of these small cells may be combined to form solar

modules which in turn make up a PV array. As previously stated, only solar energy which is absorbed

by the cells within the array contributes to the useful power output. Hence, sunlight which is

reflected from the array plays no part in electricity generation. [87]

The diagram in Figure 4.1 is that of a PV cell [88], and agrees with that shown in [89]. As previously

stated, a solar cell is made of semiconductor material. In order to adequately explain the operation

of a solar cell, it is first necessary to illustrate some basic principles of semiconductor physics in

order to outline the manner in which the device is constructed. A semiconductor is an element

which exhibits characteristics between those of an insulator and a conductor. The most commonly

used semiconductor element is silicon. [90] A semiconductor diode is formed when a p-type and an

n-type semiconductor material are brought together (forming a p-n junction which defines the

divide between the p-region and n-region [91]). This is effectively the principle behind the solar cell.

[89] In order to create a silicon solar cell, it is first necessary to start with what is called intrinsic-

silicon. [92] This is pure silicon with no added impurities. Impurities are subsequently added to the

intrinsic semiconductor to change the properties of the semiconductor. This process is termed

"doping". [89] In order to explain the formulation of the p-n junction, it is imperative to understand

that silicon has 4 valence electrons in its outer shell. This is one electron more than is present in the

outer shell of an element in Group III of the Periodic Table of the Elements, and one less electron

than is present in the outer shell of a Group V element. Hence, the formation of p-type silicon is

achieved by exposing the intrinsic-silicon to a Group III element (e.g. boron). This material is

positively charged in comparison to the silicon material, and is said to possess a hole (i.e. lack of an

electron). Therefore this is termed the p-region. Once the p-region is formed, it is necessary to

expose the semiconductor to Group V elements (e.g. phosphorous), which results in the formation

of the n-region, which for each phosphorus atom introduces results in the addition of one negatively

charged electron. Hence, the resulting semiconductor is divided into two regions which are

respectively positively charged and negatively charged compared to the original intrinsic-silicon

material. The p-region is said to contain acceptor impurities (which will accept electrons), and

conversely the n-region is said to contain donor impurities with donate electrons). The boundary

between these two regions is termed the p-n boundary. [92] The PV cell is completed by the

implementation of metallic conductors at each end of the semiconductor (i.e. both p and n regions).

A metallic grid is used on the part of the solar cell which is facing the sun. This serves the purpose of

allowing sunlight to make contact with the semiconductor. [88]

Figure 4-1: Physical Construction of a PV Cell [87]


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4.2 Operational Procedure Sunlight is made up of packets of electromagnetic energy called photons, which travel through space

at the speed of light. Photons are radiated from the surface of the sun and upon absorption by a

solar cell the generation of electrical energy occurs. It is important to note that the energy levels of

photons differ and the depth of penetration into the semiconductor material is a function of this

energy level (i.e. deeper penetration is achieved by lower energy photons). [92]Upon being

absorbed by the semiconductor material, photons of light will cause electrons of semiconductor

atoms to be knocked from their respective atoms. In doing so, an electron-hole pair is created, the

electron of which will be attracted to the n-region and the hole of which is attracted to the p-region.

[86]. This process is illustrated in the diagram below [91]:

Figure 4-2: Principle of Operation of a PV Cell [89]

As shown, when connected to a load, an electron displaced by an incident photon is seen to initially

gravitate towards the metallic grid at the edge of the n-region and subsequently flow through the

connected load, finally reaching the metal contact at the edge of the p-region. [92] Subsequent to

crossing this metallic contact, the electron "recombines" with the hole which was created due to the

incident photons. [86] It is logical to conclude that if the electron-hole pair is produced in the n-

region, that the electron produced will reach the metallic conductor at the edge of the n-region, and

similarly that if the electron-hole pair is produced in the p-region of the semiconductor, the resulting

hole will reach the base conductor of the cell with ease. One might question the prospects of holes

leaving the n-region/electrons leaving the p-region prior to recombination due to the high respective

levels of free electrons and holes in each of these regions. However, the design of PV cells is such

that holes produced in the n-region of the material are highly likely to escape the n-region prior to

recombination, and similarly for electrons produced in the p-region of the material- hence the

majority of recombination is confined to the area near the p-layer metallic contact. [91]

Once recombination occurs, the electron fills the hole, hence restoring the initial state of the system.

This process recurs over time provided the supply of sunlight (i.e. photons) is not discontinued. It is

important to realise that this effect only occurs provided that the incident photon carries enough

energy to free an electron from the outer shell of its associated atom. [91]


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4.3 Full Set of Modelling Equations The full set of modelling equations for the solar array is:

The complete derivation of these equations can be found in Section 9.8 of this report.


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4.4 Parameterization The values of cell parameters have been chosen to image the performance of the Shell SP70 solar

panel. The datasheet of this panel is shown in Section 9.9, however the cell-specific parameters used

in the model are shown in this section:


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4.5 Implementation of Newton-Raphson Algorithm A solution for cell output current is obtained for the implicit current equation of the device via

implementation of the Newton-Raphson algorithm (illustrated in Section 9.8). This is achieved by

emulating the continuous process using zero order holds at the input and output of the solar cell

model. It is important that the sample time chosen for these components is selected to be greater

than the minimum sampling time of the simulation configuration parameters.

Within the solar cell model, a delay block is used to set an initial condition for the output current of

the solar cell. The sampling time of this integrator must be chosen to be less than that of the zero

order holds used within the system (ideally more than 5 times less). This is imperative to the

successful implementation of the algorithm. The function of the delay block is to provide the

previously sampled value for cell output current to the and blocks. If the last sample of

current is assigned the variable , this process leads to the acquisition of .

At this point it is important to realise that the Newton-Raphson algorithm is an iterative solution.

Hence, after feeding back the current once through the and blocks, the solution has not

been attained, but the value of current has moved closer to the correct value. This is the reason for

the importance of the correct selection of the sampling times of the zero order hold and delay block.

Within the model created by the students, the sampling time of the zero order hold was selected as

0.1 seconds and the sampling time of the delay block was chosen as 0.01 seconds. Hence, 10

iterations will occur between two samples of the zero order hold.

It was found that the model created by the students achieved convergence to the desired value of

output current in 7 iterations if the initial condition of the delay block was set to 1.5A. In this case

the terminal voltage was maintained constant at:

And the current was seen to converge to the value:

The result is shown below:

Figure 4-3: Solution of the Implicit Current Equation via Using the Newton Raphson Method


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4.6 Solar Panel Performance The solar cell which was modelled by the students is a 125mm*125mm silicon solar cell. The

completed model of this component is illustrated below, and consists of a constant series resistance

of 0.4387Ω calculated in Section 9.8.3. The delay block and input and output zero order holds can

also be seen in the diagram:

The model is based on the solar cell used within the Shell SP70 70W Solar Panel. The datasheet

[93]of this product can be located within Section 9.9 of this report. The inner workings of each of the

subsystems shown in the above diagram are also shown within Section 9.10 of the report. The input

terminal voltage and output current were subsequently scaled in order to acquire a complete solar

panel model consisting of 4 parallel rows of 9 series cells. Hence, input voltage to the panel is

divided by 9 to acquire the voltage across a single solar cell and the output current from the solar

cell is scaled up by a factor of 4 to account for the number of parallel rows of solar cells.

4.6.1 Selection of Diode Ideality Factor

In order to meet the specifications on the product datasheet, and to achieve realistic solar panel I-V

and P-V curves, it was first necessary to select an ideality factor for the solar cell. As previously

mentioned, these typically range from 1-1.5. The solar panel was tested for numerous ideality

factors at a constant solar irradiance of 1000W/m2. The results are shown below:

Figure 4-4: Solar Cell Model


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Figure 4-5: Power- Voltage Characteristic of Solar Panel

Upon closer inspection of the point (P=70.13W, V=16.5V):

Figure 4-6: Maximum Power point (1000W/m2)

This point in particular is worth examining as the datasheet of the solar panel specifically states that

a rated power of 70W should be attainable at 16.5V. This is achieved regardless of the ideality factor

chosen as the model which was built by the students specifies this as an obligatory requirement.

However, only in the case of a=7 is this the maximum power point for the given irradiance of


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1000W/m2. Hence, although not within the usual recommended limits (1-1.5), a value of 7 will be

chosen for the ideality factor of the diode.

The need for such a large ideality factor may have arisen for the following reasons:

Simplification of the solar cell model (i.e. omission of shunt resistance and additional parallel

diodes).

Possible inaccuracy in the calculation of series resistance of the solar cells within the module.

A high level of non-ideality associated with the physical solar cell being examined.

For this choice of ideality factor, the I-V and P-V characteristic of the panel was subsequently tested

at different levels of solar irradiance as shown below. To gather these results, the temperature of

the cell was maintained constant and equal to the reference temperature (25oC):

Figure 4-7: I-V Curve of Solar Panel for Different Levels of Irradiance

At this point, it is clear that the similarity of the Simulink model produced by the students is highly

similar to the real solar panel as the I-V curves from the product datasheet are almost identical to

those achieved above:


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Figure 4-8: Shell SP70 I-V Curves for Different Levels of Irradiance (From Datasheet) [93]

The acquisition of such a high level of accuracy therefore indicates that the ideality factor chosen by

the students was correct. The power curves achieved for the model are shown below:

Figure 4-9: P-V Curves for Shell SP70 Solar Panel For Different Levels of Irradiance


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If the temperature of the cell is raised above the reference value, the following characteristic is

observed for a constant level of irradiance (1000W/m2):

Figure 4-10: Increase in Device Temperature Results in Increased Short Circuit Current

The above results agree with those shown by Jeffers in [94]. As the temperature of the cell increases

from the reference temperature, the short circuit current level increases. Although not clearly visible

in the upper diagram, as the temperature increases, the open circuit voltage of the device also

increases- a result which also agrees with [94].


