Shunt reactive VAR compensator for grid-connected induction ...

www.ietdl.org Published in IET Power Electronics Received on 24th September 2012 Revised on 3rd May 2013 Accepted on 22nd July 2013 doi: 10.1049/iet-pel.2012.0524

ISSN 1755-4535

Shunt reactive VAR compensator for grid-connected induction generator in wind energy conversion systems Santhi Rajendran, Uma Govindarajan, Annelyn Beulah Reuben, Aarthi Srinivasan Department of EEE, College of Engineering, Guindy, Anna University, Chennai, India E-mail: [email protected]

Abstract: This work presents the control design for compensating reactive power requirement of induction generator (IG) in wind generation systems using STATic COMpensator (STATCOM). A mathematical model of IG is developed in synchronously rotating d–q–0 axis. The STATCOM is realised using voltage source inverter for which the switching function model is derived and employed here. Instantaneous p–q theory and symmetrical components theory are considered for reference current generation. The current control uses an optimal proportional controller designed using linear quadratic regulator (LQR) approach. Comparative analysis is also made between hysteresis current control and LQR. Simulation and experimental results indicate that the suggested control techniques make the supply power factor close to unity.

1

Introduction

Squirrel cage induction generators (SCIG) are characterised by their ruggedness, absence of a separate supply for field, better transient performances, self-protection against severe overloads and short circuits. When connected to the grid, SCIGs can supply power at grid frequency irrespective of the wind speed. This facilitates them to be used in wind generating systems. Concerning the modelling of induction machine, a fifth-order model in dq0 frame presented in [1] is used for simulation of the induction generator (IG), which allows the study of stator, rotor and mechanical transients in the machine. The disadvantage of IG is that, it draws magnetising current which results in loading the grid with severe lagging volt ampere (VAR). These lagging VAR are to be compensated failing which reduction in power transmission capability and large-scale voltage collapse may occur. This may lead to change in real power demands, which may cause power oscillations in electric systems. This paper caters a solution to this problem arising because of reactive power requirement faced in wind energy conversion systems (WECSs) with grid-connected IG, by using STATic COMpensator (STATCOM). One of the main advantages of STATCOM is that it does not suffer as seriously as static var compensators (SVCs) and capacitors do, from degraded voltage. Besides this, the response time is also less when compared with SVCs and fixed capacitor banks, as instantaneous control of the semiconductor switches can be achieved in STATCOMs. They are recently being used for reactive power compensation and to deal with other power quality issues such as voltage flicker, improvement of stability etc. [2–6]. For the purpose of modelling of the STATCOM, a d–q reference frame model is used in [7]. This model decouples 1872 & The Institution of Engineering and Technology 2013

the real and reactive power control loops for output feedback control. A discrete linear time varying model of the three-phase voltage source converter (VSC) is presented in [8] with an objective to develop models for modern flexible AC transmission system (FACTS) controllers. For the ease of design and evaluation of different control strategies of converters, switching function models are preferred [9–11]. Owing to these advantages, the switching function model of STATCOM is adopted in this work. To generate reference currents, several strategies are being followed. The instantaneous p–q theory proposed in [12] uses the concept of reactive power compensation based on the instantaneous values of current and voltage instead of their root-mean-square (RMS) or average values. A generalised p–q theory for three-phase systems was presented in [13]. This theory can handle system unbalances and was validated by simulation and experimental verification in [14]. In this method, there is no direct control over the power factor angle of the source and it forces the supply current to be at unity power factor (UPF) [15]. Also p–q theory calculates the reference currents after transforming the currents and voltages from ‘abc’ frame to ‘αβ’ frame. A new approach to the problem of power factor correction was presented in [16], which suggested the use of symmetrical components theory to generate reference currents. In symmetrical components theory, no transformation is required to calculate the reference currents and it also allows the explicit setting of the power factor of the source. In this work, both instantaneous p–q theory and symmetrical components theory have been applied by considering balanced supply conditions and reference current generation methods are studied in detail. So far, these theories have been dealt for non-linear loads. Here an IET Power Electron., 2013, Vol. 6, Iss. 9, pp. 1872–1883 doi: 10.1049/iet-pel.2012.0524

