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26 IEEEP Students’ Seminar 2011 Pakistan Navy Engineering College National University of Sciences & Technology

MATLAB Simulation of a Variable Speed Controller for a Three Phase Induction Motor Shezana Zulfiqar Ali, Azka Khalil, Sumayyah Waheed,and Arshad Aziz Department of Electronics and Power Engineering National University of Sciences and Technology (NUST) H-12, Islamabad Pakistan Navy Engineering College(PNEC), Karachi-75350, Pakistan [email protected], [email protected], [email protected], [email protected]

Abstract— Speed control for induction motor is an essential part of today’s industry. Conventionally we use mechanical methods for speed control like gear box which are getting obsolete. Now a day’s digital approach is used because of its higher reliability and energy conservation. This paper describes the development and simulation of a speed controller for a three phase squirrel cage induction motor using MATLAB/ SimulinkTM. In this work we use Direct Torque Control (DTC) strategy, which is known to produce quick and robust response in speed controllers. The AC4 Simulink blockset is selected from SimPowerSystemTM library and is used to develop our controller. Internal parameters of the system are controlled to obtain the required output. The AC4 block set integrates all the required subsystems including rectifier, inverter, speed and Direct Torque Controller. The system is simulated and the torque and speed outputs of the controller are obtained. Keywords- MATLAB; Simulink; three phase power; squirrel cage induction motor; Direct Torque Control; speed controller; inverter; rectifier

I. INTRODUCTION Three phase induction motor is the prime mover for all the major industrial applications, covering each stage of manufacturing and processing. These motors are popular due to their simplicity, reliability and low cost. The squirrel cage motors are robust because the only parts of the motor that can wear are the bearings. Unlike DC motors slip rings and brushes are not required for such motors. Furthermore, their high power capability gives them an edge over Single-phase AC motors.[1][2] When 3-phase AC power is supplied to stator terminals of an induction motor, 3-phase alternating current flows in the stator windings. These currents set up a rotating magnetic field (flux pattern) inside the stator, known as stator magnetic field Bs. this magnetic field rotates at synchronous speed, ns. [1][3]

(1) Where: f is the system frequency p is the number of poles The rotating magnetic field Bs induces a voltage in the rotor. The voltage induced is given by:

(2) Hence there is flow of a lagging rotor current due to the inductive element present in the rotor. And this rotor current produces a magnetic field at the rotor, Br. The interaction between both magnetic fields produces torque: [3]

(3) Industrial systems require variable speed for different processes. Thus efficient and accurate methods of speed controlling are required. Variable speed controllers are used to control and/or adjust the speed of AC induction motor in short time and conserving energy too. Previously, speed had been controlled using various methods like throttling valves and gearbox but now the new approach is speed controlling along with energy conservation. The mathematical relationship of power and speed depends upon the type of load. For example in variable torque loads such as centrifugal fans, centrifugal pumps, HVAC systems etc the horsepower varies as the cube of speed thus speed controlling results in energy conservation.[1] II. MATLAB/SIMULINK MODEL DEVELOPED The model is developed using the AC4 block of SimPowerSystems™ library of MATLAB as shown in fig. 1. Fig.2 illustrates its connections with a 3 hp three phase induction motor (detailed parameters specified in table.1) using direct torque control (DTC) technique. A three phase power is supplied to the controller along with speed and torque reference values. The induction motor is fed by an inverter which is built using Universal Bridge Block. The speed control loop uses a proportional-integral controller to produce the flux and torque references for the DTC block. Parameters for controller and associated power electronic devices are specified in fig.3 and fig.4 respectively. The DTC block computes the motor torque and flux estimates and compares them to their respective reference. The comparators’ outputs are then used by an optimal switching table which generates the inverter switching pulses. The output of the block displays motor current, speed, and torque signals.[4]

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26 IEEEP Students’ Seminar 2011 Pakistan Navy Engineering College National University of Sciences & Technology

Figure1. Block diagram of MATLAB model for speed controller.

Figure 2. Subsystem of DTC induction motor drive (AC4).

A. Power Electronics Blocks Following blocks from the power electronics library of SimulinkTM are used: 1. Three phase diode rectifier 2. Braking chopper 3. Three phase inverter Three phase AC power is rectified and the DC power obtained is inverted to get an AC power output of the desired frequency. B. Speed Controller Inputs to speed controller block are the actual motor speed i.e. N and the speed set point i.e. N* given by the user. Speed controller compares both these speeds i.e. N and N* to give flux reference flux* and torque reference torque* as outputs. The outputs of speed controller, flux* and torque*, are applied to the DTC controller block.

Figure 3. Parameters of Power Electronics Blocks.

