wmrnun * nsmtuwa, m umA 
VOLTAGE STABILITY ANALYSIS OF A GRID 
CONNECTED WIND FARM 
A dissertation submitted to the 
Department of Electrical Engineering, University of Moratuwa 
in partial fulfillment of the requirements for the 
Degree of Master of Science 
by 
R.D. Nagodavithana 
University of Moratuwa 
102531 
Supervised by: 
Dr. Narendra De Silva 
Dr. J.P. Karunadasa 
Department of Electrical Engineering 
University of Moratuwa, Sri Lanka /0 253I 
October, 2011 
102531 
Declaration 
The work submitted in this dissertation is the result of my own investigation, except 
where otherwise stated. 
It has not already been accepted for any degree, and is also not being concurrently 
submitted for any other degree. 
R.D. Nagodavithana 
25/10/2011 
0 
We endorse the declaration of the candidate 
Dr. Narendra DeSilva 
t 
Dr. J.P. Karunadasa 
Contents 
Declaration i 
Contents ii 
Abstract v 
Acknowledgement vi 
List of Figures vii 
List of Tables ix 
1 Introduction 1 
2 Theoretical Development 4 
3 Development of system component models 6 
3.1 Transmission Line Model 6 
3.1.1 Extension to three phase system 8 
3.2 Induction motor model 13 
3.2.1 Dynamic equation of induction motor 13 
3.3 Wind turbine model 23 
3.4 Generator soft starter 23 
3.5 Capacitor bank 24 
3.6 Power transformer 24 
4 Calculation of model parameters 25 
4.1 Transmission line parameters 25 
4.1.1 Self Impedance 25 
4.1.2 Mutual impedance 27 
4.1.3 Transmission Line Capacitance 29 
4.2 Transformer impedance 31 
4.3 Capacitor bank 31 
4.4 Turbine parameters 31 
4.5 Induction Generator Parameters 34 
4.6 Conversion to per unit parameters 35 
4.6.1.1 Induction Motor Performance Data as Given by the Model 36 
4.7 Performance data for a single generator 36 
4.7.1 Simulation at Zero Wind Speed 37 
4.7.2 Simulation at 15m/s Wind Speed 39 
4.7.3 Torque vs Speed characteristics 40 
4.7.4 Simulation of Single Generator at end of long transmission line 40 
4.7.4.1 Varying voltage profile with constant wind speed 42 
4.7.4.1.1 Case 1: Wind speed 3m/s & voltage at increase from -10% to 
+10% in 2.5% steps 42 
4.7.4.1.2 Case 2: Wind speed 5m/s & voltage at increase from -10% to 
+10% in 2.5% steps 45 
4.7.4.1.3 Case 3: Wind speed 9m/s & voltage at increase from -10% to 
+10% in 2.5% steps 47 
4.7.4.1.4 Case 4: Wind speed 15m/s & voltage at increase from -10% to 
+10% in 2.5% steps 50 
5 Stability Analysis 53 
5.1 Case 1: Wind speed Om/s & voltage at increase from -10% to +10% in 2.5% 
steps 55 
5.2 Case 2: Wind speed 5m/s & voltage at increase from -10% to +10% in 2.5% 
steps 58 
iii 
5.3 Case 3: Wind speed 9m/s & voltage at increase from -10% to +10% in 2.5% 
steps 61 
5.4 Case 4: Wind speed 15m/s & voltage at increase from -10% to +10% in 
2.5% steps 64 
5.5 Low voltage ride through behavior 67 
6 Conclusions 70 
References 71 
Annexure A: Calculation and plotting of simulation data 72 
Appendix B: Simulink model of induction motor 75 
Appendix C: Simulink model of wind farm 76 
Appendix D: Calculation of model parameters within matlab 77 
Annexure E: Datasheet of Induction Generator 83 
Abstract 
Voltage instability is one of the problems that can cause a wind farm to shut down 
without any warning. The resulting sudden drop or generation can lead to large power 
system faults. The voltage instability issue mainly plagues one type of wind farm. The 
squirrel cage induction generator fed wind farms. This is due to the lack of reactive 
power support in this type of generators. 
To assess the stability of such wind farms a dynamic model of wind farm has been 
developed by accumulating the following models. 
1. Squirrel cage induction machine 
2. Wind turbine 
3. Transmission line 
4. Transformer 
5. Capacitor bank 
Model parameters were calculated and simulations were performed for a wind farm 
consisting of eight wind turbine generators each with a capacity of 1805kVA. 
