Voltage and frequency control of standalone wind-driven self-excited reluctance generator using switching capacitors

This paper presents a methodology for voltage and frequency (V–f) control of a standalone wind-driven self-excited reluctance generator (WDSERG). The methodology is based on proposing two different compensation configurations using two switching capacitors (short-shunt and long-shunt compensation) for (V–f) control. The dynamic and steady-state performances of the two configurations are discussed under different operating conditions: wind speeds, load currents and power factors. This analysis is done by developing a complete dynamic model of WDSERG including the excitation capacitors and load. Therefore, complete equivalent circuits are proposed. The values of capacitors are controlled by adjusting the duty cycle of H-bridge circuits with PI controllers. To validate the proposed configurations and their dynamic models and equivalent circuits, simulation results for a 1.5-kW standalone WDSERG and experimental results for 0.2 kW reluctance generator driven by a DC motor, emulating the wind turbine, are carried out. The results show a significant enhancement in voltage and frequency regulation with the selected optimal capacitances for each configuration; however, short-shunt compensation is the preferred configuration as it controls the output voltage and frequency with minimum values of capacitances and minimum required duty variation.

many remote locations, the grid disconnection motivates the option of utilizing standalone wind turbine with the use of self-excited induction and reluctance generators [10,36].
In both direct-driven mode and with single-or multistage gearbox, PMSG wind system could be more efficient than DFIG system [38]. High torque density, reduced rotor thermal stress and high energy conversion efficiency are the key benefits of using PMSG due to the existence of the PM in the rotor [16]. Cost of PM materials, PM demagnetization at high temperature and cogging torque effects are the major PMSG using limitations [22]. However, due to dependance of PMSG output voltage and frequency on wind speed, PMSG cannot be connected directly to grid; therefore, a power conversion system should be used to adjust the injected grid power. For variable speed, fixed pitch WECSs, torque and speed control strategies are analyzed and presented in [13], which would increase robustness and reliability of the generator.
Owing to its lowest cost, robustness, less converter rating requirements and no need for a DC source for excitation, DFIG wind turbine is the most commonly used one in the market [17]. However, the brushes and slip rings existence on the DFIG rotor require regular maintenance. Therefore, the remote and offshore application of DFIG is less reliability and more cost [24].
The concept of DFIG normal operation when connected to the grid is presented in [21]. Maximum active power extraction and reactive power control are discussed; however, the concept and enhancement techniques for fault ride through, crowbar protection, torque pulse compensation and stator unbalance are established.
The target in standalone WECS is to sustain voltage and frequency under changing wind speeds and loads. However, the DFIG is inappropriate for small standalone applications where low cost is the most priority due to its great size, high cost and massive complexity related to the DFIG design, assembly and control [28].
The most important factors in the generator's selection are cost and control simplicity. In this view, alternatives for PMSG and DFIG are self-excited generators due to their relative low cost. Therefore, in recent years, there is significant increase in the research and development of SEIG and SERG for standalone systems. The primary advantages of a SEIG are brushless construction with squirrel-cage rotor, rugged and robust rotor, no DC supply for excitation, small size and less maintenance cost. In addition, it has better transient performance [34].
For isolated SEIG, the steady-state performance is analyzed and studied taking into consideration the machine core losses and their variation with air gap flux. This study is obtained with a SEIG feeding a balanced inductive load [20]. Firstly, the machine must operate in saturation region for a stable operation of SEIG. Minimum excitation capacitance required at no load to control the generator terminal voltage at its desired constant value is calculated through this study. Besides, the study gives the required capacitance value to keep the generator terminal voltage at constant value under wind speed, load impedance and power factor variations. The variable excitation capacitance value is provided by fixed capacitor thyristor-controlled reactor. In [5], the continuously controlled shunt capacitor connected to SEIG is utilized in the proposed SEIG. The variable excitation capacitor could be done by employing back-to-back connected IGBT switches across the fixed excitation capacitors to regulate the terminal voltage. The results proved that over wide variety of loads and speed changes, a constant generator terminal voltage is achieved by the controlled shunt capacitor of SEIG and hence is a reliable and cost-effective.
SEIG simplicity makes it relatively inexpensive and popular in isolated WECS applications. In addition, it is self-protected counter to extreme overload and short-circuit possibilities [7]; however, an attendant needs for voltage and frequency stabilizing circuits to overcome poor regulation in generator output voltage and frequency with variable prime-mover speed and load. This will increase the installation cost [33].
