Comparing the Performance of Induction Machine Drive with Different Rotor-Impedance Profiles

Abstract: This paper compares the performance of a wound rotor induction motor drive (WRIM) with two rotor impedance profiles. The first system involves a diode rectifier followed by variable impedance in the rotor circuit. The second system involves a three-phase variable impedance in the rotor circuit. The comparison concerns the magnitude of starting transients of stator and rotor voltages and currents, the transients settling time of the stator and rotor voltages and currents, the stator and rotor consumed active and reactive power, the electrical torque, and the stable range of operation at sub-and super-synchronous speeds. This comparison is helpful for deciding the more efficient drive to be utilized, the drive with lower harmonics in currents and voltages, and the drive allowing wider speed stable operation range. Better results are obtained for the drive with the three-phase variable impedance connected to the rotor circuit.


Introduction
Wound rotor induction motor drives outperform the squirrel cage induction motor drives in many aspects. First, its speed can be varied through an external resistance, which allows maintaining the torque at any value, up to the pull out torque, within the entire speed range by varying the added rotor resistance. Second, high starting torque with restricted starting current for accelerating heavy rotating masses is provided by WRIM drive. Also, during starting the rotor is subjected to damage due to excessive heat, which can be shared by the external resistance, hence protecting the rotor circuit. Availability of full-rated torque at starting, high power factor, absence of line current harmonics, and wide range of operational speed, are other advantages of speed control via rotor resistance [1][2][3][4][5][6][7][8][9]. In fact these benefits overcome the drawbacks of WRIM higher cost and its need for frequent maintenance.
Most previous researches concerning speed control and starting of WRIM concentrated on adding capacitors to the rotor impedance to improve the power factor and dynamic performance [10,11]. Other researches considered adding chopper to the rotor circuit to vary the rotor impedance for better performance [12]. These methods add to the complexity of control and increase the cost of the drive system by adding more components to the rotor circuit.
These drawbacks are avoided in this research paper by proposing simple methods for controlling the speed of a WRIM drive. The performance of the two proposed simple rotor systems are compared to conclude the better drive from the point of view of operating speed range, harmonics, starting transients, and settling time. The rotor circuit of the first proposed system is connected to a diode bridge rectifier with a variable single-phase impedance at its output. The rotor of the second system is connected to a three-phase variable impedance. The two systems are modeled and simulated using MATLAB/Simulink software. The comparison concerned the voltage and currents transients and their settling time, the stable range of operation, the active and reactive power consumed from the grid, the rotor active and reactive power, and the electric torque response. The simulation results proved that the performance of the system with the three phase rotor impedance is better than the performance of the system with the diode bridge. Lower harmonics, short settling time, and lower voltage and current transients are observed in the drive with three phase impedance in the rotor circuit.

Mathematical Model of WRIM
The machine dynamical equations in the d-q axis can be written as [13]: Where …⅄, v, i, ω, Te denote flux, voltage, current, angular speed and electromagnetic torque respectively.
Subscripts d and q denote d-axis component and q-axis component in arbitrary d-q reference frame, respectively. r and L denote resistance and inductance, respectively Suffixes s, r and m denote stator, rotor and mutual quantities respectively; P is the number of pole pairs.

The Drive System with Three Phase Impedance In The Rotor Circuit
The per-phase rotor impedance is:

Zr= Rr +Xr+ Zext
Where Zext is the external impedance that can be varied to improve the dynamic performance of the system and to widen the stable speed range of operation. Figure 1 shows the bridge rectifier with the variable impedance at its output.

The Drive System with a Rectifier and Single-Phase Impedance
Under the balanced conditions, the three-phase sinusoidal voltages at ac side of the rectifier VA, VB and VC can be written as follows: Where Va, Vb, and Vc are the rotor circuit voltages. The DC component of the output voltage is given by: Where Vm is the peak rotor voltage magnitude.

