The Camparison of Harmonic Distortion Self-Excited Induction Generator with Isolated Synchronous Generator Under Non-linear Loads

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 6, No. 4, December 2015, pp. 759~771
ISSN: 2088-8694  759
Journal homepage: http://iaesjournal.com/online/index.php/IJPEDS
The Camparison of Harmonic Distortion Self-Excited Induction
Generator with Isolated Synchronous Generator Under
Non-linear Loads
Refdinal Nazir1
, Krismadinata2
, Rizka Amalia1
1
Electrical Engineering Department, Andalas University, Indonesia
2
Electrical Engineering Department, Padang State University, Indonesia
Article Info ABSTRACT
Article history:
Received Jul 31, 2015
Revised Nov 18, 2015
Accepted Nov 29, 2015
In this paper, the harmonic distortion for Self-Excited Induction Generator
(SEIG) and an isolated synchronous generator (ISG) under non-linear load
during steady state conditions are analyzed. The voltage and current
harmonics distortion for both generators are calculated using the transfer
function method in frequency domain for SEIG and phasor diagram method
for ISG. This analysis is done independently one by one component for all
harmonic components appear. The analysis results for both generators are
verified to the laboratory test results. For loading with the same non-linear
load to both generators, the harmonics distortion on the stator windings of
SEIG was smaller than compare ISG. In addition, the harmonic distortion
effects on other loads connected to PCC point of SEIG was lower than the
other loads connected to ISG.
Keyword:
Harmonic Distortion
Non-linear Load
SEIG
Synchronous Generator
Total Harmonic Distortion Copyright © 2015 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Refdinal Nazir,
Departement of Electrical Engineering,
Andalas University,
Limau Manis Campus, Padang 25163, Indonesia.
E-mail: refdinalnazir@yahoo.co.id
1. INTRODUCTION
Currently, the applications of Self-Excited Induction generator (SEIG) are more common in small-
scale power plants using renewable energy sources, including: wind, mini/microhydro, tidal wave, biomass,
biogas, etc. [1],[2]. Meanwhile, the isolated synchronous generators (ISG) are widely applied in diesel
electric generating sets (Genset). In its application, the two generators are often employed to drive non-linear
loads, including: uninterruptible power supply (UPS), variable frequency drives (VFD), switched mode
power supply (SMPS), energy-saving lamp (ESL), etc. The imposition of generator with non-linear loads will
have an impact on the generation of harmonic currents and voltages distortion. The generation of harmonic
currents in the generator has adverse effects upon its performance. It can give the effect of decreasing
efficiency, heating and reducing the life time of the generator [3]-[5]. Harmonic distortion of the voltage
generator will be able to create a harmonic disturbance to other loads, which are connected in parallel to the
same source.
The levels of harmonic distortion incurred due the employed of non-linear loads on SEIG and ISG
will be different. This level of harmonic distortion is influenced by the equivalent circuit structure of the
generator and its parameters. Generators for Genset usually have higher the reactance than the distribution
transformers on utility networks [3]. Consequently, the rate for the harmonic distribution of the generator
voltage is higher than the utility source, if both sources operate with the same non-linear load. The equivalent
circuit structure of SEIG has the combination between magnetization inductance and excitation capacitance
that can reduce the distortion harmonics. In the previous study, analysis of harmonic propagation on SEIG

