Optimal reactive power controller for wind-driven stand-alone doubly fed induction generators

Abstract

A control strategy has been proposed for minimising the machine loss by optimally sharing the reactive power at the stator and rotor terminals of stand-alone doubly fed induction generator. For achieving this, fixed capacitor along with static synchronous compensator at the stator terminals has been employed apart from battery inverter system at the rotor terminals. A TMS320LF2407A digital signal processor–based controller has been developed for maintaining the stator voltage magnitude and frequency. A method has been developed for calculating the optimal reactive power at the stator terminals using the steady-state equivalent circuit of the proposed system. An analogue circuit–based optimal reactive power controller has been designed and fabricated in the laboratory for supplying this optimal reactive power at the stator terminals for all operating conditions. The salient feature of the proposed optimal reactive power controller is that it needs to monitor only the reference value of reactive power at the stator terminals for any operating conditions. The successful working of the proposed controller has been amply demonstrated through extensive analytical and experimental results obtained on a three-phase, four-pole, 415 V, 50 Hz, 5 kVA doubly fed induction generator.

Keywords

AC machines doubly fed induction generator electric power generation electric generators induction generators static synchronous compensator

Introduction

Over 20% of the world’s population are still without access to electricity (World Bank, 2015). This includes 56% of rural households and 400 million people without electricity access in India (Central Electricity Authority of India, 2014). Providing electricity to these people living in remote areas must be environmentally and socially sustainable. Renewable energy sources play a major role in providing immediate and sustainable power supply to these people living in such remote locations (Rudnick et al., 2014; Zomers, 2014). In this context, stand-alone wind energy electric conversion system (WEECS) is one of the options for supplying power to such remote locations. Self-excited induction generators (SEIGs) and permanent magnet synchronous generators (PMSGs) were proposed by various authors for supplying such isolated loads. It is known that the output voltage and frequency of the SEIGs/PMSGs vary with the rotational speed and load (Alnasir and Kazerani, 2013; Bansal, 2005; Kumaresan et al., 2004; Rakesh et al., 2012; Vijayakumar et al., 2009). So, a variety of power electronic configurations were proposed in the literature to obtain a constant DC/AC voltage from such stand-alone WEECS (Alnasir and Kazerani, 2013; Geng et al., 2011; Kumar et al., 2012, 2014; Perumal and Chatterjee, 2008; Valenciaga and Puleston, 2008; Venkataraman et al., 2014). The rating of the power converters used in these systems has to be equal to or slightly above that of the machine capacity. Even after the inclusion of suitable power converters, machine terminals will not have the constant frequency operation. Hence, to have reduced power converter rating, wide rotor speed operation, constant stator voltage and frequency operation, doubly fed induction generators (DFIGs) are becoming popular for power generation from wind energy (Alnasir and Kazerani, 2013; Bagarty and Kastha, 2013; Bhattacharya and Umanand, 2009; Cheng and Zhu, 2015; Ganti et al., 2012; Gyawali et al., 2011; Iwanski and Koczara, 2008; Nehrir et al., 2011; Phan and Lee, 2012; Qu and Qiao, 2011; Sam et al., 2015; Tazil et al., 2010; Vijayakumar et al., 2012, 2013; Yang, 2008; Zhou et al., 2015). However, DFIG system for off-grid applications will be economical for ratings more than 5 kVA since it employs wound rotor induction machine.

It is known that the fluctuating power output of wind turbine with varying nature of wind speed would affect the operation of stand-alone DFIGs in supplying power to the isolated loads. So, to improve the reliability of continuous power supply for such isolated loads from wind energy, integration of other renewable sources is suggested by various researchers in addition to the use of energy storage devices such as battery (Bhattacharya and Umanand, 2009; Ganti et al., 2012; Gyawali et al., 2011; Nehrir et al., 2011; Qu and Qiao, 2011; Vijayakumar et al., 2012, 2013; Yang, 2008). When battery energy storage system is employed with stand-alone operation of DFIGs, battery will be charged at times of excess energy from the wind compared to the load requirement. On the other hand, battery will support partially or fully at times of less or no wind energy. Thus, with such energy storage components, DFIGs can be operated either in super-synchronous or sub-synchronous rotor speeds for smoothing out the intermittent power from the wind, by observing or supplying slip power at the rotor side (Vijayakumar et al., 2012, 2013).

Most of the literature available on the operation of stand-alone DFIGs for supplying isolated loads have concentrated on the closed-loop control for maintaining constant voltage magnitude and frequency with less harmonics (Alnasir and Kazerani, 2013; Bhattacharya and Umanand, 2009; Geng et al., 2011; Iwanski and Koczara, 2008; Kumar et al., 2012, 2014; Nehrir et al., 2011; Perumal and Chatterjee, 2008; Phan and Lee, 2012; Tazil et al., 2010; Vijayakumar et al., 2012, 2013). The load may be of either linear or nonlinear type with balanced or unbalanced condition. Less attention is given on operating the power converter for minimising the machine loss of such stand-alone systems (Bagarty and Kastha, 2013; Sam et al., 2015). In this context, Bagarty and Kastha have presented an algorithm for determining the optimal share of reactive power for stator side and rotor side converters of the stand-alone DFIGs for minimising the machine and converter losses (Bagarty and Kastha, 2013). MATLAB environment with dSPACE controller board has been employed for dynamically distributing the supply of reactive power between the two converters to minimise the losses without disturbing the stator flux. As the DC-link is common, control of these two back–back converters is coupled to each other. This DC-link voltage has to be maintained on the higher value when transformer is not connected between the stator side converter and load. This necessitates to employ an additional power converter for interfacing the battery storage systems to provide a continuous power to the isolated load and also for smoothing out the intermittent nature of the wind (Bhattacharya and Umanand, 2009). In this context, Vijayakumar et al. have proposed a simple system for the operation of DFIG involving only single voltage source inverter (VSI) for supplying isolated loads with battery. The advantages of this configuration are (1) self-starting, (2) simple control strategy with only one inverter at rotor side, (3) absorbing the excess power/supplying the deficit power from the wind using battery, (4) very low-voltage harmonics and (5) possibility of supplying loads even at no wind condition (Vijayakumar et al., 2012, 2013). However, the reactive power requirement of the generator and load has been supplied only by battery inverter system (BIS) connected at the rotor terminals.

