Infokum Vol.
No.
03, 2026, pp.
ISSN 2722-4635
Impact of Stator Resistance Unbalance on the Efficiency and Torque of Three-Phase Induction Motor Muhamad Vickry Almuhtadi Billah1*.
Siti Anisah2.
Parlin Siagian3 Universitas Pembangunan Panca Budi.
Medan.
North Sumatera.
Indonesia Email: 1vickryab19@gmail.
com, 2sitianisah@dosen.
id , 3parlinsiagian@yahoo.
Three-phase induction motors are key components in industrial power systems, but their performance is susceptible to internal disturbances such as stator resistance imbalance caused by aging, overheating, or manufacturing defects.
This study aims to systematically analyze the impact of stator resistance imbalance on the efficiency and torque characteristics of squirrel cage rotor induction motors using equivalent circuit-based mathematical modeling.
Unlike previous studies that used external resistors, this study modifies the stator resistance parameters directly in the model to represent more realistic internal degradation.
Simulations were performed on a 3.
73 kW, 400 V, 50 Hz motor with resistance imbalance variations from 0% to 20%.
The results show that the imbalance causes uneven current distribution and an increase in stator copper losses of up to 5.
94% at 20% conditions, although the percentage of current imbalance remains below 1%.
As a result, the efficiency decreases linearly from 92.
97% to 62%, while the mechanical torque experiences a small decrease from 95.
88 Nm to 95.
28 Nm.
This phenomenon also has the potential to increase torque ripple and uneven heating.
This study demonstrates that stator resistance imbalance, even small ones, has a significant impact on motor performance and lifespan, and therefore needs to be considered in predictive maintenance strategies and energy efficiency optimization.
Keywords: Unbalance.
Resistance.
Stator.
Mechanical Torque.
Motor Efficiency This is an open access article under theCC BYNClicense Corresponding Author:
Muhamad Vickry Almuhtadi Billah Universitas Pembangunan Panca Budi.
Medan.
North Sumatera.
Indonesia vickryab19@gmail.
Introduction Three-phase induction motors, particularly the squirrel cage rotor (SCIM) type, are the most widely used electromechanical machines in the industrial and commercial sectors globally.
Their dominance in a wide range of applications, from pumps and fans to compressors and conveyor systems to heavy machine tools, is based on their inherent advantages: simple and robust construction, relatively low cost, high reliability, and the ability to operate in harsh environments.
From the perspective of global energy consumption, these motors play a vital role.
It is estimated that electric motor systems consume approximately 40-50% of the total electricity generated worldwide, with three-phase induction motors accounting for the largest proportion.
(B et al.
, 2.
Therefore, improving the operational efficiency of induction motors is not only a technical objective, but also a strategic imperative for industrial energy efficiency and global carbon footprint reduction.
The performance of an induction motor, measured through efficiency () and torque characteristics, depends on various factors.
Efficiency is defined as the ratio of mechanical output power (Pou.
to electrical input power (Pi.
, = Pout/Pin.
The total input power consists of the mechanical output power plus the total power losses in the motor, namely copper losses (IAR) in the stator and rotor, iron core losses .
ysteresis and eddy curren.
, and mechanical and friction losses.
Among these, stator copper losses are very significant and directly depend on the square of the stator current and the stator winding resistance (R_.
Stator resistance imbalance occurs when R_sa O R_sb O R_sc, caused by overheating.
Impact of Stator Resistance Unbalance on the Efficiency and Torque of Three-Phase Induction Motor.
Muhamad Vickry Almuhtadi Billah et.
Infokum Vol.
No.
03, 2026, pp.
ISSN 2722-4635
aging, or manufacturing defects.
This condition results in uneven current distribution, increased slip, decreased speed, and an undesirable increase in torque, which negatively impacts motor efficiency and Overheating also accelerates insulation degradation, creating a cycle of progressive degradation.
Most previous research has focused on source voltage unbalance.
oltage unbalanc.
