Speed Control of a Squirrel Cage Induction Motor with A balanced Capacitor Voltage Fed Multi-Level Diode Clamped Converter

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Speed Control of a Squirrel Cage Induction Motor with A balanced Capacitor Voltage Fed Multi-Level Diode Clamped Converter

Crescent Onyebuchi Omeje1,

1 Electrical/Electronic Engineering, University of Port Harcourt, Rivers State Nigeria

Marcel Ugwuoke Agu2

2Electrical Engineering,

University of Nigeria Nsukka, Enugu State Nigeria

Abstract: This paper analyzes the concepts of a well-balanced capacitor voltage fed multi-level diode clamped converter driving a three phase squirrel cage induction motor at a varying load. The speed operations in motoring and in generating modes are considered. Speed control of the asynchronous machine is analyzed with pertinent to variable voltage and frequency (V/F) ratio at a low frequency boost- voltage. The effect of load variation on the motor speed in modified closed loop drive system with a low-frequency boost voltage is also examined in this paper. A comparison of the results obtained for the two modes of operation is presented. The simulation results indicate that a closed loop control system proffers a better and an efficient speed control at variable voltage and slip-frequency when operated with a multi-level diode clamped converter at a modulation index of

    1. It is also shown that the induction machine runs at a very high speed above the synchronous speed value under a generating mode of operation. All simulation processes were

      with magnitude above the synchronous speed value is achieved at the generating state whereas a lower speed magnitude below the synchronous speed is achieved at the motoring state.

      1. ANALYSIS OF LOW FREQUENCY STATOR VOLTAGE BOOST.

        The modified voltage-frequency control ( ) provides a

        boost-voltage at low frequencies below the rated value. This boost-voltage compensates for the stator impedance

        drop that allows a constant flux operation and maximum motoring torque from zero to rated speed [12]. The exact equivalent circuit shown in Figure 1a is applied in determining the low frequency boost voltage 0 that sustains the motor flux from zero to rated speed.

        R

        achieved in MATLAB 7.14.

        Keyword: Capacitor Voltage Balancing, Multi-Level Diode Clamped Converter, Squirrel Cage Induction Motor, Constant V/F, Motor Speed and Torque.

        1. INTRODUCTION.

          Speed control of an induction machine is a very significant

          Rs jaXLs

          Is

          aE

          aE

          Vs '

          ar

          IM

          jaXM

          jaX r

          r

          L

          L

          s

          I'r

          aspect in most industrial applications since induction motor is used in number of applications such as steel mills, pump operation, cranes, hoist drives, conveyors and traction systems [1,2,3]. Generally, the speed of a squirrel cage

          Figure 1a. Steady State Equivalent Circuit of a Squirrel Cage Induction Motor for Variable V/ F control.

          The ratio of the operating speed to the rated speed which is also a function of the frequency ratio is given by (1).

          induction machine can be controlled to operate either in a

          motoring state or in a generating state [4-5]. Conventionally, variable voltage and variable frequency

          Foperating frequency

          a = =

          Frated frequency

          s

          sr

          (1)

          methods have been applied in the speed control of induction machine [6-7]. In automobile applications, speed control is the most crucial aspect of effective machines

          Applying Kirchhoffs Voltage Law in Figure 1a gives rise

          to (2).

          r

          r

          Vs = aEar + (Im + I) × (Rs + jaXLs ) (2)

          operation. This is achieved through the following methods:

          (i) Pole changing of the machine, (ii) Supply Frequency

          Where:

          I

          Ear aEar

          R

          R

          + I = +

          (3)

          Control, (iii) Stator Voltage Control and (iv) Rotor Resistance Control [8, 9, 10]. The frequency and voltage

          m r jXm

          Lr

          Lr

          r + jaX s

          control methods can be analyzed in scalar and in vector

          Substituting (3) into (2) gives rise to (4).

          form [11]. In this paper, analysis is based on scalar control. This involves a low-frequency stator boost voltage control with a well-balanced capacitor voltage fed five-level diode

          Ear

          m

          m

          R

          R

          r

          r

          VS = aEar + (jX +

          s

          aEar

          Lr

          Lr

          + jaX

          ) (Rs + jaXLs) (4)

          clamped converter. This converter drives the squirrel cage induction machine in a closed loop system under a varying machine load and speed. The speed variation which is as a consequence of change in mechanical load is considered in motoring and in generating states. These operational states are compared with respect to the motor speed. A high speed

          At a low frequency of 0.1 1, a plot of the terminal

          voltage Vs within this range of a is presented in Figure 1b. The linear graph in Figure 1b can be represented in a linear form as shown in (5).

