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Self-excited induction generator w i t h excellentvol tage and frequency control

R. BonertS. Rajakaruna

Indexing terms: Induction generator, Stand-alone generation,Load governing

Abstract: capacitor-excited induction generatorused with a hydraulic turbine in a stand-alonegenerating system can provide a high qualityvoltage and frequency control not matched byother small generating units. This is achievedwithout a turbine governor by using acontrollable additional impedance on the loadside. The control is achieved using a staticconverter. The analysis of the system and thedesign of the power and control system arepresented. Measurements from an experimentalunit are provided to verify the predictedperformance.

List of symbols

List of symbols and their definition, units are metricusing the SI unit syslem.

Variables

C capacitancei currentIm imaginary part of

i complex componentJ inertiak , m constantL inductanceR resistancet timeTsh, To torque; shaft, constantV voltagea control angle of bridge6 pulse width (ofchopperY flux linkagew frequency in radiansQ mechanical ,peed n radiansIndices

ct controller

EE, 1998

IEE Proceedings online no. 19981680

Paper first received 10th October 1996 and in revised form 26th August1997R. Bonert is with the Department of Electrical Engineering, University ofToronto, Toronto, Ont., M5S 3G4, Canada

S. Rajakaruna is with the Department of Electrical Engineering, Univer-sity of Moratuwa, Katubedda Moratuwa, Sri Lanka

R rotor

S stator

a orthogonal component aP orthogonal component P

1 Introduction

The proposed generator system consists of a capacitor-excited induction generator driven by an unregulatedhydraulic turbine without a speed governor as shownin Fig. 1. The generator supplies an isolated electricsystem indicated as an inductive resistive load in Fig. 1.The voltage and frequency control of the system isachieved by an impedance controller at the terminals ofthe generator. This principle is sometimes called electricload governing.

n

gate open/close

'

Fig. 1

1p h a s e Icontrolled Ibridge

impedancecontroller

Ichopper I

I_ _

Turbine generator system and electric circuit

As can be seen in Fig. 1 the impedance controllerconsists of a phase controlled bridge and a chopperswitch connected to a resistor. This controller can con-sume real and reactive power. The amount of power iscontrolled by control of the bridge and the pulse widthcontrol of the chopper. The principle of operation isthat the impedance controller picks up the real powerand reactive power not used by the load, so that theload or the impedance seen by the generator at ils ter-minals is always constant. The voltage and frequency

at the terminals of the generator will then be constantas well. Any change in load is immediately compen-

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sated by the impedance controller thus holding theimpedance and therefore voltage and frequency at thegenerator terminals constant.

The advantage of this system is that an expensiveand slow turbine governor is not needed and theimpedance controller is a three-terminal device con-nected to the generator providing a high quality volt-age and frequency control. The disadvantage is therestricted use of the principle of this control forhydraulic generation at rivers or dams with sufficient

water, where it does not matter whether water spillsover the dam or some generated energy is dissipated inthe resistor of the impedance controller.

2system

Dynamic model of th e tur bine-generator

Using the space phasor description and selecting a ref-erence system rotating synchronously with the statorvoltage the induction machine can be described by thefollowing differential equations [11. Using complex var-iables for voltage, current and flux linkage the statorand rotor equations and the mechanical equation canbe written as:

3 )

with w the electrical frequency, C2 the mechanicalspeed, J the inertia, Tsh he torque and the indices Rand S mark rotor and stator variables. For the symbolsused see the list in the Appendix, Section 11.

Using a flux linkage model with only one leakage

inductance, the flux linkage equations can be writtenas:

9 s = imL, (4)

(5)ZR s = Z R L R ~with Lm the magnetising inductance and L,, the leak-age inductance.

A resistor representing the stator core losses may beadded parallel to the magnetising inductance [2 ] . Tomodel the induction machine for operation as a self-excited generator it is necessary to introduce saturationwhich can be assigned to the magnetising inductance ineqn. 4. The value of the magnetising inductance is

modelled as depending on the magnitude of the statorflux linkage:

Lm = f l Q ~ l ) (6)The load for the induction generator is modelled as a

series to represent the true dynamic behaviour of suchloads. The differential equations describing the loadand the capacitor referred to the synchronous frame ofthe induction machine's stator voltage are:

resistive inductive load with a resistor and inductor in

( 7 )

The complete equivalent circuit describing the dynamic

34

of the system including the capacitor for excitation ofthe induction generator and the load is shown in Fig. 2.

ig 2 Dyna mic equivalent circuitof generator system

The last component to be modelled is the turbine. Itis assumed that the coupling to the generator is stiff; asa result the inertia of the turbine can be added to theinertia of the induction machine. The turbine is thenmodelled by a torque-speed characteristic. The torque-speed relation of water turbines operated with a con-stant flow and head can be expressed by the linear rela-tion [3 ] :

where To and Qo is any point on the straight linetorque-speed characteristic corresponding to the giveninput hydro power. The negative slope m variesbetween 0.6 and 1.1 depending on the type of turbine.

