Functional design for a system-wide multivariable damping controller (for power systems)

IEEE Transactions on Power Systems, Vol. 5, No. 4, November 1990 1127

FUNCTIONAL DESIGN FOR A SYSTEM-WIDE MULTIVARIABLE DAMPING CONTROLLER

S. Hirano, T. Michigami, A. Kurita Tokyo Electric Power Company

Tokyo, Japan

Abstract - The damping of large power systems may be poor at heavy system loading condltions. Thls may occur even with traditional supplementary damping controls in service. This paper presents a practical coordinated system-wide approach to this problem. Multlvariable control techniques. tnvolving many machines and associated measurements and controls, are applied on a large scale system wlth realistic dynamlcs. A unique iterative design method, with multtple tasks, is presented. Use of elgenvector based dynamic reduction, sub-optimal state space control design, reconstitution of design to full system representation, and verlflcatlon is shown. The resulting hierarchical controller Is shown, with time slmulatlons and eigenvalues. to stabilize the system for heavy power transfer without adverse slde effects.

Keywords - Dynamic Stabillty, Multivariable Control, Damping, Interarea Osclllatlons. PSS

I. INTRODUCTION

This paper presents the results of a study to develop a functional design for a system-wide multlvariable damping controller.

To provide the most meanlngful results, the study system characteristics Included:

1. Heavy Power Transfer, 2. Multlple Stations, 3. Reallstlc Apparatus Dynamics, and 4. Diverse Operating Conditions.

The system model used for the study In this paper comprises over 100 machines, and about 300 buses and 350 branches, total, for the EHV and HV transmission systems. Host machine models have power system stabilizers (PSS's), and each machine model has its own exciter and one of five types of turbine models.

System studies conducted by various utilities have Indlcated that as the system load grows, there Is the potential for reduced damping In the system. In the system studied in this project, the severest case is a

90 WM 118-0 PWRS by the IEEE Power System Engineering Committee of the IEEE Power Engineering Society f o r presentat ion a t the IEEE/PES 1990 Winter Meeting, Atlanta , Georgia, February 4 - 8, 1990. Manuscript submitted August 31, 1989; made ava i l ab le f o r p r in t ing December 27, 1989.

A paper recommended and approved

D.B. Mapper, N.W. Miller J.J. Sanchez-Gasca, T.D. Younkins

General Electric Company Schenectady, New York 12345

nighttime operating condition wlth heavy cross-system power transfer. In thls case, the result I s dynam- ically unstable operatlon. The heavy transfer results from several pumped hydro units. located on one side of the system, operating at night as motors (pumplng mode). The required power Is transferred across the system from base load units on the slde opposite the pumped hydro. During the day, the pumped hydro units operate In the generatlon mode. reduclng the power transfer relative to system load.

The undesirably low damping calculated with this detailed system model appears as different groups of machines, or different areas, swinging with respect to each other. The low darnping occurs despite the exten- slve use of PSS's.

The goal o f thls study was to deslgn a system-wide dynamic controller to improve damping. This requires a broadly based problem formulation. Because the low damping Involves several groups of machines throughout the system, It was considered that a multivariable controller would provide superlor performance. Multi- variable controllers (HVC) include measurements and control signals throughout the system, and the means to coordinate their interaction.

The use of a multivariable controller to improve damping in a three machine system was demonstrated in Reference [l]. This paper presents a signlflcant technical advance beyond the Reference [l] approach by designing a multivariable damplng controller for a large-scale power system with characterlstics ( 1 ) through (4) above.

Power system stabilizers (PSS) were included in the apparatus modeled. Their usefulness to improve damping is well known [2,3]. The multivariable controller is therefore designed to work with the PSS In service, and to provide damping beyond that posstble with the PSS alone.

11. TECHNICAL APPROACH

The technical approach for the design of the system-wide multivariable damping controller was fol- lowed in the sequence Indicated; the remaining sec- tions of this paper also follow In the same sequence.

Section of Paper Technical ADDroach SteD

111. Objectives and Constraints. Establish the technical Objectives of the design and the constralnts, or limlts, to be Imposed on the design.

IV. Model Reduction. In two steps, reduce the full system model to a size that is more manageable for use with the linear multivariable design software. Flrst, combine all slmilar machines at statlon buses.

1128

V .

V I .

Second, p e r f o r m a dynamic r e d u c t i o n t o i d e n t i f y t h e major coherent areas, w h i l e r e t a i n i n g major EHV t r a n s m i s s i o n buses. Each coherent a rea i n c l u d e s one e q u i v a l e n t genera tor , w i t h an e x c i t e r and PSS, and connect ions t o t h e r e t a i n e d EHV t ransmis- s i o n . Check by s i m u l a t i o n t h a t t h e reduced n o n l i n e a r model r e t a i n s t h e p r i n c i p a l c h a r a c t e r i s t i c s o f t h e d e t a i l e d model.

M u l t i v a r i a b l e C o n t r o l (HVC) Design. Develop a m u l t i v a r i a b l e damping c o n t r o l l e r f o r t h e reduced system u s i n g o u t p u t feedback des ign method [ 4 ] . Check des ign by e igenva lues and s i m u l a t i o n s .

R e c o n s t i t u t i o n . R e c o n s t i t u t e t h e f u l l s i z e d system models w i t h t h e MVC damping c o n t r o l l e r embedded. Th is r e q u i r e s d i s t r i - b u t i n g t h e c o n t r o l s and measurements f r o m t h e reduced system model t o each o f t h e system genera tors and c o n t r o l s i g n a l r e f e r - ence j u n c t i o n s . Us ing s i m u l a t i o n s . check t h a t t h e f u l l model performance matches t h a t o f t h e reduced system model.

V I I . V e r i f i c a t i o n . E s t a b l i s h t h e f i n a l c o n t r o l d e s i g n c o n f i g u r a t i o n and v e r i f y t h a t t h e MVC damping c o n t r o l l e r meets t h e des ign o b j e c t i v e s and c o n s t r a i n t s . Th is i n c l u d e s robustness checks, c o o r d i n a t i o n w i t h o t h e r system c o n t r o l s , and checks f o r adverse machine i n t e r a c t i o n s .

111. OBJECTIVES AND CONSTRAINTS

The o b j e c t i v e o f t h e MVC damping c o n t r o l l e r i s t o p r o v i d e 10% damping r a t i o f o r i n t e r a r e a o s c i l l a t i o n s . Th is w i l l be demonstrated by s i m u l a t i o n o f severe EHV f a u l t c o n d i t i o n s . and o t h e r cont inqenc ies . e.q.. l o s s of

1.

2.

3 .

4 .

. - a major u n i t .

The c o n s t r a i n t s on t h e d e s i g n are :

The MVC damping c o n t r o l l e r must c o o r d i n a t e w j t h t h e o t h e r system c o n t r o l s ( g e n e r a t i o n d i s p a t c h ; l o a d frequency c o n t r o l ; v o l t a g e c o n t r o l ) . F u r t h e r , t h e MVC damping c o n t r o l l e r must n o t i n t e r f e r e w i t h e x i s t l n g t r a n s i e n t s t a b i l i t y c o n t r o l s .

To account f o r c o m m u n i c a t i o n / d i g i t a l c a l c u l a t i o n de lays , a l l o w a minimum 40 ms t i m e de lay between measurements and c o n t r o l s i g n a l s .

C o n t r o l a c t i o n s h a l l n o t cause excess ive v a r i a t i o n i n ma jor system v a r i a b l e s ; e.g., v o l t a g e , power, speed, f requency.

Approx imate ly 80% o f t h e system machines a r e a v a i l a b l e f o r use by t h e MVC damping c o n t r o l l e r .

