Steady-state analysis of single-phase self-excited
induction generator
B.Singh and LB.Shilpkar
Abstract: A methodology of selection of capacitors for optimum excitation of single-phase SEIG is
explained. Computed results are validated by experimental investigations under varying loads and
various excitation capacitors. The results are explained to obtain useful guidelines for design and
improvements of small self-regulated SEIG units.
1
Introduction
In most of the remote areas where the grid supply is not
available, electric power is supplied with the help of diesel
generators. Sometimes in regions served by the grid, consumers are forced to employ standby power generating
units under emergency conditions when the supply fails for
unduly long hours. Such a situation becomes critical for
vital installations like hospitals, security systems, communication and instrumentation systems and they have to perforce the use of standby generator. Recently, interest in the
self-excited induction generator (SEIG) is gaining momentum for such applications owing to its inherent advantages
[1-3]. Since a single-phase supply is preferred for small
power applications to make the system simple and costeffective, single-phase induction machines are being used as
generators for supplying smaller loads. Hence, the singlephase SEIG is presently under intense investigation to
make it suitable for field installation and quality power
supply [4-13].
Since SEIGs are finding increased use for rural electrification in developing countries [14], the single-phase SEIG is
now being explored with a view to bring out a cost-effective
small power generator acceptable to the user. For this purpose, there appears to be a need for an analytical tool that
predicts the steady-state performance of a two-winding single-phase SEIG, without resorting to any approximation
while solving the steady-state equivalent circuit. We therefore propose a new technique of steady-state analysis of a
two-winding single-phase SEIG which avoids any approximation in solving the unknown variables such as magnetising reactance and/or capacitive reactance and frequency of
the steady-state equivalent circuit. The analytical model
solves the operating values of the unknown variables by
minimising a multivariable nonlinear objective function.
Using this method the effects of both shunt and series
capacitors on the steady-state terminal voltage of twowinding, single-phase SEIG are studied for three different
excitation capacitor topologies shown in Figs. 1 and 2. To
IEE Proceedings online no. 19990607
DOI: 10.1049/ip-gtd: 19990607
Paper first received 19th January and in revised form 9th June 1999
The authors are with the Department of Electrical Engineering, ITT Delhi, New
Delhi 110016, India
IEE Proc.-Gener. Transm. Dislrib., Vol. 146, No. 5, September 1999
examine the validity of the analytical method, detailed
experimentation is undertaken to study the variation of terminal voltage with load and also to examine the effect of
shunt and series capacitors.
induction
generator
IMT|
MA
f
t
V, Mload
t
load
Fig. 1 Schematic diagram of schemes of capacitor excitation of two-winding
single-phase self-excited induction generator
a Fixed shunt
b Fixed and variable shunt
2
Mathematical modelling
Fig. 2b shows a general connection which embodies a
fixed-shunt capacitor, fixed and variable shunt-capacitor,
and shunt- and series-capacitor schemes of a two-winding
single-phase induction generator. The external load is connected to the main winding in series with capacitor Cse.
Capacitance CLsh is connected in parallel with the main
winding. Capacitors Cse and CLsh are connected to regulate
the generator terminal voltage with load. Capacitance Csh is
connected across the auxiliary winding to provide the excitation current required for the voltage build-up at no-load.
When the excitation capacitor Csh and load are connected
to different stator windings, the burden of exciting the
machine will be taken by one winding, leaving the other to
supply more load before reaching its heating limit. Mathematical model is developed for the general system shown in
Fig. 2b. It is easy to see that the equations describing this
system can be reduced to equations that describe the excita421
tion capacitor topologies of Figs, \a-2a by substituting
suitable values of capacitors.
t
Z\2b =
Z\M + Zb + Z\2
RcjFXm
Zmf =
Rc+jFXm
R2F
load
F-u
+ jFX2
Z-l-2 =
Z1A=R1A+jX1A-jXsh/F
Zh =
t
load
Zmb =
R2F
F+u
Fig. 2 Schematic diagram of schemes of capacitor excitation of two-winding
single-phase self-excited induction generator
a Shunt and series
b General
RL jFXL
—
—rA/V
own—II
I
i
R1M
vv
ODO-
Under steady-state self-excitation, IIMMjj cannot be zero and
hence from eqn. 1
=0
(2)
In eqn. 2, Xm and F are the unknowns for the given u, Xse,
Xuh, Xsh, RL and XL. Here, a minimisation technique
solves eqn. 2. The expression of left-hand side of eqn. 2 is
complex quantity and hence its magnitude must be zero to
satisfy the equation. Let this quantity is represented in a
functional form as
Z\M
12b
f(Xm,F) =
(3)
Now the problem is to select the correct values of Xm and F
which satisfy eqn. 3 and also lie within acceptable limits.
