A DUAL STATOR WINDING INDUCTION GENERATOR WITH A FOUR SWITCH INVERTER-BATTERY SCHEME FOR CONTROL Olorunfemi Ojo
Innocent E. Davidson
Dept. of Electrical and Computer Engineering Tennessee Technological University Cookeville, TN 38505, U.S.A Tel(93 1)-372-3869, E-mail :
[email protected]
Dept. of Electrical and Electronic Engineemg University of Pretoria Pretoria, South Africa
Abstract: This paper presents a novel dual stator winding induction generator scheme in which a battery voltage sourced inverter synthesized with four switching devices is connected to the control winding for load voltage and power flow control. The required carrier-based PWM modulation for the synthesis of a balanced set of output inverter voltage, comprehensive modeling, dynamic and steady-state analyses of the new generator scheme are presented. An approach to regulate the load voltage is also discussed.
The inverter controls the load voltage, in the process of which it augments the reactive power supplied by the local shunt capacitors C, to meet the reactive power demand of the load. The frequency of the inverter modulating signals is effectively the frequency of the load voltage. The battery bank which is connected to one of the two cascade capacitors buffers the system to ensure active power balance under varying operating conditions of rotor speed and load. When the rotor speed, for a short time, is less than the required load frequency (positive slip), a properly selected battery bank size provides the active power to meet the load demand and system losses while maintaining desired load voltage and frequency. If the mechanical power supplied by the rotor is more than the load active power and system losses, the balance of the active power is sent through the inverter to charge the battery. If, on the other hand, the mechanical power from the rotor is less than the load demand and system losses, the deficit is supplied by the battery.
I. INTRODUCTION Dual stator winding machines have received renewed attention in the last few years for use in adjustable speed drives where efficiency maximization, energy conservation and increase of the power capability of machines are desirable. This class of electric machines has two stator windings wound for the same pole numbers but electrically displaced from each other. The three-phase winding set carrying the load currents is called the power winding while the other three-phase winding set is known as the control winding. The dual stator winding synchronous machine was introduced in 1930 as a means of increasing the power capability of large synchronous generators [l].In the last few years, dual stator winding synchronous machines were used as sources of both DC and AC voltages [2-51. Dual stator winding induction motors have also been used for large pumps, compressors and rolling mill drives where large power capabilities are required [4-71. In this paper, a novel dual stator winding generator scheme (shown in Figure) 1 is proposed. A three-phase voltage inverter with four switching devices sourced by a battery bank is connected to the three-phase control windings. As seen from Figure 1, the three-phase inverter is synthesized from two inverter legs with four switching devices, while the third inverter leg is comprised of two cascaded capacitors, the middle point of which is connected to the third phase of the control windings.
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II. SYSTEM MODEL The system model and the modulation strategy of the inverter-system connected to the three-phase control windings is first considered. The inverter is under carrierbased sinusoidal pulse-width modulation using triangle intersection technique. The phase ‘a’ reference modulation signal is compared with a triangular wave of unit peak and the intersections determine the switching signal Sa of the switch SI. If the switching signals of switching devices SI,S3 are sa and S b respectively, from Figure 1, the following voltage equations are determined :
230
Cd
I S’YIt
i cs4 detect
Fig. 1: Circuit diagram of the dual stator winding induction generator with reduced count inverter-battery system.
1 2
sa= - ( 1 + Ma), Sb The control winding phase voltages are Vas, v b s and Vcs; the voltage between the neutral point of the control winding of the generator and the point n in the inverter circuit is V,. Vcl and Vc2are the voltages of the upper and lower capacitors respectively. The derivative d d t = p and the control winding currents are I,, Ibs and I,, with the battery current given as I,. From equations (1-3), the neutral voltage is given in equation (6) below. Substituting equation (6) into equations (1-3), expressions for the phase voltages of the control windings in equations (7-9) result.
