ANALYSIS OF MULTI-PHASE INDUCTION MACHINE

Abstract

Prior to the advent of solid-state controllers, it was a common practice in all the three-phase ac machines to have six stator terminals out on connection plate to make it amenable for star- or delta- connections of operation. The star- or delta- connected machine is then fed through three-phase ac supply. Instead of machine being powered through three-phase ac supply or three-phase drive unit, if the six terminals of the machine (specially reconfigured for six-phase operation) are independently fed through single phase ac supply or six independent drive units with proper phase displacement, there will be a sizable increase in power rating of the machine within the safe saturation limit and heating condition. In case of fault (open circuit or short circuit) at stator terminals, the three-phase machine is unable to bear the full load (depending upon the load characteristics), however, if these faults occur in the new system, the machine will be able to bearthe load and there will be not much performance degradation. Based on the basic concept of parallel-redundancy, the techniques used as such has been termed as 'Phase Redundancy', and the machine under operation is called 'multi-phase' (more than three phases) or 'high phase order' (HPO) machine. The necessary requirement for application of this concept is that the number of stator phases must be more than the conventional three phases. An ac machine has as many stator phases as coils per pole pair, which is always greater than three, and can be easily reconfigured without any additional cost. In a phase-redundant ac drive system, each of the many stator phases is either supplied by the independent single-phase supply / drive unit or in a group of three phases (displaced by 120°) by the independent three-phase supply / drive unit to provide possible operational independence to minimize the risk of physical fault propagation from one three-phase set to another. A multi-phase machine has many advantages over conventional three-phase machine. It has capability to start and to continue to run with one or more of its many stator phases open or short-circuited. A multi-phase machine with two three-phase stator-winding sets displaced from each other by 30° eliminates all the air-gap flux time harmonics of the order (8k ± 1;k- 1,3,5 )• Consequently, all the rotor copper losses produced by these harmonics as well as all the torque harmonics of order ( 6/c; k=1,3,5, ) are eliminated. Alower current per phase without an increase in per phase voltage and high power rating in the same frame can be achieved by means of a multi-phase machine. There are other compelling reasons to increase the phase order number to six or more. With the increase in the phase number of the machine, the per phase power handling requirements are reduced and large Permanent Magnet AC (PMAC) machines designed to directly drive submarine propellers at low speed have been developed. Utilizing the key advantageous feature of the multi-phase machine, the load commutated inverter (LCI) fed six-phase (two three-phase winding sets displaced by 30°) synchronous motors were developed and are being used to drive the induced draft fans (IDF) in thermal power plants. The analysis of standard symmetrical multi-phase induction machine is set forth in several texts. This work, however, cannot be directly applied to the machines with unsymmetrical phase displacement between the multiple winding sets. It has been found that the required angular displacement between multiple winding sets for better performance should be tin for an even number of winding sets and 2tz/a7 for an odd number of sets, where n is the total number of phases. The symmetrical component method originally developed for three-phase system is one of the most effective tools for the analysis of a machine under unbalanced steady-state conditions, however, as far as the analysis of the multi-phase machine is concerned, the method loses its utility due to the unsymmetrical phase displacement between multiple winding sets and also during the fault conditions particularly under an open circuit condition. The knowledge of the dynamic behavior of a machine in modern day drive system is essential to provide precise controlled operation. A number of analytical procedures have been proposed in the past for the analysis of a multi-phase induction machine. A detailed literature survey reveals that almost all the mathematical models reported earlier, except the one by Nelson and Krause, have been developed for a specific winding configuration with 30° displacement between two three-phase stator winding sets and that the mutual leakage inductances due to the presence of the different phase windings in the same slot have been neglected in most of the models. Analytical models using the concept of vector space decomposition for modeling and control of a multi-phase induction machine with balanced winding structure and with unbalanced winding structure caused by an open circuit have been reported by Zhao and Lipo. Separate mathematical models have been proposed to analyze the machine behavior under balanced and unbalanced operating conditions. Available literature does not throw light on the modeling of a multi-phase induction machine under short circuit (ground short) condition. This dissertation, therefore, presents asimple and generalized d-q model for the analysis of amulti-phase induction machine under balanced as well as unbalanced operating conditions. The machine under consideration has six stator phases divided into two wye- connected three-phase sets, labeled abc and xyz, whose magnetic axes are displaced by an arbitrary angle. The windings of each three-phase set are uniformly distributed and have axes that are displaced by 120°. The analytical model presented in this work is considered to be superior to all the other models reported earlier for the reasons given below: (i) This single analytical model is able to simulate the dynamic, transient and steady state behavior of a multi-phase machine under balanced as well as unbalanced operating condition. (ii) Both types of electrical unbalances caused by an open circuit or a short circuit at machine's stator terminals can be simulated. (Hi) Amulti-phase machine with an arbitrary phase displacement between the two three-phase winding sets can also be simulated by simply incorporating a phase displacement between the d-q stator voltages of both the winding sets and the corresponding value of the mutual leakage reactance, x,m. (iv) This analytical model has been developed in an arbitrary reference frame hence, it is more versatile and can be easily manipulated and employed to develop the various types of control