Ideally, the function f[Xm, F) must converge to zero if the
selected variables are of correct values. There may be more
than one value of these variables which may satisfy this
equation. To calculate realistic values of the variables,
higher and lower limits of the variables known from practical experience are imposed on them.
For solving eqn. 3 by minimisation, the function j[Xm,
F) is taken as an objective function and the problem is
stated as
Minimise
Fig. 3 Equivalent circuit of two-winding single-phase self-excited induction
generator
Fig. 3 shows equivalent circuit of the general system of a
two-winding single-phase induction generator based on
double rotating field theory. This circuit is natural extension of the equivalent circuit of two-phase induction motor
[15] where the external supply source is replaced by ZL in
parallel with XLsh (=l/(cob C^ )) in main winding and Xsh
(— l/(a>b Csf,)) in the auxiliary winding. Applying KVL in
the circuit of Fig. 2c
=0
(1)
such that Fi < F < Fu and Xmi < Xm < Xmu
(4)
where subscripts / and u denote lower and upper limits. The
value of tolerance to check convergence is taken quite
small, say e = 0.0001. Having obtained the saturated magnetisation reactance Xm and the per unit frequency F that
satisfy eqn. 3, the normalised air gap voltage Vgf is identified from the curve plotted between V^F and Xm using the
data obtained from a synchronous speed test [6] and given
in the Appendix (Section 8). Once VJF, Xm and F are
known, the quantities describing the performance characteristics of the system are computed as
lMf =
Z\M
= RIM + J
(RL + jFXL) (+
zf =
•imf
+ Z2 /
z
1Mb = -7T
IM
— iMf + 1Mb
RL+j(FXL-
ZmfZ2f
YlL
f
where
-jXse/F
f(Xm,F)
_
T
lA
~
IL
- 1Mb)
a
= IM{-jXLsh/F)/{RL+j{FXL
- XLsh/F)}
IEE Proc.-Gener. Transm. Distrib., Vol. 146, No. 5, September 1999
=
IL(RL+jFXL)
VA=IA
-
F
Pout — \IL\
(5)
Based on the mathematical formulation as outlined, the
value of shunt and series capacitors are selected to keep the
voltage regulation of the system within permissible limits.
After selecting proper values for the excitation capacitances, the load characteristics, curves of Vt, F, IM, IA
against Pout, are computed.
points). Results of investigations are presented for the following three topologies of capacitor excitation:
- fixed shunt capacitor across auxiliary winding
- fixed capacitor across auxiliary winding and a variable
shunt capacitor across main winding
- fixed capacitor across auxiliary winding and a fixed
capacitor in series of main winding and load.
300 -i
o
250-
•o 2 0 0 -
S 150-
3
Computation
The objective function J{Xm, F) is minimised considering
the bounds of independent variables Xm and F as external
constraints to obtain practically acceptable solution. The
sequential unconstrained minimisation technique (SUMT)
in conjunction with a direct search method, namely, Rosenbrock's method of rotating co-ordinates, have been
employed [16]. In this method the constrained optimisation
problem is converted into a series of unconstrained problems and then Rosenbrock's minimisation technique
applied for unconstrained minimisation to find the value of
objective function sufficiently close to zero.
Using this procedure, a computer program is developed
to compute the performance characteristics of two-winding
SEIG for a given set of parameters using the relations given
in eqn. 5. These relations are general because they can be
used for performance analysis of the system for the cases of
resistive load, inductive load, with and without series
capacitor Xse and regulating shunt capacitor Q^ by assigning the proper value of the circuit parameter. The effect of
different parameters on generator performance is studied
by varying these parameters such as shunt and series capacitance, load and power factor.
4
10
20
30
40
50
60
70
shunt capacitor Csh,nF
Fig. 4 Variation of main winding terminal voltage at no-bad excitation with
shunt capacitor Cs/, across auxiliary winding
400 -i
400
Experimentation
The prototype of the SEIG considered has two phase windings, main winding M and auxiliary winding A, housed in
a 24-slot stator core built in IEC 90L TEFC frame. A diecast rotor of a standard single-phase induction motor is
used. The values of the parameters of the machine used in
the simulation are determined by standard tests and are
given in the Appendix (Section 8). The induction generator
is driven by a 3.7kW, 415V, two-pole, three-phase, induction motor to operate at no-load speed of 1.03pu (base
speed 3000 rev/min) so that the frequency of generation is
maintained close to 50Hz when the generator is loaded
from no load to full load. The drive motor is energised
through a variable-voltage, variable-frequency source to
obtain a desired and controllable mechanical power input
to the induction generator. To load the machine of varying
power factor, a load unit is devised to control both active
and reactive power of the load. The system is instrumented
to measure all electrical and mechanical quantities.