 ISSN: 2088-8694
IJPEDS Vol. 6, No. 4, December 2015 : 759 – 771
760
when its is loaded by non-linear load [6]. The results showed that SEIG rejects the high order harmonics and
attenuates low order harmonics currents on its stator windings; consequently THDI is low relatively on the
stator windings.
In this paper, the current and voltage harmonic distortion for SEIG and ISG under non-linear loads
during steady state conditions are analysed. The analysis result of harmonic distortion for two generators is
compared in order to show the impact of non-linear loads on the both generator and other loads connected to
the same sources. This paper is organized into 7 sections. In section 2, the system description of proposed
system is presented. Modeling and analysis for SEIG with non-linear load is discussed in section 3. In section
4, the harmonics distortion of ISG under non-linear loads is discussed. The experimental set-up is explained
in section 5. The section 6 discusses the results and its analysis. Conclusions are presented in section 7.
2. SYSTEM DESCRIPTION
The configuration of studied system consists of a generator, non-linear loads, and other loads that
are linearly, as shown by Figure 1. In this system, Variable Fequency Drive (VFD) and Energy-Saving Lamp
(ESL) are applied as non-linear load and resistor is employed as the other load. The harmonic currents, Ih,
flow from the non-linear loads to the generator and other load, RL. In the SEIG, the harmonic currents flow to
the stator windings and the excitation capacitors that are low impedance to high frequencies, while the
harmonic currents flow only to the stator windings in the ISG. Furthermore, the both generators also produce
the small harmonic of voltages due to the imperfection of its construction.
Figure 1a shows the configuration of studied system using SEIG. As shown in this figure, SEIG is
constructed by an induction machine and an excitation capacitor. Zim is the internal impedance of induction
machine, which will be determined in next section. Meanwhile, the configuration of studied system using an
isolated synchronous generator is shown by Figure 1b. This study uses a salient pole synchronous generator,
so the synchronous impedance Zs is constructed by a direct synchronous reactance Zd and quadrature
synchronous reactance Zq [7].
SEIG Other Load
Excitation
Capacitor
Induction
Machine
ih
iRh
iIGh
ish
Isolated Synchronous
Generator
Non-Linear Load
as
Harmonic Current
Sources
Other Load
ih
iRh
iSGh
ish
ZsZim
iCh
PCC PCC
Terminal
point
Terminal
point
Non-Linear Load
as
Harmonic Current
Sources
a. studied system using SEIG b. studied system using ISG
Figure 1. The configuration of studied system
3. HARMONIC ANALYSIS OF SEIG
The single-phase equivalent circuit of SEIG with non-linear load is shown in Figure 2. In this
circuit, the non-linear loads are modeled as a current fundamental component I1, and harmonic current
sources: I2, I3, ..., In [8]. Whereas, SEIG model is constructed by the circuit of induction machine and the
excitation capacitor Ce. Where Rs, Ls, Rr
’
, and Lr
’
are the stator resistance, stator leakage inductance, rotor
resistance, and rotor leakage inductance respectively. Eg and σ are the voltage of air gap and slip. RL is the
other load, which is the linear load connected at PCC point.

IJPEDS ISSN: 2088-8694 
The Camparison of Harmonic Distortion Self-Excited Induction Generator with Isolated .... (Refdinal Nazir)
761

Figure 2. Single-phase equivalent circuit of studied system using SEIG
The analysis is conducted using the single-phase equivalent circuit as shown in Figure 2. This circuit
contains non-linear load as n unit’s current sources and SEIG as voltage sources. Besides that, the other load
as linear load RL is connected in parallel with the non-linear load at PCC point. The response of each source
to the circuit of machine stators and other load are evaluated separately. The total response can be solved
from the summation of the current response of each source and voltage response.
3.1. Current Sources Response
For current sources response, the analysis is performed by considering one current source, Ih.
Meanwhile, the other current sources and voltage source are replaced respectively with an open circuit and
internal impedance of SEIG. Figure 3a shows the equivalent circuit for one harmonic current source. In this
analysis, the equivalent circuit is expressed in the domain frequency ω. In this condition, ω = hω1, where h
and ω1 are number of harmonics and fundamental frequency respectively. The correlation between the
currents is produced by non-linear load I(h), the other load currents IL(h), and the current in to induction
generator IIG(h) is expressed as,
IIG(h)= I(h)- IL(h) (1)
where, t
L
(h)
(h) =
R
V
I
1
jω C
( )L
h
I
( )I hI G
( )I C h
h
( )Is h
h
( )I m h
h
'
( )I hr
1
jω C
( )I C 0
h
( )Is 0
h
( )I m 0
h
a. one current source response b. no-load response
Figure 3. SEIG equivalent circuit for analysis
From the equivalent circuit of Figure 3, the induction machine impedance, Zim, can be expressed as,
 rh
im rh m s
h
'
' +
R
j L j L R j L  

   
  
   
Z s
= + / / +
︵
︶
(2)
where, a slip, σh, is defined as,

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762
1 r
h
1
-
=
h
h
 


(3)
If  mr m rh= + 'L L L and rσ r h' = 'R R  , then Eq. 5 can be solved as,
   2
rσ s m rh s mr rσ s m rσ s mr
im
rσ mr
' - ' + + ' + ' +
=
' +
R R L L L L j R L L R R L
R j L
 

Z (4)
The transfer function Ts(jhω1) or Ts(h) as a current gain between the stator current Is(h) and the
input currents of SEIG IIG(h) can be written as,
s C
s
im CIG
(h)
(h) = =
+(h)
I Z
T
Z ZI
(5)
Or
      
rσ 1 mr
s 2 2 3 3
rσ 1 rσ m e rσ s e s mr e 1 rσ s e mr 1 s mr e m r e
' +
(h) =
' - ' + ' + + ' + - + '
R jh L
R h R L C R L C R L C j h R R C L h L L C L L C