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26 IEEEP Students’ Seminar 2011 Pakistan Navy Engineering College National University of Sciences & Technology TABLE I. PARAMETERS OF INDUCTION MOTOR

Quantity

Value

Pole pairs

2

Power

2238 VA

Frequency

50 Hz

Voltage

400 V

Phase

3

Speed

1705 rpm

Current

5.6 A

Stator leakage inductance

0.002 H

rotor leakage inductance

0.002 H

Stator mutual inductance

0.0693 H

Rotor inertia

0.089 (kgm2)

Rotor friction

0.005 (Nms)

Stator resistance

0.435 Ω

Rotor resistance

0.816 Ω

Figure 4. Controller Parameters.

C. Direct Torque Control (DTC) The fundamental principle of DTC is that it uses inverter switching to directly control the motor flux and torque. DTC uses motor’s torque and stator flux as primary control variables, obtained directly from the motor. DTC can provide accurate control at a very low speed. It eliminates the need to use a separate sensor for feedback. [5][6] The measured input variables to DTC block are the line current, I_ab, and the DC bus voltage, V_abc, which calculates the exact values of flux and torque by the following formulae:[4]

(4)

The reference values of flux and torque are then compared with the calculated values of flux and torque. The Switching table inside the DTC block contains two lookup tables that select a specific voltage vector in accordance with the output of the Flux & Torque comparators. The switching table is made up of two lookup tables responsible for inverter switching thereby providing new current values to the motor. This is achieved by the gate pulses produced by the DTC block. III. CALCULATIONS Braking Torque:

(5)

(8)

(6) (7)

Where: is stator flux in direct frame is stator flux in quadrature frame Rs is stator resistance is direct axis component of stator current is quadrature axis component of stator current is direct axis component of stator voltage is quadrature axis component of stator voltage Te is electromagnetic torque

Where: Power is in hp Speed is in rpm Braking torque is in lb-ft Hence

lb-ft Nm

th

26 IEEEP Students’ Seminar 2011 Pakistan Navy Engineering College National University of Sciences & Technology

Figure 5. Simulation results viewed on the scope.

IV. SIMULATION AND RESULTS

V. CONCLUSIONS

In the model shown in Fig. 1 the stator current, the rotor speed, the electromagnetic torque and the DC bus voltage of the motor are observed on the scope. The speed set point and the torque set point blocks are used to define the speed and torque reference values at specified time.

The proposed Direct Torque Control strategy is used because of its higher reliability and quicker response. This strategy is used to control the speed of a three phase squirrel cage induction motor. MATLAB/SimulinkTM is used for the development and simulation of the controller designed. The simulation results show that the model developed has the capability of controlling the speed according to the user defined reference values. This method, especially suitable for sophisticated industrial applications like centrifugal fans and pumps etc, can conserve energy as well as stabilise the torque.

As the simulation begins, at time t = 0 s, the speed set point is 500 rpm. The speed controller alters the required speed by precisely following the acceleration and deceleration ramps. Ramping speed is specified here as 1800 rpm/s. At t = 0.4 s, the full load torque is applied to the motor shaft while the motor speed is still ramping to its final value. This forces the electromagnetic torque to increase to the user-defined maximum value 17.8 Nm and then to stabilize at 13 Nm once the speed ramping is completed and the motor has reached 500 rpm. The speed of motor remains at 500rpm until at time t = 2s, the controller attains the new set point of 800 rpm. Accelerating at the specified ramping speed that is 1800rpm/s the motor attains the required speed of 800 rpm. At t = 4 s, the speed set point is changed to 0 rpm. The speed decreases down to 0 rpm by following precisely the deceleration ramp even though the mechanical load is inverted abruptly, passing from 12.53 Nm to –12.53 Nm, at t = 1.5 s. Shortly after, the motor speed stabilizes at 0 rpm. In the course of the whole simulation the regulation of DC bus voltage is notable.

VI. ACKNOWLEDGEMENT The authors of this paper would like to thank the entire faculty of Electrical Power Engineering at Pakistan Navy Engineering College, National University of Sciences and Technology. Special thanks to Mr. Ashraf Yahya, Mr. Nusrat Hussain and Cdr (R) Riaz Mehmood for providing us with their guidance and valuable time during the entire research process.

VII. REFERENCES [1] [2] [3] [4] [5]

[6]

Malcolm Barnes, Practical Variable Speed Drives and Power Electronics. A.K. Theraja and B.L. Theraja, Electrical Technology, S Chand. Stephen J Chapman, Electrical Machinery Fundamentals. MATLAB help The MathWorks, Inc. Published with MATLAB® 7.11. R.Rajendran and Dr.N.Devarajan, “FPGA Based Implementation of Space Vector Modulated Direct Torque Control for Induction Motor Drive,” International Journal of Computer and Electrical Engineering, Vol. 2, No. 3, June, 2010 1793-8163. ABB technical guide ―Direct torque control.

