Analysis Of Voltage Control For A Self-excited Induction Generator Using A Current-controlled Vol

Analysis of voltage control for a self-excited induction generator using a current-controlledvoltage source inverter (CC-VSl) S.-C.Kuo and L.Wang

Abstract: The analysed results of both voltage regulation and current-harmonic suppression of a selfexcited induction generator (SEIG), under unbalanced and/or nonlinear loading conditions using a current-controlled voltage source inverter (CC-VSI) are presented. A hybrid induction-machine model based on the three-phase a-b-c and the d-q frames of reference is employed to describe the dynamic performance of the studied system. The three-phase a-b-c induction-machine model is employed to derive dynamic equations of the SEIG under nonlinear loading conditions. The synchronously rotating reference frame based on a d-q axis model is used to decompose three-phase load currents into active and reactive power currents. The three-phase a-b-c stator voltages of the SEIG and the DC bus voltage of the inverter are simultaneously controlled by a proportional-integral (PI) voltage controller and a harmonic compensator. The simulated results show that the performance of the SEIG under unbalanced and/or nonlinear loading conditions has been effectively improved by the proposed compensating scheme.

1

Introduction

It is well known that an externally driven induction machine can be successfully operated as an induction generator with sustained self excitation when an appropriate value of a capacitor bank is appropriately connected across the terminals of the induction machine [l]. Such an induction machine is called a self-excited induction generator (SEIG). The primary advantages of a SEIG over a

conventional synchronous generator are the brushless construction with squirrel-cage rotor, reduced size, no DC supply for excitation, reduced maintenance cost, and better transient characteristics. In the last two decades, SEIGS have received more attention and they have been widely employed as suitable isolated power sources in wind, tidal, and small hydroelectric renewable energy applications

P-41.

Although the SEIGs have many advantages as described above, a capacitor self-excited induction generator suffers from its inherent poor voltage regulation, and hence, its practical applications to power systems have been limited. A number of methods have been proposed for regulating the voltage profile of the SEIG. The long-shunt and shortshunt connections of the stator windings and the series/ parallel capacitors of a SEIG provided a simple method for improving the voltage regulation of a SEIG [5, 61. However, the series capacitors used in these configurations could result in subsynchronous resonance when the studied 0LEE, 2001 IEE Proceedings online no. 20010477 DOL 10.1049/ipgtd:20010477 Paper fxst received 19th September 2000 and in revised form 26th February 2001 The authors are with the Department of Electrical Engineering, National Cheng Kung University, 1 University Road, Tainan, Taiwan 70101, Republic of China IEE Proc.-Genes. Transni. Distrrb., Vol. 148, No. 5, September 2001

SEIG fed an inductive load or a dynamic load such as an induction motor. Ooj et al. proposed a reactive power compensation scheme using a rotating synchronous condenser [7]. Nevertheless, both the maintenance requirement and large size of the rotating synchronous machine overrode the advantages of the SEIGs. Some different types of voltage regulator act as VAr controllers, which were based on switched capacitors, variable inductors, or saturated reactors [S-lo]. These approaches employed relaykontactors or semiconductor switches that had disadvantages such as larger size and heavier weight of passive elements. The static VAr compensator (SVC) could also be employed to control the conducting angle of the thyristors, and hence, the capacitor or inductor current could be varied to regulate the voltage profile of the SEIGs. T h s method would generate low-order harmonic currents, which were caused by the switching of the line currents. Due to the fast development of high-capacity power semiconductors and power-electronics application techniques, the available solid-state switches such as MOSFETs, IGBTs, GTOs, etc. have been extensively employed as fast power switches in the field of solid-state synchronous voltage source (SVS). The SVS consists of a DC-to-AC voltage source inverter (VSI) with a pulse-width-modulation (PWM) switching technique. Such a high-frequency solidstate SVS generates the low distortion capacitodinductive reactive power from the DC bus capacitor. The function of the solid-state SVS is similar to that of a rotating synchronous condenser, and it is called a static condenser (STATCON) or a static compensator (STATCOM). In recent years, the inverter-based reactive power sources have been used for regulating the AC output voltage profile of a SEIG under balanced three-phase loading conditions. Singh et al. used the STATCON to regulate the terminal voltages of SEIG based on a d-q model under various loading conditions and changes of excitation capacitance 431

