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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 8, AUGUST 2011

Direct Voltage Control for a Stand-Alone Wind-Driven Self-Excited Induction Generator With Improved Power QualityHua Geng, Member, IEEE, Dewei (David) Xu, Member, IEEE, Bin Wu, Fellow, IEEE, and Wei HuangAbstractAn improved direct voltage control (DVC) strategy is proposed for the control of terminal voltage and frequency of a stand-alone wind-driven self-excited induction generator with variable loads. The DVC strategy, including a proportional-integral (PI) regulator, leadlag corrector, and a feed-forward compensator, is designed based on the system transfer function matrix. The PI regulator can eliminate the steady-state tracking errors of the terminal voltage. The leadlag corrector is employed to enlarge the phase stability margin of the dominant loops while the feedforward compensator is adopted to mitigate the voltage harmonics resulting from the cross-coupling dynamics. The procedures for capacity design of the excitation capacitors, the voltage source inverter, and the consumer load are also presented. The simulation and experimental results verify that the proposed strategy has a fast dynamic response and can effectively control the generated voltage with low harmonic distortions under different linear or nonlinear loads. Index TermsDirect voltage control (DVC), harmonic compensation, induction generator, stand-alone wind energy conversion systems.

I. INTRODUCTION TAND-ALONE power systems using local renewable energy sources like wind, biomass, and hydro are attractive to the remote communities [1]. Compared with grid connected counterparts, they avoid long transmission lines and thereby associate losses and cost. The self-excited induction generator (SEIG) is very suitable for such small or medium power systems compared with other generator structures, such as the doubly fed induction generator, because of its low cost, robustness, less maintenance, and inherent overload protection [2][4]. However, the magnitude and frequency of the generated voltage depend on the rotor speed, excitation current, and the load. SEIG driven by constant speed prime movers such as biogas and diesel engines has a xed rotor speed. The frequency variation of the generator terminal voltage is negligible. In order to maintain the voltage magnitude under variable consumer

S

Manuscript received December 5, 2009; revised March 20, 2010 and September 5, 2010; accepted December 25, 2010. Date of current version August 10, 2011. Recommended for publication by Associate Editor F. Blaabjerg. H. Geng is with the Department of Automation, TNList, Tsinghua University, Beijing100084, China (e-mail: [email protected]). D. Xu and B. Wuare are with the Department of Electrical and Computer Engineering, Ryerson University, Toronto, ON M5B 2K3, Canada (e-mail: [email protected]; [email protected]). W. Hung is with XJ Group Corporation company, Henan 461000, China (e-mail: [email protected]). Digital Object Identier 10.1109/TPEL.2010.2104329

loads, reactive power compensators such as static VAR compensator or static compensator are necessary [5], [6]. In the application of SEIG with constant power prime movers like micro and hydro turbines, the magnitude and frequency of the generated voltage are varying with different load conditions. In previous research, electronic load controllers (ELCs) have been proposed to balance the generator output power to control the generator voltage [1], [7], [8]. However, since the active power is controlled with a variable ac/dc load in the ELC, the system efciency is low [9]. For the wind-driven SEIG where wind speed and consumer loads are variable, both input power and rotor speed are not constant which in turn varies the magnitude and frequency of the generated voltage [6], [10]. In such a case, a shunt-connected voltage source inverter (VSI) with an energy storage unit on the dc side, typically a battery bank, can be utilized to absorb or compensate the active and reactive power produced by SEIG. As a result, the magnitude and frequency of the generator voltage can be maintained [3], [6], [9], [10]. Strategies with double control loops were proposed in [6] and [10] for the SEIGVSI system. The outer frequency and voltage loops determine the references of active and reactive power (or current components) for the inner current loops which then yield the voltage commands for the VSI. Proportional-integral (PI) regulators are normally employed in both control loops to eliminate the steady-state tracking errors. In [9] and [11], direct voltage control (DVC) strategies were presented to control the SEIGVSI system. With only a single voltage loop, DVC directly controls the voltage magnitude with PI regulators and the frequency with an open-loop phase angle generator. DVC has been validated to have a fast dynamic response with simulation and experimental results [9], [11]. However, the nonlinear load situation is not considered in the present strategy. In this paper, an improved DVC strategy for the wind-driven SEIGVSI system is proposed. The procedures for capacity matching of the excitation capacitors, the VSI, and the consumer load are presented. For the resistive load, it is generally hard to reduce the VSI capacity because it has to support the resistive load at low wind speeds. For the inductive load, more excitation capacitors can help to reduce the VSI capacity due to its ability of reactive power supply. The DVC strategy is designed based on the transfer function matrix of the SEIGVSI system. It is noticed that the diagonal dominant loops have a narrow phase stability margin in the conventional DVC. Furthermore, the cross-coupling loops have signicant effects on the dominant loops in 150400 Hz frequency bands, which leads to voltage harmonics under nonlinear load conditions. A leadlag