Furthermore, present authors have suggested to supply portion of the reactive power from the stator terminals of DFIG for minimising the power loss by connecting fixed capacitor (Sam et al., 2015). It is to be noted that the net reactive power at the stator terminals should be varied dynamically depending upon the reactive power requirement of the load for operating the system with minimum loss. Hence, the capacitor at the stator side should be varied dynamically for operating the system with minimum possible power loss. Therefore, an attempt is made in this article for achieving this by employing a static synchronous compensator (STATCOM) at the stator terminals. The schematic of the proposed system is shown in Figure 1 with two independent controllers – one for maintaining the stator voltage magnitude and frequency at the set value and the other for optimal supply of reactive power at the stator terminals. Simple and independent control of BIS and STATCOM, possibility of feeding the isolated loads continuously, smoothing out the intermittent nature of wind energy by operating the generator in sub-synchronous/super-synchronous mode and possibility of integration of battery with reduced power converter are the major advantages of the proposed configuration, as shown in Figure 1, as compared to the conventional DFIG back–back converter configuration. The detailed description and operation of the system are given in the next section.

Figure 1.

Block diagram of the proposed stand-alone DFIG configuration.

Description of the system

Figure 1 shows the proposed stand-alone configuration employing DFIG for supplying isolated loads from wind energy. Fixed capacitor, STATCOM and AC loads are connected at the stator terminals which form point of common coupling (PCC) for the present system. BIS comprising of battery and VSI is connected at the rotor terminals. The stator voltage magnitude and frequency of the DFIG are regulated by BIS through stator voltage and frequency controller (SVFC) for any operating condition. For the operation of DFIG, the slip power is injected into the rotor terminals at sub-synchronous speed and extracted at super-synchronous speed. This slip power is used for charging/discharging the batteries through the VSI at the rotor terminals. Thus, the difference between the wind power and the load power is either stored in or extracted from the battery to supply continuous power to the isolated load. When the wind power is more as compared to the size of AC load, DFIG is operated in super-synchronous rotor speed for charging the batteries. The power balance for this condition is P_m = P_L + P_B + P_TLS and direction of power flow is also indicated in Figure 1. On the other hand, DFIG is operated in sub-synchronous rotor speed for supporting the AC load from battery when wind power is less. The power balance for this condition is P_m + P_B = P_L + P_TLS.

It is to be noted that the energy handled by the battery during charging/discharging operation depends on the wind and load profiles of the site where the proposed system is going to be deployed. When the battery is fully charged, a dump load or flexible loads such as space heating and water pumping may be used for power balance. Under this condition, DFIG will be operated at slightly below the synchronous speed to avoid overcharging of batteries. On the other hand, DFIG is operated at super-synchronous rotor speed by removing a portion of loads for charging when the battery is close to the under-charged condition. So, depending upon the availability of wind energy, size of the AC load and battery condition, the generator automatically locks in super-synchronous/sub-synchronous rotor speeds. The successful working of the stand-alone DFIG for these operating conditions has been verified experimentally in the laboratory.

This work aims at operating the system with minimum loss by optimally sharing the system reactive power. Fixed capacitor and STATCOM have been used for the reactive power support from the stator terminals for minimising the machine loss. The gating pulses for the insulate-gate bipolar transistors (IGBTs) in the STATCOM are obtained from optimal reactive power controller (ORPC). The reactive power at the stator terminals has been measured using reactive power transducer PWT-9060T (Industrial Control and Drives Private Limited, 2015) and appropriately conditioned before being fed to ORPC. It is to be noted that the reactive power needed by the system has to be optimally shared by stator and rotor side. It means fixed capacitor together with STATCOM at the stator side optimally shares the reactive power with BIS at the rotor side for minimising the machine loss. The optimal value for this fixed capacitor at the stator has been chosen for supplying the reactive power at the stator under no-load or load condition with unity power factor (UPF).

Stator voltage and frequency controller

The stator voltage magnitude and frequency of DFIG can be controlled by controlling the rotor voltage magnitude and frequency for any rotor speed and load (Sam et al., 2015; Vijayakumar et al., 2012, 2013). The rotor voltage magnitude can be varied by varying the modulation index (MI) of the inverter in BIS. Similarly, the frequency of the source fed at the rotor can be varied by varying the modulating frequency (MF) of the inverter. For achieving this in a closed loop, a two-loop controller – one for calculating the required MI and other for calculating MF has been developed as shown in Figure 2. The outputs of these two loops have been multiplied for getting the required reference sine wave. This sine wave has been compared with carrier wave for generating the appropriate gating pulses to be fed to the inverter in BIS.

Figure 2.

Schematic diagram of stator voltage and frequency controller (SVFC).

Optimal reactive power controller

The reactive power supplied by the STATCOM can be controlled by varying the (1) amplitude of the AC output voltage of the STATCOM and/or (2) angle between the AC output voltage of STATCOM and the voltage at the PCC (Moran et al., 1989). In the present system, the voltage at the PCC is the stator voltage of DFIG. The reactive power output from STATCOM can be obtained rapidly through the adjustment of the MI during transient period (Chen and Hsu, 2007). Hence, in this work, the reactive power output from the STATCOM has been controlled by varying the MI. For the closed-loop operation of ORPC, the voltage at the PCC has been taken as reference. This voltage is appropriately scaled down and conditioned using the signal conditioning circuit (SCC). Then, this signal is used as reference sine wave for the generation of gating pulses to control the output voltage of STATCOM. Hence, the AC output voltage of STATCOM and voltage at the PCC are in phase.