www.ietdl.org attempt is made to compensate the reactive power requirement of the grid-connected IG, and thereby improving power factor at point of common coupling (PCC) by incorporating the above theories. A suitable control scheme is required to track the reference currents. Several control schemes have been proposed till date [17–19]. In [20], current mode control of the STATCOM was achieved through hysteresis current control (HCC). In HCC, the switching frequency depends on the hysteresis band and this form of control is always stable for first-order systems [21]. In higher-order systems, to make actual currents closer to reference currents, hysteresis band must be narrow or nearing to zero that results in perfect tracking, but very high switching frequency is required, which is undesirable. Literature survey indicated that the linear quadratic regulator (LQR) is superior in its response dynamics and control effort required [22] and it is tolerant of input non-linearities. The LQR deals with the optimisation of a cost function or performance index, in which the designer can weigh the state variables according to their influence in the control action to seek for appropriate performance. In this work, two control methods, HCC and LQR are applied for current control in STATCOM and a comparative study is presented. The paper is organised as follows, Section 2 describes the system under study and its modelling. The reference current generation is presented in Section 3. Section 4 explains the control scheme with HCC and LQR. The simulation studies, discussions on results are elaborated in Section 5. Experimental results are provided in Section 6 and this work is concluded in Section 7.

2

System description

The system under study is a WECS connected to the grid. A schematic of the various components of the system is shown in Fig. 1. In the proposed study, a grid-connected SCIG coupled to a wind turbine forms the energy conversion device. In the absence of any compensating device, the currents supplied to the grid by the IG are ias, ibs and ics. With a steady dc-capacitor voltage vdc, the STATCOM is used for reactive power control. The STATCOM is connected at the PCC through an inductor L which acts as a filter. R is the leakage resistance of the inductor. The switches in the STATCOM are fired appropriately, so that

the STATCOM injects the compensating currents iac, ibc and icc into the system. 2.1

Modelling of wind turbine

The model is based on the steady-state power characteristics of the turbine. The output power and torque of the turbine are given by (1) and (2), respectively
 rA v3 Pm = cp l, bp 2 wind

(1)

Torque Tm =

Pm vm

(2)

where Pm is the mechanical output power of the turbine, cp is the performance coefficient of the turbine, ρ is the air density (kg/m3), A is the turbine swept area (m2), vwind is the wind speed (m/s), βp is the blade pitch angle (°), λ is the tip speed ratio of the rotor blade tip speed to wind speed and ωm is the speed of the generator shaft. The performance coefficient of the turbine is given in (3)  
 c2 cp l, bp = c1 − c3 bp − c4 e(−c5 /li ) + c6 l li 1 1 0.035 = − li l + 0.08bp b3p + 1

2.2

(3)

Modelling of IG

Literature suggests the use of ‘dq0’ reference frame theory to analyse electrical machines, which have variable inductances [23]. To simplify the analysis, the stator and rotor variables of IG are transformed into equivalent parameters in synchronously rotating reference frame. The three-phase quantities in the ‘abc’ frame are transformed to ‘dq0’ quantities using (4) fdq0 = Kfabc

(4)

where f is any quantity such as voltage, current or flux linkage

Fig. 1 Wind energy conversion system with STATCOM IET Power Electron., 2013, Vol. 6, Iss. 9, pp. 1872–1883 doi: 10.1049/iet-pel.2012.0524

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www.ietdl.org and the transformation matrix used is given in (5) 

  ⎞ 2p 2p cos u + cos u cos u − ⎜ 3 3 ⎟ ⎜    ⎟ 2⎜ 2p 2p ⎟ ⎟; u = v dt K= ⎜ sin u sin u − u + sin 3⎜ 3 3 ⎟ ⎜ ⎟ ⎝ ⎠ 1 1 1 2 2 2 (5) ⎛

Here ω is the speed of the reference frame with respect to the variable under consideration. Since the IG is connected to the grid, the stator voltages vas, vbs and vcs follow that of the grid. The stator currents in dq0 axes are given in (6) i0s =

c0s ; Xls

iqs =

cqs − cmq ; Xls

ids =

cds − cmd Xls

(6)

where ψds, ψqs and ψ0s are the flux linkages of the stator along the dq0 axes. ψmd and ψmq are used to account for the saturation of flux along the d and q axes, respectively. The stator currents transformed back into the ‘abc’ quantities ias, ibs and ics cause the real (P) and reactive power (Q) flow in the system. The real and reactive powers are given in (7) P = vds ids + vqs iqs ;

Q = vqs ids − vds iqs

(8)