The SERG with wind energy is practically utilized in electric power generation [31]. SERG is commonly used with standalone wind turbine. However, it can be also utilized in gird-connected wind turbine system. When SERG is connected to an isolated load, a capacitor bank should be connected to the generator terminals to achieve successful excitation. In case of grid-connected wind system, a local capacitor bank connected at the generator terminals or leading power factor loads could be the methodology for getting the required excitation [32]. In [9], the criteria of selecting the suitable excitation capacitance for a SERG driven by regulated turbine (constant frequency) are presented. By applying this methodology, AC constant output terminal voltage would be produced under changing the connected load.
Since the most works are based on PMSG and SEIG for standalone WECS, the use of SERG has paucity literature with standalone WECS. Besides having almost all the induction generator advantages, the frequency of SERG output voltage could be directly adjusted through controlling the rotor speed [30]. The performance characteristics of SERGs have been determined by different proposed methods [23]. In [14], the two-axis theory is used to study the steady-state model of SERG, which supplies an inductive load. Core losses are neglected, and magnetic saturation is assumed to be confined to the direct axis and is accounted for by a variable direct-axis magnetizing reactance. The theory developed also enables a direct computation of the minimum capacitance required to initiate self-excitation for a given value of load impedance. The value of minimum load resistance, connected to the stator's terminals of SERG in standalone mode, could be determined by eigenvalue and eigenvalue sensitivity [35]. The effect on the SERG performance due to variation in excitation capacitor, wind speed, and load is introduced in [4]. Moreover, under open-circuit, resistive and pure inductive loads, expressions for the cutoff speed value are also derived and presented in [3]. In [25], the effect of rotor cage on the performance of SERG supplying loads of different power factors is presented. The cageless SERG can only deliver less than half the rated power, while more than twothirds of the rated power could be produced by SERG with a cage. This is due to the inability of the cageless machine to excite at capacitance values high enough to circulate the rated current in the machine windings. New methods of studying the machine characteristics are based on equations between SERG parameters and external load. Then, comparisons between these methods and conventional methods are held for machine parameter measurements [11].
A mathematical model that can successfully predict the dynamic performance of single-phase SERG is presented in [2]. This model is used to study the dynamic stability of the generator under different operating conditions. The minimum excitation capacitance required for single-phase SERG is affected by the speed fluctuations [1]. Due to its poor reactance ratio, poor power factor is one of the major disadvantages of synchronous reluctance machine with simple salient rotor. Improving the performance characteristics, by improving the effective reactance ratio, can be achieved by splitting the stator winding to two three-phase windings. The grid is connected to one-stator winding, and the other winding is attached to a balanced capacitor bank [26]. In [27], dual winding reluctance generator with mixed poles is analyzed to determine its performance characteristics. In this paper, two different capacitors connections (short-and long-shunt compensation configuration) for a WDSERG are presented. Dynamic models and equivalent circuits for each configurations of compensation are developed. For most practical application, it is always required to obtain efficient energy production and constant output voltage and frequency from a WDSERG. Regulating voltage and frequency of SERG are obtained by using shunt and series switched capacitors at a certain value under different wind speeds and/or loads. A selection method of optimal capacitor values, to maintain an efficient energy production, which can be implemented in a controller, is presented. The value of each capacitor is controlled by adjusting the duty cycle of H-bridge circuit with PI controllers. PI controller gains are selected using the trial-and-error method to get the best response. Comparison between capacitor values in the two configurations is obtained to determine which one is preferable. To validate the theoretical analysis and the model of the two different compensation configurations, single-point experiments for a given value of shunt capacitor, series capacitor and load impedance were performed in the laboratory. Figure 1 shows the schematic of WDSERG system connected to an isolated load. The system consists of unregulated wind turbine coupled with the reluctance generator through a gearbox. The generator output voltage and frequency are fluctuating with wind speed changing and load variation. So, two capacitors, connected in series and shunt, are used to regulate the output voltage and frequency. The two compensation capacitors could be connected in two different configurations. The two configurations are short-shunt and long-shunt compensations as shown in Fig. 1.

