In recent years, the induction machines are increasingly being used as selfexcited induction generators (SEIG). This generator is especially widely employed for smallscale power plants driven by renewable energy sources. The application of power electronic components in the induction generator control (IGC) and the loading of SEIG using nonlinear loads will generate harmonic currents. This paper analyzes the propogation of harmonic currents on the SEIG with nonlinear loads. Transfer function method in the frequency domain is used to calculate the gain and phase angle of each harmonic current component which are generated by a nonlinear loads. Through the superposition approach, this method has also been used to analyze the propagation of harmonic currents from nonlinear load to the stator windings. The simulation for the propagation of harmonic currents for a 4 pole, 1.5 kW, 50Hz, 3.5A, Yconnected, rotorcage SEIG with energysaving lamps, have provided results almost the same with the experiment. It can prove that the validity of the proposed models and methods. The study results showed that the propagation of harmonic currents on the stator windings rejects high order harmonics and attenuates low order harmonics, consequently THDI diminish significantly on the stator windings.
1. Introduction
Nowaday, the induction generator is more popular used for smallscale power plants driven by renewable energy sources, including: wind, mini/microhydro, tidal wave, biomass, biogas, etc.
[1]
. The popularity of induction generator mainly is due to a number of advantages compared to conventional generators, such as: low cost, high reliability, rugged construction, maintenance and operational simplicity, selfprotection against faults and overload, not needed dc supply for excitation, etc.
[1
,
2]
. The application of induction generators in commercial biogas driven power has been successfully analyzed
[1]
. Some experts have successfully designed the induction generator control (IGC), consequently this generator can be used commercially on a micro hydro power plant
[3

5]
. In the meantime, the minimum excitation capacitor connected auxiliary windings of a single phase SelfExcited Induction Generator (SEIG) have been successfully calculated for suitable for stanby power system
[6]
.
However, the operation of the induction machine as a generator requires reactive power, which is supplied either from the grid or compensation capacitors. It will leads the generator to produce power with low power factor. In addition, the utilization of power electronics components on the IGC and/or nonlinear loads will generate harmonics current and voltage on the generator output. The harmonics distortion can give the effect of a decrease in efficiency, heating and reducing the lifetime of the machine
[7]
.
Currently, the performance analysis of SEIG was more focused supplying linear loads. The publications about the study of SEIG with nonlinear loads is little relatively. Only in literature
[8]
, the behaviour of SEIG with nonlinear loads has been analyzed specifically using the dynamic model. In this paper, the propagation of harmonic currents on SEIG with nonlinear load is analyzed using the steady state model. Again, the superposition approach is employed to analyze the effects of each source voltage generated by the generator and source of harmonic currents generated by the nonlinear load. Transfer function in the frequency domain is used to calculate the current gain of each harmonic component generated by nonlinear load. Simulation and experimental results are compared to test the validity of the model and method used.
This paper is organized into 5 sections. Modeling and analysis of SEIG with nonlinear load is discussed in section 2. The experimental setup are explained in section 3. The section 4 discusses the results and its analysis. Conclusions are presented in section 5.
2. The Steady State Analysis of SEIG with Nonlinear Loads
The configuration of single line diagram of the SEIG with nonlinear loads is shown in
Fig. 1
. The SEIG is constructed by an induction machine and an excitation capacitor, and is connected to nonlinear loads. In this case, nonlinear load is load equipped with electronic device, such as: uninterruptable power supply (UPS), adjustable speed drives (ASD), variable frequency drive (VFD), savingenergy lamps, etc. SEIG, either as generator set or micro hydro generator, supply nonlinear loads that generated harmonic currents.
Cofiguration of SEIG with nonlinear load
 2.1 The modelling and analysis of SEIG with nonlinear loads
In the previous study, the perphase equivalent circuit of SEIG has been employed permanently to analyze the steady state performance of SEIG with linear loads
[9

11]
. The perphase equivalent circuit of SEIG with necglecting core loss is shown in
Fig. 2
. Where,
R
_{s}
,
X
_{s}
,
R
_{r}
,
X
_{r}
, and
X
_{m}
are the stator resistance, stator leakage rectance, rotor resistance, rotor leakage rectance, and magnetizing reactance respectively. Furthermore,
R
_{L}
,
X
_{L}
, and
X
_{c}
represent the load resistance, load reactance, and excitation capacitor reactance.
