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.

Multiphase electrical machines are inherently fault tolerant due to the higher number of phases. An important step in achieving a fault tolerant control is the ability to detect and identify the fault. In variable phase-pole drives, which are a class of multiphase machines that change the number of pole pairs during real-time operation, there are further unexplored possibilities. Based on the harmonic plane decomposition theory for variable phase-pole machines, a fault detection and identification algorithm is proposed, which analyzes the spatial harmonics of the current distribution. The fault detection is fast, operation independent, non-invasive, parameter-insensitive, and computationally simple. Experimental tests validate the proposed method.

Automotive applications are revisiting the use of induction machines as magnet-free propulsive solutions due to theirintrinsic robustness and reliability. Special multiphase configurations are under investigation to reduce the losses further andfulfill the stringent energy-efficiency and compactness requirements of the automotive industry. One of these configurations isknown as variable-pole machines, which allows the number ofmagnetic pole pairs to change on the fly. These machines canstretch the torque-speed operating region, exploit the maximumtorque capability, and exhibit competitive efficiency. Althoughfault tolerance has been widely explored for multiphase machines,the same cannot be said for variable-pole machines because,until recently, complete models to describe their dynamics under any condition, including magnetic pole changing and faultoccurrences, were unavailable. This paper presents a post-faultcontrol strategy for variable-pole machines with an open-phasefault, which can operate during pole changing and addressesthe issue of fault-tolerant operation. The effectiveness of thecontrol system is verified by experimental tests carried out withan eighteen-phase variable-pole induction machine prototype.

Induction machine-based multiphase electrical ma-chines combine the robustness and reliability of well-knowninduction machines with the benefits of additional degrees offreedom, such as potential higher torque density and true faulttolerance. The subcategory of variable phase-pole machinesallows extending the operational torque and speed range withthe same voltage and current limits by changing the number ofmagnetic poles through control without hardware reconfigura-tion. Maintaining the torque throughout the operation is vital formany applications. The question of maintaining torque during apole transition still needs to be answered, especially concerningthe electric limitations. This paper’s proposed pole transitionstrategy minimizes the torque dip during the pole transition.Field weakening is added to the control scheme to accommodatethe voltage limitation. Experimentally controlled, loaded, andscheduled pole transitions demonstrate the capabilities of theproposed strategy with and without voltage limitation.

This paper presents a sensorless motor drive for a seven-phase induction machine that exploits the degrees of freedom of the multiphase system. The proposed solution involves the injection of a low-frequency current to excite the spatial third harmonic component of the magnetic field in the airgap, thereby enabling the estimation of the third spatial harmonic component of the flux linkage. The injection of a low-frequency current enables the precise estimation of rotor flux position at zero and at very low speeds, without torque ripple, which is a critical aspect for the effectiveness of a sensorless drive. 

The experimental tests conducted under different operating conditions verify the robustness of the proposed solution, as well as its promising dynamic response and stable behavior at zero and low speeds.

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.

In this first paper of a two-part series, the harmonicplane decomposition is introduced, which is an extension of the vector-space decomposition. In multiphase electrical machines with variable phase-pole configurations, the vector-space decomposition leads to a varying numbers of vector spaces when changing the configuration. Consequently, the model and current control become discontinuous. The method in this paper is based on samples of each single slot currents, similarly to a discrete Fourier transformation in the space domain that accounts for the winding configuration. It unifies the Clarke transformation for all possible phase-pole configurations such that a fixed number of orthogonal harmonic planes are created, which facilitates the current control during reconfigurations. The presented method is not only limited to the modeling of multiphase electrical machines but all kinds of existing machines can be modeled. In the second part of this series, the harmonic plane decomposition will be completed for all types of machine configurations.

In this paper, lumped parameters for a variable phase-pole induction machine with wound independently controlled stator coils are computed using finite-element simulations. Differently from finite-element simulations of conventional electrical machines, this solution uses a per-solenoid approach.

Multiphase electrical machines have the inherentadvantage of fault tolerance as compared to conventional threephasemachines. A special category of multiphase electricalmachines are variable phase-pole machines, which allow a changebetween phase-pole configurations without hardware reconfiguration,but merely through current control. This paper proposesan open-fault detection method for variable phase-pole machines; fast, non-invasive, parameter- and operation-independent. Themethod analyzes the space harmonics of the current distributionusing the harmonic plane decomposition theory, which isalready used to perform a seamless switch between phase-poleconfigurations. Simulation results demonstrate the feasibility ofthe approach.

Multiphase electrical machine are inherently truefault tolerant, which is a key difference as compared to conventionalthree-phase machines. The subgroup of variable phase-polemachines have the ability to change phase-pole configurationsonly through current control. Due to the higher availabilityand simpler construction, three-phase voltage source invertersmodules are often used for multiphase electrical machines.While many approaches exist for one single open-phase fault,this paper proposes an open-fault detection method capable todetect the failure of an entire three-phase module for variablephase-pole machines. It is an extension to the harmonic-planedecompositionfault detection analyzing the instantaneous spaceharmonic content of the current distribution. Simulation resultsdemonstrate the feasibility of the approach.

A special subcategory of multiphase electrical ma-chines are the so called variable phase-pole machines. They have the ability to electronically change the number of pole- pairs without any hardware reconfiguration. Moreover, they are inherently fault tolerant due to the higher number of independent windings. These two virtues offer new possibilities for a drivetrain with higher power density and a new level of reliability. This paper presents an adapted post-fault controller performing a pole transition with an open-phase fault. The drive changes the number of pole-pairs without loosing the torque during the transition and minimizes the stator copper losses simultaneously. The validity of the presented control is shown in simulations.

Multiphase machines offer more degrees of freedom than conventional three-phase machines. Thus, a multiphase drive can control multiple spatial harmonics independently of each other. With the torque generation in the 1st vector space, this paper proposes to inject currents in the 3rd vector space for the speed estimation thus realizing a sensorless control scheme. At lower mechanical speeds, the back-EMF decreases and becomes more difficult to estimate as the signal-to-noise ratio decreases. Injecting a slip increases the stator frequency, which in turn allows a better estimation of the back electromotive force. An experiment showing a start from standstill conditions demonstrates the proposed control.

The Clarke transformation is mathematically a Vandermonde matrix of a discrete Fourier transformation. Its purpose is to transform space-vector quantities in the space domain. One necessary condition is that the base function forms an n-th root of unity. This condition translates into requiring all sampling points to be equally spaced. However, manufacturing constraints and imperfections in electric machines may result in non-equally spaced magnetic axes, especially in the case of multiphase electrical machines, making the conventional inverse Clarke transformation used in classic vector control inaccurate. The mathematical inverse Clarke transformation solves this issue, and the existence of this matrix is always ensured. This avoids additional control action and for model predictive controllers, an accurate model is crucial. Analytical results and a simple experimental validation on a multiphase induction machine show the improvements introduced by changing the transformation matrix.

This work proposes a variable switching frequency scheme for a flying capacitor multilevel (FCML) converter in dc-ac operation to better utilize the output inductor for its rated peak-to-peak current ripple and substantially reduce converter losses over the ac line cycle. The proposed technique holds the inductor current ripple constant by leveraging the duty-cycle dependent inductor current ripple, and variably changes the switching frequency to hold this constant at its rated design value. Practical lower switching limits are taken into consideration in developing this approach, and experimental results validate the feasibility in a common micro-controller framework. Hardware results are provided for a 400 Vdc to 240 Vrms 6-level FCML inverter and showcase loss reductions on the order of 10 − 35% across the measured power range, compared to conventional control with fixed frequency operation.

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.