Fuzzy Efficiency Enhancement of Induction Motor Drive

Zineb Rouabah, Fatiha Zidani Department of Electrical Engineering, Faculty of Technology,

Laboratoire des Systèmes de Propulsion-Induction Electromagnétiques (LSPIE Laboratory),

Batna, Algeria e-mails: zinebroua@ieee.org, fati_zidani@lycos.com

Bachir Abdelhadi Department of Electrical Engineering, Faculty of Technology,

Laboratoire des Systèmes de Traction Électriques (LSTE Laboratory),

Batna, Algeria e-mail: abdelhadi3b@yahoo.com

Abstract— Efficiency improvement of motor drives is important not only from the viewpoints of energy loss and hence cost saving, but also from the perspective of environmental pollution. Several efficiency optimization methods for induction motor (IM) drives have been introduced nowadays by researchers. Distinctively, artificial intelligence (AI)-based techniques, in particular Fuzzy Logic (FL) one, have been emerged as a powerful complement to conventional methods. Design objectives that are mathematically hard to express can be incorporated into a Fuzzy Logic Controller (FLC) using simple linguistic terms. The merit of FLC relies on its ability to express the amount of ambiguity in human reasoning. When the mathematical model of a process does not exist or exists with uncertainties, FLC has proven to be one of the best alternatives to move with unknown process. Even when the process model is well-known, there may still be parameter variation issues and power electronic systems, which are known to be often approximately defined. The purpose of this paper is to demonstrate that a great efficiency improvement of motor drive can be achieved and hence a significant amount of energy can be saved by adjusting the flux level according to the applied load of an induction motor by using an on-line fuzzy logic optimization controller based on a vector control scheme. An extensive simulation results highlight and confirm the efficiency improvement with the proposed algorithm.

Keywords— Induction Motor Drive; Indirect Field Oriented Control (IFOC); Efficiency Enhancement; Losses Minimization;Optimization; Fuzzy Logic.

I. INTRODUCTION The level of prosperity of a community is related to its

capability to produce goods and services by using efficiently and rationally the provided energy. Such use of energy means higher productivity with lower losses at moderate costs. This losses reduction leads to lower environmental impact where the motor works at lower thermal and chemical impact at the electric power plant that produces the required electrical energy [1]. In this regard, since electrical machines consume most of the world’s electrical energy, any amount of electrical drive efficiency improvement leads not only to a significant energy saving but also to environmental protection and preservation [2]. Among these electrical machines, induction motor is the most robust so the most widely used and is also a high efficiency machine when operating close to its rated working steady state point. However, at torque and/or speed far from the rated values, the efficiency is greatly reduced [3].

In order to solve this problem and reducing the IM losses, one has to search for an optimum balance between copper and iron losses. This balance can be ensured by optimally controlling the IM magnetic flux.

Many approaches have been developed in order to obtain a highly efficient IM drives. These drives constitute the most attractive and active subjects in the field of motion control. The techniques allowing efficiency improvement can be divided into two categories. The first one is called loss-model – based approach (LMC); which consists of computing losses by using the machine model and selecting a flux level that minimizes theses losses. The second category is the power measure based approach, also known as search controllers (SCs), in which the flux is decreased until the electrical input power settles down to the lowest value for a given torque and speed [4-8, 10].This task can be carried out by indirect field oriented control (IFOC) scheme with appropriate algorithm as described in the present work. On the other hand, simplicity and less intensive mathematical design requirements are the main features of intelligent controllers, which are suitable to deal with nonlinearities and uncertainties of electric motors [16], such as fuzzy controllers.

In this investigation, Fuzzy logic is adopted to design the on-line efficiency improvement algorithm. The motor model includes core losses and uses Razek’s and Mendes series model. Simulation results show that this approach can greatly improve the efficiency particularly at low loads.

II. OPTIMIZATION SCHEME To improve the motor drive efficiency, it requires

application of the optimal magnetizing current (rotor flux) reference value [9]. Hence the optimization mechanism is based on the machine total losses expression, according to the magnetizing current and the electromagnetic torque.

A. Induction Motor Loss The total dominant losses of an IM consist of stator and

rotor copper losses, core losses Pfe and mechanical losses Pm. The stator and rotor copper losses are defined as follows:

Pjs=Rs i2s = Rs(i2

sd + i2sq) (1)

Pjr=Rs i2r = Rr/(1+σr)2[(iμr-isd)2+i2

sq] (2)

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The core losses including eddy current and hysteresis

losses are given by:

Pfe= (kh e�2 + ke e2�2) (3)

The coefficients of hysteresis and eddy current losses are

expressed by kh and ke respectively and can be determined from standard no-load test data [10]. These iron losses can be expressed according to the equivalent circuit of the IM in steady state shown by Fig. 1 as follows:

Fig. 1, Equivalent circuit of the IM

Pfe= I2μRfs/(σr+1)2 (4)

Where: Rfs=Afs +Bfs

2 (5)

where, A and B and fs are respectively constants and stator current frequency. As a reasonable approximation, the mechanical losses depend on the rotor speed.