Conventionally, for varying the MI of STATCOM, the reference sine wave magnitude will be varied keeping the magnitude of the carrier wave constant. The MI will be multiplied with unit sine wave for obtaining reference sine wave. For three-phase STATCOM, three such multipliers are needed for closed-loop control. In the present system, the voltage magnitude and frequency at the PCC are maintained constant by SVFC. Hence, the reference sine wave given to ORPC is always constant. To use this reference signal as such, the magnitude of carrier wave has been proposed to vary for varying the MI. To get the required carrier wave signal, the constant magnitude triangular wave is divided with the value obtained from the proportional–integral (PI) controller. For achieving this, a closed-loop controller has been developed and the schematic of the proposed ORPC is given in Figure 3. Only one divider is sufficient in the proposed method against three multipliers in the conventional method. This is an added advantage for the closed-loop control of three-phase STATCOM.

Figure 3.

Schematic diagram of optimal reactive power controller (ORPC).

The logic for setting the reference reactive power (Q_ref) for supplying the optimal reactive power output from STATCOM for minimising the machine loss is explained in next section. This Q_ref is given as one of the inputs to a summer in ORPC. The actual reactive power (Q_act) at the stator terminal has been computed using PWT-9060T VAR measurement transducer and details of these calculations are given in next section. Then, this Q_act is given as other input to the summer. The error signal obtained from the summer is given to the PI controller. As mentioned earlier, the constant magnitude triangular wave of 5 kHz is divided with the output of PI controller. The output of divider is the variable magnitude carrier wave of 5 kHz. This magnitude depends on the value of reactive power needed to be supplied by the STATCOM. Once the required magnitude carrier wave is generated from the controller, this carrier wave and the constant sine wave obtained from the PCC have been compared to generate the sinusoidal pulse width modulation (SPWM) pulses for STATCOM. These SPWM pulses are the required gating pulses for controlling the reactive power output from STATCOM. The proposed ORPC has been developed using analogue circuits and its implementation details are given in the experimental investigations section.

Steady-state analysis of stand-alone DFIG with ORPC

The reactive power needed for the proposed system has been met by the fixed capacitor along with STATCOM at the stator terminals and BIS at the rotor terminals. The ORPC proposed in this work closely monitors the reactive power at the stator and adjusts it to the required optimal value. This in turn automatically supplies the optimal reactive power required at the rotor terminals through BIS. So, for analysing the stand-alone DFIG with the addition of a capacitor, STATCOM and BIS, steady-state equivalent circuit has been developed as shown in Figure 4. STATCOM delivers a variable reactive power and its equivalent value has been represented as a variable capacitive reactance, −jX_STA. Similarly, −jX_C is included for representing the fixed capacitor. The equivalent voltage source (referred to stator) has been inserted in Figure 4 for representing the output voltage of BIS at the rotor terminals.

Figure 4.

Equivalent circuit of stand-alone DFIG with ORPC.

In the proposed system, the stator voltage magnitude and frequency have been maintained constant by SVFC. Hence, analytical expressions have been derived for various performance quantities of the proposed system by taking stator voltage as the reference phasor. Then, the stator current is given by

{\bar{I}}_{1 P} = {\bar{I}}_{L} + {\bar{I}}_{C} + {\bar{I}}_{STA} = {\bar{V}}_{1 P} (\frac{1}{R + jX} + \frac{1}{- {jX}_{C}} + \frac{1}{- {jX}_{STA}})

(1)

The air-gap voltage can be calculated by adding the phasor value of stator voltage and voltage drop in the stator winding impedance as follows

\bar{E} = {\bar{V}}_{1 P} + {\bar{I}}_{1 P} (R_{1} + j X_{1})

(2)

The rotor current (referred to stator) is given by

{\bar{I}}_{2 P}^{1} = {\bar{I}}_{1 P} + \frac{\bar{E}}{R_{m}} + \frac{\bar{E}}{j X_{m}}

(3)

Similarly, the rotor voltage, rotor frequency and other performance quantities can be calculated using the steady-state equivalent circuit of stand-alone DFIG shown in Figure 4. The expressions for these performance quantities are given in Appendix 2.

The real and reactive power at the stator terminals are as follows

P_{1} = 3 R e ({\bar{V}}_{1 P} {\bar{I}}_{1 P}^{*}) and Q_{1} = 3 Im ({\bar{V}}_{1 P} {\bar{I}}_{1 P}^{*})

(4)

If Q₁ is positive, stator supplies reactive power and if Q₁ is negative, reactive power is injected into the stator terminals. Injecting reactive power at the stator terminals has been achieved by the combination of capacitor and STATCOM.

The real and reactive power at the rotor terminals are as follows

P_{2} = 3 R e ({\bar{V}}_{2 P} {\bar{I}}_{2 P}^{*}) and Q_{2} = 3 I m ({\bar{V}}_{2 P} {\bar{I}}_{2 P}^{*})

(5)

If P₂ is positive, then real power is injected into the rotor terminals; if P₂ is negative, real power is extracted from the rotor terminals. Q₂ given in equation (5) is the reactive power supplied by the BIS at rotor terminals.