value [ll]. In this method, both the AC voltage and DC side voltage of the inverter are controlled with a reactive power and active power control loop, respectively. To improve the Steadystate and dynamic impact of a wind farm on the netwoik, the optimal power flow of a wind farm equipped with a STACOM has been investigated in [ 121. A simplified synchronously rotating reference d-q model of SEIG wii:h field-oriented controlled inverter is also proposed to control the generated voltage with variable speed and load 1131. Nevertheless, the analyses of voltage control for a SEIG under unbalanced and/or nonlinear loading conditions have not yet been examined. A new induction machine inodel called the a& stationary reference frame model has been proposed for voltage and frequency control of a SEIG by a VS-PWM converter, and simulated by using the PSpice program [14]. In such a method, the SEIG suffering from the unbalanced and/or nonlinear loading conditions had been dealt with in the experimental results. but has not evidently been expressed in the model and in the simulated results. Since most of the residential loads are single-phase types such as lamps, pumping motors, air conditioners, and heating loads, etc. unbalanced operation of an isolated SEIG will frequently occur. In fact, these single-phase loads with different VA ratings and various power factors cannot uniformly be connected to a practical three-phase system. When an isolated SEIG feeds power to an unbalanced load, both the three-phase terminal voltages and stator currents are also unbalanced. In general, the unbalanced currents tend to increase the power losses, create unequal heating in the windings, de-rate the output capacity, and cause torque pulsation on the shaft of the studied SEIG. On the other hand, if a rectified load such as a battery-charging system is connected to the terminals of a SEIG, the undesired problems caused by the harmonic currents, such as additional power losses, high-frequency pulsating torque, etc. will also happen in the SEIG. Meanwhile, the unbalanced threephase voltages and current harmonics severely affect the performance and characteristics of the facilities, which are also connected to the same output terminals of the SEIG. This paper deals with voltage regulation and current harmonic suppression for a SEIG using a current-controlled n

&(abc)

voltage source inverter (CC-VSI). A hybrid machine model based on both a three-phase a-b-c frame of reference and a d-q axis frame of reference is employed to describe the dynamic equations of the studied system under unbalanced and/or nonlinear loading conditions. The effective method based on a synchronously rotating d-q axis reference frame is used to decompose three-phase load currents into instantaneous active power and reactive power currents. The three-phase voltages of the SEIG and the DC bus voltage of the inverter are controlled by two PI voltage controllers. All models are described and simulated in real-time using MATLAB simulator software. The analysed results show that the voltage quality of the studied SEIG under unbalanced and/or nonlinear loading conditions has been effectively enhanced by the proposed compensating method.

2

System description

The block diagram of the proposed voltage regulator and current harmonic suppression for a SEIG feeding an arbitrary three-phase load is shown in Fig. I . The prime mover is assumed to be an unregulated micro-hydro turbine, and can be simulated by a separately excited DC motor. A fixed capacitor bank ( C ) supplies the exciting currents to sustain the voltage generation of the studied SEIG under no-load condition. The CC-VSI provides the reactive power and/or compensating harmonic currents to regulate the terminal voltage profile of the SEIG under various loading conditions. The AC side of the inverter is connected to the stator terminals of the SEIG through the inductor (Lf).Combining the inductor (Lf)with the capacitor bank (C), a second-order filter is used to filter out the high-order harmonic components, which are caused by the switching action of the inverter. The DC link of the inverter is composed of an electrolytic capacitor as the DC side voltage source. Since the VSI has no real power source in the DC link, a small active power fed from the SEIG is required for compensating the losses of the inverter to maintain the voltage of the DC capacitor at a specified level. The vector form of the terminal voltage is calculated from the components of the d-q axis reference frame. Then, threephase load currents are decomposed into active and 4

k(abc)

Rf

prime mover

031

‘(abc)

:“I-

&(l23)

-U /t

ic*(123)