5
100
Results and discussion
The steady-state results obtained through computation and
experimentation are presented, the theoretical results (continuous curves) being verified by test results (symbol
IEE Proc.-Gener. Trcmsm. Distrib., Vol. 146, No. 5, September 1999
0.0
100
200
300
400
power output, W
Fig. 5 Voltage and current performance of main and auxiliary winding circuits, PF= 1
5.7 Fixed sh unt capacitor excitation scheme
Fig. 4 shows the variation of no-load terminal voltage
across the main winding with shunt capacitor Csh connected across the auxiliary winding when the single-phase
SEIG is driven at a constant speed of 1.03pu. Capacitance
Csh is selected to be 30 ^iF as it results in a no-load terminal
voltage of 1.06pu (base voltage 230V). The limits of load
terminal voltage are chosen to be ±6% of rated voltage in
compliance with the utility company and user requirements. Fig. 5 shows the voltage and current performance of
the main and auxiliary winding circuits for the fixed shuntcapacitor excitation scheme (Fig. la). It is observed that the
scheme has poor voltage regulation and the output power
423
of the generator is limited to 0.45pu (base power 750 W) of
its power rating for unity power factor load. However, for
a lagging power factor load the maximum output power of
SEIG is further reduced to lower value. The system faces
voltage collapse when the generator is loaded beyond the
attainable maximum steady-state output power. With the
value of Csh selected, the voltage in auxiliary winding builds
up to 330V. Since the current in both windings are still less
than rated current (6A) it does not affect the safe operation
of the machine so far as loading is concerned.
90-i
807060"k 50-
J403020100
800
400
1200
1600
power output, W
Fig. 6 Capacitance requirement across main winding for regulating the terminalvoltage of two-winding single-phase SEIG at rated level, PF = /
300 •*
©
o
To counter the limitations of poor voltage regulation of the
fixed capacitor excitation scheme, another scheme with a
fixed and variable shunt capacitor is investigated (Fig. \b).
Since the single-phase SEIG is an unsymmetrical machine,
capacitors of different value can be connected across the
two windings of the single-phase SEIG. The fixed capacitor
across auxiliary winding Csh is selected at 30 ^F which
builds up the EMF across the main winding of the machine
at no-load to l.Opu of rated voltage. Variable capacitor
Cuh is used to support the excitation required to keep the
voltage across the main winding constant at rated value.
Fig. 6 shows the variation of the capacitance Cuh required
for regulating the load terminal voltage at constant level of
230V (rated voltage). The generator performance with the
fixed and variable shunt-capacitance excitation of the twowinding single-phase SEIG is shown in Fig. 7. It is
observed that the load voltage remains constant while there
is a small rise in voltage across the auxiliary winding. It is
interesting to note that the machine is utilised to deliver a
power output of 1.5pu of its rated capacity while keeping
the current in the main winding within the rated current.
However, the system observes a small vibration and noise
which may be attributed to interaction of forward and
backward fields in the machine owing to unbalanced winding currents. The predicted results match with the experimental points with maximum error of 2% and hence it
verifies the mathematical technique.
5.3 Shunt and series-capacitor excitation
scheme
Although the fixed and variable capacitor excitation
scheme as discussed gives good performance, the requirement of a variable capacitor to regulate the terminal voltage makes the single-phase SEIG system complex and
costly. It restricts the very advantage of recommending the
system for small portable power units. In a bid to make the
single-phase SEIG system simple and cost-effective, a
detailed investigation is carried out to study the compounding effect of shunt- and series-capacitor excitation on regulating the load terminal voltage of the system (Fig. 2a).
