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A knowledge based model for the study of power system steady-state operation
Electric Power Systems Research, 21 (1991) 231 - 239
231
A K n o w l e d g e B a s e d Model for t h e S t u d y of P o w e r S y s t e m Steady-State Operation T. M. P E N G , G. G. K A R A D Y a n d D. K. R A N A W E E R A
Department of Electrical Engineering, Arizona State University, Tempe, A Z 85287 (U.S.A.) ( R e c e i v e d F e b r u a r y 21, 1991)
ABSTRACT
This paper presents a knowledge based model for power system steady-state studies. In this model, a power system is represented by three components: power system states, power system operations, and the knowledge base which contains the knowledge about the use of the operations. In the proposed model, the knowledge representation and inference are different from the existing approaches in this area in three aspects. First, the knowledge about power system states and operations is represented by two sets of predicates and frame based structures. This allows efficient data exchange between the model and power flow software. Second, in this model, power system operations are represented by the data structures which are similar to bus and branch data structures used in a power flow program. Third, a special-purpose inference algorithm is developed to manipulate the process of analysis, calculation, and modification of power flow studies. This model is implemented on the I B M 4381 computer and shows high efficiency when used to study a practical power system problem.
Keywords: artificial intelligence, inference, knowledge representation, power system steady state, power flow. 1. I N T R O D U C T I O N
In power system steady-state studies, it is very imp o r tan t to investigate how to use operations to control bus voltage and load flows under normal and contingency conditions. Traditionally, engineers would calculate power flows, analyze the computed results and suggest remedial actions whenever necessary. 0378-7796/91/$3.50
A vast amount of experience and time is needed to perform these tasks. In recent years, expert system approaches have been proposed to integrate numerical calculation and logic reasoning in this field [1-4]. The efficiencies of these expert systems depend on the organization and representation of their knowledge bases. In ref. 1, an expert system method was proposed to assist in the decisionmaking of voltage/VAR control problems; empirical rules were used to generate control actions to alleviate the slight voltage violation problems. In ref. 2, an expert system was proposed for the same problem; sensitivity trees were used to represent the relationship between voltage control devices and the system buses. A rule based approach for decentralized voltage control was presented in ref. 3. In these existing approaches, the knowledge is represented as a group of production rules which are coded in such languages as Prolog, Lisp, OPS5, etc. This type of knowledge representation provides a convenient way to construct, manage, and modify the knowledge base. However, when integrated with power flow software, it has limited ability to control the executions of the power flow calculations and to handle a large amount of data exchanged between the numerical software and the expert system. In this paper, a new knowledge based model is presented. The knowledge representation in the model consists of two parts: (1) a power system steady-state and operation representation, which is comprised of a set of predicates (logic forms) and frame based structures; (2) a special-purpose inference algorithm. The implementation of the model into a real power system computer environment shows t hat it can achieve a highly ~'~ Elsevier S e q u o i a / P r i n t e d in T h e N e t h e r l a n d s
232
efficient p e r f o r m a n c e in p o w e r s y s t e m problems.
solving
practical
the bus states and b r a n c h states, respectively. X is a direct sum of all the bus states, g i v e n by X = Ix~ ® x ~ ® " "
2, M O D E L D E S C R I P T I O N
In the p r o p o s e d model, a p o w e r s y s t e m is described by t h r e e c o m p o n e n t s : s y s t e m states, s y s t e m o p e r a t i o n s , a n d k n o w l e d g e base.
a n d Y is the direct s u m of all the b r a n c h states, g i v e n by Y = {Yl ®Y2®" " ' ®Ym S is the direct sum of X a n d Y, given by S -- {s(x~, x2 . . . . .
2.1. L o g i c a l n o t a t i o n
®x,,
xn ; y~, y2 . . . . .
Ym)} = X O Y
T h e following logical n o t a t i o n [5] is used t h r o u g h o u t this paper: A AND (conjunction) V u n i v e r s a l q u a n t i f i e r (for all) e x i s t e n t i a l q u a n t i f i e r (for some)
w h e r e n is the n u m b e r of buses in the p o w e r system, m is the n u m b e r of b r a n c h e s in the system, and x~ ( i = 1 , 2 . . . . . n) a n d yj ( j = 1, 2 . . . . . m) s t a n d for the i t h bus s t a t e a n d the j t h b r a n c h state, respectively.
2.2. S y s t e m s t a t e s
2.3. S y s t e m o p e r a t i o n s
Let S be the set of s y s t e m states. E a c h system s t a t e in S c o r r e s p o n d s to a specified p o w e r flow case, w h i c h is defined by its netw o r k description, t h a t is, bus a n d b r a n c h data, a n d the p o w e r flow solution. A c e r t a i n e l e m e n t so e S is the i n i t i a l s t a t e a n d a c e r t a i n subset G ~ S is the set of g o a l states. T h e r e is a set of system o p e r a t i o n c o n s t r a i n t s , s u c h as m a x i m u m a n d m i n i m u m bus v o l t a g e s , a n d m a x i m u m b r a n c h load flows. The goal s t a t e is a s t a t e w h i c h satisfies all of these c o n s t r a i n t s . A p o w e r s y s t e m s t a t e c a n be described by the c o n f i g u r a t i o n a n d s t a t e s of the b u s e s a n d b r a n c h e s in the system. Let x~ s t a n d for the s t a t e of the i t h bus. It is defined by a set of p a r a m e t e r s , such as bus name, load, generation conditions, bus v o l t a g e a n d v o l t a g e p h a s e angle. This c a n be e x p r e s s e d as
Besides the state, the model h a s a second c o m p o n e n t O called o p e r a t i o n s . E a c h operation describes the r e l a t i o n s h i p b e t w e e n its p r e v i o u s s t a t e a n d the s u b s e q u e n t state. In a r e a l p o w e r system, an o p e r a t i o n , s u c h as opening a s h u n t r e a c t o r or c h a n g i n g a t r a n s f o r m e r t a p position, modifies the s y s t e m state. In this model, e a c h o p e r a t i o n is described by two parts. One is the c o n d i t i o n of the o p e r a t i o n a n d the o t h e r is the effect of the o p e r a t i o n . F r o m a m a t h e m a t i c a l viewpoint, an operation is a f u n c t i o n t h a t t r a n s f e r s the p o w e r s y s t e m f r o m an old s t a t e to a new state. Let o s t a n d for an o p e r a t i o n , t h e n if
X i ~- Cil
t h e n an o p e r a t i o n , o: S ~ S, is defined as
A
Ci2
A
" " " A
Cik
w h e r e k is the n u m b e r of p a r a m e t e r s used to describe the s t a t e of the bus, a n d c~j is the j t h ( j = 1, 2 . . . . . k) p a r a m e t e r of the i t h bus. In the s a m e way, we c a n define a b r a n c h s t a t e by a set of p a r a m e t e r s s u c h as resistance, r e a c t a n c e , a n d MW, M V A R load flow in the b r a n c h . Let y~ s t a n d for the s t a t e of the ith b r a n c h . It c a n be e x p r e s s e d as follows: Yi
=
rail
A
mi2
A
• • • A
mis
w h e r e s is the n u m b e r of p a r a m e t e r s used to describe the s t a t e of the b r a n c h , a n d m~j is the j t h ( j = 1 , 2 . . . . . s) p a r a m e t e r in the i t h branch. L e t S s t a n d for the s p a c e of p o w e r s y s t e m s t a t e s a n d let X a n d Y s t a n d for the spaces of
{Xl' X2 . . . .
' Xrt }' [21' X2 . . . . .
Xn
e X
and ~Y, , Y2 . . . . .
o(sl (x~ . . . . .
Y., }, [:Yl , Y2 . . . . .
xn ; Yl . . . . .
= s2(2~ . . . . .
:Y.n e Y
Y,,))
2,, ; ~ . . . . .
