Simplified simulation methods for polyphase brushless DC motors

Abstract

This paper presents a simulation method for brushless DC motors. The purpose of this method is to provide a solution to the initial design process, where the simulation speed is important due to the numerous variables that have to be considered. The method requires a reduced number of parameters in order to simplify it and to facilitate the design process. It is applicable to polyphase motors regardless of its connection or phase number. The simulation method can simulate the phase current control system or a DC bus current feedback system. The later control system is widely used in low-cost brushless DC motors. The simulation method is based upon the average value modelling of the inverter leg, at the PWM scale, in different modulation conditions, modelling almost all the inverter structures with transistors as active elements. The experimental results from a seven-phase brushless DC motor with one uncontrolled phase validate the modelling method. The comparison of the average torque, the current, voltage and torque waveforms in several operating conditions shows that the simulation method can predict the comportment of a brushless DC motor without an excessive computational burden, so it can be readily used as a design tool for this kind of motor.

Introduction

The time constants involved in the operation of a drive are varying on a wide range. For example, the thermal time constants used to study the thermal behaviour of the drive under specific application operation cycles can be up to 10⁵ times higher than the time steps witch are necessary to study the detailed commutation of the inverter switches. A global simulation approach taking account of all the thermal, mechanical and electrical transient operations of the drive is not applicable because the simulation speed will be totally inefficient. Suitable simplifying assumptions must be adopted to model the system on a frequency range adapted to the kind of specific behaviour to study. When a simulation tool is used as a part of a global optimisation process with a lot of iterations, it is very important to use specific methods which present a good compromise between precision and computation speed.

According to these problems, this paper presents a general simulation method for an efficient computation of the torque-speed characteristics of the drives using polyphase brushless DC motors fed by a PWM inverter with a current regulation. The method is based upon an estimation of the average value of voltages and currents on each PWM period to improve the simulation speed. The use of average variables has been widely used for the simulation of static converters or for the design of their control system [4], [6]. The averaging method has been extended to resonant converters [7], [12], to study of the discontinuous conduction operation mode [9] and even for SPICE equivalent circuits [1], [11].

Several methods have been proposed in the literature for the modelling of brushless motor drives by use of the average variables. In [5], an analytical approach is developed with some numerical approximations. The model is using the abc variables, and the neutral-point voltage to determine the motor phase voltages. In [10], a model with Park variables adapted to three phase machines and square wave currents is presented. In this paper, the authors report that there are several problems to predict the behaviour with a phase angle advance. This motor model assumes that there is no zero sequence of emf and it calculates the neutral voltage to obtain the individual phase voltage. Reference [2] shows that it is possible to use the neutral voltage in the control system to improve the performance. Another approach to the polyphase brushless DC motor modelling is presented in [3] with an exhaustive approach for a five-phase motor. It is possible to model a hysteresis controller using an optimisation process as in [4]. Reference [8] presents a combined simulation system with variable degrees of complexity.

The simulation method presented in this paper is using a linear function to approximate the non-linear behaviour of the voltage inverter. When it is compared to the previously developed approaches, the proposed model is different.

• It is independent of the number of phases and of the machine winding connections.

• It can be used to simulate many modulation and control strategies like the DC bus current control strategy widely used in brushless DC drives.

• It takes into account the commutation of the phase currents and the electromagnetic torque pulsations.