Super-Synchronous Speed Range
The stator current, rotor voltage, rotor current, stator active and reactive power, rotor active and reactive power, and electric torque are given in figures 2a-6a for the drive with rotor rectifier (system A), while these parameters are given in figures 2b till 6b for the drive with 3-phase rotor impedance (system B) at slip equal -0.08 (170rpm). Comparing results shows that the starting transients of the stator current of system A are lower than system B, but its settling time is longer and its steady state value contains higher harmonics than system B. The rotor voltage starting transients and settling time for system A are considerably higher than those for system B and its steady state value contains higher harmonics, resulting in a nearly triangular voltage profile. Similar argument applies for the rotor current as demonstrated in the figures. Consequently, the starting transient, the settling time, and the steady state harmonics of stator active and reactive power in system A are higher than its corresponding values in system B. In spite of the higher transient in the electric torque of system B, its steady state magnitude is smooth in system B while it contains ripples in system A.
The stator current, rotor voltage, rotor current, stator active and reactive power, rotor active and reactive power, and electric torque are given in figures 7a-11a for the drive with rotor rectifier (system A), while these parameters are given in figures 7b till 11b for the drive with 3-phase rotor impedance (system B) at slip equal -0.21(190rpm). Comparing results shows the higher starting transient of rotor current in system A and higher harmonics of its steady state magnitude than for Int. Res. J. Multidiscip. Technovation, 3(2) (2021) 26-34 | 28 system B. It is worth noticing that the stator active and reactive power consumed from the grid is very high during starting for system A, but settles down to the same value of system B at steady state. Also torque ripples for system A are higher with slightly higher transient magnitude than the value in system B.

Sub-Synchronous Operation
The stator voltage, stator current, rotor voltage, rotor current, stator active and reactive power, and electric torque are given in figures 12a-16a for the drive with rotor rectifier (system A), while these parameters are given in figures 12b till 16b for the drive with 3-phase rotor impedance (system B) at slip equal 0.0445 (150rpm). The starting transient of the stator current of system A is lower than system B, but its settling time is longer and its steady state value contains higher harmonics than system B.
The rotor voltage starting transients and settling time for system A are considerably higher than system B and its steady state value contains higher harmonics, resulting in a nearly triangular voltage profile. Similar argument applies for the rotor current as demonstrated in the figures. Consequently, the starting transient, the settling time, and the steady state harmonics of stator active and reactive power in system A are higher than its corresponding values in system B. The steady state The stator current, rotor voltage, rotor current, stator active and reactive power, rotor active and reactive power, and electric torque are given in figures 17a-21a for the drive with rotor rectifier (system A), while these parameters are given in figures 17b till 21b for the drive with 3-phase rotor impedance (system B) at slip equal 0.172 (130rpm). It is clear that the steady state stator current of system A contains more ripples and its transient peak and settling time are higher than those of system B. The transient magnitude and the settling time of the rotor voltage are also higher for system A than in system B. The steady state rotor current of system B is pure sinusoidal, while it contains harmonics leading to a rectangular shape for system A. This is expected due to the rotor diode rectifier. Consequently, high transients and longer settling time in the stator active and reactive power occurred in system A are due to the high harmonics of the rotor current. Also torque ripples for system A are higher with slightly higher transient magnitude than its value in system B.

Conclusion
Results of comparing the performance of a wound rotor induction motor drive (WRIM) with two rotor impedance profiles are given. The first system involves a diode rectifier followed by variable impedance in the rotor circuit. The second system involves a three-phase variable impedance in the rotor circuit. The comparison concerns the magnitude of starting transients, the transients settling time for the stator voltage and current, the rotor voltage and current, the profile of the stator active and reactive power, the profile of the rotor active and reactive power, and the electric torque at sub-and super-synchronous speed. This comparison is helpful for deciding the more efficient drive to be utilized, and the wider speed range stable operation. Results proved the superiority of the system with three phase rotor impedance concerning the starting transient peaks, the settling time, and the lower harmonics of the steady state stator current, rotor voltage and rotor current. The range of stable operation is wider in the three phase rotor impedance system, which can be concluded from the higher distortion that occurs in the voltages and currents of the system involving the rectifier as the speed range is widened.