International Journal of Electrical and Electronics Engineering Research (IJEEER) ISSN 2250-155X Vol. 3, Issue 2, Jun 2013, 131-146 © TJPRC Pvt. Ltd.
PERFORMANCE AND ANALYSIS OF INDUCTION MOTOR USING CONVENTIONAL SVM CONTROLLER AND FUZZY LOGIC CONTROLLER SRINIVASA RAO JALLURI1 & B.V.SANKER RAM2 1
Assistant Professor, Department of Electrical and Electronics Engineering, VNR VJIET, Hyderabad, Andhra Pradesh, India
2
Professor, Department of Electrical and Electronics Engineering, JNT University Hyderabad, Andhra Pradesh, India
ABSTRACT In this Paper the speed control scheme of indirect vector controlled induction motor (IM) drive involves decoupling of the stator current into torque and flux producing components. In this Paper fuzzy logic control (FLC) scheme is implemented and it is applied to a two d-q current components model of an induction motor to achieve maximum torque with minimum loss. An intelligent control based on Fuzzy logic controller is developed with the help of knowledge rule base and membership functions are chosen according to the parameters of the motor model for efficient control. The performance of Fuzzy logic controller is compared with that of the conventional Space vector Modulation (SVM) controller in terms of dynamic response to sudden load changes. The analysis of electrical transients that occur during the failure of the open circuit breaker in a three-phase inverter power supply of a DTC induction motor broke down with the fuzzy logic control scheme. The performance of the induction motor (IM) drive has been analyzed under steady state and transient conditions. The simulation model is tested using various tool boxes in MATLAB. Simulation results of both the controllers are presented for comparison.
KEYWORDS: Induction Motor, SVM Control and Fuzzy Control INTRODUCTION In many of the industrial applications, an electric machine is the most important component. A complete production unit consists primarily of three basic components, an electric machine, and energy – transmitting device and the working (or driven) machine. An electric machine or motor is the source of motive power. An energy transmitting devices delivers powers from electric motor to the driven machine (lathes, centrifugal pumps, drilling machines, lifts, conveyer belts, food – mixers etc) An electric motor together with its control equipment and energy – transmitting devices forms an electric drive. Drive means “System’s employed for the motion control”. Or A motor with suitable speed control equipment is called drive. Because of the disadvantages of dc drive, Most of the industries are prefer ac drive than the dc drive. Induction motors are being applied today to a wider range of applications requiring variable speed. Generally, variable speed drives for Induction Motor (IM) require both wide operating range of speed and fast torque response, regardless of load variations. This leads to more advanced control methods to meet the real demand. In high-performance drive systems, the motor speed should closely follow a specified reference trajectory regardless of any load disturbances, parameter variations, and model uncertainties. In order to achieve high performance, field oriented control of induction motor (IM) drive is employed [1]. The motor control issues are traditionally handled by switching table of svm controller. However, the switces are very sensitive to parameter variations, load disturbances, etc.thus, the controller parameters have to be continually adapted [2]-[5]. To develop an accurate system mathematical model due to unknown load variation, unknown and unavoidable parameter variations due to saturation, temperature variations, and system disturbances [6]. In
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order to overcome the above problems, the fuzzy logic controller (FLC) is used for motor control. The implementation of a fuzzy logic control scheme applied to a two d-q current components model of an induction motor [4]. In this Paper indirect vector control method is used for the control of induction motor. In the vector control, the induction motor can be controlled like a separately excited dc motor. Because of the inherent coupling problem, an induction motor cannot give such a fast response, this problem can be eliminated by, machine control is considered in the synchronously rotating reference frame (de- qe), where the sinusoidal variables appear as dc quantities in steady state, thus giving fast transient response. To implement conventional control, the model of the controlled system must be known. The usual method of computation of mathematical model of a system is difficult. When there are system parameter variations or environmental disturbance, the behavior of the system is not satisfactory. Usually classical control is used in electrical motor drives. The classical controller designed for high performance increases the complexity of the design and the cost.