0885-8993/$26.00 2011 IEEE

GENG et al.: DIRECT VOLTAGE CONTROL FOR A STAND-ALONE WIND-DRIVEN SELF-EXCITED INDUCTION GENERATOR

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Fig. 1.

Block diagram of the SEIGVSI system. Fig. 2. Typical C p versus curve.

phase corrector is employed to enlarge the phase stability margin of the dominant loops and a feed-forward compensator loop is proposed to suppress the harmonics due to cross-coupling. The simulation and experimental results verify that the proposed strategy has a fast dynamic response and can effectively suppress the harmonic voltages under various load conditions. II. SYSTEM CONFIGURATION AND MODELS Fig. 1 shows the block diagram of the SEIGVSI system. The wind turbine is connected to the rotor of the induction generator through a step-up gear box. At the stator side of the generator, there is an excitation capacitor bank in parallel with the VSI and the consumer load. The VSI has an energy storage device, which can be battery or supercapacitor, connected at its dc bus and offers variable controlled impedance across the SEIG terminals to retain the terminal voltage. A. Modeling of the Wind Turbine The mechanical power available in a x-pitch wind turbine, neglecting the losses in the gear box, is given by Pwt = 0.5R2 Cp ()V 3 (1)

vdr = Rr idr + vq r = Rr iq r

ddr (e r )q r dt dq r + (e r )dr . + dt

(2)

The stator and rotor ux can be computed as functions of the d-and q-axes stator and rotor currents as follows: ds = Lls ids + Lm (ids + idr ) q s = Lls iq s + Lm (iq s + iq r ) dr = Llr idr + Lm (idr + ids ) q r = Llr iq r + Lm (iq r + iq s ). (3)

The SEIG excitation capacitors introduce the following state equations in the dq frame: idc = Ce iq c dvds e Ce vq s dt dvq s + e Ce vds = Ce dt

(4)

where air density (kg/m3 ); R radius of the wind turbine (m); Cp power coefcient of the wind turbine; v wind speed (m/s); tip speed ratio. The power coefcient Cp varies nonlinearly with the tip speed ratio which is dened as the ratio of the turbine rotational speed and the wind speed. A typical Cp versus curve for a threeblade wind turbine is shown in Fig. 2 and the detailed equation is described in [12]. It shows that Cp has a unique maximal value in which point the turbine can yield the maximal wind power. B. Modeling of the SEIG The model of the induction generator can be developed in the synchronous reference (dq) frame as follows [2], [13]: vds = Rs ids + vq s = Rs iq s dds e q s dt dq s + e ds + dt

where subscripts d and q direct and quadrature axes; subscripts s and r stator and rotor variables; subscripts l and m leakage and mutual components; subscript c excitation variables; v and i instantaneous voltage and current; L inductance; R resistance; excitation capacitance; Ce synchronous rotational speed; e electrical rotor speed. r It should be noted that the mutual inductance Lm is not a constant and it depends on the nonlinear magnetization characteristics of the SEIG [9], [10]. C. Modeling of the VSI and Consumer Load For the high-frequency switching converters, it is reasonable to describe the converter dynamics with its state-space averaged model [14]. In view of this, the VSI model can be expressed in

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Fig. 3.

Single-phase equivalent circuit of the SEIGVSI system

the dq frame as follows: vds = vdi L vq s didi + e Liq i dt diq i e Lidi = vq i L dt

(5)

where the subscript i represents the VSI variables and L is the lter inductance. The model of a typical RL load can be represented in the dq frame as follows: vds = RL idL + LL vq s = RL iq L didL e LL iq L dt diq L + e LL idL + LL dtFig. 4. Flow chart of the incremental search algorithm.

