Analysis of Balanced Three-Phase Induction Motor Performance under Unbalanced Supply using Simulation and Experimental Results

Unbalanced voltage is one of the most frequent disturbances in electrical systems. An induction motor supplied by unbalanced three-phase power system has been investigated to obtain its quantities by resolving into the balanced three-phase components. This is called as symmetrical components method. The circuit quantities of three-phase squirrel cage induction motors fed from unbalanced three-phase system cannot be determined by classical methods, whereas the symmetrical components method should be used. This method introduced by Fortescue is widely utilized for rotating electrical machines. In this method, an unbalanced supply can be defined as combination of zero, forward and reverse sequence components similar to that of a balanced system [1–5]. In this work, A squirrel cage induction motor with short-circuited rotor and the plate values of P = 1.5 kW, 380 V, 3.9 A Y, n= 1470 min, f=50 Hz, cos¢=0.8 is used. This machine has been supplied by balanced and unbalanced power systems respectively for both experimental and modeling methods. Their voltage, current and power parameters are subsequently measured with their harmonic values. The comparisons have been also made for both analysis techniques [1–6].


Introduction1
Unbalanced voltage is one of the most frequent disturbances in electrical systems.An induction motor supplied by unbalanced three-phase power system has been investigated to obtain its quantities by resolving into the balanced three-phase components.This is called as symmetrical components method.The circuit quantities of three-phase squirrel cage induction motors fed from unbalanced three-phase system cannot be determined by classical methods, whereas the symmetrical components method should be used.This method introduced by Fortescue is widely utilized for rotating electrical machines.In this method, an unbalanced supply can be defined as combination of zero, forward and reverse sequence components similar to that of a balanced system [1][2][3][4][5].
In this work, A squirrel cage induction motor with short-circuited rotor and the plate values of P = 1.5 kW, 380 V, 3.9 A Y, n= 1470 min -1 , f=50 Hz, cosφ=0.8 is used.This machine has been supplied by balanced and unbalanced power systems respectively for both experimental and modeling methods.Their voltage, current and power parameters are subsequently measured with their harmonic values.The comparisons have been also made for both analysis techniques [1][2][3][4][5][6].

Symmetrical components of balanced alternating current machines
If the voltages applied to the motor stator windings are unbalanced, the motor characteristics may vary considerably.The three-phase unbalanced voltages (V 1 , V 2 , V 3 ) can be resolved into forward (V d , a 2 V d , aV d ), reverse (V t , aV t , a 2 V t ) and (V 0 , V 0 , V 0 ) zero three-phase balanced components with the aid of symmetrical components transformation.[3][4][5][6] In general, symmetrical components transformation can be defined as follows In steady-state sinusoidal operation: If the equations below are defined as follows In equations (3), V o , V d and V t represent zero, forward and reverse components respectively.Matricial Equation (4) gives the relation between symmetrical components phasors and their instantaneous values.An unbalanced three-phase system can be resolved into balanced forward, reverse and zero sequence components by using the above relations and unbalanced phasors.The forward component induces currents that are balanced and in the same phase sequence of the three-phase supply currents.The reverse component generates currents balanced as well but in the opposite phase sequence due to the voltages in reverse phase sequence in the stator.The phasors of the zero sequence are in equal amplitudes and the same phase for all phase sequences of a three-phase power supply.

The equivalent circuit of an induction motor for unbalanced supplies
Let's consider that the rotor speed in rpm and the slip of a motor operating from unbalanced voltage supply are n, σ respectively.Since the phase sequence of forward component is identical to that of the supply, this component induces a magnetic field which rotates in the same direction of the motor shaft.The per phase equivalent circuit for the rotating field is the normal equivalent circuit of an induction motor where the slip in this circuit is σ.The reverse component produces a magnetic field that rotates in the opposite direction with respect to the rotor, whereas the slip is 2-σ.Generally, the reverse magnetic field should be at minimum amplitude, because it causes a large amount of power loss in the motor.If the amplitude of reverse magnetic field is less than that of 5% of the forward component, such a three-phase power system can be supposed as symmetrical in practice.No rotating field is induced by zero component currents, because they are in the same direction for each phase.Any torque is not therefore produced since the resultant field is zero.However a motor fed from V 1 , V 2 , V 3 unbalanced voltage supply can be considered to consist of two motors operating individually.The first motor operates from forward component of balanced system at V d1 , V d2 , Vd 3 voltages with σ slip in normal rotation direction.The second motor operates from reverse component of balanced system at Vt 1 , Vt 2 , Vt 3 voltages with 2-σ slip in opposite direction.The main and two separate motors are shown in Fig. 1.The per phase equivalent circuit for the forward component is obtained by placing σ as the slip, sd I as the stator current and rd I as the rotor current in the equivalent circuit of symmetrical components of an induction motor operating at unbalanced supply.Similarly, the equivalent circuit for the reverse component can be derived, where 2-σ, st I , rt I represent the slip, the stator current and the rotor current respectively as illustrated in Fig. 1

