Investigation of capacitor-excited induction generators and permanent magnet alternators for small scale wind power generation

Renewable Energy Vol. I, No. 3/4, pp. 381-388. 1991 Printed in Great Britain.

0960-1481/91 $3.00+.00 Pergamon Press pie

INVESTIGATION OF CAPACITOR-EXCITED INDUCTION GENERATORS A N D PERMANENT MAGNET ALTERNATORS FOR SMALL SCALE WIND POWER GENERATION C. V. NAYAR, J. PERAHIA a n d F. THOMAS School of Electrical and Computer Engineering, Curtin University of Technology, GPO Box U1987, Perth, Western Australia 6001, Australia and S. J. PHILLIPS, T. PRYOR a n d W. L. JAMES Murdoch University Energy Research Institute, Murdoch University, Murdoch, Western Australia 6150, Australia

(Received 18 July 1990; accepted 3 March 1990) Abstract--This paper examines two electric generator options for use in autonomous wind systems producing asynchronous electric power. The first makes use of a capacitor-excited squirrel-cage induction generator feeding a battery bank and an induction motor driven centrifugal pump. The second uses a permanent magnet alternator. Results obtained from field tests and laboratory experiments are included. A model to calculate the wind energy captured by a commercial 5 kW wind turbine, used in the field tests, is presented. This information is then used in a cost benefit analysis based on the present value method.

1. INTRODUCTION A large potential market exists for small isolated wind generator systems used to supply asynchronous loads such as battery banks which in turn supply power to household appliances, water pumping, water desalination, remote communication equipment, cathodic protection for buried pipelines, direct space heating, and domestic hot water heating. These wind generators have been small in size, usually less than 5 kW, and have usually been located in remote villages around the world which are not connected to any electricity grid. The three most common electric generators used for isolated wind power generation are the d.c. generator, the alternator (field wound or permanent magnet) and the capacitor-excited induction generator. The d.c. generator and the field wound alternator have maintenance problems associated with commutators and brush gear. Schemes based on permanent magnet alternators and induction generators are receiving close attention because of the qualities like ruggedness, low cost, manufacturing simplicity, and low maintanance requirements. This paper describes a wind powered capacitorexcited induction generator water pumping system, and a permanent magnet alternator for battery charg-

ing. Results based on laboratory experiments and field tests are included.

2, CAPACITOR-EXCITED INDUCTION GENERATORS

The capacitor-excited induction generator obtains its magnetising current from capacitors connected across its output terminals [2]. As the rotor is driven by a prime mover residual magnetism induces a small EMF in the stator windings at a frequency proportional to the rotor speed, circulating a current through the capacitors. If the capacitors are of sufficient value the voltage builds up, its final value being limited by saturation of the machine. The speed at which capacitor-excitation occurs is dependent on the amount of residual magnetism in the rotor. Increasing the capacitance connected to the machine reduces the speed at which excitation occurs. A curve of voltage build-up at the instant of excitation is shown in Fig. 1. Steady state operation of the generator can be explained through Fig. 2. Figure 2 gives the per phase steady state equivalent circuit of a capacitor-excited induction generator supplying a resistive-inductive load where: 381

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operational equivalent circuit derived by substituting F = - j P in the steady state circuit of Fig. 2, with 1, becoming i+ . Here i[ is the instantaneous positive sequence current, its negative sequence equivalent being the complex conjugate of the positive sequence current. Using the operational equivalent circuit the following loop equation can be written :

Fig. 2. Equivalent circuit of the capacitor-excited induction generator with load. R~, X~ R,, X~, Xm X~ R, X

stator resistance, leakage reactance per phase (f~) ; rotor resistance, leakage reactance per phase (referred to stator, f2) ; magnetizing reactance per phase (~) ; per phase capacitive reactance of terminal capacitor C (~) ; load resistance, reactance per phase (fl);