To measure progress toward t h e damping o b j e c t i v e s w i t h c o n s t r a i n t s , t h e s tudy was organ ized t o examine performance under t h e f o l l o w i n g c o n d i t i o n s :

C o n d i t i o n Stud ied Base

Day Yes Yes N i g h t Yes Yes

I nc rea s ed Opera t ion - Load Power T r a n s f e r

I V . MODEL REDUCTION

A. F i r s t Reduct ion

The f i r s t model r e d u c t i o n combined i n d i v i d u a l machines a t power s t a t i o n s t h a t met t h e f o l l o w i n g c r i - t e r i a : i. connected t o a common bus; 11. same pr ime mover type ; iii. s i m i l a r i n e r t i a s ; and i v . no major d i f f e r e n c e s I n machine parameters, e x c i t e r s , and P S S ' s . T h i s f i r s t r e d u c t i o n decreased t h e number o f machines f rom over 100 t o 65.

There a r e f i v e r e p r e s e n t a t i v e prtme mover types, a l l w i t h speed governors, as f o l l o w s :

1 .

2.

3 .

4 .

5 .

F o s s i l f u e l reheat steam t u r b i n e , cross-compound, w i t h i d e n t i c a l power r a t i n g s and very s i m i l a r i n e r t i a s f o r b o t h s h a f t s . (These two t u r b i n e - genera tors can be combined.)

F o s s i l f u e l reheat steam t u r b i n e . cross-compound, w i t h an i n e r t i a r a t i o o f 1:6 between p r i m a r y and secondary s h a f t s . (These two t u r b i n e - g e n e r a t o r s cannot be combined.)

F o s s i l f u e l reheat steam t u r b i n e . tandem compound.

Nuc lear steam t u r b i n e , w i t h m o i s t u r e s e p a r a t o r / r e - h e a t e r .

Hydro t u r b i n e , i n c l u d i n g pumped hydro, w i t h i n a c - t i v e governor when pumping.

A l l p r ime movers were reduced t o s i m p l i f i e d two- s t a t e I E E E t y p e models, except f o r t h r e e s t a t e s f o r t h e second t y p e cross-compound u n i t s . A l l genera tors were reduced t o f o u r - s t a t e models w i t h o u t f i e l d s a t u r a t i o n , b u t w i t h XA a d j u s t e d f o r s a t u r a t i o n e f f e c t s .

A l l e x c i t e r s were reduced t o one o f f i v e non-IEEE types . Two o f t h e f i v e a r e shown i n F i g u r e 1 . A l l e x c i t e r models have t h r e e o r f o u r s t a t e s . Func t ion G1(s) i s a s imp le l a g f u n c t i o n , wh ich was n o t used f o r a l l a p p l i c a t i o n s ; I n a d d i t i o n , about 25% o f t h e machines do n o t have PSS's. The i n p u t f u n c t i o n V i s a compensation s i g n a l used on some cross-compoun! u n i t s t o min imize c u r r e n t o s c i l l a t i o n s between t h e two genera tors ; V o i s modeled t o be D r o D o r t f o n a l t o t h e change i n g e f e r a t o r genera tor t e r m i n a l some o f t h e e x c i t e r f i e l d f o r c i n g .

r e a c t i v e power o 'utput d i v i d e d by v o l t a g e . F i n a l l y , t h e l i m i t s on models were s e t t o p e r m i t n e g a t i v e

r

vO Pk s

A s t h e s tudy progressed, i t was found t h a t n i g h t - t i m e o p e r a t i o n w i t h inc reased power t r a n s f e r was t h e l i m i t i n g c o n d i t i o n . F i g u r e 1 . E x c i t e r Model Types

1129

PSSIs were modeled w l t h a t r a n s f e r f u n c t i o n o f up t o f i v e s t a t e s . The PSS o u t p u t s were l i m i t e d t o e i t h e r +5% o r +lo%. A l l PSSls use genera tor a c t i v e power as I n p u t s , except f o r two P S S ' s , which use machlne speed as I n p u t s .

B. Dynamic Reduct ion

The dynamic r e d u c t i o n o f t h e 65 machine system was performed i n two stages: f i r s t , t h e power network and genera tors were dynamica l l y reduced; second, e q u i v a l e n t models f o r t h e c o n t r o l elements, I .e . , e x c i t e r s . PSS's, and governors were ob ta ined.

The f i r s t s t e p I n t h e r e d u c t i o n process c o n s i s t s o f I d e n t i f y i n g coherent groups o f genera tors . The frequency domain s low coherency method i n [5,6] was used t o i d e n t i f y t h e coherent areas I n t h e system based on t h e i r modal p a r t l c l p a t t o n . The dynamic e q u i v a l e n t o f t h e network and genera tors was t h e n ob ta ined u s i n g t h e E P R I dynamlc e q u l v a l e n c i n g methodology [7]. F i c t l - t i o u s l i n e s a r e I n t r o d u c e d by t h e r e d u c t l o n process. The Impedances o f these l i n e s were s l i g h t l y m o d l f l e d t o Improve t h e system response. The a c t u a l r e t a l n e d l l n e s were n o t changed.

coherent areas i n c l u d e d :

I. HVC and Non-HVC machines. Where p o s s i b l e , gener- a t o r s n o t a v a i l a b l e t o t h e MVC were grouped I n separa te areas t o f a c i l i t a t e t h e des ign o f t h e HVC .

11. Pumped-hydros. Machines w l t h pumped hydro were k e p t separate, whenever p o s s l b l e .

l i t . System S t r u c t u r e . Host o f t h e EHV buses were r e t a l n e d t o p reserve t h e u n d e r l y l n g s t r u c t u r e o f t h e system.

l v . Topology. To f a c i l i t a t e t h e c o n t r o l des ign imp le- menta t ion i n t h e unreduced system, t h e coherent areas were s e l e c t e d p r e s e r v i n g t h e i r genera l t o p o l o g t c a l l o c a t i o n .

Once t h e r e d u c t i o n descr ibed above was completed, t h e dynamic e q u i v a l e n t s o f t h e e x c l t e r s and PSS's f o r each coherent a rea were ob ta ined. Severa l techniques have been proposed f o r t h l s [8,9,10]. I n t h l s work, a p r a c t i c a l approach was used c o n s i d e r l n g t h e f o l l o w i n g t h r e e f a c t o r s : I. frequency response o f t h e excl ter /PSS models; 11. genera tor MVA r a t l n g ; and iil. genera tor HVC a v a l l a b i l l t y .

The e x c l t e r and PSS models whose frequency response was r e p r e s e n t a t i v e o f t h e o r l g i n a l models I n each area were se lec ted . Th ls f requency response was chosen from one o f t h e l a r g e s t genera tors i n t h e area a v a l l - a b l e f o r MVC c o n t r o l . The t i m e cons tan ts and ga ins were ad jus ted , I f necessary, t o y i e l d a f requency response r e p r e s e n t a t i v e o f t h e models i n t h e coherent area. The governor model f o r t h e genera tor t o which t h e exc l te r /PSS s e t was connected was chosen f o r t h e e q u l v a l e n t model.

The e q u i v a l e n t reduced system c o n s i s t s o f 15 coherent areas and i t i s shown I n F l g u r e 2. The dynamic behav io r o f t h l s system c l o s e l y resembles t h e response o f t h e unreduced system. S p e c i f i c a l l y . t h e reduced model r e t a l n e d t h e c h a r a c t e r l s t i c s o f t h e i n t e r a r e a power o s c i l l a t i o n s w l t h s l m i l a r low damping p r e s e n t i n t h e o r l g i n a l system.