(Aderibigbe et al.
, which has serious but different impacts from the stator resistance imbalance originating within the Some related studies have limitations.
(Dani & Erivianto, 2.
simulated the impact of adding an external rheostat to one stator phase, showing a decrease in RPM and efficiency and an increase in torque, but this approach is unrealistic because it uses external components, not the internal degradation of the motor, and the efficiency calculations are not physically consistent.
(Elbabo Mohammed et al.
, 2.
Mikarius Bukit et al.
conducted physical experiments by adding external resistors .
1 to 4.
to the stator terminals, found a decrease in speed, an increase in slip, and an increase in torque, but also used external resistors and did not calculate the efficiency accurately.
(Bukit et al.
, 2.
using a similar approach that is more relevant for wound rotor motors(Situngkir, 2.
From this review, there is a need for a systematic and quantitative study on the impact of variations in stator resistance unbalance .
s a degraded paramete.
on the efficiency and torque-speed curve of a three-phase squirrel cage rotor induction motor through mathematical modeling and simulation.
This study uses a theoretical framework based on the induction motor equivalent circuit model and the symmetric component theorem.
The per-phase equivalent circuit model consists of stator resistance (RCA), stator width reactance (XCA), reflected rotor resistance (RCC'/.
, reflected rotor width reactance (XCC'), and magnetizing reactance (X_.
This model allows the calculation of stator current, rotor current, input power, output power, losses, torque, and efficiency.
To analyze the stator resistance imbalance, the symmetric component theorem.
Positive sequence components produce a synchronous magnetic field and the desired torque, while negative sequence components produce a counter-current magnetic field, negative torque .
raking torqu.
, and additional IAR losses in the stator and rotor.
(Elbabo Mohammed et , 2.
The zero-sequence component produces a pulsating magnetic field that produces no useful rotational torque but can increase losses.
By modifying the stator resistance in the model, the impact of this unbalance on the current component and motor performance can be isolated and analyzed.
(Dani & Erivianto, 2.
Based on the literature review, there are studies that have not systematically and quantitatively analyzed the impact of various levels of stator resistance unbalance .
s a representation of internal degradatio.
on the efficiency and torque characteristics of three-phase squirrel cage rotor induction motors.
Previous studies often use external methods .
heostats/additional resistor.
that are less realistic, fail to calculate accurate efficiency, or do not provide replicable mathematical models.
This study aims to fill this gap by developing a mathematical model that considers stator resistance unbalance, implementing it in MATLAB for functional and accurate simulations, and conducting systematic simulations to evaluate the motor's performance response.
Thus, this study is expected to provide a clear quantitative understanding of the impact of stator resistance unbalance on the efficiency and torque characteristics of induction motors, which can be used as a reference in predictive maintenance and energy efficiency optimization.
Literature Review Basic Principles of Induction Motors Three-phase induction motors are the most dominant AC motors in industrial applications due to their simple construction, low cost, and high reliability.
(Chandra Sekhar et al.
, 2.
This motor consists of two Impact of Stator Resistance Unbalance on the Efficiency and Torque of Three-Phase Induction Motor.
Muhamad Vickry Almuhtadi Billah et.
Infokum Vol.
No.
03, 2026, pp.
ISSN 2722-4635
main components: a stator .
tationary par.
and a rotor .
otating par.
, which interact through magnetic fields to produce mechanical torque.
Stator The stator consists of a ferromagnetic laminated core and three sets of coils .
hases A.
C) mounted with an electrical angular shift of 120A.
When a symmetrical three-phase voltage is applied, the current flowing in the coils produces a rotating magnetic field at synchronous speed .
, formulated as:
/ p where f is the source frequency (H.
and P is the number of poles (Fitzgerald et al.
, 2.
This field forms the basis of voltage induction in the rotor through the principle of Faraday's law .
= Oedi/d.
The stator resistance (R.
and leakage reactance (X.
in the coil determine the impedance per phase (Zs=Rs jX.