3

Since the STATCOM is basically a voltage source inverter (VSI), it is modelled using the equations given in [11]. The state variables are the voltage across the capacitor and the compensator current in each phase. With the switching functions of the three phases being sa, sb and sc, the ac output voltages of the STATCOM are derived as in (9) va

statcom

vb

statcom

vc

statcom

3.1

Instantaneous p–q theory

This theory derives the reference currents from the instantaneous powers in ‘αβ’ frame using Clarke’s transformation [12]. The instantaneous real and reactive powers ( p, q) in ‘αβ’ frame are given in (11) p = va ia + vb ib ;

q = vb ia − va ib

(11)

The reference grid currents in αβ frame are derived as in (12) 

i∗a i∗b

 =


1



v  a v 2 b

v2a + vb

vb −va

  p 0

(12)

Here, p is the average real power to be supplied to the grid. These currents i∗a and i∗b transformed by inverse Clarke’s transformation become the reference grid currents in the ‘abc’ frame. 3.2

i∗a

Symmetrical components theory



 va + vb − vc b vb + vc − va b ∗ = 2 p; ib = 2 p; va + v2b + v2c va + v2b + v2c

 v + v −v b i∗c = c 2 a2 b2 p va + vb + vc

(13)

√ where b = tan f 3 , φ is the desired phase angle between supply voltages (vas, vbs and vcs) and line currents (ias, ibs and ics) for the balanced system. p is obtained from the instantaneous power calculated from phase voltages and currents as given in (14)

(9)

Here R and L are the resistance and inductance of the filter through which the STATCOM is connected in shunt to the system. From the above equations, the compensating 1874 & The Institution of Engineering and Technology 2013

Reference current generation

The calculation of reference currents from the instantaneous p–q theory and the symmetrical components theory are presented in brief here. In this work, these calculations are implemented as shown in Figs. 2a and b.

Modelling of STATCOM

  diac (2sa + sb + sc ) + iac R + vdc =L dt 3   dibc (sa + 2sb + sc ) + ibc R + vdc =L dt 3   di (s + sb + 2sc ) = L cc + icc R + vdc a dt 3

(10)

In this method, the power factor angle can be set to any desired value. Based on this formulation, the reference currents for the grid are derived as given in (13) [21]

where Tm is the torque developed by the wind turbine. 2.3

1 vdc = i dt c cap

(7)

The electrical torque developed (Te) and rotor speed (ωr) are given in (8)  
 
 3 pn 1 Te = cds iqs − cqs ids ; 2 vb 2  Te − Tm vr = dt 2H

currents supplied to the system are derived. The dc voltage across the capacitor is given by (10)

p = va ia + vb ib + vc ic

4

(14)

Control scheme of STATCOM

The PWM pulses for STATCOM are generated by using two control methods HCC and LQR through which the grid currents are made equal to reference currents. IET Power Electron., 2013, Vol. 6, Iss. 9, pp. 1872–1883 doi: 10.1049/iet-pel.2012.0524

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Fig. 2 Flow diagram for reference currents calculation a Using instantaneous p–q theory b Using symmetrical components theory

4.1

HCC

HCC, also known as ON–OFF control, switches on the lower or upper set of VSC switches according to the difference in the actual and reference currents. The switching function Sa for phase ‘a’ is expressed as follows (15) sa = 0, sa = 1

if if

 ia , i∗a − HB ;

 ia . i∗a + HB

(15)

where HB is the hysteresis bound. The switching functions for the phases ‘b’ and ‘c’ are generated similarly. Using HCC technique, the controller keeps the control system variable between boundaries of hysteresis area with variable switching frequency that may vary in wideband in the inverter. 4.2

LQR

In commercial applications, a fixed switching frequency is preferred because it reduces the acoustic noise which is present with variable switching frequencies. The current control with fixed switching frequency is realised using LQR, in which the current error is compared with a fixed frequency triangular carrier wave. The duty cycle of the IET Power Electron., 2013, Vol. 6, Iss. 9, pp. 1872–1883 doi: 10.1049/iet-pel.2012.0524

resultant PWM signal is such that the current error tends towards zero. To apply linear quadratic state regulation, the single-phase equivalent of the system shown in Fig. 3a is considered and the state equations are derived. Here ‘v’ is the grid voltage of one phase. The IG is represented by its equivalent resistance (Req) and inductance (Leq) calculated from its single-phase equivalent circuit. The STATCOM is incorporated into the circuit as a current controlled voltage source, u.vdc, in which ‘u’ is the switching control of the STATCOM. Rf and Lf denote the feeder resistance and inductance, respectively. The current from the STATCOM is filtered through a filter of resistance R and inductance L. The state equation of the system is given in (16) X˙ = AX + BU