The f o l l o w i n g observa t lons can be made about t h e reduced system:

I. The adjustments and approx imat ions were made I n

Other f a c t o r s cons idered I n t h e s e l e c t l o n o f

t h e d l r e c t i o n o f c r e a t i n g a more c o n s e r v a t i v e model ( i . e . , one w i t h l e s s damping), t o produce a more e f f e c t i v e c o n t r o l l e r .

1'1. A model w l t h fewer coherent areas c o u l d have been ob ta ined. However, I n o rder t o r e t a i n as much f i d e l i t y as p o s s i b l e , w i t h o u t undu ly c o m p l l c a t l n g t h e reduced system, w i t h t r a n s m i s s i o n model " f i l l - I n " elements f rom t h e r e d u c t l o n process, 15 areas were r e t a l n e d .

iii. An e s s e n t l a l requ i rement t o o b t a i n a success fu l c o n t r o l l e r I s t o develop a h i g h f i d e l i t y dynamic e q u l v a l e n t model.

F l g u r e 2. 15 Machine E q u i v a l e n t Model

V . MULTIVARIABLE (HVC) DESIGN

A. Method

The c o n t r o l des ign method used f o r t h e MVC Damp C o n t r o l l e r i s based on t h e l i n e a r i z e d r e p r e s e n t a t o f t h e reduced system descr ibed I n S e c t i o n 1V.B. l i n e a r i z e d model takes t h e f o l l o w i n g fo rm

= Ax t Bu

y = cx

where x i s t h e n-dlmenslonal s t a t e v e c t o r , U i s t h e m d lmens lona l c o n t r o l v e c t o r , and y i s t h e r -d imens iona l o u t p u t (measurement) v e c t o r . The problem I s t o d e s i g n a c o n t r o l system o f t h e f o r m

U = Ky (2)

t o s a t i s f y t h e performance requ i rements . T h l s can be

1130

fo rmula ted as a l i n e a r q u a d r a t i c r e g u l a t o r problem t o o b t a i n a f u l l s t a t e feedback c o n t r o l [ll]. T h i s o p t i - mal f u l l s t a t e feedback I s t h e n mapped i n t o a s t a t l c o u t p u t feedback c o n t r o l l e r u s l n g t h e techn ique descr ibed i n References [4.12,13]. T h i s techn ique r e t a i n s r o p t i m a l e igenva lues and e igenvec tors w i t h t h e r measurements (assumed independent) y. T h i s y i e l d s a c l o s e d l o o p system o f t h e form:

The m a t r i x A c l has t h e d e s i r e d r e igenva lues and e lgenvec tors . I f t h e remain lng n - r e lgenva lues of A c l have n e g a t i v e r e a l p a r t s , t h l s c o n t r o l I s t h e s o l u t i o n t o a subopt imal o u t p u t feedback prob lem [13 ] . Once an acceptab le c o n t r o l l e r i s ob ta ined I n t h e f r e - quency domain i t s performance I s eva lua ted i n t h e a c t u a l n o n l i n e a r system. T h i s c o n t r o l des ign methodo- l o g y i s an I t e r a t i v e process i n t h a t t h e c o n t r o l l e r i s r e f l n e d as t h e des ign progresses. These re f lnements a r e based on t h e c h a r a c t e r i s t i c s o f t h e f u l l s t a t e and o u t p u t feedback systems, and a l s o on t h e o v e r a l l system performance. The frequency domain c o n t r o l methodology o u t l i n e d I n t h i s s e c t i o n has been s u c c e s s f u l l y a p p l l e d t o d i f f e r e n t systems [1,14-181, y i e l d i n g s imp le and e f f e c t i v e c o n t r o l l e r s .

B. MVC Damping C o n t r o l l e r Design

System Representa t lon (Open LOOD C h a r a c t e r i s t i c s )

The des ign o f t h e MVC Damping C o n t r o l l e r was based on t h e l i n e a r i z e d r e p r e s e n t a t i o n o f t h e n i g h t t i m e system. T h l s c h o i c e was based on t h e f a c t t h a t t h e swlng modes f o r t h i s system e x h i b i t much l e s s damping t h a n d u r i n g dayt ime opera t ton . A success fu l c o n t r o l des tgn f o r n i g h t t i m e o p e r a t i o n was expected t o a l s o be succes- s f u l f o r dayt ime opera t ion . However, s i n c e t h e n i g h t and day o p e r a t i n g c o n d l t l o n s r e p r e s e n t v e r y d i f f e r e n t o p e r a t i n g p o i n t s , t h e MVC must be designed such t h a t t h e system performance does n o t d e t e r i o r a t e d u r i n g t h e day case.

The open l o o p c h a r a c t e r i s t i c s . o f t h e reduced system e x h l b i t t h e complex i ty o f t h e damping problem, s i n c e many i n t e r a r e a modes e x i s t and must be cons ldered. The main mode o f I n t e r e s t i s a ma jor I n t e r t l e mode w i t h a damping r a t i o of .4% a t . 7 Hz. There a r e o t h e r i n t e r t i e modes t h a t a r e a l s o l i g h t l y damped, r a n g i n g i n damping f rom 5% t o 7% and I n f requency f rom 1.Hz t o

1.3 Hz. An e f f e c t l v e s e l e c t i o n o f c o n t r o l s and measurements i s then r e q u i r e d t o improve t h e system performance by damplng these modes.

Measurements and C o n t r o l s

The measurements and c o n t r o l s used i n t h e MVC d e s l g n were chosen t o be p r a c t l c a l , as w e l l as e f f e c - t i v e , based on t h e o b s e r v a b i l i t y , c o n t r o l l a b i l i t y and s e n s i t i v i t y o f t h e modes o f i n t e r e s t w i t h r e s p e c t t o these s i g n a l s .

Because o f a r e l a t l v e l y h l g h number o f I m p o r t a n t modes, I t was decided t o use measurements t h a t d i r e c t l y c h a r a c t e r i z e these modes t o o b t a l n an e f f e c t l v e con- t r o l l e r capable o f a f f e c t i n g them. These measurements a r e t h e genera tor power and speed o f t h e e q u i v a l e n t machines i n t h e areas i n v o l v e d i n t h e i m p o r t a n t modes. Some areas a r e n o t a c c e s s i b l e t o t h e MVC; t h e r e f o r e t h e modes m a i n l y r e l a t e d t o t h e non-MVC areas a r e n o t g r e a t l y a f f e c t e d by t h e MVC.

I t i s d e s i r a b l e t o keep t h e c o n t r o l s imple; a t o t a l o f 12 measurements ( s i x speeds and s i x powers) were used. These correspond t o t h e coherent areas 2 , 6, 8, 9, 10, 13 i n F i g u r e 2. To p r e v e n t steady s t a t e r e s e t - t i n g , t h e measurements were passed th rough r a t e wash- ou ts w i t h a t i m e c o n s t a n t o f 2 s.

The c o n t r o l s used were t h e i n p u t s t o t h e v o l t a g e r e g u l a t o r s o f t h e machines i n t h e same s i x areas used f o r measurements. These s i g n a l s were l i m i t e d t o +0.1 p.u. t o a v o i d d e t r i m e n t a l c o n t r o l a c t l o n f o r l a r g e s i g n a l excurs ions . T h l s I s t y p l c a l o f more conven- t i o n a l PSS a p p l i c a t i o n s [2].

