an expert system for switching operations for blackout restoration—line, bus-bar and feeder...

Pergamon S0952-1976(95)00010-3

Engng Applic. Artif. lntell. Vol. 9, No. 2, pp. 195-203, 1996 Copyright ~ 1996 Elsevier Science Ltd

Printed in Great Britain. All rights reserved 0952-1976196 $15.00 + 0.00

Contributed Paper

An Expert System for Switching Operations for Blackout RestorationmLine, Bus-Bar and Feeder Switching

KWANG-HO LEE Dankook University, Korea

YOUNG-MOON PARK Seoul National University, Korea

(Received May 1995; in revised form January 1996)

An expert system has been developed for switching operations of network restoration of power systems. The proposed method restores the blackout area in a power system by using sensitivity analysis and heuristic rules. The rules are categorized into flow-control rules, energization rules, line and bus-bar switching rules, and load-shedding rules. The switching (opening~closing) operations of transmission lines, transformers, substation feeders and bus-bars are used for the network restoration described in this paper. A new model for bus-bar switching in a substation is also proposed. The representation o f the power-system equipment has hierarchical data structures for the real-time recognition o f a network topology. Copyright © 1996 Elsevier Science Ltd

Keywords: Expert system, blackout restoration, bus-bar switching, switching sensitivity.

1. INTRODUCTION

Major system failures are rarely the result of a single catastrophic disturbance causing the collapse of an apparently secure system. Such failures are usually brought about by a combination of circumstances that strain the network beyond its capability. Natural distur- bances, equipment malfunctions, human error, and inadequate design combine to weaken a power system and eventually lead to its breakdown. As a counter- measure for such outages, a fast and reliable restoration algorithm is required.

Studies on blackout restoration started in the early 1980s. The restorative state is classified into two cate- gories: the state of complete collapse; and the state of partial outage. 1'2 The restoration for a complete collapse deals with a number of complicated and difficult problems such as: appropriate sectionalization of the blackout area, energizing transmission lines, and considering the dynamic characteristics and restart conditions of generators, etc. The network restoration of partial outages, however, usually deals with the reconfiguration of the networks from the restorative state to the normal state. In practice, blackout areas are res-

Correspondence should be sent to: Kwang-Ho Lee, Department of Electrical Engineering, Dankook University, 140-714 Seoul, Korea.

tored by power system operators using off-line data and their previous experience. 3 Some papers 4'5 classify the power balance into three, viz. power surplus or deficit, or blackout of the isolated area. The line power flow in these papers is checked by load flow calculation. However, since the load flow calculation requires excessive time, these methods do not seem appropriate for emergency operations.

This paper proposes a method to restore the blackout areas of a partial outage, at the same time preventing line overloads by network switching and load shedding. Load shedding has been one of the topics of recent interest. 6 In this paper, since the load denotes the feeder power in a substation, load shedding decreases the load power discretely by opening the feeder switches o-mected to the low-voltage buses in substations. For the estimation of line overloads and for the determination of the lines, feeders and bus-bars to be switched, switching sensitivities are used for calcu- lating the line power flows. Such approximate calculation contributes to speedy restoration planning, and leads to efficient performance, as compared to the approaches with no line-power calculation, but only heuristics.

This paper proposes a new modeling method for bus- bar switching in a substation. A bus-bar breaker which operates bus separation is substituted by a "virtual

195

196 KWANG-HO LEE and YOUNG-MOON PARK: BLACKOUT RESTORATION

line", having a small reactance. The operation of bus separation is equivalent to virtual switching; therefore, bus-bar switching and transmission line switching can be considered at the same time.

The research on power-system restoration was activated by applications of expert systems in the mid- 1980s. A number of papers 4'7 using expert systems for restoration problems, based on the heuristics of operators and the patterns of restorative operations, were presented. However, since the possible heuristics and patterns are pre-defined, they are not always appropriate in all cases. Also, the effective selection of switching depends on the state of the power system. The proposed scheme has an expert-system structure which is suitable for programming the operational knowledge to handle the difficulties of an analytical approach and the requirements of operators' heuristics. In this system, the numerical data of switching sensitivities are incorporated with the inference and the restoration knowledge in the power system.