σ= a−b
, is slip, where
a
and
b
represent per unit (p.u.) frequency and rotor speed respectively. The equivalent circuit of SEIG with nonlinear loads can be obtained from the modification of this equivalent circuit. In this modification, the branch of linear load (
R
_{L}
/a dan
X
_{L}
) in
Fig. 2
is changed with nonlinear load model.
Equivalent circuit perphase of SEIG under linear load with neglecting core loss
The equivalent circuit simplified of SEIG with nonlinear load is shown in
Fig. 3
. In this circuit, the amplitude and frequency of the load voltage
V
_{L}
is assumed a constant at the nominal rating. Consequently, the value of
a
in this equivalent circuit is always one. As shown in
Fig. 3
, the nonlinear load is modeled as harmonic current sources,
I
_{1}
,
I
_{2}
,…
I
_{h}
, where
h
(2
^{nd}
, 3
^{rd}
, 5
^{th}
, 7
^{th}
,....) is known the order of the harmonics. While, SEIG is formed as the single voltage source,
V
_{ig}
, that connected in series an internal impedance,
Z
_{ig}
. The voltage source of SEIG is the open circuit voltage across the load terminals 12 (see
Fig. 2
),
V
_{ig}
=
V
_{L}
(OC). Whereas, the internal impedance of SEIG is the impedance across the load terminal 12 in
Fig. 2
.
Equivalent circuit simplified of SEIG with nonlinear loads
The superposition approach is used to analyze the propagation of harmonic currents. In this approach, each source is considered to evaluate the current through the stator windings seperately.
2.1.1 Voltage source response
In voltage source response, the analysis is conducted by replacing all current sources with an open circuit. This situation can occur in SEIG under noload condition. The equivalent circuit of SEIG under noload condition is shown in
Fig. 4
. In this conditions, the stator current
I
_{s0}
is equal with the excitation current
I
_{C}
.
Equivalent circuit of SEIG for voltage sources response
Due to saturation effects, the value of
X
_{m}
is influenced by the magnetizing current
I
_{m}
, which can be expressed as follows,
There is constant value of
α
_{i}
resolved from the polynomial curve fitting using saturation test results and
n
is the degree of polynomial equation.
2.1.2 Current Sources Response
For harmonic current sources response, the analysis is performed considering one current source
I
_{h}
. While, the other current sources and voltage source are replaced respectively with an open circuit and and internal impedance of SEIG. The equivalent circuit for one harmonic current source response is given in
Fig. 5
. This circuit is expressed in the domain
s
in order to simplify the analysis. In this condition, the inductive reactances are expressed by
sL
and the capacitive reactances are presented as 1/
sC
.
SEIG equivalent circuit for current source response
The harmonics distortion on SEIG will effect on its parameter and variable values. The stator parameters (
R
_{s}
and
L
_{s}
) have a constant value, while the value of rotor parameters (
R
_{r}
′ and
L
_{r}
′) depend on the order of harmonics, due to skin effect
[12
,
13]
. Meanwhile, the amount of total rms of magnetizing current
I
_{m}
(rms) can be calculated as follow
[14]
,
Where,
I
_{mh}
is the rms value of magnetising current for
h
^{th}
order harmonic. In addition, the effect of harmonics on the slip is expressed by the following Eq.
[2]
:
where
σ
_{h}
is the slip at harmonic order
h
, and
ω
_{1}
&
ω
_{r}
are fundamental frequency and rotor speed respectively.
To referring
Fig. 4
, the rotor impedance
is connected parallel to the magnetization impedance,
Z_{m}
=
sL
_{m}
, hence the total impedance for these branches are:
The impedance
Z
_{rm}
is connected in series with the stator impedance,
Z_{s} = R_{s} + sL_{s}
, so the total impedance at this branch is:
If
and (
L_{m}
+
L′_{rh}
) =
L_{mr}
, then Eq. (5) can be modified as:
or
The equivalent circuit in
Fig. 5
can be simplified to
Fig. 6
.
Simplified representation of the equivalent circuit of Fig. 5.
From the equivalent circuit of
Fig. 6
, the transfer function
T
(s) as a current gain between the load and stator currents can be written as,
or
In the frequency domain
s
=
j
ω, the transfer function (Eq. 9) can be expressed as:
or
The magnitude of the transfer function can be solved from the following equation:
where
ω=hω
_{1}
,
ω
_{1}
is the fundamental frequency of generator.
