Effect analysis of residual magnetism availability level on the success of voltage generation processes in self-excited induction generators

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 11, No. 3, September 2020, pp. 1211~1219
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v11.i3.pp1211-1219  1211
Journal homepage: http://ijpeds.iaescore.com
Effect analysis of residual magnetism availability level on the
success of voltage generation processes in self-excited induction
generators
Refdinal Nazir, Syafii, Andi Pawawoi, Fajril Akbar, Yudi Arfan
Department of Electrical Engineering, Andalas University, Indonesia
Article Info ABSTRACT
Article history:
Received Nov 16, 2019
Revised Feb 4, 2020
Accepted Apr 26, 2020
The voltage generation process is a very crucial initial stage for the
successful operation of the self-excited induction generator (SEIG). The
availability of residual magnetism and the adequacy of excitation capacitor
value are factors that determine the success of the voltage generation process
on the SEIG. This paper analyzes the effect of the availability of residual
magnetism on the rotor's magnetic core. With a simple approach, the terminal
voltage on the SEIG can be solved through the intersection between the
magnetization curve (Xm) and the excitation curve (Xce). The shape and
equation of the magnetization curve will be affected by the availability of
residual magnetism. The change in residual magnetism availability will cause
a change in the intersection point between the magnetization curve (Xm) and
the excitation curve (Xce), which will determine the value of voltage
generated by the generator. In this study, Newton Rhapson's method with
numerical iteration approach has been used to analyze the effect of changes
in the availability of residual magnetism on the success of voltage generation
on the SEIG. The analysis results have been shown that the availability of
residual magnetism with residual voltage values below 1.04 Volt will cause
the failure of the SEIG to generate the terminal voltage at its nominal value.
Meanwhile, the availability of residual magnetism in SEIG with residual
voltage values above 1.04 Volt, will succeed in generating terminal voltage
at its nominal value. For SEIG used as the object of this study, the value of
Eres = 1.04 Volt is a critical value of the availability of residual magnetism.
Keywords:
Excitation curve
Magnetization curve
Residual magnetism
SEIG
Voltage generation
This is an open access article under the CC BY-SA license.
Corresponding Author:
Refdinal Nazir,
Department of Electrical Engineering,
Andalas University, Indonesia
Jalan Dr. Mohammad Hatta Padang 25163, Indonesia.
Email: refdinalnazir@yahoo.co.id
1. INTRODUCTION
Currently, the application of induction generators in power plants is increasingly rivaling the use of
synchronous generators, especially in small scale power plants that are driven by renewable energy sources,
such as micro hydro power plants, wind power, biomass power, etc. [1-4]. This is mainly due to the induction
generator (squirrel-cage rotor) has a number of advantages over synchronous generators, including: strong
and simple rotor construction, minimal maintenance, simple operation, has the ability to self-protection. In
addition, induction generators are more resistant to harmonic currents generated by non-linear loads or
electronic load controllers (ELC) [5-8]. There are 2 operating patterns of induction generators applied,
namely: operation as a stand-alone generator and operation as a generator connected to the grid [3,9].