INDUCTION MOTOR MODELING In modeling of three phase induction motor, it is necessary to derive the equations which are required to design induction machine model. After the mathematical modeling we implement in the simulink. To design the indirect vector control of I.M. drive, we have to know about vector control principle is based on the dynamic d-q model of the machine. The dynamic performance of an ac machine is somewhat complex because the three phase rotor windings move with respect to the three-phase stator windings as shown in figure 3.4. Basically, it can be looked as a transformer with a moving secondary. Where that coupling coefficients between the stator and rotor phase change continuously with the change of rotor position θ, the machine model can be described by differential equations with time-varying mutual inductances. But such a model tends to be very complex. A three phase machine can be represented by an equivalent twophase machine as shown in Figure 3.4. Where
ds qs
correspond to stator direct and quadrature axes, and
dr qr
correspond to rotor direct and quadrature axes. Although it is somewhat simple, the problem of time – varying parameters still remains. R.H. Park, in the 1920s, proposed a new theory of electric machine analysis to solve this problem. He transformed referred the stator variables to a synchronously rotating reference frame fixed in the rotor. With such a transformation (called park’s transformation). Later, in the 1930s H.C. Stanley showed that time – varying inductances in the voltage equations of an induction machine to electric circuits in relative motion can be eliminated by the rotor variables are transformed to a stationary reference frame fixed on the stator. Axes Transformation In this discuss about transform the three – phase stationary reference frame (as-bs-cs) variables in to two – phase stationary reference frame ( d \( d
e
q e ),
s
qs )
variables and then transform these to synchronously rotating reference frame
and vice versa.
Three Phase Stationary Reference Frame (as-bs-cs) Variables Into Two Phase Stationary Reference Frame (ds-qs) Assume that the ds-qs axes are oriented at angle, The voltages
Vdss
and
Vqss
components and corresponding inverse relation can be represented in the matrix from as.
can be resolved into as-bs-cs
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Performance and Analysis of Induction Motor Using Conventional SVM Controller and Fuzzy Logic Controller
Vqss 2 Vdss = V 3 oss
cosθ cosθ 120 cosθ 120 sinθ sin θ 120 sin θ 120 0.5 0.5 0.5
Where
V0ss
Vas V bs Vcs
(1)
is added as the zero sequence component, which may or may not be present. We have considered
voltage as the variable. The current and flux linkages can be transformed be similar equation. It is convenient to set θ =0, so that the qs -axis is aligned with the as -axis, Ignoring the zero sequences component, the transformation can be simplified, and gives as
Vqss 2 ss 3 Vd 0
1 3 1 3
-
1 3 1 3
Vas V bs
(2)
This is the conversation matrix of the equation. These equations are in two phase stationary reference frame. [6] Two Phase Reference Frame (ds - qs) to Two Phase Synchronously Rotating Reference Frame (de- qe) Figure 4 shows the synchronously rotating the
ds qs
axes and the angle
winding mounted on the
de qe
The voltage on the
θ ω e t The
de qe
two phase
axes, which rotate at synchronous speed ωe with respect to
ds qs
windings are transformed into the hypothetical
axes.
ds qs
axes can be converted or resolved into the
de qe
frame and corresponding
inverse relation can be represented in the matrix from as.
Vqse e Vds
=
cos θ e sin θ e sin θ cos θ e e
Vqss s Vds
(3)
Synchronously Rotating Reference Frame For the two phase machine shown in Figure 3.4 we need to represent both synchronously rotating reference frame d converted in to
de qe
Vqs R s i qs
e
qe .
d s q s and d r q r
We write the following stator circuit equations
ψ sqs
variables in
and
ψ sds
are
frame as:
d ψ qs ω e ψ ds dt
(4)
The above equation belongs to Figure 1.
Vds R s i ds
d ψ ds ωe ψ qs dt
(5)
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Srinivasa Rao Jalluri & B.V. Sanker Ram
Figure 1: Stationary Frame ds – as to Synchronously Rotating Frame de – qe Transformation The last terms in Equations (4) & (5) can be defined as speed emf due to rotation of the axes, that is, when
ω e 0 , the equations revert to stationary frame, Note that the flux linkage in the d e and
de
and
axes, respectively, with π/2 lead angle. If the rotor is not moving, that is, ω r
q e axes induce emf in the q e
0 , the rotor equations
for a
doubly – fed wound rotor machine will be similar to equations (4) & (5) .Where all the variables and parameters are referred to the stator, since the rotor actually moves at speed
ωe - ωr
ω r , the d r q r
relative to the synchronously rotating frame. Therefore, in
de qe
axes fixed on the rotor move at a speed frame, the rotor equations should be
modified as
Vqr R r i qr
d ψ qr ωe ω r ψ dr dt
(6)
The above equation belongs to Figure 2.