The reactive power supplied by the fixed capacitor and STATCOM, respectively, are as follows

Q_{C} = 3 I m ({\bar{V}}_{1 P} {\bar{I}}_{C}^{*}) and Q_{S T A} = 3 I m ({\bar{V}}_{1 P} {\bar{I}}_{STA}^{*})

(6)

The stator copper loss (P_SCL), rotor copper loss (P_RCL) and iron loss (P_IL) of the DFIG, respectively, are as follows

P_{SCL} {= 3 (I}_{1 P})^{2} R_{1}; P_{RCL} {= 3 (I}_{2 P}^{1})^{2} R_{2} and P_{IL} = \frac{{3 (E)}^{2}}{R_{m}}

(7)

Then, total electrical loss (TEL) of DFIG is given by

P_{TL} = P_{SCL} + P_{RCL} + P_{IL}

(8)

Estimation of Q_ref for ORPC

It can be noted from Figures 1 and 4 that the both fixed capacitor and STATCOM supply the optimal reactive power needed at the PCC for minimising the machine loss. The reactive power supplied by this combination will vary based on the load at PCC. The equivalent values of capacitances, that is, C (−jX_C) and C_STA (−jX_STA) have been used in Figure 4 for representing this variable value of reactive power. For making the calculation simple, the parallel combination of C and C_STA is taken as C_P and V_1P as reference. So, the stator current, air-gap EMF and rotor current given in equations (1) to (3), respectively, can be written as

{\bar{I}}_{1 P} = K_{1} + j (K_{2} + K_{3} C_{P})

(9)

\bar{E} = K_{4} - K_{5} C_{P} + j (K_{6} + K_{7} C_{P})

(10)

{\bar{I}}_{2 P}^{1} = K_{8} - K_{9} C_{P} + j (K_{10} + K_{11} C_{P})

(11)

where the constants K₁–K₁₁ are given in Appendix 3.

It is clear from equations (9) to (11) that the stator current, air-gap EMF and rotor current expressions are the functions of C_P for any operating conditions. Then, these expressions have been substituted in stator copper loss, iron loss and rotor copper loss expressions given in equation (7) for determining TEL of DFIG. After simplification, the TEL of DFIG with variable C_P can be shown to be

P_{TL} = K_{A} C_{P}^{2} + K_{B} C_{P} + K_{C}

(12)

where the constants K_A, K_B and K_C are also given in Appendix 3.

For determining the value of C_P to give minimum TEL of DFIG, equation (12) is differentiated with respect to C_P and equated to zero. Then, the optimal value of C_P (i.e. C_opt) is as follows

C_{opt} = \frac{- K_{B}}{{2 K}_{A}}

(13)

The reactive power supplied by C_opt is given by

Q_{opt} = 3 Im ({\bar{V}}_{1 P} {\bar{I}}_{C, opt}^{*})

(14)

where ${\bar{I}}_{C, opt}^{*} = {\bar{V}}_{1 P} / (- j 2 π f_{s} C_{opt})$

It can be noted from equation (13) that the value of C_opt is independent of slip. This means that the Q_opt given in equation (14) is independent of rotor speed or wind velocity. However, Q_opt depends on R₁, X₁, R_m, X_m and load parameters. To show the variation of Q_opt and TEL of DFIG, a three-phase, four-pole, 415 V, 50 Hz, 5 kVA, delta-connected slip-ring induction machine with three-phase star-connected rotor of 200 V, 19 A and turns ratio of 3.6 has been considered. The equivalent circuit parameters of the machine are R₁ = 5.3 Ω, R₂ = 2.4 Ω, X₁ = X₂ = 14.9 Ω, R_m = 4871.1 Ω and X_m = 208.5 Ω. Figure 5(a) shows the variation of Q_opt required at the stator terminals for minimising the loss with different loading conditions (i.e. value of load real power and PF). It can be seen from Figure 5 that the value of Q_opt is (1) constant for any value of UPF load including no-load condition and (2) variable for loads other than UPF. Predetermination was also carried out using the performance equations (1) to (8) for validating the calculation of Q_opt given in equation (14). Figure 5(b) shows the variation of TEL of DFIG with reactive power supplied by the capacitor connected at the stator terminals. It is observed from Figure 5 that the TEL of DFIG is minimum at Q_opt (calculated using equation (14)) for the given load real power and PF. Table 1 shows the predetermined values of Q_opt and Q₁ for various operating conditions. It can be noted from Table 1 that (1) the value Q₁ is same for all speeds and load conditions for operating DFIG with minimum TEL and (2) this value has to be injected at the stator. Hence, this constant value, that is, Q₁ is used as a Q_ref for the ORPC described in the previous section.

Figure 5.

Steady-state characteristics of DFIG (V_1P = 415 V and f_s = 50 Hz): (a) variation of Q_opt against P_L and (b) variation of P_TL against reactive power supplied by capacitance.

Table 1.

Predetermined values of Q_opt and Q₁ for all speeds V_s = 415 V and f_s = 50 Hz.

P_L, kW	Q_L, kVAR	Q_opt, kVAR	Q₁, kVAR
No-load condition		−0.981	−0.981
1	0	−0.981	−0.981
	0.4	−1.381
	0.6	−1.581
2	0	−0.981	−0.981
	0.5	−1.481
	1.0	−1.981
3	0	−0.981	−0.981
	0.5	−1.481
	1.0	−1.981

Performance of DFIG with ORPC

It is noted from Table 1 that a constant value of reactive power needs to be injected for operating the machine with minimum loss. So, a fixed capacitor of 6 µF per phase (delta-connected) available in the laboratory has been connected at the stator terminals for supplying constant value of reactive power. The balance reactive power is variable for any operating condition and this will be supplied from STATCOM. Of course, the net reactive power supplied by the combination of a capacitor and STATCOM is Q_opt and is given by

Q_{opt} = Q_{C} + Q_{STA}

(15)

To show the benefits of the proposed stand-alone configuration with ORPC, performance of the system was predetermined for two different loading conditions at the stator terminals for various values of speed and the results are furnished in Figure 6. It can be observed from Figure 6 that the TEL of DFIG reduces considerably by supplying Q_opt at the stator terminals. A delta-connected capacitor of 6 µF per phase supplies the reactive power of 0.973 kVAR for all speeds, both in sub-synchronous and super-synchronous regions. Similarly, the STATCOM supplies the balance reactive power of 0.128 kVAR for P_L = 1 kW and Q_L = 0.12 kVAR and 0.968 kVAR for P_L = 2.8 kW and Q_L = 0.96 kVAR for all speeds. However, the reactive power supplied by the BIS varies with operating speed.