Stability was assed for normal 33kV national grid level network voltage variations of 
± 10% of rated Voltage. The wind farm is shown to be stable for this variation and 
operated within normal parameters. 
The wind farm was also checked for LVRT capability and found to be within CEB 
specifications. 
Acknowledgement 
My sincere gratitude is extended to Dr. Narendra DeSilva and Dr. J.P. Karunadasa for 
their guidance in completing this work. Further I would like to mention my course 
coordinators Professor Ranjith Perera and Dr. 'Asanka Rodrigo for making the M.Sc 
program an enjoyable one to me. 
My thanks also goes to my parents for their encouragement to pursue this program. 
Further I would also like to thank all the lecturers that have thought me at the M.Sc. 
program. 
vi 
List of Figures 
Figure Page 
Figure 3.1: Single Phase Transmission Line Model 7 
Figure 3.2: Cascaded Single Phase Transmission Line Model 7 
Figure 3.3: Three Phase Line Section 8 
* Figure 4.1: Transmission Line Capacitance 29 
Figure 4.2: Turbine Power Curve 33 
Figure 4.3: Simulation of Single Generator at Zero Wind Speed 37 
Figure 4.4: Simulation of Single Generator at 15m/s Wind Speed 39 
Figure 4.5: Torque Vs Speed characteristics at various terminal voltages 40 
Figure 4.6: Grid Voltage - Case 1 42 
Figure 4.7: Grid Current - Case 1 43 
Figure 4.8: Transformer Voltage - Case 1 43 
Figure 4.9: Active & Reactive Power - Case 1 44 
0 Figure 4.10: Rotor Speed - Case 1 44 
Figure 4.11: Grid Voltage - Case 2 45 
Figure 4.12: Grid Current - Case 2 45 
Figure 4.13: Transformer Voltage - Case 2 46 
Figure 4.14: Active & Reactive Power - Case 2 46 
Figure 4.15: Rotor Speed - Case 2 47 
Figure 4.16: Grid Voltage - Case 3 47 
Figure 4.17: Grid Current - Case 3 48 
Figure 4.18: Transformer Voltage - Case 3 48 
• Figure 4.19: Active & Reactive Power - Case 3 49 
Figure 4.20: Rotor Speed - Case 3 49 
Figure 4.21: Grid Voltage - Case 4 50 
Figure 4.22: Grid Current - Case 4 50 
Figure 4.23: Transformer Voltage - Case 4 51 
Figure 4.24: Active & Reactive Power - Case 4 51 
Figure 4.25: Rotor Speed - Case 4 52 
Figure 5.1: Grid Voltage - Case 1 55 
vii 
Figure 5.2: Grid Current - Case 1 55 
Figure 5.3: Voltage at Common Point - Case 56 
Figure 5.4: Current at Common Point - Case 1 56 
Figure 5.5: Active & Reactive Power - Case 1 57 
Figure 5.6: Rotor Speed - Case 1 57 
Figure 5.7: Grid Voltage - Case 2 58 
Figure 5.8: Grid Current - Case 2 58 
Figure 5.9: Voltage at Common Point - Case 2 59 
Figure 5.10: Current at Common Point - Case 2 59 
Figure 5.11: Active & Reactive Power - Case 2 60 
Figure 5.12: Rotor Speed - Case 2 60 
Figure 5.13: Grid Voltage - Case 3 61 
Figure 5.14: Grid Current - Case 3 61 
Figure 5.15: Voltage at Common Point - Case 3 62 
Figure 5.16: Current at Common Point - Case 3 62 
Figure 5.17: Active and Reactive Power - Case 3 63 
Figure 5.18: Rotor Speed - Case 3 63 
Figure 5.19: Grid Voltage - Case 4 64 
Figure 5.20: Grid Current - Case 4 64 
Figure 5.21: Voltage at Common Point - Case 4 65 
Figure 5.22: Current at Common Point - Case 4 65 
Figure 5.23: Active & Reactive Power - Case 4 66 
Figure 5.24: Rotor Speed - Case 4 66 
Figure 5.25: Grid Voltage - LVRT 67 
Figure 5.26: Grid Current - LVRT 68 
Figure 5.27: Voltage at Common Point - LVRT 68 
Figure 5.28: Current at Common Point - LVRT 68 
Figure 5.29: Active & Reactive Power - LVRT 69 
Figure 5.30: Rotor Speed - LVRT 69 
viii 
List of Tables 
Table Page 
Table 4.1: Turbine Power Curve Data 32 
Table 4.2: torque coefficients of turbine 34 
Table 4.3: Generator Details 35 
Table 4.4: Comparison of Datasheet values and Simulation values 36 
ix