(all reactances referred to above relate to base frequency f ) P = l/o) d / d t and co = 2nf(radians see- ~) ; F, V per unit frequency, per unit speed ; 1~, L, IL per phase stator, rotor (referred to stator), and load currents (A) ; V, V~ per phase terminal voltage, per phase air gap voltage (V). The process of transient voltage build-up under capacitor-excitation can be explained through the

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Investigation of capacitor-excited induction generators real part and so Xm is varied until this condition occurs. F becomes the magnitude of the imaginary term of the root with a positive real part. By experimentally driving the induction machine at synchronous speed corresponding to the line frequency (F = 1), the magnetizing reactance for different input voltages at line frequency Xm can be calculated. A curve of Vg/F versus Xm may then be plotted. Knowing F and Xm the air gap voltage Vg can be found from the curve. At this stage Fig. 2 may be used to form the following equations to determine other variables :

-v~ L

F

(2)

Rr F - V +jX~,~

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~ + /X~ +

F X,:(XF-jR) RF~--X,:)

(3)

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(4)

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(5)

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(6)

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(8)

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where the input power is P~, (W), input torque T,n (N m), ~o~ synchronous speed (radians sec-i), and Pou, (W) the output power to the load. The magnitude and frequency of the voltage generated depend on shaft speed, terminal capacitance, and system load. This power may be used directly for

voltage-frequency-insensitive loads such as space and water heaters, or on converting to d.c. it may be used for battery charging as in Fig. 3. The laboratory test machine was a wound rotor induction machine having the following name plate data : 4 pole, 50 Hz, 440 V, 7.3 A, 5 hp. The prime mover was a d.c. machine. The stator was star connected while the rotor windings were short circuited. The test machine was run at constant speed of 1200 rpm and had three 65/IF capacitors delta connected to its terminals. A three phase transformer was used to step down the generated voltage (turns ratio 4.3 : 1) for compatibility with a 110 V battery bank. Per phase primary and secondary voltages, battery voltage and current, and firing angle were measured and plotted in Fig. 4. The power generated by a capacitor-excited induction generator may also be used for water pumping using a centrifugal pump powered by a three phase squirrel-cage induction motor. Laboratory tests have shown that two induction machines plus external capacitors suffered from voltage build-up problems due to the high reactive power demand of the two machines, unless high values of capacitance were used. A scheme that provides battery charging as well as water pumping and overcomes excitation problems is shown in Fig. 5. Switch $2 is initially held in the closed position to give maximum capacitance. Voltage build-up is made to take place at no load by initially having switch SI in the open position. Switch SI is only closed after 90% of rated voltage has been reached. The combined capacitance must be reasonably high to avoid voltage collapse when the motor is connected. At the instant SI is closed the motor starts from rest and its impedance only increases as the motor begins to accelerate. The demand for reactive power decreases during acceleration. Once the motor reaches normal running speed the reactive power demand is reduced and overexcitation problems including large terminal voltage causing extra iron losses and high magnetising cur-

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Fig. 5. Relay-switch capacitance.

rents due to saturation arise. It is then necessary to switch out some of the capacitor bank which is done by switch $2. Rather than using switches and a divided capacitance, a smooth variation in capacitance can be obtained by a thyristor-switched inductor and a single capacitance. The basic circuit of the controller in each phase is shown in Fig. 6. By altering the firing angle of the thyristors it was possible to control the terminal voltage. Test results of a 4 pole, 50 Hz, 415 V induction generator feeding a resistive load at 800 rpm are seen in Fig. 7. A variation of this scheme is to replace the inductors by a pump motor, making the controller deliver voltage control as well as useful mechanical power. Small inductors may be placed in series with the pump to fine tune the performance of the controller over a preferred speed range.

