The paper assesses the determination of the inductances of five-phase permanent magnet machines with magnets not directly facing the airgap but surrounded by a laminated steel rim to secure the magnets (interior permanent magnet synchronous machines, IPMSM). This particular design increases the mechanical robustness of the rotor but precludes the use of known analytical expressions to estimate the inductances. Therefore, we estimate self and mutual inductances through static analysis with the Finite Element Method under different working conditions, thus obtaining three sets of parameters. As an approximation, we assumed that the inductances can be considered independent of the rotor position. However, they can change under the influence of the stator currents and saturation of the stator and rotor iron parts. To assess the accuracy and correctness of each set of inductances, we used them in an analytical model of an existing prototype; subsequently, we compared the stator currents and the electromagnetic torque under steady state with corresponding results obtained through the Finite Element Method using the package ANSYS-Maxwell®. From this comparison, we concluded that the most appropriate inductances are those obtained without magnets in the rotor.

This work presents a new method to estimate the electrical parameters of five-phase permanent magnet synchronous machines, including those related to the third-harmonic of the air gap induction, based on the instantaneous impedance of the stator. Besides rotor speed, the proposed procedure requires the measurement of stator phase voltages and currents during a transient no-load startup. The estimates of the parameters are the solution of an optimization problem that compares experimental instantaneous impedances of d-q models with their analytical counterparts. Simulation results indicate the potential of the proposed method to provide accurate estimates of the electrical parameters and flux linkages produced by the permanent magnets. Finally, an accurate knowledge of electrical parameters is essential to several high-performance applications.

This work presents a method to estimate the electrical parameters of the double-cage model of induction motors using only data available in manufacturer data sheets. The parameters are obtained by solving a numerical optimization problem based on the steady-state equations of the induction motor and the manufacturer data through the Genetic Algorithm. To test and validate the method, we present experimental results of 100 motors with power ranging from 35 to 75 kW. These results prove the validity of the proposed method to provide adequate parameters that can be used to accurately reproduce the main steady-state performance characteristics of induction motors.

We propose a method to estimate the electrical parameters of the single-, double- and triple-cage models of induction motors using manufacturer data, such as starting torque, breakdown torque, rated torque, starting current, rated current, power factor, and efficiency. The method is based on a numerical optimization problem involving the equations of the single-, double- and triple-cage steady-state models and manufacturer data available to end-users usually in form of data sheets. To validate the method, we compare theoretical with experimental results obtained for a 75 kW motor. Both types of results prove the validity and accuracy of the proposed method to assess the main performance characteristics of induction motors.

The distribution of the induction in the airgap of five-phase induction machines operating with an open phase is investigated. Analytical expressions are given in terms of steady-state symmetrical components which are related directly to the airgap induction. It is shown that under fault, third harmonic induction components arise which can potentially produce extra magnetic losses in the stator and rotor. Three operation modes are assessed: uncontrolled, current control with joule losses minimization, and current control with equal stator currents. The results for a prototype machine are discussed considering winding losses, torque pulsations, and the distortion of the airgap induction compared with the normal operation.

The unbalanced operation of five-phase induction machines is described using the method of steady state symmetrical components and including aspects not yet considered, such as the changes in the airgap induction. Starting from the dynamic equations, described by instantaneous symmetrical components, sequence equations are obtained in terms of steady state symmetrical components, thus establishing a clear relationship between these two methods. The sequence equations allow to determine the machine performance under any unbalanced operation in a simple and direct way. Furthermore, the approach followed here allows to analyze the machine from the point of view of positive- and negative-rotating fields, as each symmetrical component can be associated with a distinct rotating field in the airgap. Analytical expressions are derived for the mean and pulsating torque produced by each steady state symmetrical component. Further, analytical expressions of the induction in the airgap are also derived as a function of sequence currents. It is demonstrated that, besides a positive- and a negative-rotating fundamental induction wave, two additional waves with triple pole pair number are created in the airgap, rotating at 1/3 of the speed of the fundamental wave. Finally, it is shown that, similar to three-phase machines, currents with high-frequency components are induced in the rotor. The model presented is useful not only to analyze but also to design five-phase machines capable of working under unbalance. The second part of the paper presents typical applications of the model described here.

