DEVELOPMENT OF AN EQUIVALENT CIRCUIT AND PERFORMANCE CHARACTERISTICS ANALYSIS OF SINGLE- PHASE PERMANENT MAGNET SYNCHRONOUS MOTORS

Abstract

Single phase permanent magnets synchronous motors are those motors that are operated from a single phase AC supply, runs at a constant speed and have the ability to remain magnetised even when external magnetic field is removed. An equivalent circuit of single-phase permanent magnet synchronous motor (SPPMSM) is proposed in this work.

A combination of the symmetrical component theory, d-q axes model of induction motor and two-reaction theorem based on the salient pole synchronous motor to realize positive and negative sequence voltage equations were applied. The resulting positive and negative sequence voltages were used to formulate the proposed equivalent circuit of this machine which is capable of induction motor action and synchronous motor action during starting and running respectively thereby offering more physical interpretation of the machine.

Identification of physical characteristics performances of this machine was carried-out through simulation in the MATLAB environment and the interpretations of these performances were given and analysed. From the performance characteristics, it suggests that the current value required to attain maximum power (730 watts) value is 4.376A. This in effect implies that the developed circuit offers a single-phase permanent magnet synchronous motor (SPPMSM) that is energy-efficient.

CHAPTER ONE

INTRODUCTION

1.1 Background of the Study

Single  phase  permanent  magnets  synchronous  motors  are  those  motors  that  are operated from a single phase AC supply, runs at a constant speed and have the ability

to remain magnetised even when external magnetic field is removed. The permanent

magnets embedded in  the  steel  rotor  of  these  motors helps  to  create  a  constant

magnetic field. The stator carries windings connected to sinusoidal AC supply which produces a pulsating rotating magnetic field in uniformly distributed stator winding. Since pulsating magnetic field can be assumed as two oppositely rotating magnetic fields, there will be no resultant torque produced at the starting and due to this deficiency, the Single phase permanent magnets synchronous motor does not start without external force. After giving the supply, if the rotor is made to rotate in either direction by external force, then the motor will start to run. Because of the constant magnetic field in the rotor, these cannot use induction windings for starting. These motors  require  a  variable-frequency power  source  to  start,  hence  a  capacitor  is required.   The   capacitor   can   be   electrolytic   for   starting   or   ceramics   for starting/running. The electrolytic start capacitor helps the motor achieve the most beneficial phase angles between auxiliary and main phase windings for the most locked-rotor torque per locked rotor current. It is disconnected from the start circuit when the motor reaches about 75% of full-load speed. The start capacitor is designed

for short-time duty. Extended application of voltage to the capacitor will cause premature failure, if not immediate destruction of the motor. Typical ratings for motor start capacitors ranges from 100 to 1,000-microfarads (μF) capacitance and 115 to 125

VAC. Though, special applications require 165 to 250-VAC capacitors, which are physically larger than capacitors of lower voltage rating for the same capacitance. The run capacitors are constructed similarly to start capacitors, except for the electrolyte. They are designed to serve continuously in the run circuit of capacitor- start/capacitor-run motors. They withstand higher voltages, in the range of 250 to 370

VAC. They also have lower capacitance, usually less than 65 μF. A typical configuration of the single phase permanent magnet motors can be represented as

shown in figure 1.1 below;

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Figure 1.1: Configuration of Single-Phase Permanent Magnet Synchronous Motors

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However, single-phase permanent magnet synchronous motors (SPPMSM) are fractional horse  power motors that are structurally similar to induction motors, except that permanent magnets are embedded in the caged rotor of the former [1, 2, 3-5]. In fact, it is a machine at which the excitation field is produced by permanent magnets instead of by dc field winding.   Some studies have indicated that neodymium iron boron (Nd-Fe-B) permanent magnet synchronous motors are around two-percent more

efficient  than  the  highest-efficiency  induction    motors  with  the  same  stator

laminations  and  similar  variable-frequency speed  controllers.  The  rotor  of  these motors can have many types of configurations since the inserted permanent magnets may vary in shapes, materials, sizes and positions which influence the performance of these motors [6, 7, 8]. This important modification allows such motors to have higher efficiency than the conventional induction motors and also makes the motor to operate at near unity power factor. With recent emphasis on high efficiency in electric motors, and the development of high energy power magnets, permanent magnet (PM) synchronous motors have been receiving much widespread interest over the last past few years [1, 3, 9]. Government legislations around the world to force the efficiency of the motor designs upwards and the gradual reduction in the cost of high-energy density permanent magnet materials, has made a significant growing interest that single-phase permanent magnet motors would be economically viable [10]. The use of Permanent  magnet  motors  can  help  to  achieve  the  new  requirements and  hence became a competitor to caged rotor induction motor in general purpose industrial applications due to its high efficiency, high power factor and its ability to self start from the  fixed frequency supply [3,  8,  11-14]. Unlike conventional synchronous

motors, a permanent magnet motor develops considerable break torque during its asynchronous mode of operation. The buried PM makes braking torque that weakens the asynchronous starting torque by means of cage bars in start-up operation [15].

