pmsg documentation.docx

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4.5 PMSM AND MODELING OF PMSM

4.5.1 INTRODUCTION

A synchronous machine is an ac rotating machine whose speed under steady state

condition is proportional to the frequency of the current in its armature. The magnetic field

created by the armature currents rotates at the same speed as that created by the field current on

the rotor, which is rotating at the synchronous speed, and a steady torque results. Synchronous

machines are commonly used as generators especially for large power systems, such as turbine

generators and hydroelectric generators in the grid power supply. Because the rotor speed is

proportional to the frequency of excitation, synchronous motors can be used in situations where

constant speed drive is required. Since the reactive power generated by a synchronous machine

can be adjusted by controlling the magnitude of the rotor field current, unloaded synchronous

machines are also often installed in power systems solely for power factor correction or for

control of reactive KVA flow. Such machines, known as synchronous condensers, may be more

economical in the large sizes than static capacitors.

With power electronic variable voltage variable frequency (VVVF) power supplies,

synchronous motors, especially those with permanent magnet rotors, are widely used for variable

speed drives. If the stator excitation of a permanent magnet motor is controlled by its rotor

position such that the stator field is always 90o (electrical) ahead of the rotor, the motor

performance can be very close to the conventional brushed dc motors, which is very much

favoured for variable speed drives. The rotor position can be either detected by using rotor

position sensors or deduced from the induced emf in the stator windings. Since this type of

motors does not need brushes, they are known as brushless dc motors.

4.5.2 Synchronous Machine Structure:

The armature winding of a conventional synchronous machine is almost invariably on the

stator and is usually a three phase winding. The field winding is usually on rotor and excited by

dc current, or permanent magnets. The dc power supply required for excitation usually is

supplied through a dc generator known as exciter, machine which is often mounted on the same

shaft as the synchronous. Various excitation systems using ac exciter and solid state rectifiers are

used with large turbine generators. There are two types of rotor structures: round or cylindrical



rotor and salient pole rotor as illustrated schematically in the diagram below. Generally, round

rotor structure is used for high speed synchronous machines, such as steam turbine generators,

while salient pole structure is used for low speed applications, such as hydroelectric generators.

The pictures below show the stator and rotor of a hydroelectric generator and the rotor of a

turbine generator.

Fig 4.1: Cylindrical rotor and Salient rotor structures

4.5.3 Permanent magnet synchronous machine:

The diagram below illustrates the cross sections of two permanent magnet synchronous

machine. The development of advanced magnetic materials, power electronics and digital control

systems are making permanent magnet (PM) machine as an interesting solution for a wide range

of applications. The advantages of PMSM compared to other AC machines are its simple

structure, high-energy efficiency, reliable operation, high power density and possibility of super

high speed operation. Recent important applications of permanent magnet synchronous machineare in the area of distributed generation, mainly in wind and micro turbine generation systems.

An advantage of a high speed generator is that the size of the machine decreases almost in

directly in proportion to the increase in speed, leading to a very small unit. Super high speed

PMSM is an important component of single shaft MTG system. In a permanent magnet

generator, the magnetic field of the rotor is produced by permanent magnets. Other types of

generator use electromagnets to produce a magnetic field in a rotor winding. The direct current in

the rotor field winding is fed through a slip-ring assembly or provided by a brushless exciter on

the same shaft. Permanent magnet generators do not require a DC supply for the neither

excitation circuit nor do they have slip rings and contact brushes. However, large permanent

magnets are costly which restricts the economic rating of the machine. The flux density of high

performance permanent magnets is limited. The air gap flux is not controllable, so the voltage of

the machine cannot be easily regulated. A persistent magnetic field imposes safety issues during



assembly, field service or repair. High performance permanent magnets, themselves, have

structural and thermal issues. Torque current MMF vectorially combines with the persistent flux

of permanent magnets, which leads to higher air-gap flux density and eventually, core saturation.

In this, permanent magnet alternators the speed is directly proportional to the output voltage of

the alternator.

Fig 4.2: Permanent Magnet Synchronous Machine

4.5.4 Advantages of synchronous generator

They are more stable and secure during normal operation and they do not require

an additional D.C supply for the excitation circuit.

The permanent magnet synchronous generators avoid the use of slip rings, hence

it is simpler and maintenance free.

Higher power coefficient and efficiency. Synchronous generators are suitable for

high capacities and asynchronous generators which consume more reactive power

are suitable for smaller capacities.

Voltage regulation is possible in synchronous generators where it is not possible

in induction types. Condensers are not required for maintaining the power factor

in Synchronous generators, as it is required in induction generators, closed gap

induction.

