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DEMO TITLES

Vector Control of Induction Motor Controllers design step by step

Author: Tshibain Tshibungu Simsmart Technologies Inc.

Brossard, Quebec Canada

Software used: Simsmart Engineering Suite V6 (ES V6)

A-PDF Merger DEMO : Purchase from www.A-PDF.com to remove the watermark

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1. OBJECTIVE AND DESCRIPTION

The following document will help the user in designing step by step a drives of Induction Motor without flux weakening. Three test cases are done in order to test and validate the design using the power electronics components from the Engineering suite V6 Electrical library. The motor will be driven using Current-Sourced Inverter (2-Level Voltage) and Voltage-Sourced Inverter (Cascaded H-Bridge or CHB 7-Level Voltage).

2. Electrical and mechanical equations

The following equations described the behavior of an induction motor in arbitrary reference frame (without saturation):

(1)

(2)

(3)

(4)

(5)

Fluxes linkages are given by: (6)

(7) (8) (9)

(10)

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3

The electromagnetic torque developed by the motor

(

) (11)

The mechanical equation is given by:

(12)

Where

3. Indirect Field Oriented Control

If we choose a new dq axis rotating at synchronous speed and aligned with the rotor field, that means , the electromagnetic torque will be:

(

) (13)

If is constant, the electromagnetic torque will depend only on .

Equation (9), gives:

(14)

Equation (14) into (13) yields,

(

)

(15)

Since , equation (5) gives:

(16)

Since we want to be constant which implies that (using equation (4)), we have: (17) Hence, (14) and (17) into (16) gives:

(18)

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4

Equation (18) represents the slip between the rotor field versus the rotor position. If the magnitude of has to be changed, (4), (10) and knowing that , we have:

(19)

Where

4. Current-Sourced Inverter

The inverter is controlled by hysteresis control. Thus, only the speed and flux controllers will be designed. Speed controller design Using (12) and (15), and assuming that the load torque is proportional to the speed, the mechanical equation in Laplace form is given as:

Where

(

)

,

,

The following diagram block is used to design the speed controller.

Since (15) shows that the torque depends only on q axis current, the open loop transfer function is given as follows:

(21)

Hence, the closed loop transfer function is given as:

(22)

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By using the pole placement method, one can place poles at and and it will

be assumed that is the dominant pole, we have:

,

Thus, we have:

,

Flux controller design Using equation (19), the open loop transfer function is given as follows:

( )

(23)

The following diagram block is used to design the flux controller.

Thus, the flux PI controller is calculated using the IMC and is given as follows:

Where

Time constant of the flux closed loop transfer function

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The diagram block control of Current-Sourced Inverter

5. Voltage-Sourced Inverter

The inverter is controlled by a carrier-based PWM technique. Thus, current, torque, flux and speed controllers will be designed. From (9)-(10), we have:

(24)

(25)

So, (24)-(25) into (6)-(7), we have:

(26)

(27)

With

7

7

Since and substituting equations (24)-(25) into (4)-(5) in synchronous reference

frame, we have:

(

) (28)

(

) (29)

Using (26)-(27) and the motor equations (1)-(2) in synchronous reference frame, we have:

(30)

(31)

Using (28)-(29) into (30)-(31), we have:

(

)

(

)

We know that , the above equations become:

(

)

(

)

Current controller design Since the system is coupled, let’s decoupled it by using the following new variables:

(30)

(31)

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8

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 d and q axes

Where

Time constant of the current closed loop transfer function with

Switching frequency

Flux controller design The speed controller is designed using the following block:

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The open loop transfer function is given as follows:

( )

If , the open loop transfer function as follows:

( )

Thus, the flux PI controller is calculated using the IMC and is given as follows:

Where

Time constant of the flux closed loop transfer function

Suggestion: Select

A complete flux controller is designed by using the symmetrical optimum criterion. Thus, we

have:

Torque controller design Since the flux must be constant, the torque controller is designed using the following block:

The open loop transfer function will be:

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10

Where

(

)

Thus, the PI torque controller is calculated using the IMC and is given as follows:

Where Time constant of the torque closed loop transfer function

Suggestion: Select

Speed controller design The speed controller is designed using the following block:

The open loop transfer function is given as follows:

Where

Knowing that near crossover frequency, we have:

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

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Applying the symmetrical optimum criterion, we have:

( ) ( )

( )

Hence, we have:

,

The diagram block control of Voltage-Sourced Inverter

Note that for CHB (Cascaded H Bridge) m-Level, the modulation index is calculated as follows:

(

)

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2. PROCESSES DATA

Example I An Induction Motor has the following parameters: ,

,

At t = 0 s the reference speed is set to 120 rad/s and reverse to -120 rad/s at t = 1.6 s. The maximum torque allows is 300 Nm. Simulate the motor drives using a Voltage-Sourced Inverter (CHB 7-Level Voltage) and Current-Sourced Inverter (2-Level Voltage).

Example II The motor selected is an ABB M3BM 450 LB [1] and the average motor parameters are taken from [2] (See table 6.3.). (Mechanical power), .

