Performance Analysis of Standalone Wind Driven

Induction Generator Feeding Unbalanced Loads

Benhacine Tarek Zine-Eddine, Mekhtoub Said, Nesba Ali*

Ibtiouen Rachid Laboratoire des Systèmes Intégrés à base de Capteurs
Laboratoire de Recherche en Electrotechnique Ecole Normale Supérieure de Kouba, Vieux Kouba
Ecole Nationale Polytechnique, El-Harrach Algiers, Algeria
Algiers, Algeria

Abstract—This paper presents the steady-state performances In the literature, many papers have addressed the steady
of a self-excited induction generator under unbalanced state operation of the SEIG under balanced conditions [7-11].
conditions. Particular interest was given to an extreme unbalance The difference between these works lies in the method adopted
condition where a three-phase induction generator is supplying a for solving the equations of the used model. Two models are
single-phase load. The computation approach used simplifies the mainly adopted: the impedance model [8] and the admittance
mathematical equations governing the operation of the generator. model [9]. The literature about the steady state of SEIG under
The adopted model for the generator-load assembly is based on unbalanced conditions is very sparse, however. The most
the symmetrical components method. An optimization technique interesting papers dealing with unbalanced mode are listed
is used for solving the equations. Then, the performances of the
below. The authors in [12] used the admittance model to
generator are determined. The results for the star and delta
connections are given. The computed results are validated by an
determine the operating conditions of the SEIG for the two star
experimental test bench. and delta configurations. Chan et al. [13] proposed a different
approach consisting in determining the equivalent total
Keywords : Induction generator, Wind energy, Unbalance, Self- impedance seen at the terminals of one phase of the load. The
excitation, Magnetic saturation. generator-load assembly is simplified to a combination of
passive elements at the terminals of the phase in question. A
I. INTRODUCTION numerical minimization method then determines the operating
The growing environmental concerns and the depletion of point of the SEIG. To avoid the mathematical calculations
fossil fuels are encouraging the rationalization of the use of developed in [13], Murthy et al. [14] used a direct method to
conventional energy resources and the exploration of establish an expression in complex numbers as a function of
unconventional energy sources such as wind, solar, the parameters of the machine. The resolution of the equations
hydropower, biomass and Geothermal energy [1]. Particularly, of the real and imaginary parts of this expression makes it
wind energy has grown strongly, which has led researchers in possible to evaluate the performances of the SEIG.
electrical engineering to carry out intensive research in order to The authors in [15-18] have studied another unbalance
increase the efficiency of electromechanical conversion on the configuration which consists in feeding single-phase loads
one hand and to improve the quality of the energy supplied on from a three-phase SEIG. This mode of operation gives rise to
the other hand. In rural and isolated areas, where the extension an extreme unbalance in the generator. In spite of this
of the electrical network is not cost-effective or impossible, the disadvantage, three-phase SEIGs are often used to supply
self-excited induction generator (SEIG), consisting of the single-phase loads. This can be explained by the fact that three-
induction machine associated with capacitors to provide the phase induction machines are standardized and available for
reactive energy required for the operation of the generator, different power ranges as well as by their competitive prices
offers several advantages in terms of reduced maintenance compared to single-phase induction machines of the same
cost, good dynamic responses and self-protection against faults power [15].
[2].
In the works cited above, the determination of the equations
The operation of the SEIG is based on the phenomenon of of the models governing the operation of the SEIG implies a
magnetic saturation [3-4]. In addition to non-linearity related to notable mathematical complexity. To remedy this drawback, a
magnetic saturation, the SEIG presents other difficulties in the different approach that permits to simplify the equations of the
unbalanced mode. Usually, unbalance occurs at the level of model is presented in the present paper. The resolution of the
excitation capacitors and/or the loads [5-6]. The study of the model equations makes it possible to determine the operating
steady state operation of unbalanced SEIG is usually based on point of the SEIG in balanced and unbalanced modes. In
the use of symmetrical components theory [4]. addition, a comparison of the performances of the two star and