The single phase permanent magnet motor starts asynchronously like induction motor and run synchronously as any other synchronous motor type. The induced currents in the rotor bars during the asynchronous operation will interact with the stator flux- linkages and a cage torque will be produced. This torque ensures the capabilities of the  motors.  Permanent  magnetisation of  the  rotor  makes  starting  more  difficult. Current generated by the rotating magnets causes a Joule loss in the stator circuit resistance, which results in a drag torque or magnet braking torque [15, 16, 17]. Torque oscillations during starting are not only higher, but also persist longer than those of induction motors. The DC offset responsible for transient oscillatory torque in the induction motor decays according to the rotor time-constant, but the permanent magnet sustains a non-decaying offset that causes oscillatory torques that persist until the motor has synchronised. For steady state (synchronous) operation of such motors, the permanent magnet provides an increased electromagnetic torque. The operation of these motors is complicated by the imbalance between the main and auxiliary winding voltages. The normal unbalanced stator excitation of this motor, results in positive and negative sequence components. The positive sequence components contribute to the synchronous motor action while the negative sequence components contribute to the induction motor action. The unbalanced stator impedances offer mutual coupling between these two symmetrical component circuits. For synchronous operation of the motor,  the  motor  is  represented by  torque  dependent impedance  [18].  It  is  also

interesting to  note  that  the  positive impedance takes  into  account the  degree  of excitation and saliency effects of the single-phase permanent magnet synchronous motor.

It is well known that induction motors suffer from relatively poor power factor, slip losses and low efficiency as compared to conventional synchronous motors [19-21]. Typically, a conventional synchronous and a dc commutator motors have some limitations such as extra dc source, noise, electromagnetic interference, etc. because of the application of commutator and brush gear assemblies [22]. The aforementioned problems have led to the development of internal permanent magnet (IPM) motors which have permanent magnet excitation in the rotor. The inherent limitations of induction motors and conventional synchronous motors are overcome by singly fed internal permanent magnet synchronous motors [22]. The popularity of IPM synchronous  motors  is  increasing  by  the  day  due  to  the  availability of  magnet materials with high energy density and cost-effective like Nd-Fe-B, Sm-Co and hard ferrites. One obvious change with the replacement of the electrical excitation with permanent magnet is the elimination of copper losses, simpler construction, lower weight and size for the same performance, and high efficiency.

Electric energy is very much essential in modern society and its availability and accessibility are the greatest engineering achievements in the past century. Modern life needs electric energy technologies that can control homes and workplaces climatic problems. To maintain and develop this energy-consuming technologies, availability of sustainable energy resources and their effective utilization through efficiency improvements  are  of  utmost  importance.  60-65%  of  the  generated  electricity  is

consumed by electric motors and about 15-20% of motor loads are used by single phase  motors [22].  Single-phase motors  are  widely used  in  small  and  fractional horsepower form in domestic, utility, and special purpose commercial markets. Compared with other motor types of the same size, single-phase permanent magnet synchronous motors are most efficient and powerful in terms of either synchronous pull out torque or torque angle with less noise or pulsating torque [22, 23]. Thus improvements in efficiency of these motors are one of the most effective ways to reduce primary energy consumption which causes global warming. Interior permanent magnet (IPM) synchronous motors are the latest choice of researchers due to their high efficiency, high power density, less noise operations, compact size compared to motor of the same performance, high reliability and low maintenance requirements. Interior permanent magnet (IPM) synchronous motor drives have been increasingly developed and widely used to meet the high efficiency and performance needs. As an awareness of the need for improved energy efficiency increases, there is a growing pressure for motors with increased efficiency even in household appliances. Over the past few years, permanent magnet synchronous (PMS) motors have received much wide   spread   interest   in   many   industrial   applications   which   require   precise synchronous operation with higher degree of rotational stability [24-45]. The line-start PMS motor requires a cage winding to develop the starting torque. The squirrel cage winding also protects the magnets from demagnetization during the start up transient and short circuit condition and also acts as a damper to the machine oscillations. Therefore, the line start PMS motor runs up toward synchronous speed, using its rotor cage winding for torque generation, and then attains synchronous speed through the