/ L f),

1

A

L

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-

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deqe-abc

id7 iqe*

ue

ide*

ieql

VDC

Fig. 1 Block diugrum qfproposed voltage regulator rmd h w n i c compnsatwnfor SEIG 432

IEE Proc.-Gener. Trwsm. Distrih.. Vol. 148, No. 5. September 2001

reactive components (id/ and iqr) using a synchronously rotating reference frame. The voltages of the AC mains and the DC bus voltage of the inverter are controlled by two PI voltage controllers. The desired active and reactive components, ide* and iqe*are transformed into three-phase current commands for CC-VSI in order to inject calculated threephase currents into the lines of the SEIG system.

and 0, (= q t ) is the angle between the machine rotor and the reference frame, which is in the direction of the magnetic flux axis of the winding of phase a. The mechanical torque equations of the SEIG can be described by

2Hp(w,) = T, - T,

(7)

p@r = wr (8) where H i s the inertia constant, and the electrical torque Te can be expressed by

rotor stator

Fi .2 Three-ple connection d b g w n of SEIG with capacitor bunk, CC-

In eqn. 7, Tmis the mechanical torque of the prime mover, and it can be simulated by a separately-excited DC motor. The mechanical torque T, can be expressed by the following equation:

V# and arbitrary loud

3

Model

Although the d-q axis model of an induction machine has been widely used in the field of induction motor control, the model is usually adapted to analyse the machine performance under three-phase balanced conditions. If the studied system is under an unbalanced three-phase operating condition, the results obtained from the d-q axis induction-machine model will become very complicated, since a zero-axis quantity corresponding to a zero-sequence component will be generated. For an insolated SEIG application, the connected loads are practically unbalanced in nature. Hence, the three-phase a-b-c frame of reference is preferred to describe the dynamics of the studied SEIG under unbalanced andor nonlinear loading conditions. Fig. 2 shows the three-phase connection diagram of a SEIG with a Y-connected excitation capacitor bank, a CCVSI, and an arbitrary load. The rotor windings of the studied SEIG are Y-connected and their terminals are shortcircuited together. The three-phase voltage equations of the stator and rotor windings of the induction machine can be expressed by the following equations [15]: us(abc)

+icl Cbp(vb) = i b s - i L b + ic2 C , P ( V c ) = i c s - i L c + ic3

C,P(V,) = 2,s

-iLa

(11) (12)

(13) where iLa, iLb and iLc are, respectively, the three-phase line currents of an arbitrary load, icl,ic2and ic3are, respectively, the compensating currents generated by the CC-VSI. The voltages of the capacitor bank, v,, v b and v, are also the voltages of the mains, since these voltages are identical to the line-to-line voltages of the SEIG.

I110 2O

+PAs(abc) R v ( a b c ) i v ( a b c )+ P A r ( a b c )

(1)

Rs(abc)is(abc)

i

100

(2) The stator and rotor flux-linkage vector in eqns. 1 and 2 can be written in matrix form as below: vv(abc)

where VDo RA,KOand q5 are the DC input voltage, armature resistance, machine constant, and field flux of the DC motor, respectively. The excitation capacitors of each phase are identical and their values are equal to 1OOpF. The voltage-current equations of the excitation capacitors shown in Fig. 2 can be expressed as follows:

90 G

€ 8 0 70

where

L, =

60

[

+

L1, L,, -O.5Lm, -0.5Lm,

+

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-0.5L,,

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Ll,

+

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1

50

(4)

cos(&)

1

(6) IEE Proc.-Gener Transm. Distrib., Vol. 148, No. 5, September 2001

I 1.o

I 1.5

I 2.0

I

I

2.5

3.0

I

Magnetisation curve of SEIG

The saturated characteristic of the magnetising reactance

+

cos(& +1200) cos(&.- 1200) cos(&) cos(0,+1200)

cos(& - 120.)