Vdr R r i dr
d ψ dr ωe ω r ψ qr dt
A special advantage of the
de qe
(7)
dynamic model of the machine is that all the sinusoidal variables in
stationary frame appear as dc quantities in synchronous frame. The flux linkage expressions in terms of the currents and combined with the equations (4) – (7) then the electrical transient model in terms of voltage and currents can be given matrix from as:
Vqs R s SLs Vds ωe L s Vqr SLm Vdr ω e ω r L m
ωe Ls R s SLs ωe ω r L m SLm
SLm ωe L m R r SLr ω e ω r L r
ω e L m i qs SLm i ds ωe ω r L r i qr R r SLr i dr
(8)
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Performance and Analysis of Induction Motor Using Conventional SVM Controller and Fuzzy Logic Controller
Where S is the Laplace operator, for a singly – fed machine, such as a cage motor,
Vqr Vdr 0
.
If the speed
ωr is considered constant (infinite inertia load), the electrical dynamic of the machine are given by a fourth - order liner
Vqs , Vds
system. Then, knowing the inputs dependent variables
Vqs , Vds , i qr
and
i qr
and
ωe
the currents
i qs , i ds
and
ωe
are independent. Then, the
can be solved from equation(2.8) .
The speed ωr in equation (8) cannot normally be treated as a constant. It can be related to the torques as
Te TL J Where
dω m 2 dω TL J m dt P dt
(9)
TL =load torque, J=rotor inertia, and m = mechanical speed
The development of torque will be expressed in more general form, relating the d-q components of variables. The torque can be generally expressed in the vector form as
3 P Te ψ m I r 2 2
(10)
Then the torque Equation after simplified is
Te
3 P L m i qsi dr i dsi qr 2 2
3 P Te ψ dsi ds ψ qsi ds 2 2
(11)
Equations (8), (9), (11). Give the complete model of the electro-mechanical dynamics of an induction machine synchronous frame. [6] Direct or Feedback Vector Control
I*ds
and
I*qs
which are dc values
with the help of a unit vector (Cos θ e and Sin θ e ) generated from flux vector signals
ψ sdr
and
ψ sqr .
In the direct vector control method, the principal vector control parameters,
stationary frame signals are then converted to phase current commands for the inverter. The flux signals
The resulting
ψ sdr and ψ sqr
are
generated from the machine terminal voltages and currents with the help of the voltage model estimator. The generation of a unit vector signal from feedback flux vector gives the name direct vector control. In the direct vector control, the measurement of voltages and currents are required. In this the
ψ r is estimated by observer and flux
vectors are estimated from the voltage model method and current model method. The three voltages and three current sensors are required. From
ψr
we get the speed
ωe
and then get the angle θ e .
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Srinivasa Rao Jalluri & B.V. Sanker Ram
Indirect or Feed Forward Vector Control In this modeling the indirect vector control method is used. In the indirect vector control the unit vector signals (Cos θ e and Sin θ e ) are generated in feed forward manner, indirect vector control is very popular in industrial application. Figure 3.2 explains the fundamental principle of indirect vector control with the help of phasor diagram.
d s q s axes
are fixed on the stator, and
Synchronously rotating axes
de qe
dr qr
axes are fixed on the rotor moves at speed
is rotating ahead of the
dr qr
corresponding to slip frequency ω sl . Since the rotor pole is directed on the
ωr
The
as shown.
axes by the positive slip angle
θ sl
d e axes and ω e ω r ω sl we can write
θ e ωe dt ω r ωsl dt θ r θ sl
(12)
Note that the rotor pole position is not absolute, but is slipping with respect to the rotor at frequency ω sl . The phasor suggest that for decoupling control, the stator flux component of current the torque component of current
I qs
should be on the
qe
I ds should be aligned on the d e axis, and
axis as shown.
Figure 2: Phasor Diagram Explaining Indirect Vector Control For decoupling control, we can now make a derivation of control equations of indirect vector control with the help of
de qe
equivalent circuits. The circuit equations can be written as. From equations (12) to (15)
dψdr /dt R r I dr (ωe ωr )ψqr 0
(13)
dψqr /dt R r I qr (ωe ωr )ψqr 0
(14)
From the rotor flux equations the currents
I dr 1/L r ψ dr L m /L r I ds
I dr , I qr equations as (15)
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Performance and Analysis of Induction Motor Using Conventional SVM Controller and Fuzzy Logic Controller
I qr 1/L r ψqr Lm /L r I qs
(16)
From the above equations we get,
dψdr /dt R r /L r ψdr Lm /L r R r I ds ωslψqr
=0
(17)
dψqr /dt R r /L r ψqr Lm /L r R r I qs ωslψdr 0 Where
(18)
ω sl ω e ω r has been substituted.