(6)

Applying Kirchhoff laws to the circuit in Fig. 3, we have Ir = Is = where Vg Zr (9)

where the subscript L represents the load variables. In the same reference frame, the currents of the SEIGVSI system shown in Fig. 1 are related by idi = ids + idc + idL iq i = iq s + iq c + iq L (7)

Vg Vs = Z1 Z2

Zr = Z2 = A= B=

where the subscript c represents the excitation capacitor variables. III. STEADY-STATE ANALYSIS Fig. 3 shows the per-unit per-phase steady-state equivalent circuit of the SEIGVSI system. The VSI, excitation capacitors, and the consumer load are represented by an ideal voltage source Vs since the generator terminal voltage is kept constant in steady state. It is assumed that the harmonics of the voltage and current at switching frequency are negligible. The rotor and stator resistances of the induction generator are referred to the stator side and the leakage inductances of the rotor and stator are assumed to be equal in magnitude (Xlr = Xls = Xl ). All machine parameters are assumed to be constant except the magnetizing reactance Xm and the slip frequency s. The nonlinear magnetization curve at base frequency is approximated with a piecewise function as listed in Appendix I. A. Output Power of the Induction Generator Under Different Wind Speeds In the steady state, the mechanical power introduced to the induction generator can be expressed with the slip frequency s, rotor current Ir , and resistance Rr as [13] follows: Pin = 3 1s 2 I Rr . s r (8)

(Rr /s)2 + Xl2 ;

Z1 =

A2 + B 2

(A + Rs )2 + (B + Xl )22 /s R r Xm (Rr /s) + (Xl + Xm )2 2

(Rr /s)2 Xm + Xl Xm (Xl + Xm ) . (Rr /s)2 + (Xl + Xm )2

Ignoring the losses of the shaft and gear box, the input mechanical power Pin equals to the wind power extracted by the wind turbine Pin = Pwt . (10)

An incremental search algorithm [10], [15] was implemented to solve the steady-state operation points of the SEIGVSI system with (1), (8), (9), and (10). The ow chart of the search algorithm can be illustrated in Fig. 4. The calculation starts with the rated wind speed (9 m/s) and the same procedure is repeated at other wind speeds. Based on the solutions of Xm and s at different wind speeds, the active/reactive power produced/consumed by the generator is obtained and depicted in Fig. 5. Experimental results are also presented in the gure to verify the calculations. The prototype will be introduced in Section VI. It is indicated that the generator produces more active power and consumes more reactive power with a higher wind speed.


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Fig. 5. Active/reactive power produced/consumed by the generator under different wind speeds.

Fig. 6. VSI capacity versus wind speed with different excitation capacitors and loads.

Compared with the active power variation, the reactive power varies in a relatively narrow interval (from 1.07 to 1.25 pu) within the available wind speed range. The rated active power of the induction generator is selected as the base value.Fig. 7. Control diagram of the SEIGVSI system with conventional DVC.

B. Capacity Matching of the VSI, Excitation Capacitors, and Consumer Load In Fig. 3, the power produced by the generator should equal to the power owing into the equivalent voltage source Vs due to the power balance. Since Vs represents the VSI, excitation capacitors, and the consumer load, following power equations hold true: PIG = PVSI PL QIG = QVSI + QC QL . (11)

so that a wide operation range can be guaranteed. Moreover, the average local wind speed can be further utilized to optimize the system capacities. IV. IMPROVED DVC The control objective of the VSI is to maintain the terminal voltage of SEIG even with variable wind speeds or consumer loads. In view of this, the system control inputs are selected as the VSI voltage vdi , vq i and the outputs are the generator terminal voltage vds , vq s . From (2) to (7), the I/O transfer function matrix of the SEIG VSI system is as follows: vs (s) = [G1 (s) I + G2 (s) J] vi (s) where vs (s) = [ vds (s) I= 1 0 0 1 vq s (s) ]T vi (s) = [ vdi (s) J= 0 1 1 0 vq i (s) ]T (12)