Pm= km∗ 2r (6)

where km is the mechanical loss coefficient. As the stator currents isd and isq are regulated and the motor is controlled to be field oriented to the rotor flux, according to the following relation:

iqr=(- M/Lr) isq and idr =0

In steady state, the operating losses of the machine can be expressed as follows:

Ploss= Pjs+ Pjr+ Pfe+ Pm (7)

The mechanical losses can be neglected and the motor torque can be expressed as:

Te= (3/2) p M/Lr ( r isq) (8)

By substituting (1), (2) and (4) into (7), we obtain the total losses:

Ploss=(Rs+Rfs)i2μ +[Rs +Rr/(1+σr)2] [Te/p(1-σ)Lsiμ]2 (9)

Minimizing the objective function (9) yields to calculate the partial derivative with regard to the target variable [14]. For this goal, the magnetizing current value obtained by the resolution of the equation (9) is:

Iμ=Kopt Te1/2 (10)

Where: Kopt=A/[np(1- )Ls]1/2

A=[[(Rs+Rr)/( +1)2+

= (Lr/M) -1

According to equation (10), the optimum flux depends on the developed torque, motor parameters and the frequency according to equation 5. Variations of Kopt versus frequency are illustrated in Fig. 2.

Fig.2, Variation of Kopt versus frequency According to equation (10), the optimum flux depends on the developed torque, motor parameters and the frequency (see equation 5). Therefore the optimal flux value can be obtained by tuning Kopt. The variations of Kopt versus frequency are illustrated in Fig. 2. Kopt is related to motor parameters. Therefore this term maybe considered as a core of the minimization problem, which is resolved by updating online Kopt values according to a fuzzy logic system.

III. FUZZY LOGIC APPROACH

The fuzzy logic is an aggregation of rules, based on the

input state variables condition with a corresponding desired output.

In contrast to classical knowledge systems, fuzzy logic is aimed at a formalization of modes of reasoning that are approximate rather than exact [15]. Fuzzy logic is much closer in spirit to human thinking and natural language than the traditional logical systems. Basically, it provides an effective means of capturing the approximate, inexact nature of the world.

A mechanism must exist to decide on which output, or combination of different outputs, will be used since each rule could conceivably result in a different output actions.

Fuzzy logic provides machinery for carrying out approximate reasoning processes when the available information is uncertain, incomplete or vague. The success of this methodology has been demonstrated in a variety of fields.

Several fuzzy logic based efficiency controller have been reported in literature, [9-11]. A fuzzy logic controller essentially embeds the experience and intuition of a human plant operator, and sometimes those of the designer of the plant, [12-13].

Rs

Vs

σLs

R’r/g(1-σ)Ls

Rfs/1+σr)

Is

Iμ Ir

0 0.5 1 1.5 22.2

2.21

2.22

2.23

2.24

2.25

2.26

2.27

Freqency (pu)

Kop

t

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A. Fuzzy state and Control variables The fuzzy controller is designed to have two fuzzy state

variables and one control variable for achieving optimum motor efficiency which is implemented in vector control scheme (see Fig. 3). Each variable is divided into fuzzy segments.thus the main challenge is to tune Kopt which is necessary for flux control to achieve an optimal efficiency.

Fig.3, Bloc diagram of the optimization system

The number of fuzzy segments in each variable is chosen to have maximum control with minimum number of rules .The first variable is the stator current error and the second one is the magnetizing current error. Both fuzzy inputs are defined as:

ΔIs(k)-Is(k-1) (11)

ΔIμ(k)-Iμ(k-1) (12)

The universe of discourse of the first input is divided into three overlapping fuzzy sets: Positive Small (PS), Positive (PM) Medium and Positive Big (PB). The grade of membership distribution is given in Fig. 4.a which uses a triangular distribution.

The universe of discourse of the second input is divided into three overlapping fuzzy sets: Negative (N), Zero (Z) and Positive (P). The grade of membership distribution is shown in Fig. 4.b.

The output variable is the error of Kopt variable. The universe of discourse of this fuzzy variable is divided into seven fuzzy sets.

The membership distribution of this variable is depicted in Fig. 4.c.

(a)

(b)

(c)

Fig. 4, Membership distribution

B. Fuzzy Inference The inference method used is basic and simple and is

developed from the maximum operation rule as a fuzzy implementation function [15-16]. Table 1 contains the corresponding rules of our controller.