  
T
(6)
Furthermore, the stator currents Is(h) can be solved using the following equations:
Ish(h)=Ts(h)IIG(h) (7)
The magnetizing current Im(h) can be calculated as,
rσ 1 rh
mh s
rσ 1 mr
' + '
(h) = (h)
' +
R jh L
R jh L


I I (8)
3.2. No-Load Response
No-load response is used to obtain the excitation current flowing in the stator windings to generate a
generator voltage. This can be done through direct measurement of the stator current at no-load conditions.
At this measurement, the value of excitation capacitor is kept constant, while the rotor speed is set to obtain
the fundamental frequency of 50 Hz. As shown in Figure 3b, the stator currents at no-load conditions Is0(h) is
equal to the current of excitation capacitor Ic(h) or the magnetization current -Im0(h). Assumed, the current
flowing in the rotor circuit is negligible. The harmonic components appearing at no-load conditions are
caused by the inherent nature of the generator.
3.3. Total Response
The currents flowing in the SEIG circuit are obtained from the total response of the current sources
and no-load response, as shown by the following equation:
Is(h) = Is0(h)- Ish(h);Im(h) = Im0(h)+ Imh(h) (9)
The terminal votage of SEIG in the harmonic distortion can be solved as,
Vt(h) = E(h)-Is(h)(Rs+jXs) (10)
where, E(h) is the air gap voltage that its is determined as (see Figure 3b),
E(h) = Vt0(h)+Is0(h)(Rs+jXs) (11)

763
The total rms of magnetizing current Im(rms) can be calculated as [8],
n
2
m m
h=1
(rms) = (h)I I (12)
The value of magnetizing inductance Lm applied in this section depends on the value of magnetizing
current Im, which its variation is obtained from the experimental results. In addition, the values of Rrh’ and
Lrh’ for different harmonic orders is solved using the block rotor test [6],[9],[10]. The experimental results are
resolved through curve fitting for a number of data that obtained from the experimental test. This method is
implemented with polyfit statement in MATLAB, so Rr’(h), Lr’(h) and Lm(Im) are obtained as:
Rr’(h) = c1h4
+ c2h3
+ c3h2
+ c4h+c5 ; Lr’(h) = d1h4
+ d2h3
+ d3h2
+ d4h+d5 (13)
Lm(Im) = e1Im
3
+ e2Im
2
+ e3 Im + e4 (14)
where, c,d & e are a polynomial coeficient that its values are given in Appendix. In this analysis, Eq. 13 &
Eq. 14 are applied for harmonic orders till 20th
, and can be assumed a constant for harmonic orders above
20th
.
4. HARMONIC ANALYSIS OF ISG
The analysis of harmonics distortion for ISG is conducted using the equivalent circuit and phasor
diagram that shown by Figure 4 & 5. As shown in Figure 4, the non-linear load is modelled as a fundamental
current component and harmonic current sources. Another load current that is connected to the same PCC
will also be contaminated by harmonic components IL(h). Because this study uses the salient pole
synchronous generator, the synchronous reactance Xs is split into the reactance in the direct axis Xd and the
reactance in the quadrature axis Xq, as shown in Figure 5a [7],[11]. Likewise, the current flows through the
stator windings are also decomposed into the current in the direct axis Isd and the current in the quadrature
axis Isq.
To analyze the response of harmonic current sources, each order-by-order harmonic component is
evaluated using an equivalent circuit as shown in Figure 5a. Here, E(h) is the harmonic voltage distortion of
the air gap, which is the innate nature of the generator. E(h) can be obtained from no-load test results. The
correlation between the currents is produced by non-linear load I(h), the other load currents IL(h), and the
stator current Is(h) for hth
order component is given as,
Figure 4. Equivalent circuit of studied system using ISG
Is(h)= I(h)-IL(h) (15)
where, the other load current can be calculated as,
t
L
L
(h)
(h) =
R
V
I
(16)

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[Isq(h),Isd(h)]
Vt(h)