A prototype was developed to verify the effective- ness of this approach. It has been confirmed that this can give operators appropriate restoration plans, including bus-separation operations. The local control center in the metropolitan area of Korea is applied as a case study.

2. RESTORATION PROBLEM

2.1. Problem formulation

The operating conditions of a power system can be described mathematically in terms of two sets of equations: 8 the power balance (or equality) constraints, and the operating (or inequality) constraints. The power balance constraints impose the requirement that the customer load demand be met at all times, while the operating constraints reflect the fact that the system variables (e.g. power flow) must always be kept within capabilities representing the physical limitations of the power-system equipment. Power-system operation can be described as being in one of three operating states: normal, emergency, or restorative. The restoration comprises the operations that make the transition from the restorative state to the normal state of the power system. The restoration problem is a very complex process, which typically involves all of the components of the power system, including generation, transmission and distribution. However this paper is concerned only with the restoration of a local transmission system, primarily conducted in a sub-control center. Therefore the issues in a bulk power transmission, such as Ferranti rise and resonance, are not considered in this paper. As stated, the restoration control problem can be formulated in general terms as follows: minF(x, us, ud), s.t. h(x, us,ua)<O, us, ud<U, where F represents the objective function, h denotes the inequality (operating) constraints, x denotes the system

variables (such as voltage magnitude, voltage angle, generation and load power), us denotes the discrete control variables of the switching of lines, transformers, and bus-bars, uo denotes the discrete control variables of the feeder switching at a substation which means the load shedding, and U is the feasible switching operations.

The objective function (i.e. F) is a multi-objective function, composed of at least the following two separate objectives: (i) to minimize the unserved load power including the load shedding; and (ii) to minimize the number of switchings of transmission lines for speedy restoration.

The hierarchical knowledge-base is constructed of cells and subsystems for speedy restoration. The cells and subsystems can describe the power systems fully, and can provide the expert systems with a data structure which ensures the efficient search. The strategy of determining the switching, us, and Ud, depends on their switching sensitivity data, as formulated in this paper.

2.2. Switching sensitivity

The prediction of the power flow is required for the reconfigured network after the energization process, which means the blackout restoration. The restoration plan must include overload alleviation, if any line is predicted to be overloaded. In the course of the planning the changed network by line switching and load shedding, a prediction of the power flow is also required. The sensitivities of line switching and load shedding indicate the changes of the line power flows.

The power balance equation of complex form in the ith bus is as follows:

Sg~ - Sd,- f~(y, v, 0) = 0, (1)

where f,, Sgi, Sdi are respectively the injection, generation and load power at the ith bus, y is the admittance vector of the transmission lines and the virtual lines representing bus-bars, and v and 0 are the vectors of bus voltage magnitude and angle respectively.

Line switching and load shedding at the ith bus are assumed:

Sg,- Sd,- ASd,-f,(y + Ay, v + Av, 0 + A0) = 0. (2)

Equation (2) is approximated as follows:

Sgi- Sd,--f(y, v, 0) -- ASa,- A~(Ay, Av, A0) = 0, (3)

where ASdi is the load power to be shed:

Af,(Ay, Av, A0) ~ (0ffl0y)'Ay + (0f//0v)tAv

+ (Ofi/OO)'AO + Ay'(02fJ0y0v)Av

+ Ay'(Ozfi/OyOO)AO. (4)

In equation (4) of the second-order Taylor expansion, the terms A0-A0, Av-Av and Av-A0 are ignored, and the term Ay-Ay is zero because of the linear relation

KWANG-HO LEE and YOUNG-MOON PARK: BLACKOUT RESTORATION 197

- • Virtual - - Line (X)

00000

]Virtual

0 0 0 0 7 Bus Virtual Line (-X)

(a)

b Bus-Bar Breaker ~ 1

I Load

(b)

Fig. 1. Diagram of bus-bar breaker modeling.

b (c)

Virtual Line (X)

between the bus power equation and the line admittance. From (1), (3) and (4):

AS~ + (0ffl0y)'Ay + (0ffl0v)'Av + (OfflOO)tAO

+ Ay'(02~/Oy0v)Av + Ay'(O2fi/OyOO)AO = 0. (5)

The terms of the real power in (5) is expanded to all the buses using the decoupling features of the Jacobian in the power equations. This gives the following equation:

APd + Re{f~Ay} + [H + z lA0 = o, (6)

where H is the Jacobian of Of/O0, and AH corresponds to ay'(Ozf/OyOO).

