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FUZZY LOGIC CONTROLLER-BASED

DYNAMIC VOLTAGE RESTORER

FOR MITIGATION OF VOLTAGE SAG

B.PANDA

Asst. Professor, Electrical Engg, KIIT University Bhubaneswar, Odisha, India

A.K. MAHAPATRA

Asst.Prof,Electrical Engg, PKACE Baragarh Orissa, India

D.P.BAGARTY* and S. BEHERA** *

Asso. Prof, Electrical Engg and **Professor, Instr & Electronics Engg C.E.T. Bhubaneswar

Bhubaneswar-751003, India

Abstract : Voltage sags are frequent events and are usually associated with fault in network, with energization of transformer or starting of large motors etc. Their duration is very short, but they can represent big problems of sensitive load like power electronic devices. In this paper, a fast PWM-based Dynamic Voltage Restorer (DVR) has been modeled and simulated with a Fuzzy Logic Controller (FLC) to investigate its performance and the relevant results are presented.

Keywords:. Voltage Sag, DVR, Sine PWM Technique, Fuzzy Logic Controller, Matlab/Simulink

1. Introduction

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Various control strategies have been developed to mitigate the voltage sag/swell [9-10] and the mitigation of unbalanced voltage dips using SSC(Static series compensator) has been analyzed by Awad et.al [11]. The authors also have studied the performance of DVR and improved performances with elimination of selective predominant harmonics [12]. A generalized voltage compensation strategy for mitigating the impacts of voltage sag/swells has been investigated [13,14]. DVR acting as series active filter has been focused [15]. C.S.Lam et.al [16] have used voltage swell and over voltage compensation technique with unidirectional power-flow controlled DVR. The applications of FLC have taken new dimension in various fields. In case of STATCOM as Active power filters, the FLC has taken lead role [17~19], whereas the use of Fuzzy Logic Controller (FLC) in case of DVR lacks in literature.

This paper presents the digital modeling and simulation of a FLC-based DVR under voltage sag/swell phenomena. In this case, the fuzzy logic controller has been incorporated instead of conventional PI controller. The simulation tool is the MATLAB/Simulink Power System Blockset (PSB). To mitigate the voltage sag problem, a prototype model has been considered. The mathematical model and instantaneous current control strategy are explained and discussed. The capability of DVR to mitigate the voltage sag is demonstrated by digital simulation. The addition of fuzzy logic control to conventional PI control gives added advantage of faster response as compared to the conventional one.

2. Basic Structure of DVR

The basic elements of a DVR (i.e., shown Fig.1) are dc side energy source, voltage source converter, injection series transformer and harmonic filter. The details about these components are described as follows.

2.1. DC side Energy Source

The energy storage devices are dc capacitors, batteries, super conducting magnetic storage and flywheels. The present work employs dc capacitor banks. The rating of dc side capacitor has been chosen considering the voltage sag without phase angle jump. The size of capacitors should be chosen such that during sag of maximum expected magnitude and duration, the load voltage is kept at rated value and dc voltage does not decrease below a minimum allowable selected value. In case of voltage sag Vsag (pu) with no phase angle jump,

the SSC should inject an active power in order to restore the pre-sag rated voltage Vlr at the load terminals and

this active power is given by

) V 1 ( P ) V 1 ( cos I V dt dv v C i v

PDVR  dc dc  dc dc dc  lr lr lr  sag  lr  sag (1)

where the load current Il and power factor cos r are assumed to be constant and equal to their rated value

during sag compensation. Plr is rated load power and vdc is the dc voltage across the capacitor.

If tsag is the voltage sag duration, the energy to be supplied by DVR is

dt ) V 1 ( P dt ) dt dv v C ( dt P W sag t t t lr t t t dc dc dc t t t DVR DVR sag 0 0 sag 0 0 sag 0 0    

 (2)

This simplifies to

Fig.1: Basic Structure of DVR

vg

- vi +

(3)

C

v (t t ) v (t )

P (1 V ) 2 1 sag lr 0 2 dc sag 0 2 dc

dc    

 (3)

If vdc(to) = Vdcr ( i.e., the initial dc link voltage is assumed at its rated value, and vdc(to+tsag) = kd Vdcr, where

kdVdcr is the minimum allowable dc-link voltage at the end of voltage sag (0 <kd < 1) to compensate a

maximum voltage sag magnitude Vsag,max for a maximum expected sag duration tsag.max, then value of

capacitance should be

) k 1 ( V ) V 1 ( t P 2 C 2 d 2 dcr max . sag max . sag lr dc  

 (4)

The size of dc capacitor will be reduced by increasing value of Vdcr and this voltage depends also on maximum

voltage rating of the VSC power electronic devices. The voltage rating of capacitor also limits the maximum injection voltage.