Gain M a t r i x

The o v e r a l l o b j e c t i v e o f t h e c o n t r o l des ign process i s t o o b t a i n a feedback g a i n m a t r i x K (see Equa- t i o n ( 2 ) ) t h a t p rov ides good c o o r d i n a t l o n between t h e measurements and c o n t r o l s t o improve t h e system dynamlc performance. T h i s was achieved w i t h t h e g a i n m a t r l x shown i n F i g u r e 3. The topo logy o f t h i s m a t r i x does n o t change between t h e n i g h t and day cases, whlch I s a d e s i r a b l e c h a r a c t e r l s t l c . However, t h e a l g e b r a i c s i g n o f t h e ga ins f o r t h e measurements f rom Area 2 i s changed between t h e n t g h t and t h e day systems. T h i s I s because Area 2 c o n t a i n s o n l y pumped hydro u n i t s , wh ich a r e a p p l l e d as motors f o r t h e n i g h t case and genera tors f o r t h e day case.

#8

#9

-.12 -.04 -.06 -.01 -.17 -03 .20 .08 -.12 .05 -05 -09

.03 -03 - .006 .02 -09 .04 .20 -01 -02 - .25 -02 .04

#ll -.07 -.04 s.01 -.20 .02 -.22 .12 -.03 -.03 -.08 -05 -.20

#13 -.23 -.03 -.01 .02 -003 -.17 .40 -.05 -04 -.35 .05 - . 4 5

F i g u r e 3. MVC Galn M a t r l x

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w i t h t h e MVC des ign embedded. The d i s t r i b u t i o n o f t h e MVC c o n t r o l s and measurements f o r t h e i n d i v i d u a l machines i s based on a mapping o f t h e C h a r a c t e r i s t i c s o f t h e f u l l power system t o and f r o m t h e domain o f t h e reduced system.

A requ i rement o f t h i s r e c o n s t i t u t i o n techn ique I s t h a t t h e f i n a l MVC r e a d i l y accommodate minor changes I n t h e ac system, such as a d d i t i o n o r removal o f spec i - f i c genera tors f r o m s e r v i c e , wh ich w i l l be encountered d u r i n g normal o p e r a t i o n o f t h e a c t u a l system.

I n o r d e r t o u t i l i z e t h e K m a t r i x designed on t h e reduced system, two new l i n e a r o p e r a t i o n s were c rea ted . F u n c t i o n a l l y , these two o p e r a t i o n s :

Design Performance (Reduced System)

The c h a r a c t e r i s t i c s and performance o f t h e MVC were checked b o t h i n t h e l i n e a r and n o n l i n e a r domain. The l o c a t i o n and damping o f t h e e igenva lues as w e l l as t h e modal p a r t i c i p a t i o n o f t h e genera tors i n t h e c l o s e d l o o p system were checked. The damping o f t h e main q n t e r t i e mode i s improved f r o m .4% t o 12%. The l e a s t damped i n t e r a r e a mode has a damping r a t i o o f 8%. Time s i m u l a t i o n s o f t h e n o n l i n e a r system were c a r r i e d o u t f o r a l a r g e number f a u l t s th roughout t h e system t o v e r i f y t h e dynamic performance o f t h e MVC. I t was found t h a t t h e MVC g r e a t l y enhances t h e dynamic per - formance o f t h e n i g h t system w h i l e r e t a i n i n g t h e accep- t a b l e c h a r a c t e r i s t i c s o f t h e day system. I n s e v e r a l ins tances t h e i n c l u s i o n o f t h e MVC makes an u n s t a b l e system become s t a b l e f o l l o w i n g t h e occurrence o f a severe f a u l t . F i g u r e 4 shows one o f these cases: a 3.5 c y c l e f a u l t a t bus G. The good performance o f t h e MVC was a l s o v e r i f i e d c o n s i d e r i n g communication t i m e de lays up t o 100 msec.

1. Synthes ize e q u i v a l e n t reduced system measurements f r o m p h y s i c a l l y r e a l i z a b l e measurements.

2. D i s t r i b u t e r e a l i z a b l e c o n t r o l s i n t h e r e c o n s t i - t u t e d system f r o m e q u i v a l e n t c o n t r o l s i n t h e reduced system.

Two new m a t r i c e s p e r f o r m t h e r e q u i r e d mappings, as f 01 1 ows :

52.0

51.5 ul 4 51.0

N W x 2 50.5 I

50.0 CI

t& 52.0

v1

w 51.5

X $ 1 51.0 z 50.5 4

50.0

49.5

g 49.5

- W i t h HVC I ---_- Wi thout MVC

Y = K Y

and

Y ( 4 )

u = K u U

where: a . .

U = m d imens iona l v e c t o r o f c o n t r o l s on t h e f u l l mod e 1

d imens iona l v e c t o r o f measurements on t h e f u l l model

x r measurement syn thes is m a t r i x

i . . A

y = r

i

l ' l ' i ' I ' 1 ' 1 0 2 4 6 8 10

Time - Seconds

K = r

K = m

Y

x m c o n t r o l d i s t r i b u t i o n m a t r i x

Combining Equat ions ( Z ) , ( 4 ) . and ( 5 ) y i e l d s :

u = K K K y U Y

F i g u r e 4. Reduced Order Model Response t o F a u l t on a Major T i e L i n e (Comparison w i t h Open Loop)

V I . RECONSTITUTION The f u l l y r e c o n s t i t u t e d M V C K m a t r i x i s represented

by t h e p r o d u c t o f t h e t h r e e K m a t r i c e s i n Equat ion (6 ) .

The f l o w o f i n f o r m a t i o n f o r t h i s process I s shown i n F i g u r e 5. The a c t u a l d imensions o f t h e v e c t o r s , f o r

A. General F o r m u l a t i o n

A f t e r d e s i g n i n g a v i a b l e MVC on t h e reduced system, t h e n e x t s t e p i s t o r e c o n s t i t u t e t h e f u l l system model

A

Y Y U

MEASUREMENTS CONTROLS

F i g u r e 5. I n f o r m a t i o n Flow Through M u l t i v a r i a b l e C o n t r o l l e r

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t h e maximum number o f t u r b i n e - g e n e r a t o r s i n c l u d e d i n t h e HVC, a r e no ted on t h e f i g u r e .

The r e c o n s t i t u t i o n process descr ibed up t o t h i s p o t n t i s v e r y genera l and c o u l d be a p p l i e d t o a range o f s i m i l a r problems. The c o n t e n t s o f K y and Ku a r e a p p l i c a t i o n s p e c i f i c .

8. R e c o n s t i t u t i o n Parameters

The purpose o f t h e K y m a t r i x i s t o c r e a t e a v e c t o r y wh ich i s f u n c t i o n a l l y e q u i v a l e n t t o 5 . For t h i s design, t h e e q u i v a l e n t speed o f an area was represented by t h e i n e r t i a weighted average o f t h e speeds o f t h e HVC machines i n t h a t area. The power of an area I s equal t o t h e sum o f t h e power on each o f t h e MVC machines. These values were sca led t o t h e c o r r e c t p e r u n i t va lues i n o r d e r t o be c o n s i s t e n t w i t h t h e reduced system K m a t r i x .

S i m i l a r l y . t h e purpose o f t h e Ku m a t r i x i s t o c r e a t e a v e c t o r i, which i s f u n c t i o n a l l y e q u i v a l e n t t o U. S ince t h e c o n t r o l s i g n a l s U a r e a l l v o l t a g e e r r o r s , on a p e r u n i t b a s i s , each i n d i v i d u a l HVC machine i n a p a r t i c u l a r a rea was f i r s t g i v e n t h e same s i g n a l . Thus, t h e non-zero e n t r i e s i n Ku were s e t t o u n i t y . These e n t r i e s may be r e f i n e d by s c a l i n g up o r down t o i n c r e a s e o r decrease t h e response o f p a r t i c u l a r machines i n an area. T h i s re f inement was u t i l i z e d on two machines i n Area 2 t o c o r r e c t f o r excess ive v a r i a - t i o n i n machine t e r m i n a l vo l tage. Adjustments i n q n d i v i d u a l e n t r i e s o f Ku c o u l d be used t o c o r r e c t f o r o t h e r f a c t o r s , such as s u b s t a n t i a l d i f f e r e n c e s i n ex- c i t e r response. These i n d i v i d u a l Ku e n t r i e s a l s o a l l o w f o r t h e p o s s i b i l i t y o f f i e l d t u n i n g o f s i g n a l s t o i n d i v i d u a l machines.