RL
IL(h)
Xd(h),Xq(h)
(h)
Rs Is(h)
Ef(h)
Isd(h)
d-axis (+)
jIsq(h)
Is(h)
-RsIs(h)
Vt(h)
(h)
-jXd(h)Isd(h)
-jXq(h)Is(h)
-jXq(h)Isq(h)
s(h)
E’(h)
Ef(h)
q-axis (-)
d-axis (-)
a. simplified equivalent circuit b. phasor diagram
Figure 5. Simplified equivalent circuit and phasor diagram of ISG for hth
harmonic order of non-
linear load
The phasor diagram of synchronous generator for hth
harmonic component of non-linear load is
given in Figure 5b. To determine the phase angle δ(h), the following relationship is used,
E’(h) = Vt(h)-RsIs(h)-jXq(h)Is(h) (17)
where, Xq(h)= jhω1Lq(h) and Xd(h)= jhω1Ld(h)
Here, E’(h) in phasor form can be written as,
( ) ( )h h  ' '
E E (18)
The current source harmonic in terms d-axis and q-axis can be presented as,
 0
sd s s(h) = (h)sin (h)-90 - (h)I I   (19)
 0
sq s s( ) = ( )cos ( ) -90 - ( )I h I h h h  (20)
Furthermore, the terminal voltage equation can be written as:
Ef(h)= Vt(h)- RsIs(h)-jXq(h)Isq(h)-jXd(h)Isd(h) (21)
The harmonic component of terminal voltage can be solved as:
Vt(h)= Ef(h)+RsIs(h)+jXq(h)Isq(h)-jXd(h)Isd(h), for h = 2, 3, 4....... (22)
where Ef(h) is congenital harmonic component of the induction voltage, which is determined through the no
load test.
The influence of harmonics on the direct inductance, Ld(h), and the quadrature inductance, Lq(h), are
measured based on the method meansurement in several literature [11],[12]. The variation of Ld and Lq with
the harmornic orders h is resolved through curve fitting for a number of data that obtained from the
experimental test. This method is implemented with polyfit statement in MATLAB, so Ld (h) and Lq (h) is
obtained as:
Ld(h) = k1h4
+ k2h3
+ k3h2
+ k4; Lq(h) = m1h4
+ m2h3
+ m3h2
+ m4 (23)
where, k & m are polynomial coeficient, which its values are given in Appendix. In this analysis, Eq. 23 is
used for harmonic orders till 20th
, and can be assumed a constant for harmonic orders above 20th
.

765
5. EXPERIMENTAL SETUP
The analysis results of proposed models are validated through comparisons between analysis and
experimental test results. Figure 6 shows the testing circuit for all the proposed configuration system. The
experimental test contains two steps, as shown in Figure 6. The first step is performed the testing of SEIG
under non-linear loads. The testing of ISG under non-linear loads is done on the second step. For all test
conditions, the frequency fundamental for both the generator is set at its nominal value (50 Hz) by adjusting
the rotor speed.
This test uses two generators using the machines with the same capacity, namely: 0.8 kW, 380 V, 3-
phase, 50 Hz, 4 poles. SEIG is equipped with 26 μF capacitors that connected in Y. For two generators,
testing scheme was used 405 W Energy-Saving Lamp (ESL) and Variabel Frequency Drive (VFD) as a non-
linear load and resistor 900 Ω as other load. The both machines are rotated by the DC motor with a speed of
1536 rpm for SEIG and 1500 rpm for ISG in order to obtain the frequency and the terminal voltage reaches
its nominal value. The measured machine parameter were: Rs = 8,20 Ω and Xs= 6,97 Ω for SEIG; Rs = 10,60
Ω for synchronous generator. And other parameters for both machines has been explained in Section 3 & 4.
The measurement of harmonic currents is carried out on three branch, namely: the non-linear load
branch (P1), the other load branch (P2), and the stator windings branch (P3). In the meanwhile, the
measurement of the harmonic voltages is performed at the PCC point. On this measure, the current flows in
the branches of non-linear load measured in the direction of leaving the load. All testing of harmonic
distortion is done using Power Analyzer CA 8220 that connected to PC.

Figure 6. The testing circuit for all the proposed system
6. RESULTS AND DISCUSSIONS
6.1. The Harmonic Produced by The Non-linear Loads
Figure 7 show measurement results for the harmonics produced by non-linear load when SEIG
encumbered with 405 W ESL. As shown by Figure 7a, the current waveform has deviated far from the ideal
sinusoidal form because of harmonics effect, but the voltage waveform is almost close to the ideal sinusoidal
form. This is in line the results shown by Figure 7b that THDI and THDV harmonic produced by ESL were
47.0% and 4.3% respectively. Figure 8 shows measurement results for the harmonics produced by non-linear
load when SEIG encumbered with variable frequency drive (VFD). As shown by Figure 8, the value of THDI
will was greater (56.3%) when SEIG burdened with VFD. The component of harmonic currents scattered
from low order to high order, wherein the component with the highest amplitude are on the order of 5,7,13.