Obtaining circuit parameters of the induction motor by experimental tests
The stator winding parameters of the motor used in this study obtained by the measurements are given in Table 1.The short-circuited impedance, equivalent resistance and reactance referred to the stator side, rotor resistance and leakage reactance of the motor have been obtained by using the quantities provided from the short-circuited experiment.The equivalent circuit parameters calculated by using the data in Table 1 and Table 2 are shown in Table 3, Table 4.The Matlab / Simulink Model The Matlab/Simulink model in Fig. 2. has been constituted by using equations 5-8 where flux linkagecurrent relations and mechanical system equations are written for the machine.

A comparison of performances of the induction machine fed from balanced and unbalanced supplies
If balanced 3-phase alternating current machines are fed from balanced three phase power systems, symmetrical phase voltages and currents are provided.In case of operating at unbalanced voltage system, in order to obtain the amplitude of any phase current, the effects of currents in the other phases to that phase should be known.The voltage and current value of the motor 10 Nm load under experiment fed from the balanced voltages and current value are: . However if the unbalanced voltage and current systems are resolved into the symmetrical components, two circle diagrams can be obtained where they are for the forward and the reverse.Zero component does not exist since the neutral point of the motor is not grounded in normal operation [1] The phasor values of the applied voltages unbalanced in experimental tests are: The electrical and mechanical torque variations at 10 Nm load under unbalanced conditions are shown in Fig. 4.Under this load, the speed variation of the motor is also illustrated in Fig. 5.The all results obtained by modeling and experiments can be seen in Fig. 4  The current waves of the motor in experiments and the currents of balanced power supply for the simulation are shown in Fig. 6 and Fig. 7 respectively.In both analyses, the peak value of motor current is 4 A approximately.It means the simulation results are in accordance with the measurement values.Fig. 8 and Fig. 9 show the motor current vs. time curves under unbalanced power supply.As can be seen from the curves, the unbalanced supply generates over distortions in the currents drawn from the source.This circumstance causes harmonics; therefore the current harmonics of I 1 phase of the motor have been measured.The current harmonic values measured in I 1 phase are completely shown in Fig. 9 and Fig. 10.As can be seen from the figures, the harmonic contents differ in balanced and unbalanced systems.A comparison of performances of the induction machine fed from balanced and unbalanced supplies If balanced 3-phase alternating current machines are fed from balanced three phase power systems, symmetrical In case of balanced supply, harmonics (11, 15, 19) do not exist obviously but the 3rd, 5th and 7th harmonics have influence in unbalanced operation.This result increases the total harmonic distortion and aggravates the quality of energy.

Conclusions
The unbalanced operation regime of a three phase supply is determined by quantities such as emf, potential difference and current.In this article, the specific equivalent circuits of an induction machine are obtained by resolving the mentioned quantities into symmetrical components.In these equivalent circuits, the opposite rotating torque occurs due to the reverse components of currents.Therefore the motor needs drawing more current from the supply to maintain the demanded mechanical power.As a result, the copper losses and the heat in the machine increase.
This result has been also seen by loading the machine at 10 Nm torque in both simulation and experimental measurements.In addition, the harmonics generated during unbalanced operation are observed as electromagnetic noise in the machine.This noise appears as pulsations in motor bearings as well.This event may cause bearing faults for-long term operations from unbalanced supply.It is clearly observed that the simulation and the experimental results are in well accordance with each other.The parameters of an induction machine operating from unbalanced supply can be obtained by the proposed model in Matlab/Simulink environment without the need for any equipment.

Fig. 11 .
Fig. 11.Current harmonic spectrum for Unbalanced power supply Table 5. Harmonic values Balanced Supply

Table 3 .
Equivalent circuit parameters

Table 4 .
Equivalent circuit parameters

Table 6 .
Data at balanced and unbalanced power supplies