978-1-5090-4947-9/16/$31.00 ©2016 IEEE

delta configurations of the generator-load assembly is , , stator line currents.
, ,
presented. Three modes of operation are studied: balanced
stator phase voltages.
, ,
operation, unbalanced operation and single-phase load
operation. In order to validate the adopted approach, the load line currents.
, ,
different modes of operation of the SEIG are examined on a
load phase voltages.
, ,
laboratory test bench. The theoretical and experimental results
are presented and compared. load impedances.
II. SEIG-LOAD MODELING , , denote the admittances of positive, negative and
zero sequences, respectively.
Where = e and , , are the admittances of the
A. SEIG model for unbalanced operation
/
The connections between the machine stator and the

shown in Figs. 1 and 2 respectively. The impedances , ,

unbalanced load for the two delta and star configurations are load-capacitor assembly of phases 1, 2 and 3, respectively.
Using the symmetrical components theory, the phase
are formed of capacitors in parallel with the loads which are
current is defined by:
assumed to be purely resistive.
The modeling is based on the symmetrical components
method in order to account for unbalanced modes of operation = (4)
of the generator. In the following, the steps necessary for
determining the equations governing the operation of the
, ,
generator-load assembly for the delta configuration are
presented. The star configuration is analyzed following the denote positive, negative and zero sequences of
same procedure. In this study, the admittances of the equivalent the load voltage .
circuits for the positive and negative sequences were used. , , denote positive, negative and zero sequences of
The equivalent admittances in symmetrical components are the load current .
defined as follows [4] The currents and may be expressed in the same

= ( + + )
manner as .
(1)
For delta configuration, zero-sequence voltage is null:

= ( + . + . ) (2) =0 (5)

= ( + . + . ) (3) The positive and negative sequences of the load line current
are expressed as:

= − = (1 − )( + ) (6)

= − = (1 − )( + ) (7)

The per-phase equivalent circuits of the induction machine

for positive and negative sequences are shown in Figs. 3 and 4
respectively [4].

Fig. 1. Connection diagram of the SEIG/load in delta configuration

Fig. 3. Positive sequence equivalent circuit of induction machine

Fig. 2. Connection diagram of the SEIG/load in star configuration

Fig. 4. Negative sequence equivalent circuit of induction machine
 #$ and #% are stator and rotor resistances respectively. Substituting (15) in (13) gives:
&$ and &% are stator and rotor leakage reactances,
-) + − 4=0
./ .3
.0 123
respectively. (16)
&' is the induction machine magnetizing reactance.
( is the slip.
For successful self-excitation process of the SEIG, the
positive sequence voltage should be non zero, then:
) , ) are the admittances of the positive and negative per ) + −
./ .3
=0
.0 123
(17)
phase equivalent circuits of the SEIG, respectively.

$ , $ are the positive and negative sequences of the stator Finally, the resolution of (17) allows determining the
phase voltage, respectively operating point of the SEIG under balanced or unbalanced
* , * are the positive and negative sequences of the air-
loading conditions.
gap voltage, respectively. B. Resolution Method
$ , $ are the positive and negative sequences of the stator
Equation (17) is expressed in terms of the slip and the
phase current, respectively. magnetizing reactance, whose, in turns, depend on the load and
the air-gap voltage, respectively. Consequently, the resolution
The parameters of the equivalent circuits are considered of (17) by classical analytical methods is not possible. To
constant except for the magnetizing reactance, which is address this problem, a numerical approach based on the
variable as a function of the saturation state of the induction Simplex Nelder-Mead method has been adopted. This method
machine. The verification of the superposition principle uses a non-linear algorithm for multivariable optimization [19].
required by the symmetrical components method implies the The resolution of (17) is performed by minimizing the
same value for the magnetizing reactance for both positive and magnitude of its left term, which makes it possible to obtain the
negative sequences [4]. The effect of magnetic saturation on values of the magnetizing reactance and the frequency. The
leakage inductances as well as iron losses is neglected. different currents and voltages can then be calculated.
From Figs. 4 and 5, positive and negative sequence Indeed, the value of the magnetizing reactance in
components of the stator current may be expressed as: conjunction with the magnetization curve of the machine will