The value of the element in the vector Ay is +y when connecting, and - y on opening, so the term can be substituted by diag(y)Aus, where Aus takes one of the values, - 1 , 0, + 1. Similarly, the load-shedding term, APd is separated out as DAud. The values in matrix D are the feeder load powers, where the row index corresponds to the buses, and the column index corresponds to all the feeders of all the buses. The value of an element in the vector AUd takes one of values, - 1 , 0.

The equation, arranged with regard to A0 from (6), is as follows:

A0 = A'Aud + B'Aus , (7)

where

A ' = - [H+ AHI-1D,

B ' = - [H+ AH1-1 Re{fly diag(y)}.

The power flow of the line between the ruth and nth buses is:

Pm,, = - V2mRe{ymn } + v,,,v,,(Re{ym,,} cos 0m.

+ Im{Ym~ } sin Ore,,). (8)

The variation of equation (8) is:

AP,~n = v,~v~( - Re{ymn } sin 0,,~ + Im{y,,, } cos Omn )A0,,~. (9)

The equation of power sensitivity is derived as follows by expanding (9) to all the lines, and by combining (7):

APi =AAud + BAus, (10)

where

A = - HI[H + A l l ] - 1D,

B = - HI[H + AH] -~ Re{fy diag(y)}.

The matrix H~ indicates the Jacobian value between both buses of each line. In the matrix B, the row index corresponds to the lines to be checked for overloads, and the column index corresponds to the lines to be switched. In the matrix A, the row index corresponds to the lines to be checked, and the column index corresponds to the buses where the load shedding is considered.

2.3. Bus-bar switch modeling

The switching algorithm can be extended to the case where a bus-bar breaker operation separates a bus. Reference 9 proposed a modeling technique in which each bus-bar breaker which is to be a candidate for corrective switching is represented as a zero-impedance circuit made up of two circuits in series, having equal but opposite reactance. The resulting network has only an additional node and two additional links for each such breaker, as shown in Fig. l(a).

This paper proposes a model where each bus-bar breaker is represented as a proper impedance circuit. The resulting network has only an additional link without an additional node for each such breaker, as shown in Fig. l(c). So the switching sensitivity equation (10) can be applied to bus-bar switching as a line switching. The algorithm in this paper treats the additional link as a virtual line, in the same way as other transmission lines in the network. Therefore, selection of the virtual line representing the breaker is equivalent to selecting the breaker itself as a corrective switching action.

A special note needs to be made considering the assignment of the proper reactance. The additional non-zero reactance of a virtual line makes the power system states deviate from the exact states. For a small deviation, the small virtual reactance is to be assigned


to the bus-bar breaker. Too small a value of the virtual line reactance may cause a divergence of the system states. Since the objective of this bus-bar model is to find the quantitative relation between the bus separation action and the system states, a slight incorrect- ness of the system-state calculation is tolerable to the emergency operation in this algorithm. The proper value of the virtual line reactance in the test system is obtained through several trial-and-error iterations. The admittance vector, y in the equations (1)-(10) is extended to the virtual lines representing bus-bar breakers.

3. DESCRIPTION OF THE SYSTEM COMPONENTS

The hierarchical knowledge-base is constructed of cells and subsystems for fast restoration. The cells and subsystems fully describe the power systems, and provide the expert systems with a data structure which ensures an efficient search.

3.1. Cells and subsystems

A cell is a conceptual object which corresponds to an element that can be isolated by opening all the switches. The cell is represented by data that can describe a particular element such as a bus, a line, a generator, a load, a transformer, etc. The entire power system can be described by the cells, but a hierarchical data structure is still needed for an efficient search. In the hierarchical structure, the cells are in the lowest level. A group of cells which are connected electrically form a subsystem which is at a higher level than that of the cells. A subsystem is defined as a group of cells or other subsystems one level lower in the hierarchical structure. So a subsystem describes some part of a power system. When a switch device operates to connect, a subsystem can be generated by combining the subsystems which are connected electrically by the switch. When a switch operates to disconnect, a subsystem can be divided into two subsystems which are disconnected electrically by the switch. Therefore, a network reconfiguration is recognized by rebuilding the subsystem hierarchies.