:~m)
w h e r e s~, s 2 e S. F o r e a c h g i v e n initial state, typically, t h e r e is a set of o p e r a t i o n s . It is defined as an o p e r a t i o n sequence, w h i c h m o v e s the s y s t e m f r o m the initial s t a t e to the goal state. T h e o p e r a t i o n s e q u e n c e c a n be e x p r e s s e d as follows. L e t :~ a n d ~" be the sets of bus s t a t e s a n d b r a n c h s t a t e s w i t h o u t a n y v i o l a t i o n s of operation c o n s t r a i n t s . A set of p o w e r s y s t e m goal s t a t e s S ~ S is defined as =
233
where 121 . . . . . 2n} c : ~ and {3~1. . . . . 3~m} ~ Y An operation sequence is defined as O = { o l , o2 . . . . .
ok }: O ( s ~ ) = S k + l e
where s~ = initial system state ol ( s , ) = s2 o2 0 2 )
= s3
ok (sk) = sk ~
c
2.4. Knowledge base In power system steady-state studies, one starts from an initial state. If the state is not a goal state, then an operation sequence must be found to move the initial state to the goal state. In this process, one must know how to use the operations to modify the system state. In our model, this knowledge is presented in the knowledge base as a set of rules. The information used in this 'knowledge base' was obtained from textbooks as well as from utility engineers. We define the rules with the relationship between an operation and its purpose. For example, if the voltage at bus A is high, then decrease the generator voltage at bus B by -0.01 p.u. 2.5. Inference algorithm To move a system from its initial state to a goal state, it is necessary to perform the following tasks: (1) evaluate the power flow solution of a system state; (2) select an operation to modify a system state if necessary; (3) run the power flow program. In our model, these tasks are performed by the inference algorithm. A detailed description of the algorithm will be given in §5 of this paper.
3. S Y S T E M S T A T E R E P R E S E N T A T I O N
In this model, the power system states are represented by two sets of binary or t er t iary predicates which describe facts about buses and branches. Binary and t er t i a r y predicates are logic forms having two and three arguments, respectively. As in a power flow program, system configurations and states are specified by two types of data: bus data and
branch data, which are described by predicates in our model.
3.1. Bus state representation A bus state can be described by a set of parameters. For example, the name of the bus is A, the load at the bus is 50MW and 12.5 MVAR; the voltage in the bus is 1.103 p.u.; the voltage phase angle is 23.33 °. These facts can be expressed by a set of predicates such as BusNamekV(A, 500), LoadMW(A, 50), LoadMVAR(A, 12.5), Voltage(A, 1.103), and VoltagePhase(A, 23.33~'). (More details about predicate and predicate logic are given in refs. 5 and 6.) A complete set of the predicates is given in the following three groups. (1) The predicates driven from the input data of a power flow case are: BusID(A, BQ) ChangeCode(A, none) BusNamekV(A, 500) LoadMW(A, 50) LoadMVAR(A, 12.5) ShuntMVAR(A, 75) ShuntMVARMax(A, 100) GenerationMW(A, 0.0) GenerationMVAR(A, 0.0) GenerationMWMax(A, *) VoltageHold(A, *) VoltageMax(A, 1.05) (2) The predicates which are driven from the computed power flow results are: Voltage(A, 1.103) VoltagePhase(A, 23.33 ~') (3) The predicates status of the bus are:
which
describe
the
VoltageStatus(A, status) ShuntStatus(A, status) GenerationMWStatus(A, status) GenerationMVARStatus(A, status) For example, the predicates VoltageStatus(A, high) and ShuntStatus(A, available) are generated by the following logic reasoning: Voltage(A, value 1) A VoltageMax(A, value 2) A value_ 1 > value_ 2 ~ V o l t a g e S t a t u s ( A , high) ShuntMVAR(A, val ue_ 1) A ShuntMVARMax(A, value_ 2) /~ value 1 < value_ 2 ~ S h u n t S t a t u s ( A , available)
234
3.2. Branch state representation T h e b r a n c h s t a t e c a n be r e p r e s e n t e d in a s i m i l a r way. Let ( A - B) s t a n d for the n a m e of a b r a n c h w h i c h c o n n e c t s bus A to bus B. T h e s t a t e of the b r a n c h c a n be described by the following t h r e e g r o u p s of p r e d i c a t e s . (1) T h e p r e d i c a t e s d r i v e n from the i n p u t d a t a of a p o w e r flow case are: B r a n c h I D ( A - B, T/L) S w i t c h S t a t u s ( A - B, A, ON) S w i t c h S t a t u s ( A - B, B, ON) R e s i s t a n c e ( A - B, *) R e a c t a n c e ( A - B, *) a / 2 ( n - B, *) B / 2 ( A - B, *) B r a n c h L o a d M a x ( A - B, *) T a p P o s i t i o n ( A - B, *) w h e r e T s t a n d s for t r a n s f o r m e r , L for line, * for a p a r a m e t e r value, O N / O F F for the s w i t c h status. (2) T h e p r e d i c a t e s driven from the comp u t e d p o w e r flow r e s u l t are: B r a n c h L o a d M W ( A - B, *) B r a n c h L o a d M V A R ( A - B, *) (3) T h e b r a n c h s t a t u s is described by the B r a n c h L o a d S t a t u s ( A - B, n o r m a l / o v e r l o a d ) p r e d i c a t e , w h i c h is d r i v e n by the following logic reasoning: B r a n c h L o a d M W ( A - B, v a l u e _ 1) A B r a n c h L o a d M V A R ( A - B, v a l u e _ 2) A B r a n c h L o a d M a x ( A - B, v a l u e _ 3) /x S q r t ( ( v a l u e 1) * 2 + ( v a l u e _ 2) * 2) > v a l u e _ 3 ~ B r a n c h L o a d S t a t u s ( A - B, o v e r l o a d )
3.3. Features of the representation The r e p r e s e n t a t i o n of the p o w e r s y s t e m s t a t e s used in this model h a s the following features. - The s a m e d a t a b a s e is used by the knowledge b a s e d model a n d the p o w e r flow p r o g r a m . As a m a t t e r of fact, w h e n the p o w e r s y s t e m d a t a are used by the k n o w l e d g e b a s e d model, t h e y are p r o c e s s e d in the f o r m of p r e d i c a t e s ; w h e n t h e y are used by the p o w e r flow program, t h e y are p r o c e s s e d in the f o r m of d a t a records or d a t a cards. - The k n o w l e d g e b a s e d model p r o v i d e s a m o r e c o m p r e h e n s i v e d e s c r i p t i o n of the p o w e r s y s t e m b e c a u s e not only are the p o w e r s y s t e m i n p u t d a t a a n d c o m p u t e d p o w e r flow r e s u l t s used, but also i n f o r m a t i o n d r i v e n by logic r e a s o n i n g .
These p r e d i c a t e s can be g r o u p e d in a n y order. As an example, they c a n be sorted acc o r d i n g to e i t h e r a c e r t a i n keyword, such as bus name, or p r e d i c a t e type, such as S h u n t M W . This p e r m i t s a m o r e flexible w a y to process s y t e m data. In a p o w e r flow p r o g r a m , the d a t a h a v e to be o r g a n i z e d by bus or b r a n c h name.
4. SYSTEM OPERATION REPRESENTATION
4.1. Types of operation T h e c h a n g e s in a p o w e r system s t a t e m a y be c a u s e d by (1) c h a n g i n g p a r a m e t e r v a l u e s at a bus, s u c h as load or g e n e r a t i o n ; (2) changing p a r a m e t e r v a l u e s in a b r a n c h , s u c h as a t r a n s f o r m e r t a p p o s i t i o n or series c o m p e n s a tion; (3) s w i t c h i n g on/off a line or a transformer. T h e s e t h r e e types of o p e r a t i o n c a n be e x p r e s s e d as the following t e r t i a r y predicates: Cha nge BusPa r a me te r ( bus name, parameter, value) C h a n g e B r a n c h P a r a m e t e r ( b r a n c h name, p a r a m e t e r , value) ChangeON/OFF(branch, switchl ON/OFF, switch2 O N / O F F ) A n y p o w e r s y s t e m o p e r a t i o n can be represented by t h e s e p r e d i c a t e s . F o r i n s t a n c e , the o p e r a t i o n t h a t o p e n s the t r a n s m i s s i o n line f r o m K y r e n e 500 to S i l v e r k g 500 c a n be represented by C h a n g e O N / O F F ( K y r e n e 500-Silv e r k g 500, OFF, OFF). Here, the second a r g u m e n t in the p r e d i c a t e i n d i c a t e s t h a t the s w i t c h at bus 1 ( K y r e n e 500) s h o u l d be in the O F F p o s i t i o n a n d the t h i r d a r g u m e n t indicates the s a m e for the s w i t c h at bus 2 (Silv e r k g 500).