=
1 - ( 1+Mb) 2
(10)
With equation (10) substituted into equatipns (1-3), with the desired balanced phase voltages are Vas , v b s * and V,,*, the modulating signals are given as :
*
2
1 2
Ma = -( 2 Vas* + v b s + - (VCZ-VCI)) v d
2
Mb = -(
: 1
2 Vbs* + V,S + - ( V C Z - ~ C I ) )
2
v d
(1 1) (12)
If vas*=VCOS (Qt+c), Vbs*=Vcos(~t+c-120) and v,,* =Vcos(~t+c+120)where the frequency of the modulating signal is a, then the modulating signals are given as:
M , , = M c o s ( ~ t + ~ - 9 0+) MO
2
Where, M = v d Vd
J
The modulating signals (Ma ,Mb) required to generate the switching signals saand sb, respectively are now determined from equations (1-3). The switching signals take values of one and zero which, expressed in terms of their low frequency components, are represented as [8]:
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= vc1
1
V, MO= - ( VC2-VcI) , v d
vc2
M is the modulation magnitude index and the modulation angle is 5, both of which are varied to achieve the required phase voltages of the control windings. It is observed that MO is the compensating component of the modulating signals that accounts for the unbalance in the capacitor voltages. The equations for the modulation signal for the inverter are similar to those given in [9]. Since the switching signal S ,
23 1
corresponding to device S4 is complementary to Sa and the switching signal Sbb of device S3 is also complementary to sb, defining v, = vc1-vc2, equations (4-5) become:
The next step in the analysis is to transform equations (7-9, 14-15) to the synchronous reference frame to convert the time-varying state variables to DC quantities. The q-d synchronous reference voltages of the inverter output (input to the control winding set) after much simplification are:
Fig. 2: Complex q-d equivalent circuit of the dual stator winding induction generator. For the impedance load shown in Figure 1, the q-d load equations with the compensating capacitors Cq are:
The sum of the capacitor voltage (14) becomes the following after simplification:
It is observed that the input voltage to the inverter (vd) inevitably has a ripple component due to the imbalance between the two cascade capacitor voltages. Since I, is almost a DC quantity and ICsis oscillating at the frequency of the control winding current, Vu is always present, independent of any control scheme. What active control does is to limit its magnitude. The q-d model equations of the dual stator winding induction motor in the synchronous reference frame are set forth [lo]. Expressed in the complex variable form, the electrical equations are given (see Figure 2) as:
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232
The load resistance and inductance are R,, and Lo, respectively.
III. CONTROL SCHEME The generator system in Figure 1 is generally stable due to the presence of the battery connected across one of the cascade capacitors of the inverter. There is a ripple component riding on the capacitor DC voltages, whose magnitude depends on the value of c d , the control winding current magnitude and the load frequency. However, a modulation scheme based on equations (13) constrains the magnitude of the ripple and keeps it within a reasonable bound. The battery must be sized appropriately to be able to augment the mechanical power from the shaft for the worst rotor speed and loading conditions. To regulate the load voltage magnitude, a simple proportional-integral gain (PI) or integral-proportional (I-P) controller suffices. The peak value of the measured load voltage is compared with desired peak load voltage; the error is fed to the controller, the output of which becomes the value of the modulation index, Mqd. With measurement of cascade capacitor voltages, MOis determined which in addition to M are used in equations (13) snynthesize the modulation signals Ma and Mb. These signals are compared with a train of triangle waveforms of unit peak value, the outputs yield the signal signals to the four switching devices. The transfer function of the generator scheme obtained from equations (1 8-22) is given as:
V@P -vqds
-Z m Z m r = &d ZqA + Zr (ZrZs - Z m Z m r ) Zr(ZpsZr
& = r p + PL, - j o , b , Z,= rs + p L - jo,Ls,
2pS= pLpS - j o , Lps Z,= r,+ p L - jusoL , & = PL-jOeLm Z,=c,p-jo,C,
L=pL,-jcisoLao,
+l/& ,Z,=%-jo,Lo+pLo
Substituting the equation for equation (23),
v@from
equation (16) into
Using an integral-proportional controller with gains KI and Kp, the magnitude of the modulation magnitude is given as :
The transfer function between the me!sured load voltage , Vqdp and the reference load voltage, Vqdp is given as:
Fig. 3: Build-up transients of the generator, (a) Battery current, (b) the load voltage.
The controller gain parameters KI , Kp are chosen to optimize the closed-loop eigenvalue locations uniformly in the left-half S-plane using the Butterworth polynomial [l 13. The sketch of the controller structure is also shown in Figure 1. Implementation of the controller requires the measurement of the load peak voltage using a fast peak detector [121.