The above equations describe the turbine generatorsystem with a typical load and the excitation capacitorcompletely. Choosing to align the real axis of the refer-ence system with the stator voltage and splitting thecomplex differential equations into real differentialequations the complete system of equations results ineight real differential equations written in state spaceform and ten algebraic equations. The equations areshown below.

The algebraic equations result directly from theequivalent circuit developed above. The eighteen equa-tions contain eighteen unknown variables.

Tsh = To m(R Ro (9)

differential equations

algebraic e quations

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In the general case of variable speed the system ofequations leads always to only one nonlinear transcen-dental equation for the frequency which has to besolved numerically. This holds true independently ofthe choice of the structure of the equation of the mag-netising characteristic. The decisive step to this generalsolution results from rewriting the steady state equa-tions such that the single phase equivalent circuit repre-senting the equations contains only elements parallel tothe magnetising inductance, as shown in Figs. 4a and band described in detail in [4].

c _ _

I II

II - - - - -

LRS

aca = --asa ~~

a,ap = - ssp L pThe magnetis ing (characteristic from which L, is

(26)

(27)

2 8 )

(29)

derived, is approximated by

Qs = k l . for 0 5 i 5 io

kl

bQs = 1 1 . io + rctan(b(im o for i o 5 i

The constants k l , 6 , io are determined such that thederivative &ldi is cclntinuous at i = io and the meas-ured curve is adequately approximated. This approxi-mation has the advantage that it matches mostmagnetising characteristics very accurately from thelinear region well into the saturation region. Further-more the derivative falls monotonously and the inversefunction is readily available. An example of the goodapproximation is shown in Fig. 3.

1.4 -

1.2

4-.

an& 1.0m

._8 -

8 0.6 -3

4-

0.4 ---

0 .

0.2 0.4 0.6 0.8 1 .O 1.2

magnetising current per unitFig.3k = 2.87,io = 0.11,b = 3.167

~ measured_ _ _ _ approximated

Appro ximation of the magnetising characteristic

3

The 18 steady state equations describing the systembehaviour are derived from eqns. 10-27 using eqns. 28and 29. The resulting system of equations is nonlinear.To solve these equations a new approach was devel-oped which results In a very elegant way to find thesteady state solution [4]. This approach includes earlier

solutions [ S 61 but is more general and the mathemati-cal formulae are much simpler.

Steady state mod el and solut ion

IEE Proc G ene r. Tuansm. Distrib., Vol. 145 No. I , January 1998

Fig.4 Steady state equivalent circuita Fullb Reduced

Based on the steady state solution it is possible tocalculate the operating conditions for any set of param-eters. On the other hand it is also possible to determine

the required settings of the torqueTs h

the speed Q thevalue of the excitation capacitor and the value of theload impedance to achieve a specific desired operatingpoint for voltage, frequency and stator current. Thesecalculations provide the base to determine the rating ofthe impedance controller.

4

Several solutions to build an impedance controller arepossible. The controller shown in Fig. 1 was proposedin [7] and was chosen for this project. The controlleroffers a wide range of fast impedance control and pro-vides a proven reliable design. To keep the voltage har-

monics injected by the impedance controller low, thechopper is switched synchronised to the pulses of thephase controlled bridge at five times the pulse fre-quency of the bridge. The remaining higher frequencyharmonics are reduced by the capacitor on the AC-side, and as a result the remaining total harmonic dis-tortion in the voltage is always less than 5 .

Modelling the selected controller is difficult, as differ-ent modes of continuous and discontinuous conduc-tions have to be analysed. The choice was made todescribe the controller as a device providing real andimaginary current components at a given AC voltageas function of the control angle a of the bridge and thepulse width 6 of the chopper.

Since the harmonics are limited, an approach whichanalyses only the fundamental components of the con-

Model o f the i mpedance contr oller

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erated in the microcontroller. The complete softwarefor the gating control, the control and regulator algo-rithms, the analog I/O and the keyboard I/O is writtenin the C-language. A 16 bit fixed point number systemis used for the arithmetic. The control is implementedas a dual rate sampled data system, with a sample rateof 3kHz in general and a slow sample rate of 60Hz forthe frequency measurement and the slow closed loopfrequency regulator and voltage regulator.

To demonstrate the system performance several tests

with different load changes have been carried out; threeof them will be discussed.

30y0 r - _ _ _1.2

1.06

steadv -I

2 1.04 I

0.6 :

1.06

1.04

; time of change0.4 , , / , I

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

I

-I

I

1.04

.96

0.94

0.98 1 Ifm

I- I

c j J I I I

time of change0.96

0.94

In the first test a load operating at 90 of rated cur-rent at power factor 0.8 is changed by sudden switchingto a load at 45 of rated current at about the samepower factor of 0.76. This is a very large change inload and rather untypical for such a system, butsmaller changes are so well controlled, that not muchcan be observed. Figs. 10a and b show the change involtage and frequency in response to this large changein load. Voltage and frequency are shown in per unit(pu) of the rated values. The values shown are the mag-nitude and frequency of the space-phasor of the statorvoltage as measured and calculated by the microcon-troller.The uncontrolled transient is indicated in thesegraphs with a dashed line. The results are very goodand confirm the predictions of the simulation.

