vector control of pmsm (step by step)

5/28/2018 Vector Control of PMSM (step by step)

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DEMO TITLES

Vector Control of Permanent Magnet Synchronous Motor

(PMSM)

Controllers design step by step

Author: Tshibain Tshibungu

Simsmart Technologies Inc.

Brossard, QuebecCanada

Software used: Simsmart Engineering Suite V6 (ES V6)


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1. OBJECTIVE AND DESCRIPTIONThe following document will help the user:

in designing step by step a drives of PMSM without flux weakening,

in designing a LC output filter.

Three test cases are done in order to test and validate using the power electronics components

from the Engineering suite V6 Electrical library.

1.1. Electrical and mechanical equations

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

using the following assumptions:

Saturation is neglected, The induced EMF is sinusoidal,

Eddy currents and hysteresis losses are negligible.

Voltage equations for Wye grounded through impedance motor under balanced conditions are

given by:

(1)

(2)

Fluxes linkages are given by:

(4) (5)Where the peak of the flux induced in the stator windings by the permanent magnetsThe developed torque motor is being given by:

(6)The mechanical torque equation is given by:

(7)


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Where Equations (4)-(5) into (1), (2) and (6) gives:

(8) (9) (10)For a constant torque angle control , we have . Hence, the electromagnetictorque will be:

(11)

Where

1.2. Current d and q axes controllers design

From (8) and (9) we have:

(12) (13)Where

Thus, the PI controllers that control both current axes (d and q) are calculated using the IMC

(Internal Model Control) and are given as follows:

For q axis


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For d axisWhere

Switching frequencyA feed forward compensation is done in order to calculate and(see diagram blockbelow).

1.3. Speed controller design

Since (11) shows that the torque depends only on q axis current, and knowing the closed looptransfer function of q axis current, the open loop transfer function is given as follows:

(14)Where

Poles placement method

We assume that the closed loop transfer function of q axis current is faster (as for a hysteresis

current control scheme), so

(15)Hence, the closed loop transfer function is given as follows:

(16)By placing poles at and and it will be assumed that is the dominant pole,we have:


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Thus, we have:

Symmetrical optimum method

Starting with equation (14) and knowing near crossover frequency, we have:

Hence, the closed loop transfer function is a third order model given as:

Applying the symmetrical optimum criterion, we have:

Hence, we have:

In order, to avoid a big overshoot the following filter should be placed after the speed

reference:


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1.4. Maximum speed before the flux weakening

Since this control is done before the flux weakening and neglecting the voltage drop, the

maximum electrical speed is obtained using the steady state equations of (8)-(9). Thus, we

have:

1.5. Diagram blocks

These diagram blocks show the overview of the motor control.

The diagram block control of VSI

The diagram block control of CSI


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1.6. LC Filter design

Assuming as the maximum frequency output by the inverter, which indirectly themaximum speed of the PMSM, the inductance is selected using the maximum voltage drop

allowed

Where

RMSThe capacitor is selected as follows:

Where Resonant frequencyMaximum frequency outputThe damping resistance is selected as follows:

The quality factor should be in the range of .Hence, for a desired , we have:


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2. PROCESSES DATAExample I

A PMSM has the following parameters:

A DC source supplies the motor through an inverter. At t = 0 s the referencespeed is set to 150 rad/s and reverse to -100 rad/s at t = 0.25 s. The maximum torque allows is

12 Nm. Simulate the motor drives using a voltage and current source drive PMSM. Repeat

voltage source drives PMSM with an input LC filter.

Example II


, A DC source supplies the motor through an inverter. At t = 0 s the referencespeed is set to 250 rad/s and reverse to -250 rad/s at t = 0.25 s. Simulate voltage source drives

PMSM with an input LC filter.

Example III


A DC source supplies the motor through an inverter. At t = 0 s the referencespeed is set to 120 rad/s. Simulate voltage source drives PMSM with an input LC filter.


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3. CONTROLLERS AND LC FILTER DESIGNExample I

Motor parameters

, , ,

Thus,

Case 1: Voltages source Inverter (VSI) drives PMSM

Current controller design

Selecting , we have: For q axis For d axisSpeed controller design

The speed reference filter is:


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Case 2: Currents Source (CSI) drives PMSM

The hysteresis control will be used where . So, only the speed controller is designed.Using the poles placement method at and , we have: Case 3: Voltages source Inverter drives PMSM with LC filter


allowed

Where


Where Resonant frequencyMaximum frequency outputSo, selecting

and knowing that

, the resonant frequency

should be in the range of: Thus, we select The damping resistance is selected as follows:


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The quality factor should be in the range of

.

Hence, for Current controller design

The capacitor and resistor of the filter can be ignored when designing the current controllers.

Hence, we have:

Selecting , we have: For q axis

For d axis

Speed controller design

The speed reference filter is simply ignored but it could be placed.


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Example II

Motor parameters

,

,

,

Thus,

Input LC filter design


allowed

Where


Where Resonant frequencyMaximum frequency output


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So, selecting and knowing that , the resonant frequencyshould be in the range of: Thus, we select

The damping resistance is selected as follows:



Hence, we have:

Selecting , we have: For q axis For d axisSpeed controller design



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Example III

Motor parameters

The max torque is

, , , Thus,

Input LC filter design


allowed

The capacitor is selected as follows:

Where

Resonant frequencyMaximum frequency output So, selecting and knowing that , the resonant frequencyshould be in the range of:


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Thus, we select The damping resistance is selected as follows:



Hence, we have:

Selecting , we have:

For q axis For d axisSpeed controller design



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4. SIMULATION PARAMETERSThe simulation was run in time domain with sample time of


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5. PROCESSES REPRESENTATION IN ES V6Case of VSI drives PMSM without LC filter

Case of VSI drives PMSM with LC filter


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Case of CSI drives PMSM without LC


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6. ENGINEERING SUITE V6 RESULTSExample I: Case of VSI drives PMSM without LC filter


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Steady state current without filter


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Example I: Case of VSI drives PMSM with LC filter


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Steady state current with filter


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Example I: Case of CSI drives PMSM without LC filter


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Steady state current without filter


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Example II: Case of VSI drives PMSM with LC filter


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Steady state current with filter


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Example III: Case of VSI drives PMSM with LC filter


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Conclusion

This document shows:

How to design controllers for PMSM drives,

How to design LC filter.

NB: All these test cases where simulated also using others well known software.

NB

In this document:

VSI (Voltage-Sourced Inverter) is simply means Voltages Control Inverter (VCI),

CSI (Current-Sourced Inverter) is simply means Currents Control Inverter (VCI).

7. REFERENCE BOOKS1. Voltage-Sourced Converters in Power Systems. Modeling,Control, and Applications.

A. Yazdani / R. Iravani.

2. Electric Motor Drives. Modeling, Analysis, and Control.

R. Krishnan.

3.

High Performance Control of AC Drives with Matlab/Simulink Models.H. Abu-Rub, A. Iqbal, J. Guzinski.

vector control of pmsm (step by step)

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