As i n d i v i d u a l machines a r e brought o n - l i n e o r removed, t h e c a l c u l a t i o n o f t h e a r e a ' s e q u i v a l e n t speed and power w i l l change; t h e r e f o r e , t h e elements o f K f o r t h a t a rea w i l l change. The reduced system m a t r i x i s n o t a f f e c t e d by these changes i n u n i t comnl t - ment s i n c e I t a c t s on s i g n a l s wh ich a r e r e p r e s e n t a t i v e of t h e response o f e n t i r e areas.

C . R e c o n s t i t u t i o n Resu l ts

A sumnary o f t h e s i z e and d i s t r i b u t i o n o f machines p a r t i c i p a t i n g i n t h e r e c o n s t i t u t e d MVC, f o r n i g h t t i m e o p e r a t i o n . I s shown i n Tab le 1. Th is d i s t r i b u t i o n i s r e p r e s e n t a t i v e of t h e v a r i o u s o p e r a t i n g c o n d i t i o n s eva lua ted . Area 14 has machines on l i n e I n t h e day o n l y .

Table 1

N i g h t t i m e Opera t ion

Number o f Machines i n Each Area Area No. - HVC Non-MVC Total

1 2 3 4 5 6 7 8 9

10 11 12 13 14

2 8 9 2

10 12

2 16 1 4

3 4 2 9 0

15 -- 4 4 T o t a l 60 37 97

F i g u r e 6 shows a comparison o f swings f o r represen- t a t i v e machines ( o f Area 9) . f o l l o w i n g a severe ac system f a u l t , f o r t h e reduced and f u l l systems.

- F u l l System ----- Reduced System c] ' 3 0.990 U w h UY

_ _ _ 1.0 __.----

b ' i ' i ' k ' I , Time - Seconds

F i g u r e 6. Comparison o f A c t u a l Machine and E q u i v a l e n t Machine Response

o f

1 .

2.

3.

4.

Some observa t ions about t h e r e l a t i v e performance

I n most areas, t h e damping i s b e t t e r i n t h e f u l l system than i n t h e e q u i v a l e n t machine i n t h e reduced system.

The HVC does n o t adverse ly a f f e c t t h e performance o f t h e cross-compound machines, even though f a s t dynamics a r e n o t represented i n t h e reduced model. T h i s may be seen i n t h e speed swings o f t h e second machine, i n F i g u r e 6, wh ich a r e well-damped.

A s expected, t h e MVC does l i t t l e t o c o r r e c t t h e l o c a l mode o s c i l l a t i o n s on machines, p a r t i c u l a r l y those which a r e n o t i n c l u d e d i n t h e MVC.

The r e c o n s t i t u t i o n techn ique s u c c e s s f u l l y p r o j e c t s t h e MVC designed on t h e reduced system onto t h e f u l l system. The success o f t h i s techn ique i s due p r i m a r i l y t o t h e good f i d e l i t y o f t h e reduced o r d e r model. S p e c i f i c a l l y , t h e behav io r o f t h e equiva- l e n t machines I s genu ine ly r e p r e s e n t a t i v e o f t h e c o l l e c t i v e response o f t h e machines i n t h a t a rea t o system d is tu rbances .

t h e f u l l and reduced system a r e :

V I I . VERIFICATION AND FINAL RESULTS

MVC Damplnq C o n t r o l l e r F i n a l Desiqn

The MVC Damping C o n t r o l l e r f i n a l design, shown s c h e m a t i c a l l y i n F i g u r e 7, comprises t h r e e types o f c o n t r o l l e r s , as f o l l o w s :

1. One C e n t r a l C o n t r o l l e r (C). w i t h s i x communication

2. S i x Reqlonal C o n t r o l l e r s ( R ) l o c a t e d i n Areas 2, 6, 8, 9. 11, and 13 ( F i g u r e 2) . Each Regional

l i n k s t o :

C o n t r o l l e r has communication l i n k s w i t h i n i t s r e g i o n t o :

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1.09

F i g u r e 7. MVC Damping C o n t r o l l e r (Schematic)

3. The Loca l C o n t r o l l e r s ( L ) a t t h e machines w i t h i n t h e r e g i o n . There a r e 60 l o c a l c o n t r o l l e r s f o r n i g h t t i m e o p e r a t i o n and 76 l o c a l c o n t r o l l e r s f o r dayt ime opera t ion .

Each Loca l C o n t r o l l e r o b t a i n s two measurements (speed; genera tor power) f r o m I t s machine, and p r o v i d e s one MVC c o n t r o l s i g n a l t o t h e summing j u n c t i o n o f t h e v o l t a g e r e g u l a t o r f o r i t s machine.

Each Regional C o n t r o l l e r combines i t s Loca l Con- t r o l l e r measurements i n t o two area measurements ( e q u i - v a l e n t p e r u n i t speed and area p e r u n i t power) and sends t h e u n i t c o n t r o l s i g n a l s t o i t s Loca l C o n t r o l - l e r s .

The C e n t r a l C o n t r o l l e r takes t h e 12 area measurements ( s i x speed, s i x power) and generates t h e s i x a rea p e r u n i t c o n t r o l s i g n a l s .

The communication network i s a double s t a r type , which was chosen because i t has f a r fewer l i n k s t h a n a p o i n t - t o - p o i n t network. and i t p r o v i d e s more s e c u r i t y t h a n a r i n g network. It appears t h a t t h e c e n t r a l and r e g i o n a l c o n t r o l l e r s should have redundant components.

Performance o f F i n a l Design

The machine speed excurs ions f o r some representa- t i v e machines a r e shown i n F i g u r e 8. The event shown i s f o r a 3.5 c y c l e f a u l t on a major t i e l i n e c l e a r e d by opening t h e f a u l t e d l i n e . T h i s d i s t u r b a n c e i s t h e w o r s t s i n g l e f a u l t f o r t h e model system and i s u n s t a b l e open loop, as seen i n t h e f i g u r e .

The q u a n t i t a t i v e r e s u l t s i n t h e f o r m o f damping r a t i o s a r e shown i n t h e t a b l e below f o r t h e c r i t i c a l n l g h t cases.

Table 2

Oampinq R a t i o

Case ( N i a h t ) O b j e c t i v e (#l) W/MVC W/O MVC

Increased Power Flow 0.10 0.10 Unstab le Base Power Flow 0.20 -0.20 0.00

cl W w PI m w z X U

3

I - W i t h HVC Wi thout MVC I , I , -----

1.01 I I .

1.0

0 . 9 4 , 1 ' 1 ' 1

0 2

Time - Seconds

F i g u r e 8. Response of F u l l System Comparison ( W i t h and Wi thout MVC) t o Severe F a u l t

The MVC a p p l i c a t i o n t o t h e I n i t i a l l y u n s t a b l e n i g h t inc reased power f l o w case n o t o n l y s t a b i l i z e d it, b u t p r o v i d e d h i g h damping (10%). Note: a 10% damping r a t i o i s e q u i v a l e n t t o p r o v i d i n g a 1O:l a m p l i t u d e r e d u c t i o n I n f o u r o s c i l l a t i o n s a t t h e f requency o f i n t e r e s t .

MVC a p p l i c a t i o n t o n i g h t base case changed p e r f o r - mance f r o m zero damping t o about 20% damping.