2.2. Voltage- Source Converter (VSC)

The Voltage Source Converter (VSC) is controlled by a Pulse Width Modulation (PWM) technique. The magnitude of modulating signal is derived from control unit and this signal is then compared with fixed carrier signal to extract the signals of switching devices of converter. When the network is at its rated value, it is therefore possible to constrain the inverter to insert a voltage identically equal to zero by properly controlling semi-conductor components.

2.3. Series Injection Transformer

As far as the rating of transformer is concerned, the following considerations can be done. Supposing to compensate a voltage sag of max depth Vi.max (Vgr) (i.e., Vi.max (pu) <1, the maximum series injection voltage and

Vgr is the grid-rated line-to-line voltage), the transformer power is given by

At Vi.max VgrIlr (5)

where Ilr is rated load current.

As the voltage sags are short compared to thermal time constant of a transformer, one can choose the rated power smaller than above calculated value. As well known [7], the RMS value of the fundamental frequency component Vc.1 of the VSC output phase voltage can be expressed as a function of PWM modulation index

ma (i.e., ma <1) and of dc side voltage vdc

Vc.1ma vdc 2 2 (6)

Similarly Vc.1max marvdcr 2 2 (7)

where mar modulation index at rated value.

Since the DVR has to compensate a voltage sag of max depth Vi.max (Vgr), the transformer turn ratio Kt can be

determined dcr ar max . i gr max . 1 c gr max . i t V m V V 2 2 V ) V ( V

K   (8)

In the present work, the modulation index at rated value mar = 0.8 has been chosen in order to work in linear

region when the maximum series injection voltage is required and to have still a compensation margin in the linear region for the voltage sags of larger depth or during compensation process, the dc side voltage falls below its rated value.

2.4. Harmonic Filter

A passive filter is needed for blocking the high-frequency harmonics generated by PWM switching. This filter can be connected either on converter side or on line side. In present case, a passive filter is considered on converter side and the cut-off frequency is decided based upon source frequency with 50 Hz.

3. Fuzzy Controller

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information for appropriate fuzzification operations, the inference mechanism and defuzzification. The rule-base consists of a set of linguistic rules relating the fuzzy input variables to the desired control actions. Fuzzification converts a crisp input signal, the error (e), and error change (e) into fuzzified signals that can be identified by level of membership in the fuzzy sets. The inference mechanism uses the collection of linguistic rules to convert the input conditions to fuzzified output. Finally, the defuzzification converts the fuzzy outputs to crisp control signals, which in the system acts as the changes in the control input.

The typical input membership functions for error and change in error are shown in Fig. 3, whereas the output membership function for change in control input is shown in Fig. 4. The output generated by fuzzy controller must be crisp which is used to control the drive unit and thus accomplished by the defuzzification block. Knowledge base involves defining the rules represented as a set of if then rules, for example if speed error is positive large ‘PL’ and error change is negative large ‘NL’, then change in output is zero ‘Z’. The control rules are evaluated by inference mechanism. Many defuzzification strategies are available, such as, the weight-average criterion, the mean-max membership, and center-of-area (centroid) method. The defuzzification technique used here is based upon centroid method that is shown in Fig. 5(a & b). Suppose the voltage error is – 20 and change in voltage error is -17, then e will be NS and the change in error will be PS or PL. So the rules relating the error and error rate are “If ‘e’ is ‘NS’ and ‘de’ is ‘PS’ then change in control input is ‘Z’ (Fig. 5(a))” and If ‘e’ is ‘NS’ and ‘de’ is ‘PL’ then change in control input is ‘PS’ (Fig. 5(b))

By using the most commonly used defuzzification method, i.e. the Center-of-area method, the defuzzified values of increment in control inputs are obtained as C* = (C1 * A1 + C2 * A2)/ (A1+A2), where C1, A1: - Centroid and area derived (i.e., from Fig. 5(a)) from membership function for change in control input. Similarly, C2 and A2 represent centroid and area shown in Fig. 5(b).

NL NS PS PL

1

Z

0 15 50 90

-15 -50 -90

NS PS PL

1

Z NL

-20 -15 -5 0 5 15 20

(a) (b)

Fig. 3. Membership function for (a) error ‘e’ (left) , (b) change in error ‘e’ (right)

Fuzzification Inference Mechanism

Defuzzification

Error Change Error

Control output(u)

Knowledge Base

Data | Rule Base | Base

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4. Fuzzy Control System of DVR

In present case, a complete control scheme will be defined for a DVR, which is connected to a linear load consisting of a resistance and inductance.

4.1. Model of Control System

In order to study DVR connected in series with line as shown in Fig.1, the network can be simplified shown in Fig.6.