Since the presented system is a xed-speed wind energy conversion system (WECS), the active and reactive power of the SEIG can be related to the wind speed as shown in Fig. 5. By further considering (11), the capacities of VSI with different excitation capacitance and consumer loads under variable wind speeds are illustrated in Fig. 6, where the nominal capacitance Cen is designed to provide the excitation currents for the induction generator at the rated wind speed (9 m/s). As shown in Fig. 6, for the resistive load (PF = 1), the VSI capacity reduces with a higher wind speed as the SEIG produces more active power. Increasing or decreasing the excitation capacitance can result in the increase of VSI capacity because the VSI is required to absorb or produce parts of the reactive power due to the capacitance mismatch. Moreover, it is hard to reduce the VSI capacity by capacity matching because it has to support the resistive load at low wind speeds. For the inductive load (PF < 1), the VSI capacity can be reduced if the excitation capacitor is properly increased. Under different wind speeds, optimal capacity of VSI exists at the point where the capacitor bank can provide all the reactive power required by the SEIG and the load. As a result, the capacity of the excitation capacitor can be designed at the rated wind speed and it is better to be higher than its nominal value in order to feed the inductive load. The VSI capacity should be designed at the minimal wind speed

G1 (s) and G2 (s) are the dominant and cross-coupling transfer functions of the I/O and they are listed in Appendix II. Here, the magnetizing saturation is not concerned because the generator should be designed to operate in the linear parts of the magnetization curve in the desired wind speed range in order to obtain a satisfactory performance. Thus, Lm is considered as a constant in this section. For such a multiinput multioutput (MIMO) system, a popular technique in the industry is to follow the control design procedures for single-input single-output (SISO) systems, in which the cross-coupling items are considered as disturbances. Motivations comes from the fact that many systems can be made diagonally dominant (i.e., interactions between loops are not

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Fig. 8.

Bode diagram of the open-loop SEIGVSI system with different load parameters: (a) d-axis; (b) q -axis; (i) dominant loop; (ii) cross-coupling loop.

Fig. 9.

Control diagram of the SEIGVSI system with improved DVC.

predominant) by designing appropriated decoupling compensators [16]. The PI controller can be applied to the dominant loops [9] resulting in the control diagram as depicted in Fig. 7, where T (s) = kp + ki /s and vdis represents the disturbances caused by the load variations. The open-loop transfer function matrix of the whole system shown in Fig. 7 is G (s) = T (s) [G1 (s) I + G2 (s) J] . (13)

Fig. 10.

Open-loop bode diagram of the dominant loops.

Usually, the generator speed responses much slower than the electrical variables due to the large turbine and generator inertias. And the operating slip frequency of the wind-driven SEIG shown in Fig. 1 is around 5 to 1%, which has negligible effects on the system characteristics. By considering the generator speed as a constant, the open-loop bode diagrams of the system (13) with different load situations are illustrated in Fig. 8. Fig. 8 shows that the d- and q-axes dominant/cross-coupling loops have the same bode magnitude properties. For the dom-

inant subsystems, the phase stability margin is very narrow (around 1 ) which is hard to improve through PI parameter design as long as a certain controller bandwidth is required. The load parameters have negligible inuence on the bode properties of the dominant loop but they can affect the cross-coupling loop in the low-frequency band (< 10 Hz). Compared with the dominant subsystem, the cross-coupling subsystem has much smaller magnitudes during all the frequency band except for 150400 Hz. As a result, the load effects on the cross-coupling loop can be restrained by the dominant subsystem. However, the


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Fig. 11.

System responses with RLload. (a) Step-up load and constant wind speed. (b) Constant load and step-down wind speed.

Fig. 12. System responses with a step-up nonlinear load and constant wind speed. (a) DVC without feed-forward compensator. (b) DVC with feed-forward compensator.

Fig. 13.

Frequency spectrum of the load voltage in Fig. 12. (a) DVC without feed-forward compensator. (b) DVC with feed-forward compensator.

cross-coupling loops may deteriorate the harmonic mitigation performance of the dominant loops. A leadlag phase corrector is effective to improve the phase stability margin of the dominant loops, which has the following transfer function:

Tc (s) =

1 + Tz s 1 + Tp s

(14)

in which Tz and Tp are the time constants of the lag and lead correctors, respectively. For the inuence of a cross-coupling subsystem, compensators are usually used in order to decouple the loops so that the overall system consists of a number of independent SISO diagonal control loops and each of them can be designed independently by classical techniques. However, the decoupling compensators tend to be of the same order of complexity of the plant itself. Moreover, exact decoupling implies that the

