A Systems Approach to Development Planning of the Fuel Power Industry of a Planned-Economy Country

A SYSTEMS APPROACH TO DEVELOPMENT PLANNING OF THE FUEL POWER

INDUSTRY OF A PLANNED- ECaNOMY CaUNTRY

L. S. BELYAEV MARCH IS76

R a c v c h Reports provide the f o r d record of research conducted by the International Institute for Applied Systems Analysis. They are carefully reviewed before publication and represent, in the Institute's best judgment, competent scientific work. Views or opinions expressed herein, however, do not necevvily reflect those of the National Member Organuations suppon- ing the h u i t u t e or of the h t i t u t e itself.

Intarnational Inrtituta for Applied Syrtamr Analyris

2361

Laxanburg, Aurtria

PREFACE

The aim of this paper is to characterize the main principles of a systems approach to development planning of the fuel power industry of a country with planned economy. The paper is based on the experience of the USSR;

in particular, it reflects results of researches of the Siberian Power Institute of the Academy of Sciences of the USSR.

The paper forms part of the IIMA Energy Project investigation into the long-term (15-50 years) energy evolution of various countries (developed and developing, with planned and non-planned economy), talung into account global interfaces and constraints.

SUMMARY

The fuel power industry (FPI) of a country ob\iously is a 5-ery large com- plex system: for countries with a planned economy, it must be considered as an entirely aggregate energy system. A special systems approach is needed for planning and forecasting its development. Such an approach has been developed in the Soviet Union since the creation of

GOELRO

~ 1 a n . l It includes the following main components:

-

Creation of a systems hierarchy and a development task hierarchy:

-

Elaboration and application of mathematical models;

-

The use of special methods for taking into account uncertainties in input data;

-

Consideration of the external interaction of e n e r g systems. their environmental impacts. etc.;

-

Improvement of organizational structure and praciical management methodology.

.& the second, fourth and fifth elements are sufficiently well known and widely accepted. attention in the pape'r is concentrated mainly o n the first and third components.

Creation of a hierarchy of systems is necessary owing to the except~onai complexity of the fuel power industry. The system must somehow be decom- posed into subsystems while at the same tune its entirety is preserved. This paper describes the FPI systems hierarchy variant based on a combination of territorial and branch indicators. Different kinds of decisions on systems devel- opment are made at various hierarchical levels: they require iarious time periods t o implement and must be made with corresponding degrees of planning (each decision at the appropriate time). A number of tasks must be solved to sub- stantiate each decision; and for development planning of the entire system.

the tasks at various hierarchical levels must be coordinated. With t h ~ s aim.

planning task hierarchies have been dekised, together with the system hier- archy. Such a task hierarchy is described in the paper using the example o f development planning for the generating capacity of electric power systems.

l ~ t a t e Plan for the Electrification of the U.S.S.R.

Special methods must be used to take information uncertainty into account.

These must be geared to complex problems, both static and dynamic, of large dimensions. Such methods have been developed in the USSR for the solution of energy problems, and their general features are described here.

Uncertain input data (i.e. whose distribution functions are not known) lead t o uncertainty in decision-making. The aim of formal mathematical methods in this regard is the best possible identification of the consequences resulting from alternative decisions, and the definition of rational ("intelhgent") decision variants from which the final choice may be made. But ultimately man himself-- the specialists--must decide on the basis of experience and intuition. To decrease information uncertainty, final decisions should be made as late as possible, immediately before their implementation; thus the "freshest" information with the smallest possible degree of uncertainty is provided. In practice this means that final decisions should normally relate only to the nearest interval of time, to priority construction projects, etc.

The methods described in thls paper take these factors into account. They are an expansion of well-known methods of decision-making under uncertainty as described in [S] to deal with complicated optimization problems. They are based on the use of a "payoff matrix" and application of special criteria (Wald, Laplace. Savage. Hunvicz. and others). The basic concepts consist of the "dis- cretization" of continuous problems. and the distinguishing of the "first step"

for dynamic problems. The sequence of operations for solving complicated optimization problems under uncertainty is given in this paper, with expla- nations for each operation.

A Systems Approach t o Development P l a n n i n g of t h e F u e l Power I n d u s t r y of a Planned-Economy Country

L.S. Belyaev

1 . INTRODUCTION

For a c o u n t r y w i t h a planned economy, t h e f u e l power i n d u s t r y ( F P I ) c a n and must be t r e a t e d a s a n e n t i r e l y u n i f i e d system.

B a s i c d e c i s i o n s c o n c e r n i n g i t s development a r e made c e n t r a l l y by t h e n a t i o n a l p l a n n i n g a u t h o r i t y . However, many p l a n n i n g and p r o j e c t o r g a n i z a t i o n s p a r t i c i p a t e i n p r e p a r i n g and s u b s t a n t i a t i c g b o t h b a s i c and lower-order d e c i s i o n s . On t h e whole, development p l a n n i n g of n a t i o n a l and r e g i o n a l f u e l power i n d u s t r y i s a complex p r o c e s s t h a t r e q u i r e s a s p e c i a l systems approach.

I n t h e S o v i e t Union, a systems approach t o e n e r g y development p l a n n i n g h a s i n f a c t been a p p l i e d f o r a l o n g time. The w i d e l y known S t a t e P l a n f o r t h e E l e c t r i f i c a t i o n of t h e USSR (GOELRO), d e v e l o p e d i n t h e e a r l y 1920s under t h e d i r e c t i o n of Academician G.M. ~ r i i i a n o v s k i j , a l r e a d y c o n t a i n e d t h e e l e m e n t s of a systems approach ( a t t h a t time c a l l e d t h e " m u l t i f a c e t e d m e t h o d " ) . S i n c e t h e n , t h e n a t u r e and methods of t h a t approach have been developed and p e r f e c t e d .

The s y s t e m s approach d e s c r i b e d i n t h i s paper h a s been formal- i z e d i n t h e USSR i n r e c e n t y e a r s . While it has n o t y e t been f u l l y implemented, it i s i n c r e a s i n g l y g a i n i n g a c c e p t a n c e and i s b e g i n n i n g t o t a k e r o o t . We w i l l f i r s t c h a r a c t e r i z e t h e approach a s a whole and t h e n e x p l a i n i t s components i n more d e t a i l .

2 . THE FPI AS A TOTALITY OF LARGE SYSTEMS

The f u e l power i n d u s t r y of a c o u n t r y might be viewed a s a t o t a l i t y of l a r g e a r t i f i c i a l systems [ I ] . Some of t h e b a s i c f e a t u r e s d i s t i n g u i s h i n g what we c a l l " l a r g e " a r t i f i c i a l systems from t h o s e t h a t a r e merely complex a r e g i v e n below.

1 ) H i e r a r c h i c a l S t r u c t u r e of t h e System

A l a r g e system c o n s i s t s o f a number of subsystems of v a r i o u s h i e r a r c h i c a l l e v e l s . Each subsystem f u l f i l l s d e f i n e d f u n c t i o n s and i s r e l a t i v e l y autonomous; i n p a r t i c u l a r , it may have i t s own management o r g a n .