In this case, the VSC is considered as a voltage source with amplitude KtVc, Lt is leakage inductance of series

transformer referred to network side. The source is represented by an ideal voltage source having amplitude Eg

and inductance Lg. The voltage available before DVR is Vg. The load is modeled as the series resistance Rl and

an inductance Ll.

In order to set up an effective control system, it is first of all necessary to adequately model the system to be controlled. To do this, the following hypotheses have been done.

A first dynamic model is considered with the filters neglected. The VSC is modeled as an ideal voltage source (i.e., with no delays)

l Rlil(t) vg(t) Kt vc(t) L Lt Ll dt

di

L      (9)

Fig.4. Memberhip function for output (change in control input ‘u’ )

NL NS PS PL

1

Z

-40 -30 -20 0 20 30 40

NS PS Z

-20 17

C1, A1

NS PL PS

-20 17

C2, A2

Fig.5. Defuzzificztion technique using centeroid method

(a)

(b)

Fig. 6 Single phase equivalent circuit of the system under study

Eg

Kt Vc Vg

Lg

Vl

Rl Ll

(6)

R i (t) dt di L ) t (

vl  l l  l l (10)

where vl(t): load phase voltage, il(t): load phase current.

Applying Park’s transformation to above two equations, one has following d-q equations from (9)

) t ( v K ) t ( v ) t ( i wL ) t ( i R dt di

L ld l ld  lq  gd  t cd (11)

R i (t) wLi (t) v (t) K v (t) dt

di

L l lq ld gq t cq

lq

(12)

and from (10)

R i (t) wL i (t)

dt di L ) t (

v l ld l lq

ld l

ld    (13)

R i (t) wL i (t)

dt di L ) t (

v l lq l ld

lq l

lq    (14)

where ‘w’ is the system angular frequency and having indicated with xd and xq, the d- and q-axis components of

each quantity.

A symmetrical voltage sag occurs at t=t0 can be represented in this reference system with a step-variation of the

network voltage vgd(q); therefore, during the sag, the equations (11,12) can be rewritten in terms of variations

with respect to pre-sag conditions, obtaining a system of ordinary differential equations, with initial conditions

ild(t0) = ilq(t0) = 0.

This allows to apply the Laplace Transform and write the following equations from (11,12).

sLild(s) Rlild(s)wLilq(s)vgd(s)Ktvcd(s) (15) sLilq(s) Rlilq(s)wLild(s)vgq(s)Ktvcq(s) (16) and from (13,14)

vld(s)  sLlild(s) Rlild(s)wLlilq(s) (17)

vlq(s)  sLlilq(s) Rlilq(s)wLlild(s) (18)

After some algebraic manipulations, one easily gets from (15,16) and (17,18) as follows.

vld(s)  G(s)

vgd(s)Ktvcd(s)Gi(s)ilq(s)

(19) vlq(s)  G(s)

vgq(s)Ktvcq(s)Gi(s)ild(s)

(20) where G(s) and Gi(s) are defined as

l l l t i l l l R sL R wL ) s ( G and R sL R sL ) s ( G    

 (21)

Hence defining the system

vcd(s)  vgd(s)Ktvcd(s)Gi(s)ilq(s) (22)

vcq(s)  vgq(s)Ktvcq(s)Gi(s)ild(s) (23)

to be controlled is simply described by

vld(s)G(s)vcd(s) and vlq(s)G(s)vcq(s) (24) The above pair of equations in (24) can be written as a single one.

vldqG(s)vcdq (s) (25)

4.2.Fuzzy Control Scheme

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5. Simulation Results

A small prototype model of DVR connected to 1-phase utility has been considered and studied analytically with a Fuzzy controller. The simulation of this model is carried out with MATLAB/Simulink based on data as given Appendix. The results from simulation are presented in Figs. 8~14. Figures 8, 9 and 10 correspond to similar condition. Input is changed keeping load parameters and its reference command constant.

TABLE-I Error (e)

PL PS Z NS NL

Change in error (de/dt)

NL PL PL PS PS Z NS PL PL NS Z NL

Z PL PS Z NS NL

PS PS Z NS NL NL PL Z NS NS NL NL

Fig.7 : Feedback control loop of DVR

Fuzzy Controller

G(s)

V

ldq,ref

V'

cdq,ref

V

ldq

de/dt

e

Time ---- (s)

Fig. 8: Voltage waveform of source voltage (vg), injected voltage(vi) , load voltage (vl)

and load current (il) ;

Vg – changes from 150 to 180 V at 0.5 sec,

Load parameters and reference load voltage remains constant throughout

vg (V)

vi(V)

vl(V)

(8)

The waveforms of source voltage (Vg), the injection voltage (Vi), load voltage and load current are shown in

Fig. 8. During simulation, the input voltage is maintained at 150 V at time ‘t’=0. The reference voltage of the controller is set at 160V. At time ‘t’=0.05 sec, the controller is activated. Before this activation, the load voltage becomes less than source voltage due to impedance drop across secondary of the series injection transformer. This drop could be avoided using a switch across secondary of injection transformer before activation of

Q

P

Time ---- (sec)

Fig.10: Active power (P) and reactive power (Q) during step change in input voltage at t= 0.4 sec without any change in load and

reference load voltage command.