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4.7 Solar Array Model In order to achieve a useful power output onto the microgrid it is necessary to connect together

multiple of the solar panels designed above. In order to achieve a higher voltage output, several

panels are connected in series:

Figure 4-11: Scaled Voltage Output Achieved by Adding Multiple Panels in Series

Alternately, by adding multiple solar panels in parallel, the current output can be scaled in a similar

manner as the voltage was by adding panels in series:

Figure 4-12: Scaled Current Output Achieved by Adding Multiple Panels in Parallel


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Hence, by combining a number of solar panels in series and parallel it is possible to choose the

power output of the array. For this project, the students desired a maximum power output of

approximately 2kW from the solar array which can play a complementary role to the wind turbine

already modelled by the students. In order to achieve this, the students consulted the datasheet of

the product. The maximum power point current and voltage at STC are given as 4.25A and 16.5V

respectively for a single solar panel. Hence, by designing for ideal operation at an irradiance level of

1000W/m2 and a cell temperature of 298.15K, by combining 5 parallel rows of 6 series solar panels, a

rated power output of 2103.75W is calculated:

The Simulink configuration used to achieve this design is shown below:

Figure 4-13: Solar Array Arrangement Consisting of 5 Rows of 6 Panels


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The resulting power curves for this array are shown below:

Figure 4-14: Power Curves of Complete Solar Array For Different Levels of Irradiance

This plot is incredibly important as it will be used in coming sections to validate the maximum power

point tracking controller which is to be designed for the array. The upper diagram shows that if the

system is constantly operating at Maximum Power Point, even at low levels of irradiance the

terminal voltage of array does not fall below 48V (the voltage at the DC bus).

Hence, this implies that the method of connection from the output terminals of the array to the DC

bus will be via a step down DC/DC buck converter.

The values of power and voltage corresponding to Maximum Power Point are given on the above

plot, as well as the trend which occurs through these points. The trend plot was achieved using the

“polyfit” and “polyval” functions in Matlab while approximating the Maximum Power Point curve as

a 2nd order polynomial:

p=polyfit([89,94.4,96.2,97.8,99],[376.9,799.6,1233,1669,2104],2);

f=polyval(p, [89,94.4,96.2,97.8,99]);

plot([89,94.4,96.2,97.8,99],f,'k')


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4.8 Maximum Power Point Tracking Controller There are a number of methods which are used to track maximum power for changing levels of

irradiance. In fact, [95] describes 19 such methods. Two methods of tracking maximum power were

attempted for the solar array designed by the student, and both will be discussed however more

detail will be given on the final control methodology used. Both of the methods which were

researched by the students are examples of "hill climbing" algorithms. Several other methods are

also possible, such as

of

feedback control, DC link capacitor droop control, current

sweep, Ripple Correlation Control (RCC), fuzzy logic control, fractional short-circuit current and

fractional open circuit voltage methodologies. [95]

4.8.1 Perturb & Observe (P&O)

The diagram below shows the control logic which is followed by the P&O control algorithm:

Figure 4-15: P&O Control Logic [96]

Effectively the algorithm will increment or decrement the voltage on the terminals of the array

based on the effect which the previous voltage perturbation had on the output power of the array.

As explained by the upper diagram, if the previous perturbation of voltage was implemented in a

positive direction (i.e. if the voltage was increased) and resulted in an increase in power output, the

algorithm will choose to further increase the terminal voltage of the array in an effort to further

increase power output. Similarly, if the previous perturbation was negative (i.e. the voltage was

decreased), and resulted in a decrease in power output, the algorithm will attempt to work in

opposite direction and “climb the hill” to the maximum power point by increasing the voltage. The

bottom half of the diagram above operates in a similar manner.

As stated above, the purpose of implementation of this algorithm is to control the power output of

the array by incrementally changing the terminal voltage of the array. It is important to realise that

in reality, this process is carried out by the DC/DC converter between the solar array and the DC bus

of the microgrid- hence the goal of the P&O algorithm is to incrementally change the duty cycle of

this converter to achieve the above task. This process is similar to the role of the DC/DC converter

within the WECS previously designed by the students.


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The operation of this algorithm is such that once the maximum power point is reached, an oscillation

occurs from the left hand side of the maximum power point to the right hand side of the max power

point. If the size of the voltage perturbation used by the algorithm. By minimizing this value, the

amplitude of oscillation which occurs at maximum power point can be minimized. Conversely,

minimizing this value has an inherent disadvantage as it causes the operation of the algorithm to

slow considerably.

For instance, if a small perturbation size is used (0.01 for instance)- performance is considerably

worsened in the case of the emergence of the sun from behind a cloud. In such a case, there is

effectively a step increase in the level of solar irradiance. If this step increase is of the order of 100’s

of W/m2, and the choice of perturbation size is small then it might take over a minute to reach

maximum power point (however this is also dependant of the sampling time of the algorithm). This

is of course an undesirable effect as due to the unpredictability of the weather, maximum power

point may not be reached at all if another cloud moves to block the sun before the minute has

passed.

Another problem associated with the operation of the P&O algorithm is that it is incapable of

determining the cause of the increase/decrease in power level. For instance, in the case that the

solar irradiance is initially at a constant level and the operating point of the device is oscillating

about the maximum power point (i.e. changing from just right to just left of the maximum power

point). If the terminal voltage of the array is initially just higher than the maximum power point

voltage, the subsequent iteration will cause the voltage at the terminals of the array to decrease to

slightly lower than the maximum power point voltage. If however, when this perturbation is made

the level of solar irradiance increases and continues to increase, then the result will be a continuous

decrease in the array terminal voltage and divergence from maximum power point. However the

extent of this decrease will be dependent on the rate and duration of increase of the solar

irradiance. The deviation will come to an end once the rate of change of irradiance decreases. This

issue is described in more detail in [97].

As well as this, it is clear that P&O is somewhat less efficient compared to other control

methodologies as the average daily efficiency of a device using P&O control is 81.5% compared to

89.9% which is achievable using the Incremental Conductance Algorithm which will now be

discussed. [97]


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4.8.2 Incremental Conductance Algorithm

The flow chart shown below clearly illustrates the control logic behind the operation of the

incremental conductance algorithm.

By analysing the power curve of the solar array, it can be found that:

It is also worth noting that the power curves shown in previous sections of the report clearly shown

that:

Figure 4-16: Incremental Conductance Algorithm Control Logic [95]


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It is also important to distinguish between the incremental conductance and the instantaneous

conductance of the array:

By comparing the instantaneous and incremental conductance it is possible to track maximum

power point. The instantaneous conductance is calculated from measured values of current and

voltage at the present time. The changes in current and voltage can be calculated by

comparison of the present values of current and voltage with those from the previous cycle. Hence,

the incremental conductance can be obtained in this manner. Decisions are made based on these

two quantities by following the flow chart shown above.

It is imperative to understand that at the maximum power point, as the rate of change of power with

respect to voltage is equal to zero. By basic calculus this is concluded by virtue of the fact that

maximum power point is a local maximum of the power function:

This condition is checked within the algorithm, and if it is seen to be true it is clear that the operating

point of the array has reached the maximum power point and no change in terminal voltage is

required.

At this point, analysing Figure 4-17 is a worthwhile activity [98]:

Figure 4-17: Rate of Change of Voltage with Respect to Voltage For a Typical Solar Array [98]


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It is clear from the above diagram that the rate of change of output power with respect to voltage is

positive for voltages less than that corresponding to the maximum power point and is negative for

voltages greater than this. Hence, rearranging the equation given earlier it is clear that:

Regardless of whether operating at voltages higher or lower than , the output voltage and

current from the array are positive. Hence, it is clear that:

Hence, when the operating point is seen to be to the left of the maximum power point, the terminal

voltage is incremented, and when the operating point is seen to be to the right of the maximum

power point, the voltage is decremented. Both of these perturbations result in movement of the

operating point of the array closer to that which corresponds to maximum power.

4.8.2.1 Implementation of Incremental Conductance Controller

The Incremental Conductance algorithm was subsequently modelled within Simulink. The

configuration used by the students is shown in the diagram below:

Figure 4-18: Control Logic of Incremental Conductance Controller

The purpose of the memory block which is present within the upper diagram is to delay the input to

the block for one integration time step. An initial condition must be set for this block so that the


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output of the block has a starting point for the first time step of the simulation. Subsequent to that

time step, the output of the block is equal to the input of the block during the previous time step.

The inclusion of this block is imperative to the successful simulation of the incremental conductance

algorithm, as its exclusion results in an algebraic error within Simulink.

The blocks shown in the upper diagram are expanded within the Appendices of the report. It is

important to note that the subsystem "First Branch" handles cases during which , and the

subsystem "Second Branch" handles cases which comply to the condition .

The controller has been implemented within the solar array as shown below:

Figure 4-19: Implementation of Incremental Conductance Controller

Within the First Branch and Second Branch subsystems, decisions are made based on current and

voltage measurements. This process was made possible by utilising multiport switch blocks and

comparison blocks. For instance, the internal configuration of the Second Branch subsystem is

shown below:

Figure 4-20: Second Branch Subsystem


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This system demonstrates the logic which was used to model the incremental conductance

algorithm For instance, if there has been no change in voltage but a change has occurred in current,

the output of the pink multiport switch will be 1. Using the yellow block, the change in current is

analysed and therefore if the change in current is greater than 0, the output of the subsystem is 1,

however is the change in current is not positive, the output of the Second Branch subsystem will be

-1. A negative number indicates that the terminal voltage is to be decremented to converge to

MPPT, and a positive output indicates that the terminal voltage of the array must be incremented in

order to converge to MPPT. Hence, in this case where over the previous two samples, no change has

occurred in terminal voltage however array current has decreased, a decrease in array voltage is

necessary. This complies with the incremental conductance flow chart which was shown at the

beginning of this section. This method of using multiport switches and comparison blocks was

replicated in order to model the entire incremental conductance algorithm.

The performance achieved by from the full system is shown below:

It is important to note that in order to achieve the above response; the level of solar irradiance was

stepped from 200W/m2 to 400W/m2 to 600W/m2 to 800W/m2 to 1000W/m2, and subsequently

stepped back down to 200W/m2 in reverse order. Comparing the above response with the plot of

the array’s P-V curves previously shown, it can be seen that the incremental conductance algorithm

tracks maximum power point perfectly at each level of irradiance tested. One should realise that

there is a very slight oscillation in system voltage at maximum power point, and hence the values

voltage values achieved in the above graph do not exactly match those shown on the array’s P-V

curves earlier in the report.