( C e r t a i n subsystems may t h e m s e l v e s be l a r g e systems, i n t u r n c o n s i s t i n g of f u r t h e r subsystems.) Subsystems of a s i n g l e l a r g e system, however, a r e s t r o n g l y i n t e r c o n - n e c t e d ; t h e i r o p e r a t i o n s a r e s u b o r d i n a t e t o a common

g o a l ; a n d , f o r purposes of s o l v i n g some of t h e i r development problems, t h e y should be viewed j o i n t l y a s a u n i t e d system.

2 ) Organic P a r t i c i p a t i o n of Man i n System O p e r a t i o n and Management

A l a r g e system i s an o r g a n i c "man-machine" e n t i r e t y , which i n c l u d e s n o t o n l y t e c h n i c a l e l e m e n t s b u t a l s o management o r g a n s . I t may comprise s e v e r a l such o r g a n s , and t h e s e may form a h i e r a r c h y t h a t c o r r e s p o n d s more o r l e s s t o a h i e r a r c h y of r e a l subsystems.

3) E x t e r n a l and I n t e r n a l Random F a c t o r s I n f l u e n c i n q System Development

F a c t o r s i n f l u e n c i n g t h e system a r i s e from n a t u r a l phe- nomena and p e c u l i a r i t i e s of t e c h n o l o g i c a l p r o c e s s e s , a s w e l l a s from t h e a c t i o n s of people ( i n c l u d i n g t h o s e involved i n system management)

.

Consequently l a r g e systems a r e s t o c h a s t i c , a s u b s t a n t i a l element of un- c e r t a i n t y being i n t r o d u c e d by t h e p a r t i c i p a t i o n of men.

I n a d d i t i o n t o t h e s e b a s i c f e a t u r e s , l a r g e systems a l s o have a number of o t h e r properties--multicriterion f u n c t i o n s , a d a p t i v e and s e l f - o r g a n i z i n g c a p a b i l i t i e s , r e l i a b i l i t y , feedback c a p a b i l i t y - - w h i c h w i l l n o t be d i s c u s s e d i n t h e paper.

T h i s c o n c e p t of l a r g e a r t i f i c i a l systems c o r r e s p o n d s b e t t e r t o r e a l i t y . The f u e l power i n d u s t r y and i t s i n d i v i d u a l branches may be viewed a s a c l a s s i c example of a l a r g e system. Obviously

t h e s e a r e very complex o b j e c t s f o r s t u d y ; t h e y c a n n o t be de- s c r i b e d w i t h e x a c t i t u d e m a t h e m a t i c a l l y , b o t h because of t h e i r e x c e p t i o n a l complexity and because of t h e p a r t played by man), whose a c t i o n s c a n n o t be p r e d i c t e d . Xoreover, random f a c t o r s , d a t a u n c e r t a i n t y , and t h e l i k e must be t a k e n i n t o account.

The approach f o r development p l a n n i n g of such systems t h a t has been developed i n t h e S o v i e t Union w i l l now be examined.

3. COPWONENTS OF THC SYSTEXS APPROACH

The nethcdology of a systems approach t o development p l a n n i n g of t h e f u e l power i n d u s t r y i s based on t h e f o l l o w i n g p r i n c i p l e s .

1 ) C r e a t i o n of a h i e r a r c h y of systems f o r t h e FPI, and i d e n t i f i c a t i o n of t a s k s f o r t h e development of each system;

2 ) E l a b o r a t i o n and a p p l i c a t i o n of mathematical models f o r s o l v i n g t h e development t a s k s ;

3) The use of s p e c i a l methods f o r t a k i n g a c c o u n t of u n c e r t a i n t i e s i n i n p u t d a t a ;

4 ) C o n s i d e r a t i o n o f t h e e x t e r n a l i n t e r a c t i o n s o f e n e r g y s y s t e m s , t h e i r e n v i r o n m e n t a l i m p a c t , e t c . ;

5 ) Improvement o f o r g a n i z a t i o n a l s t r u c t u r e and p r a c t i c a l management methodology.

The need f o r c r e a t i n g a h i e r a r c h y of s y s t e m s f o l l o w s from t h e c o m p l e x i t y o f t h e f u e l power i n d u s t r y . Decomposition i n t o s u b s y s t e m s f o r which more p r e c i s e m a t h e m a t i c a l models c a n be c o n s t r u c t e d p r o v i d e s t h e d e t a i l s r e q u i r e d f o r s o l v i n g v a r i o u s t a s k s .

F o r e a c h s u b s y s t e m o f t h e F P I - - t h a t i s , a t e a c h h i e r a r c h i c a l l e v e l , a number o f d e c i s i o n s must b e made: f o r example, d e c i s i o n s on power p l a n t d e s i g n and c o n s t r u c t i o n , d e s i g n o f new t y p e s o f e q u i p m e n t , p r o d u c t i o n r e q u i r e m e n t s , and s o f o r t h . D i f f e r e n t d e c i s i o n s demand d i f f e r e n t t i m e p e r i o d s f o r t h e i r i m p l e m e n t a t i o n and must be made w i t h v a r y i n g d e g r e e s o f p l a n n i n g . To s u b s t a n t i a t e t h e d e c i s i o n s , s p e c i f i c t a s k s must be s o l v e d . Thus a number o f development management t a s k s a r e s o l v e d f o r e a c h s u b s y s t e m , and a

h i e r a r c h y o f t h e s e t a s k s i s d e f i n e d a l o n g w i t h t h e s y s t e m s h i e r - a r c h y .

S t u d y and o p t i m i z a t i o n o f complex s y s t e m s i s u n t h i n k a b l e t o d a y w i t h o u t m a t h e m a t i c a l models. These models have been w i d e l y u s e d i n many c o u n t r i e s f o r some t i m e . We may make o n l y t h e f o l l o w i n g o b s e r v a t i o n . Models a r e c o n s t r u c t e d t o c a r r y o u t s p e c i f i c r e s e a r c h o r s o l v e s p e c i f i c problems. F o r v e r y complex s y s t e m s , i t i s i m p o s s i b l e , o r s e n s e l e s s , t o d e v e l o p " a l l - i n c l u - s i v e " models r e f l e c t i n g i n d e t a i l a l l t h e a s p e c t s o f a r e a l s y s t e m t h a t a r e of i n t e r e s t f o r s o l v i n g v a r i o u s q u e s t i o n s . T h i s i s p a r t i c u l a r l y t r u e o f o p t i m i z a t i o n models. Depending on t h e problems t o be s o l v e d , t h e v a r i o u s p r o p e r t i e s o f a s y s t e m a r e r e f l e c t e d i n t h e models w i t h v a r y i n g d e g r e e s o f d e t a i l . There- f o r e s e v e r a l d i f f e r e n t models may be needed f o r t h e same system.