3.2. A switch, and its representation

The electrical network connection of the power system depends on the on/off status of the switches (circuit breakers, line switches). In this paper, a restoration plan is determined by the simulation of many cases of switching. Therefore during restoration planning, rapid recognition of reconfigured networks is required. This recognition process is done by rebuilding the subsystems with respect to the on/off status of the switches. A CB (circuit breaker) is represented as:

CB (index, Celll, Cell2, status),

where the index gives the identification of the CB. Cell 1

and Cellz indicate the cells which are linked by the CB. A CB always relates two cells. According to the location of a CB in a subsystem, the CB can be either an external CB or an internal CB of the subsystem.

External CB: This represents a CB which the subsystem shares with another external subsystem. For example, in Fig. 2, the external CBs of SUB 6 are CB 3 and CB 4, and the external CBs of SUB 3 are CB 2 and CB 3.

Internal CB: This represents the external CB of a subsystem one level lower inside the subsystem. In Fig. 2, the internal CB of SUB 6 is CB 5, and the internal CBs of SUB 8 are CB 1, CB 2, CB 3, CB 4, CB 5.

3.3. Representation of a subsystem

The data object, SUB, which describes a subsystem, is stored in the database using the following format:

SUB(index,type,[internal SUB list], [external CB list],[data]),

where the index is the identification of the subsystem. The other components are as follows:

Type: This describes the type of subsystem. It is one of these types of equipment: bus, line, generator, load, transformer and SUB. The subsystem of SUB-type is formed by grouping the other subsystems, which are located one level lower in the hierarchical structure.

Internal SUB list (ISL): The internal SUB of a subsystem is a subsystem which is located one level lower inside the subsystem. The ISL of the subsystem lists all of the internal SUBs of the subsystem, so the ISL of a cell-type subsystem is empty. In Fig. 2, the ISL of SUB6 is {1,2}, and the ISL of SUB 8 is {3, 6, 7}.

External CB list (ECL): ECL lists all the external CBs which connect the subsystem with other, external subsystems. Since the internal CB list is not needed to rebuild the hierarchical structure, the recognition of the network reconfiguration from the

~% ~, ;,~,-,"('-,"" Sul~5,(=Gen) '', CB~i,-" s , Sub7(=Sub4+Sub5)

CB2 ),2 - ', / ' ~ Sub8( =sub3+ , , , Sub6+Sub7) ' , ~ Sub3(=Line)

', ~, CB4 CB3 ' - - - ] , - ,'

/ - ".-: -,_ Sub (=aus) ' , , CB.5-r=~-_ " )/'~f--Sub6(=Subl+Sub2) ".. (. ~ ~ ~ Subl(=Load)

Fig. 2. Diagram of sample subsystems.


switching is done only by the ISL and the ECL. In Fig. 2, the ECL of SUB 6 is {3, 4}, the ECL of SUB 4 is {1, 2}.

Data: According to the types of the subsystems, each has information of the state variables and their allowed capabilities, such as voltage, power, line capacity, etc. A SUB-type subsystem has data con- cerning the total generating power and the total load power inside it. The data are the sum of the values of the internal subsystems inside it. A subsystem is classified into energized and deener-

gized subsystems. A subsystem with a power- generation source in the data field is defined as an energized subsystem, while a subsystem without a source power in the data field is defined as a deener- gized subsystem. After the network has been modified by switching operations, the state of the separate partial systems is to be identified according to the power balances. The identification of the power states, such as blackout, surplus and deficit, is done by considering the information in the data field of the subsystem which belongs to the highest level in the hierarchical structure. From the relation between the total generation power and the total load power of the pre-fault state, the state of the power balance is defined as follows:

Blackout: If EPg = 0 and ZPL ¢ 0 in a subsystem, it is defined to be in a "blackout" state. The highest subsystem in the blackout state is called the "blackout subsystem".

Deficit: If ZPg :i/: 0 and ~Pg < ]~PL in a subsystem, it is defined to be in a "deficit" state. The highest subsystem in the deficit state is called the "deficit subsystem".