Figure 4-21: Performance Achieved Using Incremental Conductance Algorithm


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Table 4-1: Maximum Power Point Tracking- Results

Ideal MPP Achieved Values

Power (W) Voltage (V) Power (W) Voltage (V)

200W/m2 376.9 89 376.9 89

400W/m2 799.6 94.4 799.6 94

600W/m2 1233 96.2 1233 96.6

800W/m2 1669 97.8 1669 98

1000W/m2 2104 99 2104 98.8

A more detailed view of the convergence to maximum power point is shown below for a step change

in solar irradiance from 200W/m2 to 400W/m2 at 50 seconds. Convergence to maximum power point

is achieved in approximately 5 seconds which is a satisfactory response.

Figure 4-22: Convergence of Operating Point to Maximum Power Point

As shown in the upper diagram, ten incremental adjustments to the power output (and therefore

the terminal voltage) occur within a period of 1 second. This is due to the fact that a sampling time

of 0.1 seconds was chosen for the zero-order holds within the system.


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5 Battery Model

5.1 Introduction A battery was required in the microgrid model to help provide more reliability to the consumers.

With wind and solar energy being unpredictable, it was necessary to introduce a device that could

provide/consume the difference between the power being generated and the load requirement.

When the load was greater than the combined wind and solar power, the battery would be required

to provide the remainder of the power. On the other hand, when there is excess power being

generated by the renewables, this power is intended to flow into the battery for use in a period of

reduced renewable generation. This method is much more economic and useful than simply using a

‘dump’ load, which wastes the power by letting it flow to ground.

The use of a battery in the microgrid also helps to minimize the intermittency characteristic of

renewable generating sources like wind and PV. The introduction of a storage element in the

microgrid is what sets it apart from the main utility grids that currently operate globally in developed

countries [99]. The integration of renewables into the electricity generation market is hugely

benefitted by having the ability to store the excesses of power being generated when power

demand is low. Curtailment is a huge issue with having wind turbines connected to a main utility

grid. If generation of power from renewables is too high, then the operators of the grid will prevent

all of this power being supplied to the grid in order to maintain system balance and reliability [100].

Hence this renewable energy is simply ‘dumped’. During the period of January to November 2010,

26GWh of wind energy generated went unused in Ireland [101]. This report also details how, in the

absence of Turlough Hill (Irelands only pumped storage facility) there was less “room” for the wind

and hence the amount of wind energy wasted increased. This pumped storage facility acts in the

same way as the battery bank in the DC microgrid. Without the storage of the battery bank, the

amount of energy unused would increase. While there is a heavy reliance on wind and solar energy

in the microgrid, any quick variations of power being generated can be handled by the battery bank

whether it is required to supply/absorb the changes in power.


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5.2 Battery Cell Model A Lithium-Ion battery was the desired battery type for the microgrid. The initial battery cell model

was obtained from [102]. Lithium-Ion batteries are the chosen battery type for many electric vehicle

manufacturers including Nissan [103], Tesla [104] and Renault [105]. This confirms a good maturity

of the technology and gives confidence to users that the battery would be reliable. Lithium-Ion

batteries offer a host of advantages: greater energy-to-weight ratio, no memory effect and low self-

discharge when not in use [106]. The final two advantages listed are very important to the microgrid.

With no memory effect, the maximum capacity of the battery remains unchanged despite its

irregular charging and discharging. Low self-discharge is also highly advantageous as it means the

SOC within the battery varies very slowly over time. Hence in times when the battery is expected to

just remain idle and hold the charge, it can do so without much loss of energy. Many considerations

must be taken into account when choosing a battery type. For the purpose of this project, energy

capacity is the most important of these characteristics. The sole purpose of the battery in this

project is to store/supply power to the load when necessary. Hence, the more energy the battery

can store, the more advantageous the battery is to this project. A cell type with a capacity of 40Ah

was chosen and all of the details of the cells parameters were also obtained [106] and are shown

below in Table 5-1.

Table 5-1: Battery Cell Parameters

Capacity (Ah) v0(V) R (Ω) K0 (V) A (V) B (Ah)-1 Vnom (V)

40 3.5 0.01 0.0025 0.2 0.375 3.2

Where,

The values above were obtained through complex testing which requires special equipment [107].

These parameters help in determining the open-circuit voltage ( ) of the battery at a defined

charge ( ).

This equation describes how the open-circuit voltage varies as the charge on the battery varies. An

example of the variation of the can be seen in Figure 5-3. The State of Charge (SOC) of the

battery at any time is the ratio of the instantaneous charge on the battery to the nominal or

maximum charge of the battery. It is a very useful parameter for analysing the current status of the

battery. In other words the SOC of the battery indicates how full the battery is. For example, if the

battery is half full it has a SOC of 0.5.


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The SOC of the battery is the key parameter in this project. It informs the user of the backup that the

microgrid has at any period in time. This is very important when it comes to controlling the full

microgrid which is detailed further in Section 6.3.

The equivalent circuit for the battery cell is shown in Figure 5-1. The resistor in the diagram

represents the internal impedance within the battery cell.

Figure 5-1: Battery Cell Equivalent Circuit

The direction of the current in the diagram indicates that the battery is charging. The terminal

voltage ( ) is the terminal voltage and is the voltage that appears across a load when it is attached

to the terminals of the battery. Using Kirchoff’s Voltage Law, the power flow can be determined

within the battery cell. The charging current ( ) is taken as positive.

This equation is solved to find the current in the Simulink model. The resulting equation used in

Simulink is shown below:

The charge of the battery varies as the current flows in/out of it. A fundamental law of electricity is

that current is the flow of charge. This is described by the equation below.

Hence the current in the simulation can be integrated with respect to time to obtain the new charge

on the battery. This is the method used in the Simulink model. The charge on the battery is

determined in an on-going basis depending on the current flowing in/out of the battery.

This is the final equation used in the Simulink model of the battery cell. A picture of the model is

shown in


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Figure 5-2: Battery Cell Model

The battery power flow in the battery cell was controlled in order to prevent the current from

flowing when the battery reaches its maximum SOC. Without the controller the power flowed

continuously even when the battery reached maximum capacity. This is not in accordance with how

the battery acts in reality. When the battery begins to reach a SOC of 1, the current falls off to 0A

[107].

The controller itself is made up of Multi-Port Switches and Relational Operators in Simulink. Once

the limits outlined by the controller are reached, the power flow that wanted to flow into the model

would be switched off. The limits chosen for the battery were chosen in order to preserve the

lifetime of the battery. These limits maintain the SOC between 0.2 and 0.9 [107]. These restrictions

obviously have an effect on the storage capacity of the battery but they were still implemented to

preserve the health of the battery.


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5.3 Layout of Battery Bank The selected DC bus voltage was 48V (See Section 3.8.2). The battery is what maintains the DC bus at

this voltage and so the battery bank must have a nominal voltage close to 48V. As noted in Table 5-1,

the nominal battery voltage is 3.2V. In order to get a nominal battery bank voltage of 48V, the bank

requires

= 15 battery cells in series. This is the nominal voltage and so the actual voltage does

vary from this throughout the operation of the battery and is a function of the SOC. Figure 5-3 shows

the variation of the open-circuit voltage of the battery bank as the battery discharges from an SOC of

0.9 to an SOC of 0.2 (7% increase).

Figure 5-3: VOC Variation with SOC

The number of parallel branches the battery contains determines the energy capacity and power

output of the battery. Obviously the more battery cells the model has, the better it is for the stability

for the consumers. Yet it was considered to design the battery based on the requirements of the

microgrid and size the battery accordingly. Hence a nominal power of 4.8kW (close to the size of the

WECS) was decided upon for the battery bank. This value would require a current of 100A at the

nominal voltage of 48V. The recommended current for the battery cells is 0.5C [108]. The C-value is

defined as the amount of current a cell can discharge for an hour in going from a SOC of 1 to a SOC

of 0 [107] [109]. Table 5-1 shows that the capacity of the battery cells in this project is 40Ah. Hence

the C-value for these cells is 40A. This means that the desired current for each battery cell is 20A. In

order to achieve this at the nominal power, the battery bank must have

parallel branches.

Figure 5-4 shows the layout of the battery bank.


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Figure 5-4: Battery Bank Configuration

When creating the effect of a series connection for the currents, the mean value of the currents in

all of the cells is taken. When a parallel effect is desired, the sum of the currents is calculated. It is

the opposite case when considering the voltages.

This battery bank now contains 75 battery cells. With each cell having a capacity of 40Ah at a

nominal voltage of 3.2V, the battery bank has a total energy capacity of 9.6kWh. In order to have an

idea of the size of such a combination of battery cells, the capacity of the Renault Fluence ZE battery

pack was researched and found to be 22kWh [105]. Hence the battery bank used in the microgrid

corresponds to approximately 43.64% the size of an EV battery. The size of the battery can very

easily be increased by increasing the number of parallel branches in the layout.

The battery bank was sized from a nominal power of 4.8kW. The battery bank should thus be able to

discharge fully (from a SOC of 0.9 to 0.2) at this power, for 1.41 hours. This figure was arrived at by

following the calculations below.

But the battery has limits for the SOC and hence the operating capacity is 0.7 * 9.6 = 6.72kWh. The

time that the battery can supply a power of 4.8kW is:

Figure 5-5 shows how the model of the battery discharges at 4.8kW. The time corresponds with the

previously calculated value.


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Figure 5-5: Battery Bank Complete Discharge at 4.8kW


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5.4 Operation of the Battery Bank The battery bank model must have the power input defined at the beginning of the simulation. It is

the power that determines of the rest of the parameters in the battery bank. An initial value for the

charge in the battery must be set in the integrator block. This determines the initial SOC of the

battery. Once the simulation begins, the power input determines all changes in current, SOC

and .

