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# Thesis Colloquium of Sayan Paul

## January 12, 2023 @ 8:30 PM - 9:30 PM IST

**Thesis Title:** Pulse Width Modulation Techniques of Inverter Fed Split-Phase Machine Drive in Linear and Overmodulation Regions

**Degree registered:** PhD

**Guide:** Prof. Kaushik Basu

**Date and Time:** 12th January 2023, 03:00 PM

**Place:** MMCR EE,

**Meeting Link: **Teams Meeting Link

Multi-phase machines (MPMs) have more than three windings in their stator, rotor, or both. With the broader adoption of power-electronic converters for efficient driving of the machines, MPMs are gaining attention in different applications due to their certain advantages over three-phase machines. One such advantage is higher fault tolerance due to higher phase redundancy, which makes it suitable for safety-critical applications like electric vehicles (EVs), ship propulsions, electric aircraft, etc. Another advantage is that MPMs allow power splitting across multiple phases. Hence, the power rating per phase drive unit becomes low, making it suitable for high-power applications like railway traction, pumps, compressors, etc. Recent literature also proposes using the same multi-phase converter fed MPM, otherwise used for propulsion, as an onboard battery charger; it substantially reduces space, weight, and cost. During charging mode, the leakage inductance of the machine provides the required inductance for the grid connection, and MPM’s higher degrees of freedom are used to lock the rotor electronically. An asymmetrical six-phase machine (ASPM) or split-phase machine is one such MPMs and is very common in EVs. This thesis aims to devise the pulse-width modulation (PWM) techniques of a two-level six-phase inverter fed ASPM to improve the overall drive efficiency.

ASPM has two sets of balanced three-phase windings, which are spatially shifted by 30 degrees (electrical angle). In one of the popular configurations, the two three-phase winding sets are connected in star fashion with two isolated neutral points. This machine is conventionally analyzed in two two-dimensional (2D) orthogonal subspaces. One of these subspaces is associated with electromagnetic energy transfer and torque production. The other subspace doesn’t transfer energy through the air gap and the equivalent circuit in this plane, consisting of winding resistance and leakage inductance, provides a low impedance. Therefore, excitation of this non-energy-transferring subspace causes a large current and associated copper loss. Any PWM technique of ASPM aims to synthesize the desired voltages in the energy-transferring plane and minimize the applied voltage in the non-energy-transferring subspace.

Linear modulation techniques (LMTs) of ASPM apply zero average voltage in the non-energy-transferring subspace and synthesize the desired voltages in the energy-transferring plane on an average over a switching cycle. It is expected that these LMTs should avoid more than two switching transitions of an inverter leg within a carrier period to limit the instantaneous switching loss. Through an innovative approach, our work finds a way to account for all possible infinitely many LMTs that follow the rule of at most two transitions per leg. But each of them results in a different current ripple performance. Ripple current is inevitable in PWM converters and should be minimized through modulation to reduce the associated copper loss. The total ripple current RMS of ASPM is contributed by both energy-transferring and non-transferring planes. One machine parameter also impacts this performance: the ratio of high-frequency inductances in these two subspaces. For all reference voltage vectors and the whole feasible range of the machine parameter, our work finds the techniques with minimum current ripple (RMS) among the above infinite possible LMTs through numerical optimization. A hybrid PWM strategy is proposed with these optimal techniques, which outperforms all existing techniques regarding current ripple performance.

Overmodulation (OVM) techniques of ASPM attain higher voltage gain in energy-transferring subspace than LMTs by applying non-zero average voltage in the non-energy transferring subspace. This operation doesn’t cause any torque ripple, but the applied voltage in non-energy transferring subspace should be minimised to reduce unwanted current and associated loss. The existing OVM technique in the literature minimizes this average voltage from the space-vector perspective with a pre-defined set of four active vectors. To find the best technique, one needs to perform the above minimization problem with all possible sets of active vectors, which can give higher voltage gain. So, this requires the evaluation of a large number of cases. In this thesis, we have formulated the above minimization problem in terms of average voltage vectors of two three-phase inverters, where active vectors need not be specified beforehand. Thus, the analysis is more general. Following the above analysis, eight switching sequences in one part and two in another part of the OVM region are derived, which attain the minimum average voltage injection in the non-energy transferring subspace.

Although the above OVM sequences apply the same average voltages in the two subspaces, they have different high-frequency ripple currents due to different switching strategies. The current ripple study of the OVM techniques of ASPM is missing in the literature. Hence, one of our works in the thesis studies the current ripple performances of the above optimal PWM sequences in the OVM region, which apply minimum average voltage in the non-energy-transferring subspace. We find the sequence with the best switching current ripple performance for a given reference vector in the OVM region and the machine parameter. After that, a PWM technique is proposed, which substantially improves the high-frequency current ripple performance (RMS) compared to two existing OVM techniques for a given machine parameter value.

Finally, simple carrier-comparison-based implementation methods of the proposed LMTs and OVM sequences are found. The six-phase inverter is split into two three-phase inverters, and the proposed strategy implements the PWM sequences per three-phase inverter basis. In carrier-based implementations, the duty signal of the top switch of an inverter leg is compared with a triangular carrier. The bottom switch’s gating pulse complements the top switch’s pulse with a fixed dead time. The duty signal of the top switch of any leg has two components- a modulation signal and a common-mode signal. Two 180-degree phase-shifted carrier signals are required to implement the proposed sequences. The energy-transferring plane of ASPM is divided into twenty-four equivalent sectors; the carrier signals and the expressions of modulation and common-mode signals differ from one sector to another. Henceforth, a sector-independent algorithm is proposed in this thesis to derive these duty signals that substantially reduce the computational burden.

The proposed techniques are validated through simulation in MATLAB/Simulink and experiments on a hardware prototype at a power level of 4 kW.