Surplus: If ~,Pg>EP L in a subsystem, it is defined to be in a "surplus" state. The highest subsystem in the surplus state is called the "surplus subsystem".

3.4. Sequence of reconfiguration In a case where a switch is opened, the separation of

a subsystem occurs, and in a case of closure, the merging of subsystems occurs. It is impossible that the separation of a subsystem could occur in cases of closing, or the merging of subsystems in cases of opening. The reconfiguration sequences according to switching are as follows:

A. In cases of opening

(1)Find the subsystem which contains the opened switch by searching the subsystems, from the highest level downward in the hierarchical data structure.

(2) Check whether or not separation occurs in the subsystem found.

(3) If separation does not occur, there is no change in the hierarchical structure, so the procedure for opening is ended.

(4) If separation occurs, two subsystems have been generated. The indices of the newly gener-

ated subsystems are inserted in the ISL of the subsystem which is one level higher than the divided subsystem.

(5) For the higher-level subsystems than the separated subsystem, the former sequences are performed upward in the hierarchical structures and are repeated recursively, until no division occurs, or until the algorithm arrives at the highest level.

B. In cases of closing

When a switch operates to close, the hierarchical structure changes only if the changed switch is the external CB of the highest subsystem. This is obvious, since the other subsystems lower than the highest have already been merged to build the hierarchical structure.

(1) If the changed switch is not the external CB of the highest subsystem, there is no change in the hierarchical structure, so the procedure for closing is ended.

(2) If the changed switch is the external CB of the highest subsystem, find the two subsystems of the highest level which share the changed switch, and merge them.

4. KNOWLEDGE-BASED SYSTEM The knowledge base consists of the following types,

described by production rules: energization, overload alleviation and flow control knowledge. The flow control knowledge carries out the reasoning control for other types of knowledge. The overload alleviation knowledge, decomposed into line-switching and load- shedding knowledge, refers to the switching sensitivities in off-line data. The constitution of the knowledge base is explained in Fig. 3.

4.1. Flow-control knowledge The reasoning tree of the flow-control knowledge is

depicted in Fig. 4. Each node has the truth value "true" or "false". The task of restoration is ended when the root node "System Restoration" has the value "true". As the inference engine traces the AND/OR tree, each node is evaluated to have one of the truth values.

[ F low-Cont ro l K n o w l e d g e ]

Energizatio" Overload Alleviation Knowledge]

Knowledge / Switching / / Shedding I / L Knowledge J L KnowledgeJ J

I[ Network Reduction~-*[Off.LineSWitching Data Sensitivity]

Fig. 3. Knowledge configuration.


I _ System 1 Restoration

[Energization/ [Overload Alleviation/

I ine S ,o i. l [ oad S oddin J Fig. 4. Flow-control knowledge tree.

The node "Energization" has the value "true" when the plan for energizing the blackout areas is determined, or when no blackout areas arise. After the plan for line switching has been determined, if it alleviates all the overloads, then the node "Overload Allevi- ation" has the value "true" without executing the load- shedding knowledge; otherwise, load-shedding is exe- cuted to terminate the restoration procedure.

4.2. Energization knowledge

After a fault occurs and the protection devices are operated, the subsystems in the highest level belong to one of three states, viz. blackout, deficit and surplus according to power balance. A blackout area corresponds to the highest subsystem in which the total generation power equals zero, and the total load power does not. To recognize the blackout area, the only thing to do is to check the data field of the highest subsystems. After recognition of the blackout area, this expert system activates the following rules, denoted by the "Energization" node in Fig. 4.

(1) Surplus subsystems are sought, that can feed the blackout area by transmission lines, bus-bars and transformers. If there are several such subsystems, the one that has the maximum surplus power is selected to feed the blackout area with electrical power.

(2) The lines between the selected surplus subsystem and the blackout subsystem are considered. The one which has the maximum capacity of line flow is selected.

(3)The selected line is determined to link the surplus and the blackout subsystems. These heuristics are performed for all the blackout

subsystems, if there are more blackout areas.

4.3. Line-switching knowledge

After the line switching for energizing the blackout areas, the power flows of the changed networks are predicted, to check for line overloads according to the switching sensitivities of the lines (including transformers and bus-bars). If overloads are predicted, sup- plementary line switching is considered to alleviate the overloads. For speedy restoration, the number of lines to be switched must be minimized, while satisfying the

operating constraints which mean that the networks contain no overloads.