          Vs = V0 + Ka (5)

          Where Vs is the low frequency stator boost voltage. V0 is the offset voltage or stator voltage which is chosen to give the rated magnetizing current at zero speed when a = 0. By extrapolation V0 = 13.33V which represents the low frequency stator boost voltage. The slope of the linear graph is given by K = 218.35. Substituting the value of K and V0 into (5) gives rise to (6).

          Terminal Voltage VT[Volt]

          Terminal Voltage VT[Volt]

          Vs = 13.33 + 218.35a (6)

          Per-Unit Frequency a

          Figure 1b. Stator Terminal Voltage Variation against per unit frequency ratio (a).

          controlled by controlling the rate of change in supply frequency (ii) A wider stable speed operating region is achieved (iii) A good running and transient performance is easily obtained (iv) Voltage and frequency can easily attain rated values at base speed.

          In the closed loop analysis of squirrel cage induction motor, the dynamic equations are essential in the prediction of transient characteristics of the machine speed. The following assumptions as reported in [13-14] are made in the development of transient equations for the conventional squirrel cage induction machine model:

          1. Machine stator voltages are balanced with a sinusoidally distributed magneto-motive force (mmf)

          2. Saturation effect of the magnetizing core is neglected

          3. Harmonic contents of the magneto-motive force (mmf) wave are neglected.

          4. The machine is symmetrical with a linear air-gap and magnetic circuit

          The differential equations that describe the dynamic performance of an ideal symmetrical induction machine in a stationary reference frame is presented in (7).

          Vqs

          Vds

          0

          The expression in (6) formed the basic equation for the low frequency stator boost voltage which was applied in the

          [ 0 ]

          (Rs + Ls) 0 Lm 0

          closed loop speed control of the squirrel cage induction

          machine shown in Figure 2.

          0 (Rs

          =

          + Ls) 0 Lm

          Lm rLm (Rr + Lr) rLr

      2. CLOSED LOOP SPEED CONTROL OF SQUIRREL CAGE INDUCTION MOTOR.

        A closed loop speed control can be implemented with the variable voltage and frequency method through a slip speed

        [

        iqs

        ids

        ×

        i

        rLm Lm rLr (Rr + Lr)]

        (7)

        regulation. A proportional integral controller is applied to regulate the slip speed of the motor to a set value. The major blocks that make up the components of the electric drives for the speed control as presented in Figure 2 include: (i) The d.csource of supply (ii) The power semi- conductor converter (iii) The induction motor and (iv) The controllers. Frequency control is achieved through the speed feedback loop which generates a slip speed =

        . The slip speed difference is acted upon by a

        qr

        [idr]

        Where: Ls = LLs + Lm (8) Lr = LLr + Lm (9)

        For simulation purposes, (7) can be compressed and

        represented by (10).

        [i] = [L]1 ([R] + r[G])[i] + [L]1[V] (10)

        Where:

        [V] = [Vqs Vds 0 0] (11)

        R 0 0 0

        PI-controller to reduce the error in speed. A slip limiter set at ±0.7Smaxis applied to regulate the slip speed of the motor to a permissible value. The resultant speed is summed with a mechanical speed from the rotor sensed through a tachometer to produce a slip frequency. The slip frequency is then supplied to the pulse-width modulator of

        the five-level diode clamped converter shown in Figure 2. Voltage Control is achieved by summing the values of the adjusted low frequency stator boost voltage in (6) with the actual stator supply voltage obtained from the five-level diode clamped converter. The voltage error produced is regulated with a PI-controller to produce the desired voltage applied in the pulse width modulator of the five- level diode clamped converter. This process continues until

        [R] =

        [L] =

        [G] =

        s

        0 Rs 0 0

        0 0 Rr 0

        [ 0 0 0 Rr]