, which affects the current distribution and operating efficiency.
Under ideal conditions, the stator resistances of all three phases are identical (Rs,A = Rs,B = Rs,C), resulting in a uniform magnetic flux distribution.
However, in practice, stator resistance imbalances can occur due to insulation degradation, manufacturing limitations, or uneven operating temperatures (Mponwana & Barendse, 2.
These imbalances disrupt the symmetry of the system, causing uneven current distribution and increased power losses.
Rotor The rotor of an induction motor is generally a squirrel cage made of copper or aluminum conductor bars short-circuited by end rings.
When the stator magnetic field cuts the rotor conductors, a voltage is induced according to Lenz's law, producing a rotor current (I.
that interacts with the stator flux to produce torque:
T=kUIiUIIrUIcosr with k the motor constant, i the magnetic flux, and r the phase angle of the rotor current.
(Nadir et al.
The critical characteristic of the rotor is slip .
, which measures the relative speed difference between the stator and rotor fields:
Slip determines the magnitude of the rotor current and the resulting torque.
Under full load conditions, typical slip is in the range of 2Ae5% (Gupta & Singh, 2.
Rotor resistance (R.
plays a critical role in the motor's torque-slip characteristics.
At low slip .
ormal operatio.
, torque is directly proportional to slip, while at high slip .
tart-u.
, torque is inversely proportional to slip.
Stator and Rotor Interaction The stator-rotor electromagnetic interaction is represented by a per-phase equivalent circuit model that forms the basis for the motor performance analysis.
This model consists of Stator impedance (Rs jX.
Stator copper losses and leakage flux.
Magnetizing impedance .
: Representation of the magnetizing current to generate the main flux.
Stator-related rotor impedance (Rr/s jX.
: Rotor resistance (R.
modulated by slip .
(Mponwana & Barendse, 2019.
Nadir et al.
, 2.
The active power converted to mechanical power (Pme.
is given by:
which shows a strong dependence on rotor slip and resistance.
This mechanical power is then related to torque through the equation:
Impact of Stator Resistance Unbalance on the Efficiency and Torque of Three-Phase Induction Motor.
Muhamad Vickry Almuhtadi Billah et.
Infokum Vol.
No.
03, 2026, pp.
ISSN 2722-4635
with rotor angular velocity in rad/s and rotor rotor speed in rpm.
Motor efficiency () is defined as the ratio of output mechanical power to input electrical power:
Induction Motor Model with Stator Resistance Unbalance The unbalanced stator resistance (Rs,AORs,BORs,C) disrupts the symmetry of the basic design of the induction motor, which was originally designed for balanced stator impedance.
Under ideal conditions.
Rs,A=Rs,B=Rs,C, so that the current and magnetic flux distribution are uniform.
(Jassim et al.
However, factors such as insulation degradation, manufacturing limitations, or uneven operating temperatures cause resistance deviation, modeled as:
Zs,A= Rs,A jXs.
Zs,B = Rs,B jXs.
Zs,C= Rs,C jXs Research by Alnasser et al.
confirmed that a 5% resistance imbalance results in a current imbalance of up to 15%, violating the symmetrical operating principle of an induction motor.
This changes the characteristics of the rotating magnetic field and induces unwanted flux components, potentially detrimental to motor performance.
The stator resistance imbalance also affects the total impedance per phase (Ztotal,phas.
, which is the sum of the stator impedance and the rotor magnetization-equivalent This change in total impedance is key to understanding how stator resistance imbalance triggers current imbalance and reduced motor performance.
(Jassim et al.
, 2.
Current Unbalance and Power Loss Mechanism The stator impedance imbalance results in uneven current distribution across the three phases, as explained by Ohm's Law for an unbalanced system.
(Nadir et al.
, 2.
VA = Ztotal,AUIHE.
VB = Ztotal,BUIIB.
VC = Ztotal,CUII As a result, the current in the phase with the lower stator resistance will increase, while the phase with the higher resistance will experience a decrease in current.