(16)

The state and input vectors are given in (17) 

 i1 ; X= i2



v U= uc

 (17)

i1 and i2 are state variables, v is the input and uc is a state feedback control variable. The system matrix, A and the 1875

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Fig. 3 LQR design implementation a Simplified single-phase equivalent circuit of the system b Implementation of LQR for STATCOM (i∗jc = i js − i∗j , where j = a, b, c)

input matrix, B are as follows in (18)

designed as in (21)

 ⎤ R + Rf 0 ⎢ − L + L  ⎥ ⎢ f
⎥ ⎢ ⎥ A=⎢ R + Req ⎥ ⎢ ⎥ ⎣ ⎦ 0 −
L + Leq ⎡ ⎤ 1

 0 ⎢ L + Lf ⎥ ⎢ ⎥ B=⎢ ⎥ V ⎣
dc  ⎦ 0 L + Leq

 uc = −K z − z∗

⎡

Here K is the feedback gain matrix and z* is the desired state vector. The selection of the feedback gain matrix involves minimisation of the linear quadratic cost function and finding the steady-state solution of the Riccati equation shown in (22) [21] (18)

Converting the above state variables to local variables namely the source current and STATCOM current for ease of measurement under practical conditions, the transformation given in (19) is used  z=

ig iSTAT





1 = −1

 0 X = TX ; 1

∗



z =

(21)

i∗g

i∗STAT



(20)

Assuming full control over uc, a state feedback controller is 1876 & The Institution of Engineering and Technology 2013

(22)

 K = R−1 BTI P

(23)

In the above equations, Q is a symmetric positive semi-definite matrix that defines the weights of each state variable to be controlled and R puts a penalty on the maximum control action. Q and R are diagonal matrices of the form as shown in (24) and (25) 

(19)

Transforming the state equation given in (16), the z˙ is obtained as follows z˙ = TAT −1 z + TBU = AI z + BI U

0 = ATI P + PAI − PBI R−1 BTI P + Q

Q=

wig

0

0

wiSTAT

 ;

 R=

r1 0

0 r2

 (24)

Once a suitable gain matrix is selected, the switching control, u is obtained from (25) u = −hys(uc )

(25)

IET Power Electron., 2013, Vol. 6, Iss. 9, pp. 1872–1883 doi: 10.1049/iet-pel.2012.0524

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Fig. 4 Simulated results for the wind speed of 5 m/s a Grid voltage and current in phase ‘a’ for an uncompensated system b Grid voltage, current and spectrum of grid current in phase ‘a’ using instantaneous p–q theory with HCC c Grid voltage, current and spectrum of grid current in phase ‘a’ using instantaneous p–q theory with LQR

Fig. 5 Simulated waveforms using symmetrical components theory with φ = 0 a Grid voltage, current and spectrum of grid current in phase ‘a’ with HCC b Grid voltage, current and spectrum of grid current in phase ‘a’ with LQR IET Power Electron., 2013, Vol. 6, Iss. 9, pp. 1872–1883 doi: 10.1049/iet-pel.2012.0524

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Fig. 6 Real power fed to grid by IG and reactive power supplied by STATCOM to IG a Real power supplied by IG to grid b Reactive power supplied by STATCOM to IG c Power factor for various wind speeds with instantaneous p–q theory d Power factor for various wind speeds with symmetrical components theory

where the hys function is defined by if uc . lim

then hys(uc ) = 1

elseif uc < −lim then hys (uc) = −1. The selection of the ‘lim’ determines the switching frequency while tracking the reference. In this control law, since the switching decision

Fig. 7 Simulation results obtained for symmetrical component theory with φ = 5° a Grid voltage, current and spectrum of current in phase ‘a’ with HCC b Grid voltage, current and spectrum of current in phase ‘a’ with LQR 1878 & The Institution of Engineering and Technology 2013

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Fig. 8 Simulation results obtained for symmetrical component theory with φ = 10° a Grid voltage, current and spectrum of current in phase ‘a’ with HCC b Grid voltage, current and spectrum of current in phase ‘a’ with LQR

is based on a linear combination of multiple states, switching band tracking control is adopted.