Figure 6.

Reactive power supplied by BIS and TEL of DFIG against speed (V_1P = 415 V, f_s = 50 Hz, V_dc = 144 V, C = 6 µF and Q_C = 0.973 kVAR): (a) P_L = 1.0 kW, Q_L = 0.12 kVAR and Q_STA = 0.128 kVAR and (b) P_L = 2.8 kW, Q_L = 0.96 kVAR and Q_STA = 0.968 kVAR.

Predetermination was also carried out for TEL of DFIG for various loading conditions and the results are given in Figure 7. As the stator voltage magnitude and frequency are maintained constant by SVFC, the results furnished in Figure 7 are same for all operating speeds. It can be observed from Figure 7 that the TEL of DFIG increases with the increase in load and load PF. Figure 7 also shows the considerable reduction in TEL of DFIG with ORPC (i.e. Q_opt at the stator terminals). The improvement in the performance of the system is less for the generator supplying UPF loads as compared to lagging PF loads.

Figure 7.

TEL of DFIG against load power.

From Figure 6, it can be noted that the reactive power supplied by the BIS reduces with ORPC for a given operating condition. This further reduces the VA burden and conduction loss of the BIS. However, there will be a loss due to the inclusion of capacitor and STATCOM at the stator terminals. So, to show the overall benefit of the proposed system, the conduction loss and switching loss of the SPWM inverter and STATCOM are calculated using the steady-state expressions given in Graovac and Purchel (2009) and Nicolai (2014) and these expressions are given in Appendix 4.

Then, power loss in the capacitor can be calculated by

P_{CL} {= 3 I}_{C}^{2} X_{C} DF

(16)

where DF is the dissipation factor and its typical value of 1e−3 has been used for the estimation of power loss in the capacitor.

Then, the total loss in the system can be estimated by adding the TEL and mechanical loss of DFIG, total loss of inverter connected at the rotor terminals, total loss of STATCOM and power loss in the capacitor.

Using the steady-state analysis of the proposed system and equations (8), (16), (34), power loss at various stages is calculated with and without ORPC and the results are furnished in Table 2 for typical loads. From Table 2, it can be observed that the improvement in the efficiency of the generator is relatively more for lagging PF loads with ORPC. Similarly for the same PF with ORPC, the efficiency of the generator increases with load. Furthermore, it can be noted from Table 2 that the total loss of the proposed system decreases with the addition of ORPC for all operating conditions.

Table 2.

Calculation of power loss with and without ORPC: V_1P = 415 V and f_s = 50 Hz.

Sl. No.	Load	ORPC	P_TL, W	η_DFIG, %	P_TLI, W	P_CL + P_STAL, W	Total loss, W
1	No-load	Without ORPC	163.2	–	30.6	–	344
1	No-load	With ORPC	119.5	–	19.0	3.4	292
2	1 kW, 0.8 PF (lag)	Without ORPC	185.9	74.85	42.0	–	378
2	1 kW, 0.8 PF (lag)	With ORPC	138.8	77.59	23.0	15.9	328
3	1 kW, 0.6 PF (lag)	Without ORPC	223.0	72.83	48.9	–	422
3	1 kW, 0.6 PF (lag)	With ORPC	138.8	77.59	23.0	22.9	335
4	3 kW, 0.8 PF (lag)	Without ORPC	435.5	83.67	69.6	–	655
4	3 kW, 0.8 PF (lag)	With ORPC	269.9	87.77	42.0	32.9	495
5	3 kW, 0.6 PF (lag)	Without ORPC	661.3	78.71	89.7	–	901
5	3 kW, 0.6 PF (lag)	With ORPC	269.9	87.77	42.0	50.3	512

ORPC: optimal reactive power controller.

For the calculation of generator efficiency and total loss in the system, the mechanical loss is taken as 150 W and η_DFIG is the efficiency of DFIG.

Experimental investigations

In order to validate the working of the proposed system shown in Figure 1, a three-phase SPWM inverter has been connected at the rotor terminals to control stator voltage and frequency constant, whereas STATCOM has been connected at the PCC for ORPC. Both SPWM inverter and STATCOM have been made with dual IGBT modules SKM300GB125D along with suitable gate driver circuits. The SVFC has been implemented with TMS320LF2407A digital signal processor (DSP). This DSP has a maximum operating frequency of 40 MHz. A 100 µs sampling time is used for analogue-to-digital conversion and other operations needed for the development of the closed-loop controller. LEM make voltage transducer (LV-25) has been employed to sense stator voltage magnitude and frequency and given to SVFC. The output voltage magnitude from the transducer has been scaled down to a value compatible to the analogue-to-digital converter (ADC) with a 12-bit resolution available in TMS320LF2407A DSP by SCC. Then, the digital equivalent of RMS value of stator voltage magnitude has been computed and this is given as one input to the summer present in the voltage control loop. The digital equivalent of reference stator voltage magnitude has been given as another input to the summer. The error obtained from summer in the voltage control loop has been given to the PI controller with proportional and integral gain of 40 and 0.1, respectively. Similarly, the actual and reference values of frequency have been given to the summer in the frequency control loop. The error obtained from summer in the frequency control loop has been given to the PI controller with proportional and integral gain of 3.5 and 0.03, respectively. The PI controller gains in the voltage and frequency control loop have been tuned by trial and error method to achieve the satisfactory dynamic performance of the DFIG for the step change in the load and speed. The outputs obtained from the voltage and frequency control loops have been processed as per the SVFC discussed in the description of the system section for obtaining reference signal. This reference signal has been compared with the carrier frequency to get SPWM pulses. The generated SPWM pulses are given to the IGBTs in the inverter connected at the rotor terminals through gate driver circuits.