While, the phase angle of the transfer function can be calculated as:
To rereferring
Fig. 5
, the current
I
_{sh}
propagate to the magnetizing inductance
L
_{m}
can be determined as:
or
 2.2 Induction machine parameter test
In this study, 4 pole ; 380420V, 1.5 kW, 50 Hz; 3.5A; Yconnection; rotorcage induction machine is used. The DC test, noload test and blockedrotor test are conducted to determine the machine parameters. In addition, saturation test and testing the influence of harmonics on the rotor resistance and inductance are also performed. Through the parameter test is obtained
R
_{s}
= 4.70 Ω and
X
_{s}
= 5.07 Ω.
The variation of the magnetizing inductance
L
_{m}
against the magnetizing current
I
_{m}
can be completed from saturation test results, as shown in
Fig. 7
. The procedure test is explained in Appendix. By using the curve fitting, this relationship can be presented in 7
^{th}
order polynomial equation, as:
Variation of magnetizing inductance L_{m} against magnetizing current I_{m}
The influence of harmonics on the rotor resistance,
R
_{rh}
’, and inductance,
L
_{rh}
’, are measured through blockedrotor test. Generally, the induction machines is operated at low slip (24%), therefore the frequency of rotor currents is in the range from 1 to 2 Hz
[15]
. During blockedrotor test, slip is one, hence the stator frequency is equal with the rotor frequency. In this test, the fundamental rotor frequency is taken 5 Hz, and 10 Hz, 15 Hz, 20 Hz,... are used as harmonics frequency in 1
^{st}
, 2
^{nd}
, 3
^{rd}
, 4
^{th}
,... order. The variation of the rotor resistance,
R
_{rh}
’, and inductance,
X
_{rh}
’ against the harmonics order,
h
, are shown in
Figs. 8
and
Fig. 9
respectively. By using the curve fitting, this relationship can be presented in 6
^{th}
order polynomial equation, as follow:
Variation of rotor resistance R_{rh}’ against h
Variation of rotor inductance X_{rh}’ against h
and
In the simulation, Eqs. 17 and 18 are used for harmonics number till 20
^{th}
, and can be assumed a constant for harmonics number above 20
^{th}
.
 2.3 Computer Simulation
The computer simulation is designed to solve the spectrum of transfer function and the propagation of harmonic currents on the stator windings. The design of computer program is developed from the flow chart in
Fig. 10
. The initial magnetizing current 
I
_{m0}
 is assumed similarly with the excitation current at noload condition 
I
_{c0}
.
L
_{m0}
is solved ploting 
I
_{m0}
 on the magnetising curve (see
Fig. 5
). In addition,
ε
is a small quantity (
ε
= 10
^{−6}
).
Flow chart for computation of spectrum transfer function and stator current
3. Experimental Set Up
In order to validate the results of the modeling and analysis, a series of experiment are performed in the laboratory. The experiment set up for the SEIG with nonlinear is shown by
Fig. 11
. In this test, a 3hp induction motor supplied by a frequency regulator is used as an activator of SEIG. The excitation capacitors used in this test is 3 × 34μF, which are connected in Y connection. The generator is burdened by nonlinear load, which is an energysaving lamps of 1200 Watt. The harmonic measurements are performed using Power Analyzer type CA 8220 with data transfer to a PC/Laptop. The measurements were taken at two points of measurement, namely: on the load side (P2) and on the stator windings side (P1). During testing, both in the noload condition and the nonlinear load condition, the fundamental frequency of terminal voltage generator is kept a 50 Hz constant by adjusting the speed rotor. The rotor speed for noload condition is 1507 rpm, while rotor speed for load condition is 1539 rpm.
Experiment set up for the proposed system
4. Results and Discussion
 4.1 Simulation results of transfer function analysis
The transfer function analysis is employed to investigate the propagation of harmonic currents generated by nonlinear load to the stator windings of SEIG. In theory, the analysis of the transfer function has been carried out in section 2.1 (Eqs. 12 and Eq. 13). The simulation results for magnitude and phase angle of the transfer function are shown in
Fig. 12
. As shown in
Fig. 12(a)
, the magnitue of transfer function has significantly its value for low order harmonics, and above order 20
^{th}
harmonics are negligible. The phase angle of transfer function has always a positive value, and can be negligible for higher than order 20
^{th}
(see
Fig. 12(b)
).
Simulation results for values of the transfer function
 4.2 Experimental results of SEIG under no load
Fig. 13
shows the output of SEIG under noload test. As shown in
Fig. 13a
, the stator current
I
_{s0}
is leading against the output voltages
V
_{0}
. At noload condition, the stator windings is only flowed the current that generated by the excitation capacitor. In this condition, the generator has generated harmonic currents and voltages, with THD by 5.7% and 4.9% respectively (see
Fig. 13(b)
). The generated harmonics are relatively low and are the innate nature of SEIG.