= )
permit to deduce the positive sequence of no-load stator air-gap
$ $ (8) voltage. The value of the slip will make it possible to calculate

= )
the frequency of the stator quantities. Thus, the positive
$ $ (9) sequence of the stator voltage can be determined from the
equivalent circuit of Fig. 3 as follows:

5/
=
Hence, the positive and negative sequence components of
(67 1897 )2/
stator line current may be written as follows: (18)

= (1 − ) )
* : positive sequence of the air-gap voltage
(10)

= (1 − ) ) (11) :$ : stator pulsation :$ = 2<=

The currents and voltages of the three phases may be
From Fig. 1, the positive sequence components of the
derived from their respective symmetrical components as
load/stator line currents are equal and opposite, which makes it
follows:
possible to write:

= −
For phase voltages:

= +
(12)
(19)

= +
By replacing the currents and by their respective
expressions (6) and (10), one obtains: (20)

+ + ,=− ) (13) = + (21)

Similarly to (12), Fig.1 states that the negative sequence For line currents:

=) +)
components of the load/stator line currents are equal and
opposite. Combining this with (7) and (11) permits to write: (22)

( + ) = − ) (14) = () ) + () ) (23)

= - 4 = () )+ () )
./
.0 123
(15) (24)
 The power consumed by the load is given by:

>= + 6C + 6D
?@A ?A ?A
6B A E
(25)

Two coefficients quantifying the degree of unbalance are

introduced as:

?3
FG = × 100 %
?/
(26)

K73
JFG = / × 100 %
K7
(27)

VUF : Stator voltage unbalance factor.

Fig. 5. Laboratory test bench
CUF : Stator current unbalance factor.
III. RESULTS AND DISCUSSIONS
The experimental validation was carried out on a laboratory
test bench consisting of a 3.5 kW three-phase induction
machine, driven by a DC machine of the same power. The
experimental device is shown in Fig. 5. The parameters of the
induction machine, determined from the conventional tests, are
given in the Appendix.
The variation of the magnetizing reactance as a function of
no-load air-gap voltage is shown in Fig. 6. This curve, obtained
experimentally from no-load test, was modeled by the
following polynomial expression:

&' = L (* ) + L (* ) + L (* ) + LM (28)

Where:
L = 5.49. 10 Q , L = −0.0017 , L = 0.3341 ,LM = 41.73 Fig. 6. Magnetizing reactance as a function of air-gap voltage

Two important areas can be distinguished on the 25

(for * < 100 V) and the saturated zone (for * > 100 V). The
magnetization characteristic illustrated in Fig. 6; the linear zone 250

linear zone is of no interest in the operation of the SEIG. 20

200
Indeed, the phenomenon of self-excitation of the induction I-sim
generator can only occur in the saturated zone. 15
I-exp
V-sim
V-exp 150
For all the tests carried out, the speed of the generator is
kept equal to 1500 rpm and the value of the capacitors is
10
maintained at 80 µF. These two values make it possible to have 100

a self-excited operating point close to the nominal conditions of

the generator. It is obvious that these tests can be carried out at 5 50
different speeds and with different capacitances. However, the
self-excitation conditions and the rated values of the generator
should be taken into account. 0
500 1000 1500 2000 2500
0

Power (W)
A. Balanced Operation
The balanced regime carried out in the present study Fig. 7. Performances of SEIG with balanced load in delta configuration
consists in supplying a purely resistive balanced three-phase
load. The values of the load resistances used are between 38.7 The stator voltage decreases as the power consumption
and 204.6 Ω. Fig. 7 represents the variation of the stator increases. This is due to the reduction in the level of
voltage and current as a function of the powers consumed for magnetization of the generator, which is in turn due to the
the delta configuration. Similar results are obtained in the case reduction in the supply of reactive energy provided by the
of the star configuration. capacitors.
 It can also be noted that the power supplied by the
16
generator reaches a point of maximum power (2560 W) above 250