I

0.5

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Fig.3

Lsr

cos(0,)

'

40 0.0

X, plays a very important role in the voltage buildup process of a SEIG. The nonlinear characteristic relating X,(Q) and the magnetising current I,(A) of the studied SEIG is obtained from an experimental test, and is shown in Fig. 3. Such a nonlinear relationshp can be fitted with a continuous function

X m = a[arctan(pI, - y)

+S]/I,

(14) 433

where the coefficients in eqn. 1, a, 0, y and 6, are determined as below:

a = 69.386, p = 1.797, y = 0.96 and 6 = arctan(y) and the value of thlz initial magnetising reactance can be derived from eqn. 14. using L’HBpital’s rule. Once the magnetising inductance M(= Xm/mb)is found, the mutual inductan’ceused in the above equations can be determined by:

The voltage of the DC bus can be calculated from the inductor currents as follows:

2 C ~ c p ( v o c= ) FAi,l

+ FBic2 + FCic3

(22) The set point of the VDcmust be greater than the peak value of the generated phase voltage in order to generate the desired line currents. 4

Control strategy

0

L,,

= ‘3 M

(15)

Since only a small capacity of the M-G set is available in our laboratory, it is expected that the laboratory prototype will be implemented in future work to verify the effectiveness of the proposed method. The employed induction machine has the following specifications on its nameplate: 1.1kW, 127(A)/220(Y) V, 8.3(A)/4.8(Y) A, 60H2, 2 poles, 3600rpm. The base values of the studied SETG are: V, = 127V, I,, = 4.8A, Zb = 26.462Q Nb = 3600rpm, and w, = 377rads. It is also possible to simulate the performance of a larger generator wii h the proposed method, if its parameters are available. The schematic diagram of a typical CC-VST is shown in Fig. 4. The DC link of the inverter is composed of an electrolytic capacitor as the DC side voltage source. The switching function E4 is defined as follows: FA = 1 when the upper switch (either SI or DI) is conducting, and FA = -1 when the lower switch either (S4 or D4) is conducting. The switching functicins of other legs are defined by a similar way.

The concept of voltage regulation for a SEIG is considered as being that the controlled reactive currents, which are supplied by the CC-VSI, are injected into the line currents of the SEIG. The three-phase voltages of the SETG are sensed and transferred into vector form as a feedback voltage, whose absolute value is a DC quantity, and it is compared with the prespecified reference voltage. After the error voltage is processed by the controller, the output signal of the controller is used to control the reactive power flow of the studied system. If the feedback voltage is larger than the reference voltage, the CC-VSI provides the lagging reactive power for reducing the degree of saturation of the SEIG, and hence, the magnitude of the output voltage of the SETG is also decreased. On the contrary, the leading reactive power is required when the feedback voltage is smaller than the reference voltage. The function of this control strategy is operated well when the system is under a balanced condition. Nevertheless, the loads distributed among thee-phase terminals of the SEIG are practically unbalanced. The SElG may feed the nonlinear loads with a front-end AC-to-DC converter such as a battery-charging system. The feedback voltage is no longer a pure DC quantity when the system is under a three-phase unbalanced condition. A significant ripple quantity corresponding to the unbalanced three-phase voltages is superimposed on the feedback voltage. Hence, the complete concept of voltage control is not only that the feedback DC quantity should be regulated, but also the ripple of the generated voltage should be reduced using the proposed CC-VSl. To get the space vector form of the generated voltages, the three-phase voltages are transformed into orthogonal two-axis components based on a stationary d’-q&reference frame. The transformation equation is of the form: Us(dq0)

= Ksu(abc)

(23)

where the transformation matrix, K,, is given by

I Fig. 4

I

I

Schemtic diugruw of cwrent-controlledvol~ugesource mverter

The voltage
= va - e a - R ~ i c l

L f P ( i c 2 ) = vb

-

eb - R f i c 2

(18)

(19)

Lfp(ics) = - - Rfics (20) where e,, eh and e, are the output voltages as a function of both the capacitor voltage and state of the switches, and they can be expressed as:

With this matrix, the transformation between the threephase a-b-c frame of reference and the ds-qJaxis frame of reference is power invariant. Since the ds-qs axes are orthogonal co-ordinates and the dJ-axis is aligned with a-axis of the three-phase a-b-c frame of reference, the stator voltages vdT and v can be converted to a polar form. The absolute value o r t h e vector stator voltage, I V , ~ ~ , and its vector angle, e,, are, respectively, expressed as:

LO, = arctan % vds

(25)

The sensed voltage 1v.J is compared with the reference voltage I v , ~ ~ * and the error is sent to the input point of the 434

IEE Pro,.-Gener. Trunsm.Distrib.. Vol. 148, N a 5 , September 2001

first PI controller (PI-AC), and its output is denoted as &*, which is the reactive current command for regulating the voltages of the mains. In addition to the AC voltage being regulated, the DC bus voltage should also be regulated. Since the switching losses and conductor losses of the inverter cause the DC bus voltage to be varied, the additional power supplied from the SEIG is needed to keep the DC bus voltage at a constant value. The control loop for the D C bus voltage regulation is also shown in Fig. 1. The error between the DC bus voltage, VDc,and the reference voltage, VDc*,is fed to the second PI controller (PI-DC), whose output is denoted by iCic*. The effect of the control scheme using these two controllers has a good performance under a balanced condition. As mentioned above, the controlled voltage still has the ripple when the studied SEIG feeds unbalanced three-phase loads or nonlinear loads. A solution for this problem is that three-phase load currents should be balanced by injecting the desired compensating currents into the line of the SEIG. If the three-phase load currents are transformed into d-q axis currents according to the stator voltage vector phase, e,, then the load currents in terms of synchronously rotating d'-q' frame of reference are derived as:

ig(&o) = K e i L ( a b c )

(26)

where

Ke =

Again, the voltages of the mains based on synchronously rotating d'-q' axis frame of reference is given as: Then, the expression for the active and reactive power of the load based on the synchronously rotating de-q' axis frame of reference are given by:

With the orientation of the reference frame stated above, the q'-axis voltage is equal to zero (v; = 0), and hence, iCf is regarded as the active power current, and iq; is considered as the reactive power current. Both currents can be decomposed into a DC component and an AC component, and they can be represented as:

If the load currents listed above are entirely supplied by the CC-VSI, the currents of the mains could be balanced and are equal to the three exciting currents of the capacitor bank. Under this condition, the three-phase voltages are no doubt balanced. However, the CC-VSI can only supply reactive power and ripple active power since there is no other active energy storage component except the electrolytic capacitor at the DC side. The DC term of the active power current, i,,,must be supplied by the SEIG. From the discussion given above, the reference signal of the complete compensation currcnt based on the de-qe axis frame of IEE Proc.-Geiier. Tr(m~ii7.Dktrih.. Vu1 148. No. 5, September 2001

reference can be represented as:

+

iZe = 5 d l dc* (32) Here, the DC term of the active power current is extracted by using a fourth-order Butterworth low-pass filter with cut-off frequency at 15Hz. The reference currents of the CC-VSI can then be obtained by transferring and it,e* back to the three-phase system, i.e.

(33) The switching patterns of the CC-VSI are generated according to the compared results between the actual currents and the reference currents with a small hysteresis current band. The complete block diagram of the proposed voltage regulator and harmonic compensation for the SEIG system is shown in Fig. 1. The differential equations of the SEIG and the CC-VSI compensating model are calculated using the Runge-Kutta method of integration. Combining the PI controllers and a low-pass filter, the proposed algorithm is simulated by using a system-oriented MATLAB in real time. 5