400 -i
-«
5.2 Fixed and variable shunt capacitor
excitation scheme
o
i, 200-
100-
15-,
0.8
400
800
1200
1
1600
10-
•PF=1.0
5-
4)
60 $ 0
4/
100 120 140
160 180
Cse, nF
-5-
-10400
800
1200
1600
power output, W
Fig. 7 Voltage and current performance of main and auxiliary winding circuits of two-winding single-phase SEIG with fixed and variable shunt-capacitor
excitation
A 4
Fig. 8 Effect of series capacitor on voltage regulation of single-phase SEIG
Csh = 30MF
Fig. 8 depicts the effect of series capacitor Cse on the full
load voltage regulation of the single-phase SEIG with the
IEE Proc.-Gener. Transm. Distrib., Vol. 146, No. 5, September 1999
shunt- and series-capacitor excitation scheme at different
load power factors. The full load voltage regulation of the
generator remains within the limit of ±6% of the rated
value for the values of Cse falling in a range. This range of
Cse is 80 to 180uF for a unity power factor load, 55 to
100|iF for 0.9 power factor load, and 70 to 90\xF for 0.8PF
load. In this selection range, the full load voltage regulation
is minimum for Cse of 80 uF.
The selection of series capacitance should be justified not
only on the basis of full load voltage regulation but also
from the viewpoint of load voltage profile and maximum
utilisation of the machine as the generator. The load voltage profile is examined for unity power factor load and
0.8PF R-L load. Fig. 9 shows the effect of series capacitor
on variation of terminal voltage. The scheme is observed to
be self-regulative as there is small change in voltage with
load. The voltage profile is more flat for Cse at lOOjiF than
at 70 and 80 \xF and hence the system may sustain overloading for short period. However, maximum power
attainable of a generator with Cse at 80 [xF is limited due to
the main winding current which crosses the rated limit as
shown in Fig. 10a.
Figs. 11-13 show the effect of series capacitance on the
performance of the generator for R-L load of 0.8PF. The
system observes voltage sag at light load as shown in
Fig. 11. This sag in voltage is as high as 25% of rated voltage for Cse of 100[iF, which is more severe than that of
14% for Cse at 80 uF. Nevertheless, the system displays selfregulation when loaded to a higher load. The voltage profile of both main and auxiliary windings is concave as seen
in Figs. 12a and 13a and the concavity in the voltage profile increases with higher values of series capacitance.
Therefore the selection of a lower value Cse is better than a
higher one so long as other constraints are satisfied. There
is not much change in the auxiliary winding current with
load (Fig. \2b) because the capacitor in the auxiliary circuit
supports exciting the machine up to the level of no-load
voltage. The current in the main winding reaches rated
value when the machine is safely loaded to 160% of the
rated power, Fig. 13£>, demonstrating the overload capability of the scheme. As the series capacitor of 80 ^iF gives better performance for unit power factor load as well as an RL load and maximises the output power of the SEIG, it is
selected as an optimum value.
280-i
240-
240-'
200-
^
>-—7^-
200-
160-
>
;*• 160-
120-
>
-''(iii)
120-
80-
80-
40-
40-
0
200
400
600
800
1000
1200
00
power output, W
Fig. 9 Effect of series capacitor on terminal voltage of single-phase SEIG
supplying unity power factor load
(i) 70nF; (ii) 80nF; (iii) lOO^F
200
400
600
800
1000
1200 1400 1600
power output, W
Fig. 11 Effect of series capacitor on terminal voltage of single-phase SEIG,
supplying R-L load, 0.8 PF lagging
(i) 7 0 F ; (ii) 80(jF; (iii) 100(JF
8.0-•
400-1
6.0-<
-<
300-
4.0-
< 200-
2.0-
1000.0
200
400
800
600
1000
1200
500
400
n
1000
1500
1000
1500
4.0 n
300-
3.0^
5? 200-
i
100-
^™»J^
2.0-
1.00.0
0
200
400
600
800
1000
1200
power output, W
F i g . 1 0 Effect of series capacitor on voltage and current of main and auxiliary windings of single-phase SEIG, unity power factor
Cx 80MF
IEE Proc.-Gener. Transm. Distrib., Vol. 146, No. 5. September 1999
500
power output, W
Fig. 12 Effect of series capacitor on voltage and current of auxiliary winding,
detail as Fig. 10
425
the frequency of generation when the machine delivers noload to its maximum attainable output power remains
within ±3% limits of the rated frequency.
300-1
200-
6
100-
500
1000
1500
500
1000
power output, W
1500
Fig. 13 Effect of series capacitor on voltage and current of main winding,
detail as Fig. 10
The steady-state performance of the two-winding singlephase SEIG has been predicted and verified with experimental results for three different schemes, namely, fixedshunt capacitor excitation, fixed and variable capacitor
excitation, shunt- and series-capacitor excitation. The generator with fixed shunt-capacitor excitation scheme delivers
lower output power at a reduced voltage and hence it can
only be used in limited practical applications. With the case
of fixed and variable shunt-capacitor excitation scheme the
generator can safely be loaded to 150% of rating of the
machine while restricting the winding currents within rated
value. The compounding effect of the series capacitor with
the shunt capacitor has resulted in the self-regulated load
characteristics and the machine can safely be loaded to
140% of its rating. The series capacitor should be judiciously selected such that the requirement of the voltage
regulation is satisfied while the voltage sag at part load is
reduced to minimum and the power output is maximised.