The SOC is the most important parameter in the battery when it comes to this project. As stated

earlier it defines the backup that the microgrid has. In Section 6.3, it will become apparent how

important the SOC is when it comes to making decisions on the power flows in the complete

microgrid model. Section 6 also introduces the concept of grid connection for the microgrid which

provides alternative charging options for the battery.


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6 Complete Microgrid

6.1 Compilation of Models With all of the distributed generation and storage elements now modelled, they are all put together

to commence the complete model of the microgrid. Figure 6-1 shows the complete model in

Simulink. The picture shows a close up of all the major elements. The rest of the model just contains

scopes, summing blocks etc.

Figure 6-1: Complete Microgrid Model on Simulink

The power being generated by the solar (orange) and wind (green) models are output from their

respective blocks depending on the parameters defined in their individual blocks. In contrast to this

the battery (blue) has its power as an input, which is decided by the supervisor controller (yellow).

This controller also takes the loads (grey) into account when making decisions. The controller is

further described in Section 6.4.

An m-file with all of the parameters for each individual block was created and hence changes for all

of the blocks are made easily. The code in this m-file is shown in the Appendices (Section 9.11). The

m-file allows the following common changes to be made in a simple manner:

Critical and non-critical load changes

Initial SOC of battery

Wind speed

Solar Irradiation

Buying/Selling prices to/from the utility grid


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6.2 Modelling of Loads Loads are required in the microgrid model to make it as realistic as possible. The main purpose of

the microgrid is to supply these loads with the power they require. For the main utility grids, the

loads are made up of households, commercial buildings, hospitals etc. The loads can generally be

broken down into two sectors: Critical and non-critical loads.

6.2.1 Critical and Non-Critical Loads

Critical loads must always be supplied with electricity, regardless of the method for which the

electricity has to be obtained. So in times of low electricity generation the first and most important

loads to be supplied will be critical loads. In the event that all loads cannot be supplied power, some

of the non-critical loads will be shed. These loads can be shed incrementally depending on how

much power the generators can supply. If the generators cannot supply the critical load, then the

grid will have to use extra generators or import the electricity from elsewhere. Data centres are an

example of a critical load in a commercial building, while within a main utility grid a hospital would

be considered a critical load.


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6.3 Grid Imports/Exports As mentioned earlier, a microgrid can be completely islanded which means no grid connection is

available. In this project though, the microgrid has the ability to import/export electricity from/to

the grid.

In reality connections to the main utility grids are quite complex. A Point of Common Coupling (PCC)

is required as a connection point for both systems. A grid forming unit is usually used to regulate the

voltage and set the system frequency before the microgrid can be connected with the main grid [21].

Frequency-droop and voltage-droop controls are used to share real and reactive power components.

For electricity export, a DC-AC inverter would be required to convert the DC power into AC power

before the electricity could be sent to the grid. When importing electricity, an AC-DC rectifier would

be used to change the AC power to DC power before it can be sent to the DC bus. A DC-DC converter

would also be required more than likely to change the voltage level to that of the DC bus.

With the DC microgrid in this project, the implementation of the utility grid is very simply achieved.

The supervisory control decides when the grid is required to receive/supply power. There is no code

built to allow for the converters and control. Hence the presence of the utility grid in this project is

more about giving an understanding of how the microgrid would operate in grid-connected mode, as

opposed to modelling a detailed connection point. Its presence in the microgrid is similar to that of

the loads. The grid connection is important in this microgrid due to the heavy reliance on the

intermittent renewable generators. If the microgrid was to be completely islanded then a much

larger battery would be required in order to secure power for the loads for prolonged periods of

time.


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6.4 Supervisor Control With all the different situations that can occur in the microgrid, some sort of controller had to be

implemented to decide on the power flows. The loads are the centre of the microgrid as they are the

reason the microgrid is needed. So the most important aspect for the controller to consider is to

ensure supply power to the loads. Once the loads are receiving the required power, the microgrid

can decide on what to do with any remaining power.

There are two main sections in the supervisor control:

1.

2.

Where = Power Generated by Wind and Solar and = Load Power Requirement

These two scenarios have completely different implications for the microgrid. When the power

being generated within the microgrid exceeds the power required by the loads, then the microgrid

must decide what to do with the excess power. The only options for this are to send the power to

the battery or export the electricity to the utility grid. When the load power cannot be supplied by

the renewables in the microgrid, then the remaining power must be sourced from elsewhere. Once

again the two options are the battery and the grid. As mentioned earlier though, the microgrid has

the ability to shed non-critical loads in this event. There are three key parameters within the

microgrid which facilitate decision making:

1. SOC of the battery

2. Import price from the grid

3. Export price to the grid

The ability of the microgrid to make decisions on import and export prices means that the economic

effects for the microgrid operators are now also being considered. Similarly to the introduction of

loads and the utility grid, the prices being introduced are more about the concept than the actual

modelling. In other words real prices and figures were not used. Instead price levels were introduced

which are summarised in Table 6-1.

Price Level M-File Value Range Price Level M-File Value Range

High > 2 High > 3

Medium 1-2 Low < 3

Low < 1 Table 6-1: Supervisory Control - Price Levels

In the importing scenario, a high price is representative of as being very expensive and would only

be purchased when absolutely necessary. The medium level is just an average price. If electricity is

required for non-critical loads then the microgrid will import the electricity. Finally the low price

represents a bargain. The electricity is extremely cheap and should be exploited when available.

The exporting scenario is different as it generally is not desired of the microgrid to export electricity

to the main grid. The only times power will be exported are when the battery is full and the excess

power might as well be sold. Or else if the price of electricity export is extremely high and a lot of

money is to be made.


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In order to implement the decisions that would be made by the controller, Multi-port switches were

used. These switches decide on the output for a particular power flow based on a list of indexes.

Each index describes a particular condition of the microgrid. Table 6-2 is an example of how the

indexes operate.

Pws < Pload

Grid-Load SOC High Price Medium Price Low Price 0.2 7 140 -7

Conditionally Supplied

0.2-0.4 15 300 -15

Supply Total Load - WS Supplied Loads

0.4-0.6 10 200 -10

No Supply

0.6-0.9 2 40 -2 0.9 1 20 -1 Table 6-2: Index Example for Supervisor Control

This table shows how the power will flow from the utility grid to the loads for all possible scenarios

while the renewable power is lower than the load power requirement. The green cells illustrate the

events that will cause power to flow to the loads from the grid while the orange cells indicate when

there will be no power flow from the grid to the loads. The blue cell is a special scenario. In this

event, the loads need more power but the battery is completely discharged (0.2). Hence the only

other source of power is the grid. Yet the price is too high for importing and so the grid will shed

some non-critical loads instead. The rest of the index tables are shown in Section 9.12.

The corresponding Multi-Port Switch in Simulink is shown below in.

Figure 6-2: Example of Multi-port Switch in Simulink


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6.5 Scenario Analysis

6.5.1 Introduction to Scenarios

In order to illustrate the application of all the above decisions and events, several scenarios were

simulated and the results analysed. Real life situations were simulated in order to give an idea as to

how the microgrid model could be utilised.

It should be noted that simulation times are very prolonged for the complete microgrid. This is due

the long time it takes for changes to occur in the battery (hours) in comparison the quick changes

that happen in the wind and solar models (seconds). Previously it was seen that the battery model

completely discharges in about 1.41 hours (at 4.8kW, see Figure 5-5). When analysing the battery on

its own, this wasn’t an issue as the battery model could be simulated having the simulation time as

hours. But when the models are required to be simulated in one complete model, the simulation

must have one defined simulation time scale. The resulting solution involved adjusting the battery

model to operate in terms of seconds instead of hours (Capacity of 40Ah now defined as 144000As).

So now in order to see the battery complete an entire discharge, the model is required to simulate

for 5076 seconds. In real time, this would take close to nine hours.

Each scenario is simulated for 1000 simulation seconds (Approx. 17 minutes). The aim of the

scenarios is to show all of the capabilities of the complete microgrid including wind/solar power

variations, load shedding, impact of price changes etc.

The initial conditions will be stated at the beginning of the scenarios. Next the changes that occur

and the times that they occur will be noted. Finally a brief synopsis of the scenario will detail what

happened at each key point with the aid of the resulting graphs.

A convention was agreed upon to ensure the correct direction of the power flows could be

understood easily. If power is flowing into a module (e.g. Battery charging, loads being supplied etc.)

then the power flow for that module is positive. If the power is flowing out of a module (e.g. Power

generated by renewables, Battery supplying power etc.) then the power for the module is taken as

negative.

*Note that while some of the changes seem to look like ramp changes, they actually occur as step changes. This may be

confusing like in the case in Scenario 1 where it appears as though the battery and grid are simultaneously charging (circa.

200 seconds). The reason for this occurrence is due to the sample time being 10. This had to be introduced to reduce the

memory being taken up by the results. It was attempted previously to run the simulations as normal but the program kept

crashing.

6.5.2 Scenario 1

As stated in Section 6.5.1, the scenarios try to relate to common real-life events that may happen to

a microgrid. Scenario 1 deals with the event in which the battery becomes fully charged by the

renewables, when the wind speed drops off and the microgrid needs to call on an alternative source

of power.

6.5.2.1 Initial Conditions

Wind Speed 12.629ms-1 SOC 0.88

Solar Irradiance 1000W/m2 Critical Load 2kW

Buying Price High Non-Critical Load 3kW

Selling Price High


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Table 6-3: Scenario 1 Initial Conditions

6.5.2.2 Changes

Change Made In: Initial Value Final Value Time of Change (s)

Selling price High Low 200

Wind Speed (m/s) 12.629 8 700 Table 6-4: Changes made throughout Scenario 1

6.5.2.3 Analysis

Before the analysis begins the results of the simulation are shown in Figure 6-3 and Figure 6-4.

Figure 6-3: Scenario 1 – Power Flows

Figure 6-4: Scenario 1 - SOC Variation

At the beginning of the simulation, it is evident that the power being generated by the

renewables (pink) was greater than the power required by the loads (blue). Hence the


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supervisor control had to decide what to do with the excess of power. The two options that

can absorb this power were the grid and the battery. Table 9-2 details how the decision was

made in this case. The result is seen as the excess power being generated flows to the grid

(black). This means the microgrid was availing of the extremely good prices for exporting at

that time. The SOC of the battery was an important parameter to consider in this decision

also. In this case, the battery had enough charge to allow exporting to the grid to occur.

