In this paper the harmonic plane decomposition from part I is completed. Multiphase electrical machines with independently controlled stator coils benefit from a fixed amount of current controllers and unified models. In part I, the foundation for such models was laid. This paper shows that the choice of the base case has to fulfill certain criteria to properly represent vector-space quantities. More specifically, phase-pole configurations with an even number of pole pairs need adapted base cases with reduced rank as compared to the odd base case. Continuous modeling and control requires retention of the dimensionality of Clarke matrices. A different number of stator and rotor slots can lead to aliasing in the transformation, when keeping the dimension consistent. Therefore, a specific Clarke transformation for rotor quantities based on the developed theory is elaborated. Finally, it is demonstrated how the harmonic plane decomposition can be used to model each harmonic plane of an arbitrary phase-pole configuration with conventional machine equivalent circuits, e.g. the T-equivalent or inverse-Γ models.

Variable phase-pole machines are envisioned in applications requiring a large torque-speed operating area. The control of these machines relies on accurate models and parameters but research on their parameter identification is scarce. This paper presents an offline parameter-identification method for variable phase-pole machines adopting a harmonic-plane decomposition model. The method employs standard tests with single-frequency three-phase excitation in multiple pole configurations and uses the results to minimize a constrained, regularized weighted least-squares problem. It relies on identifying a set of parameters common to all phase-pole configurations and transforming them into the adopted model. Good agreement is exhibited when comparing experimental results to an analytical harmonic-plane decomposition model using the inferred parameters. Steady-state, as well as pole transitions, are compared. The paper emphasizes the importance of performing measurements in multiple pole configurations and weighing these measurements appropriately to render an accurate set of parameters.

This paper analyzes the sensitivity of the rotor parameter estimation of an advanced Γ−model for multiphase induction machines. These machines exhibit inter-plane cross saturation and certain sub-topologies, such as variable phase-pole machines, may operate briefly with high rotor frequencies, which warrants the use of such models. It is shown that accurate non-linearity compensation of the voltage vector and characterization of the drive's input/output-delays is paramount for the rotor parameter estimation. Moreover, standstill experiments using a simple inverter excitation signal are designed to improve on the offline parameter estimation by means of a prediction error method. The presented method may find usage in (self-) commissioning of multiphase induction machines.

Variable phase-pole machines are envisioned in applications requiring a large torque-speed operating area. The control of these machines relies on accurate models and parameters but research on parameter identification methods is scarce. This paper presents an offline parameter-identification method for variable phase-pole machines adopting a harmonic plane decomposition model. The method employs standard tests with single-frequency excitation in multiple pole configurations and uses the results to minimize a constrained, regularized weighted least-squares problem. Good agreement is exhibited in simulations when comparing a harmonic-plane decomposition model of a variable phase-pole machine using the inferred parameters to a benchmark vector-space decomposition model implementing parameters identified in the standard tests. The paper emphasizes the importance of performing measurements in multiple pole configurations and weighing these measurements appropriately to render an accurate set of parameters.

Magnet-free variable phase-pole machines are competitive alternatives in electric vehicles where torque-speed operating region, reliability, cost, and energy efficiency are key metrics. However, their modeling and control have so far relied on existing fixed-phase and pole-symmetrical models, limiting their drive capabilities especially when switching the number of poles on the fly. This paper establishes the harmonic plane decomposition theory as a space-discrete Fourier transformation interpretation of the Clarke transformation, decomposing all pole-pair fields into a fixed number of orthogonal subspaces with invariant parameters. The model remains unaltered for all phase-pole configurations, guaranteeing continuity even under phase-pole transitions. Relations of the state and input space vectors, and model parameters to those of the vector space decomposition theory used for multiphase machines are established via the use of the complex winding factor. Experiments confirm the modeling theory and demonstrate its practical usefulness by performing a field-oriented-controlled phase-pole transition. Non-trivial configurations with more than one slot/pole/phase and a fractional phase number are also demonstrated.

Active short-circuit is a standard emergency procedure applied to three-phase permanent-magnet synchronous machine drives in battery-electric and hybrid electric drivetrains to comply with stringent automotive safety standards, such as the ISO 26262. Unfortunately, the ensuing torque and current transients can harm the passengers and the driveline itself. This paper develops and validates a mathematical and graphical method to determine the safe operating area of pre-fault current conditions to guarantee that the torque remains within user-defined acceptable bounds and that the permanent magnets do not demagnetize during the short-circuit transient. The new method utilizes an inductance-based dynamic model of the motor, including magnetic saturation. The proposed methodology promises to be useful in the design, initial testing, and commissioning of permanent-magnet synchronous machines used for the propulsion of automobiles.

To exploit the benefits of field-oriented controlled variable phase-pole machines, optimal current references need to be generated.This article proposes a steady-state Joule-loss minimization obeying inverter constraints and air-gap flux-density limitations.Different from previous attempts, the phase-pole configuration is not limited to exciting a single pole order. Instead, multiplepole-order fields are superimposed to accomplish the optimal current injection at all evaluated torque-frequency operating points.Two main conclusions are drawn from the solution to the optimization problem using experimentally identified parameters of avariable phase-pole machine. To begin with, adequate current injection extends the operating range. Secondly, the RMS currentis reduced, particularly in the high-torque region.

The active short-circuit is a standard safety measure for permanent-magnet synchronous machine drives in electric vehicles, but it can lead to harmful torque and current transients. This paper introduces a mathematical and graphical method to determine the safe operating area of pre-fault current conditions, complying with user-defined torque bounds and preventing magnet demagnetization during short-circuit transients. The method incorporates an inductance-based motor model considering magnetic saturation, which is used to outline a strategy for transitioning to safe initial conditions in the minimum time for the available voltage. Experiments on a 35 kW permanent-magnet synchronous machine support the efficacy of the proposed strategy, offering promise for its use in automotive propulsion where compliance to safety standards such as the ISO 26262 is paramount.

Variable phase-pole machines have the potential to extend the operational range to higher speeds through magnetic pole changes. The state-of-the-art vector space decomposition cannot model the transient behavior of the pole change for any possible phase-pole configuration as it creates a discontinuity. The proposed harmonic plane decomposition theory solves this issue by generalizing the vector-space decomposition to the fullest extend by using its discrete Fourier transformation interpretation. The theory for indirect rotor field-oriented control is developed using the harmonic-plane decomposition. A controlled, loaded pole change on a wound independently-controlled stator-coils machine using two transition strategies shows the harmonic-plane decomposition-based controller’s ability to maintain torque in the transition. Additionally, the proposed controller accomplishes real harmonic injection and balanced steady-state operation.