In the first part of the paper, a complete model to describe the unbalanced operation of five-phase induction machine is presented. To show the application and validity of this model, in this second part, it is applied to study two typical cases: voltage unbalance and loss of one stator phase. The data used here refer to a five-phase prototype machine of 5.5 kW. Special attention is given to those effects not yet fully addressed in other works, such as additional harmonic induction components in the airgap and high-frequency currents in the rotor windings. These effects can increase the winding and magnetic losses and also change the saturation of the iron parts, thus changing the machine parameters and torque capability. The determination of the additional rotating fields created in the airgap under unbalance helps understand the way pulsating torques and rotor induced currents are produced. The cases studied show that the approach followed can help not only to better understand how the machine works under unbalance, but also provides a powerful tool to design and analyze multiphase machines.

Computer aided design tools are nowadays important for a variety of engineering fields. One of the most used tool is MATLAB/Simulink®, which has a broad variety of libraries and is recognized by its reliability. This paper presents a toolbox library for simulation and prototyping of control techniques for three and five phase induction machines, developed in MATLAB/Simulink®and to be used with dSPACE®DS-1104 platform. The software tools and the hardware platform are both described and provide an integrated environment which allows the user to develop and evaluate control techniques for induction machines by means of pure simulation as well as executing them on an underlying hardware platform connected to the machine. The transition from simulation to a hardware platform are done transparently for the user using rapid prototyping tools.

The steady state operating curves of three design variants of a five-phase induction machine are assessed and compared to a standard three-phase induction machine of the same size which is taken as the basis for the comparison. The performance in terms of torque, power factor, stator current and efficiency are analyzed for different load conditions. The operating curves are determined by means of an electrical model that includes the effects of the third-harmonic component of the airgap induction, iron saturation and magnetic losses as well. The electrical parameters used in this model are obtained analytically. Based on the data of the machines considered, it is shown that five phase machines can have a slightly better performance than an equivalent three-phase machine, even when they have less conductor volume in the stator and rotor windings. The results also show that five-phase machines considered can present a higher peak torque and thus a better overload capacity.

The paper addresses a comparison between the performance of a five phase and a three phase prototype induction machine under steady state. The main aspects included in the comparison are: torque capability, efficiency, power factor, losses and active volume. An analytical model for steady state including losses and saturation is also presented; the model also considers the effect of the third harmonic airgap induction, which in the case of five phase machine can be used to reshape the airgap induction and increase the torque capability. The comparison is based on the data of two prototypes having the same frame size and about the same volume of conducting material and iron. The performance comparison shows that some advantages of high phase machines are in fact limited by losses and demand a specific design to be effectively achieved.

The paper assesses the torque capability of high phase induction machines taking a conventional three phase machine as the basis for comparison; analytical expressions for torque as a function of phase number for machines with sinusoidal and trapezoidal airgap field are derived and discussed. A trapezoidal field is assumed to be produced through the imposition of a third harmonic current in the stator current besides the fundamental. The torque capability comparison is performed keeping the airgap peak induction and the linear stator current constant, thus resulting about the same amount of magnetic and winding losses for variable phase number. It is shown that the main factors influencing the torque capability of machines with sinusoidal airgap field are the winding characteristics - including number of slots per phase and pole - and the winding pitch. Higher torques are associated with windings without pitch shortening and with low values of slots per phase and pole. It is also shown that machines with trapezoidal field can have higher torque capability than sinusoidal field machines, being the greatest torque improvement associated with low values of slots per pole and phase. Under the assumptions made, torque improvements from 10% to 15% can be obtained. The paper also shows that for sinusoidal field machines, the maximal torque practically obtained with seven phases, while for trapezoidal field the maximal torque is obtained with eleven phases.