Even t h e b e s t m a t h e m a t i c a l model c a n n o t g i v e c o r r e c t r e s u l t s i f s u p p l i e d w i t h i n s u f f i c i e n t l y d e f i n e d d a t a ; f o r t h e f o r e s e e - a b l e f u t u r e s u c h u n c e r t a i n t y w i l l c o n t i n u e t o e x i s t . T h a t b r i n g s u s t o t h e t h i r d p r i n c i p l e of o u r s y s t e m s a p p r o a c h - - t h e need f o r d e a l i n g w i t h u n c e r t a i n i n f o r m a t i o n . By u n c e r t a i n t y i n i n p u t d a t a we mean t h a t n e i t h e r t h e i n p u t d a t a n o r t h e i r d i s t r i b u t i o n f u n c t i o n s a r e known t o u s e x a c t l y . T h i s c a n u l t i m a t e l y l e a d t o u n c e r t a i n t y i n d e c i s i o n - m a k i n g , and m a t h e m a t i c a l models become p o w e r l e s s h e r e . U l t i m a t e l y man h i m s e l f - - t h e s p e c i a l i s t s - - m u s t d e c i d e on t h e b a s i s o f e x p e r i e n c e and i n t u i t i o n . The aim, t h e r e - f o r e , o f f o r m a l s t u d i e s i s t h e b e s t p o s s i b l e i d e n t i f i c a t i o n of t h e c o n s e q u e n c e s r e s u l t i n g from a l t e r n a t i v e d e c i s i o n s . They a r e a l s o used t o d e f i n e r a t i o n a l v a r i a n t s from which t h e f i n a l

c h o i c e may be made. ,

S p e c i a l methods a r e a p p l i e d f o r t h e s o l u t i o n o f complex o p t i m i z a t i o n problems u n d e r u n c e r t a i n t y . L a t e r w e w i l l b r i e f l y d e s c r i b e methods d e v e l o p e d i n t h e S o v i e t Union f o r a p p l i c a t i o n t o e n e r g y problems. Note t h a t t h e u n c e r t a i n t y f a c t o r

i n d a t a and decision-making must be t a k e n i n t o a c c o u n t when c o n s t r u c t i n g a h i e r a r c h y o f development t a s k s f o r t h e FPI, i n d e t e r m i n i n g t h e s t r u c t u r e and c o n c e r e t e s t a t e m e n t s of t h e t a s k s , c o m p i l i n g mathematical models, and d e l i n e a t i n g t h e f u n c t i o n s of men and computers.

The f o u r t h p r i n c i p l e - - c o n s i d e r a t i o n o f t h e e x t e r n a l i n t e r - a c t i o n s o f energy systems w i t h o t h e r b r a n c h e s of t h e n a t i o n a l economy, t h e i r e n v i r o n m e n t a l impact, etc.--obviously r e q u i r e s no s p e c i a l e x p l a n a t i o n . C o n s i d e r a t i o n o f t h e v a r i o u s consequences of a g i v e n program i s a widely a c c e p t e d e l e m e n t of t h e systems approach. However, r e a l i z a t i o n o f t h i s p r i n c i p l e o f t e n e n c o u n t e r s s e r i o u s m e t h o d o l o g i c a l and p r a c t i c a l d i f f i c u l t i e s w i t h r e s p e c t t o t h e c o m p i l a t i o n and comparison o f c r i t e r i a , n u m e r i c a l e s t i - mation o f l o s s e s i n o t h e r b r a n c h e s of t h e economy, changes i n t h e b i o s p h e r e , and s o on. S p e c i f i c methods f o r c o n s i d e r i n g conse- quences w i l l depend on t h e p e c u l i a r i t i e s of t h e t a s k s b e i n g

s o l v e d and may d i f f e r f o r d i f f e r e n t subsystems o f t h e FPI. A s a r u l e , e x t e r n a l i n t e r a c t i o n s o f t h e energy systems a r e t a k e n i n t o a c c o u n t by i n t r o d u c i n g c o r r e s p o n d i n g r e s t r a i n t s whose q u a n t i - t a t i v e c h a r a c t e r i s t i c s a r e determined by t r e a t i n g t h e n a t i o n a l economy a s a whole, o r by s t a n d a r d i z i n g b i o c h e m i c a l , s o c i a l and o t h e r i n d i c a t o r s .

F i n a l l y , t h e f i f t h p r i n c i p l e d e a l s w i t h t h e p r a c t i c a l r e a l i z a t i o n o f t h e o t h e r p r i n c i p l e s o f t h e systems approach. A s t h e FPI d e v e l o p s and t h e methodology o f t h e systems approach con- t i n u e s t o be p e r f e c t e d w i t h r e s p e c t t o t h e o r y , t h e r e i s a need f o r c o n t i n u o u s improvement o f p l a n n i n g p r a c t i c e s . It i s n e c e s s a r y t o r e f i n e , f o r example, t h e s t r u c t u r e and f u n c t i o n s o f management o r g a n s and t h e f l o w o f i n f o r m a t i o n , and t o d e v e l o p new mathematical models. P r a c t i c a l r e a l i z a t i o n of t h e systems approach t a k e s p l a c e more s l o w l y t h a n i t s t h e o r e t i c a l development and i s much more l a b o r i o u s . E x p e r i e n c e , i n t u r n , i s a c o n s t a n t s t i m u l u s f o r t h e development of t h e t h e o r y and i s t h e b a s i c means f o r v e r i f y i n g t h e e f f e c t i v e n e s s of t h e methods proposed.

Some of t h e p r i n c i p l e s o f t h e s y s t e m s approach under examina- t i o n w i l l be i l l u s t r a t e d l a t e r i n more d e t a i l .

4 . A HIERARCEIY OF FPI SYSTEMS; THE TIME ASPECT

I n t h e USSR a t p r e s e n t , p r e f e r e n c e i s g i v e n t o a v a r i a n t of t h e FPI h i e r a r c h y t h a t i s based on a combination of t e r r i t o r i a l and branch i n d i c a t o r s [ I

,

21

.

T h i s v a r i a n t i s d e p i c t e d i n F i g u r e 1 i n a somewhat s i m p l i f i e d form. On t h e t e r r i t o r i a l s i d e , systems a r e d i v i d e d i n t o t h e l e v e l s : c o u n t r y , economic r e g i o n , i n d u s t r i a l c e n t e r , p l a n t . F e a t u r e s o f t h e b r a n c h e s i n c l u d e : a g g r e g a t e

energy s y s t e m s , e l e c t r i c power s y s t e m s , g a s s u p p l y s y s t e m s , o i l s u p p l y s y s t e m s , and systems f o r t h e c o a l i n d u s t r y and atomic power i n d u s t r y . The " c r o s s - c u t t i n g " of some t e r r i t o r i a l and branch l e v e l s forms systems; some of t h e s e a r e shown i n t h e d i a - gram. For o t h e r c o u n t r i e s , some h i e r a r c h i c a l l e v e l s - - f o r example, t h e economic r e g i o n i n c o u n t r i e s w i t h s m a l l e r t e r r i t o r y - - o r

b r a n c h e s might be o m i t t e d .