An analogue-based ORPC described in the description of the system section has been designed and fabricated in the laboratory as per the circuit diagram as shown in Figure 8. The reference sinusoidal waveform required for the generation of SPWM pulses for the three legs of STATCOM has been obtained from the SCC connected at the PCC and scaled down to get a maximum magnitude of 4.1 V. A 5 kHz triangular waveform has been generated employing TL084 op-amp integrated circuits (ICs) with the fixed magnitude of 15 V. TL084 op-amp IC has a slew rate of 13 V/µs and band width of 3 MHz. As mentioned in the description of the system section, to get the required carrier wave signal, the constant magnitude triangular wave is divided with the value obtained from the PI controller. For carrying out this division operation, divider circuit using AD633JN multiplier/divider IC has been constructed as per the connection details given in Figure 8. An inverting amplifier circuit is included between the output of PI controller and divider circuit to compensate the additional negative gain of 10 incurred with this divider circuit.

Figure 8.

Analogue-based ORPC circuit diagram.

The actual value of reactive power (Q_act) to be injected at the stator terminals has been measured using PWT-9060T VAR measurement transducer. The output of the VAR transducer has been conditioned and calibrated so that the output voltage varies from (0 to 9) V for (0–3) kVAR leading. This (i.e. Q_act) has been given as one of the inputs to the error amplifier with unity gain. As described in the previous section, the value of Q_ref for the experimental machine of three-phase, four-pole, 415 V, 50 Hz, 5 kVA rating is 0.981 kVAR leading. The equivalent value of voltage for this reactive power is 2.94 V. This constant value of voltage (i.e. Q_ref) is the other input to the error amplifier given in Figure 8. The output of error amplifier is given to the analogue-PI controller circuit designed for this purpose with proportional and integral gains of 4.5 and 0.002, respectively. These gains are tuned in the analogue circuit by appropriately varying the pots employed in the PI controller circuit to get the satisfactory performance of the STATCOM. For varying the MI of the STATCOM to supply the required reactive power, the 15 V magnitude triangular wave of 5 kHz is divided with the output of PI controller. Thus, the output of the divider circuit is the variable magnitude carrier wave corresponding to the required MI. Then, this carrier waveform and the constant magnitude reference sinusoidal waveforms are given as inputs to the three comparator circuits, one for each leg of STATCOM. The outputs of comparator circuits are the required SPWM pulses to be applied to the IGBTs of STATCOM for ORPC at the stator terminals.

To demonstrate the successful working of the proposed ORPC along with SVFC for the stand-alone operation of DFIG, experiments have been conducted on the same three-phase, four-pole, 415 V, 50 Hz, 5 kVA, delta-connected induction machine considered in the previous section. A separately excited DC motor is used to drive the generator and suitable number of batteries was connected at the DC side of the inverter in BIS. The experiment was conducted for various rotor speeds by maintaining the two values of constant load power (i.e. one at 1.0 kW and 0.12 kVAR and other at 2.8 kW and 0.96 kVAR). It was observed that for any value of load and speed, (1) SVFC maintains the stator voltage magnitude and frequency constant and (2) ORPC adjusts the reactive power supplied by the STATCOM so that the optimal value of reactive power is supplied by the fixed capacitor and STATCOM at the PCC. Variation of rotor reactive power, TEL of DFIG and reactive power supplied by the STATCOM with rotor speeds of the generator were observed and these experimental values are also given in Figure 6 along with the corresponding predicted values. Various electrical quantities at the stator terminals with and without ORPC have also been observed using Fluke make power harmonic analyser (Fluke 345 PQ Clamp meter) for various rotor speeds with this load setting. It has been observed that the similar values were obtained for various rotor speeds. For the sake of brevity, the experimentally recorded values of electrical quantities at 1300 r/min are given in Figure 9. From Figure 9, it can be observed that (1) the SVFC maintains the set voltage magnitude (415 V ± 1.0%) and frequency (50 Hz ± 0.5%) at PCC, (2) ORPC maintains the set Q_ref (0.981 kVAR ± 0.5%) and (3) voltage total harmonic distortion (THD) is well below the acceptable limit, at the stator terminals for any load and speed.

Figure 9.

Steady-state performance quantities of the proposed system with ORPC recorded using power harmonic analyser: (a) P_L = 1 kW and Q_L = 0.12 kVAR and (b) P_L = 2.8 kW and Q_L = 0.96 kVAR.