which the increase in load (R> 45.9 Ω) causes a decrease in 14

power and voltage. 200
12
The stator current is almost constant (10.5A), this can be Ia-sim
Ib-sim
explained by the fact that the stator current is the sum of the 10 Ic-sim
150
capacitive and load currents. Thus, by increasing the load, the Ia-exp
Ib-exp
8
voltage decreases causing the capacitive current to decrease, Ic-exp
and since the current in the load increases as the power is 6
Va-sim
Vb-sim
100

increased, the load current compensates for the capacitive Vc-sim

current, which makes it possible to have a stator current quite 4 Va-exp
Vb-exp 50
constant. 2
Vc-exp

B. Unbalanced Operation
0 0
In this part, the unbalanced three-phase load is chosen so 1600 1800 2000 2200 2400 2600 2800
Power (W)
that two phases of the load are kept constant at 75.3 Ω, while Fig. 8. Performances of SEIG with unbalanced load in star configuration
the third phase is variable. Six resistance values are examined:
38.7 Ω, 45.9 Ω, 57.3 Ω, 108.3 Ω, 204.6 Ω and 650 Ω.
Figs. 8 and 9 illustrate the variations of the voltages of the
three loads and that of the stator currents as a function of the
power consumed for the star and delta configurations,

Load voltages (V)

Stator currents (A)
respectively. The simulation results are very close to the
experimental results, hence the validity of the adopted model.
The values of the voltages at the terminals of the three loads
are quite close, for the configuration in delta, unlike the case of
the star configuration.
Fig. 10 shows the variations of the coefficients CUF and
VUF as function of the total power. The values of CUF and
VUF decrease proportionally with the increase of the power, up
to a limit value (5% for CUF and 1% for VUF). These limit
values characterize an almost balanced load. Indeed, in a
balanced mode operation CUF and VUF are zero. By further Fig. 9. Performances of SEIG with unbalanced load in delta configuration
increasing the power through the load of the variable phase, the 22 22
values of CUF and VUF retake increasing values up to 18% for
20 20
CUF and 3% for VUF. VUF-star
CUF-star
18 VUF-delta
18
The CUF and VUF curves obtained for the two star and 16
CUF-delta
16
delta configurations are essentially similar. It should also be
14 14
noted that the VUF values are lower than those of CUF.
12 12
C. Single-Phase Operation
10 10
In this section, the performances of the three-phase 8 8
induction generator feeding a single-phase load are examined.
6 6
For this particular operation, several capacitor and load
connection configurations are reported in the literature [15]. 4 4

2 2
In this study, the configuration of the generator with three
capacitors is adopted. The single-phase load (R) is connected to 0
1400 1600 1800 2000 2200 2400
0

J , J , J represent the self-excitation capacitors. Fig. 11

the terminals of one of the three phases (here phase b). Power (W)

Fig. 10. Variations of CUF and VUF in unbalanced operation

shows the connections of the SEIG with single-phase resistive
load in the case of delta configuration. The results of the delta configuration are given for three
Figs. 12 and 13 represent respectively the variations of the values of the single-phase load 38.7, 57.3 and 75.3 Ω.
voltages at the terminals of the capacitors as well as the According to Figs. 12 and 13, the simulation results agree
variations of the stator currents obtained for the star and delta well with those obtained experimentally, which proves the
configurations. The three capacitors are identical with a validity of the elaborated model even for cases of extreme
capacity of 80µF each. The star configuration results are given unbalance (single-phase operation).
for six values of the single-phase load: 38.7 Ω, 45.9 Ω, 57.3 Ω,
75.3 Ω, 108.3 Ω and 204.6 Ω.
 configuration are less unbalanced compared to those of the star
configuration.
For single-phase operation, the generator has current and
voltage characteristics close to nominal values, which makes
this type of generator suitable for supplying single-phase loads.
35 400