Wind turbine model
The wind turbine output mechanical power can be defined by [37]: (1)

Dynamic model of SERG at no load
The self-excitation of the SERG is done using shunt capacitor. The machine must operate in the saturation region, and sufficient rotor speed and residual flux are required to initiate the self-excitation of SERG, and then, voltage starts building up which will be limited by the core saturation at steady state.
The following assumptions are taken in consideration in steady state and dynamic models: 1. MMF and flux density distributions are sinusoidal 2. Balanced operation of SERG 3. Neglect core losses

Magnetic saturation in the d-axis only
The current equations for SERG, without damper windings, in the d-q rotor reference frame are given by [19]: where the current equations, in the d-q rotor reference frame, of the shunt capacitor are described by [19]: The electromagnetic torque of the generator can be given by: where the stator flux linkages in the d-q axes are given by: The mechanical equation of the generator can be written as: When the SERG operates at no load, a closed-form solution for minimum capacitor value (C min ) could be obtained if the core loss is neglected [14].
When the armature resistance is very small, This means that the machine will self-excite if X c is less than X dun .

Dynamic model of short-shunt compensation with load
The mathematical model of the short-shunt compensation configuration of WDSERG shown in Fig. 1a can be derived using the equivalent circuit of the system shown in Fig. 3. The current equations for reluctance generator, without damper winding, in the d-q rotor reference frame are same as Eqs. (3) and (4). The differential equations of the shunt capacitor with parallel-connected load in the d-q rotor reference frame are described by: The differential equations, in the d-q rotor reference, of the load are given by: The differential equations, in the d-q rotor reference, of series capacitor are illustrated as:

Dynamic model of long-shunt compensation with load
The equivalent circuit shown in Fig. 4 is used to derive the mathematical model of the long-shunt compensation configuration of WDSERG. As given in Eqs. (3) and (4), the cageless reluctance generator has current equations in the d-q rotor reference frame like short-shunt compensation. Where the differential equations, in the d-q rotor-reference frame, of the shunt capacitor are described by: The differential equations, in the d-q rotor-reference frame, of the load are given by: The differential equations of series capacitor in d-q rotor-reference frame are illustrated as:

Determination of optimal capacitors
In standalone WDSERG system, the output stator voltage and frequency are controlled to certain levels by variable three-phase shunt and series capacitors bank. The capacitance variation can be accomplished by utilizing switched capacitor principle, which is a three-phase capacitors bank connected to the reluctance generator through a threephase inverter, and the capacitance value changes with duty ratio of the switches as follows: where C e is effective capacitance value, C is fixed capacitance value, d is duty ratio of the switches, t 1 is the on-time period and T is the total switching time. To keep the output voltage and frequency of WDSERG at certain value, two PI controllers are used to control the inverter switches for adjusting the desired value of series and shunt capacitors. The controller gains tuning is achieved via using the trial-and-error method.

Simulation results
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 X ds for each value of d-axis current i ds is obtained from magnetization curve, which are represented by 6 th -order polynomial equation as shown:

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 MAT-LAB/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 (27) X ds = −0.002839i 6 ds +0.10299i 5 ds −1.1798i 4 ds + 5.5572i 3 ds −7.9918i 2 ds −30.4452i ds +182.1 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 longshunt 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.