F i e 1. The energy systems hierarchy.

A s has been s a i d , f o r each system--any t e r r i t o r i a l o r branch l e v e l - - t h e s t r u c t u r e o f management development t a s k s must be determined. The s p e c i f i c i m p l i c a t i o n s of t h e s e t a s k s depend n o t o n l y on t h e p e c u l i a r i t i e s o f t h e g i v e n system, b u t a l s o on t h e p e r i o d of t i m e f o r which t h e y a r e b e i n g s o l v e d . For n e a r e r t i m e p e r i o d s , t h e t a s k s a r e c o n n e c t e d w i t h t h e c o n s t r u c t i o n of s p e c i f i c p r o j e c t s . Those f o r more d i s t a n t p e r i o d s c o n c e r n system d e s i g n t a s k s , development of new equipment, s c h e d u l i n g of s c i e n t i f i c r e s e a r c h , and s o f o r t h . The f o l l o w i n g t i m e p e r i o d s a r e d e f i n e d i n t h e S o v i e t Union f o r P P I development ( s e e F i g u r e 2) :

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Long-term f o r e c a s t i n g d o e s n o t r e l a t e t o p l a n n i n g i n t h e s e n s e o f d e t e r m i n i n g r e a l c o n t r o l a c t i o n s . I t s aims a r e t o i d e n t i f y l o n g - t e r m r e g u l a r i t i e s and t e n d e n c i e s i n t h e f i e l d of e n e r g y , and problems whose s o l u t i o n s t a k e l o n g p e r i o d s t o r e a l i z e : new a r e a s f o r f u t u r e s c i e n t i f i c r e s e a r c h , p o s s i b i l i t i e s f o r

a p p l y i n g new methods i n t h e p r o d u c t i o n , d i s t r i b u t i o n and u t i l i - z a t i o n o f e n e r g y , g e o l o g i c a l e x p l o r a t i o n f o r new r e s o u r c e s , and t h e l i k e . A l s o , lonr-Lerm f o r e c a s t s s u p p l y a r e f e r e n c e p o i n t f o r more d i s t a n t ~ ~ e r s p e c t i v e s d u r i n g t h e c o m p i l i n g o f 15-year p l a n s . I n l o n q - t e r n f o r e c a s t i n g , t h e c o u n t r y ' s f u e l power

i n d u s t r y i s c o n s i d e r e d a s a whole, w i t h a rough v i e w o f economic r e g i o n s and e n e r g y b r a n c h e s .

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I n 15-year p l a n n i n g , t h e t i m e p e r i o d c o n s i d e r e d i s t r e a t e d i n 5-year s e g m e n t s . The f o l l o w i n g a s p e c t s a r e d e t e r m i n e d f o r t h e s e c o n d and t h i r d segment: t h e r a t i o n a l p r o p o r t i o n s f o r t h e d e v e l o p m e n t o f i n d i v i d u a l b r a n c h e s , t h e d e v e l o p m e n t s c a l e f o r v a r i o u s f u e l r e s o u r c e d e p o s i t s , t e r r i t o r i a l s i t i n g o f m a j o r p l a n t s and i n d u s t r i a l complexes, d i s t r i b u t i o n o f f u e l and e n e r g y , a n t i c i p a t e d demands f o r power e q u i p m e n t , and o t h e r a n a l o g o u s l a r g e - s c a l e p r o b l e m s . I n t h i s c a t e g o r y o n l y two h i g h t e r r i t o r i a l l e v e l s a r e u s u a l l y examined: t h e c o u n t r y a s a whole and t h e economic r e g i o n .

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I n 5 - y e a r p l a n n i n g , more c o n c r e t e problems a r e t r e a t e d : f o r example, t h o s e r e l a t e d t o t h e d e s i g n and c o n s t r u c t i o n o f e n e r g y p r o j e c t s , i n c l u d i n g t r a n s p o r t , and t h e d e t e r m i n a t i o n o f equipment and m a t e r i a l demands. Here a l l t h e t e r r i t o r i a l l e v e l s a r e

examined.

I n y e a r l y p l a n n i n g , s t a r t times f o r power i n s t a l l a t i o n s and f o r t h e d e v e l o p m e n t o f t h e i r o u t p u t c a p a c i t i e s a r e d e f i n e d . Annual l e v e l s o f i n v e s t m e n t a n d o f p r o d u c t i o n and consumption o f e q u i p m e n t , f u e l , and e n e r g y a r e a l s o d e t e r m i n e d .

The t a s k s t o be s o l v e d f o r development p l a n n i n g o f e a c h s y s - tem a r e new d e f i n e d i n a c c o r d a n c e w i t h t h e a p p r o p r i a t e t i m e s c a l e . A t t h e same t i m e , t h e t a s k s a t v a r i o u s h i e r a r c h i c a l l e v e l s must be c o o r d i n a t e d w i t h r e s p e c t t o t i m i n g and s e q u e n c e f o r t h e e f f e c t i v e - n e s s of t h e FPI a s a whole. T h i s i m p l i e s c o n s t r u c t i o n o f a t a s k h i e r a r c h y .

A s a n e x a m p l e , F i g u r e 3 shows a h i e r a r c h y o f d e v e l o p m e n t t a s k s f o r t h e g e n e r a t i n g c a p a c i t i e s o f e l e c t r i c power s y s t e m s . For t h e USSR, t h e s e t a s k s encompass t h r e e l e v e l s : t h e c o u n t r y ' s a g g r e g a t e e n e r g y s y s t e m , i t s i n t e r c o n n e c t e d e l e c t r i c power s y s t e m , and t h e u n i t e d r e g i o n a l e l e c t r i c power s y s t e m s . The t a s k s a r e s o l v e d f o r v a r i o u s p e r i o d s o f t i m e , d e p e n d i n g on t h e n a t u r e o f t h e d e c i s i o n s t o be made. The a r r o w s show t h e t r a n s m i s s i o n o f i n f o r m a t i o n a b o u t t h e d e c i s i o n s made ( " d i r e c t " i n f o r m a t i o n ) . Of c o u r s e t h e r e a r e b a c k - a n d - f o r t h f l o w s o f i n f o r m a t i o n from t a s k t o t a s k .

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P i e 3. Task hierarchy for the pi?Mmg of electric power system capacity.

F o r e l e c t r i c power s y s t e m s , d e v e l o p m e n t t a s k s f o r e l e c t r i c power n e t w o r k s must a l s o b e s o l v e d ; t h e s e t o o a r e d i v i d e d by h i e r a r c h i c a l l e v e l and s h o u l d be c o o r d i n a t e d w i t h t a s k s a l r e a d y c o n s i d e r e d f o r g e n e r a t i n g c a p a c i t i e s .

The s i t u a t i o n i s s i m i l a r f o r o t h e r FPI s y s t e m s .