For decoupling control, it is desirable that
ψ qr =0
(19) That is,
dψ qr /dt = 0
(20)
So that the total rotor flux ψ r is directed on the
d e axis.
Substituting the above conditions in equations (16) & (17), and simplified we get
ˆr L r dψ ˆ r L m i ds ψ R r dt
(21)
L i qs ωsl m ˆr τ r ψ
(22)
Where
τr
If rotor flux
Lr Rr
ˆr ψ
= rotor time constant,
ψ r ψ dr has been substituted.
= constant, which is usually the case, i.e.
ˆ r /dt dψ
=0 and
ˆ r /Lm I ds = ψ In other words, the rotor flux is directly proportional to current
(23)
I ds in steady state.
The I qs is estimated as follows. From equation (16) of d-q model derivation The Torque is given by
Te (3/2)(P/2) (ψ dr I qr ψ qr I dr ) From the Equation (8) and substitute in the above equation we get
(24)
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Srinivasa Rao Jalluri & B.V. Sanker Ram
Te (3/2)(P/2) (ψdr I qr )
(25)
after substitution the value of
I qr
then the equation I qs as
ˆ r) I qs (2/3)(2/P) (L r /L m )(Te ψ
(26)
From these equation we can write The field component of the stator current
ˆ r /L m I ds ψ *
(27)
Similarly, *
The torque component of the stator current I qs
I qs
ˆr = (2/3) (2/p) (Lr/Lm) (Te*/ ψ
est
)
(29)
Therefore the slip speed ωsl* = Lm/ τr. (Iqs*/
ˆ rest ψ
)
(30)
To implement the indirect vector control strategy, it is necessary to take equations (12), (22), (23), (29), & (30) into consideration and these equations are implemented in simulink. [1]
FUZZY CONTROL SYSTEM A Fuzzy control system essentially embeds the experience and intuition of a human plant operator. If accurate mathematical model is available with known parameters it can be analyzed, but it is time consuming and tedious
Figure 3: Fuzzy Speed Controller in Vector Drive System The Figure 3 shows the Fuzzy control of indirect vector control. The controller observes the pattern of speed loop error signal and correspondingly updates the output DU. So that the actual speed There are two inputs signals to the Fuzzy controller, one is error E =
ω*r - ω r
ωr
matches the commanded speed ω r . *
and another one is change in error CE
which is integrating of error. These two inputs are converted to per unit signals e and ce by dividing respective scale
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Performance and Analysis of Induction Motor Using Conventional SVM Controller and Fuzzy Logic Controller
factors i.e. e=E/GE & ce=CE/GC. Similarly output of plant control signal U is derived from DU by multiplying the scale factor GU i.e. DU=du*GC. After that it is derivate to generate the output signal U. In vector controlled drive this controlled output U is
ΔI*qs
current. The advantage of fuzzy control in terms of
per unit variables is that the same control algorithm can be applied to all the plants of same family. Their scale factors can be constants or programmable. The Figure 4 shows that the inputs are normalized and then applied to Fuzzy controller. The defuzzified output is de - normalized and it will be derivated to generate the output signal.
Figure 4: Structure Fuzzy of Control in Feedback System. Figure 5 shows GE and GDE are the normalized inputs to Fuzzy logic controller. Where GE=1/reference input and GDE=1/ (reference input*10). After normalization these inputs are becomes to E and IE i.e. Error and Integrated Errors. Output GU is the denormalized to generate the output signal U. which is saturated in range of +400 to -400. All the MFS are symmetrical for positive and negative values of variables.
Figure 5: Fuzzy Controller Rule Matrix Figure 6 shows corresponding rule table for the speed controller. The top row and left column of the matrix indicate the fuzzy sets of variables E, IE, respectively, and the Mfs of output variable GU are shown in the body of matrix. There may be 7*7 = 49 possible rules in the matrix.