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Fig. 6. Single line schematic of three phase voltage controller. 3. PERMANENT MAGNET ALTERNATOR Figure 8 shows the 5 kW wind generator built by the local company Westwind Turbines. and erected on Curtin campus. Also, a test rig consisting of an

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identical 5 kW alternator coupled to a variable speed d.c. drive motor was set up in the laboratory to evaluate the performance of the generator under simulated wind conditions. A thyristor bridge controller was used to run the d.c. motor at variable speeds. The test rig was instrumented to measure shaft speed, shaft torque, terminal voltage, current, and power. As shown in Fig. 9 the wind generator consists of a rotating drum to which the three blades are attached. The magnets are of ferrite type and are glued to the inner surface of the drum. Housed inside the drum is the stator which is a normal three phase star connected single layer winding. Using the test rig the droop characteristics and

Fig. 8.5 kWtestmachine.

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efficiency of the alternator were obtained and are shown in Fig. 10. The experimental power curve, obtained when a microprocessor based half controlled thyristor bridge rectifier was used to charge a 110 V battery bank, is shown in Fig. 11. A personal computer was used as a data logger to record wind speed, shaft speed, battery voltage and current.

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4. COST BENEFIT ANALYSIS The cost (in Australian dollars) of the capacitorexcited induction generator scheme comprises of $500 for the induction machine, $300 for a gear box needed to step-up the speed of the turbine, capacitors $300, and $1000 for an electronic controller, totalling 5;2100. The permanent magnet alternator option in comparison has costs of $4000 for the permanent magnet alternator and $1000 for the electronic controller. It is noted that the alternator was custom built but once commercially available their cost will be reduced. To evaluate economic viability of the 5 kW windturbine-driven permanent magnet alternator for battery charging a model was developed to predict the annual energy output. It was assumed that wind speed follows a Weibull distribution [1, 4]. Details of the model are given in Appendix I. Numerical data used in the calculations are shown in Table 1. Results obtained from the model for different mean wind speeds are seen in Fig. 12. A model using a form of cost benefit analysis based on the present value method was then developed [5], see Appendix II. The model was applied to a system comprising of the 5 kW wind turbine generator, and an electronic

0.5 1 1.5 2 2.5 3 POWER OUTPUT(kW)

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2 3.1 (m sec -1)

VR

12.1 (m sec -1)

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15.7 (m sec -1)

p R Cpmax PR CO e i m ec

1.225 (kg m -3) 3.5 (m) 0.35 5000 (W) 15000 ($A) 0.4 (S/kWh) 0.15 0.03 0.08 0.x6

13

Table 2: Results of Cost Benefit Analysis. Mean Wind Speed (m/sec) 4 5 6 7 8

Pay-back Period (years) 20 9 5 3 2

A model to calculate the wind energy c a p t u r e d by a wind t u r b i n e was used in a cost benefit analysis. Acknowledgements--The authors are grateful to the Minerals and Energy Research Institute of Western Australia for funding the project, Venco Products/Westwind Turbines, Curtin University of Technology and Murdoch University Energy Research Institute for providing the facilities.

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controller for battery charging, totaling $15,000. T h e model used the values o f a n n u a l energy o u t p u t s h o w n in Fig. 12. The m o d e l gave the p a y - b a c k periods s h o w n in Table 2 w h e n the p a r a m e t e r s of the model were assigned the values s h o w n in T a b l e 1.

5. CONCLUSION This p a p e r presented two p r o m i s i n g schemes for small scale stand alone wind p o w e r g e n e r a t i o n : one using a capacitor-excited i n d u c t i o n generator, a n d the other a p e r m a n e n t m a g n e t alternator. Both arrangements can supply resistive-heating loads where voltage and frequency need not be regulated, or a rectifier may be attached for battery charging.

