Adaptive Fuzzy Control for Uninterruptible Power Supply with Three ...

Adaptive Fuzzy Control for Uninterruptible Pow4 Supply with Three-phase P W M Inverter Feng-Yih Hsu' and Li-Chen F'u'*~ Dept. of Electrical Engineering' Dept. of Cornpu ter Science & Information Engineering2 National Taiwan University, Taipei, Taiwan, R.O.C. Abstract The major problems of uninterruptible power supply (UPS) with three phc PWM inverter arise from unknown nonlinear loading to and phase couplings the inverters. I n this paper, an adaptive fuzzy control is proposed to solve tht problems. The control objective is to track the desired sine waveform regardless the versatile nonlinear loading, whose bound can be represented b y a fuzzy rule-ba: The algorithm embedded in the proposed architecture can automatically update t h z z y control rules and, consequently, drive the tracking errors to a designated nedg borhood of zero.

I

Introduction

To provide the reliable uninterruptible power supply (UPS) for the use of COI puters or factory automation systems has become more and more important. T: most common configuration of a UPS system consists of a dc source, a dc-ac invert( and an inductance-capacitance (L-C) filter. To establish a clean and reliable U P the waveform of tlie output voltage of the UPS system can only contain low tot harmonic distortion (THD) and can only have little variation even in the face varied nonlinear load. To achive the above characteristics, a well designed control1 is needed in a UPS system to compensate for the different system characteristi resulting from the various (nonlinear) loads to and phase couplings of the invertei A straightforward approach to improve the performance is to use a feedforwai compensator to cancel the dynamics of the unknown load. Dead beat control hq been proposed for the simple linear system load [1]-[4]. For a complex or ill-define load model, repetitive control can assure high performance in the steady-state col dition but results i n poor transient response because of the long period to learn proper control law [5]. On the other hand, the conventional control in an analc UPS is to raise the control gain properly to robustify the stability as well as tk perforinance for unknown load [GI. An dternntive, however, exists which is to U: an intellignet control metli(1ology to suitably iicljust tlie control gain in a responsh 0-780%3687-9/9681996

IEEE

188

,y so i l s to compensate for the variation of characteristics due to load change. llowiiig this stremi of thought, in this paper, AII adaptive fuzzy control for a UPS ;tern is proposed to achieve the aforementioned control goal.

Problem Formulation A UPS system equipped with a three-ph,we PWM inverter is depicted in Figure which consists of an L-C filter at the inverter output, IGBT's t o play as switching vices, a dc capacitor filter at tlie inverter input, and an unknown load at the G C ;er output. The variables v r l , U,? and vr3, are the PWM modulation signals iich are the inputs to the PWM moduliitor in the figure, whereas the variables , wi2 and w i 3 , are tlie inverter outputs satisfying the following equality:

,

lere

Wi

= [ w i ~ , ~ i ~ , w ; ~w,. ] "= ' , [ V , . ~ , V , ~ , V , ~ ]o~h, = [ v h l , v 1 , 2 , v h ~which ]~ denotes

e voltage-drop vector at the on-state of IGBT, and Ed is the dc voltage of the

verter. From Fig. 1, the mathematic model of the UPS system can be formulated follows:

- ir, Wi - 11, - V N

Cpii, = L,fi =

= ii

2,.

here w, = [ ? J , ~ ,v,z ,q.;3]'" is the vector of output voltages, U N = [U,, vn, u , , ] ~with = ~ ( w I l+v,2 1 1 ; ; ~ ) bring the neutral voltage, i, = [icl,icP,ic3]T is the vector of e capacitor currents, i, = [irL,ii2,ir3]7' is the vector of the inverter currents, and = [if,l, i,,3]' is the vector of the load currents. By differentiating equation ), we can get the following equation:

+

r .

..

I),

3

1:

= -2,

cp

1 .

-(it

c:,

. - il,)

1

----(Vi

1

CpL,

1: - 21, - U N ) - -2L

(4)

CP

substitute equiLtio11 (1) into equation (4),we can then obtain the dynamic equaof the C'PS syste1n ;U follows:

311

1 Ed ij, = -( w,. - 111, - w, - PIN - L s i L ) C,L, 2

(5)

The control goal is to let the ,. output-voltage vector w, track the desired sineave vector IJE = [vf , U : , , uzB] = [w;,(27rfwt),vf +27rfwt),U; +27rfwt)IT,

,

l(y

(T

liere fu is t h e frequenc;y of the clasired sinewave voltage. Let the tracking error x t o r be denoted ;U e , = wf - w, = [evc eve ,ev,3]'r and its time derivative as

,, = Sz - 6, = SE - &iC. 5

Then, the error dynamics of the system can be derived

follows: cu + 2, and are some positive constants. where gf3 =

gtJ

1gt,l

Et

ell

et

To remove the effect of U,, + U , 2 + U .

-

-(U,,, +UJ,l +U,,

3

El,,

Izilr,I

3

3l.

+

+

u,.~ vr2 u,.~ = 0 so that we can derive U,, Now, let the control law be designed as follows:

f ~ , ~let ,

n r

Vry

where K,, =

111

=

& - 7",-is r

;I

(

-(url f u r ? ) ,

constant gain, f is the proposed adaptive fuzzy controll

Adaptive Fuzzy Control

Let f ( v C kq,k ) be rewritten

:ISfollows:

f ( W x , a )=

+ (lick1 + €)7f(Uck,qk),

(1

(cl+*) where E is i i sinall constant satisfying E 2 h . l , for ~ k = 1 , 2 and 7f(wCk,qk) the key adaptive fuzzy function. To simplify the notations, let U = [ u l ,u2IT w1 U I = v c k , U? = q k , and TU = 7 f ( v C k , q k ) ,where vCkand q k are the k-th elements U, and q , respectively.

190

s a general description of the fuzzy knowledge representation [lo], a fuzzy rule

consists of a collection of fuzzy If-then rules. Let U denote as an input fuzzy i)r in the discourse universe U,,and L = {L;,. ,LTi . * ., Ly } x i a family m y sets associated w i t h tlie membership functions p L ; j (see Fig. 2) corre+

ding to the variable 1 4 , j = 1,2, where Ly' is obviously a fuzzy set in L j . In tion, tlie centers of tlie family of fuzzy sets, L j , are grouped into a set as 'iij = 1. -1. * * * U / 1, wlit?re E? is a center satisfying E; < . . < G? < . . < U; ) see Fig. 2). Let L and a be both defined as product sets, L = Lj and of 2 iij, respectively, consisting of the families of fuzzy sets Lj and the sets of ers i i j , j = 1,2. Then, an example of the i-th fuzzy rule is expressed as follows:

- q,

n,'=,

nj=,

-

is L a ( ; ) , then

w is Q b ( ; ) , (13) re La(;)E L , a(i)= cyI (i) x is a product index associated with the i-th rule, : ~f ( U ) is denoted as an output fumy variable. Let Q = {Q', ,Q O , . ,Q'} jenoted as a family of fumy sets associated with the membership functions corresponding to the output variable ?ut with QO being a fuzzy set in the ily Q and Qfl(;) E Q with p(i) being an integer index associated with the ixle. Furthermore, let the sets of centers of the family of fuzzy sets, Q, be oted as z = {d,. . . ,WO, - .. ,iij"}l where d is a center of the fuzzy set satisfying < . .. < < .. . < ID''. Generally speaking, w can be expressed as follows: be ritten as: R[i] : If

U

I-

mO(;)&(u) = oT