A change in the price at 200s, caused the microgrid to reconsider the previous decision

made. The price of exporting was no longer such a good deal and so the supervisor control

changed the path of power flow to the battery. This is shown by the decaying of the grid

power to zero and the increase in battery power (red) to a value of about 2kW. It is here that

the problems with the large sampling time are experienced as referred to in the note at the

end of Section 6.5.1. The effect of this power flow to the battery is shown in Figure 6-4 also

as the SOC began to ramp up.

This increase in SOC came to a halt at around 560 seconds, as the battery reached the

maximum allowable SOC of 0.9. The excess power could no longer flow to the battery bank.

Hence the next most advantageous choice was to export the power to the grid (Decisions

detailed in Section 9.12 again). This is seen in the stepping up of the black line in Figure 6-3.

At 700 seconds, the wind speed decayed to 8m/s. The result was that the power delivered

by the renewables was not large enough to supply all of the loads. Hence backup was

required to provide the difference in power. The battery is seen to track the difference in

power and hence maintained the supply of power to the loads at 5KW. This particular action

is the key to the operation of the microgrid. The battery allows changes in the wind speed to

occur while having no impact on the power supplied to the loads. Hence the intermittency

effects of the renewables are minimised. The effect of the battery supplying power is also

seen in Figure 6-4 with the SOC decaying at a constant rate.

6.5.3 Scenario 2

This scenario deals with a more complicated issue for the microgrid. The battery runs out of charge

and the solar irradiance drops for a period, as if a cloud is passing over the PV panels. The scenario

shows how the microgrid deals with this incident.

6.5.3.1 Initial Conditions

Wind Speed 12.629ms-1 SOC 0.21

Solar Irradiance 1000W/m2 Critical Load 5kW

Buying Price High Non-Critical Load 1.8kW

Selling Price Low Table 6-5: Scenario 2 Initial Conditions

6.5.3.2 Changes

Change Made In: Initial Value Final Value Time of Change (s)

Solar Irradiance (W/m2) 1000 200 20

Buying Price High Medium 430

Buying Price Medium Low 550

Solar irradiance (W/m2) 200 1500 700 Table 6-6: Changes made throughout Scenario 2


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6.5.3.3 Analysis

As in Scenario 1, the results from the simulation are shown in Figure 6-5 and Figure 6-6.

Figure 6-5: Scenario 2 - Power Flows

Figure 6-6: Scenario 2 - SOC Variation

The ‘cloud’ passes over the sun causing the solar irradiance to decay almost immediately in

the simulation causing the power being generated to decrease accordingly (Pink). Before this

change occurred the renewable were able to supply the full load requirement (Blue) but the

reduction in solar irradiance has resulted in the need of backup. With the price of electricity

import being high, the microgrid does not want to import to supply non-critical loads. There

is some charge left in the battery though, so the battery acts as the backup (Red).

This is fine until the battery runs out of charge, which is seen to occur at around 260

seconds. The result of this is seen in Figure 6-5. The power being supplied to the load is seen


90 | P a g e

to drop, illustrating that some of the loads have been shed. The critical load of 5kW is still

being supplied by the renewables. The renewables also supply as many of the non-critical

loads as possible. Taking a close look at the Total Power Flow (turquoise), a small increase

can be seen. This is a characteristic of the load shedding. In the model, the non-critical loads

are made up of 100W loads. The microgrid supplies as many of the 100W loads as possible in

this case. When there is an excess left over (< 100W) then the remaining power cannot

supply any of the loads. Hence there is a small amount of power leftover. The power can

simply be ‘wasted’ to ground via a dump resistor. Alternatively these excess powers may be

used for Combined Heat and Power for the local area or some other alternative which uses

the power more efficiently.

At 430 seconds the price of importing from the grid changes to medium. The supervisory

control now decides that it is acceptable to import electricity from the grid. This is seen in

Figure 6-5 where the Load Power Flow increases again to the magnitude of the full load

requirement. The power can also be seen to be flowing from the grid (black).

At 550 seconds, there is a further decrease in import prices which causes the price to enter

the Low level. The result of this is seen immediately. The power being imported from the

grid increases dramatically. The microgrid is availing of the cheap import prices to charge the

battery and increase the reliability of the system. With the battery being charged again at a

cheap price, the microgrid doesn’t have to fear the prices of importing electricity increasing

again.

The ‘cloud’ has now passed and the solar irradiance increases accordingly. This causes the

power being generated to jump beyond the load requirement and so the operation of the

microgrid is changed by the supervisor controller again. The battery continues to charge but

now the energy is ‘free’. The microgrid no longer requires power from the grid and so the

black line in Figure 6-5 falls to zero again.

Operations experienced in Scenario 2:

Load Shedding

Battery Discharge to minimum SOC

Decrease in Solar Irradiation

Varying Import Prices and their Impacts

Balancing of Power


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7 Potential Project Improvements Predictive Control on Battery With predictive control on the battery, a more accurate and sensible plan of energy storage can be

obtained. The use of this control scheme has the ability to make economic savings in the operation

of the microgrid. For an example of how this control is designed and implemented see [102].

Introduction of Real Wind and Solar Data The wind and solar models in this project is very complex and accurate. The control systems in place

help the microgrid extract the maximum power from the natural resources. By inputting real wind

and solar data from a certain period of time, the performance of the microgrid can be analysed

under those conditions. An example of an application for this could be in the testing of a site for the

construction of a microgrid. Wind and solar data from the area in question could be recorded. By

providing this data to the models, it would be possible to examine the power outputs of the

generators and hence the feasibility of the site.

Modelling of Realistic Loads (Critical and Non-Critical) A continuation of the previous idea in Section 0 would be to model the loads in the microgrid in

question. The ability of the microgrid to supply the loads on daily basis could be tested. Daily load

curves from similar buildings could be obtained and the performance of the microgrid could be

analysed (in terms of its ability to supply the loads). Different days with different characteristics

could give an indication of how favourable the weather must be in order to supply the loads. By

viewing weather sheets, it can be seen how often these conditions would actually occur in the

desired area. The models could be adjusted to suit different sized sites. The feasibility tests outlined

above could also give an indication into whether the microgrid would require further generators

(including fossil fuelled generators to increase reliability) and also may help in sizing the DC battery

bank.

Extension of the Current Generating Sources In line with Section 0, the group of generators in this project could be extended to enhance reliability

and capacity of the Microgrid. The list of potential additions is long and varied depending on the

requirements. Fossil fuel generators may help in extending reliability of supply and supplement the

intermittency of the renewables especially if the microgrid is intended for islanded operation.

Augmentation of the Microgrid Models Another point raised in Section 0 was increasing the size of the models. For the battery this is a

simple matter. The number of parallel branches in the battery bank can be increased to improve the

energy storage capacity. It must be noted that battery cells are expensive and limit the size of a

practical battery bank. The wind model would prove to be a bit more complicated considering the

model is based on a particular wind turbine which was obtained from [75]. If changing the turbine a

new set of parameters would be required along with a vs. curve. Also, the very fact that the

wind turbine model is non-linear implies that in order to scale up the model, linearization about a

new system operating point would be necessary. This would be used to find the operating point of

the new machine. Obviously new controllers would have to be designed but the same method could

be followed as outlined in Section 3. The solar array was modelled by first designing a solar cell

model, and then scaling the current and voltage from the device- hence creating a larger model

would not be a significant challenge.


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Improvement of the Supervisor Control The supervisor controller is very basic. The operation of the full microgrid is satisfactory in the model

but the controller could definitely be improved. It basically has a set of ‘if’ statements deciding on

the power flows. Due to its simplicity, further improvement may be possible.

Introduction of Real Electricity Import/Export Prices Similarly as outlined in Sections 0 and 0, real data could be introduced to give a more realistic look at

scenarios. Once again this could help optimise feasibility tests.


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9 Appendices

9.1 Appendix A: Derivation of Modelling Equations for WECS

9.1.1 Derivation of Available Wind Power [110]

Before the characteristics of the turbine are inspected, it is important to gain an understanding of

the nature of the wind from which the turbine acquires energy/power. Firstly, it is necessary to

acquire an expression for the maximum available power in the wind.

Given a cylindrical volume of wind flowing towards a wind turbine rotor disk as shown below:

The kinetic energy of the wind is clearly:

Where:

The mass of the wind is expressed as:

This leads to:

This is an expression for the power contained within a cylindrical stream of wind, prior to making

contact with the wind turbine blades. However, it is important to realise that the power that is

extractable by the wind turbine is much lower than this, and is limited by the Betz Limit.

Figure 9-1: Cylindrical Volume of Wind


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9.1.2 Derivation of Extractable Wind Power [111]

Figure 9-2: Control Volume for Derivation of Extractable Wind Power

The above diagram shows a control volume, containing wind flowing in the direction of a wind

turbine rotor disk. The vertical red line denotes a wind turbine rotor through which the wind flows

resulting in power extraction. This analysis is in many ways simplified compared to the operation of a

wind turbine in reality, for instance:

Assumptions:

-An infinite number of rotor blades.

-Homogenous, incompressible, steady state flow.

-Non rotating rotor wake.

-Uniform thrust on rotor area.

-Static pressure upstream is equal to static pressure downstream.

-No frictional drag.

Clearly, each of these assumptions takes away from the accuracy of the derivation, however the

analysis of wind turbine power extraction characteristics is not the objective of this report- hence, by

taking into account each of these assumptions, a desirable level of accuracy is still attainable.

The thrust on the rotor disk may be expressed as:

The rate of change of mass may be expressed as:

* Note that the term thrust is effectively the rate of change of momentum of the wind between the cross-sections 1 & 4


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Using Bernoulli’s Equation to balance the pressures within each section of the stream tube:

And as:

From earlier, this equals:

Hence:

Now introduce the axial induction factor:

This implies that:

&

And so:

Therefore:

Now introducing the power coefficient of the wind turbine [111], [75]:

By letting = and = :

It will be shown at a later stage in the report that an optimum tip speed ratio exists at which power

extraction is constantly a maximum:


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Also, it is clear that:

Via differentiation with respect to the axial induction factor:

This is the Betz Limit, which states that a maximum of 59.26% of the power in a wind gust can be

extracted by a horizontal axis lift based wind turbine. Note that in reality, it is impossible to reach

this value for , due to the assumptions made at the beginning of the derivation.