The MVC c o n t r o l s i g n a l s a r e l i m i t e d t o +lo%, whereas most o f t h e PSS s i g n a l s a r e l i m i t e d t o 55%. I n c r e a s i n g t h e PSS l i m i t s t o +lo% does n o t change t h e e igenva lues and t h e r e f o r e t h e damping o f t h e system. Furthermore, t i m e s i m u l a t i o n s w i t h a l l t h e PSS l i m i t s s e t t o 510% show v e r y s i m i l a r performance, b o t h open and c l o s e d loop, t o those presented here.

C o o r d i n a t i o n w i t h Other C o n t r o l s

C e r t a i n i n h e r e n t des ign c h a r a c t e r i s t i c s o f t h e MVC Damping C o n t r o l l e r p r o v i d e good c o o r d i n a t i o n w i t h t h e g e n e r a t i o n d ispatch . l o a d frequency, and v o l t a g e con- t r o l systems, as f o l l o w s :

1. The MVC damping c o n t r o l l e r p rov ides no c o n t r o l s i g n a l s t o t h e t u r b i n e s (steam, gas, hydro) i n t h e system. I n a d d i t i o n , t h e MVC damping c o n t r o l l e r p r o v i d e s no s t e a d y - s t a t e c o n t r o l s i g n a l s t o t h e genera tors .

2. The c o n t r o l s i g n a l s t o t h e MVC des ignated e x c i t e r s a r e i n h e r e n t l y t r a n s i e n t , by u s i n g r a t e t y p e wash- ou ts on t h e two types o f measurements ( g e n e r a t o r power and speed) used by t h e g a i n m a t r i x o f t h e MVC damping c o n t r o l l e r .

The f i r s t i n h e r e n t d e s l g n c h a r a c t e r i s t i c means t h a t t h e MVC damping c o n t r o l l e r has no s teady-s ta te e f f e c t on g e n e r a t l o n c o n t r o l . For those t u r b i n e s w i t h governors b e i n g used i n l o a d frequency c o n t r o l , t h e MVC w l l l have a b e n e f i c i a l e f f e c t on t r a n s i e n t g e n e r a t i o n changes, s i n c e t h e MVC adds damping t o speed o s c i l l a - t i o n s .

The second i n h e r e n t c h a r a c t e r i s t i c means t h a t t h e HVC damping c o n t r o l l e r has no s teady-s ta te e f f e c t on system v o l t a g e c o n t r o l . For a few machines, t r a n s i e n t

1134

v o l t a g e v a r i a t i o n s a r e s l i g h t l y h i g h e r w i t h MVC i n use t h a n w i t h o u t MVC. However, t h e o v e r a l l e f f e c t o f MVC i s b e n e f i c i a l on t r a n s i e n t v o l t a g e v a r i a t i o n s , s i n c e t h e MVC adds damping.

The MVC des ign a l s o i n h e r e n t l y p rec ludes e x c i t i n g I n t e r a c t i o n s among p a r a l l e l machines because t h e i n d l - v i d u a l speed and power measurements f rom each MVC machine a r e n o t used d i r e c t l y i n t h e MVC. I n s t e a d , t h e i n d i v i d u a l measurements f r o m each MVC machine i n an area a r e combined i n t o one e q u i v a l e n t measurement, as shown i n F i g u r e 7, b e f o r e b e i n g used t o produce t h e MVC feedback c o n t r o l s i g n a l s .

F l n a l l y , f o r I n t e r a r e a i n t e r a c t i o n s , i t shou ld be no ted t h a t t h e r e i s o u t s t a n d i n g c o o r d i n a t i o n o f t h e MVC Damping C o n t r o l l e r w i t h e x i s t i n g t r a n s i e n t s t a b i l i t y c o n t r o l s . Th is i s I l l u s t r a t e d i n S e c t i o n V f o r n i g h t - time o p e r a t i o n . Wi thout MVC, t h e f a u l t (3LG) on one EHV c i r c u i t near Bus G causes t r a n s i e n t i n s t a b i l i t y . Wi th t h e MVC Damping C o n t r o l l e r , t h t s f a u l t case i s s t a b l e , w i t h good damping. Th ls exceeds t h e d e s i g n o b j e c t i v e s o f t h e MVC Damping C o n t r o l l e r .

I n t r a - A r e a I n t e r a c t i o n s

The MVC Damplng C o n t r o l l e r p r o v i d e s good damping f o r d i s t u r b a n c e s t h a t occur w i t h i n a coherent area. T h l s i s i l l u s t r a t e d by t h e s i m u l a t i o n r e s u l t s o f F i g u r e 9 f o r a f a u l t w i t h i n Area 2, wh ich i s o f p a r t i c u l a r i n t e r e s t because: t h e Area 2 machines a r e pumped hydro; Area 2 a c t u a l l y i s between Area 1 (non-MVC Machines) and t h e remainder o f t h e system; Area 2 c o n t r i b u t e s s t r o n g l y t o t h e MVC damping.

1.010

' l . d I \

o.9!Jr , , , 0 2 I 10 1 ' 1 ' 1

Time - Seconds

F i g u r e 9. Response t o a I n t e r a r e a F a u l t (Representa t ive Machines i n Area 2)

A f a u l t was a p p l i e d a t an EHV bus w i t h i n Area 2, and was c l e a r e d b y opening t h e a f f e c t e d c i r c u i t , wh ich a l s o f o r c e d t h e t r i p o u t o f two MVC machines i n Area 2, and a cor respond ing change i n t h e Area 2 MVC s t r u c - t u r e . F i g u r e 9 shows n o t o n l y no adverse machlne i n t e r a c t i o n s , b u t good damping d e s p i t e t h e change i n t h e MVC s t r u c t u r e .

Robustness

The MVC Damping C o n t r o l l e r adapts e a s l l y t o changes i n u n i t commitment and accommodates l a r g e changes i n system g e n e r a t i o n and load; e.g., 60 machines and

l i g h t e r g e n e r a t i o n f o r n i g h t t i m e o p e r a t i o n , and 76 machines and heavy g e n e r a t i o n f o r dayt ime o p e r a t i o n .

On a l i n e a r b a s i s , t h e MVC was checked f o r l o s s of t h e f o l l o w i n g area s i g n a l s a t each MVC area: speed measurement, power measurement, c o n t r o l s l g n a l , b o t h measurements p l u s c o n t r o l s i g n a l . I n a l l cases, t h e reduced system e igenva lues remain s t a b l e . Also, f o r a l l s i g n a l l o s s cases except t h r e e , t h e damping remains above 5%. The t h r e e cases w i t h minimum damping l e s s t h a n 5% i n v o l v e Areas 2 and 13.

V I I I . CONCLUSIONS

The main c o n c l u s i o n i s t h a t a system-wide m u l t i - v a r i a b l e damping c o n t r o l l e r has been s u c c e s s f u l l y designed on a l a r g e s c a l e system w i t h r e a l i s t i c param- e t e r s t h a t meets t h e des ign o b j e c t i v e and s a t i s f i e s a l l t h e imposed c o n s t r a i n t s . The c o n t r o l l e r uses measurement and c o n t r o l s i g n a l s t h a t a r e a v a i l a b l e and prac- t i c a l . The c o n t r o l l e r i s c o n c e p t u a l l y s imp le and coor - d i n a t e s w e l l w i t h a l l o t h e r system c o n t r o l s . The con- t r o l l e r adapts e a s i l y t o changes i n u n i t commitment and accommodates l a r g e changes i n system g e n e r a t i o n and load.