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 11, No. 3, September 2020 : 1211 – 1219
1212
The operation of a stand-alone induction generator, better known as the Self-Excited Induction Generator
(SEIG), is generally used in small-scale power plants in off-grid areas. While the operation of induction
generators with grid-connected patterns is generally applied to the distributed generation (DG) in on-grid
areas. The study in this paper is focused to analyze the operation of SEIG.
Besides the rotation of the prime mover, there are two variables that determine the success of
the SEIG operation, namely: the availability of the residual magnetism at the time of initiation and
the adequacy of the reactive power during the excitation process. The reactive power needs of the induction
generator are used to generate a magnetic field in the air gap, which is needed to produce the induced voltage
[10]. In SEIG, the reactive power requirements are supplied from the excitation capacitor, which is connected
in parallel with the generator terminal. The availability of residual magnetism in the iron core of the SEIG
rotor is absolutely necessary to generate the initial voltage of the generator (Eres), and then as a trigger for
the initial excitation current (Ie0) [11]. The unavailability of residual magnetism or the reduction in its value
lower than the critical value will cause the failure of the voltage generation process in the SEIG. The value of
residual magnetism availability in the SEIG can be change due to short circuit fault, extra reactive load, and
its operated at its critical point [12,13].
The effect of the availability of residual magnetism on the success of voltage generation on SEIG is
analyzed in this paper. Graphically, the generation of SEIG terminal voltages at nominal values can be
determined from the intersection between the magnetization curve (Xm) and the excitation curve (Xce) [14].
The magnetization curve equation will be affected by the availability of the residual magnetism, while the
excitation curve equation is determined by the value of the excitation capacitor. The change in the residual
magnetism availability will cause a change in the intersection point between the magnetization curve (Xm)
and the excitation curve (Xce), which will determine the amount of voltage generated by the generator. In this
study, Newton Raphson's method with a numerical approach is applied to analyze the effect of changes in the
availability of residual magnets on voltage generation by SEIG.
2. THE PROCESS OF VOLTAGE GENERATION ON SEIG
In the induction generator connected to the grid, the voltage generation process can occur
immediately when the generator is paralleled to the grid. This happens because the reactive power needs for
the excitation process are directly provided by the grid system. Unlike the induction generator connected to
the grid, the reactive power supply in the SEIG is obtained from the excitation capacitor. And the excitation
process in SEIG begins with the availability of residual magnetism in its rotor. Therefore, the voltage
generation process in SEIG can be broken down into two stages, namely: synchronous operation stage and
asynchronous operation stage [15-17].
2.1. Synchronous mode operation
The excitation process at the synchronous operating mode stage is triggered by the availability of
residual magnetism in the SEIG. The availability of residual magnetism can be checked from the voltage
generated at the machine terminals it caused. Measurement of the machine terminal voltage caused by the
residual magnetism is performed in the condition that the machine has not been connected to the excitation
capacitor and its rotor is rotated in synchronous rotation, as shown in figure 1. The value of the voltage
generated by the residual magnetism in the stator is proportional to the residual magnetism density and the
number of rotor rotation. Figure 2b. shows the waveform of the terminal voltage due to residual magnetism
for machines used as study objects and rotated at synchronous rotation. The residual magnetism is formed
because of the magnetizing process that has been carried out before the machine is operated, as shown in
figure 2. For generators, the magnetizing process is usually implemented until it reaches the flux saturation
value (ψs). When the magnetization current is reduced to zero, there is still a magnetic flux stored on the
magnetic core of machine rotor. The remaining flux in the magnetic core is known as the remanence flux
(ψr). The comparison between the magnitude of the remanence flux with the saturation flux is known as the
remanence factor (Kr) [18]. The remanence factor value of an induction generator is determined by the
magnetic core material used [19-21]. The magnitude of the magnetization current will affect the amount of
residual magnetism, which automatically also affects the magnitude of voltage that its forms. Figure 3 shows
the variation between the magnetization current Im and the voltage generated at the machine terminal due to
residual magnetism Eres. As this figure shows, the magnitude of voltage due to the residual magnetism is
proportional to the magnitude of current injected into one of the phase windings of machine stator.

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Effect analysis of residual magnetism availability level on the success of voltage … (Refdinal Nazir)
1213
(a) (b)
Figure 1. Voltage due to the induction of residual magnetism (a) equivalent circuit (b) voltage waveform
Figure 2. The process of forming residual
magnetism
Figure 3. Magnetizing current (Im) versus the voltage
due to residual magnetism (Eres)
2.2. Asynchronous Mode Operation
The asynchronous operating mode of SEIG in the voltage generation process starts after
the excitation capacitor (Ce) is connected on the generator terminal. The SEIG equivalent circuit in the no-
load condition and the asynchronous operating mode is shown in Figure 4.
In no-load conditions, the rotor current is very small and can be ignored. In this condition, the rotor
circuit branch becomes an open circuit, so that the equivalent circuit of SEIG can be simplified as shown in
Figure 4b. In this circuit, Im = Is = Ie applies. The air gap voltage curve (Eg) as a function of Im is obtained
from the saturation test results. The terminal voltage curve (Vt) as a function of Im can be solved through
the following equation:
2
s
m
2
s
m
g
t )
(
)
( R
I
X
I
E
V +
+
=
(1)
Figure 5 shows the relationship between the magnetization curve (Xm) and the excitation curve (Xce)
in the voltage generation process of SEIG. Magnetization curves can be expressed in terms of air gap voltage
(Eg) versus magnetizing current (Im) or terminal voltage (Vt) versus magnetizing current (Im), as shown in
Figure 5a. For the same machine, the initial value of the magnetization curve will change according to the
value of the voltage generated due to residual magnetism. The excitation curve is a linear curve with changes
directly proportional to the excitation reactance (Xce) or inversely proportional to the excitation capacitance
(Ce). The voltage generation process in SEIG can be completed from the intersection of the magnetizing
curve with the excitation curve [15,22], as shown in Figure 5b. The point of intersection of these two curves
can occur in the region of saturation, linear or initial region. The voltage generation process is claimed to be
successful if the intersection of the two curves occurs in the saturation region. If the two curves intersect in a
linear region, intersection will occur at many points, which triggers the voltage generation process to become
unstable. Meanwhile, if the intersection occurs in the initial area, then the generator will only generate a very
small voltage.
jXs
Rs
jXm
Eres
Eg
Vt
Im
Is