4.5.5 PMSM driven Wind turbine

An analytical model of a small PMSM is used to investigate the effect of controlling the dc link

voltage on the capture of maximum power. The model relates the dc link voltage of the machine

to its rotor speed. It neglects magnetic saturation. The effective air gap in a PMSM with magnets

mounted on the rotor surface can be considered constant and relatively large. This is due to the

relative permeability of the PM material being close to unity. The d and q-axis synchronous



reactances are consequently identical. The generator armature current can be related to the torque

and induced voltage as follows:

T=K tIa (4.1)

E=K eIa (4.2)

Control over the rotor speed can be achieved simply by varying the generator terminal voltage.

The steady state terminal voltage of the generator can be determined for a machine with

negligible saliency can be expressed as:

V = ( ) aR a sin (4.3)

It is assumed that the generator is connected to a diode rectifier and assumed that the phase

voltage and fundamental component of the armature current of the generator are in phase. Then

the above equation can be written as

Va= IaR a ( 4.4)

The rectified dc-link voltage may be obtained using the standard equations for a three-phase full-

bridge diode rectifier taking the effect of commutation overlap into account as

√

V-2 (4.5)

Using above equations, it is possible to obtain a prediction for the dc-link voltage as a function of

the terminal phase voltage or mechanical speed and TSR. The figure shows the optimum relation

between the dc voltage and the rotor speed for the capture of maximum power when the

generator operates at the peak power coefficient Cp max and TSR. Considering the previous

equations, a sudden increase in wind speed will decrease both TSR and Cp . An increase in the

wind speed will result an increase in the torque transmitted from the turbine to the generator.

Then, the turbine will try to accelerate in response to an increase in wind speed. An acceleration

of the turbine will result in an increase in the commanded dc-link voltage (i.e., dc-link voltage

will increase in response to an increase in wind speed). When the wind speed falls rapidly, a

sudden decrease in wind speed will result in a high TSR and C p

will decrease, decreasing the

torque. With low applied torque to the generator, the inductance and inertia of the system will

result in a braking torque being applied, slowing the generator and turbine. The reduction in

speed will lower the dc – link voltage.

4.6 MODELING OF PM DRIVE SYSTEM



This chapter deals with the detailed modelling of a permanent magnet synchronous motor. Field

oriented control of the motor in constant torque and flux-weakening regions are discussed.

Closed loop control of the motor is developed using a PI controller in the speed loop. Design of

the speed controller is discussed.

4.6.1 Detailed Modelling of PMSM

Detailed modelling of PM motor drive system is required for proper simulation of the system.

The d-q model has been developed on rotor reference frame as shown in figure 4.3. At any time

t, the rotating rotor d-axis makes and angle ¸r with the fixed stator phase axis and rotating stator

mmf makes an angle ± with the rotor d-axis. Stator mmf rotates at the same speed as that of the

rotor.

Figure 4.3 The d-q model has been developed on rotor reference frame

The model of PMSM without damper winding has been developed on rotor reference frame

using the following assumptions:

1) Saturation is neglected.

2) The induced EMF is sinusoidal.

3) Eddy currents and hysteresis losses are negligible

4) There are no field current dynamics

Voltage equations are given by: (4.6)

(4.7)

Flux Linkages are given by

(4.8)

(4.9)

Substituting equations 4.8 and 4.9 into 4.6 and 4.7

( ) (4.10)



( ) (4.11)

Arranging equations 4.10 and 4.11 in matrix form

[

] [

] [

] (4.12)

The developed torque motor is being given by

()( ) (4.13)

The mechanical torque equation is

(4.14)

Solving for the rotor mechanical speed from equation 4.14

∫ )dt (4.15)

And

= (4.16)

In the above equations r is the rotor electrical speed m

is the rotor mechanical speed.

4.6.2 Parks transformation and d-q modellingThe dynamic d-q modelling is used for the study of motor during transient and steady state. It is

done by converting the three phase voltages and currents to dqo variables by using parks

transformation. Converting the phase voltages Vabc to Vdq0 variables in rotor reference frame the

following equations are obtained.

=

(4.17)

Convert Vdq0 to Vabc

=

(4.18)

4.6.3 Equivalent circuit of permanent magnet motor



Equivalent circuits of the motors are used for study and simulation of motors, from the d-q

modelling of the motor using the stator voltage equations the equivalent circuit of the motor can

be derived. Assuming rotor d axis flux from the permanent magnets is represented by a constant

current source as described in the following equation,

(4.20)

Figure 4.4 permanent magnet motor electric circuits without damper windings

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