Another i m p o r t a n t c o n c l u s i o n i s t h a t t h e t e c h n i c a l approach, o r p l a n , developed f o r t h i s des ign p r o j e c t I s b o t h t e c h n i c a l l y v a l i d and e f f e c t i v e f o r dynamic a n a l y s i s and des ign u s l n g a l a r g e power system.

REFERENCES

J.J. Sanchez-Gasca, N.W. M i l l e r , A . K u r i t a . and S. H o r i u c h i , " M u l t i v a r i a b l e C o n t r o l f o r Damping I n t e r a r e a O s c i l l a t i o n s i n Power Systems." C o n t r o l Systems Magazine. Vo l . 9, No. 1, January 1989, pp. 28-32.

E.V. Larsen. D.A. Swann. "ADDlVina Power Svstem S t a b i l i z e r s : . P a r t I, P a r t '11; {ar t 111, Trans. on Power Apparatus and Systems. Vol . PAS-100, No. 6. June 1981, pp. 3017-3046.

I E E E T u t o r l a l Course, "Power System S t a b i l i z a t i o n V ia E x c i t a t i o n Cont ro l , " I E E E 81 EH0 175-0 PWR, 1980.

J. Medanlc. "On S t a b i l i z a t i o n and O p t i m i z a t i o n by Output Feedback." 1 2 t h Annual As i lomar Conference on C i r c u i t s and Systems, P a c i f i c Grove, C a l i f o r - n i a . November 1978.

8. Avramovic, P.V. Kokotov ic , J.R. Winkelman, J.H. Chow, "Area Decomposi t ion f o r Electromechan- i c a l Modes o f Power Systems." presented a t Sympo- sium on Larqe-Scale Systems. IFAC. Tolouse, France, 1980.

J.H Chow, E d i t o r . Time-Scale Model ing o f Dynamic Networks w i t h A p p l i c a t i o n s t o Power Systems, Spr inger -Ver lag , New York, 1982.

"Development o f Dynamic E q u i v a l e n t s f o r T r a n s i e n t S t a b i l i t y Studies, ' l EPRI EL-456, RP763, F i n a l Repor t 1977.

A.J. Germond, R . Podmore. "Dynamic Aggregat ion o f Genera t ing U n i t Models," I E E E Trans. on Power Apparatus and Systems. Vol . PAS-97, No.4, July/August 1978. pp. 1060-1069.

S . Geeves, "A Modal-Coherence Technique f o r D e r i v i n g Dynamic Equ iva len ts . " I E E E Trans. on Power Systems, Vol . 3, No. 1, February 1988, pp. 44-51.

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[ l o ] S .E .M. de D l i v e i r a , J.F. de Q u e l r o z , "Modal David B. Klapper ( M ' 46 ) r e c e i v e d t h e B.S. degree I n Dynamic E q u t v a l e n t f o r E l e c t r i c Power Systems," E l e c t r l c a l Eng lneer ing f r o m Purdue U n i v e r s i t y i n 1948, P a r t I, I E E E Trans. on Power Systems, v o l . 3, a B.S. degree i n Mathematics, and a M.S. degree i n No. 4, November 1988. pp. 1723-1730. E l e c t r i c a l Eng ineer ing from t h e I l l i n o i s I n s t i t u t e o f

Technology i n 1955. B.D.O. Anderson and J.B. Moore, L i n e a r Dpt lma l C o n t r o l , P r e n t i c e H a l l , New Jersey, 1971.

J . Medanic, "Design o f Low Order Opt imal Dynamic Regu la to rs f o r L i n e a r T ime- Invar ian t Systems." Conf. on I n f o r m a t i o n Science and Systems. 1979.

W . E . Hopklns, J r . , J. Medanic, and W.R. Perk ins , "Output Feedback Pole Placement i n t h e Design o f SuboptImal L l n e a r Q u a d r a t i c Regu la to rs , " I n t . J . o f C o n t r o l , Vo l . 34, pp. 593-612. 1981.

A.S. Brower, S.H. J a v i d , A.S. P a t e l , T.D. Younkins, and G.H. Q u e n t i n , "A New Coord ina ted C o n t r o l Design Method and I t s A p p l l c a t i o n t o a Coal G a s i f l c a t t o n P l a n t , " Proceedlngs o f t h e 1984 American C o n t r o l Conference, 'San Diego, C a l i - f o r n i a , June 6-8, 1984, pp. 1805-1810.

T.W. T e r w i l l i g e r , A.S. Brower, R.S. Bahet i , R .E . Smith, and G.H. Quent in , "Advanced C o n t r o l Aspects o f t h e I G C C Concept," Proceedings o f t h e American C o n t r o l Conference, San Diego. C a l i - f o r n i a . June 6-8, 1984, pp. 1526-1533.

T.O. Younkins and J.H. Chow, l ' M u l t l v a r i a b l e Feed- water C o n t r o l Design f o r a Steam Generator," IEEE C o n t r o l Systems Magazine, Vol . 8, No. 2, A p r i l 1998, pp. 77-79.

T.D. Younkins, J.R. Wlnkelman, J .J . Sanchez-Gasca, and J.A. McGrady, "Output Feedback M u l t i v a r i a b l e C o n t r o l f o r an Advanced B o i l i n g Water Reactor." I E E E Trans. on Energy Conversion, Vol . EC-2, No. 3, September 1987, pp. 349-354.

T. Hara, A . K u r i t a . T.D. Younkins, J .J . Sanchez-Gasca, and J.H. Chow, " A Coord ina ted M u l t i v a r i a b l e C o n t r o l System Deslgn f o r an HVDC L inked Remote ABWR Nuc lear Power Park," IEEE Trans. on Energy Conversion. Vo l . EC-2, No. 4, December 1987, pp. 542-548.

T. Mlchigami was born i n Ish ikawa Japan, on June 16. 1943. He r e c e i v e d t h e B.S. degree I n e l e c t r i c a l eng i - n e e r i n g f rom M e i j i U n i v e r s i t y i n 1966, and t h e M.S. degree f r o m Tokyo Denki Co l lege i n 1969. I n 1962, he j o i n e d Tokyo E l e c t r i c Power Company (TEPCO), Tokyo, Japan, where he has been engaged i n t h e d i s p a t c h l n g and t h e o p e r a t i o n o f t h e e l e c t r i c power system. He i s a deputy manager o f D l s p a t c h l n g D l v i s j o n Power System Opera t ion Department. He i s a member o f t h e I n s t i t u t e o f E l e c t r l c a l Engineers o f Japan, and a member o f t h e work ing group SC-39 o f C I G R E .

A tsush i K u r i t a was born I n Japan i n 1955. He gradu- a t e d f rom I b a r a g i U n i v e r s i t y i n 1979 and f r o m t h e Master Course o f Shizuoka U n i v e r s i t y , m a j o r i n g I n e l e c t r i c a l eng ineer ing . He j o i n e d t h e Tokyo E l e c t r i c Power Company (TEPCO) i n 1981. M r . K u r i t a i s p r e s e n t l y a Research S t a f f Sen ior Engineer o f t h e Power System Department o f t h e TEPCD Eng ineer ing Research Center . He I s a member o f t h e I n s t i t u t e o f E l e c t r l c a l Engineers o f Japan.

Sumio H i rano graduated f rom Saitama U n i v e r s i t y i n 1982 and r e c e i v e d t h e B.S. degree o f e l e c t r i c a l e n g i n e e r i n g . He j o i n e d t h e Tokyo E l e c t r i c Power Company i n 1982, where he has been engaged I n power system p l a n n l n g . (He I s n o t a member o f I E E E . )

M r . K lapper was w i t h t h e Commonwealth Edlson Com- pany i n Chicago, I l l i n o i s . f r o m 1948 u n t i l 1966. He h e l d a v a r i e t y o f p lann ing , design, and s u p e r v i s o r y p o s l t i o n s i n t h e e n g i n e e r i n g area. M r . K lapper j o i n e d GE's Systems Development and Eng ineer ing Department i n 1971. H i s p r i n c i p a l a c t i v i t y has been development and a p p l i c a t i o n of new methods f o r system s t a b i l i z a t i o n . He has been t h e P r o j e c t Manager o f t h e j o i n t Tokyo E l e c t r i c Power Company-GE s t u d i e s s i n c e t h e i n c e p t i o n i n 1978.