Note t h a t t h e need t o a s s i g n s y s t e m s d e v e l o p m e n t t a s k s t o d i f - f e r e n t h i e r a r c h i c a l l e v e l s , i n s t e a d o f s o l v i n g what seems t o b e a

s i n g l e o p t i m i z a t i o n t a s k , a l s o seems from t h e u n c e r t a i n t y i n i n p u t d a t a . D i f f e r e n t d e c i s i o n s r e q u i r e d i f f e r e n t t i m e p e r i o d s f o r t h e i r implementation. To r e d u c e d a t a u n c e r t a i n t y , d e c i s i o n s should be made a s l a t e a s p o s s i b l e , immediately b e f o r e being implemented, s o t h a t t h e " f r e s h e s t " i n f o r m a t i o n w i t h t h e s m a l l e s t d e g r e e of u n c e r t a i n t y i s provided. Each d e c i s i o n i s t h u s made a t t h e b e s t p o s s i b l e t i m e , t h e s p e c i f i c t a s k s u b s t a n t i a t i n g it having f i r s t been s o l v e d . One i s d e a l i n g w i t h a number of i n t e r c o n n e c t e d development t a s k s r a t h e r t h a n a s i n g l e o p t i m i z a - t i o n t a s k which, g i v e n t h e d a t a u n c e r t a i n t y , would be unmanageable.

5. MATHEMATICAL MODELS FOR FPI DEVELOPMENT PLANNING

We have s e e n t h a t many models must be used t o o p t i m i z e t h e f u e l power i n d u s t r y complex. To c l a r i f y t h i s , l e t u s r e t u r n t o F i g u r e 1 , p r e s e n t i n g t h e FPI systems h i e r a r c h y . For each system i n d i c a t e d h e r e ( e a c h s q u a r e i n t h e t a b l e ) , s e v e r a l mathe- m a t i c a l models have been o r a r e b e i n g developed i n v a r i o u s c o u n t r i e s t o c a r r y o u t t h e c o r r e s p o n d i n g systems development t a s k s . Of c o u r s e , t h e many models c a n n o t be d i s c u s s e d h e r e . Some of them a r e d e s c r i b e d i n [ 3 , 41, and a r e v i e w of USSR e n e r g y models i s t o be p r e p a r e d a t IIASA i n t h e n e a r f u t u r e . The most

i m p o r t a n t and i n t e r e s t i n g a r e models e l a b o r a t e d on a n a t i o n w i d e l e v e l . These a r e mainly o p t i m i z a t i o n models, sometimes dynamic, u t i l i z i n g l i n e a r programming methods. Some of them, p a r t i c u l a r l y t h o s e f o r t h e c o u n t r y ' s a g g r e g a t e energy system, may i n c l u d e s e v e r a l thousand e q u a t i o n s and t e n s of t h o u s a n d s o f v a r i a b l e s . U s u a l l y t h e y c o n s i s t o f s e v e r a l b l o c k s r e p r e s e n t i n g t e r r i t o r i a l o r b r a n c h subsystems.

Mathematical models f o r o p t i m i z a t i o n o f systems o f lower t e r r i t o r i a l l e v e l s (economic r e g i o n s , i n d u s t r i a l c e n t e r s , p l a n t s ) a r e c o n s i d e r a b l y more v a r i e d . Mainly n o n l i n e a r models a r e used h e r e , which may a l s o be dynamic, d i s c r e t e , o r s t o c h a s t i c , depending on t h e t a s k t o be c a r r i e d o u t . The most c o m p l i c a t e d models a r e now r e a l i z e d on computers a s program-information camplexes, which i n c l u d e d a t a banks and c o n t r o l and s e r v i c e programs a l o n g with t h e b a s i c model programs. These complexes a r e u s u a l l y cornprisad i n a n automated management system.

6. ACCOUNTING FOR UNCERTAINTY OF INPUT INFORMATION

To t a k e a d e q u a t e a c c o u n t of i n f o r m a t i o n u n c e r t a i n t y when s o l v i n g development t a s k s of t h e FPI, s p e c i a l methods f o r s o l v i n g complex t a s k s of l a r g e dimensions must be a p p l i e d . Before t h e methods t h e m s e l v e s a r e d i s c u s s e d , t h r e e i m p o r t a n t p o i n t s should be s t r e s s e d .

F i r s t , a s I have a l r e a d y mentioned, u n c e r t a i n t y i n i n i t i a l i n f o r m a t i o n l e a d s t o u n c e r t a i n t y i n decision-making. Conse- q u e n t l y formal methods c a n n o t o f f e r s i n g l e o p t i m a l s o l u t i o n s ; t h e y can o n l y p r o v i d e c l e a r e r and f u l l e r a n a l y s e s and e l u c i d a t e r a t i o n a l d e c i s i o n v a r i a n t s .

Second, s i n c e i n p u t d a t a a r e n o n - d e t e r m i n i s t i c , t h e i r many p o s s i b l e combinations must be c o n s i d e r e d , and t h e v a r i a n t s o f f e r e d must be compared f o r a l l t h e s e combinations. T h i s makes t h e s e c a l c u l a t i o n s v e r y l a b o r i o u s and r e q u i r e s t h e s i m u l a t e d a d a p t a t i o n of each v a r i a n t t o d i f f e r e n t p o s s i b l e development c o n d i t i o n s . I n a d d i t i o n , p r o c e d u r e s must be used t h a t s a t i s f y b a l a n c e and t e c h n i c a l c o n s t r a i n t s .

F i n a l l y , a s n o t e d e a r l i e r , d e c i s i o n s should be made inrmediately b e f o r e t h e i r implementation in o r d e r t o d e c r e a s e i n f o r m a t i o n u n c e r t a i n t y . I n p r a c t i c e t h i s means t h a t f i n a l d e c i s i o n s should r e l a t e o n l y t o t h e n e a r e s t i n t e r v a l of t i m e , t o p r i o r i t y c o n s t r u c t i o n p r o j e c t s , e t c . When p o s s i b l e , d e c i s i o n s s h o u l d be made i n s e p a r a t e s t a g e s - - f o r example, f o r t h e s t a r t o f a d e s i g n s t a g e and t h e s t a r t of a p r o j e c t c o n s t r u c t i o n , o r f o r t h e d e s i g n of new equipment, p r o d u c t i o n o f p r o t o t y p e s , and connnercial p r o d u c t i o n . Thus, d u r i n g r e a l i z a t i o n of t h e f i r s t s t a g e s , technical-economic i n d i c a t o r s f o r p r o j e c t s and equipment a r e made more p r e c i s e , and o t h e r e x t e r n a l c o n d i t i o n s underqo r e f i n e m e n t .

The methods d e s c r i b e d below t a k e t h e s e t h r e e s t a t e m e n t s i n t o account.