4.2. Conditions of operation T h e s u c c e s s f u l l y e x e c u t e d o p e r a t i o n requires the s a t i s f a c t i o n of p r e d e t e r m i n e d conditions, w h i c h are also d e s c r i b e d in the form of p r e d i c a t e s . T y p i c a l e x a m p l e s are the following. (1) T h e g e n e r a t i o n or VAR c o n t r o l equipm e n t o u t p u t c a n be c h a n g e d only if t h e y are in ' a v a i l a b l e ' status. To describe this, we have: ShuntStatus(bus, status) GenMWStatus(bus, status) G e n M V A R S t a t u s ( b u s , status)
235 Here, the status of generator, shunt or seties capacitors may be obtained by comparing their actual outputs with the maximum. (2) The change in a br a nc h switch ON/ OFF status requires t ha t the switch is in a proper position. For example, a line switch can be opened when it is in a closed status. To define this, we have SwitchStatus(branch, bus, ON/OFF status)
4.3. Script based operation representation The power system operations can be described by a set of script based structures which are driven by using the previously defined operations and operation conditions. Each of the script based structures consists of two parts which are the preconditions and effects of the operations. For example, ChangeON/OFF(A - B, OFF, OFF) Precondition: SwitchStatus(A - B, A, ON) SwitchStatus(A - B, B, ON) Effect: SwitchStatus(A - B, A, OFF) SwitchStatus(A - B, B, OFF) This script describes an operation t hat opens a branch from bus A to bus B. The 'precondition' part of this script says t h a t the branch switches at bus A and bus B are in the ON (closed) positions. The 'effect' part says t h at the operation changes the switch positions from ON to OFF. The energization of the above transmission line can be described as a two-step operation. First, ChangeON/OFF(A - B, ON, OFF) Precondition: SwitchStatus(A - B, A, OFF) SwitchStatus(A - B, B, OFF) Effect: SwitchStatus(A - B, A, ON) This step of the operation closes the switch of branch A - B at the A side. Then, ChangeON/OFF(A - B, ON, ON) Precondition: SwitchStatus(A - B, A, ON) SwitchStatus(A - B, B, OFF) Effect: SwitchStatus(A - B, B, ON)
This step of the operation closes the switch of branch A- B at the B side. The operation t hat changes the bus param et er values, for example, increasing the shunt reactive power at bus A from 75 MVAR to 100 MVAR, can be expressed as: ChangeBusParameter(A, Shunt VAR, 100) Precondition: ShuntStatus(A, available) Effect: ShuntMVAR(A, 100)
4.4. Integration of the operation with power flow These script based representations of the operations are integrated with a power flow program [5, 6]. This is performed by converting the predicates of the script based structure into a format t hat can be read and interpreted by the power flow program. In this project, we use the Interactive Power Flow System (IPS) of Western Systems Coordinating Council (WSCC) [10]. The effect of the operation has to be verified by the rerun of the power flow. For example, the predicate which increases the reactive power at Silverkg 500 to 100 MVAR requires the rewriting of ChangeBusParameter(Silverkg 500, shunt VAR, 100) in the following format: B
M
Silverkg500
100
where B stands for bus and M is a change code in IPS which means 'modify'. The predicate describing the operation t hat opens the transformer switches at Kyrene 500 and Kyrene 345 is ChangeON/OFF(Kyrene 500- Kyrene 345, OFF, OFF) which can be written in the format T
O
Kyrene 500
Kyrene 345
1
where T stands for transformer and O for 'open' in the IPS.
4.5. Modification of system states by operations An operation or operation sequence can be used to modify a system state to eliminate overvoltage, low voltage, and overload.
236 This can be described by the following rules: AdjustVoltage(A, increase/decrease) ~ C h a n g e B u s P a r a m e t e r ( B , shunt VAR, value) AdjustVoltage(A, increase/decrease) ~ C h a n g e B u s P a r a m e t e r ( B , gen VAR, value) AdjustVoltage(A, increase/decrease) ~ C h a n g e B r a n c h P a r a m e t e r ( B - Z, tap position, ratio)
5.1. Analysis of the given power system state This analysis finds the bus voltage or branch load flow violations in the system state. (1) The voltage violations are identified by the following inference rules: Vx.
Voltage(x, value 1) A VoltageMin(x, value_ 2) A value_ 1 < value_ 2 ~VoltageStatus(x, low)
Vx.
Voltage(x, v a l u e _ l ) A VoltageMax(x, value_ 2) A value_ 1 > value_ 2 ~VoltageStatus(x, high)"
AdjustLoadFlow(A - B, increase/decrease) ~ C h a n g e O N / O F F ( Z - W, ON/OFF, ON/OFF) In most cases the adjustment of a system state (voltage or load flow) requires several operations. This forms an operation sequence. For example, the voltage at b u s A may be decreased by: (1) changing the shunt reactive power at A to value 1; and (2) changing reactive power generation at bus B to value_2. This operation sequence can be described by: ChangeBusParameter(A, shunt VAR, value_ 1) ChangeBusParameter(B, gen VAR, value_ 2)
5. INFERENCE ALGORITHM An inference algorithm has been developed for the identification of voltage and load violations and the selection of the required operation sequences. Before a detailed description of the algorithm is given, a definition of a set of power system voltage and load flow violations is presented:
where x is a logic variable which can be matched with any bus name in the system. (2) The branches with overload can be found by the following inference rule: ¥y.
BranchLoadMW(y, v a l u e _ l ) A BranchLoadMVAR(y, value 2) A BranchLoadMax(y, value_ 3) A Sqrt(value_ 12 + value_ 22) > value_ 3 ~ B r a n c h L o a d S t a t u s ( y , overload)
where y is a logic variable which can be matched with any branch name in the system. (3) If the bus voltage status and branch load status are normal, then V = {0}. The given power system state is in the goal state• This terminates the procedure. The operation sequence set is also empty: O = {0}. (4) Otherwise, a set of the predicates which describe the voltage and the load flow violations is formed. It is defined as V = { v , , t
V 2 , . . . ~'.
V = {vl, v2 . . . . .
v~ }
where k is the number of violations t ha t occur in the system; each element in V is a predicate describing a violation, which has two forms: BusVoltageStatus(bus name, high/low) or B r a n c h L o a d S t a t u s ( b r a n c h name, overload) The task of the algorithm is to reach a goal state which has an empty set of the voltage and load flow violations. This goal state can be reached by finding and applying the proper operation sequence. The algorithm terminates when the goal state is obtained. This is indicated by V = {0}.
(5) For the adjustment of the vo]tage and load flow, a set of subtasks T = {tl, t2. . . . } is formed. Each element in T is a predicate having the form AdjustVo]tage(x, increase/decrease) AdjustLoadFlow(y, decrease) The predicates are driven from the inference rules be]ow: Vx. VoltageStatus(x, high) ~AdjustVoltage(x, decrease) Vx. Vo]tageStatus(x, low) ~AdjustVo]tage(x, increase) Vy. BranchLoadStatus(y, overload) ~AdjustLoadF]ow(y, decrease)
237
The p r e d i c a t e s in set T may be a r r a n g e d a c c o r d i n g to t h e i r priorities, which can be d e t e r m i n e d by sensitivity analyses.
5.2. Search for possible operations If the set of v i o l a t i o n s V is not empty, t h e n a set of o p e r a t i o n s has to be found to modify the system state. (1) Select the first e l e m e n t t in set T and find the o p e r a t i o n s t h a t perform the desired voltage or load flow adjustment. This operation set is defined as F = {f~, f2 . . . . }, in w h i c h each e l e m e n t stands for an operation. A set of i n f e r e n c e rules is developed to p e r f o r m this step. F o r example: Vx. AdjustVoltage(x, i n c r e a s e / d e c r e a s e ) r 3 s 3 t. C h a n g e B u s P a r a m e t e r ( r , s, t) Vx. AdjustVoltage(x, i n c r e a s e / d e c r e a s e ) ~ 3 r ~ s 3 t. C h a n g e B r a n c h P a r a m e t e r ( r , s, t) Vy. A d j u s t L o a d F l o w ( y , decrease) w. C h a n g e B r a n c h P a r a m e t e r ( w , ON/OFF, ON/OFF) (2) If o p e r a t i o n set F is given by
F={fi Ii =1,2,...} t h e n a set of feasible o p e r a t i o n s
0 1 = {0ili----1,2 . . . . } ~ F can be found by using the following i n f e r e n c e rule: Vf~ e F ( i = 1 , 2 . . . . ) and f/=ClAC2A''" if
ck(k=l,
AelAe2A''"
2. . . . ) e S .