To ascertain the dynamic performance of the proposed system with SVFC and ORPC, experiments have been conducted for step change in load at PCC for a given speed. The experimental waveforms have been observed using Agilent make (DSO1002a) digital storage oscilloscopes. Figure 10 shows the waveforms of stator voltage and current; rotor voltage and current; STATCOM voltage and current for step change in load from no-load to (1.0 kW and 0.12 kVAR) load with two operating speeds, one at sub-synchronous and other at super-synchronous speed. Similarly, the above-mentioned waveforms have been observed for step change in load from (1.0 kW and 0.12 kVAR) to (2.8 kW and 0.96 kVAR) for different operating speeds. For the sake of brevity, experimentally obtained results are given in Figure 11 for the rotor speed of 1200 r/min. It is noted from Figures 10 and 11 that for all speeds, the (1) stator voltage magnitude and frequency are maintained at the set value for any load, (2) stator and rotor currents are 0.7 and 4.1 A, respectively, at no-load and these currents increase to 1.1 and 5.4 A for (1.0 kW and 0.12 kVAR) load and 2.3 and 10.0 A for (2.8 kW and 0.96 kVAR) load and (3) reactive power supplied by the STATCOM is 0.008 kVAR at no-load and this value increases to 0.128 kVAR for (1.0 kW and 0.12 kVAR) load and 0.968 kVAR for (2.8 kW and 0.96 kVAR) load. Figure 12 illustrates the experimental results on the system for simultaneous step change in the load and speed. Figure 12 gives step change in load from (1.0 kW and 0.12 kVAR) to (2.8 kW and 0.96 kVAR) and speed from 1400 to 1300 r/min. It has been observed that the controller tracks the set value of stator voltage magnitude and frequency as well as the Q_ref at the stator terminals even for the simultaneous step change in load and speed. For the sake of clarity, the enlarged stator voltage and current waveforms at the instant of step change in load or speed are also given in Figures 10 to 12. Thus, Figures 10 to 12 show the satisfactory dynamic performance of the SVFC and ORPC for step change in load and speed.

Figure 10.

Dynamic response of the proposed system for the step change in load: from no-load to (1.0 kW and 0.12 kVAR) load: (a) N = 1300 r/min and (b) N = 1700 r/min.

Figure 11.

Dynamic response of the system for the step change in load: from (1.0 kW and 0.12 kVAR) to (2.8 kW and 0.96 kVAR) load at N = 1200 r/min.

Figure 12.

Dynamic response of the system for the simultaneous change in load and speed: from (1.0 kW and 0.12 kVAR) to (2.8 kW and 0.96 kVAR) load and N = 1400–1300 r/min.

Observation has also been made through experiment that the proposed system performed satisfactorily even for a step change in speed through synchronous speed (Vijayakumar et al., 2013). Furthermore, to ascertain the response of the controller for step change in light load to medium load and back, experiments have been conducted with UPF load at the stator terminals (1) from no-load to 1 kW, (2) 1 kW to 2 kW and (3) 2 kW to 1 kW. It has been observed for these cases that the controller could track the set values of stator voltage and frequency within few cycles. However, controller took a little more time for simultaneous large step change in the load and speed than that with only step change in load (Vijayakumar et al., 2012). The experimental set-up of the proposed wind-driven stand-alone DFIG system is shown in Figure 13.

Figure 13.

Photograph of the experimental set-up.

Conclusion

A topology consisting of STATCOM along with fixed capacitor at the stator terminals and BIS at the rotor terminals has been proposed for operating the stand-alone DFIG with minimum machine loss. Two independent controllers, namely SVFC and ORPC, have been developed for operating the proposed DFIG configuration supplying isolated loads from wind energy. SVFC has been implemented using TMS320LF2407A DSP for maintaining the stator voltage magnitude and frequency at the set value. On the other hand, an analogue circuit–based ORPC has been designed and fabricated for supplying optimal reactive power at the stator terminals.

A method has been developed and presented in this article for estimating the value of optimal reactive power at the stator terminals for minimising the machine loss. It has been shown that for the given machine, (1) the optimal reactive power at the stator terminals is independent of rotor/wind speed for the given load and (2) the reactive power needs to be injected at the stator terminals is constant (Q_ref) for supplying the optimal reactive power for any operating condition. Thus, this Q_ref is continuously monitored by the ORPC. If the load reactive power demand changes, then the extra/deficit reactive power tends to get supplied from the stator terminals. The ORPC senses this change and controls the STATCOM to bring the stator side Q_ref back to the set value (981VAR in this case). Hence, through ORPC, always a constant amount of reactive power is injected to the stator terminals of DFIG to optimise the losses. The predetermined performance characteristics and experimental results obtained on a three-phase, four-pole, 50 Hz, 5 kVA, slip-ring machine with the proposed controllers confirm the successful working and usefulness of the proposed stand-alone DFIG configuration.

Footnotes

Appendix 1

Appendix 2

The required rotor voltage (referred to stator) can be evaluated using the following equation

(17)

{\bar{V}}_{2 P}^{1} = \bar{E} + {\bar{I}}_{2 P}^{1} ((\frac{R_{2}}{s}) + j X_{2})

The operating slip of the stand-alone DFIG is given by

(18)

s = \frac{N_{s} - N}{N_{s}}

Then, the rotor voltage required to be applied from BIS to maintain constant stator voltage can be calculated using the machine turns ratio and operating slip. This expression is given by

(19)

{\bar{V}}_{2 P} = {\bar{V}}_{2 P}^{1} (\frac{s}{a})

Similarly, the rotor current can be estimated by

(20)

{\bar{I}}_{2 P} = a {\bar{I}}_{2 P}^{1}

To maintain the stator frequency constant for a given rotor speed and load, the frequency of the rotor voltage to be injected is given by f_r = sf_s and this rotor frequency can be shown as follows

(21)

f_{r} = f_{s} - (\frac{PN}{120})

where P is the number of poles.

After evaluating the rotor voltage magnitude using (19), the MI of the inverter is determined using the following expression

(22)

m = 2 \sqrt{2} \frac{{\bar{V}}_{2 P}}{V_{DC}}

where V_DC is the battery voltage.