This phenomenon causes a disproportionate increase in stator copper losses, formulated as:
PC_stator=OHEO2Rs,A OIBO2Rs,B OICO2Rs,C Experimental studies by proved that a 10% resistance imbalance increases copper losses by 25% compared to balanced conditions.
(Malik et al.
, 2.
This increased loss further reduces the output mechanical power (Pme.
based on the principle of conservation of energy:
PMEK = Pinput Oe Pcu_stator Oe Pcore Oe Pfriction so that the motor efficiency (=y100%) decreases exponentially.
Test results show that a 15% resistance imbalance can reduce efficiency by up to 9.
5% at full load.
Research by (Zhang et al.
, 2.
revealed that increased copper losses not only reduce efficiency but also cause uneven heating of the stator.
Phases with higher currents experience significant temperature increases, accelerating insulation degradation and potentially leading to premature failure.
Using infrared thermography, they measured temperature differences of up to 18AC between phases at a 12% resistance imbalance.
Impact of Stator Resistance Unbalance on the Efficiency and Torque of Three-Phase Induction Motor.
Muhamad Vickry Almuhtadi Billah et.
Infokum Vol.
No.
03, 2026, pp.
ISSN 2722-4635
Impact on Torque Characteristics Stator resistance imbalance not only reduces efficiency, but also disrupts the stability of mechanical Slip .
), defined as s=.
sync Oe nroto.
/nsync , becomes unstable due to current fluctuations.
The resulting mechanical torque (T ) is directly related to slip through the equation:
Slip instability causes undesirable torque variations, especially at low speeds.
Furthermore, symmetric component analysis reveals that the current imbalance produces a negative sequence component (I2 ), which interacts with the positive sequence component (I1 ) to produce torque ripple:
I1=1/3(IA aIB a2IC).
I2=1/3(IA a2IB aIC) with as a symmetric operator (Rodriguez et al.
, 2.
Research (Mponwana & Barendse, 2.
proves that a 10% increase inOI2Oincreased the torque ripple amplitude by 21%, potentially causing excessive vibration, noise, and shaft wear.
Using acceleration sensors and spectral analysis, they identified a 100 Hz frequency component in the motor with an 8% resistance imbalance, which is consistent with the predictions of torque ripple theory.
To quantify the impact of stator resistance unbalance, recent research recommends using the percentage current unbalance:
In addition, the power factor .
f ) is also affected by the stator resistance unbalance:
where Pinput is the total active power and Sinput is the total apparent power.
Research(Aderibigbe et al.
shows that a 10% resistance imbalance can reduce the power factor by 0.
06 pu, which has implications for increasing reactive power requirements and operational costs.
Research Methods Impact of Stator Resistance Imbalance on the Efficiency and Torque of Three-Phase Induction Motor: This study uses a numerical analysis method based on an equivalent circuit model to evaluate the impact of stator resistance unbalance on the performance of a three-phase induction motor.
This approach was chosen because it allows for high-precision variation of stator resistance parameters without requiring physical modifications to the motor, while providing a deep understanding of the unbalance mechanism.
The method consists of three main stages:
Development of a mathematical model based on an equivalent circuit with stator resistance Numerical simulations for various imbalance scenarios Quantitative analysis of the relationship between resistance unbalance, efficiency, and torque ripple This approach is superior to previous studies (Bukit et al.
, 2024.
Dani & Erivianto, 2.
because it does not use unrealistic external resistors, but rather modifies the stator resistance parameters directly in the mathematical model as a representation of the internal degradation of the motor.
A mathematical model is developed based on the per-phase equivalent circuit of an induction motor with modifications to incorporate stator resistance unbalance.
Based on a literature review, this model is represented as:
Impact of Stator Resistance Unbalance on the Efficiency and Torque of Three-Phase Induction Motor.
Muhamad Vickry Almuhtadi Billah et.
Infokum Vol.
No.