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Srinivasa Rao Jalluri & B.V. Sanker Ram
Figure 6: Rule Table
RESULTS AND DISCUSSIONS First the indirect vector control of induction motor drive with SVM controller is designed, by Proper adjustments of the gains to get simulated results. After this indirect vector control drive with Fuzzy controller is designed by proper adjustments of membership functions to get simulated results. At Load Conditions In this the machine is stepped up to speed using the speed reference after that which is subjected to a step change at 0.6sec, and also load disturbance at 0.3sec.Drive with SVM controller speed response has small peak at 0.02sec, but in case of fuzzy controller speed response quickly and smoothly responds to the programmable speed reference, as shown in Figure 7.1. After a sudden load disturbance at 0.3 sec the speed response of the drive with SVM controller has small decrement in speed from 122 R.P.M to 118 R.P.M as shown in Figure 7.2 (a). But in case of fuzzy controller the speed decrement is small compared to the conventional SVM controller as shown in Figure 7.2 (b).Drive with svm, Fuzzy controller current responses are sinusoidal throughout the simulation period, as shown in Figure 7.3. Slightly small disturbance of currents occurred at initial start up of motor from standstill, at step change also the current response changes slightly but with in short time it reaches to a previous position, and at the
sudden load disturbance at 0.3sec there is a
slight change in current as shown in Figure 7.3.d-axis current of the drive with SVM and Fuzzy controller is constant throughout the simulation period as shown in Figure 7.4. At the initial start up of the motor from standstill, Drive with SVM controller torque response has a larger peak compared to drive with fuzzy controller as shown in Figure 7.6.Q-axis current is constant except at step change, as shown in Figure 7.5.Drive with SVM controller rotor flux has peak over shoot, but in case of fuzzy controller it can be eliminated, as shown in Figure 7.7.
LOAD RESULTS
Figure 7. 1 (a): Commanded & Achieved Speeds of Induction Motor Drive with SVM Controller at Variable Load
Performance and Analysis of Induction Motor Using Conventional SVM Controller and Fuzzy Logic Controller
141
Figure 7.1 (b): Commanded & Achieved Speeds of Induction Motor Drive with Fuzzy Controller at Variable Load
Figure 7.2 (a): Commanded & Achieved Speeds of Induction Motor Drive with SVM Controller at Variable Load
Figure 7.2 (b): Commanded & Achieved Speeds of Induction Motor Drive with Fuzzy Controller at Variable Load after Zoom
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Srinivasa Rao Jalluri & B.V. Sanker Ram
Figure 7.3 (a): Achieved three Phase Currents of Induction Motor Drive with SVM Controller at Variable Load
Figure 7.3 (b): Achieved Three Phase Currents of Induction Motor Drive with Fuzzy Controller at Variable Load
Figure 7.4 (a): D-Axis Current (Synchronous Frame) of the Induction Motor Drive with SVM Controller at Variable load
Performance and Analysis of Induction Motor Using Conventional SVM Controller and Fuzzy Logic Controller
Figure 7.4 (b): D-Axis Current (Synchronous Frame) of the Induction Motor Drive with Fuzzy Controller at Variable Load
Figure 7.5 (a): Q-Axis Current(Synchronous Frame) of the Induction Motor Drive with SVM Controller at Variable Load
Figure 7.5(b): Q-Axis Current(Synchronous Frame) of the Induction Motor Drive with Fuzzy Controller at Variable Load
143
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Srinivasa Rao Jalluri & B.V. Sanker Ram
Figure 7.6 (a): Load Torque & Electromagnetic Torque Developed by the Induction Motor Drive with SVM Controller at Variable Load
Figure 7.6 (b): Load Torque & Electromagnetic Torque Developed by the Induction Motor Drive with Fuzzy Controller at Variable Load
Figure 7.7 (a): Commanded & Achieved (Estimated) Rotor Flux of the Induction Motor Drive with SVM Controller at Variable Load
Performance and Analysis of Induction Motor Using Conventional SVM Controller and Fuzzy Logic Controller
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Figure 7.7 (b): Commanded & Achieved (Estimated) Rotor Flux of the Induction Motor Drive with Fuzzy Controller at Variable Load
SCOPE FOR THE FUTURE WORK The Indirect vector control of induction motor with Fuzzy logic controller has advantages over SVM controller. For improve the dynamic performance of Indirect vector control of induction motor will implement by using the soft computing techniques like Fuzzy-Neural network method, GA based control algorithms.
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