The tip speed ratio is the ratio of the linear speed at the tip of the wind turbine rotor to the linear

speed of the oncoming wind. [111], [75]

This implies that:

Now letting = and = for simplicity: [111], [75]

Where:


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9.1.3 Derivation of Clarke and Park Transformations

Figure 9-3 and Figure 9-4 above show two different sets of co-ordinate systems. Figure 9-3 illustrates

a positive sequence configuration. This is the standard representation used to analyse balanced

systems. Figure 9-4 however shows a negative sequence network, which is used in the analysis of

Figure 9-3: Positive Sequence Network

Figure 9-4: Negative Sequence Network


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unbalanced systems, and also for the derivation of the Clarke and Park Transformations as in within

[112] and [113]. From [114], positive and negative sequences are defined as:

Positive Sequence:

“Three vectors of equal magnitude but displaced in phase from each other by 120o and has the same

phase as the original vectors”

Negative Sequence:

“Three vectors of equal magnitude but displaced in phase from each other by 120o and has the phase

sequence opposite to the original vectors"

There is a need to define these alternate coordinate systems, as the derivation of the Clarke and

Park Transformations is carried out using negative sequence notation as will be shown below. The

purpose of the Clarke Transformation is to represent a 3 phase system ( ) in terms of a 2 phases

( ). The first step in carrying out this transformation, is to define the and axes. The

representation used within this report will take the and axes to point in the directions shown

below:

The positioning of the and axes shown in Figure 9-5 is equivalent to that used within [112] ,

[113] and [115]. This pair of axes is stationary, and can be perceived as being fixed to the stator of

the machine. The transformation procedure effectively consists of resolving 3 phase , and

vectors onto the and axes. It is important to note that in doing this, a scaling factor is included.

The purpose of incorporating this scaling factor is to yield certain relationships between

variables and variables, depending on the value of the scaling factor. This facilitates easier

analysis of certain machine properties such as voltage and power, depending on what is desired by

the operator. This will be explained in more detail subsequent to the derivation of the Clarke and

Park Transformations

Figure 9-5: Orientation of Alpha and Beta Axes with Respect to abc

Axes


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As stated above, in order to convert from to representation, it is necessary to resolve the

phase components onto the α and β axes, while incorporating a scaling factor. This process is shown

in Figure 9-6 and is illustrated mathematically below, using phase vectors , and

corresponding αβ vectors and . A scaling factor is utilised.

By resolving phase components onto the axis it is clear that:

- Where a superscript implies the projection of the non-superscripted variable onto the axis in

the superscript. Hence:

Similarly by following the same procedure for the axis:

Figure 9-6: Projection of abc Phase Components for Clarke Transformation


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In order to form a 3x3 invertible matrix, it is necessary to include the “zero sequence” component

within the transformation. The zero sequence component within a balanced system is always equal

to zero. Hence, assuming balanced operation:

These three equations define the Clarke transformation, which can represent a set of 3 phase

components on two stationary α and β axes:

- Which is equivalent to the transformations developed in [115] and [113].

Therefore, the Clarke Transformation Matrix has been defined as:

Now that the phase components can be represented on this pair of fixed axes, it is possible to re-

represent them on the axes (direct) and (quadrature), which rotates about the origin at an

angular frequency of . In order to carry out this transformation it is again necessary to define the

orientation of the and axes within the coordinate system.

Figure 9-7: Orientation of d and q Axes


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The axes will be positioned as shown in Figure 9-7. It is important to note however, that carrying out

research on the topic, it is clear that different authors position the and axes differently and

consequently, the resulting transformation is slightly different (for instance incorporates a change of

sign (and use of sine as opposed to cosine and vice versa) in one or more directions). An example of

this is the representation used in [113], which is not the same as that used within this report, or

within [112] which is equivalent to the representation shown in Figure 9-7.

The transformation from the and axes to the and axes will be carried out from first

principles using trigonometry. A detailed diagram which explains the derivation is shown in Figure

9-8 below, where:

(rad) is the initial electrical angular displacement at 0 seconds.

Also:

Figure 9-8: Development of Park Transformation


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But:

This implies that:

Therefore:

Similar to when deriving the Clarke Transformation, a third equation must be included which defines

the zero sequence component. As this has already been defined within the Clarke Transformation,

there is no need to redefine it, as the zero sequence does not change when changing representation

from to . Regardless of whether the components are being viewed in or

representation, the zero sequence component is exactly the same.

Hence:

However by combining this expression and the previously derived Clarke Transformation:

Now, by selecting the scaling constant , to yield an amplitude invariant transformation (i.e. letting

), [68], the following transformation takes the following form:


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This is the Park Transformation (also known as the Blondel-Park Transformation) [68].

If the reference frame is set up as shown in the below diagram, as done by Krause in [116], the

following version of the transformation is obtained:

This transformation is clearly different to that derived above; however the only reason for these

differences arising is the initial choice of axis directions.

Figure 9-9: Alternative Reference Frame Used in [116]


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9.1.4 Amplitude Invariance

It is important to be aware that there are multiple options for the choice of the scaling factor . As

stated, this effectively means that the value of a quantity (for example voltage/current), will be

equal to the magnitude of the phase value of this quantity, effectively acting as an envelope for the

sinusoid. Other values for the scaling constant can be chosen in order to yield different

transformation properties as shown in the below table [117].

In order to demonstrate the phenomenon of amplitude invariance, a set of 3 phase sinusoids was

transformed into representation using the Park Transformation. To demonstrate the useful

nature of the amplitude invariant quality, this procedure was also carried out for an exponentially

damped set of sinusoids, and the envelope was maintained. Hence, throughout reading the report it

is useful to note that the component of currents/voltages is effectively a negative envelope of the

sinusoidal quantities.

Figure 9-10: Choices of Scaling Factor and Resulting Transformation Properties [117]

Figure 9-11: Amplitude Invariant Park Transformation for 3 Phase Balanced Sine Waves

Figure 9-12: Amplitude Invariant Park Transformation for 3 Phase Exponentially Damped Sine Waves


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9.1.5 Derivation of Inverse Park Transformation

Defining a 3x3 matrix A as:

Letting = , the Park Transformation is:

However, in order to use this matrix practically, it is necessary to find the inverse matrix :

From matrix theory, the inverse of the matrix A is:

Where:

Note the trigonometric identities:

By comparison of the matrices A and :


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First it is necessary to form the determinant of matrix A:


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This implies that:


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Therefore:


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9.1.6 Modelling the Permanent Magnet Synchronous Generator

9.1.6.1 Voltage Equations

In order to obtain a correct model of the PMSG, it is first necessary to define the equivalent circuit of

the machine. The stator electrical equivalent circuit for a synchronous machine operating in

generating mode is as shown in Figure 9-13 below. Assuming a generator convention (current out of

machine terminals taken as positive), it can be found that (if the stator winding resistance per phase

is assumed to be constant), the stator voltage equations of the machine may be expressed as:

These equations which agree with the method shown in [76], are a result of summing the voltages in

each phase of the machine. This also correlates to [118], although a motoring convention (current

into machine terminals taken as positive), is assumed in this case. It is important to note that is

the resistance of each stator winding, and is the total flux linking the nth stator winding. Note

that the above terms of the form

represent the back emf in each of the windings due to a

changing flux. Due to the relationship:

- It is also possible to express this term as the voltage across an inductance as shown in [73].

However, for the purposes of this derivation, the key reference exploited was [119], and hence the

equations listed above are used. The above equations can also be represented in vector form as

shown below:

Figure 9-13: Equivilent Stator Circuit of a Synchronous Generator [76]


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Which could also be written as: [76]

Letting:

,

,

,

Clearly, the flux linking each stator winding will be the sum of the flux from the rotor magnets and

from the stator winding itself. At this point it is necessary to define the as the flux linkage in the

nth winding due to the rotor magnets. The flux linkage related to the rotor magnets as seen by each

of the stator windings is hence:

Where:

At this juncture, it is useful to note that magnetic flux linkage due to the rotor magnets is at a peak

when the magnetic axis of the rotor and the stator are aligned, which is the reason for the

cosinusoidal nature of the above functions. As the goal of this section is to express the voltage

equations of the machine in terms of and variables, it seems appropriate at this stage to convert

into notation, using the Park Transformation which was derived earlier.

Therefore:

Clearly by utilising Park and Inverse Park Transformations:

Now denote:


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From previous work:

By carrying out matrix multiplication (utilising the Inverse Park Transformation developed in Section

9.1.5), the following expression for the inductance matrix in terms of and variables ( ) can be

developed:

Now, the original voltage vector equation can now be reintroduced:

It then follows that:

From matrix theory:

Where is the Identity Matrix:


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Letting:

This implies that:

So:


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Hence, as stated in [75]:

&

At this stage it is possible to draw the direct and quadrature equivalent circuits for the generator:

Figure 9-14: Direct Axis and Quadrature Axis Circuits for PMSG


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9.1.7 Derivation of Electromechanical Power Equation

It is clear that:

Hence, it is now necessary to express this equation in terms of direct and quadrature current/back-

emfs:

Now, using a well-known matrix equation:

This implies that [68]:

Therefore:


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9.1.8 Electromechanical Torque Equation

Hence, it is now possible to quantify the back-emf on each winding in terms of and components.

It is important to note that assuming balanced conditions; the back-emf has no zero sequence

component. Noting that the back-emf vector is:

The electromechanical torque in a synchronous motor is produced solely by the stator back-emf as

stated my Wallmark [68]. Hence, it is straightforward to assume that in the case of a synchronous

generator, the electromechanical torque of the machine is the sole contributor to the generation of

the back-emf (which from the earlier explanation of machine operation, is a simple deduction).