We have extended well-known methods of decision-making under u n c e r t a i n t y t o c o v e r c o m p l i c a t e d o p t i m i z a t i o n problems. Those methods ( s e e f o r example [ S ] a r e based on t h e u s e of a "payoff m a t r i x " and t h e a p p l i c a t i o n of s p e c i a l c r i t e r i a (Wald, L a p l a c e , Savage, H u w i c z , and o t h e r s ) . They assume t h a t decision-making t a k e s p l a c e i n one t i m e o r s t a t i c s i t u a t i o n w i t h a f i n i t e numbez of a c t i o n s and s t a t e s of n a t u r e . But i n t h e r e a l - w o r l d develop- ment o f energy systems, one u s u a l l y e n c o u n t e r s a n i n f i n i t e m u l t i t u d e of both d e c i s i o n p a r a m e t e r s and n o n - d e t e r m i n i s t i c

i n p u t i n d i c a t o r s ; many t a s ~ s being dynamic in n a t u r e . T h i s f a c t r e q u i r e s t h e development o f s g e c i a l methods.

One b a s i c i d e a c o n s i s t s in t h e " d i s c r e t i z a t i o n " of con- t i n u o u s problems. Here one s e l e c t s a f i n i t e number of " r e p r e - s e n t a t i v e " p o i n t s from t h e i n f i n i t e domain o f d e c i s i o n p a r a m e t e r s o r p a r a m e t e r s c h a r a c t e r i z i n g s t a t e s of n a t u r e . For t h e s e p o i n t s t h e n e c e s s a r y c a l c u l a t i o n s a r e made, t h e payoff m a t r i x i s ccn- p i l e d , and t h e a n a l y s i s i s c a r r i e d o u t .

The scheme o u t l i n e d h e r e i s based on r e s e a r c h and on p r a c t i c a l s o l u t i o n s of some energy t a s k s . I t p r o v i d e s f o r t h e f o l l o w i n g o p e r a t i o n s :

1 ) S t a t e m e n t of t h e problem;

2 ) S e l e c t i o n o f a r e p r e s e n t a t i v e set o f s t a t e s of n a t u r e , ( i . e . of p o s s i b l e c o n d i t i o n s f o r system d e v e l o p m e n t ) ; 3 ) S e a r c h f o r and p r e l i m i n a r y a n a l y s i s of v a r i a n t s f o r

problem s o l u t i o n ;

4 ) C a l c u l a t i o n o f t h e p a y o f f m a t r i x ;

5 ) A n a l y s i s o f t h e p a y o f f m a t r i x a n d s e l e c t i o n o f r a t i o n a l a c t i o n s ;

6 ) F i n a l c h o i c e o f t h e a c t i o n t o be t a k e n f o r r e a l i z a t i o n . F o r e a c h o p e r a t i o n , methods o f i m p l e m e n t a t i o n h a v e b e e n i n v e s t i g a t e d and recommended, [ I , 6 , 7 , 8 , 91, w h i c h I s h a l l n o t d i s c u s s h e r e i n d e t a i l . R e l a t e d work w i l l be d o n e a t IIASA. Below I s h a l l b r i e f l y e x p l a i n t h e s e o p e r a t i o n s .

S t a t e m e n t o f t h e p r o b l e m i s t h e f i r s t s t e p , a n d a v e r y i m p o r t a n t o n e . Here o n e must e s t a b l i s h :

-

I d e n t i f i c a t i o n o f p a r a m e t e r s (components o f v e c t o r x ) c h a r a c t e r i z i n g t h e d e c i s i o n t o be made,

-

I d e n t i f i c a t i o n o f t h e p r o b a b i l i s t i c i n p u t d a t a c h a r a c t e r i z i n g t h e s t a t e s o f n a t u r e ,

( X a n d Y a r e domains o f p o s s i b l e v a l u e s f o r v e c t o r s x a n d y ) ;

-

^*An e v a l u a t i n g f u n c t i o n f o r e s t i m a t i n g t h e e f f e c t o f a c t i o n s ( o r e x p e n d i t u r e s ) u n d e r d i f f e r e n t s t a t e s o f n a t u r e ;

-

E x i s t i n g c o n s t r a i n t s a n d p r o c e d u r e s t o s a t i s f y them.

F u n c t i o n E ( x , y ) i s n o t a n o b j e c t i v e f u n c t i o n i n t h e u s u a l s e n s e . W e c a n n o t t a l k a b o u t m i n i m i z i n g it ( i f it r e p r e s e n t s e x p e n d i t u r e s ) , s i n c e e a c h v a l u e o f v e c t o r x may a t t a i n i t s minimum u n d e r a d i f f e r e n t s t a t e o f n a t u r e . We c a n t r y ! however, t o make t h e v a l u e s o f f u n c t i o n E ( x , Y ) a s s m a l l a s possible.

I f we a r e d e a l i n g w i t h a dynamic p r o b l e m , f o r m u l a t i o n o f t h e e v a l u a t i o n f u n c t i o n E ( x , y ) becomes more c o m p l i c a t e d . T h i s w i l l be d i s c u s s e d a t t h e end o f t h e p a p e r .

The s e c o n d and t h i r d o p e r a t i o n s a r e i n f a c t t h e " d i s - c r e t i z a t i o n " o f t h e problem I m e n t i o n e d e a r l i e r . I n t h e d i s - c o n t i n u o u s s e t s Y and X , a f i n i t e number o f p o i n t s m u s t be c h o s e n t h a t c h a r a c t e r i z e t h e s e t a s a whole s u f f i c i e n t l y w e l l . A s a n e x a m p l e , l e t u s c o n s i d e r t h e s e t o f p o s s i b l e s t a t e s o f n a t u r e Y .

The f o l l o w i n g methods o f f o r m a l d e s c r i p t i o n ( s e e F i g u r e 4 ) may be u s e d f o r n o n - d e t e r m i n i s t i c i n p u t d a t a (components o f v e c t o r y ) t h a t a r e o f a c o n t i n u o u s n a t u r e :

1 ) F o r s t o c h a s t i c d a t a w i t h a known d a t e - g e n e r a t i n g p r o c e s s , a d i s t r i b u t i o n f u n c t i o n ;

2 ) For p a r t l y u n c e r t a i n d a t a , a s e r i e s o f p o s s i b l e d i s t r i b u t i o n f u n c t i o n s ^;

3 ) For u n c e r t a i n d a t a , a n i n t e r v a l of p o s s i b l e v a l u e s .

1. STOCHASTIC-DEFINITE DATA

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Figure 4. Quantitative description of nondeterministic data.

For e a c h o f t h e s e methods o f d e s c r i p t i o n we c a n , o r m u s t , show a r a n g e ( f r o m A t o B ) o f p r a c t i c a l l y p o s s i b l e v a l u e s o f t h e d a t a c o n s i d e r e d . For v e c t o r y w i t h a l l i t s components we s h o u l d o b t a i n a c o n t i n u o u s f i e l d Y ( n - d i m e n s i o n a l p a r a l l e l - e p i p e d o r some o t h e r s p a c e ) , and i n t h a t s p a c e c h o o s e a d e f i n i t e number o f p o i n t s a s i t s r e p r e s e n t a t i v e s .