 ISSN: 2088-8694
1214
(a) (b)
Figure 4. The SEIG equivalent circuit on the asynchronous operating mode (a) equivalent circuit on no load
conditions, (b) simplified equivalent circuit
(a) (b)
Figure 5. The relationship between the magnetization curve (Xm) and the excitation curve (Xce) in the voltage
generation process of SEIG. (a) magnetizing curve in terms Eg and Vt (b) intersection of the magnetization
curve with several exc. Curves
3. ANALYSIS AND EXPERIMENTAL SET-UP
3.1. Analysis
As discussed in session 2.2, the process of voltage generation at the SEIG can be simply solved
from the intersection between the magnetization curve (Xm) and the excitation curve (Xce). The function of the
magnetization curve can be defined by the following equation:
Xm:Vt = g(Im) ; Xce : Vce = h(Im) (2)
If the magnetization curve equation is approximated by the polynomial interpolation method, then
its function can be expressed by the following equation:
g(Im) = a0+a1Im+a2Im
2
+a3Im
3
++an-1Im
n-1
+an
Im
n
(3)
The constant values of a1, a2, a3, ………., an-1, an can be solved using the polyfit function in
MATLAB [23]. The excitation curve can be expressed by the following function:
h(Im)=XceIm (4)
The difference between the magnetization curve and the excitation curve can be solved by this
following equation:
f(Im) = g(Im) - h(Im) (5)
The intersection of these two curves can be solved by determining the root of
the following equation:
Ls
Rs
Lm
Eres
Eg
Vt Ce
im
ie
Ls
Rr
ir
is
jXs
Rs
jXm
Eres
Eg
Vt -jXce
Im
Ie
Is

1215
f(Im) = a0+(a1-Xce) Im+a2Im
2
+a3Im
3
++an-1Im
n-1
+anIm
n
= 0 (6)
while,
f’(Im) = (a1-Xce) +2a2Im+3a3Im
2
+.+(n-1)an-1Im
n-2
+nanIm
n-1
(7)
To determine the root of equation (6), Newton Raphson's iteration method is used, with the equation
for solving each iteration as follows [24,25]:
)
(
'
)
(
m
m
m
m
I
f
I
f
I
I new
−
=
(8)
Im
new
= value of magnetization current at the k-iteration
Im = value of magnetization current at the (k-1)-iteration
Overall, the analysis of the effect of residual magnet availability on the generation of SEIG terminal
voltages is completed through the steps arranged in the flowchart in Figure 6. As shown in Figure 6, the
magnetization curve data in variations of Eg (i) and Im (i) are obtained from saturation measurements (see
Appendix). Whereas the magnetization curve data in the variation Vt (i) with Im (i) is calculated through (1).
The determination of the value of the excitation capacitor by operating the generator with the availability of
sufficient residual magnetism and zero load conditions, so that the terminal voltage reaches a nominal value.
The frequency value of the voltage generated by the generator is set at 50 Hz. In this iteration, the initial
condition I0 can be set to zero. For each iteration step k, a new value of the Im
new
magnetization current is
calculated. The iteration process is stopped, if | Im-Im
new
| reach smaller or equal to , where in the process of
this diagram set  = 10-5
. The analysis process is carried out for a variety of residual magnetism conditions,
ranging from the availability of strong residual magnetism to the availability of very low residual magnetism,
so that no more voltage can be generated. In this study, there are 6 effects of the availability of residual
magnet conditions analyzed on the generation voltage of SEIG. All results of the analysis will be
discussed in session 4.
Figure 6. Flow chart for effect analysis of the residual magnetism availability to
the voltage generation process
Start
|Im – Im
new
|<  Im = Im
new
End
No
Yes
k, Im, Vt
Caculate : Vt (Im)
(Eq. 1 )
Polynomial Interpolation :
Vt (Im) : g(Im) = a0+a1Im+a2Im
2
+ +anIm
n
Data Magnetizing Curve :
Im(i), Eg(i)
Excitation Curve :
Vce (Im) : h(Im) =XceIm
f(Im)= g(Im)-h(Im)
Set Exc. Capacitor & frequecy:
Ce & fg
Xce = 2πfgCe
a
a
k=k+1
Im = Im
new
Vt (Im) = a0+a1Im+a2Im
2
+ +anIm
n
Initial Condition :
Im = I0 ; k = 0

