The performance of a 1.5-kW WDSERG with series and shunt capacitors is examined using MATLAB/Simulink. Table 1 gives the SERG parameters used in the simulation. The simulation results are obtained with variable wind speeds, load impedances and power factor. The output load voltage is controlled at 220 V with a desired output load frequency at 50 Hz.
The corresponding value of Xds for each value of d-axis current ids is obtained from magnetization curve, which are represented by 6th-order polynomial equation as shown:
$$X_{ds} = - 0.002839i_{ds}^{6} + 0.10299i_{ds}^{5} - 1.1798i_{ds}^{4} + \,\,5.5572i_{ds}^{3} - 7.9918i_{ds}^{2} - 30.4452i_{ds} + 182.1$$
(27)
Minimum capacitor required for SERG at no load
At no load, the value of minimum capacitance required to build up the generator terminal voltage depends on the generator output frequency, i.e., rotor speed, variation as shown in Eq. (11). Furthermore, using the differential equations stated in the previous sections, a dynamic model of SERG at no load and constant speed is created using MATLAB/Simulink. PI controller is used to control the speed of generator by toque variation. The excitation capacitance value is decreased gradually until the terminal voltage of SERG disappeared and minimum capacitor value is recorded. The relation between minimum capacitance and the SERG rotor speed, which is shown in Fig. 5, can be obtained by repeating the above procedure for other generator speeds. A good agreement between the calculate and simulation results is shown in Fig. 5, which provides a straightforward validation of the dynamic model of SERG and the mathematical study presented in Eq. (11) to determine the minimum capacitor for output voltage generation.
Optimal capacitance required with variable load impedance for WDSERG
The study is performed for two configurations under variable load characteristic with constant power factor 0.9 lag and constant wind speed equal to 8.5 m/s. The generator will run at no load for 25 s; then, a lagging power factor load (R = 300 Ω and L = 450 mH) is connected to the generator terminal. Finally, the load is changed to R = 200 Ω and L = 300 mH at t = 45 s. Under no-load condition, the two configurations gradually build their voltages.
Figure 6 shows the simulation results for short-shunt compensation with variable load impedance. In this configuration, the shunt capacitor is used to control the output frequency at 50 Hz and the series one is used to control the output load voltage at 220 Vrms. Under no-load condition, the generator voltage builds up and the voltage level increased in no-load period to 240 V because there is no control on voltage level due to disconnection of series capacitor as shown in Fig. 6a. At any load current increasing instant, there will be an increase in the generator current, which will increase the voltage drop on the stator impedance of the generator. Therefore, there is a drop in the load voltage, with each load current increasing, before the voltage controller takes action and restores the load voltage again to its desired value by changing the series capacitor value. Figure 6b shows the rotor speed; it is noticed that there is a decrease in the speed (undershoot) with each load current increasing step because of the increase in generator current; therefore, the load torque on the turbine is increased. So, the speed control will decrease the shunt capacitor value as shown in Fig. 6c. The reduction of the shunt capacitor will decrease the shunt capacitor current, which will decrease the overall generator current. The decrease in the generator current leads to decrease generator losses and the rotor speed increases across the wind turbine characteristics shown in Fig. 2. The rotor speed increases until the summation of the load power and generator losses are equal to the value before the load variation and the rotor speed restore its desired value at 1500 rpm.
Figure 6c shows also the required series capacitance value to maintain the load voltage constant. At no load, it is observed that the series capacitor value reaches its maximum limit as it is not connected in this period. The change in generator, shunt capacitor and load currents with load current increasing is shown in Fig. 6d. The generator voltage value depends on the reactive power from series and shunt capacitor that build field in SERG. Therefore, the reduction in shunt capacitor value will cause decrease in shunt capacitor current, reactive power supplied to the generator, and hence, generator voltage decreases as shown in Fig. 6e.
In long-shunt compensation, the series capacitor is used to control the output frequency at 50 Hz, and the shunt one is used to control the output load voltage at 200 V. In Fig. 7a, there is a reduction in load voltage with increasing the load current until the controller decreases shunt capacitor value in order to decrease shunt capacitor current and generator current. As a result, the voltage drop on series capacitor and stator impedance will decrease so the load voltage will increase again. Unlike short-shunt compensation, the load voltage can be controlled even in no-load condition because the shunt capacitor is always connected to the generator.
In Fig. 7b, it observed that the increase in load current would result in increased speed. The generator speed can be controlled at 1500 rpm with increasing loading current by increasing the capacitance of the series capacitor as shown in Fig. 7c.
Using series capacitor, the wind turbine output power can be controlled to adjust speed again. The value of shunt capacitor should be decreased to maintain the output voltage at 200 V as shown in Fig. 7c as increasing the load current connected to SERG would reduce load voltage. Figure 7d shows the change in generator, shunt capacitor and load currents with load current increasing. Furthermore, there will be drop in generator voltage due to decrease in shunt capacitor value as shown in Fig. 7e. This decease results in drop in reactive power supplied from shunt capacitor that represents the field in SERG.
It can be noticed that generator and load currents in two configurations are the same. However, long-shunt compensation configuration yielded higher-shunt capacitor current and required higher capacitors value. Hence, short-shunt configuration is a preferable choice.
Optimal capacitance required under variable load current and lagging power factor for WDSERG
Series and shunt capacitors are used to achieve constant voltage level in short- and long-shunt compensation, respectively. In case of short-shunt compensation, series capacitor value is directly proportional to loading current and power factor. The increase in the capacitor value, with increased loading conditions, is large with higher power factor as shown in Fig. 8a.
For long-shunt compensation, Fig. 8b shows the relation between shunt capacitor value and loading current. Generally, for constant output voltage, the more increase in loading current and power factor, the less capacitance required. There will be change in speed when the load is increased as discussed in previous section and controllers will take actions to maintain speed at a desired level. Figure 8c, d shows shunt and series capacitors required to adjust frequency at 50 Hz in the short- and long-shunt compensations, respectively. In short-shunt compensation configuration, the required shunt capacitor value to adjust speed is inversely proportional to load current and power factor. On the other hand, series capacitor value has a direct relationship with the load current and power factor in long-shunt compensation configuration.
It is seen from Fig. 8 that the change in the shunt and series capacitors in long-shunt compensation is higher than in short-shunt compensations. This will reflect in a large variation in the duty cycle of the inverter switches to get the overall required range of capacitances.
Optimal capacitance required under varying wind speed and lagging power factor
When wind speed is increased, the load voltage will also increase and the controllers will take action to make load voltage profile constant. In short-shunt compensation, series capacitor value drops with increasing wind speed to adjust voltage level at a desired value as shown in Fig. 9a. On the other side, Fig. 9b illustrates that the shunt capacitor value requirement is significantly increased with rise in wind speed to adjust voltage profile also for long-shunt compensation.
The increase in wind speed will increase in generator speed and frequency of output voltage. As a result, the controller will try to change the capacitance value to adjust the frequency again. Figure 9c, d illustrates the value of shunt and series capacitors, which are needed to keep generator speed constant in the short- and long-shunt compensations, respectively. In particular, under constant voltage profile, low power factor requires low series capacitor value in the long-shunt compensation; in contrast, low power factor requires high shunt capacitor value in the short-shunt compensation. It is noticed that the variation of load power factor has a very small effect on the values of the shunt and series capacitors.