S e v e r a l s e l e c t i o n methods have been p r o p o s e d , g e n e r a l l y based on t h e ( i n some s e n s e ) r e g u l a r d i s t r i b u t i o n of a g i v e n number of p o i n t s i n a n n-dimensional p a r a l l e l e p i p e d o r s i n g l e cube. I n p a r t i c u l a r , l i n e a r c o d e t h e o r y i s used f o r c h o o s i n g p o i n t s e v e n l y o r u n i f o r m l y d i s t r i b u t e d on a g r i d o r i n t h e c e n t e r s of s p h e r e s having e q u a l and maximum p o s s i b l e d i a m e t e r s . F i g u r e 5 i l l u s t r a t e s s u c h s e l e c t i o n w i t h i n a two-dimenasional s i n g l e cube. F i g u r e 5a shows t h e s e l e c t i o n of s e v e n p o i n t s on a r e g u l a r g r i d , and F i g u r e 5b t h a t o f t h r e e p o i n t s in t h e c e n t e r s of s p h e r e s .

0.5 1

Figure 5. Selection

0

o f uniformly situated points.

To s e l e c t p o s s i b l e a c t i o n s f o r s u b s e q u e n t e x a m i n a t i o n , i . e . t o c o m p l e t e t h e t h i r d o p e r a t i o n , a n o t h e r method may a l s o be used. I t i n v o l v e s making d e t e r m i n i s t i c o p t i m i z a t i o n c a l c u - l a t i o n s f o r s e v e r a l s t a t e s of n a t u r e s e l e c t e d d u r i n g t h e second o p e r a t i o n . The " l o c a l " o p t i m a l v a r i a n t s s o o b t a i n e d c a n be i n c l u d e d among t h e a c t i o n s c o n s i d e r e d .

A s a r e s u l t of t h e s e two o p e r a t i o n s we o b t a i n a f i n i t e number ( S ) of c o n s i d e r e d s t a t e s of n a t u r e ys ( s = 1 , 2 ,

. . . ,

^{S )}

-

and a f i n i t e number ( I ) of p o s s i b l e a c t i o n s x i ( i = 1

,

2 ,

. . .

^{I )}

.

C a l c u l a t i o n of t h e payoff m a t r i x means e s t i m a t i n g t h e v a l u e s o f f u n c t i o n E ( x , y ) f o r a l l p o s s i b l e a c t i o n s xi and a l l s t a t e s of n a t u r e ys. ^A payoff m a t r i x i s r e p r e s e n t e d i n F i g u r e 6 . On t h e r i g h t s i d e of t h e f i g u r e , c h a r a c t e r i s t i c v a l u e s of f u n c t i o n E ( x , y ) a r e shown which may be o b t a i n e d from t h e payoff m a t r i x .

Because o f t h e u n c e r t a i n t y of f u t u r e system development c o n d i t i o n s we c a n n o t o b t a i n a s i n g l e ( d e t e r m i n i s t i c ) e s t i m a t e f o r each p o s s i b l e a c t i o n xi; t h e s e r i e s o r v e c t o r o f e s t i m a t e s

o b t a i n e d depends on t h e s t a t e s o f n a t u r e . S i n c e t h e p r o b a b i l i t i e s o f d i f f e r e n t s t a t e s o f n a t u r e a r e n o t known e i t h e r , we a l s o

c a n n o t d e t e r m i n e t h e m a t h e m a t i c a l e x p e c t a t i o n o f e x p e n d i t u r e s . Only c e r t a i n c h a r a c t e r i s t i c v a l u e s can t h e r e f o r e be determined:

t h e maximum e x p e n d i t u r e

EY,

t h e minimum e x p e n d i t u r e

y,

^and

t h e a r i t h m e t i c mean

Ei.

I n a d d i t i o n , we can dete-mine t h e maximum r i s k ( r e g r e t ) v a l u e (Rimax)

.

The s e l e c t i o n o f r a t i o n a l a c t i o n s c a n be made u s i n g t h e above-mentioned c r i t e r i a f o r u n c e r t a i n c o n d i t i o n s . The most l o g i c a l and i n t e r e s t i n g c r i t e r i a a r e shown below.

Wald's c r i t e r i o n ( o f minimax e x p e n d i t u r e s ) : 0

min _i

TX

^-in _i ^max _s ^E i s

- Xi;

Savage s c r i t e r i o n (of minimax r i s k ) : 0 r n i n _i

RY

^{= min max} _{i s} ^Ris

-

^X~

L a p l a c e ' s c r i t e r i o n :

1 0

min _i

Ei

= rnin _{i S s = l}

1

E~~

-

_L

Hurwicz's c r i t e r i o n (of pessimism-optimism) 0

min _{i 1} + ⁽ 1

-

^a

~ y ~ ~ ] - ^XH

w a l d ' s and S a v a g e ' s c r i t e r i a a r e minimax, t h e r e m a i n i n g two u s e a c e r t a i n a v e r a g e e s t i m a t i o n o f e x p e n d i t u r e s . A c e r t a i n

g e n e r a l i z e d c r i t e r i o n (K) c a n a l s o be c o n s t r u c t e d on t h e b a s i s of c h a r a c t e r i s t i c v a l u e s of t h e p a y o f f m a t r i x :

min ⁰

min _i Ki = min _i

[olqax

^{+ a2Ei}

⁺

^{o J ~ i +} a 4 R y x ]

-

K

Figurc 6. T l ~ c payoff matrix atid its charactcristic values.

Depending on t h e a c c e p t e d v a l u e s of c o e f f i c i e n t s a , one may p a s s from t h i s c r i t e r i o n t o each of t h e f o u r p r e c e d i n g ones o r o b t a i n v a r i o u s combinations of c r i t e r i a .

Note t h a t each of t h e c r i t e r i a h a s d e f i n i t e drawbacks. None i n s p i r e s complete c o n f i d e n c e , and no d e c i s i o n based on a s i n g l e one is allowed. These c r i t e r i a merely p r o v i d e t h e p o s s i b i l i t y t o

i d e n t i f y r a t i o n a l a c t i o n s t h a t a r e d e s i r a b l e i n some r e s p e c t . A s s t a t e d b e f o r e , t h e f i n a l c h o i c e of a d e c i s i o n from m o n o a number of r a t i o n a l v a r i a n t s must b e made by man h i m s e l f . Here a d d i t i o n a l o b j e c t i v e s , n o t c o n s i d e r e d d u r i n g t h e e a r l i e r exami- n a t i o n of t h e problem, may be t a k e n i n t o a c c o u n t , u s e may b e made of e s t i m a t i o n s by e x p e r t s , and t h e l i k e . Without d w e l l i n g on t h e s e , I w i l l merely n o t e t h a t d e s p i t e a " s u b j e c t i v e " c h o i c e a t t h e f i n a l s t a g e , t h e p r e c e d i n g a n a l y s i s g u a r a n t e e s o n l y r a t i o n a l v a r i a n t s and i n s u r e s u s a g a i n s t g r o s s e r r o r s .