        Ls 0 Lm 0

        0 Ls 0 Lm

        Lm 0 Lr 0

        [ 0 Lm 0 Lr ]

        0

        0

        0

        0

        0

        0

        0

        0

        0

        0

        0

        0

        0

        0

        (12)

        (13)

        (14)

        the machine is shut-down. The various advantages of variable voltage and frequency control include but not limited to the followings: (i) Motor acceleration is easily

        0 Lm 0 Lr

        [Lm 0 Lr 0 ] [i] = [iqs ids iqr idr] (15)

        o

        o

        V = 13.33 Vs = V0 + Ka

        Voltage

        Error

        K

        PI Voltage Controller

        Kp + Ki

        s

        Vm

        Kp + Ki

        s

        Vm

        Slip

        DC Supply

        PWM Control for the Five- Level DCC

        *

        m

        Speed Reference

        (Rad/Sec) SL

        PI Speed Controller

        Kp + Ki

        Slip Limiter

        sSL

        =

        218.35

        e = Frequency

        m

        Mechanical Speed (Rad/Sec)

        Speed Error

        s a

        e

        Electrical Speed (Rad/Sec)

        P

        2

        Vsf

        Stator Supply

        = Voltage

        Induction Motor

        m

        Mechanical Speed (Rad/Sec)

        Tachometer for Speed Sensing

        Figure 2 Block diagram of the closed loop speed control of squirrel cage induction motor with V/F scheme.

        s

        s

        Where: = d , R

        dt

        is the stator resistance, Rr is the rotor

        The chopper current limiting inductors are represented by L1 and L2 while the source capacitors are represented by

        resistance referred to the stator side, LLs and LLr are the

        stator and rotor leakage inductance. Lm is the magnetizing inductance, is synchronous speed in Rad/Sec.

        The mechanical model of an induction motor is composed of the equations of motion and the driven load of the motor. This is presented in equation (16).

        2J dr

        Cd1, Cd2, Cd3 and Cd4. The inductor L1 is applied to transfer

        excess capacitor stored energy between capacitors Cd1 and Cd2 in the upper part of the circuit. Similarly, L2 is applied to exchange capacitor stored energy between capacitors Cd3 and Cd4 in the lower part of the circuit as presented in Figure 3.

        Tem = TL + P

        (16)

        dt

        i1

        Sa1

        Where: P is the number of pole pairs, J is the moment of

        inertia, r is the rotor electrical speed, TL is the Load torque and Tem is the electromechanical torque. The machine parameters used for the simulation is presented in Table 1.

        Sca1

        L1

        Dc2

        icp

        Vcd1

        Vcd2

        Cd1

        i2

        Cd2

        Sa2

        Sa3

        Table 1. Simulation Parameters.

        +VdcDC

        Dc3

        Vcd3

        i3

        Cd3

        Sa4

        c

        Sa1

        Van

        MACHINE PARAMETERS

        VALUES

        Rated Power

        5H.P = 3730W

        Rated Input Voltage

        400 V

        Stator Resistance

        2.2

        Rotor Resistance

        0.87

        Stator Leakage Inductance L

        Ls

        0.0052 H

        Rotor Leakage Inductance L

        0.0052 H

        Lr

        Magnetizing Inductance

        0.0955 H

        Number of Pole

        4

        Frequency (Hertz)

        50

        Motor Speed (RPM)

        1440

        Coefficient of Viscosity (Nms)

        0.0008

        Motor Inertia (Kg-M2)

        0.07

        Load Torque (Motoring)

        0, -20 and -10

        Load Torque (Generating)

        0, 20 and 10

        MACHINE PARAMETERS

        VALUES

        Rated Power

        5H.P = 3730W

        Rated Input Voltage

        400 V

        Stator Resistance

        2.2

        Rotor Resistance

        0.87

        Stator Leakage Inductance L

        Ls

        0.0052 H

        Rotor Leakage Inductance L

        0.0052 H

        Lr

        Magnetizing Inductance

        0.0955 H

        Number of Pole

        4

        Frequency (Hertz)

        50

        Motor Speed (RPM)

        1440

        Coefficient of Viscosity (Nms)

        0.0008

        Motor Inertia (Kg-M2)

        0.07

        Load Torque (Motoring)

        0, -20 and -10

        Load Torque (Generating)

        0, 20 and 10

        L2 icp

        Sa2

        R + jL

        Sca2

        Vcd4

        i4

        Cd4

        i5

        Sa3

        Sa4

        Figure 3. A Five-Level Diode Clamped Converter with an interconnected Buck-Boost Chopper Circuit.