IV. SYSTEM SIMULATION AND DYNAMICS .....
In this section, computer simulations showing the responses of the controlled generator system to changes in load impedance and rotor speed are presented. The electrical build-up transient dynamics are shown in Figure 3 where the reference peak voltage is 80 Volts. The peak phase voltage gradually builds up and attain the steady-state desired values. The response to a change of the load impedance from 50 Ohms (low power) to 5 Ohms (high power) is demonstrated in Figure 4. It is observed that after an initial dip in the peak voltage, the controller restores the voltage to the reference point. Before the change of load, the battery was being charged (current flowing into the battery) while after the load impedance has been changed, the battery supplies positive current to balance the active power requirement of the load.
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233
I
Iu I
KJI
I
I
P.1
a. 4
1
0.6
I
I
I
D. e
ISCC1
Fig. 4: Response to change of load impedance from 50 to 5 Ohms. (a) The battery current, (b) the peak voltage.
Y
I
.
.. .
. .
I
I
I
I I
’
VI. CONCLUSIONS This paper has presented a novel dual-stator winding induction generator scheme with a reduced count voltage source inverter which with a small battery source has the capability of load voltage regulation and buffering the active load power demand. The dynamic control and steady-state performance are demonstrated through a detailed model and computer simulations results.
VII. REFERENCES [l]
P. L. Alger, E. H. Freiburghouse and D. D. Chase, “Double windings for turbine altemators,” AIEE Transactions, vol. 49, January 1930, pp. 226-244.
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E. F. Fuchs and L. T. Rosenberg, “Analysis of altemator with two displaced stator windings,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-93, no. 6, November/December 1974, pp. 432439. r31 Schiferl, Detailed analysis of a six-phase synchronous machine with AC and DC connections, MS Thesis, Purdue University, West Lafayette, Indiana, 1982. [41 P. W. Franklin, “A theoretical study of the three phase salient pole type generator with simultaneous AC and bridge rectified DC output,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-92, no. 2, M=h/April 1973, pp. 543-557. T. Kataoka, E. H. Watanabe and J. Kitano, “Dynamic control of a current-sourceinverteddouble wound synchronous machine system for AC power system,” IEEE Transactions on Industry Applications, vol. IA-17, no. 3, May/June 1981, pp. 314-320. K. Gopakumar, V. T. Ranganathan and S. K. Bhat, “Split-phase induction motor operating from PWM voltage source inverter,” LEEE Transactions on Industry Applications, vol. IA-29, no. 5, September/October 1993, pp. 927-932. r71 J. C. Salmon and B. W. Williams, “A split-phase induction motor design to improve the reliability of PWM inverter drives,” IEEE Transactions on Industry Applications, vol. IA-26, no. 1, JanuaryFebruary 1990, pp. 143-150. [81 Peter Wood, Switching Power Converters, Van Nostrand Reinhold Company, New York, 1981. r91 G. Kim and T. A. Lipo, “VSI-PWM rectifiedinverter system with a reduced switch count,” IEEE Transactions on Industry Applications, vol. 32, no. 6, NovemberlDecember 1996, pp. 1331-1337. T. A. Lipo, “A q-d model for six phase induction machines,” Intemational conference on electrical machines, Athens, Greece, 1980, pp. 860-867. r111 Friedland, Control System Design, An Introduction to State-Space Methods, McGraw-Hill Inc , New York, 1986. B. Kwom, J. Youm and J. Choi, “Automatic voltage regulator with fast dynamic speed,” IEE Proceedings, Electric Power Applications, vol. 146, no. 2, March 1999, pp. 201-207. r21
The steady-state waveforms of the generator when the rotor slip is negative are shown in Figure 5 above. The sum of the capacitor voltages (V,) is observed to have a constant component with a ripple component having the same frequency as that of the control winding voltage. This observation is actually confirmed by equations (17). The phase voltage of the load is very clean without significant inverter voltage induced component. In this instance, the average battery current (not shown) is negative, signifying that the generator is charging the battery while satisfying the load demand.
1.25
1 [Sec]
Fig. 6: Steady-state generator waveforms. (a) Capacitor voltage, (b) load voltage.
Fig. 5 : Dynamics to change of rotor slip from negative (0.02) to positive slip (0.02). (a) The battery current, @) the load voltage.
V. STEADY-STATE ANALYSIS
1.20
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