There are many possible combinations of lines to be switched. This means that the search space to find the best switching is vast. However, the information on line-switching sensitivity, the matrix B in equation (10), confines the searching space by selecting the effective lines which have negative values of sensitivities, and by avoiding combinations of switching lines which increase the overloads. Since the searching proceeds from cases of single lines switching to those involving more lines, the solution switching that is first found in the searching process satisfying the line power constraints has the minimum number of switchings. These heuristics help reduce the time required to determine the switching lines. The procedural heuristics denoted by "Line Switching" node are as follows:

(1) The sensitivity matrix B in equation (10) is calculated when the power system is in the normal state. In each row of the matrix, the elements are rearranged in ascending order, and stored, together with the line numbers.

(2) Let the ith and jth lines be overloaded after the blackout restoration. The set of the candidate lines to be switched is made up on the basis of the ith row and jth row in the matrix B. The elements corresponding to the candidate lines in the matrix have negative values in the ith row or the jth row.

(3) The number of switching lines is one at first, and is increased by one until the operating (line power) constraints are satisfied. Now let the number of switching lines and the candidate lines be N and Nc respectively.

(4) Nc is then the maximal number of switching lines to be considered. For an efficient search, the order of candidate lines is important. In this study, a more effective line takes a higher priority. The effective lines are the ones which are effective in alleviat- ing the overloads. In other words, these lines have lower values in the ith and jth rows of matrix B.

(5) In the process of searching the switching lines, if the operating constraints are satisfied with respect to all the lines, then they are determined to be the switching controls for overload alleviation, and the restoration plan is completed; otherwise, step (6) is applied.

(6) The solution of N lines which leads to the minimum remaining overloads is stored. If the minimum remaining overloads of N lines are less than those of the N - 1 lines which are stored already, step (7) is applied; otherwise, step (8) is applied.

(7) In this case, the solution of N lines is better than that of N - 1 . Therefore it is considered for more lines of N+ 1, and the steps (5) and (6) are performed again. If N equals Nc, all the candidate lines are determined to be switched, and then the load shedding is performed.


23

B

A 67

l

70 72

> , = , 1 1 2 4 < 71

...... .... 68 >12 ---_

16 56

26

27

1 4 6 ~ ~" 6 9 20 19 58 < < • "'7- ~ I 64

35

r 3 ~ " <__ 38 > [ 43 <

163 39 [ 62

41

40 ~ _[_10 2~2 - - - 21

Fig. 5. Network diagram of local control center.

18

(8) In this case, the solution of N lines is worse than that of N - 1. It can be thought that the more switching lines, the more the overloads. Therefore the lines stored in N - 1 lines are determined to be switched, and then the load shedding is performed.

4.4. Load-shedding knowledge When a severe fault occurs, it is possible that line

switching will be insufficient to alleviate all the overloads. In the case, after the overloads have been maxi- mally decreased by line switching, load-shedding is considered to alleviate the remaining overloads. The loads in this paper are modeled by the feeders connected to the bus in a substation. The load power of a bus is the load power sum of the feeders at the bus, and decreases discretely according to the load-shedding, which is done by disconnecting the feeder switches. Since the minimization of the unserved power is the objective of the restoration plan, it is efficient that the amount of load shedding power should be minimized, while satisfying the operating constraints at the same time. Information of the load-shedding sensitivity, the matrix A in equation (10), confines the searching space, and reduces the amount of the shedded power. The procedural heuristics denoted by "Load Shedding" in Fig. 4 are as follows:

(1) The sensitivity matrix A in equation (10) is calculated when the power system is in normal state. In each row of the matrix, elements are rearranged in ascending order, and stored, together with the feeder numbers.

(2) Let the ith line remain overloaded after line switching. The set of the candidate feeders is made up on the basis of the ith row in the matrix A. The elements corresponding to the candidate feeders are the negative values in the ith row. The number of the candidate feeders is denoted by Nc.

(3) The search for the feeders proceeds from the switching of one feeder to the switching of Nc feeders. The search space is confined by the follow-

ing steps. (4) If the load-shedding power of a set of feeders is

less than the maximum overload, the switching of the feeders cannot alleviate all the overloads, so consideration of them is skipped; otherwise, the set of feeders is checked for satisfaction of the constraints of all the overloaded lines.