T h i s , in b r i e f , i s t h e g e n e r a l scheme f o r s o l v i n g problems under c o n d i t i o n s of u n c e r t a i n t y . W e have n o t c o v e r e d h e r e many d i f f i c u l t i e s t h a t o c c u r d u r i n g t h e v a r i o u s s t e p s , n o r how t o d e a l w i t h them. The scheme we have o u t l i n e d h a s been v e r i f i e d by a p p l i c a t i o n t o p r a c t i c a l problems and c o n t i n u e s t o be developed and r e f i n e d .

Now l e t u s c o n s i d e r b r i e f l y t h e s t a t e m e n t o f dynamic prob- lems, t o which t h e m a j o r i t y of power systems development t a s k s a r e r e l a t e d . On f o r m u l a t i n g dynamic ~ r o b l e m s , i t i s i m p o r t a n t t h a t t h e p r i n c i p l e o f t a k i n g o n l y p r i o r i t y d e c i s i o n s be r e f l e c t e d - - t h a t i s , d e c i s i o n s c o n c e r i n g t h e n e a r e s t time i n t e r v a l ( t h e

" f i r s t s t e p " ) . For a c o r r e c t e v a l u a t i o n of t h e consequences of p r i o r i t y d e c i s i o n s , an a d d i t i o n a l t i m e p e r i o d ( " a f t e r - a c t i o n "

p e r i o d ) must be examined. D i f f e r e n t s t a t e m e n t s f o r dynamic problems a r e p o s s i b l e , depending on t h e ways cnosen t o a c c o u n t f o r system development d u r i n g t h e " a t e r - a c t i o n " p e r i o d [9]

.

^The

most l o g i c a l and f l e x i b l e s t a t e m e n t i s t h e f o l l o w i n g [ 8 , 91.

The g i v e n p e r i o d i s d i v i d e d i n t o T t i m e i n t e r v a l s ( t = 1 ,

. . . ,

T I . I t i s assumed t h a t t h e f i n a l d e c i s i o n i s made o n l y f o r v a l u e s o f d e c i s i o n p a r a m e t e r s i n t h e f i r s t i n t e r v a l x l

.

These a l o n e c h a r a c t e r i z e a l t e r n a t i v e c o u r s e s o f a c t i o n , and :or them t s e p o s s i b l e v a r i a n t s a r e o u t l i n e d ( d u r i n g t h e t h i r d o p e r a t i o n ) :

The s t a t e s of n a t u r e a r e c h a r a c t e r i z e d by t h e s p e c i f i c r e a l i - z a t i o n s of v e c t o r 7 f o r t h e whole p e r i o d T examined:

The economic impact of some v a r i a n t xi f o r a c e r t a i n s t a t e of n a t u r e ys i s d e t e r m i n e d by t h e f o l l o w i n g c a l c u l a t i o n o f t h e payoff m a t r i x :

E~~ = El (xi,y1 s ) + min E~ (xt,.ytS)

,

X t

t-2

where El and Et a r e e x p e n d i t u r e f u n c t i o n s f o r t h e l s t and tth i n t e r v a l s r e s p e c t i v e l y , and x, i s t h e v a l u e o f t h e d e c i s i o n p a r a m e t e r s i n - t h e 2nd-and s u b i e q u e n t t i m e i n t e r v a l s . The f i r s t t e r m of t h e r e l a t i o n s h i p e s t i m a t e s t h e e f f e c t i n t h e f i r s t t i m e i n t e r v a l f o r which a f i n a l d e c i s i o n i s s o u g h t . The second t e r m t a k e s i n t o a c c o u n t t h e e f f e c t i n t h e " a f t e r - a c t i o n " p e r i o d . Here it i s assumed t h a t i n t h e " a f t e r - a c t i o n " p e r i o d t h e s y s t e m would d e v e l o p o p t i m a l l y depending on t h e a c t i o n s e l e c t e d i n t h e f i r s t s t e D , and on t h e c o n d i t i o n s y t h a t i n f a c t o c c u r . _S

A l l s u b s e q u e n t decision-making, a f t e r o n e o b t a i n s t h e p a y o f f m a t r i x , w i l l be a s c o n s i d e r e d above. T h i s s t a t e m e n t i s a v e r y time-consuming o n e s i n c e it demands t h e c o m p l e t i o n o f IxS d e t e r - m i n i s t i c o p t i m i z a t i o n c a l c u l a t i o n s . Note, however, t h a t dynamic problems a r e always more complex t h a n s t a t i c o n e s .

R e f e r e n c e s

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(21 Makaroff, A.A., and L.A. Melentyev, M e t h o d s f o r I n v e s t i - g a t i o n and O p t i m i z a t i o n o f t h e E n e r g y Economy ( i n R u s s i a n ) , Nauka, N o v o s i b i r s k , 1973

[ 3 ] C h a r p e n t i e r , J . - P . , A Review of Energy Models: No. 1 , RR-74-10, I n t e r n a t i o n a l I n s t i t u t e f o r Applied Systems A n a l y s i s , Laxenburg, A u s t r i a , 1974

[ 4 ] C h a r p e n t i e r , J.-P., A Review o f Energy Models: No. 2 , RR-75-35, I n t e r n a t i o n a l I n s t i t u t e f o r Applied Systems A n a l y s i s , Laxenburg, A u s t r i a , 1975

[51 Luce, R.D., and A. X a i f f a , Games and D e c i s i o n s , Wiley, New York, 1957

(61 Accounting of I n p u t Data U n c e r t a i n t y ( i n R u s s i a n ) : Prob- l e m s o f t h e C r e a t i o n o f A u t o m a t e d I n f o r m a t i o n Manage- m e n t S y s t e m s f o r t h e D e v e t o p m e n t o f E l e c t r i c Power S y s t e m s , No. 1 , L.S. Belyaev, e d . , S i b e r i a n Power I n s t i t u t e , S i b e r i a n Department o f t h e USSR Academy of S c i e n c e s , I r k u t s k , 1973

[ 7 ] U n c e r t a i n t y F a c t o r i n D e c i s i o n - M a k i n g i n L a r g e S n e r g y S y s t e m s , Vol. 1 ( i n R u s s i a n ) , L.S. Belyaev, e d . , S i b e r i a n Power I n s t i t u t e , S i b e r i a n Department of t h e USSR Academy of S c i e n c e s , I r k u t s k , 1974

[ 8 ] Belyaev, L.S., Q u e s t i o n s of O p t i m i z a t i o n of Large Systems Under P r o b a b i l i s t i c S i t u a t i o n s ( i n R u s s i a n )

,

S c o n o m i c a i m a t e m a t i c h e s k i e m e t o d y ,

3,

6 , 1967

[91 Belyaev, L.S., Some S t a t e m e n t s and Ways of S o l v i n g Dynamic O p t i m i z a t i o n Problems Under U n c e r t a i n t y , i n P r o c e e d i n g s , I F I P C o n f e r e n c e on O p t i m i z a t i o n T e c h n i q u e s , Computer C e n t e r of t h e S i b e r i a n Department of t h e USSR Academy of S c i e n c e s , N o v o s i b i r s k , 1974