Investigations on Pulse Width Modulation Techniques for Split-Phase Induction Motor Drives

Abstract

A split-phase induction motor (SPIM) has two sets of identical three-phase windings. These two sets of windings are separated by 30◦ in space, which are, typically fed by a three-phase voltage source inverter (VSI) each. The individual voltage rating of each winding is 0.5176 times the original voltage rating of an equivalent three-phase machine, leading to a reduced DCbus voltage rating of the VSI. The DC capacitance value and size of the inverter are also reduced. However, the application of harmonic voltages on the motor is inevitable in any inverter-fed operation. The harmonic voltages of order 5, 7, 17, 19, . . . result in significant harmonic currents of the same order. While these harmonic currents do not lead to harmonic torques of order 6, 18, 30, . . ., unlike in a three-phase induction motor, these do increase the stator copper loss. The harmonic voltages of order 11, 13, 23, 25, . . . do result in harmonic currents of the same order and also harmonic torques of order 12, 24, . . .. The harmonic voltages at any given fundamental voltage depend on the pulse width modulation (PWM) technique employed. This thesis analyses various existing PWM techniques for SPIM drives, and also proposes and validates two new PWM techniques for the same. Most existing PWM techniques follow either the triangle-comparison (TC) approach or the space-vector (SV) based approach. TC-based PWM (TCPWM) techniques for SPIM drives employ two sets of modulating signals, which are phase-shifted by 30◦ from each other. These modulating signals are compared against a common triangular carrier to identify the switching instants of the six legs. In SV-based PWM techniques (SVPWM), the voltage reference is provided in terms of a revolving voltage vector. The sampled reference voltage vector is used to identify the voltage vectors to be applied in the given sub-cycle, and the corresponding dwell times of each voltage vector. While the TC-based techniques are easier to implement than the SV-based techniques, certain SV-based techniques could offer better harmonic performance than the TC-based techniques. Developing a better unified understanding of both the approaches could lead to either efficient implementation or effective performance analysis of a certain PWM technique. This could also provide insight into developing new PWM techniques. Such a unified understanding of the TC and SV-based approaches is well-developed for three-phase induction motor drives. While certain studies have been reported on SPIM drives in this context, this thesis attempts to add up further to such studies. Three continuous TC-based PWM techniques, namely sine-triangle PWM (STPWM), three-waves based common mode injected PWM (CM3PWM) and six-waves based common mode injected PWM (CM6PWM), are analysed from the space vector perspective. Every leg switches once in every half-carrier cycle in all three continuous PWM techniques. There is no simultaneous switching of more than one leg. The switching sequence starts with one zero state and ends with another zero state. Five active states get applied in between the two zero states. Among bus-clamping PWM techniques, continual clamp PWM (CCPWM) and split clamp PWM (SCPWM) are analysed in a similar fashion. Four of the six legs switch once in every half-carrier cycle in these PWM techniques. Totally, five inverter states get applied in each half-carrier cycle. Only one zero state gets applied at low modulation indices, while no zero state is used at high modulation indices. The active voltage vector, produced by each active state, is a four-dimensional one. The four orthogonal components are usually designated as α, β, µ1 and µ2. The voltage vectors applied, and the sequence in which they are applied are studied in different regions of the fundamental cycle (termed sectors) for each of the TCPWM techniques. The similarities and differences between the individual techniques and also those between continuous and bus-clamping techniques are brought out. The thesis analyses three different four-dimensional (4D) SVPWM techniques from a per-phase perspective. The switching-cycle-averaged pole voltages are evaluated for each of the SVPWM techniques. The common mode voltage (CMV) in each of the three-phase inverter voltages is determined. The relationship between this CMV and the three-phase fundamental voltages is then established. Such analysis of an SVPWM technique leads to a computationally efficient implementation of the same. The common mode or zero sequence signal is derived from the three-phase sinusoidal modulating signals of an inverter, and is added to the three-phase sinusoidal signals to obtain the equivalent modulating signals for the given SVPWM technique. These modulating signals are compared against an equivalent carrier signal, which is also obtained through analysis. Such carrier-based implementation significantly reduces the computation time required for the given SVPWM technique on a TMS320F28377S DSP platform. Experimental results of stator current waveforms under steady-state and various dynamic conditions from a 6kW, 200V, 50Hz SPIM drive are presented. Such computationally efficient implementations are also successfully extended to vector-controlled SPIM drives. Simulation and experimental results from the vector controlled drive are also presented. The performances of different PWM techniques are compared in terms of current ripple and torque ripple using the notion of stator flux ripple. The stator flux ripple vector is the time integral of the error voltage vector, which is the difference between the instantaneous applied voltage vector and the reference voltage vector. This ripple vector is a four-dimensional quantity in SPIM drives. The stator flux ripple is evaluated and compared along each of the four orthogonal axes for the different PWM techniques. The total rms harmonic distortion factor, evaluated analytically, is verified by experimental measurements of the total harmonic distortion factor (THD) in the motor currents. The switching loss pertaining to the different PWM techniques is also analysed and compared. One of the bus-clamping PWM techniques (BCPWM-1) is shown to reduce the inverter switching loss at power factors greater than 0.707. Two SV-based advanced bus-clamping pulse width modulation (ABCPWM) techniques are proposed in this thesis for SPIM drives to enhance their performance further. These ABCPWM techniques also use four active vectors in every sector, as in the case of the 4D SVPWM techniques. But, the proposed techniques apply the null vector only once, while applying one of the active vectors twice in each sub-cycle. The sequence of vectors ensures that only one leg switches at a time. The total number of switching transitions in a sub-cycle is five, which is less than the six transitions in the case of the continuous 4D SVPWM techniques. Stator flux ripple-based analysis is carried out for these special switching sequences along all four orthogonal axes. The harmonic distortion factor, thus obtained, brings out the superior harmonic performance of the proposed switching sequences over the conventional switching sequences at high modulation indices for a given average switching frequency. Switching loss factor-based analysis shows that the inverter switching loss gets significantly reduced with the proposed PWM techniques at high power factors compared to the existing 4D SVPWM techniques. Simulations and experiments on a 6kW, 200V, 50Hz SPIM drive confirm the significant reduction in the stator current THD with the proposed ABCPWM techniques at high speeds for a given average switching frequency. In particular, one of the proposed techniques improves the no-load stator current THD by 32% at the rated speed of the SPIM drive, compared to a state-of-the-art SVPWM technique.