30 350
Ia-sim
Ib-sim
300
25 Ic-sim
Ia-exp
Ib-exp 250
Ic-exp
Fig. 11. SEIG feeding single-phase load in delta configuration 20
Va-sim
Vb-sim 200
15 Vc-sim
The curves representing the variation of the voltages for the Va-exp 150
Vb-exp
two star and delta configurations show that the voltage at the 10 Vc-exp
100
terminals of the single-phase load (phase b) is almost constant
and close to the nominal value of the machine, i.e. 230 V. The 5 50
voltage of phase "a" for the star configuration increases with
the load reaching 340 V for a load of 38.7 Ω, which poses a 0 0
200 400 600 800 1000 1200 1400 1600 1800
risk for the capacitor connected to this phase. The voltages at Power (W)
the terminals of the capacitors for the delta configuration are
very close to one another and practically invariable with the Fig. 12. Performances of SEIG in single-phase operation – star configuration
power.
Fig. 14 illustrates the variations of the coefficients VUF and 25

CUF as a function of the power of the single-phase load. These 250

Ia-sim
curves show that the coefficients CUF and VUF are varying Ib-sim
20
proportionally to the power. Also, it can be seen that the Ic-sim
Ia-exp 200
current unbalance factor (CUF) is more significant than the Ib-exp
voltage unbalance factor (VUF). The CUF reaches 32% for a 15
Ic-exp
Va-sim
power of 1300 W, i.e. one third of the nominal power of the Vb-sim 150
Vc-sim
machine. The delta configuration has a higher CUF, while the Va-exp
VUFs are almost the same for the two configurations. 10 Vb-exp
100
Vc-exp

IV. CONCLUSION
5
In this work, the performances of the self-excited induction 50

generator in balanced and unbalanced modes for the star and

delta configurations were examined. The proposed new 0 0
computational approach makes it possible to simplify the 500 600 700 800 900 1000 1100 1200
Power (W)
equations governing the induction generator when feeding
unbalanced loads. The results from the simulation are validated Fig. 13. Performances of SEIG in single-phase operation – delta configuration
by experimental tests.
35 35
For balanced load operation with constant rotor speed, the
stator current is almost constant but the stator voltage varies 30 30
inversely with the increase in load, which remains a
disadvantage. 25 25

The unbalance related to the difference in power consumed 20 20

VUF-star
on each phase of the load was examined. Two coefficients for CUF-star
quantifying the degree of current unbalance (CUF) and voltage 15
VUF-delta
15
CUF-delta
(VUF) were introduced and calculated for each case of
unbalance. VUF coefficient is always lower than CUF 10 10
coefficient. The single-phase configuration has the highest
CUF; it reaches a value of 32% for one third of the nominal 5 5

power of the machine.