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a. voltage and current waveform b. spectrum harmonic
Figure 7. The harmonic produced by non-linear load when SEIG burdened ESL
Figure 8. The harmonic produced by non-linear load when SEIG encumbered with VFD
Figure 9 and 10 show measurement results for the harmonic generated by non-linear load when ISG
encumbered with 405 W ESL and VFD respectively. As shown by these figure, THDI for ISG was lower than
SEIG, namely: 29.5 % (with ESL) and 24.2% (with VFD). However, THDV was bigger when using ISG,
namely: 13.7 % (with ESL) and 24.2% (with VFD). The Harmonics generated by ISG with non-linear loads
more focused on low-order harmonic components, especially the order of 5 and 7.
The list of harmonic components produced by non-linear loads for both generators was used to
analyze the harmonic distortion on stator side and other load using analysis method in section 3 & 4. The
analysis results will be explained in next subsection.
THDI = 47.0 %; THDV = 4.3 %Vrms = 220.2 V; Irms = 0.587A
current
voltage
current
voltage
current
voltage
current
voltage
Vrms = 224.2 V; Irms = 0.582 A THDI = 56.3 %; THDV = 5.1 %

767
Figure 9. The harmonic produced by non-linear load when ISG encumbered with ESL
Figure 10. The harmonic produced by non-linear load when ISG burdened with VFD
6.2. The Impact of Non-linear Loads Against Harmonic Distortion on The Stator Windings
The impact of non-linear load on both generators can be measured from the level of harmonic
distortion for the current of stator windings. Figure 11 and 12 show the current and voltage harmonic
distortion on stator windings side and terminals when SEIG and ISG burdened with 405W ESL respectively.
As shown these figure, THDI & THDV of the current stator windings and the terminals voltage of SEIG was
lower than THDI & THDV level for ISG. The SEIG has eliminated almost all the harmonic components,
except the harmonic component order 3th
, 5th
, and 7th
. While, the stator current of ISG still has contained 3th
,
5th
, 7th
, 11t
h, 13th
, 17th
and 19th
order harmonic component.
Vrms = 221.6 V; Irms = 0.479A THDI = 37.9 %; THDV = 16.3 %
current
voltage
THDI = 29.5 %; THDV = 13.7 %
current
voltage
current
voltage
current
voltage
Vrms = 221.4 V; Irms = 0.524A

 ISSN: 2088-8694
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harmonic orders (h) harmonic orders (h)
a. measured b. analyzed
Figure 11. The current harmonic distortion on the stator windings when SEIG burdened with ESL
Figure 12. The current harmonic distortion on the stator windings when ISG encumbered with ESL
Figure 13 and 14 show the current harmonic distortion on stator windings side when SEIG and ISG
burdened with VFD respectively. Like as loading the both generators with ESL, the current and voltage
harmonic distortion of the stator windings and terminals for SEIG was lower than the current and voltage
harmonic distortion of the stator windings and terminals for ISG.
THDI = 17.25 %; THDV=16.92%
THDI = 8.05 % ; THDV= 3.23%
THDI = 17.80 %; THDV = 14.0 %
THDI = 10.1 %; THDV = 4.1 %
current
voltage
current
voltage

769
6.3. The Impact of Non-linear Loads Against Harmonic Distortion on The Other Loads
The harmonic current produced by the non-linear load also propagate to the other load connected to
the PCC point, so the other load current will also be distorted. Table 1 contained the value of odd harmonic
components & THD on other load when both generators burdened by non-linear loads. As shown this table,
the impact of non-linear load against the harmonic distortion on the other load for SEIG was better than ISG.
The THDI and THDV on the other load for applied SEIG were lower than when applied ISG.
Figure 13. The current harmonic distortion on the stator windings when SEIG encumbered with VFD
harmonic orders (h ) harmonic orders (h)
Figure 14. The current harmonic distortion on the stator windings when ISG encumbered with VFD
THDI = 8.81 %; THDV=2.66%
THDI = 23.8 %; THDV = 17.5 %
THDI = 12.2 %; THDV = 5.0 %
current
voltage
THDI = 29.6 %; THDV = 14.1 %