(Scale: 1:1)

P(W) Q(VAR)

Time ---- (sec)

Fig.9: RMS values of source voltage (Vg ), injected voltage (Vi) and load voltage (Vl)

during input change at 0.4 sec ,but with load and reference constant

Vg (V)

Vi(V)

(9)

controller. When the controller is activated at 0.05 sec, the load voltage follows reference command and sticks to reference value till the input voltage is increased to 180V at 0.4 sec. In above case, an artificial voltage swell is created intentionally at input before t<=0.4 sec and t >0.4 sec respectively to observe the action of controller at different time interval. During t=0 to 0.4 sec, the input voltage is less than reference value thus exhibiting artificial sag condition, whereas between t=0.4 to 0.8 sec, the artificial swell is created by suddenly increasing input voltage above reference value. The load parameters are kept unchanged during the variation in input voltage and the controller is found to be working satisfactorily. Corresponding to Fig. 8, the rms values of the source voltage, the injected voltage and the load voltage are shown in Fig. 9. Under same situation, the variation in load active power and reactive power are shown in Fig. 10.

Now it is further investigated with step change in load without any change in input and reference command. With these conditions, the figures 11,12 and 13 are obtained. In this case, the source voltage of 150V and load reference command of 160 V are maintained constant with step change in load at 0.5 sec. In this case also the controller is activated at t=0.05 sec. The source voltage, injected voltage, load voltage and load current are shown in Fig. 11. It shows that even if the load current increases, the controller acts in such a away so as to boost the injected voltage level in line to maintain load voltage constant. The rms values of source, injected and load voltage under this situation are shown in Fig. 12, where as Fig. 13 demonstrates the variation in load active and reactive power. It is found that the controller is acting satisfactorily under both variations in input voltage and also during step change in load.

The harmonic analysis is shown up to 500Hz considering two cycles of load voltage in Fig. 14. The predominant harmonic voltages are found to be at 250, 400 and 450 Hz. Their magnitudes are found to be 1.6%, 0.5% and 1.5% of fundamental respectively and the THD is 2.2% that lies in safe limit of IEEE std. The comparison between FLC and conventional PI controller has been given in Table-II. It is observed that the effect of fuzzy controller makes faster and reduces oscillation as compared to conventional PI, when the system is subjected to small signal perturbation.

Time ---- (sec)

Fig. 11: Waveforms of source voltage (vg), injected voltage (vi), load voltage

(vl) and load current (il) when there is step change in load at t= 0.5 sec

without any change in source and reference command

vg(V)

vi(V)

vl(V)

(10)

Time ---- (sec)

Fig.12: Waveforms of rms values of source voltage, injected voltage and load voltage current when there is step change in load at time 0.5 sec without any change

in source and reference command

Vg(V)

Vi(V)

Vl(V)

P

Q

Time ---(sec)

Fig.13: Active power (P) and reactive power (Q) when there is change in load at t =0.5 sec without change in source voltage and reference command

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5. Conclusion

The problem of voltage sag/swell which has emerged a major concern in the field of power quality has been investigated in this paper considering parameters of a prototype model. The effective algorithm has been developed in order to obtain a fast response of the device. The analysis of mitigating voltage sag of a 1-phase DVR under fuzzy controller is carried out using MATLAB Power System Blockset. The results of simulation are presented and discussed. The proposed controller of DVR exhibits a highly effective, a faster and flexible control for an efficient voltage flicker mitigation in power systems

Appendix: Simulated Data

Supply System : Rated voltage= 150~200v/ph , Frequency = 50 Hz; 1-phase Series Transformer: Rated power= 3.3KVA, Primary rated voltage=100V; Secondary rated voltage=100V; Primary/secondary parameters: R (0.0015 pu), L(0.005pu); Magnetization reactance = 1.85pu, Magnetization resistance = 10 pu VSC: PWM Based, Dc side voltage= 100 V, Frequency modulation ratio = 40; Harmonic Filter: Primary side: (T-Filter): Lf =2mH, Rating of Cf= 3 kVAR; Load: R=5 ohm, L = 25 mH; Auxiliary load: R=40 ohm. L = 1mH;

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TABLE-II

PI Controller FLC

Dynamic response of load voltage Nearly One cycle Less than a quarter cycle

Source current THD 3.46 % 2.2%

Figure 14: Harmonic analysis of load voltage

V

l

(V)

V

h

(%age of 50 Hz

(12)

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Referências

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