The second test shows a resistive load running atabout 80 of rated current being switched to about 8of rated current. This is one of the harshest conditions,as pure resistive loads cause the fastest load currentchanges possible. This kind of test indicates the behav-iour of the system at transients such as load sheddingor reclosure after the trip of a switch. Figs. l l a and bshow the change of voltage and frequency in responseto the second test transient. The dashed line indicates

I- I

c j J I I I

time of change

the disturbance for the unregulated generator. Theoffset which can be seen is due to the fact that thedisplayed traces are the response with only the feedfor-ward control active.

0.96

0.94

2

+23%

. I

: ime of change. , : J

' time of change0.94 : f I I I I I

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0time,s

,+84% a

3 1.02

1.00

0.98

Q

timeb

Fig.I Measurements test 2Variation of a generator voltage and b frequency70 load chang e, feedforward control only_ _ controlled response_ _ _ _ uncontrolled response

bc

100

V

-100

Fiy. 1250A load change

Measurements: variation of the generator line-to-line voltage at

Both examples demonstrate the superior performanceof the proposed control. Looking at the actual line-to-line voltage of the stator the small change in space-phasor amplitude and frequency can hardly be seen.Fig. 12 shows the stator line-to-line voltage Vb, and aload transient of 50 from full load to half load atabout constant power factor.

8 Nonsymmetri cal loads and automati c start up

Using the experimental set-up and the established sim-ulation further studies were carried out [IO]. The firststudy concentrated on the feasibility of handling non-symmetrical loads and compensating by the impedancecontroller. The result of this study is that due to thefast switching chopper, it is possible to reduce theimpact of nonsymmetrical loads on the symmetry of

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the stator voltages considerably. The control strategydeveloped holds the voltage and frequency variationsof the stator voltage within 2% at 25 nonsymmetry.The nonsymmetry is defined as the amplitude of thenegative sequence current to the positive sequence cur-rent. This is a very good result.

A second study developed a control strategy forautomatic start up of the generator turbine set assum-ing no external pow1:r is available and the system isstarted by opening the gate of the penstock whichcauses the turbine to start up. The automatic systemsenses the sudden increase in stator voltage of the gen-erator as soon as the self-excitation process takes placeand stabilises the voltage and frequency to the desiredvalues upon which the load can be connected by themain switch to the generator system.

9 Conclusions

The self-excited induction generator in a stand-alonegenerating system W Ith a hydraulic turbine using theprinciple of electric load governing by an impedancecontroller can provide excellent voltage and frequencycontrol. With state of the art electronics and the appro-

priate control concept, it is possible to achieve a volt-age and frequency regulation not offered by othersmall generating systems.

The principle of the proposed impedance controller isgeneral and can be used for other impedance control

tasks. The proposed system is also applicable to syn-chronous generators including generators with perma-nent magnet excitation.

10 References

SLEMON, G.R.: ‘Electric machines and drives’ (Addison-Wes-ley, 1992)MALIK, N.H., and HAQUE, S.E.: ‘Steady state analysis andperformance of an isolated self-excited induction generator’,ZEEE Trans., 1986, EC-I, 3) , pp. 134139GULLIVER, J.S., and ARNDT, R.E.A.: ‘Hydropower engineer-

ing handbook’ (McGraw-Hill, 1991), pp 4.404.43RAJAKARUNA, S., and BONERT, R.: ‘A technique for thesteady state analysis of a self-excited induction generator withvariable speed’, ZEEE Trans. Energy Convers., 1993, 8 (4), pp.

ARILLAGA, J., and WATSON, D.B.: ‘Static power conversionfrom self-excited induction generators’, Proc. IEE, 1978, 125, (8),

MURTHY, S.S., MALIK, O.P., and TANDON, A.K.: ‘Analysisof self-excited induction generators’, ZEE Proc. C, 1982, 129, (6),

BONERT, R., and HOOPS, G.: ‘Stand alone induction generatorwith terminal impedance controller and no turbine controls’,IEEE Trans. Energy Convers., 1990, 5 (I), pp. 28-31RAJAKARUNA, S.: ‘Control of a stand-alone self-excited induc-tion generator driven by an unregula ted turbine’. PhD thesis,Department of Electrical Engineering, University of Toronto,1993

757-161

p p ~ 43-746

pp. 260-265

BONERT, R.: ‘Inte ractive simulation of dynamic systems on apersonal computer to support teaching’, ZEEE Trans. Power

10 RUYTER, E.: ‘Automatic start-up and unbalanced load behav-iour of an electronically controlled induction generator system’.Diplomarbeit, University of Toronto and University of Karl-sruhe, Germany, 1995

S y ~ t . , 989, 4, (l), pp. 380-383

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