Results and discussion

Since the studied SEIG must be excited by injecting a leading reactive power into the stator, a fixed capacitor bank with 100pF/phase is used to supply the required reactive power under the over-excitation condition, which ensures the generated voltage can be sustained under a no-load condition. The function of voltage regulation is achieved by injecting the proper amount of reactive power from CCVSI. The effects of voltage regulator and harmonic compensator with CC-VSI are examined and illustrated using the following three loading conditions. (i) A three-phase resistive load. The resistance values of both phases b and c are lOOQ, while the resistance value of the phase a is 25 k 0 . It is used to simulate an open-circuit condition on phase a as compared to that of phases b and c. (ii) A three-phase inductive load. Originally, a 120R resistor and a 132.6mH inductor are connected in series in each phase to constitute a balanced three-phase inductive load. The impedance of phase a is suddenly changed to be a 2600Q resistor and a 5mH inductor to obtain an unbalanced three-phase loading condition. (iii) A nonlinear rectified load. A three-phase diode bridge rectifier with a resistive load of 1000 connected at the D C side is employed to simulate a nonlinear loading condition. Fig. 5 shows the transient responses of the studied system under the loading condition of (a) with a voltage regulator but without harmonic compensation. The three-phase voltages of the mains are shown in Fig. 5a. The highest voltage in the three phases in Fig. 5 n is the voltage of phase a, since the magnitude of the load impedance of phase a is the largest one in the three phases. The function of voltage regulation is started at r = 0.1 s, and the three-phase voltages still exhibit unbalanced waveforms since the function of current harmonic compensation does not activate. Fig. 5b shows that the absolute value of the vector voltage, Iv,I has an apparent ripple component about 0 . 0 6 ~ ~ and 1 , it would be enlarged a little after the voltage regulator is included. It is found from Fig. 5b that the average of the vector voltage is indeed close to the reference voltage, which is set to be 0.9pu when the voltage regulator is oper435

ating under the steady-state condition. Fig. 5c shows the voltage waveform of phase a of the mains and the compensating current of phlase a supplied by the CC-VSI. It is found that the compensating current lags the voltage, and therefore, the CC-VSI supplies the lagging reactive power for regulating the vector voltage. This is due to that fact that the absolute value of the vector voltage is larger than the reference one before compensation. 1 .o

2 ai 2

0.5

5

unavoidable when the harmonic current is compensated by the CC-VSI. Fig. 6d shows the active current component, id?, and the reactive current component, iJ, which are decomposed from the three-phase load currents. The upper portion is the active current, while the lower one is the reactive power current. It is found that the DC term of the active power current is about 0.2pu, while the DC term of the reactive power current is null. Since the average reactive power is not required for the purely resistive load, the AC term of the active and reactive power current, which are caused by the unbalanced loads, must be compensated completely. 1 .o

0.0

0

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2

-0.5

0.5

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7 0.0 c

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0.00

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0.15

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0.25

0.30

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t. s

a

1

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0.10

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0.30

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Fig.5 , Trunsient res

otzsei' o SEIG under unbulanced resistive loding cowltwn (with voliuge regdtor a mains voltages b absolute value o f vector voltage c voltage and compensating current of phase a

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The effects of the voltage regulator and harmonic compensation are shown in Fig. 6. It can be seen from Fig. 6a that the amplitulrles of the three-phase voltages are nearly equal when the voltage regulation and harmonic compensation are simultaneously employed. The ripple of the vector voltage is significant reduced to be a very small amount, as shown in Fig. 6b and its average value approaches a steady-state condition within 0.1s after the complete compensation works. The response time is mostly influenced by the time constant of magnetising inductance of the studied SEIG. The transient response of the DC voltage of the CC-VSI is shown in Fig. 6c. The reference voltage on the DC side, VD,* is chosen to be 2.0pu, which is nearly equal to 360V in an actual system. It is obvious from Fig. 6c that the control loop for DC voltage has good performance, except that the ripple component is

I

0.25

-0.2

iqle

-0.3I 0.00

I

I

0.05 0.10

I

0.15

I

0.20

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0.25

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0.30

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0.35

1

0.40

t, s

d Trmient reA omes of SEIG under unbulanced resistive loading c o d twn (with voltage regultor mi Iw"nic compemator) a mains voltages b absolute value o f vector voltage c voltage at DC bus d active current and reactive current of load

