Vector Control of PMSM (step by step)
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Transcript of 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 PMSM has the following parameters:
, 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 PMSM has the following parameters:
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
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 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
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 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, 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 axisSpeed controller design
The speed reference filter is:
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Example III
Motor parameters
The max torque is
, , , Thus,
Input 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
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, 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 axisSpeed controller design
The speed reference filter is:
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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.