03, 2026, pp.
ISSN 2722-4635
For each unbalance scenario, the motor performance is calculated using the following equation:
Current per phase Stator Copper Loss Input Power Mechanical Power Efficiency PMEK= Pinput Oe Pcu_stator Oe Pcore Oe Pfriction Mechanical Torque Motor parameters are taken from the literature for a 5 HP .
73 kW), 400V, 50 Hz, 4-pole induction motor as per Ie 112-2017 procedure, which is consistent with the data available in the current literature.
Table 1.
Motor Data Parameters Parameter Mark Parameter Mark Rated Power 73 kW Rotor Resistance (R.
30 Line-to-Line Voltage (VLL) Stator Leakage Reactance (X.
Frequency .
50 Hz Rotor Leakage Reactance (X.
Number of Poles (P) Magnetizing Reactance (X.
40 Speed .
1450 rpm Core Loss (Pcor.
Balanced Stator Resistance (R.
Friction Loss To analyze the impact of stator resistance unbalance, four main scenarios were simulated:
Table 2.
Imbalance Scenarios No Description Stator Resistance %R_Unbalance Balanced .
Rs,A=Rs,B=Rs,C=0.
5% imbalance Rs,A=Rs,B=0.
48 ,Rs,C=0.
10% imbalance Rs,A=Rs,B=0.
48 ,Rs,C=0.
15% imbalance Rs,A=Rs,B=0.
48 ,Rs,C=0.
20% imbalance Rs,A=Rs,B=0.
48 ,Rs,C=0.
Impact of Stator Resistance Unbalance on the Efficiency and Torque of Three-Phase Induction Motor.
Muhamad Vickry Almuhtadi Billah et.
Infokum Vol.
No.
03, 2026, pp.
ISSN 2722-4635
Results and Discussion Resistance Imbalance Analysis The analysis is carried out by following the motor data for a 5 HP .
73 kW), 400 V, 50 Hz, 4-pole induction motor.
The following calculations are carried out to analyze the motor at a Resistance unbalance of 5% (Rs,A = Rs,B = 0.
Rs,C = 0.
504 ):
Basic Motor Parameter Calculation Synchronous Speed .
Motor Operation Slip Phase Voltage (Vp.
Equivalent Circuit Model Calculation (Rs,C = 0.
Unbalanced Stator Impedance Rotor Impedance Rotor Magnetizing Impedance ( Total Impedance Per Phase ( Current and Power Calculation Current Per Phase assuming Impact of Stator Resistance Unbalance on the Efficiency and Torque of Three-Phase Induction Motor.
Muhamad Vickry Almuhtadi Billah et.
Infokum Vol.
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Current RMS Value Current Imbalance Percentage Stator Winding Loss Complex Power Per Phase Total System Power Power Factor Calculation of Mechanical Power and Efficiency Mechanical Power ( Mechanical Torque Efficiency () Impact of Stator Resistance Unbalance on the Efficiency and Torque of Three-Phase Induction Motor.
Muhamad Vickry Almuhtadi Billah et.
Infokum Vol.
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03, 2026, pp.
ISSN 2722-4635
From the calculation results above,The performance analysis of three-phase induction motors was carried out through numerical simulations based on equivalent circuit models, by varying the level of stator resistance unbalance.
For each scenario .
%, 5%, 10%, 15%, and 20%), the parameters of current, power, efficiency, torque, and percentage of current unbalance were calculated using a mathematical approach and then simulated using the Matlab program to view all scenarios.
From the results of running the Matlab program, the results of all scenarios are presented in Table 3.
Induction Motor Performance Simulation Results.
Table 3.
Induction Motor Performance Simulation Results Torque Input Power Unbalanced Current RMS Current Imbalance Efficiency Cu loss (N.
(W) (%) (A) Impact of Resistance Imbalance on Current Distribution and Power Losses The simulation results show that the unbalanced stator resistance causes uneven current distribution, even though the difference in current values between phases is relatively small.