The mechanical power input to the rotor of the generator is as follows

(23)

P_{m} = 3 {(I_{2 P}^{1})}^{2} R_{2} (\frac{1 - s}{s}) - P_{2} (\frac{1 - s}{s})

Appendix 3

\begin{array}{l} K_{1} = \frac{V_{1 P} R}{R^{2} + X^{2}}, K_{2} = - \frac{V_{1 P} X}{R^{2} + X^{2}}, K_{3} = 2 π f_{S} V_{1 P} \\ K_{4} = V_{1 P} + K_{1} R_{1} - K_{2} X_{1}, K_{5} = K_{3} X_{1}, K_{6} = K_{2} R_{1} + K_{1} X_{1} \\ K_{7} = K_{3} R_{1}, K_{8} = K_{1} + \frac{K_{4}}{R_{m}} + \frac{K_{6}}{X_{m}}, K_{9} = \frac{K_{5}}{R_{m}} - \frac{K_{7}}{X_{m}} \\ K_{10} = K_{2} + \frac{K_{6}}{R_{m}} - \frac{K_{4}}{X_{m}}, K_{11} = K_{3} + \frac{K_{5}}{X_{m}} + \frac{K_{7}}{R_{m}} \\ K_{A} = 3 [R_{1} K_{3}^{2} + \frac{1}{R_{m}} (K_{5}^{2} + K_{7}^{2}) + R_{2} (K_{9}^{2} + K_{11}^{2})] \\ K_{B} = 6 [K_{2} K_{3} R_{1} + \frac{1}{R_{m}} (K_{6} K_{7} - K_{4} K_{5}) + R_{2} (K_{10} K_{11} - K_{8} K_{9})] \\ K_{C} = 3 [R_{1} (K_{1}^{2} + K_{2}) + \frac{1}{R_{m}} (K_{4}^{2} + K_{6}^{2}) + R_{2} (K_{10}^{2} + K_{12}^{2})] \end{array}

Appendix 4

The conduction loss of the IGBTs and diodes in the inverter can be calculated by

(24)

P_{C I} = 6 (V_{CE 0} I_{C (av)} + R_{C (on)} I_{Crms}^{2})

(25)

P_{C D} = 6 (V_{D 0} I_{D (av)} + R_{D (on)} I_{Drms}^{2})

The average and RMS value of currents in the IGBT in the inverter are given by

(26)

I_{C (av)} = \sqrt{2} I_{2 P} (\frac{1}{2 π} + \frac{m \times P F}{8})

(27)

I_{C (rms)} = I_{2 P} \sqrt{2 (\frac{1}{8} + \frac{m \times P F}{3 π})}

The average and RMS values of currents in the diode in the inverter are given by

(28)

I_{D (av)} = \sqrt{2} I_{2 P} (\frac{1}{2 π} - \frac{m \times P F}{8})

(29)

I_{Drms} = I_{2 P} \sqrt{2 (\frac{1}{8} - \frac{m \times P F}{3 π})}

where V_CE0 and V_D0 are the on-state collector-emitter voltage of IGBT and on-state voltage of diode in V, respectively. R_C(on) and R_D(on) are the on-state resistance of IGBT and diode in Ω, respectively.

The switching loss of the IGBTs in the inverter is as follows

(30)

P_{swI} = {6 E}_{swI} f_{sw}

where E_swI is the energy dissipation of IGBT in the inverter during switching and it can be calculated by

(31)

E_{swI} = E_{swIref} (\frac{I_{C (av)}}{I_{Iref}}) {(\frac{V_{dc}}{V_{Iref}})}^{1.2}

The switching loss of the diodes in the inverter is as follows

(32)

P_{swD} = {6 E}_{swD} f_{sw}

where f_sw is the switching frequency (5 kHz for both inverter and STATCOM) and EswD is the energy dissipation of diode in the inverter during switching and it can be calculated by

(33)

E_{swD} = E_{swDref} {(\frac{I_{D (av)}}{I_{Dref}})}^{0.6} {(\frac{V_{dc}}{V_{Dref}})}^{0.6}

Then, the total loss of inverter can be estimated by

(34)

P_{TLI} = P_{CI} + P_{swI} + P_{CD} + P_{swD}

Equations given in this section have been used for calculating the conduction and switching losses in the STATCOM also. In this work, two IGBT-based Semikron make three-phase inverter modules (Semikron make) have been used. These inverter modules have Semitron dual IGBT module (SKM300GB125D) in each leg. The parameters given in SEMIKRON Electronics Private Limited (2015), namely, R_C(on) = 9 mΩ, R_D(on) = 4.5 mΩ, V_CE0 = 1 V, V_D0 = 1 V, f_sw = 5 kHz, E_swIref (at I_Iref = 200 A, V_Iref = 600 V) = 26.75 mJ and E_swDref (at I_Dref = 200 A, V_Dref = 600 V) = 13.75 mJ are used for calculating power loss in the inverter.

Acknowledgements

The authors gratefully acknowledge the authorities of the National Institute of Technology, Tiruchirappalli, India for all the facilities provided for carrying out the experimental and simulation work in the preparation of this article.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported in part by the National Institute of Wind Energy (Formerly Centre for Wind Energy Technology), Chennai, India, an autonomous Research and Development Institution under the Ministry of New and Renewable Energy, Govt. of India.

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Optimal reactive power controller for wind-driven stand-alone doubly fed induction generators

Abstract

Keywords

Introduction

Description of the system

Stator voltage and frequency controller

Optimal reactive power controller

Steady-state analysis of stand-alone DFIG with ORPC

Estimation of Qref for ORPC

Performance of DFIG with ORPC

Experimental investigations

Conclusion

Footnotes

Appendix 1

Appendix 2

Appendix 3

Appendix 4

Acknowledgements

Declaration of conflicting interests

Funding

References

Estimation of Q_ref for ORPC