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26 IEEEP Students’ Seminar 2011 Pakistan Navy Engineering College National University of Sciences & Technology

MATLAB Simulation of a Variable Speed Controller for a Three Phase Induction Motor Shezana Zulfiqar Ali, Azka Khalil, Sumayyah Waheed,and Arshad Aziz Department of Electronics and Power Engineering National University of Sciences and Technology (NUST) H-12, Islamabad Pakistan Navy Engineering College(PNEC), Karachi-75350, Pakistan [email protected], [email protected], [email protected], [email protected]

Abstract— Speed control for induction motor is an essential part of today’s industry. Conventionally we use mechanical methods for speed control like gear box which are getting obsolete. Now a day’s digital approach is used because of its higher reliability and energy conservation. This paper describes the development and simulation of a speed controller for a three phase squirrel cage induction motor using MATLAB/ SimulinkTM. In this work we use Direct Torque Control (DTC) strategy, which is known to produce quick and robust response in speed controllers. The AC4 Simulink blockset is selected from SimPowerSystemTM library and is used to develop our controller. Internal parameters of the system are controlled to obtain the required output. The AC4 block set integrates all the required subsystems including rectifier, inverter, speed and Direct Torque Controller. The system is simulated and the torque and speed outputs of the controller are obtained. Keywords- MATLAB; Simulink; three phase power; squirrel cage induction motor; Direct Torque Control; speed controller; inverter; rectifier

I. INTRODUCTION Three phase induction motor is the prime mover for all the major industrial applications, covering each stage of manufacturing and processing. These motors are popular due to their simplicity, reliability and low cost. The squirrel cage motors are robust because the only parts of the motor that can wear are the bearings. Unlike DC motors slip rings and brushes are not required for such motors. Furthermore, their high power capability gives them an edge over Single-phase AC motors.[1][2] When 3-phase AC power is supplied to stator terminals of an induction motor, 3-phase alternating current flows in the stator windings. These currents set up a rotating magnetic field (flux pattern) inside the stator, known as stator magnetic field Bs. this magnetic field rotates at synchronous speed, ns. [1][3]

(1) Where: f is the system frequency p is the number of poles The rotating magnetic field Bs induces a voltage in the rotor. The voltage induced is given by:

(2) Hence there is flow of a lagging rotor current due to the inductive element present in the rotor. And this rotor current produces a magnetic field at the rotor, Br. The interaction between both magnetic fields produces torque: [3]

(3) Industrial systems require variable speed for different processes. Thus efficient and accurate methods of speed controlling are required. Variable speed controllers are used to control and/or adjust the speed of AC induction motor in short time and conserving energy too. Previously, speed had been controlled using various methods like throttling valves and gearbox but now the new approach is speed controlling along with energy conservation. The mathematical relationship of power and speed depends upon the type of load. For example in variable torque loads such as centrifugal fans, centrifugal pumps, HVAC systems etc the horsepower varies as the cube of speed thus speed controlling results in energy conservation.[1] II. MATLAB/SIMULINK MODEL DEVELOPED The model is developed using the AC4 block of SimPowerSystems™ library of MATLAB as shown in fig. 1. Fig.2 illustrates its connections with a 3 hp three phase induction motor (detailed parameters specified in table.1) using direct torque control (DTC) technique. A three phase power is supplied to the controller along with speed and torque reference values. The induction motor is fed by an inverter which is built using Universal Bridge Block. The speed control loop uses a proportional-integral controller to produce the flux and torque references for the DTC block. Parameters for controller and associated power electronic devices are specified in fig.3 and fig.4 respectively. The DTC block computes the motor torque and flux estimates and compares them to their respective reference. The comparators’ outputs are then used by an optimal switching table which generates the inverter switching pulses. The output of the block displays motor current, speed, and torque signals.[4]

th

26 IEEEP Students’ Seminar 2011 Pakistan Navy Engineering College National University of Sciences & Technology

Figure1. Block diagram of MATLAB model for speed controller.

Figure 2. Subsystem of DTC induction motor drive (AC4).

A. Power Electronics Blocks Following blocks from the power electronics library of SimulinkTM are used: 1. Three phase diode rectifier 2. Braking chopper 3. Three phase inverter Three phase AC power is rectified and the DC power obtained is inverted to get an AC power output of the desired frequency. B. Speed Controller Inputs to speed controller block are the actual motor speed i.e. N and the speed set point i.e. N* given by the user. Speed controller compares both these speeds i.e. N and N* to give flux reference flux* and torque reference torque* as outputs. The outputs of speed controller, flux* and torque*, are applied to the DTC controller block.