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phase stability margin at the prior cutoff frequency (1 kHz) is increased to 58 which is enough for the stable operation of the SEIGVSI system. Additional damping on the sixth voltage harmonics is also provided with the dominant loops that can help to suppress the harmonic voltages in nonlinear load applications. V. SIMULATION RESULTS The simulations are carried out in MATLAB/SIMULINK to verify the effectiveness of the improved DVC. The models of the SEIGVSI system shown in Fig. 1 are developed in the simulations. The SEIG is modeled as a ve-order system in the abc reference frame. The VSI and its controller are modeled as a digital system with a 5-kHz switching frequency and a 10kHz sampling frequency. The excitation capacitor is selected to provide the needed reactive power to the SEIG at the rated wind speed. The rotating frequency of the dq frame for the DVC is set by a constant reference. System and control parameters for the simulations are listed in Appendix I. The system responses under different wind speed and load conditions are presented. A. Operation With Linear RL Load Under the rated wind speed 9 m/s, the RLload is applied to evaluate the performance of the proposed DVC. The load changes at t = 0.2 s from RL = 44 , LL = 340 mH to RL = 22 , LL = 340 mH. The simulation results are shown in Fig. 11(a). It shows that the DVC has very fast dynamic responses. When the load increases, the VSI provides more currents to sustain the load voltage and the generator output currents preserve the same since the wind speed does not change. Although onecycle transients appear in the VSI and generator currents after t = 0.2 s, the load currents have negligible transients. The system responses with a step wind speed is illustrated in Fig. 11(b). At t = 0.2 s, the wind speed steps from 9 down to 7 m/s while the consumer load remains at RL = 44 , LL = 340 mH. The VSI increases the output currents after the wind speed changes but the load voltage and current reserve a constant. Because of the large inertias of the wind turbine and generator, the current response of the VSI is slower than that in the constant wind speed situation. In both simulations with linear loads, the generated voltages have very low total harmonic distortions (THD). B. Operation With Nonlinear Load The performances of the DVC for nonlinear load applications are evaluated with the simulations. The nonlinear load congures with a three-phase diode rectier powering a resistor. The load resistance changes at t = 0.2 s from RL = 44 to RL = 22 and the wind speed is 9 m/s. Two DVCs without and with feed-forward compensators are implemented in the SEIG VSI system and the simulation results are depicted in Figs. 12 and 13. As shown in Fig. 12, the nonlinear load currents are provided by the generator and VSI. Similarly with Fig. 11(a), the

Fig. 14. System responses with a constant nonlinear load and step-down wind speed employing improved DVC.

knowledge of an exact plant model is necessary to cancel the coupling dynamics. In view of these, such a strategy seems to be unpractical for the SEIGVSI system. Since the cross-coupling loops have signicant effects on the dominant dynamics only in 150400 Hz frequency bands, the harmonic components in the disturbance vdis within the frequency bands are expected to be amplied and coupled into the system outputs. In order to obtain a satisfactory harmonic mitigation performance, a feed-forward compensator is proposed to the dominant loops to provide active damping on the voltage harmonics resulting from the cross-coupling loops. The harmonics components in vdis can be extracted from the load voltage. Considering a three-phase balanced nonlinear load, only fth- and seventh-order harmonics, both having a frequency of 360 Hz (sixth order) in the synchronous rotational frame, are within the 150400-Hz frequency bands. Hence, a band-pass lter is employed to detect the sixth voltage harmonics from the feedback signals and formulate the feed-forward compensator F (s) = 2cut s 2 s2 + 2cut s + 0 (15)

where cut and 0 are the cutoff and center frequencies of the band-pass lter. Because of no current control loops, the output currents of VSI with DVC may exceed its rating due to lower wind or during overloading. In order to improve the current controllability, additional current limiter loop is introduced into the DVC [17]. When the VSI current exceeds its rating value, the current limiter will decrease the output voltage reference in the allowed range. The block diagram of the proposed DVC is shown in Fig. 9. Compared with the indirect schemes, the diagram is simple to implement since only voltage loop is required to tune. Moreover, the dynamic response of DVC is faster than that of an indirect scheme which can be affected by a large turbine and generator inertias [11]. Compared with conventional DVC, the improved DVC can further improve the power quality. The corresponding open-loop bode plots of the dominant loops [corresponding to Fig. 8(i)] are shown in Fig. 10. It shows that the load changes hardly affect the controller design and the


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Fig. 15.