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The maximum torque allows is 4500 Nm. Simulate the motor drives using a Voltage-Sourced Inverter (CHB 7-Level Voltage) and Current-Sourced Inverter (2-Level Voltage). For VSI, at t = 0 s the reference speed is set to 120 rad/s and to 70 rad/s at t = 3.5 s. For CSI, at t = 0 s the reference speed is set to 200 rpm and to 1492 rpm at t = 1 s. Example III An Induction Motor has the following parameters [3]: ,

, , , ,

At t = 0 s the reference speed is set to 1189 rpm and to 200 rpm at t = 3 s. The maximum torque allows is 7490 Nm. Simulate the motor drives using a Voltage-Sourced Inverter (CHB 7-Level Voltage) and Current-Sourced Inverter (2-Level Voltage).

3. CONTROLLERS DESIGN

3.1. RATED FLUX CALULATION

Example I

, , ,

√

√ ,

Under no load and in rated condition, the slip is zero. From (1)-(10) we have:

(

) (

)

(

)

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14

(

) (

)(

) (

)

So, the rotor rated flux is calculated as follows:

√ ( )

Example II For this example, we assume what follows: , From the table 6.3., the base power, impedance and inductance are:

So, the average parameters for 962 HP motor in per unit are:

Assuming that , we have:

Hence, the Induction Motor parameters in real values are:

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The rotor rated flux is calculated as follows: , ,

√

√ ,

(

) (

)

(

)

(

) (

)(

) (

)

√ ( )

Example III For this example, we assume what follows:

The rotor rated flux is calculated as follows:

, ,

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√

√ ,

(

) (

)

(

)

(

) (

)(

) (

)

√ ( )

Notice that the rotor flux calculated is nearly equals to the rated value given.

3.2. CURRENT-SOURCED INVERTER

Example I

(

)

,

,

The hysteresis control:

Flux controller

Since , and with

Speed controller

For

,

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DC voltage Selection For a 2-level voltage, we have: Since , we have:

The inverter is built as 2-level with Example II

(

)

,

,

The hysteresis control:

Flux controller

Since , and with

Speed controller

For

Hence, we select

DC voltage Selection The inverter is built as 2-level with

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Example III

(

)

,

,

The hysteresis control:

Flux controller

Since , and with

Speed controller

For

Hence, we select

DC voltage Selection The inverter is built as 2-level voltage with

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3.3. VOLTAGE-SOURCED INVERTER

Example I

, (

)

(

)

,

Current controller

Flux controller

Since , we have:

Torque controller

Speed controller

ABC to dq measured current can be filter out with following filter

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Cross coupling terms

DC voltage Selection For a CHB m-level, we have: Since , we have:

The inverter is built as CHB 7-level voltage with by H Bridge The switching frequency Example II

, (

) ,

(

)

,

Current controller

Flux controller

Since , we have:

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Torque controller

Speed controller

ABC to dq measured current can be filtred out with following filter

Cross coupling terms

DC voltage Selection For a CHB m-level, we have: Since , we have:

The inverter is built as CHB 7-level voltage with by H Bridge The switching frequency

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Example III

(

)

(

)

,

Current controller

Flux controller

Since , we have:

Torque controller

Speed controller

ABC to dq measured current can be filtered out with following filter

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Cross coupling terms

DC voltage Selection For a CHB m-level, we have: Since , we have:

The inverter is built as CHB 7-level voltage with by H Bridge

The switching frequency

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4. PROCESSES DESIGN IN ENGINEERING SUITE V6

See the end of the document

5. SIMULATION PARAMETERS

The simulation was run in time domain with sample time of

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6. ENGINEERING SUITE V6 RESULTS FOR CSI

Example I

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Example II

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Example III

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¡

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7. ENGINEERING SUITE V6 RESULTS FOR VSI

Example I

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Example II

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Example III

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Conclusion

This document shows:

How to design controllers for Induction Motor drives,

How to select the appropriate DC voltage level. 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).

8. REFERENCE BOOKS

1. ABB High Voltage Induction Motors.

Technical Catalogue. HV Induction Motors IEC catalogue EN 12-2007

2. Analysis of Faulted Power Systems. Paul M. Anderson

3. High-Power Converters and AC Drives. Bin Wu

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Speed controller

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ITL

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d

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Flux calculation

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Theta calculation

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q axis current

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Torque controller

Iqs

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Ws*La*Ids

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Torque limiter

sbb

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CHB 7-LEVEL VOLTAGE DRIVES INDUCTION MOTOR

≥

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31a

b

c

≥

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≥

≥

≥

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Carrier phase 0 deg

Carrier phase 180 deg

Carrier phase 60 deg

Carrier phase 240 deg

Carrier phase 120 deg

Carrier phase 300 deg

VΦV C

T

V Van Voltage

VΦV C

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V

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Ungrounded

Motor

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Speed controller

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Flux calculation

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Theta calculation

Speed reference

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Speed Measured

3

A

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Flux controller

Torque_ref

Torque limiter

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2-LEVEL VOLTAGE DRIVES INDUCTION MOTOR

Hysteresis

control

Iabc

Ungrounded

Motor