M r . K lapper I s a member o f t h e I E E E Power Englne- e r i n g S o c i e t y and ORSA. He i s a Reg is te red Pro fes- s i o n a l Engineer i n t h e s t a t e o f I l l i n o i s .

N icho las W. M i l l e r r e c e i v e d t h e B.S. and M.Eng. degrees i n e l e c t r i c power e n g l n e e r i n g f rom Rensselaer Poly- technic I n s t i t u t e i n 1979 and 1980. r e s p e c t l v e l y . He j o i n e d GE i n 1980 as an A p p l i c a t i o n Engineer i n t h e Systems Development and Eng ineer ing Department. He i s a member o f t h e I E E E Power Eng lneer ing S o c i e t y and o f t h e Working Group on Harmonics i n Power Systems. He i s a l s o a l i c e n s e d P r o f e s s i o n a l Engineer i n t h e s t a t e o f New York.

Juan J. Sanchez-Gasca r e c e i v e d M.S. degrees i n computer sciences and e l e c t r i c a l e n g i n e e r l n g and a Ph.D. i n e l e c t r i c a l e n g i n e e r i n g f r o m t h e U n i v e r s i t y o f Wisconsin-Madison I n 1978, 1983, and 1983, respec- t i v e l y . I n 1983, he j o i n e d GE as an A p p l i c a t i o n Engi- neer i n t h e Systems Development and Eng ineer ing Department. He i s a member o f t h e I E E E Power Engine- e r i n g S o c i e t y .

Thomas D . Younkins r e c e i v e d a B.S.M.E. degree f r o m t h e Pennsylvania S t a t e U n i v e r s i t y I n 1954. He has worked f o r GE s i n c e t h a t t i m e and qraduated f rom t h e GE Advanced Eng ineer ing Program <n 1957. From 1959 t o 1978, he h e l d a v a r i e t y o f e n g i n e e r i n g d e s i g n and management assignments w h i l e work ing on nava l n u c l e a r power p l a n t s a t t h e K n o l l s Atomic Power Labora tory . Since 1978, he has been a Sen ior A p p l i c a t i o n Engineer w i t h t h e Systems Development and Eng ineer ing Depar t - ment, work ing on t h e dynamic i n t e r a c t i o n and c o n t r o l o f power p l a n t s and power systems. M r . Younkins i s a Reg is te red P r o f e s s i o n a l Engineer i n New York S t a t e . He I s an A d j u c t Pro fessor a t Unlon Co l lege and has t a u g h t a r e a c t o r techno logy course a t Union f o r many years.

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DISCUSSIOti

C.D.VOURNAS,National Technical University, Athens, Greece: The authors should be congratulated for a very interesting paper applying to an actual power system the concept of a multivariable stabilizer. A similar controller was suggested 11 years ago for the particular configuration of a multimachine power plant [ A ] . The "modal stabilizer" presented in [A] increased the damping of all the electromechanical oscillation modes without affecting the other eigenvalues of the system. This was achieved by feeding back speed, power, as well as terminal voltage of all the machines to the AVR input of each machine.

The authors' comments on the following remarks would be greatly appreciated:

It seems that the control design proposed in the paper specifies the exact location of r eigenvalues but does not guarantee the stability of the remaining eigenvalues of the system. Have the authors considered an alternate design method that would yield stable and adequate eigenvalues for all the modes of the linear model? It is a well known principle of PSS design a certain degree of phase advance should be present in the stabilizing signal so that it can be effective. In the case of multivariable proportional feedback the necessary phase advance of the stabilizing signal is provided by combining a number of weighted measurements, each having a different phase. It is therefore evident that all the measurements should be present for this synthesis to be effective. Loss of any measurement could have unforseen effects on the overall performance. The Gain Matrix given in Fig.3 of the paper is far from being diagonally dominant. In particular, the dependance of the stabilizing signal for machine no.2 on the response of machine no.13, and vice versa, is exceedingly pronounced. This exemplifies the remark made above and easily explains why the "cases with damping less than 5%" involve loss of measurement from these two areas, as stated in the paper.

that

Reference

[A] C.D.Vournas, R.J.Fleming, " A Multivariable Stabi- lizer for a Multimachine Generating Plant", paper

A 79 009-2, presented at the IEEE/PES Winter Power Meeting, New York, NY, Feb. 4-9, 1979.

Manuscript received March 2 , 1990.

S . HIRANO, T. MICHIGAHI, A. KURITA, 0.6. KLAPPER, N.W. MILLER, J . J . SANCHEZ-GASCA, T.D. YOUNKINS: The a u t h o r s thank t h e d l s c u s s e r f o r h i s I n t e r e s t I n o u r work and h i s remarks. We have t h e f o l l o w i n g comnents:

1. The c o n t r o l d e s l g n proposed i n t h e paper y l e l d s s t a b l e and adequate e igenva lues f o r a l l t h e system modes under a wide range o f system o p e r a t l n g c o n d l t l o n s . The c o n t r o l l e r does r e t a l n r modes, a sub-set o f t h e modes o f a f u l l s t a t e feedback c o n t r o l d e s l g n . These modes a r e t h e modes o f I n t e r e s t . t h e l r l n t e r a c t l o n s w l t h o t h e r modes a r e eva lua ted b e f o r e and d u r l n g t h e d e s l g n process. t o a v o l d d e t r l m e n t a l modal l n t e r a c t l o n s .

2. Not a l l t h e measurements need t o be present f o r t h e c o n t r o l l e r t o be e f f e c t l v e . However, as no ted by t h e d l s c u s s e r . t h e l o s s o f some measurements have a g r e a t e r Impact t h a n o t h e r s on t h e c o n t r o l l e r performance. The l o s s o f measurements and/or c o n t r o l s l g n a l s was t h o r o u g h l y eva lua ted based on t h e l l n e a r a n a l y s i s and n o n - l i n e a r s l m u l a t l o n s o f a l a r g e number o f cases l n v o l v l n g a l l t h e o p e r a t l n g c o n d l t l o n s o f I n t e r e s t .

3. The main o b j e c t l v e o f t h e c o n t r o l l e r p resented i n t h e paper, l . e . , o f t h e g a l n m a t r l x , I s t o c o o r d l n a t e t h e measurement s l g n a l s w l t h t h e c o n t r o l s l g n a l s , t o ach leve t h e s p e c l f l e d c o n t r o l o b j e c t i v e s . T h l s o b j e c t l v e was met w l t h t h e g a l n m a t r l x g l v e n I n t h e paper. The d l s c u s s e r I s c o r r e c t I n n o t l n g t h e c o r r e l a t l o n between areas 2 and 13. A lso , as noted by t h e d lscusser , t h e f l n a l g a l n m a t r l x I s n o t d l a g o n a l l y dominant. The a u t h o r s c o n s l d e r t h a t t h l s I l l u s t r a t e s a v l r t u e o f t h e m u l t l v a r l a b l e c o n t r o l d e s l g n method used: a good c o n t r o l des tgn i s developed w l t h o u t r e q u l r j n g o f f - d l a g o n a l compensators t o produce d iagona l domlnance.

Manuscript received Apri l 2 , 1990.

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Functional design for a system-wide multivariable damping controller (for power systems)