Fig.6

IEE Prw-Gener. Transm. Distrib.. Vol 148, No. 5, September 2001

Fig. 7 shows the transient responses of the studied system under the loading condition of (b). The inductive load changes from a three-phase balanced condition to an unbalanced one at 0.1 s. It can be found from Fig. 7a that the three-phase voltages have no evident change when the load is suddenly switched to an unbalanced condition. The mains phase voltage and compensating phase current are shown in Fig. 7b. It is seen that the compensating current leads the mains voltage before 0.1 s, while the compensating current lags the mains voltage after the change of the loading condition. T h s means that the CC-VSI provides the reactive power to the system under a balanced condition and it absorbs the reactive power from the system under an unbalanced condition. The active current power component, $, and the reactive power current component, iJ, of inductive load currents are shown in Fig. 7c. It is found that both currents contain the purely DC quantities for the balanced loading condition and they also have AC components under an unbalanced load condition, which must be compensated by the CC-VSI. i* .” n -

2

0.5

ai cn c 5 0.0

Fig. 8. At the beginning of the simulation, the compensating function is not applied to the studied system and the mains currents are the distorted currents of the rectifier load as depicted in Fig. 8a. Once the control scheme starts at t = 0.1 s, the mains current of phase a, which is almost in phase with the mains voltage, approaches a pure sinusoidal waveform but with high-order harmonics. Fig. 8b shows the actual compensating current of phase a with respect to the mains voltage. After three cycles, the system approaches its steady-state condition. The timescalar zoomed waveforms of mains voltage and reference compensating current of phase a are shown in Fig. 8c. Comparing Fig. 86 and c, it is obvious that the actual compensating current follows the reference current in a very good manner. Besides, the voltages of the mains are actually compensated and modified from a distorted waveform to a nearly pure sinusoidal waveform after 0.1 s. The stator current, load current and capacitor current waveforms of the nonlinear loading condition are also shown in Figs. 90, b and c, respectively. It is found that the shape of the stator current waveform is improved after compensation. It is also noted that the high-order harmonics generated by the CC-VSI are sunk into the exciting capacitor.

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I

0.20

I

0.25

I

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I

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I

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t, s C

Fig.7

Trmiennt responses of SEIG under on unbahced uzrluctive loudirg

condition a mains voltages h voltage and compensating current of phase a c active current and reactive current of load

-1.0-1 0.05

I

1

1

0.10

0.15

0.20

1, s C

Fig.8

The ability of the proposed control scheme for handling the nonlinear loading condition of (c) is illustrated in IEE Proc.-Gener. Trunsm. Distrib , Vol. 148. No. 5, September 2001

Trmient responws of’SEIG d e r nonlinear loudmg condition a voltage and current of phase U b voltage and compensating current of phase a c zoomed results of voltage and reference compensating current of phase a 437

1.o

0.5 0 3

&

0.0

.-m

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t, s

a

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7

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t, s

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4 0.0 .-0.5 -1..o +, 0.00

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Fig.9 CI

Cui~eizti t ~ r r w j i m u nfplu~~ Ue LII&Y

nunlitwur lo~uringcutzc/itiun

stator current

b load current c capacitor current

6

Conclusions

This paper has presented the voltage control strategy of employing a voltage regulator and harmonic compensator to regulate and balance the generated voltage of an isolated self-excited induction generator (SEIG), subject to unbalanced and/or nodi near loading conditions. The hybrid induction-machine model based on a three-phase a-b-c reference frame and a d-q axis reference frame has been proposed to describe dynamic characteristics of the studied SEIG with the proposed current controlled voltage source inverter (CC-VSI). AI1 models associated with PI controllers and a low-pass filter are simulated in real time using MATLAB simulator software. Transient responses of the studied system subject to balanced and unbalanced resistive and inductive loading perturbations have been examined. Dynamic characteristics of the studied SEIG with harmonic compensal ion feeding a three-phase bridge diode rectifier have also been performed. The analysed results show that the performance of the studied SEIG under unbalanced and/or nonlinear loading conditions has been effectively improved by the proposed compensating method.