Experimental results
A 0.2-kW, 380-V synchronous reluctance generator is used to demonstrate experimentally the validity of the SERG dynamic model and equivalent circuit. Figure 10 shows the experimental setup picture at the laboratory, where a wind turbine is emulated by using a DC motor. The parameters of the SERG are listed in Table 2. The results are obtained with variable load impedances and power factor. An inductive load of 244 Ω resistance and 0.5 H inductance is used in the test for both short-and long-shunt compensations. A single-point test is performed to prove the validity of dynamic models and equivalent circuits of the two configurations (short-and long-shunt compensation). The values of two series and shunt capacitors are inserted in MATLAB Simulink model, and the speed of SERG is adjusted to confirm the value in hardware test by changing the prime mover toque applied on SERG.
For short-shunt compensation, a shunt capacitor of 18 µf and a series capacitor of 4 µf are used. These capacitors controlled the output phase voltage of the generator to 183 V (rms) and the generator speed to 1320 rpm (output frequency equals 44 Hz). Figures 11  and 12 show the simulation and experimental results for SERG connected to short-shunt configuration.
For long-shunt compensation, a shunt capacitor of 59 µf and a series capacitor of 46 µf are used. These capacitors controlled the output phase voltage of the generator to 139 V (rms) and the generator speed to 1230 rpm (output frequency equals 41 Hz). Figures 13 and 14 show the simulation and experimental results for SERG connected to long-shunt configuration. It is noticed that the experimental results have nearly the same RMS value for the generator phase voltage and current and load current as the simulation results, but the generator current is not pure sinusoidal waveform. Table 3 presents percentage of error between experimental and simulation results. Furthermore, there is a good correlation between simulation and experimental results, which validates the dynamic model and supports the assumption made in the model.

Conclusions
This paper presents a control technique to regulate the output voltage and frequency of WDSERG connected to an isolated load. Dynamic model of SERG with excitation capacitors at variable wind speed, load current and power factor is developed. Simulation results for a 1.5-kW WDSERG system are performed to verify the control scheme effectiveness. From the simulation results, it can be proved that the output voltage and frequency of WDSERG could be controlled by two series and shunt switching capacitors with different configurations (long-and short-shunt compensation).
In short-shunt compensation, series capacitor requirement increases as the loading current and power factor increase. However, lower series capacitor is required for high wind speed value. On the other hand, the value of shunt capacitor decreases with increasing load current and power factor. Furthermore, there is a direct relationship between wind speed and shunt capacitor. In the long-shunt case, shunt capacitor value and wind speed value are in direct proportion, but it is inversely proportional to loading current and power factor. On the other side, series capacitor value requirement increases as loading current and power factor increase. However, series value capacitor decreases with increasing wind speed value.
It is observed from the results that the load power factor variation has a more significant effect on the value of the optimal required capacitances with load current variation than changing of wind speed. The values and variation range of shunt and series capacitors for long-shunt compensation are higher than that for short-shunt compensation; these lead to a large variation in the duty cycle of the inverter switches, which requires a complicated control algorithm, and the cost is increased because of the large value of capacitor. Furthermore, long-shunt compensation configuration has higher shunt capacitor current. Hence, short-shunt configuration is the best choice to control the voltage and frequency of SERG.

List of symbols
A: Turbine swept area; C p : Performance coefficient of the turbine; C se , C sh : Series and shunt capacitors; i dl , i ql : d-q axes components of the load current; i ds , i qs : d-q axes components of the stator current; L ds , L qs : d-q axes components of the stator inductance; P: Number of pair poles; R: Radius of the turbine blade; R l , L l : Load resistance and inductance; R s : Stator resistance; T e : Electromagnetic torque; T pm : Prime mover torque; v cd , v cq : d-q axes components of the capacitor voltage; v dl , v ql : d-q axes components of the load voltage; v ds , v qs : d-q axes components of the stator terminal voltage; V w : Wind speed; X dun : Unsaturated value of d-axis synchronous reactance; X q : q-axis synchronous reactance; β: Moment of inertia; J: Blade pitch angle; λ: Tip speed ratio; λ ds , λ qs : d-q axes components of the stator flux linkage; ρ: Air density; ω o : Rated (base) synchronous speed; ω r : Angular speed of rotor; ω t : Rotor blade speed.