The ouput of SEIG under noload condition
 4.3 Experimental results for SEIG with nonlinear load
Fig. 14
shows the measurement results of the harmonic spectrum for current and voltage on the load side (P2). As shown by
Fig. 14(b)
, the component of harmonic currents spread from low to high order, with THD
_{I}
of 35.4%. This is obvious from results recording the waveform of load current (
Fig. 14(a)
), which showed a distorted badly from the ideal sinusoidal shape. Meanwhile the voltage waveform is slightly distorted, with THD
_{V}
only reached 9.5%.
The measurement results on the load side (P2)
The Spectrum of harmonic currents and voltages on the stator windings side (P1) are shown by
Fig. 15
. As shown by this figure, the propagation of harmonic currents that generated by nonlinear load (P2) on the stator winding have filtered significantly by SEIG, so that its THD
_{I}
is only 17.9%. In this case, the SEIG circuit has eliminated nearly all high order harmonic components. Whereas, harmonic current in order 5
^{th}
, 3
^{rd}
, and 7
^{th}
are still emerging, but its amplitude has reduced.
Current and voltage stator harmonics spectrum on the stator side (P1)
 4.4 Simulation results of SEIG with nonlinear load
The spectrum of harmonic currents on the stator windings of SEIG can be solved from the summation of all current sources and voltage source response. For the current sources response, the propagation of all harmonic currents generated by nonlinear loads on the stator windings are determined by multiplying each component of the transfer function spectrum (
Fig. 12
) and the load current spectrum (
Fig. 14(b)
). Meanwhile, the response of the voltage source is harmonic currents spectrum on the stator windings of SEIG in the noload condition (
Fig. 13(b)
). All above calculation have performed using computer program based the flow chart in
Fig. 10
. The simulation results of the spectrum for harmonic currents on the stator windings is shown in
Fig. 16
. As shown this figure, the component of harmonic currents that appear on the stator windings is only order 5
^{th}
and 7
^{th}
, while the component of higher order harmonics does not arise at all. THD
_{I}
of the stator current from simulation is 13.38 %.
Simulation results for spetrum harmonics of stator current I_{s}
 4.5 Discussion
The simulation and experiment results have provided the same conclusion, that SEIG rejects or attenuates the propagation of harmonic currents from the load to the stator windings. As shown in
Figs. 15
and
Fig. 16
, SEIG rejects almost all the high order component of hamornic currents on the stator windings, and attenuates the low order component.
On other hand, the current on the stator windings is the sum of the current of excitation capacitor and the load current containing harmonic components. In the stator windings, the current component of excitation capacitor is greater than the current generated by nonlinear load. Consequentially, the contribution of the load current containing harmonic on the stator winding is small relatively, so THD
_{I}
is small too
For loading SEIG with the energysaving lamps of 1200 Watt, the propagation of harmonic currents reduced from THD
_{I}
of 35.4 % on the loads side to 17.9 % (experimental result) or 13.38 % (simulation result) on the stator windings side.
5. Conclusions
The transfer function method in frequency domain has been successfully used to calculate a current gain and its phase angle of each harmonic current component is generated by a nonlinear load. Through the superposition approach, this method has also been successfully used to analyze the propagation of harmonic currents generated by nonlinear load to the stator windings of SEIG.
The simulation and experiment have provided similar results. This shows that the models and methods used has adequate validity. Generally, The study results showed that the propagation harmonic currents created by loads on the stator widings of SEIG are rejected for high order components, and attenuated for lower order components. Consequently, the THD
_{I}
of stator current will be reduced significantly. In this study, the reduction percentage of harmonic current distortion on the stator windings reached 49.44% (experimental results) or 62.20% (simulatian results). It can be showed that SEIG has a friendly nature to the harmonics distortion generated by nonlinear loads.
Acknowledgements
Author would like thanks to Engineering Faculty, Andalas University for the financial support this work, through DIPA Funding (No. 032/PL/SPK/PNP/FTUnand/ 2013).
BIO
Refdinal Nazir received B.E. and M.T. degree in electrical engineering from Bandung Istitute of Technology, Indonesia, in 1985 and 1991 respectively, and Ph.D degree from University Technology of Malaysia in 1999. He is currently a senior lecture in Dept. of Electrical Engineering, Andalas University, Indonesia. His research interests are electric machines, renewable energy, distributed generation, and microgrid.
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