(5) For a set of feeders, if the constraint of any line is violated, the set is discarded, and step (4) is performed for the rest of the set. If all the constraints are met, and the load-shedding power of the feeders is less than that of the temporary optimum feeders, the feeders are substituted for the temporary optimum feeders.

(6) If the load-shedding power of the feeders is larger than that of the temporary optimum feeders, consideration of the feeders is skipped.

(7) When the searching reaches the Nc feeders, the switching of the temporary optimum feeders is determined as the final load-shedding.

5. CASE STUDY

The test results were obtained on a 25-bus system, comprising the networks of a local control center in Seoul, Korea as shown in Fig. 5. The internal network of the area A in the figure is the 154 kV system, while the external network of the area B is the 345 kV system. The externals of three and six lines are equivalenced by using network-reduction techniques. Line 66 is a virtual line representing a bus-bar breaker, so bus 8 and bus 9 are in the same substation. The total load power of 19 substations inside the local control center is about 1600 MW. Each lumped load consists of several feeders in a substation, and the total number of feeders in the 19 substations is 198.

In the pre-fault normal operation, lines 39, 41, 42, 43, 46 and 47 are open to suppress single-phase short- circuit capacity. The feeder power of the substations concerned to the switching operation buses is listed in Table 1.


Table 1. Feeeder load data (MW)

Bus number 5 6 7 9 10 11 13 14 15 20 Lumped load 49.7 79.4 98.4 53.5 82.3 92.2 125.0 93.8 26.3 96.8 Number of feeders 6 9 11 7 9 10 11 9 5 10

Feeder 1 7.3 7.2 10.1 4.7 9.1 8.2 12.7 11.4 5.3 8.9 2 8.4 8.6 8.5 8.9 7.8 10.1 8.2 15.2 4.1 11.3 3 4.8 12.1 6.3 6.3 8.2 9.3 9.8 7.8 7.0 14.2 4 12.2 7.8 9.0 5.1 12.5 5.0 13.8 9.5 3.2 6.7 5 7.2 11.4 4.7 10.1 12.1 6.5 15.1 10.7 6.7 10.4 6 9.8 9.2 8.8 6.9 13.7 12.4 8.7 13.2 - - 11.8 7 - - 6.4 9.3 11.5 2.8 17.1 9.3 8.4 - - 9.4 8 - - 10.4 11.2 - - 11.4 3.3 15.2 11.7 - - 7.7 9 - - 6.3 7.5 - - 4.7 4.8 8.6 5.9 - - 10.6

10 - - - - 1 2 . 4 - - - - 15.5 12.9 - - - - 5.8 1 1 - - - - 1 0 . 6 - - - - - - 1 0 . 7 - - - - - -

Fault and blackout

Double lines (from bus 12 to bus 13) are dropped by line faults. This causes buses 13, 14 and 15 to be blacked out, as shown by the area C in Fig. 5, because lines 52 and 53 have opened in prefault operation. The pre-fault load power of the blackout area is 245.1 MW, as shown in Table 1.

Energization and overload

The result of the energization routine shows connection of line 52 or 53 (from bus 14 to bus 15). The power flow capacity of a single line (line 52 or 53) is not enough to supply the blackout load power, 245.1 MW; therefore the double line 52 and 53 are to be closed together. It is predicted, by using a sensitivity matrix, that this double line switching will cause an overload on line 32 (from bus 4 to bus 5). This line is loaded to about 150% of its rating.

Overload alleviation

The overload alleviation routine by means of line and bus-bar switching shows a connection of line 39 (from bus 7 to bus 8) and lines 42 and 43 (from bus 20 to bus 9), and opening of the bus-bar breaker which is represented by the virtual line 66 (from bus 8 to bus 9). This means that the load at bus 9 is to be transferred from bus 8 to bus 20. This switching alleviates the overload on line 32. But the lines 34 and 35 are predicted to be loaded to about 102% of their rating.

