. Discussion of Results

The convergence characteristics of the newly developed simultaneous method of power flow is compared with the existing sequential method of power flow analysis and it is found that the simultaneous method results in less number of iterations.

For the particular WECS modelled, the effect of increasing the number of turbines with and without compensation is summarized in Table 7.2. From Table 7.2 it is seen that when the transmission line between the PCC and the grid is strengthened (with 5 parallel lines), 13 turbines can be connected and thus more power can be fed into the grid. The voltage profile at the WECS terminals is also found to improve, although the reactive power drawn from the grid is very large. Yet such strengthening is not cost effective, being the equivalent of having 5 lines in parallel. Therefore, the effect of different types of compensation is studied.

Table 7.2 shows that with shunt compensation, there is improvement in voltage profile and decrease in the reactive power demand. The line current reduces
thereby reducing transmission losses. The net effect is an improvement in power factor. With series compensation, there is improvement in voltage profile, although there is increase in the reactive power demand. The line current drawn is com­paratively large, yet more turbines can be connected on-line. The net effect is an improvement in real power penetration. With series-shunt compensation there is a considerable improvement in voltage profile. At the same time, the reactive power demand and the line current drawn are both reduced compared to series com­pensation alone and are comparable with shunt compensation. A combination of series compensation equal to 50 % of line reactance and shunt compensation of 150 kVAR, shows better performance as compared to either series or shunt compensation alone, for the 9-bus radial system considered. Thus with the correct choice of capacitor sizes, a combination of series and shunt compensation can be used to improve the overall system performance.

In Table 7.2, V—voltage at WECS terminals at rated speed, P—Real power generated at rated speed, Q—Reactive power demand at rated speed, I—Line current at rated speed, A—Uncompensated system (1—without line strengthening, 2—with double circuit line, 3—with 5 lines in parallel), B—Shunt Compensation (1-150, 2-200, 3-250 kVAR), V, P, Q and I values with 5 turbines on-line, C— Series Compensation (1-0.5 Xline, 2-0.75 XUne)—V, P, Q and I values with 10 turbines on-line, D—Series-shunt Compensation (1-Xse = 0.5 Xline and Qsh = 150 kVAR, 2-Xse = 0.75 Xline and Qsh = 200 kVAR)—V, P, Q and I values with 10 turbines on-line.

To summarize, the following are recommended:

1. To strengthen the grid to evacuate the maximum power output from the wind farms, corresponding to installed rated capacity. This is to ensure harvesting of the wind power in the windy seasons.

2. To go in for appropriate value of series-shunt capacitor compensation with grid connected induction generators.

Appendix I

Data for 9-Bus Radial System 1. Transmission Line Data (All Lines)

Подпись: 0.24 X/km 0.48 X/km 2.80 pS/km 20.0 kmResistance




Table A.1 Transformer data


Load transformer data (all)

Step up transformer data (at the wind bus)


transformer data

Rated apparent power

0.63 MVA

1.0 MVA

25 MVA

Rated voltage of MV side

15 kV

15 kV

110 kV

Rated voltage of LV side

0.4 kV

0.69 kV

15 kV

Nominal short-circuit voltage

6 %


11 %

Copper loss at rated power

6 kW

13.58 kW

110 kW

2. Load Data (All Loads)

0.150 ? j0.147 MVA


Подпись: Fig. A.1 Cp—k curve for the considered wind turbine

Coefficients of Cp—k Curve













Gear box ratio


Asynchronous Generator Data (D-Connection)

Stator resistance

0.0034 X

Rotor resistance

0.003 X

Stator leakage reactance

0.055 X

Rotor leakage reactance

0.042 X

Magnetizing reactance

1.6 X

Appendix II

Jacobian Matrix for the 9-bus System

For the system considered the Jacobian is a (17 x 17) matrix as below. The numbers in the matrix represent the row and column of the elements. The ana­lytical expressions for these elements are given in the subsequent sections.

(1, 1)



(1, 16)


(8; 1)



. . ,J2. . .


. . .J5 . . .


(9; 1)






(16, 8)


. . J4. . .


.. J..



. . ■ J7. . ■

(17, 8)





1 Elements of J1

Подпись: OPi . rn = imag X vj

. J¥=i



. Discussion of Results Подпись: + 2ViLreal{Yij)

Elements of J2

O D, г

OV|Vj| = rea^V;VjY(j Diagonal element for WECS bus (bus 9),

J(8; 16)= J(8, 16)- 22V9| ?2Є (r2 + x2)

3 Elements of J3

Подпись: realX/ ViVjYy

_ jV*’

Подпись: OQi 00j real[XV* VY

. Discussion of Results

4 Elements of J4


. Discussion of Results

— 2| Vi|2rea/(Yy)


. Discussion of Results

Diagonal element for WECS bus (bus 9),


. Discussion of Results
. Discussion of Results
. Discussion of Results

9 Elements of J9


. Discussion of Results

These are given by Eqs. (7.13) to (7.18).




1. Liangzhong Y, Phill C, Laurent S, Xiao-Ping Z (2005) Congestion management of transmission systems using FACTS. In: IEEE/PES transmission and distribution conference and exhibition, Asia and Pacific, Dalian, China, pp 1-5

2. Slootweg J, Polinder H, Kling W (2001) Initialization of wind turbine models in power system dynamics simulations. In: IEEE Porto power tech proceedings, p 7


Updated: October 23, 2015 — 12:41 pm