Then
f/e01
Here, s is a given system state; ci (i = 1, 2 . . . . ) is a set of p r e d i c a t e s which describes the prec o n d i t i o n p a r t of fi ; ei (i -- 1, 2 . . . . ) is a set of p r e d i c a t e s which describes the effect p a r t of fiF o r a given system state and o p e r a t i o n , this rule says t h a t if all the p r e d i c a t e s in the p r e c o n d i t i o n p a r t of the o p e r a t i o n are satisfied by the system state, t h e n the o p e r a t i o n is a feasible o p e r a t i o n .
form the system into the goal state. The procedure is the following: (1) The elements in O1 are sorted according to t h e i r o p e r a t i o n priority. (2) The first e l e m e n t in Ol, which is the first o p e r a t i o n , is applied to the initial state. This g e n e r a t e s a new state. T h e power flow of the new state is calculated. (3) These new results are evaluated. If the v i o l a t i o n set V is not empty, it is n e c e s s a r y to go b a c k to the p r e v i o u s step to find the n e x t o p e r a t i o n which modifies the system state. Repeat the same p r o c e d u r e until V becomes an empty set.
6. IMPLEMENTATION AND TEST RESULTS
A r e d u c e d power system model of WSCC was used to test the p e r f o r m a n c e of the proposed system. The initial WSCC system contains more t h a n 2000 buses. This r e d u c e d model consists of 502 buses and a b o u t 1000 b r a n c h e s . The p r o g r a m s are w r i t t e n in Computation Oriented Program Environment (COPE) and i m p l e m e n t e d on the IBM 4381 c o m p u t e r of the Salt River Project. F i g u r e 1 shows p a r t of the above system. This gives an idea of the voltage/VAR c o n t r o l facilities available in the C h o l l a - C o r o n a d o area. For the d e m o n s t r a t i o n of the proposed model, the e n e r g i z a t i o n of the Cholla 500C o r o n a d o 500 line is selected as an example. It is assumed t h a t the s h u n t r e a c t o r at the Coronado 500 kV bus (93 MVAR) is out of service. The e x p e r t system is used to solve this problem and the results of the first r u n (state 1) are p r e s e n t e d in Table 1.
(
EI
5.3. Evaluation of the effect of the operation In this step, the effect of the o p e r a t i o n is e v a l u a t e d by i n v e s t i g a t i n g the power flow results of the new power system state. If no v i o l a t i o n is identified, these o p e r a t i o n s trans-
palo
oo oo.0o o0
vrde500
'=" Isil-'~erkg 500
Fig. 1. Voltage/VAR control facilities in the Cholla Coronado area.
238 TABLE 1
TABLE 3
Cholla 500-Coronado 500 line major bus voltage results with the shunt reactor at Coronado 500 out of service: open end at the Coronado 500 kV bus
Cholla 500 Coronado 500 line major bus voltage results with the shunt reactor at Coronado 500 out of service: open end at the Coronado 500 kV bus; generator voltage at Coronado reduced by 0.01
Bus name
Voltage
Status Bus name
Kyrene Silverkg Coronado Coronado Palovrde Cholla Cholla Navajo Westwing Westwing Saguaro Fourcorn Fourcorn Springr Open end
(kV)
Max.
Real
500 500 500 345 500 500 345 500 500 345 500 500 345 345 500
1.099 1.099 1.099 1.060 1.099 1.099 1.060 1.099 1.099 1.060 1.099 1.099 1.060 1.060 1.150
1.073 1.077 1.085 1.036 1.073 1.087 1.062 1.081 1.072 1.046 1.057 1.069 1.028 1.041 1.100
Yes Yes Yes Yes Yes Yes High Yes Yes Yes Yes Yes Yes Yes Yes
Kyrene Silverkg Coronado Coronado Palovrde Cholla Cholla Navajo Westwing Westwing Saguaro Fourcorn Fourcorn Springr Open end
Voltage
Status
(kV)
Max.
Real
500 500 500 345 500 500 345 500 500 345 500 500 345 345 500
1.099 1.099 1.099 1.060 1.099 1.099 1.060 1.099 1.099 1.060 1.099 1.099 1.060 1.060 1.150
1.073 1.080 1.098 1.046 1.073 1.069 1.050 1.081 1.072 1.046 1.045 1.069 1.027 1.046 1.111
Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
TABLE 2 c o n t r o l d e v i c e to s o l v e t h e a b o v e p r o b l e m . I t is p o s s i b l e to a c h i e v e t h e g o a l s t a t e b y r e d u c i n g t h e g e n e r a t o r v o l t a g e a t C o r o n a d o by 0.01 p.u. T h e r e s u l t is s h o w n i n T a b l e 3. T h e c o m p u t e r r e s p o n s e t i m e f o r t h i s c a s e is 0.38 m i n u t e w h i c h i n c l u d e d t h e t i m e o f e v a l u a t i n g p o w e r flow, s e l e c t i n g o p e r a t i o n , e d i t i n g t h e p o w e r flow d a t a , c a l c u l a t i n g p o w e r flows, and displaying the results. F o r most of our test cases, a goal state could be r e a c h e d i n o n e o r t w o s t e p s ( o p e r a t i o n s ) .
Cholla 500-Coronado 500 line major bus voltage results with the shunt reactor at Coronado 500 out of service: open end at the Cholla 500 kV bus Bus name
Kyrene Silverkg Coronado Coronado Palovrde Cholla Cholla Navajo Westwing Westwing Saguaro Fourcorn Fourcorn Springr Open end
Voltage
Status
(kV)
Max.
Real
500 500 500 345 500 500 345 500 500 345 500 500 345 345 500
1.099 1.099 1.099 1.060 1.099 1.099 1.060 1.099 1.099 1.060 1.099 1.099 1.060 1.060 1.150
1.074 1.081 1.103 1.049 1.073 1.069 1.050 1.081 1.072 1.046 1.046 1.069 1.027 1.048 1.116
Yes Yes High Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
It c a n be s e e n t h a t t h e r e is a v o l t a g e v i o l a t i o n a t t h e C h o l l a 345 k V bus. T h e o p e r a t i o n s e l e c t e d by t h e e x p e r t s y s t e m t o m o d i f y t h i s s t a t e is t o e n e r g i z e t h e l i n e f r o m t h e o t h e r end. Table 2 shows the v o l t a g e s in this new state. This time, a v o l t a g e v i o l a t i o n at the Coron a d o 500 k V b u s o c c u r s . T h i s t i m e t h e e x p e r t s y s t e m s e l e c t e d a C o r o n a d o g e n e r a t o r as a
7. CONCLUSIONS In this paper, we p r e s e n t a k n o w l e d g e based model for p o w e r system steady-state studies. This model has the following features. T h e k n o w l e d g e is r e p r e s e n t e d by p r e d i c a t e s and frame based s t r u c t u r e s . This kind of k n o w l e d g e r e p r e s e n t a t i o n allows the model to h a n d l e a l a r g e a m o u n t o f d a t a p r o d u c e d by p o w e r flow c a l c u l a t i o n s e f f i c i e n t l y . P o w e r s y s t e m o p e r a t i o n s a r e r e p r e s e n t e d by frame based d a t a s t r u c t u r e s . This type of d a t a structure provide a complete description about the conditions and effects of the operations. A s p e c i a l - p u r p o s e i n f e r e n c e a l g o r i t h m is dev e l o p e d to h a n d l e b o t h s y m b o l i c a n d n u m e r i cal processes. -
-
239
A practical power system is used to test the performance of the model and the results show a high efficiency.
ACKNOWLEDGEMENTS
We would like to express our gratitude to the Salt River Project (SRP), to James Tang and James Hsu of the Department of Power System Analysis and Joe Giles of the Department of Computer Applications of the SRP, and to Greg Lewis of Arizona State University for their valuable discussions which were very helpful for the formulation of the model. The work reported in this paper has been sponsored by the SRP.
REFERENCES 1 C. C. Liu and K. Tomsovic, An expert system assisting decision making of reactive power/voltage control, IEEE Trans., PWRS-1 (1986) 195-201.
2 S. J. Cheng, O. P. Malik and G. S. Hope, An expert system for voltage and reactive power control of a power system, IEEE Trans., PWRS-3 (1988) 1449- 1455. 3 W. R. Wagner, A. Keyhani, S. Hao and T. C. Wong, A rule based approach to decentralized voltage control, IEEE Trans., PWRS-5 (1990). 4 Z. Z. Zhang, G. S. Hope and O. P. Malik, Expert systems in electrical power systems - a bibliographical survey, IEEE Trans., PWRS-4 (1989) 1355 - 1362. 5 A. Thayse, From Standard Logic to Logic Programming, Wiley, New York, 1988. 6 W. Bibel and A. W. Biermann, Fundamentals of Artificial Intelligence: An Advanced Course, Springer, New York, 1986. 7 J. Allen, Natural Language Understanding, Benjamin/ Cummings, Menlo Park, CA, 1987. 8 T. M. Peng, G. G. Karady and J. C. Hsu, An expert system for voltage control integrated with existing solftware environment, Proc. 2nd Symp. Expert Sys-
tems, Application to Power Systems (ESAPS), Seattle, U.S.A., 1989, University of Washington, pp. 444- 450. 9 T. M. Peng, G. G. Karady and J. C. Hsu, A natural language representation of knowledge base integrated with power flow program, Proc. IOth Power Systems Computation Conf., Graz, Austria, 1990, Butterworth, London, pp. 972 - 978. 10 Western Systems Coordinating Council, Interactive
Power Flow Systems User's Reference Manual, Version 4.0.11, Salt Lake City, UT.