However, as shown in of Wallmark's document :

And as:


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9.1.9 General Torque Expression

The equation relating the mechanical speed of the rotor to the torques acting on the system is as

shown below:

This equation effectively states that the rate of change of rotor rotational speed is directly

proportional to the torques acting on the system. For the purpose of analysing this machine, only

two torques are acting on the rotor- a driving mechanical torque (from the wind turbine rotor), and

a electromechanical load torque. This analysis is similar to that used in [112], although this

document also takes into account friction and cogging torque. Clearly a machine working in

generating mode will have a mechanical torque greater than the electromechanical torque which

produces the generator output voltages. Hence:

where is the mechanical torque due to the rotation of the wind turbine rotor and is the inertia

of the rotational system. However:

Hence:

However, as shown earlier, the turbine torque can be expressed as:

Utilising MPPT however the expression becomes:

Therefore:


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9.1.10 Derivation of Rectifier Output Voltage and the Phase Voltage

in Figure 3-15 has the following equation:

So in order to get the DC output voltage, the equation above must be integrated for the time that it

is the conducting [120]:

This is the average voltage output from the six-pulse rectifier. is the rms line-line voltage on the

input side of the rectifier- i.e. it is equal to the rms line to line voltage across the terminals of the

PMSG.

Hence:

The resulting voltage output from the DC/DC buck converter is therefore (Note the conversion from

to

):

where

and is the peak phase to neutral voltage output from the PMSG [120] [121](It is

important to note also, that this implies that the generator is star connected). This also correlates

with the per-phase equivalent circuit shown in the next section. It is important to note that this

implies that the quantities shown in this figure are all peak- phase values.


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9.1.11 Derivation of Current Injected onto DC Busbar

The phasor diagram for the PMSG in terms of and components is shown in Figure 9-15. From

this diagram it is easy to conclude that the variables and can be expressed as:

and:

At this point it should also be noted that:

As shown in the below diagram, it can be deduced that:

This method of scaling is illustrated in the below diagram. These results can be used to modify the

voltage equations for the WECS:

Figure 9-15: Per-Phase Equivalent Circuit and Phasor Diagram for PMSG [18]


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Figure 9-16: Scaling Procedure Required for Derivation

and as:

it is clear that: [75]

and:

Now, if the current flowing onto the DC Bus from the WECS is defined as , the operation of the

WECS in full can be described by the diagram in Figure 9-15. In order to complete the model of the

WECS, it is necessary to perform a power balance between the output terminals of the generator

and the output of the DC/DC converter. It is essential to realise that the power flow at each of these

stages in the system is exactly the same. The power coming from the DC/DC converter is:


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Therefore this is equal to the output power of the PMSG. This power can be expressed as:

And using the equation derived for generator power, it can be deduced that:

No zero sequence current flows in balanced 3 phase operation- hence:

Hence:


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9.2 Appendix B – Calculation of the Optimum Operating Conditions The power coefficient of the turbine is defined as follows:

In order to find the max possible we must differentiate it with respect to :

This yields the following:

For the model being used this yields:

And:


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9.3 Appendix C - Calculation of the Initial Conditions for WECS Model Constants

Vbus Pn P J Rs Ls

48V 5kW 28 7.856kgm2 0.3676Ω 3.55mH Φsr r Λopt Cp,opt ρ

0.2867Wb 1.84m 7.198 0.381 1.225kgm-3

Now that we have , can be found:

Now seeing as

During steady state

Letting and , yields a quadratic equation in :

This yields:

,

By letting

, the following equation is obtained:

These two results for will give two values for , given respectively:

,

9.4 Appendix D – Linearization of WECS This section details the linearization of the three characteristic non-linear equations that describe

the operation of the model, shown below:

In order for the equation to be linear we need the equation in the form:

AND

Begin with linearizing the equation:

Working out the individual elements:


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So,

Therefore,

To make the maths easier, some of the constants were combined to give one single constant. These

constants are detailed below.


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So,

By using simultaneous equations with the three main equations derived, the following equation is

obtained. In the Laplace domain:

Using this, the transfer function for the linear system is obtained:


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9.5 Appendix E- Subsystems of the WECS

Figure 9-17: Inside the "Find Tt" Subsystem

Figure 9-18: Inside the "Find Cp" Subsystem

Figure 9-19: Inside the "Find ωe" Subsystem

Figure 9-20: Inside the "Find ωm and tipspeed" Subsystem


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Figure 9-21: Inside the "Find Iq" Subsystem

Figure 9-23: Inside the "Find K" Subsystem

Figure 9-22: Inside the "Find Id" Subsystem

Figure 9-24: Inside the "Find Iw" Subsystem


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9.6 Appendix F- WECS Current Controller Test Configuration

Figure 9-25: Linear and Non-Linear System under Zeigler Nichols PI Controller


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9.7 Appendix G- Code for WECS Current Controller Design A=[-242.905, -52.655, 77.09; 1330.66, -3033.61, 16.81; -10.73, 0, -0.26];

B=[-7987.14, -1074.94, 0; -1741.87, -234.43, 0; 0, 0, 43.162];

C=[1,0,0];

D=[0,0,0];

[num, den]=ss2tf(A,B,C,D,1);

G=minreal(tf(num, den));

Td=1*10^(-3);

s = zpk('s');

d = exp(-Td*s);

L=d*G;

nyquist(L);

w=logspace(-2,4,100000);

[mag,phase]=bode(-G,w);

M(1:length(mag))=mag(1,1,1:length(mag));

MdB=20*log10(M);

P(1:length(phase))=phase(1,1,1:length(phase));

semilogx(w,P)

subplot(211), semilogx(w,M)

subplot(212), semilogx(w,P)

phi=-w.*Td.*180/pi();

New_P=phi+P;

subplot(211), semilogx(w,M)

subplot(212), semilogx(w,New_P)

bode(-L);

hold on

subplot(211), semilogx(w,MdB,'r'), grid, title('Magnitude Bode Plot of Inverted Linearized Model Incorporating Time Lag (dB)'), xlabel('Frequency (rad/s)'), ylabel('Magnitude (dB)')

subplot(212), semilogx(w,New_P,'r'), grid, title('Phase Bode Plot of Inverted Linearized Model Incorporating Time Lag (Degrees)'), xlabel('Frequency (rad/s)'), ylabel('Phase (Degrees)')


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9.8 Appendix H: Modelling of Solar Array

9.8.1 Shockley Diode Equation

Due to the doped nature of the semiconductor material which makes up a solar cell, the

concentration of free electrons within the n-region of the material is higher than that of the p-

region. Similarly, the concentration of free holes in the p-region is much higher than that of the n-

region. [92] This difference in concentration causes electrons to diffuse from the n-region to the p-

region. Similarly holes follow a path of negative concentration gradient, diffusing from the p-region

to the n-region. The resulting current densities are quantified below [122]:

At this point, it is important to note that between the p and n-regions, there exists an area of

separation called the depletion region. [92] Respectively, within the p and n-regions the density of

free holes and free electrons decreases with distance from the depletion region. The depletion

region contains no free charge carriers due to the effect of recombination which occurs due

diffusion of the high density of holes and electrons on either side of the gap. The result is as shown

in Figure 9-26. [123].

Figure 9-26: Concentration of Holes and Electrons within a Solar Cell [123]


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The depletion layer is divided into two regions- one containing negative ions and one containing

positive ions. Due to the electric charge differential caused by these ions, an electrostatic potential

which acts conversely to the effect of diffusion. The electric field produced causes holes from the n-

region to cross over into the p-region, and electrons from the p-region to cross into the n-region.

[92] The "drift" current density resulting from the respective crossings of holes and electrons due to

this effect is quantified in terms of the particles' mobility, concentration, and the magnitude of the

electric field [89]:

The Einstein equation shown below relates the mobility of holes and electrons to the diffusion

constants [124]:

The expressions for the total hole and electron current densities are shown below:

By conservation of electric charge, it can be found that:

*where is the saturation current density.

This is known as the diode equation. However, it is important to realise that this equation only

represents a portion of the current flowing in the PV cell. The photo current flow generated by

illumination ( ) is the sum of the diode current and the load current-hence:

*where, is the saturation current, and is the solar cell load current. This results in the ideal solar cell model shown in

Figure 9-27. [125]

Figure 9-27: Ideal Solar Cell Model


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The current through the p-n junction is therefore:

In order to improve this model, it is possible to take into account other factors which have been

ignored thus far [126]:

A series resistance is included in order to account for the resistance of the metallic grid/base

contacts at the edge of the p and n regions, as well as the resistance of the conductor used to

connect adjacent cells in the array. The resistance is often neglected as it is normally very small.

A parallel shunt resistance can be incorporated in order to account for the effect of leakage

within the semiconductor. This resistance is usually neglected as it generally has a very large

value, and hence results in a low level of leakage current which is often disregarded. [127]

Additional diodes are added to the equivalent circuit in order to account for additional effects.

For instance, the two diode model (so called “double exponential model”) used in [128]

accounts for the recombination of charge carriers. [88] A three diode model has also been

designed which incorporates the effects of grain boundaries within the model. [129]

Despite the additions which can be made to the solar cell model, the goal of this project does not

involve the detailed analysis of the performance of solar cells. It is generally accepted that a single

diode model incorporating a series resistance gives satisfactory and relatively accurate performance.

The equivalent circuit of such a solar cell is shown below:

Hence, now the equation for the current through the p-n junction becomes:

The thermal voltage of the diode is expressed as: [129]

Therefore this implies that:

Figure 9-28: Equivalent Circuit of Solar Cell Analysed (Single Diode & Series Resistance Only) [127]


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By incorporating the diode ideality factor ( ), this becomes:

This is known as the Shockley Diode Equation. [127] The diode ideality factor is included for the

purpose of accounting for diode non-idealities. For instance, in the case of the ideal diode, ,

however a non-ideal device usually has an ideality factor of . The effect of varying

from its ideal value of 1 is the curvature of the device I-V (and hence P-V) characteristic. The value of

should be chosen in order to optimise the accuracy of the model once it has been designed. [88]

Hence, the equation for the diode current of a single solar cell is:

9.8.2 Current Flow within the Equivalent Circuit

As stated earlier it is clear that:

It is now necessary to obtain expressions for the photo current and saturation current of the solar

cell. The photo current corresponding to the reference temperature of the device is given by the

expression below: [131]

At this point it is important to note that reference conditions (i.e. irradiance and temperature) are

specified on the device data sheet and correspond to STC (Standard Test Conditions) of: [132]

The actual photo current can be expressed as: [131], [133]

The upper expression shows that when the actual temperature of the device equals the reference

temperature, the actual photo current is equal to the reference photo current which is to be

expected. The short circuit temperature coefficient is given on some datasheets of the in terms of

. As expected, the photo current of the device is directly proportional to the level of solar

irradiance absorbed by the solar cell:


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However for the Shell SP70 solar panel which is being analysed in this report, the temperature

coefficient is instead given in terms of . Hence, the equation can be modified as follows:

Where is given in .