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770
6.4. Discussion
As explained in section 6.1, the synchronous generator produced the harmonic current components
fewer than SEIG, especially for high-order harmonic components. However, the harmonic distortion of PCC
voltage on the synchronous generator was greater than SEIG. The harmonic currents generated by non-linear
loads were depended on the generator impedance. The impedance of synchronous generator contains a large
enough inductive reactance, which connected in series with non-linear loads (see Figure 1a.). For high order
frequency, the reactance synchronous became large, so the harmonic components generated by non-linear
load were reduced.
Tabel 1. The current odd harmonic components & THD on other load when the both generator burdened non-
linear load
As described in section 6.2, the harmonics distortion of the stator windings current and terminal
voltage was smaller when SEIG applied. This condition may occur due to a combination of the stator
windings inductance and capacitor excitation may have eliminated the high-order harmonic currents and has
attenuate the low-order harmonic currents on the stator windings. Moreover, because of the stator windings
of synchronous generator is connected in series with the harmonic current source, then currents flowing in
the stator windings was equal to the line current of synchronous generator. Furthermore, the low harmonic
current distortion in the stator windings will be produced the minor harmonic deviations in the terminal
voltage of SEIG..
As elaborated in section 6.3, the impact of the non-linear loads against the harmonic distortion on
other loads connected to the same source will be better when used SEIG. The harmonic distortion on the other
load is affected by two things, namely: the harmonic distortion on the terminal voltage and the current
harmonics propagation of a nonlinear load.
7. CONCLUSION
This paper has presented and analysis the harmonic impact of non-linear load against the harmonic
distortion on the generator windings and the other load connected to the same source. It proved the impact of
non-linear load to the harmonic distortion on SEIG was smaller than ISG. The analysis results were verified
by experiment results of laboratory testing. The harmonic current and voltage distortion in the stator
windings of SEIG were lower than ISG. Furthermore, the harmonic current distortion effects on other loads
connected in parallel to the terminals of SEIG was also lower than the other loads connected to ISG.
ACKNOWLEDGEMENT
Author would like thanks to Engineering Faculty, Andalas University for the financial support this
work, through DIPA Funding (No. 014/PL/SPK/PNP/FT-Unand/2014).
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h
Measured (%) Analyzed (%)
SEIG Synchronous SEIG Synchronous
ESL VFD ESL VFD ESL VFD ESL VFD
1 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
3 0.5 1.1 1.8 2.4 0.9 1.0 1.9 2.6
5 3.2 4.2 11.6 13.8 4.1 5.8 11.9 14.6
7 0.5 0.9 4.4 6.9 0.9 1.5 4.2 7.1
9 0.4 0.5 0.3 0.4 0.1 0.1 0.6 0.5
11 0.6 0.7 3.5 0.2 0.5 0.7 3.6 0.8
13 0.2 0.3 3.3 0.6 0.3 0.5 3.1 0.3
THD (%) 3.9 4.4 13.10 14.90 4.34 6.11 13.75 16.5

771
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APPENDIX
The polynomial coeficient of machine parameters
i
SEIG Synchronous Machines
ei ci di ki mi
1 0.019656014 8.05042818e-06 1.33095094e-07 0.000019106 0.000004881
2 -0.088230362 -0.00046874 7.88155364e-06 -0.000520051 -0.000180807
3 -0.013005548 0.01006005 -0.00017248 0.005088344 0.002307599
4 0.578249237 - 0.09657362 0.00168943 -0.022509893 -0.013318719
5 - 0.45742845 -0.00713447 0.239759872 0.177835792
6 - 3.72274449 0.02690408 - -
BIOGRAPHIES OF AUTHORS
Refdinal Nazir received B.Eng. 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.
Krismadinata received the B.Eng. degree in electrical engineering from Andalas University,
Padang, Indonesia, in 2000 and the M.Eng. degree from the Bandung Institute of Technology,
Bandung, Indonesia, in 2004, and the Ph.D. degree from the University of Malaya, Kuala
Lumpur, Malaysia, in 2012, and Post-doctoral at UMPEDAC within 2012-2014. He is currently
with Dept. of Electrical Engineering, Universitas Negeri Padang, Indonesia. Dr. Kris has
international patents and also as reviewer for many international journal in electrical engineering
and energy fileds. His research interests are power electronics, control system and renewable
energy.
Rizka Amalia, was born in Bukittinggi, West Sumatra, Indonesia in 1983. Received B.Eng.
degree in electrical engineering from Andalas University, Indonesia, in 2006. From 2003 to 2006
active as an assistant Electrical Energy Conversion Laboratory. She is currently master students
in Andalas University, Indonesia.

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