It is concluded that the two-winding single-phase SEIG
with shunt and series excitation is an attractive option for
small single-phase power generation for standby or autonomous system.
7
1
2
3
200
400
600
800 1000
output power, W
1200
1400
Fig. 14 Load characteristic of self-regulated single-phase SEIG
(i)PF=0.8;(ii)0.9;(in)
1.0
The load characteristics of the shunt- and series-capacitor
excitation of single-phase SEIG with excitation capacitors
Csh and Cse selected at optimum values of 30 and 80|iF,
respectively, and supplying a load of power factors 1.0, 0.9
and 0.8pu are compared in Fig. 14. The main winding current and frequency are also shown in this Figure. The generator delivers rated power output at a load voltage of 0.9
and l.Opu, respectively, for unity power factor load and
0.8PF load. Comparison of the results shows that the connection of a series capacitor permits maximum utilisation
of the generator. The load voltage is self-regulated from noload to maximum power output in all three cases of load
power factor. The maximum attainable power output keeping the main winding current within rated value is more for
the case of a nonunity power factor load than the resistive
load. The self-regulating feature of the scheme significantly
reduces the cost and complexity of the SEIG system as it
avoids the use of a voltage regulator. The frequency of generation varies from 51.5Hz at no-load to 49.5Hz at 1.4pu
load. There are two distinct advantages of setting the noload speed of the generator at 1.03pu. First, the increased
operating frequency (51.5 Hz) at no-load reduces the magnetising current and hence improves the efficiency and
loading capability of the machine. Secondly, excursion in
Conclusions
4
5
6
7
8
9
10
11
12
13
14
15
16
References
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self excited induction generators', IEE Proc, 1982, 129, (6), pp. 260265
ELDER, J.M., BOYS, J.T., and WOODWARD, J.L.: 'The process
of self excitation in induction generators', IEE Proc, 1983, 130, pp.
103-107
QUAZENE, L., and MCPHERSON, G.: 'Analysis of self excited
induction generators', IEEE Trans., 1983, PAS-102, (8), pp. 27932797
SINGH, B.: 'Optimum utilization of single phase induction machine
as a capacitor self-excited induction generator', Electr. Mack Power
Syst., 1987,13, pp. 73-85
SINGH, B., SAXENA, R.B., MURTHY, S.S., and SINGH, B.P.: 'A
single phase self-excited induction generator for lighting load in remote
areas', Int. J. Electr. Eng. Educ, 1988, 25, pp. 269-275
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induction generator-part-I: Basic system and theory', IEEE Trans.,
1993, EC-8, (3), pp. 377-382
MURTHY, S.S., RAI, H.C., and TANDON, A.K.: 'A novel selfexcited self regulated single-phase induction generator part II: Experimental verification', IEEE Trans., 1993, EC-8, (3), pp. 383-388
RAHIM, Y.H.A., ALOLAH, A.I., and AL-MUDAIHEEN, R.I.:
'Performance of single phase induction generator', IEEE Trans., 1995,
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(3), pp. 484-492
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IEE Proc.-Gener. Transm. Distrib., Vol. 146, No. 5, September 1999
8
Appendix
The machine used for the test is a two-winding single-phase
induction generator rated as follows: 750W, 230V, 6A,
50Hz, 3000 rev/min. The parameters obtained from the
results of the standard test and referred to respective stator
windings
g are
Rm = 4.0 ohms, R2 = 3.2 ohms, Xm = X2 = 4.6 ohms, Rc
= 932 ohms
IEE Proc.-Gener. Transm. Distrib., Vol. 146, No. 5, September 1999
R\A = 5.5 ohms, Xu = 6.95 ohms, X™ = 235.00 ohms
t u m s ratl0> a = N N = L 1 7
^ i
The magnetisation curves are modelled based on test data
as
yjF = m5 _ QQm3 x if x < 1 6 0 . 0 ohms
&
mm
V= 491.9 - 1.5602 Xm if Xm < 210.0 ohms
J / / F = 731.4 - 2.6091 Xm if Xm > 210.0 ohms
427