The phase with the higher resistance .
hase C) experiences a decrease in current, while phases A and B remain constant because their resistances remain unchanged.
In balanced condition .
%), all three phases have identical current .
46 A).
At 20% unbalance, the C-phase current drops to 24.
22 A, resulting in a current unbalance of 98%, but significant enough to affect efficiency.
Stator copper losses increase linearly as the resistance unbalance increases:
From 861.
6 W .
%) to 912.
8 W .
%), or an increase of about 5.
This increase occurs because even though the phase C current decreases, the higher resistance results in greater losses in that phase, while phases A and B continue to contribute dominant This phenomenon shows that an internal resistance imbalance, even if small, can cause a disproportionate increase in power losses, thereby reducing the operational efficiency of the motor.
Impact on Motor Efficiency Motor efficiency decreases consistently as the percentage of stator resistance unbalance increases.
Under balanced conditions, the motor reaches a peak efficiency of 92.
At 20% unbalance, the efficiency drops to 92.
62%, as shown in Figure 1.
Impact of Stator Resistance Unbalance on the Efficiency and Torque of Three-Phase Induction Motor.
Muhamad Vickry Almuhtadi Billah et.
Infokum Vol.
No.
03, 2026, pp.
ISSN 2722-4635
Figure 1.
Graph of the effect of stator resistance imbalance on efficiency Although the decrease in efficiency appears small .
35%), this phenomenon has important The decrease in efficiency is caused by increased power losses, particularly copper losses in the stator.
As shown in the table, stator copper losses increase significantly from 861.
12 W at balanced conditions to 912.
14 W at 20% unbalance.
This increase occurs because, although the current in the higher resistance phase .
hase C) decreases slightly, the increase in its resistance value (Rs,C) causes the IAR power losses in that phase to increase disproportionately.
This larger total power loss reduces the output mechanical power (Pme.
and lowers the efficiency ratio ( = Pmek / Pi.
Impact on Mechanical Torque Characteristics Figure 2.
Graph of the effect of stator resistance imbalance on Mechanical Torque Mechanical torque also shows a similar trend to efficiency.
As seen in Table 3 and Figure 2, torque decreases from 95.
88 Nm at balanced conditions to 95.
28 Nm at 20% unbalance.
The decrease in torque is a direct consequence of the decrease in output mechanical power (Pme.
In this analysis model, the rotor speed .
_roto.
is considered constant, so the change in torque (T = Pmek / O) is directly proportional to the change in mechanical power.
Because resistance unbalance increases copper losses, there is less mechanical power left to be converted into torque.
Although the decrease in torque is numerically small, this trend indicates that the motor produces lower output power under unbalanced Impact of Stator Resistance Unbalance on the Efficiency and Torque of Three-Phase Induction Motor.
Muhamad Vickry Almuhtadi Billah et.
Infokum Vol.
No.
03, 2026, pp.
ISSN 2722-4635
Conclusion The analysis of stator resistance unbalance on the performance of a three-phase induction motor shows that even small deviations in phase resistance can significantly affect motor operation.
The presence of resistance unbalance leads to unequal current distribution among phases, which in turn causes negative sequence components in the system.
As a result, the motor experiences increased losses, particularly copper losses, leading to a reduction in overall efficiency.
Additionally, the unbalanced condition produces torque pulsations due to the interaction between positive and negative sequence magnetic fields.
These torque fluctuations can cause mechanical vibration, noise, and long-term degradation of motor The study also indicates that the greater the degree of stator resistance unbalance, the more severe the reduction in efficiency and the instability of the electromagnetic torque.
This condition not only decreases energy performance but also shortens the operational lifespan of the motor.
Therefore, maintaining balanced stator resistance is essential for ensuring optimal efficiency, stable torque output, and reliable motor operation.
Preventive maintenance, periodic resistance testing, and early fault detection are strongly recommended to minimize the impact of resistance unbalance in industrial applications.
Reference