5

Simulation results and discussion

In this work, the system as dealt with in the previous sections is simulated in MATLAB/SIMULINK and its steady-state

analysis is done. The specifications of the SCIG used for simulation in this work are as follows: three phase, 4 kW, 400 V, 50 Hz, four pole and 1430 rpm. The STATCOM has a dc-link capacitor of 600 µF. While regulating states using LQR, since the current injected from STATCOM (iSTAT) plays a vital role in reactive VAR compensation, it is given more weight of

Table 1 System performance parameters for ‘φ’ variations φ = 5°

power factor VAR supplied from STATCOM THD, %

φ = 10°

φ = 15°

HCC

LQR

HCC

LQR

HCC

LQR

0.9615 1100 3.32

0.9743 1050 2.0346

0.9545 1010 3.5263

0.9642 949 2.2315

0.9373 800 3.63

0.9457 776 2.213

Fig. 9 Hardware setup – schematic and snapshot IET Power Electron., 2013, Vol. 6, Iss. 9, pp. 1872–1883 doi: 10.1049/iet-pel.2012.0524

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www.ietdl.org Variation of real and reactive power with rotor speed – uncompensated case

Table 2

Rotor speed, rpm 1513 1520 1537 1546 1556 1565 1570 1575

Real power supplied, W

Reactive power drawn (VAR)

60 100 165 224 286 350 365 408

150 220 290 323 369 432 479 515

wiSTAT = 100. The weight of IG current is chosen as wig = 5. The elements of the R matrix are chosen as r1 = r2 = 0.1. Solving the Riccati equation, the gains K1 and K2 are found to be 0.0795 and 31.6709, respectively. The frequency of triangular carrier is set as 2.5 kHz. The LQR is realised for STATCOM as shown in Fig. 3b. The STATCOM is connected to the PCC through a filter of resistance 0.4 Ω and inductance 0.01 H. The power generated from IG is fed to the grid through a feeder of resistance 1 Ω and inductance 0.01 mH in each phase. The system is simulated for wind speeds ranging from 4 to 7 m / s. STATCOM is connected at t = 2 s. The system is simulated separately for each control method with the reference currents generated by instantaneous p–q theory and symmetrical component theory with φ = 0. The results confirm the UPF operation at

Fig. 10 Grid voltage and currents a Before compensation b Instantaneous p–q theory with HCC c Instantaneous p–q theory with LQR (va is the grid voltage of phases ‘a’, ia, ib and ic are currents flowing through the grid in each phase), (voltage sensor gain = 200 and current sensor gain = 5) 1880 & The Institution of Engineering and Technology 2013

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Fig. 11 Grid voltage and currents a Symmetrical components theory with HCC b Symmetrical components theory with LQR (va is the grid voltage of phases ‘a’, ia, ib and ic are currents flowing through the grid in each phase), (voltage sensor gain = 200 and current sensor gain = 5)

PCC. The simulated results for the wind speed of 5 m / s are illustrated in Figs. 4 and 5. From the responses, the following observations are made: † Fig. 4a shows the phase relationship between grid voltage (va) and current (ia) in phase ‘a’ without STATCOM which reveals that the reactive power is drawn from the grid. † In Figs. 4b and c, the UPF operation in phase ‘a’ with HCC- and LQR-based control of STATCOM using instantaneous p–q theory are illustrated in sequence. The spectrum of grid current in phase ‘a’ for both control methods are also presented from which it can be identified that the LQR and HCC provide total harmonic distortion (THD) of 2.0887 and 3.4733%, respectively. † In Figs. 5a and b, the UPF operation in phase ‘a’ with HCC- and LQR-based control of STATCOM using symmetrical components theory are illustrated in sequence. The spectrum of grid current in phase ‘a’ for both control methods are also presented from which it can be viewed that the THD with LQR and HCC are 3.8099 and 2.3399%, respectively. Figs. 6a and b illustrate the real power fed to grid by IG and reactive power supplied by STATCOM to IG, respectively. The proficiency of the reference current generation theories and the control methods HCC and LQR to attain UPF are depicted in Figs. 6c and d. As observed from these figures, more enhancement of power factor and reduction in %THD are achieved with LQR compared with HCC. Since the symmetrical components theory provides the freedom of setting desired power factor angle (φ), the system is simulated for non-zero ‘φ’ values which reduce the power IET Power Electron., 2013, Vol. 6, Iss. 9, pp. 1872–1883 doi: 10.1049/iet-pel.2012.0524

rating of STATCOM compared with UPF. The simulation results are shown in Figs. 7 and 8 for φ = 5 and 10°. From the responses, it can be viewed that the preset ‘φ’ is achieved between va and ia. The power factor attained, VAR supplied from STATCOM and THD for different ‘φ’ are listed in Table 1.