231
A K n o w l e d g e B a s e d Model for t h e S t u d y of P o w e r S y s t e m Steady-State Operation T. M. P E N G , G. G. K A R A D Y a n d D. K. R A N A W E E R A
Department of Electrical Engineering, Arizona State University, Tempe, A Z 85287 (U.S.A.) ( R e c e i v e d F e b r u a r y 21, 1991)
ABSTRACT
This paper presents a knowledge based model for power system steady-state studies. In this model, a power system is represented by three components: power system states, power system operations, and the knowledge base which contains the knowledge about the use of the operations. In the proposed model, the knowledge representation and inference are different from the existing approaches in this area in three aspects. First, the knowledge about power system states and operations is represented by two sets of predicates and frame based structures. This allows efficient data exchange between the model and power flow software. Second, in this model, power system operations are represented by the data structures which are similar to bus and branch data structures used in a power flow program. Third, a special-purpose inference algorithm is developed to manipulate the process of analysis, calculation, and modification of power flow studies. This model is implemented on the I B M 4381 computer and shows high efficiency when used to study a practical power system problem.
Keywords: artificial intelligence, inference, knowledge representation, power system steady state, power flow. 1. I N T R O D U C T I O N
In power system steady-state studies, it is very imp o r tan t to investigate how to use operations to control bus voltage and load flows under normal and contingency conditions. Traditionally, engineers would calculate power flows, analyze the computed results and suggest remedial actions whenever necessary. 0378-7796/91/$3.50
A vast amount of experience and time is needed to perform these tasks. In recent years, expert system approaches have been proposed to integrate numerical calculation and logic reasoning in this field [1-4]. The efficiencies of these expert systems depend on the organization and representation of their knowledge bases. In ref. 1, an expert system method was proposed to assist in the decisionmaking of voltage/VAR control problems; empirical rules were used to generate control actions to alleviate the slight voltage violation problems. In ref. 2, an expert system was proposed for the same problem; sensitivity trees were used to represent the relationship between voltage control devices and the system buses. A rule based approach for decentralized voltage control was presented in ref. 3. In these existing approaches, the knowledge is represented as a group of production rules which are coded in such languages as Prolog, Lisp, OPS5, etc. This type of knowledge representation provides a convenient way to construct, manage, and modify the knowledge base. However, when integrated with power flow software, it has limited ability to control the executions of the power flow calculations and to handle a large amount of data exchanged between the numerical software and the expert system. In this paper, a new knowledge based model is presented. The knowledge representation in the model consists of two parts: (1) a power system steady-state and operation representation, which is comprised of a set of predicates (logic forms) and frame based structures; (2) a special-purpose inference algorithm. The implementation of the model into a real power system computer environment shows t hat it can achieve a highly ~'~ Elsevier S e q u o i a / P r i n t e d in T h e N e t h e r l a n d s
232
efficient p e r f o r m a n c e in p o w e r s y s t e m problems.
solving
practical
the bus states and b r a n c h states, respectively. X is a direct sum of all the bus states, g i v e n by X = Ix~ ® x ~ ® " "
2, M O D E L D E S C R I P T I O N
In the p r o p o s e d model, a p o w e r s y s t e m is described by t h r e e c o m p o n e n t s : s y s t e m states, s y s t e m o p e r a t i o n s , a n d k n o w l e d g e base.
a n d Y is the direct s u m of all the b r a n c h states, g i v e n by Y = {Yl ®Y2®" " ' ®Ym S is the direct sum of X a n d Y, given by S -- {s(x~, x2 . . . . .
2.1. L o g i c a l n o t a t i o n
®x,,
xn ; y~, y2 . . . . .
Ym)} = X O Y
T h e following logical n o t a t i o n [5] is used t h r o u g h o u t this paper: A AND (conjunction) V u n i v e r s a l q u a n t i f i e r (for all) e x i s t e n t i a l q u a n t i f i e r (for some)
w h e r e n is the n u m b e r of buses in the p o w e r system, m is the n u m b e r of b r a n c h e s in the system, and x~ ( i = 1 , 2 . . . . . n) a n d yj ( j = 1, 2 . . . . . m) s t a n d for the i t h bus s t a t e a n d the j t h b r a n c h state, respectively.
2.2. S y s t e m s t a t e s
2.3. S y s t e m o p e r a t i o n s
Let S be the set of s y s t e m states. E a c h system s t a t e in S c o r r e s p o n d s to a specified p o w e r flow case, w h i c h is defined by its netw o r k description, t h a t is, bus a n d b r a n c h data, a n d the p o w e r flow solution. A c e r t a i n e l e m e n t so e S is the i n i t i a l s t a t e a n d a c e r t a i n subset G ~ S is the set of g o a l states. T h e r e is a set of system o p e r a t i o n c o n s t r a i n t s , s u c h as m a x i m u m a n d m i n i m u m bus v o l t a g e s , a n d m a x i m u m b r a n c h load flows. The goal s t a t e is a s t a t e w h i c h satisfies all of these c o n s t r a i n t s . A p o w e r s y s t e m s t a t e c a n be described by the c o n f i g u r a t i o n a n d s t a t e s of the b u s e s a n d b r a n c h e s in the system. Let x~ s t a n d for the s t a t e of the i t h bus. It is defined by a set of p a r a m e t e r s , such as bus name, load, generation conditions, bus v o l t a g e a n d v o l t a g e p h a s e angle. This c a n be e x p r e s s e d as
Besides the state, the model h a s a second c o m p o n e n t O called o p e r a t i o n s . E a c h operation describes the r e l a t i o n s h i p b e t w e e n its p r e v i o u s s t a t e a n d the s u b s e q u e n t state. In a r e a l p o w e r system, an o p e r a t i o n , s u c h as opening a s h u n t r e a c t o r or c h a n g i n g a t r a n s f o r m e r t a p position, modifies the s y s t e m state. In this model, e a c h o p e r a t i o n is described by two parts. One is the c o n d i t i o n of the o p e r a t i o n a n d the o t h e r is the effect of the o p e r a t i o n . F r o m a m a t h e m a t i c a l viewpoint, an operation is a f u n c t i o n t h a t t r a n s f e r s the p o w e r s y s t e m f r o m an old s t a t e to a new state. Let o s t a n d for an o p e r a t i o n , t h e n if
X i ~- Cil
t h e n an o p e r a t i o n , o: S ~ S, is defined as
A
Ci2
A
" " " A
Cik
w h e r e k is the n u m b e r of p a r a m e t e r s used to describe the s t a t e of the bus, a n d c~j is the j t h ( j = 1, 2 . . . . . k) p a r a m e t e r of the i t h bus. In the s a m e way, we c a n define a b r a n c h s t a t e by a set of p a r a m e t e r s s u c h as resistance, r e a c t a n c e , a n d MW, M V A R load flow in the b r a n c h . Let y~ s t a n d for the s t a t e of the ith b r a n c h . It c a n be e x p r e s s e d as follows: Yi
=
rail
A
mi2
A
• • • A
mis
w h e r e s is the n u m b e r of p a r a m e t e r s used to describe the s t a t e of the b r a n c h , a n d m~j is the j t h ( j = 1 , 2 . . . . . s) p a r a m e t e r in the i t h branch. L e t S s t a n d for the s p a c e of p o w e r s y s t e m s t a t e s a n d let X a n d Y s t a n d for the spaces of
{Xl' X2 . . . .
' Xrt }' [21' X2 . . . . .
Xn
e X
and ~Y, , Y2 . . . . .
o(sl (x~ . . . . .
Y., }, [:Yl , Y2 . . . . .
xn ; Yl . . . . .
= s2(2~ . . . . .
:Y.n e Y
Y,,))
2,, ; ~ . . . . .