process of synchronization. The run-up torque is composed basically of a steady-state time averaged torque and a pulsating torque [46, 47]. The average torque is mainly responsible for driving the rotor to synchronous speed, while the pulsating torque produces noise and vibration during starting. The average and pulsating torques have their own individual components [46]. The average torque is composed of two components, namely the cage torque and magnet torque.

An equivalent circuit of this motor was sought to simplify calculation, and more broadly present the complex circuit in its simplest form in order to aid the steady state analysis. In its most common form, an equivalent circuit is made up of linear, basic passive elements resistance, inductance, and capacitance in a simple arrangement such that its performance would duplicate that of a more complicated circuit or network for proper physical interpretations of the motors. The equivalent circuit analysis gives all the  characteristics of  original  complex  circuit.  The  purpose  of  equivalent circuit analysis is to understand and analyze the complex electrical circuits in a simple and easy way. In electrical engineering, the characteristics and behaviour of electrical machines such as transformer, motors, and generators can be analyzed easily by this equivalent circuit analysis. The non linear parameters are the causes for complexity in the system. If any nonlinear complex parameters exist in the circuit, the equivalent circuit can be depicted by approximating that nonlinear parameter to an equivalent value of linear behaviour. Steady state and asynchronous performance evaluation can easily be evaluated with the aid of the equivalent circuit to identify the different torque components involved.

1.2  Statement of Problem

The single-phase permanent magnet synchronous motors (SPPMSMs) have received far less attention in the literature than the three-phase type even though the machine has higher potential for efficient improvement even at low ratings. Currently, there is a paucity of researches concerning the design of the motors. The difficulty of start-up and the longer start-up time result from the overlapping of the torque produced by permanent magnets and the torque produced by electromagnetic induction in the rotor bars. In particular, the torque produced by permanent magnet decreases the start-up torque, resulting in start-up problems. The design procedure and the design method of these motors are concentrated on the permanent magnet, the windings and the capacitors. The permanent magnet greatly affects the start-up and the synchronization and the windings and capacitors should be designed considering the output power and the symmetrisation conditions. A condition for balanced operation of this machine based on symmetrical component theory is needed to be derived for the equivalent circuit development and  steady state  analysis. The  complexity in  the  analysis is attributed to the unbalanced stator as well as electric asymmetries in the rotor. An equivalent circuit for this motor is proposed in this work to predict more physical interpretation of the motor and also to help in evaluating the steady state performances characteristics  of  these  machines.  Identification  of  the  physical  significance  of different torque components and arrival at an expression for this torques, which can be used in the preliminary design, is needed to ascertain the motor performances.

1.3  Research Objective

In this work, an equivalent circuit of single-phase permanent magnet synchronous motors (SPPMSMs) is proposed which gives more physical interpretation of this machine. The use of separate treatment based on the symmetrical component, d-q axes model of induction motor and two-reaction theorem based on the salient pole synchronous motor to realize positive and negative sequence voltage equations are to be applied. The voltage equations that evolves, will formulate the proposed equivalent circuit  of  this  machine.  This  will  then  help  us  in  analysing  the  steady  state performance characteristics of this machine.

1.4  Significance of the Study

As awareness of the need for improved energy efficiency increases, there is a growing pressure for motor with increased efficiency even in the household appliances. Single phase permanent magnet motors has a number of features which makes it an attractive choice for this type of high efficiency motor application. There is great potential for these types of motors to replace conventional single-phase induction motors in many domestic applications on account of their higher efficiencies when properly designed. With the proposed equivalent circuit of the machine, the physical interpretation of this machine can easily be seen and the steady state analysis can be performed. This in essence will help the researchers and more importantly the motor designers in carrying out future works.

1.6  Scope of the Study

The scope of this work is the application of accurate mathematical model of the motor characteristics arising from the unbalanced stator field and the rotor saliency. The

model relies on the combination of  symmetrical components to  cope with stator imbalance and reference frame transformations in the d-q axes to cope with the rotor saliency. Realisation of the various components of forward and backward voltage equations, formation of the proposed equivalent circuit in the steady state and performance analysis of the motor will summarise the research.

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