Experimental setup of the SEIGVSI system.

Fig. 16.

System responses with RLload. (a) Step-up load and constant wind speed. (b) Constant load and step-down wind speed.

VSI provides more currents after the load variation while the generator currents preserve unchanged due to the constant wind speed. Without feed-forward compensator, the generator voltage is highly distorted with fth- and seventh-order harmonics and the THD is higher than 5% as illustrated in Fig. 13(a). The fth and seventh harmonics are effectively damped with the compensators and the power quality is highly improved as shown in Fig.13(b). The results correspond well with the analysis in Section IV. The system responses with the step wind speed are illustrated in Fig. 14. At t = 0.2 s, the wind speed steps from 9 down to 7 m/s while the load resistance remains at RL = 44 . Similarly, the VSI increases the nonlinear output currents after the wind speed changes and the currents provided by the SEIG reduce. The load voltage reserves a constant magnitude and frequency after the wind speed steps.

A back-to-back converter is employed for the experiment in which one side operates as the rectier to function as the dc energy storage unit and the other as the VSI to maintain the local bus voltage. The wind turbine simulator is driven by a acdc converter. Both the VSI and acdc converter are controlled with the same DSPFPGA digital control system. The eld programmable gate array (FPGA) implements the digital phase-locked loop and all necessary protections. The TMSF2812 xed-point DSP is applied to realize the necessary mathematical algorithms and generate pulse-width modulation gate driving signals for the power devices. Appendix I gives the rating and parameters of the experimental system. A. Operation with Linear RL Load With the same conditions as in the simulation, the experimental results are shown in Fig. 16, which are consistent well with the simulation results. It shows that the DVC has very fast dynamic responses and the load voltage is controlled to be a constant with load or wind speed variations. B. Operation With Nonlinear Load Employing the same conditions as in Simulation B, the performances of the DVC for nonlinear load applications are experimentally evaluated and the results are depicted in Fig. 17(a)(f).

VI. EXPERIMENTAL RESULTS Fig. 15 shows the experimental setup built to verify the proposed DVC strategy. The setup consists of two shaft-coupled machines: one is the dc motor operating as the wind turbine simulator and the other is the induction generator. A capacitor bank is connected in parallel with the generator to provide the excitation.

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Fig. 17. System responses with a step-up nonlinear load and constant wind speed. (a) DVC without feed-forward compensator. (b) Enlarged load voltage and current of (a). (c) Frequency spectrum of the load voltage in (b). (d) DVC with feed-forward compensator. (e) Enlarged load voltage and current of (d). (f) Frequency spectrum of the load voltage in (e).

VII. CONCLUSION This paper has presented the procedures for the capacity and controller design of the stand-alone wind-driven SEIGVSI system. The VSI capacity can be optimized following the capacity matching calculations for a given load range. For the inductive load, more excitation capacitors can help to reduce the VSI capacity because its ability of reactive power supply. In the industry, the conventional technique for the controller design of a MIMO system such as the SEIGVSI is to follow the procedures for SISO systems, in which the cross-coupling loops are considered as disturbances or compensated with decoupling items. However, as shown in this paper, it is difcult to execute the decoupling compensations for the SEIGVSI system since the system parameters are normally unknown. Moreover, the inuences of the coupling dynamics cannot be ignored in some frequency bands. In such a case, the compensation can be implemented in the diagonal dominant loops, which provides active damping on the effects of coupling dynamics. The proposed control strategy has been veried with simulation and experimental results. APPENDIX I PARAMETERS OF THE SEIGVSI SYSTEM The parameters of the wind turbine model are as follows: Number of blades 3 Turbine radius (m) 2 Rated power (kW) 2 Rated wind speed (m/s) 9 Gearbox ratio 31

Fig. 18. System responses with a constant nonlinear load and step-down wind speed employing improved DVC.

Without feed-forward compensator, the DVC can also have a fast response even with the nonlinear load as shown in Fig. 17(a). But the generated voltage is highly distorted as illustrated in Fig. 17(b). Based on the fast Fourier transform analysis [see Fig. 17(c)], fth and seventh harmonics are the dominant harmonic components in the generator voltage and the THD is as high as 7.66%. With additional feed-forward compensator, the fth and seventh harmonics are effectively damped as shown in Fig. 17(e) and the voltage THD is reduced to 2.74%. With a step wind speed, the experimental result is illustrated in Fig. 18. The VSI increases the nonlinear output currents after the wind speed change and the load voltage reserves a constant magnitude and frequency. All the experimental results correspond well with the theoretical analysis and the simulations.