:~m)
w h e r e s~, s 2 e S. F o r e a c h g i v e n initial state, typically, t h e r e is a set of o p e r a t i o n s . It is defined as an o p e r a t i o n sequence, w h i c h m o v e s the s y s t e m f r o m the initial s t a t e to the goal state. T h e o p e r a t i o n s e q u e n c e c a n be e x p r e s s e d as follows. L e t :~ a n d ~" be the sets of bus s t a t e s a n d b r a n c h s t a t e s w i t h o u t a n y v i o l a t i o n s of operation c o n s t r a i n t s . A set of p o w e r s y s t e m goal s t a t e s S ~ S is defined as =
233
where 121 . . . . . 2n} c : ~ and {3~1. . . . . 3~m} ~ Y An operation sequence is defined as O = { o l , o2 . . . . .
ok }: O ( s ~ ) = S k + l e
where s~ = initial system state ol ( s , ) = s2 o2 0 2 )
= s3
ok (sk) = sk ~
c
2.4. Knowledge base In power system steady-state studies, one starts from an initial state. If the state is not a goal state, then an operation sequence must be found to move the initial state to the goal state. In this process, one must know how to use the operations to modify the system state. In our model, this knowledge is presented in the knowledge base as a set of rules. The information used in this 'knowledge base' was obtained from textbooks as well as from utility engineers. We define the rules with the relationship between an operation and its purpose. For example, if the voltage at bus A is high, then decrease the generator voltage at bus B by -0.01 p.u. 2.5. Inference algorithm To move a system from its initial state to a goal state, it is necessary to perform the following tasks: (1) evaluate the power flow solution of a system state; (2) select an operation to modify a system state if necessary; (3) run the power flow program. In our model, these tasks are performed by the inference algorithm. A detailed description of the algorithm will be given in §5 of this paper.
3. S Y S T E M S T A T E R E P R E S E N T A T I O N
In this model, the power system states are represented by two sets of binary or t er t iary predicates which describe facts about buses and branches. Binary and t er t i a r y predicates are logic forms having two and three arguments, respectively. As in a power flow program, system configurations and states are specified by two types of data: bus data and
branch data, which are described by predicates in our model.
3.1. Bus state representation A bus state can be described by a set of parameters. For example, the name of the bus is A, the load at the bus is 50MW and 12.5 MVAR; the voltage in the bus is 1.103 p.u.; the voltage phase angle is 23.33 °. These facts can be expressed by a set of predicates such as BusNamekV(A, 500), LoadMW(A, 50), LoadMVAR(A, 12.5), Voltage(A, 1.103), and VoltagePhase(A, 23.33~'). (More details about predicate and predicate logic are given in refs. 5 and 6.) A complete set of the predicates is given in the following three groups. (1) The predicates driven from the input data of a power flow case are: BusID(A, BQ) ChangeCode(A, none) BusNamekV(A, 500) LoadMW(A, 50) LoadMVAR(A, 12.5) ShuntMVAR(A, 75) ShuntMVARMax(A, 100) GenerationMW(A, 0.0) GenerationMVAR(A, 0.0) GenerationMWMax(A, *) VoltageHold(A, *) VoltageMax(A, 1.05) (2) The predicates which are driven from the computed power flow results are: Voltage(A, 1.103) VoltagePhase(A, 23.33 ~') (3) The predicates status of the bus are:
which
describe
the
VoltageStatus(A, status) ShuntStatus(A, status) GenerationMWStatus(A, status) GenerationMVARStatus(A, status) For example, the predicates VoltageStatus(A, high) and ShuntStatus(A, available) are generated by the following logic reasoning: Voltage(A, value 1) A VoltageMax(A, value 2) A value_ 1 > value_ 2 ~ V o l t a g e S t a t u s ( A , high) ShuntMVAR(A, val ue_ 1) A ShuntMVARMax(A, value_ 2) /~ value 1 < value_ 2 ~ S h u n t S t a t u s ( A , available)
234
3.2. Branch state representation T h e b r a n c h s t a t e c a n be r e p r e s e n t e d in a s i m i l a r way. Let ( A - B) s t a n d for the n a m e of a b r a n c h w h i c h c o n n e c t s bus A to bus B. T h e s t a t e of the b r a n c h c a n be described by the following t h r e e g r o u p s of p r e d i c a t e s . (1) T h e p r e d i c a t e s d r i v e n from the i n p u t d a t a of a p o w e r flow case are: B r a n c h I D ( A - B, T/L) S w i t c h S t a t u s ( A - B, A, ON) S w i t c h S t a t u s ( A - B, B, ON) R e s i s t a n c e ( A - B, *) R e a c t a n c e ( A - B, *) a / 2 ( n - B, *) B / 2 ( A - B, *) B r a n c h L o a d M a x ( A - B, *) T a p P o s i t i o n ( A - B, *) w h e r e T s t a n d s for t r a n s f o r m e r , L for line, * for a p a r a m e t e r value, O N / O F F for the s w i t c h status. (2) T h e p r e d i c a t e s driven from the comp u t e d p o w e r flow r e s u l t are: B r a n c h L o a d M W ( A - B, *) B r a n c h L o a d M V A R ( A - B, *) (3) T h e b r a n c h s t a t u s is described by the B r a n c h L o a d S t a t u s ( A - B, n o r m a l / o v e r l o a d ) p r e d i c a t e , w h i c h is d r i v e n by the following logic reasoning: B r a n c h L o a d M W ( A - B, v a l u e _ 1) A B r a n c h L o a d M V A R ( A - B, v a l u e _ 2) A B r a n c h L o a d M a x ( A - B, v a l u e _ 3) /x S q r t ( ( v a l u e 1) * 2 + ( v a l u e _ 2) * 2) > v a l u e _ 3 ~ B r a n c h L o a d S t a t u s ( A - B, o v e r l o a d )
3.3. Features of the representation The r e p r e s e n t a t i o n of the p o w e r s y s t e m s t a t e s used in this model h a s the following features. - The s a m e d a t a b a s e is used by the knowledge b a s e d model a n d the p o w e r flow p r o g r a m . As a m a t t e r of fact, w h e n the p o w e r s y s t e m d a t a are used by the k n o w l e d g e b a s e d model, t h e y are p r o c e s s e d in the f o r m of p r e d i c a t e s ; w h e n t h e y are used by the p o w e r flow program, t h e y are p r o c e s s e d in the f o r m of d a t a records or d a t a cards. - The k n o w l e d g e b a s e d model p r o v i d e s a m o r e c o m p r e h e n s i v e d e s c r i p t i o n of the p o w e r s y s t e m b e c a u s e not only are the p o w e r s y s t e m i n p u t d a t a a n d c o m p u t e d p o w e r flow r e s u l t s used, but also i n f o r m a t i o n d r i v e n by logic r e a s o n i n g .
These p r e d i c a t e s can be g r o u p e d in a n y order. As an example, they c a n be sorted acc o r d i n g to e i t h e r a c e r t a i n keyword, such as bus name, or p r e d i c a t e type, such as S h u n t M W . This p e r m i t s a m o r e flexible w a y to process s y t e m data. In a p o w e r flow p r o g r a m , the d a t a h a v e to be o r g a n i z e d by bus or b r a n c h name.
4. SYSTEM OPERATION REPRESENTATION
4.1. Types of operation T h e c h a n g e s in a p o w e r system s t a t e m a y be c a u s e d by (1) c h a n g i n g p a r a m e t e r v a l u e s at a bus, s u c h as load or g e n e r a t i o n ; (2) changing p a r a m e t e r v a l u e s in a b r a n c h , s u c h as a t r a n s f o r m e r t a p p o s i t i o n or series c o m p e n s a tion; (3) s w i t c h i n g on/off a line or a transformer. T h e s e t h r e e types of o p e r a t i o n c a n be e x p r e s s e d as the following t e r t i a r y predicates: Cha nge BusPa r a me te r ( bus name, parameter, value) C h a n g e B r a n c h P a r a m e t e r ( b r a n c h name, p a r a m e t e r , value) ChangeON/OFF(branch, switchl ON/OFF, switch2 O N / O F F ) A n y p o w e r s y s t e m o p e r a t i o n can be represented by t h e s e p r e d i c a t e s . F o r i n s t a n c e , the o p e r a t i o n t h a t o p e n s the t r a n s m i s s i o n line f r o m K y r e n e 500 to S i l v e r k g 500 c a n be represented by C h a n g e O N / O F F ( K y r e n e 500-Silv e r k g 500, OFF, OFF). Here, the second a r g u m e n t in the p r e d i c a t e i n d i c a t e s t h a t the s w i t c h at bus 1 ( K y r e n e 500) s h o u l d be in the O F F p o s i t i o n a n d the t h i r d a r g u m e n t indicates the s a m e for the s w i t c h at bus 2 (Silv e r k g 500).