TABLE I. RULES MATRIXE

N Z P Is

PS PS Z NS PM PM Z NM PB PG Z NB

-1 -0.5 0 0.5 1

0

0.2

0.4

0.6

0.8

1

DKopt

Deg

ree

of m

embe

rshi

p

NG NM NP Z PP PM PG

I

ref

Speed PI d (q)PI Inverter

3/2

Te

Iμopt

IMI

sqref

Usqref

Isq

Iμ Optimization

algorithm

Fuzzy

Controller

Usdref

P

ΔIsq

ΔIμ

-

+

-1 -0.5 0 0.5 1

0

0.2

0.4

0.6

0.8

1

DImu

Deg

ree

of m

embe

rshi

p

N Z P

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

DIs

Deg

ree

of m

embe

rshi

p

P P P M P G

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00.2

0.40.6

0.81

-1

-0.5

0

0.5

1

-0.5

0

0.5

DIsDImu

DK

opt

C. Fuzzy controller Design The configuration of the proposed controller is shown in

Fig. 5 and the controller surface is illustrated in Fig. 6.

Fig.5, The proposed fuzzy controller

Fig. 6, Optimizing control law mapping

IV. SIMULATION RESULTS

Simulations are performed using MATLAB/SIMULINK

software for energy efficient control of the IM fed by a voltage source inverter. The specifications and parameters of the simulated IM are given in Table 2. Fig.3 depicted block diagram of the proposed system, more details of fuzzy block are given in Fig.5. As an example for efficiency optimization, consider the following load profile. From 0 to 1 second 0.25TL load torque is applied then from 2 to 4 second it is 0.5 TL, then from 4 to 6 second it is TLnominal and finally from 6 to 8 second it is 0.75 TL.Fig.7b represents electromagnetic torque of machine. As it is seen, the electromagnetic torque follows the load torque rather accurately. We can see also from this figure the torque is not affected by the using of the optimization algorithm. Fig.7c shows the rotor flux magnitude, with variation of load torque profile the rotor flux grows larger and vice versa with

fuzzy proposed approach .With conventional method the rotor flux magnetic reaches the rated value and it still attains to this value under different operating conditions such as sudden change in load torque. Efficiency of motor is drawn in Fig.7d with IFOC method effectiveness of loss minimization depends on load torque and it is more efficient at light load. This could be explained as further capability of loss minimization algorithm to decrease copper loss in comparison to iron loss with the proposed approach; efficiency optimization algorithm based on fuzzy logic remains under different load torque. As it is seen in Fig.7d and Fig.8, under different operating conditions (change in reference speed and load torque) fuzzy efficiency optimization control incorporated in IFOC scheme provide on effective means for overall improvement of IM motor drive performance.

When the IM load decreases, the output power decreases and the input power is remaining constant. As a consequence, the IM efficiency decreases.. In order to increase this IM efficiency, the input power has to be reduced. This target can be accomplished by adjusting the rotor flux reference to its optimal value.

Fig.7, Motor Performances Comparison

Fuzzy System

G

G-1

G-1

Z-1

Z-1

Σ

Σ

Σ

Z-1

+-

+-

+

+

ΔIμ

ΔIs

Kopt

0 1 2 3 4 5 6 7 80

5

10 L

oad

(Nm

)( a )

0 1 2 3 4 5 6 7 80

1

2( c )

F

luxe

(wb)

0 1 2 3 4 5 6 7 80

10

20( b )

Tor

que

(Nm

)

0 1 2 3 4 5 6 7 80

0.5

1( d )

T i m e ( s )

Eff

icie

ncy

(pu)

F u z z yF O C

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As can be noticed, Fig. 8 compares the efficiency of the IM

drive system under the losses minimization strategy based on fuzzy control and the conventional field oriented control. It shows clearly the effective improvement of efficiency over light load region for all operating speeds. It is obvious that the amount of energy saving has a considerable value especially beyond the rated load and at all range speeds.

Fig.8, Motor efficiency evolution with motor load

V. CONCLUSION

This paper aims to improve the induction motor drive efficiency that leads to a significant amount of energy saving. This efficiency enhancement is carried out by adjusting the flux level depending on the applied load of an induction motor by using an on-line fuzzy logic optimization controller based on a vector control scheme. A series of the induction motor drive performances are obtained with a variable load under this proposed algorithm. The application of the proposed algorithm yields to a series of simulation performances of the induction motor drive with a

variable load. They present the IM drive efficiency evolution with a certain load profile with the suggested losses minimization strategy based on fuzzy control and the conventional field oriented control. The comparison between these two control schemes reveals that the achieved results are of a great interest. Indeed, the fuzzy control contributes with a great deal to the efficiency improvement for all operating speeds particularly in light load region. This contribution conducts to a paramount energy saving and hence to environment protection.

Appendix

TABLE II. RATING AND PARAMETERS OF IM

Parameters Symbols Values Units power P 1.1 kW Number of pairs of poles np 2

Stator resistance Rs 8 Rotor resistance Rr 3.1 Mutual inductance M 0.443 H Stator self inductance Ls 0.47 H

Rotor self insuctance Lr 0.47 H

Inertia j 0.06 IS Viscose friction coefficient f 0.0 IS

Rated load torque TL 7 Nm

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0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.2

0.4

0.6

0.8

175 rad / s

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0.7

0.8

0.9

1157 rad / s

Effic

ienc

y

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0.7

0.8

0.9

1314 rad / s

Load (pu )

Fuzzy

FOC

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