1. G. L. Johnson, Wind Eneryy Systems, Prentice-Hall, U.S.A. (1985). 2. N. H. Malik and S. E. Haque, Steady state analysis of an isolated self-excited induction generator, IEEE Trans. on Energy Conversion, Vol. EC-I, No. 3, pp. 134-140 (1986). 3. T. Nejat Veziroglu, Alternative Energy Sources VI, Vol. 3, Hemisphere Publishing Corporation, U.S.A. (1985). 4. S. Rahman, A microcomputer-based planning tool for wind energy development, Proceedings o.f the Sixth Miami International Conference on Alternative Energy Sources (also found in Alternative Energy Sources V1, Vol. 3, Hemisphere Publishing Corporation, U.S.A.) (1983). 5. J, Van Leuven, Autonomous wind power systems are economically competitive, Proceedings o.f the Sixth Miami International Conference on Alternative Energy Sources (also found in Alternative Energy Sources V1, Vol. 3, Hemisphere Publishing Corporation, U.S.A.) (1983).

APPENDIX I: PREDICTION OF AVAILABLE WIND ENERGY

Since the wind speed was taken to be Weibull distributed, the wind speed probability density function is given by : .f'(I') :

(k/c)(z!/c) k-

i exp (--(t!/c)

k-

i)

(A1)

where r = wind speed, c = scale factor, and k = shape factor. Parameters c and k are found from the following two equations : V = cF(1 + ( l / k ) )

(A2)

cr2 = c2{F(l + ( 2 / k ) ) - F 2 ( 1 +(l/k))}

(A3)

where V = mean wind speed, ~ = standard deviation, and F = gamma function. The power available from a wind turbine is P = (1/2)C~pgR~'v 3

(A4)

where power P is in watts, Cp = power coefficient, p = air

C. V. NAYAR et al.

388

density (kg m-3), R = radius o f wind turbine (m), v = wind speed (m sec-~). Due to the nature o f a wind turbine the predicted value of power is calculated in two p a r t s - - t h e first part (P~) between cut-in (Vc) wind speed and rated (VR) speed and the other (P2) between the rated and furling (Vr) speeds.

P, = (1/2)pnR 2

fi:

Cpv3f(v) dr.

(A5)

Wind turbines can be designed to give the best Cp at one of several operating speeds, and one such design where weights are used to place a true maximum of C~ at VR is given by :

Cp = P.[(l/Z)p~tR2v3)(V~ - V~)]- '[(1 - w)(v k - V ~ ) + w(v 2k-- Vc~)(Z~ + V~)- ']

(A6)

where k --I w = [ 2 Vh¢ V k~ - Vc)l [V~-2V~V~-3V~

k]

(A7)

with k defined as above, PR is the rated power of the wind turbine. Equation (6) is substituted into the equation for P~, eq. (AS)

and the annual energy output is AEO = C F * PR * 8760 (in units ofWh).

APPENDIX 1I: COST BENEFIT ANALYSIS

The relative cost of wind turbine generator during its life, discounted to present values, is :

C/Co= l + m ~ [ ( l + ~ ) / ( l + i ) ] j

(A8)

The C r in P2 is a constant and may be taken as the maximum value of C~ (Cp,,,x). The capacity factor is given by CF = (Pi + P2)PR

(A9)

(All)

where Co is the base year capital cost, m is the fraction of capital cost for maintenance and operating per year, n is the lifetime of the wind turbine generator, cc is the capital cost inflation rate, and i is the annual interest rate of borrowing funds. In this case the wind turbine is complemented by an auxiliary fuel base power plant and so the benefit (total cash fuel savings per base year annual benefit) over the same number of years, discounted to an equivalent value of today, is:

B/Bo = ~ [(1 +//)/(1 +i)]~ P2=(l/2)CppTrR2V~;'iFf(v)dv.

(A10)

i=

(AI2)

I

where ,8 is the fuel escalation rate. The first year saving (B0) was taken to be Bo = e* W where e is the cost per kWh o f fuel replaced, and W is the annual energy output of the wind turbine. The break-even condition occurs when C - - B = 0, where C is found from eq. (AI 1) and B is found from eq. (AI2).