        4.1. Control Scheme of the Five-Level Capacitor Voltage Diode Clamped Converter.

        Two stages are considered in this section. The first stage is focused on keeping the output voltage constant using a

        reference voltage tracking of

        =

        while the second

        4

      3. DC CAPACITOR VOLTAGE BALANCING IN DIODE CLAMPED CONVERTER.

Several multi-level inverter configurations with a d.c capacitor voltage balance and pulse-width modulation (PWM) techniques have been reported in [15-21]. This section shows a simple buck-boost chopper circuits that are connected to the input d.c capacitors of a single phase mid- point five-level diode clamped converter. The buck-boost chopper circuit ensures that the d.c capacitor voltage is always balanced through the energy exchange in the inductor and the source capacitors. 1 and 2 are the chopper bidirectional switches. Each switch is made up of a unidirectional transistor switch and an anti-parallel diode.

stage involves the generation of the switching signals for Sa1 Sa2 Sa3 and Sa4. The complementary switching is obtained by inverting the respective signals.

First Stage: If Vcd1 Vcdr + V and V = cd1 Vcd2,

1 is turned on. The overcharged energy on capacitor Cd1 is transferred to the inductor L1 by the flow of chopper current 1 through the loop Vcd1 1 1 Vcd1. When Cd1 is discharged to an acceptable level of Vcdr

V < 1 < Vcdr + V, 1 is turned off and 2 is simultaneously turned on to charge Cd2 to a level of Vcdr

V < 2 < Vcdr + V by transferring the energy built up in the inductor L1 to charge Cd2. Similarly, when Cd2 is

discharged to an acceptable level of Vcdr V < 2 <

Vcd1 and Vcd4 increased progressively from at the same

Vcdr + V, 2 is turned off while 1 is turned on to 4

charge Cd1by transferring the energy built up in the

rate that Vcd2 and Vcd3 decreased from . The increase and

4

inductor L1 to charge Cd1. The same process applies to the energy exchange between capacitors Cd3 and Cd4 respectively.

Second Stage: Switching signals for Sa1 Sa2 Sa3 and Sa4 are generated using the phase-disposition sinusoidal pulse- width modulation technique. The signals are achieved by comparing four carrier waves with a reference (modulating) wave. The four carrier waves are obtained with the aid of equations (17)-(20) having different offset values.

decrease in the capacitor voltage is as a result of the flow of unequal branch currents i1 to i5 of Figure 3. This therefore implies that under steady state operation, only Cd1 and Cd4 need to be discharged from their excess voltages to =

. The excess energy recovered from the chopper

4

inductors is then applied to charge up Cd2 and Cd3 to =

. Figure 5 represents the output voltage waveform for

4

the balanced capacitor voltage and five-level inverter

tr1 = [ 0

1 1

2F F

] (17)

output phase voltage under steady state condition. In Figure

5, it is observed that each of the four capacitor voltages

c c

closely track the reference voltage

= = 100.

2x 1 2x 2x 1 4

tr2 = [

1

0

2Fc

1

Fc ] (18)

This gives a high quality inverter output voltage under a prolonged steady state condition as against Figure 4

tr3 = [

x 1 x x 1

1 1

0

2Fc Fc

] (19)

waveform. The simulation results for the squirrel cage induction motor showed that there is an overshoot in the speed of the machine during starting as shown in Figures 8

(x 1) x (x 1) and 15. At start, the machine speed rises to 164.8 Rad/Sec

tr4

= [ 0

1

2Fc

1

Fc ] (20)

at 0.053second in motoring condition whereas the rise in speed in generating condition is 331.4 Rad/Sec. which is

equivalent to twice the value obtained in motoring state on

(2x 1) 2x (2x 1)

tr1 tr4 represent the carrier waves. X represents the amplitude of the carrier wave. At every condition X 1, Fc represents the switching frequency of the carrier,

The reference (modulating) wave is derived from (21).