4.2. Conditions of operation T h e s u c c e s s f u l l y e x e c u t e d o p e r a t i o n requires the s a t i s f a c t i o n of p r e d e t e r m i n e d conditions, w h i c h are also d e s c r i b e d in the form of p r e d i c a t e s . T y p i c a l e x a m p l e s are the following. (1) T h e g e n e r a t i o n or VAR c o n t r o l equipm e n t o u t p u t c a n be c h a n g e d only if t h e y are in ' a v a i l a b l e ' status. To describe this, we have: ShuntStatus(bus, status) GenMWStatus(bus, status) G e n M V A R S t a t u s ( b u s , status)
235 Here, the status of generator, shunt or seties capacitors may be obtained by comparing their actual outputs with the maximum. (2) The change in a br a nc h switch ON/ OFF status requires t ha t the switch is in a proper position. For example, a line switch can be opened when it is in a closed status. To define this, we have SwitchStatus(branch, bus, ON/OFF status)
4.3. Script based operation representation The power system operations can be described by a set of script based structures which are driven by using the previously defined operations and operation conditions. Each of the script based structures consists of two parts which are the preconditions and effects of the operations. For example, ChangeON/OFF(A - B, OFF, OFF) Precondition: SwitchStatus(A - B, A, ON) SwitchStatus(A - B, B, ON) Effect: SwitchStatus(A - B, A, OFF) SwitchStatus(A - B, B, OFF) This script describes an operation t hat opens a branch from bus A to bus B. The 'precondition' part of this script says t h a t the branch switches at bus A and bus B are in the ON (closed) positions. The 'effect' part says t h at the operation changes the switch positions from ON to OFF. The energization of the above transmission line can be described as a two-step operation. First, ChangeON/OFF(A - B, ON, OFF) Precondition: SwitchStatus(A - B, A, OFF) SwitchStatus(A - B, B, OFF) Effect: SwitchStatus(A - B, A, ON) This step of the operation closes the switch of branch A - B at the A side. Then, ChangeON/OFF(A - B, ON, ON) Precondition: SwitchStatus(A - B, A, ON) SwitchStatus(A - B, B, OFF) Effect: SwitchStatus(A - B, B, ON)
This step of the operation closes the switch of branch A- B at the B side. The operation t hat changes the bus param et er values, for example, increasing the shunt reactive power at bus A from 75 MVAR to 100 MVAR, can be expressed as: ChangeBusParameter(A, Shunt VAR, 100) Precondition: ShuntStatus(A, available) Effect: ShuntMVAR(A, 100)
4.4. Integration of the operation with power flow These script based representations of the operations are integrated with a power flow program [5, 6]. This is performed by converting the predicates of the script based structure into a format t hat can be read and interpreted by the power flow program. In this project, we use the Interactive Power Flow System (IPS) of Western Systems Coordinating Council (WSCC) [10]. The effect of the operation has to be verified by the rerun of the power flow. For example, the predicate which increases the reactive power at Silverkg 500 to 100 MVAR requires the rewriting of ChangeBusParameter(Silverkg 500, shunt VAR, 100) in the following format: B
M
Silverkg500
100
where B stands for bus and M is a change code in IPS which means 'modify'. The predicate describing the operation t hat opens the transformer switches at Kyrene 500 and Kyrene 345 is ChangeON/OFF(Kyrene 500- Kyrene 345, OFF, OFF) which can be written in the format T
O
Kyrene 500
Kyrene 345
1
where T stands for transformer and O for 'open' in the IPS.
4.5. Modification of system states by operations An operation or operation sequence can be used to modify a system state to eliminate overvoltage, low voltage, and overload.
236 This can be described by the following rules: AdjustVoltage(A, increase/decrease) ~ C h a n g e B u s P a r a m e t e r ( B , shunt VAR, value) AdjustVoltage(A, increase/decrease) ~ C h a n g e B u s P a r a m e t e r ( B , gen VAR, value) AdjustVoltage(A, increase/decrease) ~ C h a n g e B r a n c h P a r a m e t e r ( B - Z, tap position, ratio)
5.1. Analysis of the given power system state This analysis finds the bus voltage or branch load flow violations in the system state. (1) The voltage violations are identified by the following inference rules: Vx.
Voltage(x, value 1) A VoltageMin(x, value_ 2) A value_ 1 < value_ 2 ~VoltageStatus(x, low)
Vx.
Voltage(x, v a l u e _ l ) A VoltageMax(x, value_ 2) A value_ 1 > value_ 2 ~VoltageStatus(x, high)"
AdjustLoadFlow(A - B, increase/decrease) ~ C h a n g e O N / O F F ( Z - W, ON/OFF, ON/OFF) In most cases the adjustment of a system state (voltage or load flow) requires several operations. This forms an operation sequence. For example, the voltage at b u s A may be decreased by: (1) changing the shunt reactive power at A to value 1; and (2) changing reactive power generation at bus B to value_2. This operation sequence can be described by: ChangeBusParameter(A, shunt VAR, value_ 1) ChangeBusParameter(B, gen VAR, value_ 2)
5. INFERENCE ALGORITHM An inference algorithm has been developed for the identification of voltage and load violations and the selection of the required operation sequences. Before a detailed description of the algorithm is given, a definition of a set of power system voltage and load flow violations is presented:
where x is a logic variable which can be matched with any bus name in the system. (2) The branches with overload can be found by the following inference rule: ¥y.
BranchLoadMW(y, v a l u e _ l ) A BranchLoadMVAR(y, value 2) A BranchLoadMax(y, value_ 3) A Sqrt(value_ 12 + value_ 22) > value_ 3 ~ B r a n c h L o a d S t a t u s ( y , overload)
where y is a logic variable which can be matched with any branch name in the system. (3) If the bus voltage status and branch load status are normal, then V = {0}. The given power system state is in the goal state• This terminates the procedure. The operation sequence set is also empty: O = {0}. (4) Otherwise, a set of the predicates which describe the voltage and the load flow violations is formed. It is defined as V = { v , , t
V 2 , . . . ~'.
V = {vl, v2 . . . . .
v~ }
where k is the number of violations t ha t occur in the system; each element in V is a predicate describing a violation, which has two forms: BusVoltageStatus(bus name, high/low) or B r a n c h L o a d S t a t u s ( b r a n c h name, overload) The task of the algorithm is to reach a goal state which has an empty set of the voltage and load flow violations. This goal state can be reached by finding and applying the proper operation sequence. The algorithm terminates when the goal state is obtained. This is indicated by V = {0}.
(5) For the adjustment of the vo]tage and load flow, a set of subtasks T = {tl, t2. . . . } is formed. Each element in T is a predicate having the form AdjustVo]tage(x, increase/decrease) AdjustLoadFlow(y, decrease) The predicates are driven from the inference rules be]ow: Vx. VoltageStatus(x, high) ~AdjustVoltage(x, decrease) Vx. Vo]tageStatus(x, low) ~AdjustVo]tage(x, increase) Vy. BranchLoadStatus(y, overload) ~AdjustLoadF]ow(y, decrease)
237
The p r e d i c a t e s in set T may be a r r a n g e d a c c o r d i n g to t h e i r priorities, which can be d e t e r m i n e d by sensitivity analyses.
5.2. Search for possible operations If the set of v i o l a t i o n s V is not empty, t h e n a set of o p e r a t i o n s has to be found to modify the system state. (1) Select the first e l e m e n t t in set T and find the o p e r a t i o n s t h a t perform the desired voltage or load flow adjustment. This operation set is defined as F = {f~, f2 . . . . }, in w h i c h each e l e m e n t stands for an operation. A set of i n f e r e n c e rules is developed to p e r f o r m this step. F o r example: Vx. AdjustVoltage(x, i n c r e a s e / d e c r e a s e ) r 3 s 3 t. C h a n g e B u s P a r a m e t e r ( r , s, t) Vx. AdjustVoltage(x, i n c r e a s e / d e c r e a s e ) ~ 3 r ~ s 3 t. C h a n g e B r a n c h P a r a m e t e r ( r , s, t) Vy. A d j u s t L o a d F l o w ( y , decrease) w. C h a n g e B r a n c h P a r a m e t e r ( w , ON/OFF, ON/OFF) (2) If o p e r a t i o n set F is given by
F={fi Ii =1,2,...} t h e n a set of feasible o p e r a t i o n s
0 1 = {0ili----1,2 . . . . } ~ F can be found by using the following i n f e r e n c e rule: Vf~ e F ( i = 1 , 2 . . . . ) and f/=ClAC2A''" if
ck(k=l,
AelAe2A''"
2. . . . ) e S .