strategy, (v) Effect of mutual leakage coupling between the two-stator winding sets has been included in this analytical model. To sum up, our model is more generalized and versatile. Fault studies form an important step in the design of adequate protective schemes for drive systems. The types of fault that can occur increases with the increase in number of phases. Open circuit (/, = 0 if the fault is occurring at stator input phase terminal 'a') and short circuit (va = 0 if the fault is occurring at input phase terminal 'a') are the most common faults that can occur at the stator input phase terminals of the in machine. The type of supply system and the impedances across the unexcited winding terminals are the two parameters, which together determine the basic drive configuration and performance of the machine during fault. For the purpose of this dissertation, the theoretical values of torque at different slip under steady state have been calculated for the following discrete cases that provide important criteria for (n-1) phase excitation performance analysis: (i) Voltage Source excitation and the Short Circuit occurring at input stator phase terminal (VS-SC); (ii) Voltage Source excitation and the Open Circuit occurring at input stator phase terminal (VS-OC); (iii) Current Source excitation and the Short Circuit occurring at input stator phase terminal (CS-SC); (iv) Current Source excitation and the Open Circuit occurring at input stator phase terminal (CS-OC). There are very few references available on the phase-redundant systems and the multi-phase machine drives. In most of the references available so far, (i) the key quantities giving the torque production characteristics of the four cases of (n-1) phase excitation as well as balanced excitation have been determined for six-phase machine without considering the saturation level or normal working voltage of the existing machine when it is converted to operate on high phase order, (ii) While comparing the torque-slip relation of the machine configured to operate on six-phase or more with its three-phase counterpart, magnetic loading (voltage per turn) has not been taken into account. The variation of efficiency, current and power factor with output, for balanced as well as unbalanced excitation and the improvement in power rating of the machine in the same frame are the key points, which had not been addressed yet. In this work, all these points have been paid due attention to during the experimental verifications. If a machine operating at a constant speed under steady load conditions is subjected to a step function or impulse-function change of load or terminal voltage, it will normally return to steady state constant speed conditions with or without oscillations of speed and current about the steady state values. Again, if a machine is subjected to periodic variations of voltage or torque about a mean value, there will be associated IV periodic variations of speed and current. This phenomenon termed as 'small oscillations' has been investigated in details. The effect of various motor parameters such as magnetizing reactance, stator and rotor resistance, and moment of inertia on the stability ofthe multi-phase machine has also been included in this thesis. For the purpose of experimental verification, a 220 V, 1.5 kW, 3-phase squirrel cage induction motor frame, with 36-slots in armature was selected for 4-pole operation with a coil pitch of seven slots. All the stator coil terminals were taken out on a connection table to yield alternative winding schemes for different number of phases and poles. The armature terminals were reconnected for six-phase and were excited by sixphase balanced supply simulated from the three-phase v/f controller with PWM waveform with the help of autotransformer. To determine the working voltage of the machine within the safe saturation level, the test motor was subjected to no-load test for its no-load magnetization characteristic. Another test was also conducted with varying applied voltage for its no load loss calculation for the three cases given below: (i) Motor connected for six-phase; (ii) Motor connected for six-phase but with one phase open (unbalanced fivephase), (iii) Motor connected for three-phase. The load test on the motor was also conducted to analyse the variation of efficiency, power factor and current as a function of output for the three cases given below: (i) Motor connected to six-phase with rated phase voltage, 210 Vand with the load varied from no-load to a value of 3.0 kW. (ii) Motor connected to six-phase but with one phase open (unbalanced fivephase) with rated phase voltage 210 V and with the load varied from noload to a value of 2.25 kW. (iii) Motor connected to three-phase with rated phase voltage of 220V and with the load varied from no-load to a value of 1.72 kW. Results of theoretical and experimental analyses clearly demonstrate several advantageous features of the multi-phase machine. A large percentage of the induction motor balanced excitation performance can be retained following loss of excitation to one stator phase. Tests also reveal that post-fault (n-l)-phase excitation performance characteristics of the induction motor improve with the increase in number of stator phases approaching balanced excitation levels at a given slip for large value of n. Apart from this, following observations are also made based on the test results: (i) Improved reliability as the machine continues running with one of its many phases open- or short-circuited and there is not much performance degradation. This property of the multi-phase machine will be advantageous in nuclear power plants for its circulation pumps and for other similar applications in process industries, which demand high reliability; (ii) Reduced iron loss leading to an improved overall performance; (iii) Lower current per phase without increase in per phase voltage. This advantageous feature may be useful for electric vehicles and similar applications where lower, upper limit of voltage and current is desirable, (iv) The most advantageous feature is increase in power rating of the machine on high phase order connection in the same frame. In other words, there is a reduction in per phase power handling requirement though with enhanced modularity and fault tolerance. Based on this research work, one paper has been published in International Journal of Electric Machines and Power Systems. One has been accepted for publication in National Journal and one (revised manuscript) is under review. In addition, two papers in International and one paper in National Conference have already been presented and published. One paper has been accepted in International Conference, ICEE2001 to be held in China in July 2001.