 ISSN: 2088-8694
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3.2. Experimental set-up
In order to verify the results of the analysis, a series of experiment are conducted in the laboratory.
This test applies the squirrel-cage induction machine of 1.5 kW, 380 V, 3-phase, 50 Hz, 4 poles, which is
equipped with 12 mF excitation capacitors that connected in delta. This machine parameters obtained from
the test results are Rs = 4,38  and Xs = 3,61.
The laboratory testing process begins with the demagnetization process of the SEIG through loading
the generator at its critical point, so that the generator voltage drops to zero suddenly. In this condition, the
voltage caused by the residual magnetism is close to zero. The next process, the dc current is injected into
one of the stator phase windings from the SEIG, so that Eres can be obtained at the expected value. Then, the
rotor of SEIG is rotated with the motor at 1506 rpm and Eres are measured. Next, the excitation capacitor is
switched on the SEIG terminal under no-load condition, and the terminal voltage generated (Vt) and the
magnetization current (Im) is measured. The testing process is repeated, each for the availability of strong,
weak, and critical residual magnetism.
4. RESULTS AND DISCUSSION
4.1. The analysis results of voltage generation processes under strong residual magnetism availability
conditions
Figure 7 has shown the analysis results of the voltage generation process in the SEIG under
conditions of availability of strong residual magnetism, namely Eres = 4.27 Volts and Eres = 2.73 Volts. As
shown in figure 7, the intersection of the curve only occurs in the saturation region area, namely: at (Im =
2,831 A, Vt = 220, 07 Volts) for Eres = 4.27 Volts and at (Im = 2,799 A, Vt = 217, 54 Volts) for Eres = 2.73
Volts. Whereas in the initial region, the two curves do not intersect. This has shown that the voltage
generation process at SEIG has been successful for both conditions of the availability of residual magnetism.
Figure 7. The analysis results of voltage generation process under strong residual
magnetism availability conditions
4.2. The results of the analysis of voltage generation processes under critical residual magnetism
availability conditions
The analysis results of the voltage generation process on the SEIG in conditions of critical residual
magnetism availability, namely Eres = 1.04 Volts and Eres = 0.993 Volts, are shown in figure 8. As shown in
this figure, for Eres = 1.04 Volts, the process of voltage generation is still successful because at the initial
area does not occur at the intersection of the curve. However, when the residual voltage of residual
magnetism decreases to Eres = 0.993 Volts, the voltage generation process cannot have reached the expected
value (nominal value). This happens because there are 2 intersection points of the curve, namely in the initial
area (Im1 = 0.109 A, Vt1 = 8.47 Volts) and the saturation area (Im2 = 2.761 A, Vt2 = 214.58 Volts).

1217
Figure 8. The analysis results of voltage generation process under critical residual
4.3. The analysis results of voltage generation process under weakening residual magnetism
availability conditions
Figure 9 have shown the analysis results of the generation voltage process on the SEIG under weak
residual magnetism availability conditions, namely Eres = 0.487 Volts and Eres = 0.088 Volts. As shown in
figure 9, for both conditions, the intersection of the magnetization curve and the excitation curve occurs at
two points. Therefore, in both of these conditions, the generator only generates a small voltage, namely Vt =
10.54 Volts in the residual magnetism state with Eres = 0.487 Volts and Vt = 10.54 Volts in the residual
magnetism state with Eres = 0.088 Volts. This means that the voltage generation process to reach nominal
voltage was not successful for both conditions of the residual magnetism availability.
Figure 9. The analysis results of voltage generation process under weak residual
4.4. Comparison of analysis and testing results
The experimental tests are conducted to check the validity of the results of the analysis discussed in
sessions 4.1 to session 4.3. Figure 10 shows the comparison between the analysis results and the test results
for various variations in the availability of residual magnetism to the voltage generated by SEIG. As shown
in this figure, the simulation results and experiment results both show that the generator failed to generate a
terminal voltage at its nominal value for an Eres value below 1.04 Volt. At Eres values above 1.04 volt, both
curves have indicated the generator succeeded in generating its terminal voltage at nominal value. The
simulation results and the test results show that the critical value of the remaining magnetic availability
occurs at the value of Eres = 1.04 Volt. From the description above, the analysis results are in line with the test
results, so the validity of the model and the analysis method are sufficiently tested.

 ISSN: 2088-8694
1218
Figure 10. The comparison of simulation and test results
5. CONCLUSION
The effect of the availability of residual magnetism on the success of the terminal voltage generation
process for SEIG on its nominal value has been successfully analyzed using Newton Raphson's iteration
method. The availability of residual magnetism with residual voltage values below 1.04 Volt will cause the
failure of the SEIG to generate the terminal voltage at its nominal value. Meanwhile, the availability of
residual magnetism in SEIG with residual voltage values above 1.04 Volt, will succeed in generating
terminal voltage at its nominal value. For SEIG used as the object of this study, the value of Eres = 1.04 Volt
is a critical value of the availability of residual magnets (Ecritical). The decrease in Eres value of SEIG can be
caused by various conditions, such as: short circuit fault, lack of reactive power, operation of the generator at
the critical point etc. Therefore, for the voltage generation process in SEIG to be successful, it must be
ensured that the residual voltage value must be above its critical value.
ACKNOWLEDGEMENTS
Author would like thanks to Andalas University for the financial support this work, through PDUPT
Funding (No. T/5/UN.16.17/PT.01.03/PD-EET/2019).
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