Then
f/e01
Here, s is a given system state; ci (i = 1, 2 . . . . ) is a set of p r e d i c a t e s which describes the prec o n d i t i o n p a r t of fi ; ei (i -- 1, 2 . . . . ) is a set of p r e d i c a t e s which describes the effect p a r t of fiF o r a given system state and o p e r a t i o n , this rule says t h a t if all the p r e d i c a t e s in the p r e c o n d i t i o n p a r t of the o p e r a t i o n are satisfied by the system state, t h e n the o p e r a t i o n is a feasible o p e r a t i o n .
form the system into the goal state. The procedure is the following: (1) The elements in O1 are sorted according to t h e i r o p e r a t i o n priority. (2) The first e l e m e n t in Ol, which is the first o p e r a t i o n , is applied to the initial state. This g e n e r a t e s a new state. T h e power flow of the new state is calculated. (3) These new results are evaluated. If the v i o l a t i o n set V is not empty, it is n e c e s s a r y to go b a c k to the p r e v i o u s step to find the n e x t o p e r a t i o n which modifies the system state. Repeat the same p r o c e d u r e until V becomes an empty set.
6. IMPLEMENTATION AND TEST RESULTS
A r e d u c e d power system model of WSCC was used to test the p e r f o r m a n c e of the proposed system. The initial WSCC system contains more t h a n 2000 buses. This r e d u c e d model consists of 502 buses and a b o u t 1000 b r a n c h e s . The p r o g r a m s are w r i t t e n in Computation Oriented Program Environment (COPE) and i m p l e m e n t e d on the IBM 4381 c o m p u t e r of the Salt River Project. F i g u r e 1 shows p a r t of the above system. This gives an idea of the voltage/VAR c o n t r o l facilities available in the C h o l l a - C o r o n a d o area. For the d e m o n s t r a t i o n of the proposed model, the e n e r g i z a t i o n of the Cholla 500C o r o n a d o 500 line is selected as an example. It is assumed t h a t the s h u n t r e a c t o r at the Coronado 500 kV bus (93 MVAR) is out of service. The e x p e r t system is used to solve this problem and the results of the first r u n (state 1) are p r e s e n t e d in Table 1.
(
EI
5.3. Evaluation of the effect of the operation In this step, the effect of the o p e r a t i o n is e v a l u a t e d by i n v e s t i g a t i n g the power flow results of the new power system state. If no v i o l a t i o n is identified, these o p e r a t i o n s trans-
palo
oo oo.0o o0
vrde500
'=" Isil-'~erkg 500
Fig. 1. Voltage/VAR control facilities in the Cholla Coronado area.
238 TABLE 1
TABLE 3
Cholla 500-Coronado 500 line major bus voltage results with the shunt reactor at Coronado 500 out of service: open end at the Coronado 500 kV bus
Cholla 500 Coronado 500 line major bus voltage results with the shunt reactor at Coronado 500 out of service: open end at the Coronado 500 kV bus; generator voltage at Coronado reduced by 0.01
Bus name
Voltage
Status Bus name
Kyrene Silverkg Coronado Coronado Palovrde Cholla Cholla Navajo Westwing Westwing Saguaro Fourcorn Fourcorn Springr Open end
(kV)
Max.
Real
500 500 500 345 500 500 345 500 500 345 500 500 345 345 500
1.099 1.099 1.099 1.060 1.099 1.099 1.060 1.099 1.099 1.060 1.099 1.099 1.060 1.060 1.150
1.073 1.077 1.085 1.036 1.073 1.087 1.062 1.081 1.072 1.046 1.057 1.069 1.028 1.041 1.100
Yes Yes Yes Yes Yes Yes High Yes Yes Yes Yes Yes Yes Yes Yes
Kyrene Silverkg Coronado Coronado Palovrde Cholla Cholla Navajo Westwing Westwing Saguaro Fourcorn Fourcorn Springr Open end
Voltage
Status
(kV)
Max.
Real
500 500 500 345 500 500 345 500 500 345 500 500 345 345 500
1.099 1.099 1.099 1.060 1.099 1.099 1.060 1.099 1.099 1.060 1.099 1.099 1.060 1.060 1.150
1.073 1.080 1.098 1.046 1.073 1.069 1.050 1.081 1.072 1.046 1.045 1.069 1.027 1.046 1.111
Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
TABLE 2 c o n t r o l d e v i c e to s o l v e t h e a b o v e p r o b l e m . I t is p o s s i b l e to a c h i e v e t h e g o a l s t a t e b y r e d u c i n g t h e g e n e r a t o r v o l t a g e a t C o r o n a d o by 0.01 p.u. T h e r e s u l t is s h o w n i n T a b l e 3. T h e c o m p u t e r r e s p o n s e t i m e f o r t h i s c a s e is 0.38 m i n u t e w h i c h i n c l u d e d t h e t i m e o f e v a l u a t i n g p o w e r flow, s e l e c t i n g o p e r a t i o n , e d i t i n g t h e p o w e r flow d a t a , c a l c u l a t i n g p o w e r flows, and displaying the results. F o r most of our test cases, a goal state could be r e a c h e d i n o n e o r t w o s t e p s ( o p e r a t i o n s ) .
Cholla 500-Coronado 500 line major bus voltage results with the shunt reactor at Coronado 500 out of service: open end at the Cholla 500 kV bus Bus name
Kyrene Silverkg Coronado Coronado Palovrde Cholla Cholla Navajo Westwing Westwing Saguaro Fourcorn Fourcorn Springr Open end
Voltage
Status
(kV)
Max.
Real
500 500 500 345 500 500 345 500 500 345 500 500 345 345 500
1.099 1.099 1.099 1.060 1.099 1.099 1.060 1.099 1.099 1.060 1.099 1.099 1.060 1.060 1.150
1.074 1.081 1.103 1.049 1.073 1.069 1.050 1.081 1.072 1.046 1.046 1.069 1.027 1.048 1.116
Yes Yes High Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
It c a n be s e e n t h a t t h e r e is a v o l t a g e v i o l a t i o n a t t h e C h o l l a 345 k V bus. T h e o p e r a t i o n s e l e c t e d by t h e e x p e r t s y s t e m t o m o d i f y t h i s s t a t e is t o e n e r g i z e t h e l i n e f r o m t h e o t h e r end. Table 2 shows the v o l t a g e s in this new state. This time, a v o l t a g e v i o l a t i o n at the Coron a d o 500 k V b u s o c c u r s . T h i s t i m e t h e e x p e r t s y s t e m s e l e c t e d a C o r o n a d o g e n e r a t o r as a
7. CONCLUSIONS In this paper, we p r e s e n t a k n o w l e d g e based model for p o w e r system steady-state studies. This model has the following features. T h e k n o w l e d g e is r e p r e s e n t e d by p r e d i c a t e s and frame based s t r u c t u r e s . This kind of k n o w l e d g e r e p r e s e n t a t i o n allows the model to h a n d l e a l a r g e a m o u n t o f d a t a p r o d u c e d by p o w e r flow c a l c u l a t i o n s e f f i c i e n t l y . P o w e r s y s t e m o p e r a t i o n s a r e r e p r e s e n t e d by frame based d a t a s t r u c t u r e s . This type of d a t a structure provide a complete description about the conditions and effects of the operations. A s p e c i a l - p u r p o s e i n f e r e n c e a l g o r i t h m is dev e l o p e d to h a n d l e b o t h s y m b o l i c a n d n u m e r i cal processes. -
-
239
A practical power system is used to test the performance of the model and the results show a high efficiency.
ACKNOWLEDGEMENTS
We would like to express our gratitude to the Salt River Project (SRP), to James Tang and James Hsu of the Department of Power System Analysis and Joe Giles of the Department of Computer Applications of the SRP, and to Greg Lewis of Arizona State University for their valuable discussions which were very helpful for the formulation of the model. The work reported in this paper has been sponsored by the SRP.
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tems, Application to Power Systems (ESAPS), Seattle, U.S.A., 1989, University of Washington, pp. 444- 450. 9 T. M. Peng, G. G. Karady and J. C. Hsu, A natural language representation of knowledge base integrated with power flow program, Proc. IOth Power Systems Computation Conf., Graz, Austria, 1990, Butterworth, London, pp. 972 - 978. 10 Western Systems Coordinating Council, Interactive
Power Flow Systems User's Reference Manual, Version 4.0.11, Salt Lake City, UT.