Vra = Am sin() (21)

Where: Am represents the amplitude of the modulating wave.

The algorithm for the switches on phase A inverter leg is presented as follows:

If ( > 1)

1 = 1; 2 = 1; 3 = 1; 4 = 1;

1 = 0; 2 = 0; 3 = 0; 4 = 0;

Else if ( Vra < tr1 and Vra > tr2 )

1 = 0; 2 = 1; 3 = 1; 4 = 1;

1 = 1; 2 = 0; 3 = 0; 4 = 0;

no-load. When a periodic load as shown in Figure 6, is applied on the machine at a varied time interval of [0.5, 1.0; 1.5; 2.0] second the motor speed drops in the sequence of [156.7; 155.5; 156.1; 159.1] Rad/Sec. as presented in

Figure 8 for motoring condition and [315.5; 312.7; 313.4; 312.7] Rad/Sec. for generating condition as shown in Figure 15. Similarly, the electromechanical torque in motoring condition changes in line with the speed in the sequence [73.72; 49.96; 25.92; -24.94] Nm and [-19.59;

s e g

)

a 2

t d

l

o c

VV

r& o t 1

i d

c c a p(V a

C

s e g

)

a 2

t d

l

o c

VV

r& o t 1

i d

c c a p(V a

C

    1. ; 9.693; 19.6] Nm for generating condition. The simulation result presented in Figure 9 also showed that during start-up, the machine on no-load and on periodic loading operation draws much current and produces oscillatory torques which is presented in Figure 7 and in Figure 14.

      Vcd1

      Vcd2

      Vcd1

      Vcd2

      Capacitor Voltage Vcd1 & Vcd2 (Volts)

      Capacitor Voltage Vcd1 & Vcd2 (Volts)

      115

      Else if ( Vra

      < tr2

      and Vra

      > tr3

      ) 110

      105

      1 = 0; 2 = 0; 3 = 1; 4 = 1;

      1 = 1; 2 = 1; 3 = 0; 4 = 0;

      100 (

      95

      90

      Else if ( Vra

      < tr3

      and Vra

      > tr4

      ) 85

      0 0.1 0.2 0.3 0.4 0.5 0.6

      1

      = 0; 2

      = 0; 3

      = 0; 4

      = 1;

      s e g

      )

      a 4

      t d

      l

      o c

      VV

      r& o t 3

      i d

      c c a p(V a

      C

      s e g

      )

      a 4

      t d

      l

      o c

      VV

      r& o t 3

      i d

      c c a p(V a

      C

      Capacitor Voltage Vcd4 & Vcd3 (Volts)

      Capacitor Voltage Vcd4 & Vcd3 (Volts)

      115

      Time t(secs)

      1 = 1; 2 = 1; 3 = 1; 4 = 0;

      115

      110

      110

      Vcd4

      Else ( Vra

      < tr4

      105

      )

      )

      105

      101000

      1 = 0; 2 = 0; 3 = 0; 4 = 0;

      = 1; = 1; = 1; = 1;

      9595

      9090

      Vcd3

      End

      1

      2

      3

      4

      8585

      0 0

      2 5 0

      0.01.1

      0.02.2

      0.03.3

      Time t(secs)

      0.04.4

      0.05.5

      0.06.6

      2 0 0

      1. SIMULATION RESULTS AND DISCUSSION. The simulation result for the five-level diode clamped converter (DCC) with a disconnected chopper circuit is presented in Figure 4. It is evidently shown that in the absence of the chopper circuit (disconnected buck-boost chopper circuit), an unbalanced state of the capacitor voltage is obtained. This is observed in the rising with time of the unbalanced state of the dc capacitor voltage waveforms shown in Figure 4 where the capacitor voltages

        1 5 0

        e g

        a t l

        o V

        t

        u p n

        t a

        u v

        O

        r

        e t r

        e v

        n I

        e g

        a t l

        o V

        t

        u p n

        t a

        u v

        O

        r

        e t r

        e v

        n I

        Phase Voltage Van (Volts)

        Phase Voltage Van (Volts)

        1 0 0

        5 0

        (

        0

        – 5 0

        – 1 0 0

        – 1 5 0

        – 2 0 0

        – 2 5 0 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6

        Time (Sec.)