Load-shedding

No other line switching can be found to relieve the remaining overloads, so the load-sheddding routine is activated. Since the prediction of line power flow by sensitivities is slightly different from the correct value, 98% of its rating is used as the overload criterion in approximate line power. Considering this margin, the line power to be suppressed on lines 34 and 35 is 11.88 MW respectively. The result of this routine shows two feeders should be opened, at buses 7 and 10, of 8.5 and 4.7 MW respectively. Then the load power of this combination is the minimum for overload alleviation within this criterion.

As the final result of the restoration planning, the

following sequential operations are presented to the operators at the local control center:

• connect lines 42 and 43; • disconnect line 66; • connect line 39; • disconnect the second feeder at bus 7; • disconnect the ninth feeder at bus 10; • connect lines 46 and 47.

As the inference engine traces the knowledge tree, the planning of switching operations is achieved at each step. Table 2 indicates the line power of the lines concerned in the switching operation at each step. Column A in Table 2 is the 100% rating of each line.

The change of line power flow in the table is shown as the following sequence: Column B corresponds to the pre-fault state. Column C corresponds to the case after the energization switching (lines 46 and 47 close) which causes a line overload. Column D corresponds to the case after the overload-alleviation routine by line switching (line 39 closed), and column E corresponds to that achieved by bus-bar switching (line 66 open). Column F shows the state with all overloads suppressed by load-shedding.

6. CONCLUSION

This paper proposes an expert system which cannot only restore blackout areas, but also prevent line overloads. A blackout area is restored by line switching, that interconnects the blackout areas and the energized

Table 2. Line power at each step (MW)

Line A B C D E F

32 215.0 173.6 343.7 218.1 201.7 197.8 33 218.5 101.3 177.2 121.2 113.9 112.2 34 165.0 90.6 90.6 181.7 166.7 162.6 36 206.1 21.9 97.7 41.8 34.5 32.7 37 216.6 72.9 195.7 105.0 93.2 90.4 39 258.4 0.0 0.0 181.3 151.4 157.1 40 152.0 82.3 82.3 82.3 82.3 77.6 42 216.6 0.0 0.0 0.0 26.8 26.8 44 216.6 46.1 168.8 168.8 168.8 168.8 46 160.5 0.0 122.6 122.6 122.6 122.6


areas. The overload alleviation is achieved by switching transmission lines and virtual lines, and switching feeders. A virtual line represents a bus-bar breaker for bus separation. Feeder switching means load-shedding in a substation. During the restoration plan, numerous cases of switching are generated, but a restricted set of cases is considered by using heuristic rules and numerical data about switching sensitivity. Since line switching changes the network topology, a rapid recognition scheme for the network reconfiguration is needed. The suggested method of data representat ion is adequate for rapid recognition of a changed topology. The line powers of post switching play a key role in determining the restorative switching. These states of a power system are easily predicted by the switching sensitivities formulated in this paper.

This restoration-guidance system was applied to a local control center in the neighborhood of Seoul, Korea. This expert system gives appropriate solutions, that are applicable by the power-system operators.

REFERENCES

1. TASK FORCE Report, Power system restoration. IEEE Trans. Power Systems 2, No. 2 (1987).

2. Kafka R. J. Role of interactive and control computers in the development of a system restoration plan. IEEE Trans. PAS 101, No. 1 (1982).

3. Kato M. The development of power system restoration method for a bulk power system by applying knowledge engineering techniques. IEEE Trans. Power Systems 4, No. 3, 1228-1235 (1989).

4. Sakaguchi T. Development of a knowledge based system for power system restoration. IEEE Trans. PAS 102, No. 2 (1983).

5. Wang Shi-Mo, An expert system for bulk power system restoration. Second Symposium on Expert System Application to Power Systems, Seattle (1989).

6. Adibi M. M. Local load shedding. Trans. Power Systems 3, No. 3 (1988).

7. Fukui S. A knowledge-based method for making restoration plan of bulk power system. IEEE Trans. Power Systems 7, No. 2 (1992).

8. Dy Liacco. A hierarchical interactive approach to electric power system restoration. IEEE Trans. Power Systems 7, No. 3 (1992).

9. Wollenberg B. F. Corrective control of power system flows by line and bus-bar switching. IEEE Trans. Power Systems 1, No. 3 (1986).

an expert system for switching operations for blackout restoration—line, bus-bar and feeder...

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