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Lift to drag ratio 30 0.461 Cp, m ax 3.43. m Ratings and data of the SEIG are listed as follows: Power (kW) 2 Line voltage (V) 208 Current (A) 5.55 Frequency (Hz) 60 Shaft speed (rpm) 1720 Pole pairs 2 Stator, rotor resistances (pu) 0.032 Stator, rotor leakage inductances (pu) 0.061 Mutual inductance (pu) 0.875 Excitation capacitance (pu) 1.15. Parameters of the VSI and DVC are as follows: DC bus voltage (V) 400 Filter inductance (pu) 0.2 Proportional parameter 10 Integral parameter 20 Feed-forward loop gain 1 Time constant of lag corrector 4.68 104 Time constant of lead corrector 5.488 105 Cutoff frequency of the band-pass lter (rad/s) 314 Center frequency of the band-pass lter (rad/s) 2261.94. Magnetization curve at base frequency is Vg = 0.9758 0.0401Xm for Xm 0.6727 pu Vg = 0.9847 0.0537Xm for 0.6727 Xm 0.8117 pu Vg = 1.0254 0.1038Xm for 0.8117 Xm 1.0104 pu Vg = 0 for Xm > 1.0104 pu. APPENDIX II TRANSFER FUNCTION MATRIX OF THE SEIGVSI SYSTEM The transfer function matrix of the SEIGVSI system can be deduced from (2) to (7).1 G1 (s) I + G2 (s) J = [I + Ai (s) A L (s) + Ai (s) Ac (s) 1 1 + Ai (s) A g (s)]

(16)

[2] M. G. Simoes and F. A. Farret, Alternative Energy Systems: Design and Analysis With Induction Generators, 2nd ed. Boca Raton, FL: CRC Press, 2007. [3] J. Chatterjee, B. Perumal, and N. Gopu, Analysis of operation of a selfexcited induction generator with generalized impedance controller, IEEE Trans. Energy Convers., vol. 22, no. 2, pp. 307315, Jun. 2007. [4] K. Protsenko and D. Xu, Modeling and control of brushless doubly-fed induction generators in wind energy applications, IEEE Trans. Power Electron., vol. 23, no. 3, pp. 11911197, May 2008. [5] B. Singh, S. Murthy, and S. Gupta, Analysis and design of statcom-based voltage regulator for self-excited induction generators, IEEE Trans. Energy Convers., vol. 19, no. 4, pp. 783790, Dec. 2004. [6] B. Singh and G. Kasal, Solid state voltage and frequency controller for a stand alone wind power generating system, IEEE Trans. Power Electron., vol. 23, no. 3, pp. 11701177, May 2008. [7] B. Singh, S. Murthy, and S. Gupta, Analysis and design of electronic load controller for self-excited induction generators, IEEE Trans. Energy Convers., vol. 21, no. 1, pp. 285293, Mar. 2006. [8] J. M. Ramirez and M. E. Torres, An electronic load controller for the self-excited induction generator, IEEE Trans. Energy Convers., vol. 22, no. 2, pp. 546548, Jun. 2007. [9] B. Venkatesa Perumal and J. Chatterjee, Voltage and frequency control of a stand alone brushless wind electric generation using generalized impedance controller, IEEE Trans. Energy Convers., vol. 23, no. 2, pp. 632641, Jun. 2008. [10] L. Lopes and R. Almeida, Wind-driven self-excited induction generator with voltage and frequency regulated by a reduced-rating voltage source inverter, IEEE Trans. Energy Convers., vol. 21, no. 2, pp. 297304, Jun. 2006. [11] W. Huang and D. Xu, Direct voltage control for standalone wind energy conversion systems with induction generator and energy storage, in Proc. IEEE Electric Power Conf.(EPEC), Oct. 2008, pp. 18. [12] G. Stavrakakis and G. Kariniotakis, A general simulation algorithm for the accurate assessment of isolated diesel-wind turbines systems interaction. i. a general multimachine power system model, IEEE Trans. Energy Convers., vol. 10, no. 3, pp. 577583, Sep. 1995. [13] B. K. Bose, Modern Power Electronics and AC Drives. Upper Saddle River, NJ: Prentice Hall, 2002. [14] D. Maksimovic, A. Stankovic, V. Thottuvelil, and G. Verghese, Modeling and simulation of power electronic converters, Proc. IEEE, vol. 89, no. 6, pp. 898912, Jun. 2001. [15] S. Singh, B. Singh, and M. Jain, Performance characteristics and optimum utilization of a cage machine as capacitance excited induction generator, IEEE Trans. Energy Convers., vol. 5, no. 4, pp. 679685, Dec. 1990. [16] D. Chen and D. Seborg, Multiloop PI/PID controller design based on gershgorin bands, IEE Proc. Control Theory Appl., vol. 149, no. 1, pp. 6873, Jan. 2002. [17] R. Teodorescu and F. Blaabjerg, Flexible control of small wind turbines with grid failure detection operating in stand-alone and grid-connected mode, IEEE Trans. Power Electron., vol. 19, no. 5, pp. 13231332, Sep. 2004.