        Figure 4. Five Level DCC waveforms with a disconnected chopper circuit. Cd1 & Cd2 = Cd3 & Cd4 = 2000µF, Vdc = 400V, Fc =1.05 KHz, Fs = 50Hz, M = 0.8, ZL = (8+6j) .

        s e g)

        2

        a d t l c

        oV V

        & r

        o 1 t d i

        c c a(V p

        C

        s e g)

        2

        a d t l c

        oV V

        & r

        o 1 t d i

        c c a(V p

        C

        Vcd1

        Vcd2

        Vcd1

        Vcd2

        Capacitor Voltage Vcd1 & Vcd2 (Volts)

        Capacitor Voltage Vcd1 & Vcd2 (Volts)

        120

        100

        80 (a)

        60

        40

        0 0.1 0.2 0.3 0.4 0.5 0.6

        Timet(secs)

        s e g

        )

        a 4 t d l

        o c

        VV

        r& o t 3 i d c c

        a p(V a C

        s e g

        )

        a 4 t d l

        o c

        VV

        r& o t 3 i d c c

        a p(V a C

        Vcd4

        Vcd3

        Vcd4

        Vcd3

        Capacitor Voltage Vcd3 & Vcd4 (Volts)

        Capacitor Voltage Vcd3 & Vcd4 (Volts)

        120

        100

        80

        60

        (b)

        40

        0 0.1 0.2 0.3 0.4 0.5 0.6

        Timet(secs)

        e g

        a l

        o V

        t uV

        p t n u a

        Ov r

        e t r

        e v

        n I

        e g

        a t l

        o V

        t uV

        p t n u a

        Ov r

        e t r

        e v

        n I

        250

        200

        Phase Voltage Van (Volts)

        Phase Voltage Van (Volts)

        150

        100

        50

        0

        -50

        -100

        -150

        -200

        (c)

        -250

        0 0.1 0.2 0.3 0.4 0.5 0.6

        Timet(secs)

        Figure 5. Five Level DCC waveforms with an interconnected chopper circuit. Cd1 & Cd2 = Cd3 & Cd4 = 2000µF, Vdc = 400V, Fc =1.05 KHz, Fs = 50Hz, M = 0.8, ZL = (8+6j) .

        Figure 6. A Plot of Applied-Mechanical Load Torque (NM) against Time (Sec.) (Motoring State).

        Figure 7. A Plot of Electromechanical Torque against Time (Motoring State).

        Figure 8. A Plot of Motor Speed against Time (Motoring State)

        Vqs (Volt)

        Vqs (Volt)

        Figure 9. A Plot of Stator and Rotor qd-axes currents (A) against Time (Sec.).

        Time (Sec.)

        Figure 10. A Plot of Q-axis phase voltage (A) against Time (Sec.).

        Vds (Volt)

        Vds (Volt)

        Time (sec.)

        Figure 11. A Plot of D-axis phase voltage (V) against Time (Sec).

        Figure 12. A Plot of Electromechanical Torque against Speed (Motoring State).

        Figure 13. A Plot of Applied-Mechanical Load Torque against Time (Generating State).

        Figure 14. A Plot of Electromechanical Torque against Time (Generating State).

        Figure 15. A Plot of Motor Speed against Time (Generating State)

        Figure 16. A Plot of Electromechanical Torque against Speed (Generating State).

      2. CONCLUSION

      The concept of speed control with a low frequency stator boost voltage was analyzed with respect to variable voltage and frequency ratio. A well balanced capacitor voltage fed five-level diode clamped converter (DCC) was modeled to drive a 5Hp squirrel cage induction motor in motoring and in generating mode of operations. The simulation results obtained and presented in Figures 4 and 5 indicate that an unsymmetrical voltage distribution across the inverter leg is achieved with an unbalanced capacitor voltage. Conversely, a symmetrical and high quality voltage distribution is achieved across the inverter leg for a well- balanced capacitor voltage. This work has shown that there

      is an appreciable rise in the speed of the squirrel cage induction motor during a generating condition over the motoring condition. The results equally proved that a periodic loading of the machine always lead to sudden changes in speed with a resultant rise and fall in the electromechanical torque.

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