438

A digital processor is required to implement the transformation between three-phase a-b-c and d-q axis reference frames, in which the synchronously rotating angle can be calculated. Since the PLL (phase-locked loop) technique is not needed for tracing the voltages of the mains in this proposed control method, there is no frequency problem when the controller is operating. With the fast development of semi-conductors and the cost reduction of digital signal processor (DSP) chips, power devices have become more and more popular. A number of DSP-based vector-control schemes for induction machine drives have been implemented and are feasible for various industrial applications. The implementation of the DSP-based voltage controller for the SEIG will soon become practical. References

1 BASSET, E.D., and POTTER, F.M.: ’Capacitive excitation of induction generators’, Truns. Am. Inst. Electr. Eng., 1935, 54, pp. 540-545 2 WATSON, D.B., AMLAGA, J., and DENSEM, T.: ‘Controllable d.c. power supply from wind-driven self-excited induction machines’, IEE Pruc., 1979, 126, (12), pp. 1245-1248 3 RAMAKUMAR, R.: ‘Renewable energy sources and developing countries’, IEEE Truns. Power Appur. Syst., 1983, 102, (2), pp. 502510 4 MURTHY, S.S., MALIK, O.P., and TANDON, A.K.: ‘Analysis of self excited induction generators’, IEE Proc. C., Gener. Trumin. Distrib., 1982, 129, (6), pp. 26&265 5 SHRIDHAR, L., SINGH, B., JHA, C.S., SINGH, B.P., and MURTHY, S.S.: ‘Selection of capacitors for the self regulated short shunt self excited induction generator’, IEEE Truns. Energy Cunvers., 1995, 10, (l), pp. 1&16 6 WANG, L., and SU, J.E.: ‘Effects of long-shunt and short-shunt connections on voltage variations of a self-excited induction generator’, IEEE Truns. Energy Cunvers., 1997, 12, (4), pp. 368-374 7 001, B.T., and DAVID, R.A.: ‘Induction generator/synchronouscondenser system for wind-turbine power’, IEE Proc. C., Gener. Trun.sin. Distrib., 1979, 126, (l), pp. 69-74 8 ELDER, J.M., BOYS, J.T., and WOODWARD, J.L.: ‘Self excites induction machine as low cost generator’, IEE Proc. C., Gener. Trunsn7. DBtrib., 1984, 131, (2), pp. 3 3 4 0 9 SINGH, B., MISHRA, R.K., and VASANTHA, M.K.: ‘Voltage regulator for isolated self-excited cage generator’, J. Elecrr. Power Syst. Res.. 1992. 24., (2). DD. 75-83 \ 10 BRENNEN, M.B., and ABBONDATI, A.: ‘Static exciter for induction generators’, IEEE Truns. Ind Appl., 1977, 13, (5), pp. 422428 1 I SINGH, B., and SHILPAKAR, L.B.: ‘Analysis of a novel solid state voltage regulator for a self-excited induction generators’, LEE Proc. C., Gener. Trunsnz. Distrib., 1998, 145, (6), pp. 647455 12 SAAD-SAOUD, Z., LISPOA, M.L., EKANAYAKE, J.B., JENKINA, N., and STRBAC, G.: ‘Application of STATCOMs to wind farms’, IEE Proc. C., Gener. Tmnsnz. Distrib., 1998, 145, (3,pp. 5 11-5 16 13 LEIDHALD, R., and GARCIA, G.: ‘Variable speed field-oriented controlled induction generator’. Proceedings of 33rd IAS-IEEE annual meeting, 1998, pp. 540-546 14 MARRA, E.G., and POMILLIO, J.A:: ‘Self-excited induction generator controlled by a VS-PWM hi-directional converter for rural applications’. Proceedings of 13th APEC-IEEE annual meeting, 1998, pp. 11G112 15 KRAUSE, P.C.: ‘Analysis of electric machinery’ (McGraw-Hili Book CO,New York, 1987)

8

8. I

Appendix

Machine parameters

1.1 kW, 127(A)/220(Y) V, 8.3(A)/4.80 A, 60Hz, 2 poles, R,s= R,. = 2.067Q X, = Xi,. = 2.382C2, H = 0.082s.

8.2 CC-VSI parameters Lr = 7mH, Rf= 0.35Q2,Cdc= 7200pF.

8.3 Controller parameters Both the PI-AC and PI-DC digital controllers have the following parameters: proportional constant Kp = 0.012, integral constant Ki= 0.015.

IEE P r o c - G m e r . Trrr~srn.Distrib., Vol. 148, No. 5, Sepreniber 2001