Figure 3. Parameters of Power Electronics Blocks.

th

26 IEEEP Students’ Seminar 2011 Pakistan Navy Engineering College National University of Sciences & Technology TABLE I. PARAMETERS OF INDUCTION MOTOR

Quantity

Value

Pole pairs

2

Power

2238 VA

Frequency

50 Hz

Voltage

400 V

Phase

3

Speed

1705 rpm

Current

5.6 A

Stator leakage inductance

0.002 H

rotor leakage inductance

0.002 H

Stator mutual inductance

0.0693 H

Rotor inertia

0.089 (kgm2)

Rotor friction

0.005 (Nms)

Stator resistance

0.435 Ω

Rotor resistance

0.816 Ω

Figure 4. Controller Parameters.

C. Direct Torque Control (DTC) The fundamental principle of DTC is that it uses inverter switching to directly control the motor flux and torque. DTC uses motor’s torque and stator flux as primary control variables, obtained directly from the motor. DTC can provide accurate control at a very low speed. It eliminates the need to use a separate sensor for feedback. [5][6] The measured input variables to DTC block are the line current, I_ab, and the DC bus voltage, V_abc, which calculates the exact values of flux and torque by the following formulae:[4]

(4)

The reference values of flux and torque are then compared with the calculated values of flux and torque. The Switching table inside the DTC block contains two lookup tables that select a specific voltage vector in accordance with the output of the Flux & Torque comparators. The switching table is made up of two lookup tables responsible for inverter switching thereby providing new current values to the motor. This is achieved by the gate pulses produced by the DTC block. III. CALCULATIONS Braking Torque:

(5)

(8)

(6) (7)

Where: is stator flux in direct frame is stator flux in quadrature frame Rs is stator resistance is direct axis component of stator current is quadrature axis component of stator current is direct axis component of stator voltage is quadrature axis component of stator voltage Te is electromagnetic torque

Where: Power is in hp Speed is in rpm Braking torque is in lb-ft Hence

lb-ft Nm

th

26 IEEEP Students’ Seminar 2011 Pakistan Navy Engineering College National University of Sciences & Technology

Figure 5. Simulation results viewed on the scope.

IV. SIMULATION AND RESULTS

V. CONCLUSIONS

In the model shown in Fig. 1 the stator current, the rotor speed, the electromagnetic torque and the DC bus voltage of the motor are observed on the scope. The speed set point and the torque set point blocks are used to define the speed and torque reference values at specified time.

The proposed Direct Torque Control strategy is used because of its higher reliability and quicker response. This strategy is used to control the speed of a three phase squirrel cage induction motor. MATLAB/SimulinkTM is used for the development and simulation of the controller designed. The simulation results show that the model developed has the capability of controlling the speed according to the user defined reference values. This method, especially suitable for sophisticated industrial applications like centrifugal fans and pumps etc, can conserve energy as well as stabilise the torque.

As the simulation begins, at time t = 0 s, the speed set point is 500 rpm. The speed controller alters the required speed by precisely following the acceleration and deceleration ramps. Ramping speed is specified here as 1800 rpm/s. At t = 0.4 s, the full load torque is applied to the motor shaft while the motor speed is still ramping to its final value. This forces the electromagnetic torque to increase to the user-defined maximum value 17.8 Nm and then to stabilize at 13 Nm once the speed ramping is completed and the motor has reached 500 rpm. The speed of motor remains at 500rpm until at time t = 2s, the controller attains the new set point of 800 rpm. Accelerating at the specified ramping speed that is 1800rpm/s the motor attains the required speed of 800 rpm. At t = 4 s, the speed set point is changed to 0 rpm. The speed decreases down to 0 rpm by following precisely the deceleration ramp even though the mechanical load is inverted abruptly, passing from 12.53 Nm to –12.53 Nm, at t = 1.5 s. Shortly after, the motor speed stabilizes at 0 rpm. In the course of the whole simulation the regulation of DC bus voltage is notable.

VI. ACKNOWLEDGEMENT The authors of this paper would like to thank the entire faculty of Electrical Power Engineering at Pakistan Navy Engineering College, National University of Sciences and Technology. Special thanks to Mr. Ashraf Yahya, Mr. Nusrat Hussain and Cdr (R) Riaz Mehmood for providing us with their guidance and valuable time during the entire research process.

VII. REFERENCES [1] [2] [3] [4] [5]

[6]

Malcolm Barnes, Practical Variable Speed Drives and Power Electronics. A.K. Theraja and B.L. Theraja, Electrical Technology, S Chand. Stephen J Chapman, Electrical Machinery Fundamentals. MATLAB help The MathWorks, Inc. Published with MATLAB® 7.11. R.Rajendran and Dr.N.Devarajan, “FPGA Based Implementation of Space Vector Modulated Direct Torque Control for Induction Motor Drive,” International Journal of Computer and Electrical Engineering, Vol. 2, No. 3, June, 2010 1793-8163. ABB technical guide ―Direct torque control.

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