0 0
700 800 900 1000 1100 1200 1300
The CUF and VUF curves for the two delta and star
Power (W)
configurations are almost identical. However, the delta
configuration has a higher CUF in the case of a single-phase Fig. 14. Variations of CUF and VUF in single-phase operation
load. The voltages at the load terminals for the delta
 APPENDIX [8] S. S. Murthy,B. P. Singh, C. Nagamani, and K.V.V. Satyanarayana,
“Studies on the use of conventional induction motors as self-excited
The test bench used in the experimental investigation induction generators,” IEEE Trans. Energy Convers., vol. 3, no. 4, pp.
consists of a wound rotor three-phase induction machine driven 842–848, December 1988.
by a DC motor. The parameters of the induction machine are: [9] L. Quazene and G. McPherson, “Analysis of the isolated induction
genertor,”IEEE Trans. Power App. Syst., vol. PAS-102, no. 8, pp. 2793–
Parameters Values 2798, August 1983.
Power P = 3.5 kW [10] J. Bjôrnstedt, F. Sulla O. Samuelsson, “ Experimental investigation on
steady-state and transient performance of self-ecited induction
Voltage U = 220/380 V generator,” IET Gener. Transm. Distrib, vol. 5, Iss. 12, pp. 1233–1239,
Speed N = 1410 tr/mn 2011.
Number of poles 4 poles [11] A. Kheldoun, L. Refoufi, D. E. Khodja, “Analysis of the self-excited
Nominal stator current Is = 14/8 A induction generator steady state performance using a new efficient
Nominal rotor current Ir = 9 A algorithm,” Electr. Power Systems Res, vol. 86, pp. 61–67, 2012.
Stator resistance Rs= 1.2 Ω [12] A. H. Al-Bahrani, “Analysis of Self-Excited Induction Generators
Under Unbalanced Conditions,” Electric Machines and Power Systems,
Rotor resistance Rr = 0.88 Ω vol. 24, no. 2, pp.117-129, 1996.
Leakage inductance ls= lr=10 mH [13] T. F. Chan and L. L. Lai, “Steady-State Analysis and Performance of a
Stand-Alone Three-Phase Induction Generator With Asymmetrically
Connected Load Impedances and Excitation Capacitances” IEEE Trans
on Energy Conversion, vol. 16, no 4, December 2001.
REFERENCES [14] S.S.Murthy, B.Singh, S.Gupta and B.M.Gulati, “General steady-state
[1] F. A. Farret and M. G. Simoes, Integration of Alternative Sources analysis of three-phase self-excited induction generator feeding three-
Energy. Piscataway, NJ: IEEE Press, 2006. phase unbalanced load/ single-phase load for stand-alone applications”
IEE Proc.- Gener.,Transm., Distrib., vol 150 , no.1, pp. 49-55, January
[2] R.C. Bansal, “Three-phase self-excited induction generators: an
2003.
overview,” IEEE Trans on Energy Conversion, vol. 20, no. 2, June
2005. [15] C.P Ion C. Marinescu, “Three-phase induction generators for single-
phase power generation: An overview,” Renewable and Sustainable
[3] A. Nesba, R. Ibtiouen, S. Mekhtoub, O. Touhami, and S. Bacha, A
Energy Reviews, vol. 22, pp.73–80, 2013.
“Novel Method for Modeling Magnetic Saturation in the Main Flux
of Induction Machine,” The 6th WSEAS/IASME international [16] S.S. Murthy, Bhim Singh, V. Sandeep, “An analytical performance
Conference on Electric Power Systems, High Voltages, And Electric comparison of two winding and three winding single phase SEIGs,”
Machines (POWER'06), Spain, 16-18 December 2006. Electric Power Systems Research, vol. 107, pp. 36-44, 2014.
[4] I. Boldea and S. Nasar, The Induction Machine Handbook, CRC Press [17] S. Gao, G. Bhuvaneswari, S.S. Murthy, U. Kalla, “Efficient voltage
LLC, 2002. regulation scheme for three-phase self- excited induction generator
feeding single-phase load in remote locations,” IET Renew. Power
[5] Y.J.Wang, Y.S.Huang, “Analysis of a stand-alone three-phase self-
Gener., vol. 8, no. 2, pp. 100-108, 2014.
excited induction generator with unbalanced loads using a two-port
network model,” IET Electr. Power Appl,vol.3, Iss.5, pp. 445-452, 2009. [18] S. S Murthy, G. Bhuvaneswari, S. Gao, and R. K. Ahuja, “Self excited
induction generator for renewable energy applications to supply single-
[6] J. Radosavljevic, D. Klimenta, M. Jevtic, “Steady–state analysis of
phase loads in remote locations”. IEEE International Conference on
parallel–operated self–excited induction generators supplying an
Sustainable Energy Technologies (ICSET), pp. 1-8, Sri Lanka, 6-9
unbalanced load,” Journal of Electrical Engineering, vol. 63, no. 4, pp.
December 2010.
213–223, 2012.
[19] J.C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright,
[7] T. F. Chan, “Analysis of self-excited induction generators using an
"Convergence Properties of the Nelder-Mead Simplex Method in Low
iterative method ,” IEEE Trans. Energy Convers., vol. 10, no. 3, pp.
Dimensions," SIAM Journal of Optimization, Vol. 9 Number 1, pp. 112-
502–507, September 1995.
147, 1998.