where

Ai (s) = Ls I + e L J AL (s) = (RL + LL s) I + e LL J Ac (s) = Ce s I + e Ce J1 Ag (s) = Ag s (s) Ag r 1 (s) A g r 2 (s) Ag r 3 (s)

Ag s (s) = (Rs + Ls s) I + e Ls J Ag r 1 (s) = Lm s I + e Lm J Ag r 2 (s) = (Rr + Lr s) I + (e r ) Lr J Ag r 3 (s) = Lm s I + (e r ) Lm J. REFERENCES[1] B. Singh, S. Murthy, and S. Gupta, Transient analysis of self-excited induction generator with electronic load controller (ELC) supplying static and dynamic loads, IEEE Trans. Ind. Appl., vol. 41, no. 5, pp. 11941204, Sep./Oct. 2005. Hua Geng (S07M10) received the B.S. degree in electrical engineering from the Hua Zhong University of Science and Technology, Wuhan, China, in 2003, and the Ph.D. degree in control theory and application from Tsinghua University, Beijing, China, in 2008. From 2008 to 2010, he was a Postdoctoral Research Fellow in the Department of Electrical and Computer Engineering, Ryerson University, Toronto, ON, Canada. He has been an Assistant Professor in the Automation Department, Tsinghua University, since May 2010. His current research interests include distribution generation systems, renewable energy conversion systems, and digital control systems.

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Dewei (David) Xu (S99M01) received the B.Sc, M.A.Sc, and Ph.D. degrees in electrical engineering from Tsinghua University, Beijing, China, respectively, in 1996, 1998, and 2001. He has been working with Ryerson University, Toronto, ON, Canada, since 2001, where he is currently an Associate Professor. His research interests include renewable energy system, high power converters, electric motor drives, and advanced digital control for power electronics.

Wei Huang received the M.A.Sc. degree in electrical and computer engineering from the Ryerson University, Toronto, ON, Canada, in 2008. He joined XJ Group Corporation Company, Henan, China, in 2009, where he is currently a Senior Engineer and Project Manager. His current research interests include the control and operation of wind energy conversion systems.

Bin Wu (S89-M92SM99F08) received the M.A.Sc. and Ph.D. degrees in electrical and computer engineering from the University of Toronto, Toronto, ON, Canada, in 1989 and 1993, respectively. After being with Rockwell Automation Canada as a Senior Engineer, he joined Ryerson University, Toronto, where he is currently a Professor and the NSERC/Rockwell Industrial Research Chair in Power Electronics and Electric Drives. He has published more than 200 technical papers, authored a Wiley-IEEE Press book, and holds more than 20 issued and pending patents in the area of power conversion, advanced controls, adjustable-speed drives, and renewable energy systems. Dr. Wu received the Gold Medal of the Governor General of Canada, the Premiers Research Excellence Award, the Ryerson Distinguished Scholar Award, the Ryerson Research Chair Award, and the NSERC Synergy Award for Innovation. He is a Fellow of the Engineering Institute of Canada (EIC) and the Canadian Academy of Engineering (CAE). He is an Associate Editor of IEEE TRANSACTIONS ON POWER ELECTRONICS and IEEE CANADIAN REVIEW.

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