6

Experimental results

To validate the feasibility of the proposed control scheme under balanced supply voltages, experimental tests have been carried out. The induction machine and the voltage source inverter with the ratings of 0.75 kW and 5 kVA have been used. The inverter is built with Semikron made insulated gate bipolar transistor (IGBT) modules, SK60GM123D. Filter inductor of 8 mH is used in each phase. Voltage and current sensing are done by LEM voltage (LV25-P) and current (LA25-P) transducers. The quantities measured from the system are IG currents, grid currents and grid voltages. The prime mover action is brought about by a 1.1 kW dc shunt motor. The complete control, which involves reference current generation, HCC and LQR are realised using DS1104 R&D controller board of dSPACE which includes subsystem based on TMS320F240 digital signal processor. In Fig. 9, a schematic of the hardware setup is shown along with the snapshot of the actual system. The induction machine is excited through an autotransformer with the set voltage of 150 Vrms. Super synchronous speed is achieved by performing field control of dc shunt motor. The dc capacitor of STATCOM is precharged and maintained at constant value of 250 V using a PI control loop. The detailed parameters of hardware setup are given in the Appendix. 1881

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Fig. 12 Spectrum of experimental grid current in phase ‘a’ a For instantaneous p–q theory with HCC b For instantaneous p–q theory with LQR c For symmetrical components theory with HCC d For symmetrical components theory with LQR e Efficiency of the system

For various speeds, the real power supplied and the reactive power drawn without compensation are tabulated in Table 2. The experiment is carried out with HCC and LQR and the reference grid currents are generated using both instantaneous p–q theory and symmetrical components theory. The results are provided for the rotor speed of 1565 rpm. The grid voltage and current in phase ‘a’ before compensation are shown in Fig. 10a, which implies that the reactive VAR is drawn from the grid. Figs. 10b and c depict the compensated grid currents and UPF in phase ‘a’ with HCC and LQR, respectively, when instantaneous p–q theory is used. In Figs. 11a and b, the compensated grid currents and UPF in phase ‘a’ with HCC and LQR are presented in sequence, when symmetrical components theory is used. The achievement of reactive power compensation through the proposed compensation techniques is apparent from 1882 & The Institution of Engineering and Technology 2013

Figs. 10b, c and 11a, b. On exploring the responses, it is understood that the distortions in grid currents are considerably reduced thereby the power factor is improved with LQR control than the HCC. The frequency spectrum of measured grid current and the calculated %THD in phase ‘a’ for each compensation technique with the combination of HCC and LQR are illustrated separately in Figs. 12a–d . From these figures, it is viewed that the symmetrical components theory with LQR yields less THD and higher power factor than the other combinations. The efficiency of IG is also calculated for varying rotor speeds and plotted in Fig. 12e.

7

Conclusion

Supplying power of good power factor by wind farms is a challenge posed in real time, as the power has to conform IET Power Electron., 2013, Vol. 6, Iss. 9, pp. 1872–1883 doi: 10.1049/iet-pel.2012.0524

www.ietdl.org to certain standards. This challenge arises from the fact that the IGs used for energy conversion draw a large quantity of reactive power from the grid. Under isolated conditions, fixed capacitors can be used to provide excitation. However under grid-connected conditions, a compensating device which can provide compensation for the range of wind speeds of IG operation is required. STATCOM proves to be an effective device to serve this purpose. In this paper, the STATCOM is made to supply the entire reactive power requirement of the IG for various wind speeds ranging from 4 to 7 m / s. For all speeds within this range, the reactive power drawn from the grid is made zero and a significant improvement in power factor is achieved. The LQR has been designed for this system and the superiority of this regulator over HCC for optimal state regulation is validated. Instantaneous p–q theory and symmetrical components theory have been applied for reference current generation. Extensive simulation results and the experimental results observed from laboratory setup are presented to support and validate the suggested compensation algorithms. From the results obtained, it is identified that the combination of symmetrical components theory with LQR leads to better performance in terms of power factor as well as THD.

8

Acknowledgments

The authors are grateful to the anonymous reviewers for their critical comments and suggestions. This work has been supported by Anna Centenary Research fellowship, Anna University, Chennai-25, Tamil Nadu, India.

9

References

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Appendix

IG parameters: 0.75 KW, 2 A, 1500 rpm, four pole, dc shunt motor: 1.1 KW, 6 A, 230 V and 1500 rpm and dc capacitor: 1650 μF and 950 V.

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