At this point it is necessary to acquire an expression for the reverse saturation current in the solar

cell. In order to achieve this, it is necessary to analyse the performance of the solar cell under open

circuit conditions at the reference temperature. As there is no path for the current, under such

conditions the current flowing from the terminals of the cell is in this case. Therefore:

As there is no current flowing through the series resistance of the device, the voltage across the

diode is equal to the voltage across the terminals of the device which is the open circuit voltage of

the cell (given on the datasheet of the solar panel).

It is approximated by authors ( [127], [134]) at this point in the derivation that the photo current in

this condition is equal to the reference level of short circuit current. This implies that:

However as the temperature of the solar cell deviates from the reference value, the reverse

saturation current is given by the expression below: [135]

As previously stated, the relationship between the currents flowing in the circuit is:

It is important to realise at this point that this expression is an implicit function of . This is due to

the fact that the output current variable appears on both sides of the equation and cannot be

isolated to find a solution. In order to implement this relationship within the model of the solar


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array, it is necessary to acquire an iterative solution for the variable . This is achieved by utilising

the Newton-Raphson algorithm. This procedure is carried out below:

Hence the Newton-Raphson algorithm states that:

Where:

This leads to the iterative solution:

The implementation of this solution will be explained in detail later in the report when the formation

of the Simulink model of the process is demonstrated.

9.8.3 Series Resistance

The series resistance of a solar cell varies with temperature in reality. However, for the purposes of

this project, a simplified model of the series resistance was developed equivalent to that shown in

[135] , [94], [136]. The approximation used assumes that the series resistance of a solar cell is equal

to its value at maximum power point and reference temperature and irradiance (25oC, 1000W/m2).

The formula used is as shown below:

It is important to note that the solar cell series resistance calculated using the above formula is

0.4387 .


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9.9 Appendix I- Shell SP70 Solar Panel Datasheet

Figure 9-29: Shell SP70 Datasheet [93]


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9.10 Appendix J- Solar Array Subsystems

Figure 9-31: Inside the "Ioact" Subsystem

Figure 9-30: Inside the "Iphact" Subsystem

Figure 9-32: Inside the "Rseries (Fixed Based on Reference Values)" Subsystem


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Figure 9-33: Inside the "f(x)" Subsystem

Figure 9-34: Inside the "f(x)’" Subsystem


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Figure 9-35: Inside the "6 Panels in Series" Subsystems

Figure 9-36: Inside the "First Branch" Subsystem

Figure 9-37: Inside the "Second Branch" Subsystem


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9.11 Appendix K – M-File Example for the Complete Microgrid %%Solar Array%% Voc3=3.65; Isc2=0.856667; Voc1=7.3; Isc1=0.428333; Imp2=0.805; Vmp2=2.9333; Vmp1=5.866667; Imp1=0.4025; Ksc=2*10^-3; Koc=-76*10^-3; q=1.60217646*10^(-19); k=1.3806503*10^(-23); Eg=1.12*q; a=7; Gref=1000; Tref=25+273.15; Tact=Tref; Vtref=k*Tref/q; Vtact=k*Tact/q; Gact=1000; Nseries=9; Nparallel=4; Vocref=21.4/9; Impref=4.25/4; Vmpref=16.5/9; Iscref=4.7/4; t=1000; %seconds %%Wind Turbine%% Rwind=.3676; L=3.55e-3; P=28; J=7.856; flux=0.2867; rho=1.225; vb=48; u=6.46; v=12.629; r=1.84; tipspeedopt=7.198; pi=pi();

%%Battery%% %Lithium-Ion Battery Parameters V0=3.5; R=0.01; K=0.025; A=0.2; B=0.375; Q=144000; % As

Vnom = 3.2; %V Voc=3.675; %IC=0A ncells=15; Vbpack=ncells*Vnom; Qnom=Vbpack*Q; %------------------Integrator Parameters------------------ qhigh = 0.9*Q; qlow = 0.2*Q;


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%-------------- Function Parameters ------------------------------ tsampi = -1; tsampvoc = -1; %--------------------------------------------------------- %(CP) - Variables for Constant Power qic = 0.21*Q; tsamp = 0.01;

%------------Grid to Batter Charging Power-----------------------% Power_From_Grid_To_Battery=-4800;

%----------------------------------------------------------------%

%------------------Wind Changes -------------------------%

Wind_Slope_Time = 700;%hours.... Wind_Slope_Duration = 60; Wind_Speed_Initial=v; %Initial Condition: Do not change Desired_Final_Value=v;

Wind_Speed_Slope = (Desired_Final_Value-

Wind_Speed_Initial)/Wind_Slope_Duration; %0 for no ramp

Wind_Slope_Counter_Time = Wind_Slope_Duration + Wind_Slope_Time; Wind_Speed_Initial_Counter = 0; %Keep 0

%----------------------------------------------------------------%

%------------------Solar Array Changes---------------------------%

%---Change 1---% Gact_Slope_Desired = 200; Time_For_Slope =20;

Gact_Slope_Time =20; Gact_Slope = (Gact_Slope_Desired - Gact)/Time_For_Slope;

Gact_Slope_Counter_Time = Gact_Slope_Time + Time_For_Slope; %This stops the

intitial ramp to desired value

%------------%

%---Change 2---% Gact_Slope_Desired_2 = 1500; Time_For_Slope_2 =20;

Gact_Slope_Time_2 =700; Gact_Slope_2 = (Gact_Slope_Desired_2 -

Gact_Slope_Desired)/Time_For_Slope_2;

Gact_Slope_Counter_Time_2 = Gact_Slope_Time_2 + Time_For_Slope_2; %This

stops the intitial ramp to desired value

%------------%

%------------------Pricing -------------------------%

Buy_High = 2;


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Buy_Low = 1; Actual_Buying_Price_Initial=2.5; Actual_Buying_Price_Final = 1.5; Buying_Step_Time = 430; Buying_Step_Change_Time=550; New_Buying_Value=0.5; Buying_Change_Required=New_Buying_Value - Actual_Buying_Price_Final;

Sell_High = 3; Actual_Selling_Price_Initial = 2; Actual_Selling_Price_Final = 2; Selling_Step_Time = 9;

%--------------------------------------------------%

%------------------Load Changing -------------------------%

%-----Non-Critcial-----%

Non_Crit_Load_Size = -100;

NonCrit_Load_Change=-800; %Negative to increase load

NonCrit_Load_Step_Time = 0;

NonCrit_Load_Change2=0; %Negative to increase load

NonCrit_Load_Step_Time2 = 3;





%----------------------%

%-------Critcial-------%

Crit_Load_Init=-5000; %Negative to increase load

Crit_Load_Change=0; %Negative to increase load

Crit_Load_Step_Time = 2;

Crit_Load_Change2=0; %Negative to increase load

Crit_Load_Step_Time2 = 4;

Crit_Load_Change3=0; %Negative to increase load

Crit_Load_Step_Time3 = 6;

%----------------------% %---------------------------------------------------------%


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9.12 Appendix L – Indexes for Supervisory Switches

Pws < Pload

Grid-Battery

SOC High Price Medium Price Low Price

Supply 4.8kW to Battery

0.2 7 140 -7

No Supply

0.2-0.4 15 300 -15 0.4-0.6 10 200 -10 0.6-0.9 2 40 -2 0.9 1 20 -1

Battery-Loads SOC High Price Medium Price Low Price 0.2 7 140 -7

Supply Total Load - WS Supplied Loads

0.2-0.4 15 300 -15

No Supply

0.4-0.6 10 200 -10 0.6-0.9 2 40 -2 0.9 1 20 -1

WS - Load Condition No. Condition Condition Value

1 PWS<PLoad -6 2 PWS>PLoad -3 3 SOC = 0.2 + High Price 1 4 SOC Not Equal to 0.2 + High Price 0 5 PWS<Pcrit 20

6 PWS>Pcrit 10 Combinations Value

Supply the Complete Generated Power 1,3,5 15

1,3,6 5

Rounding the Generated Power due to Load Shedding

1,4,5 14 1,4,6 4 2,3,5 18 2,3,6 8 2,4,5 17 2,4,6 7 Table 9-1; Indexing for PL > PWS


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*Note that the combinations including option 1 apply to the top block (See Section 0) for the supervisor control while the

options including option 2 apply to the bottom block. Hence in the top block, the selections including option 2 output a

value of zero. If this did not occur, both the top and bottom blocks would output the desired value and the resulting power

to the loads would be doubled.

Pws > Pload

WS-Grid SOC High Price Low Price <=0.5 15 15

No Power to Grid

0.5<SOC<0.9 10 -10

PWS - Pload to Grid

0.9 1 -1

WS-Battery

SOC High Price Low Price <=0.5 15 15

No Power to Batt

0.5<SOC<0.9 10 -10

PWS - Pload to Batt

0.9 1 -1 Table 9-2: Indexing for PWS > PL

These tables can be quite confusing so a set of flow charts were designed to show more simply how

the decisions are made.


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9.13 Appendix M – Supervisor Control Blocks of Complete Microgrid

Figure 9-38: Display of Top and Bottom Supervisor Blocks in the Microgrid Model


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Figure 9-39: Top Supervisor Block

Figure 9-40: Bottom Supervisor Block

Documents

Co-ordinated Control of Microgrids