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An Expert System for Switching Decisions in Substations
Copyrighl © I FAC Illh Triennial World Congress, T allinn , ESlonia, USSR. 1990
AN EXPERT SYSTEM FOR SWITCHING DECISIONS IN SUBSTATIONS Z. Z. Zhang, G. S. Hope and O. P. Malik Dept.
(lI Eleetrim/
ElIg ill enillg, U lliven'it\,
Abstract
PROBLEM SPECIFICATION AND EXPERT SYSTEM
Automatic sequence switching has been an important pursuit in the field of substation automation since the introduction of computers to substations in the 1960s. Computer-based methods for substation switching have been presented previously. Early work used Boolean algebra to express the relationship between substation switches [1]. Dynamic programming [2] and substation information matrix [3] were used to search for the optimal sequence of switching operations. Computer aided interlocking of substations is attractive because it decreases cost and increases capabilities [4]. Also attention has been given to automatic restoration and rearrangement of substations following an abnormality [5] . In recent years expert systems have captured the interest of power system engineers [6,7]. Operation assistance proved to be one of the most valuable applications of expert systems [8]. Substation Switching operations have two obvious features :
(b)
Problem Specification In a substation switching decisions are made by operators or computers. The following three considerations are basic. 1.
2.
(a)
Human safety must be ensured and device operational limitations must not be overreached. (b) Normal conditions (for example, continuity of supply to loads) in parts of the substation unrelated to the task must not be affected. Safety requirements lead to the following mandatory constraints:
These features indicate that expert system technology can make a contribution to solving the above-mentioned problems. The following problems must be solved to improve the functioning of current sequence switching: (I) reduce the burden of numerical processing,
All operational interlocking rules must be followed. All power sources unrelated to the task must not be interrupted, even temporarily.
(2) improve software flexibility for ease of substation modification or extension, and
Status of components unrelated to the task must not be changed, even temporarily.
(3) provide a detailed explanation of switching operations sequence selected to fit the severity of events. 3.
An expert system used for sequence switching has three possible application benefits:
(2)
support automatic switching functions microprocessor-based protection and control,
(3)
provide the energy management system(EMS) with a tool to rapidly restore supply in emergencies.
Safety Substation switching operations must be safe in the following sense:
Experience of human operators plays an important role in decision making.
provide operators of substations with an intelligent assistant,
Functionality The objective of switching operations is to meet requirements of power transmission, transformation and distribution by opening and closing switching devices. In these tasks equipment which maintains the supply to other loads is placed in or removed from service. Fulfillment of the tasks depends upon sequence switching operations and leads to the necessity of determining the sequence.
Decision making is based on deductive inference following a definite logical sequence from some current switching pattern.
(I)
Callada
This paper presents an expert system used to help operators make decisions for sequence switching in substations. Its intelligent problem solving method is also presented. The organization of the paper is as follows. The sequence switching problem is formulated first. Then a model of substation switching network and problems solving methods are discussed. Next, a knowledge base, an inference engine, and a user interface in the expert system are described. At the end, simulation results in a substation are given in the form of application examples.
Computer-based sequence switching offers advantages of integration in substation automation. This paper presents an expert system, designed in PROLOG, for sequence switching of substations. A knowledge base for a hierarchical structure model of substation switching network, an inference engine based on suggested sequence switching strategy and a user interface with man-machine interaction are described. Also, application examples in a substation are given. INTRODUCTION
(a)
of Ca/gw )',
Switching operations must progress sequentially. Optimality
There are many switching sequences that satisfy the given goals. Selection of the minimal cost sequence is an approach to optimization. Under the assumption that individual devices' operation cost for opening or closing are equal, the total number of operations to perform the given task should be minimal. The goal is to determine a particular sequence of switching tasks which minimizes operating costs and meets the mandatory safety constraints.
with
223
r- -
-
-
-----,
i - I nference I engi ne I I
I
Component Level Fas t base Rule base
Each switching device in the SSN is described by the data: name, type, serial number, switch-on/off status, live/dead status, working conditions (normal, maintained, automatically operated). Links between switching devices in the SSN are described also. Branch Level
Knowl edge base
Shell
Branches and nodes at each end are described by the following data.
User
(a)
Fig. 1. Structure of the expert system Expert System
branch: name, type, serial number, included component names, names of end nodes, connected status, working conditions.
To deal with the sequence switching problem, an expert system designed in PROLOG [9] to assist operators to determine strategy is presented .. Fig. 1 shows the structure of the expert system. It consists of a knowledge base, an inference engine and a user interface. The latter two parts together are called an expert system shell.
node: name, type, serial number, linked branches names, live/dead status and heuristic search estimate. Connected status of a branch depends on switch-on/off status of all switching devices in the branch, and are described by corresponding logic relations. Network Level
The expert system provides the following three main functions.
The following three aspects of SSN are described at the network level. 1. Physical joint structure This gives the fixed connections between all branches and nodes of the SSN. 2. Connected status This gives the connectivity between different elements (nodes, branches) in the SSN. The current connected status in the SSN depends on the physical joint structure and the current connected status of all its branches, and are deduced through reasoning. 3. Live status This gives the description of live elements in the SSN. Current live status in electricity depends on the distribution of supplies and current connected status in the network, and can be deduced through reasoning. Topologic Graph
(b)
Knowledge acquisition Users are able to integrate new knowledge into the expert system. The model of a substation switching network can be modified according to current variations. Reasoning rules can be added or eliminated to improve implementation of the system. 1.
Problem solving Given a task of switching operations, the expert system does the following: 2.
analyses the task defines the problem in terms of switching operations suggests a sequence switching program of operations that deal with the task. 3.
Explanation The system is interactive and can answer user's question during and after the problem solving process. Thus, the reasoning and decision process as well as the switching strategy are available to the operalor. MODELING OF SUBSTATION SWITCHING NETWORK
The topologic graph (TG) of the SSN consists of a set of nodes and a set of edges. Each edge is a branch which consists of some basic components. Fig. 3 shows the TG for the SSN in Fig. 2. Concepts which are necessary to the reasoning in the TG are identified as follows. 1. Components Components in the TG are classified into the following types: st:pply components (transmission lines), load components (feeders to loads), switching components (circuit breakers and isolators), joint components (busbars) and transforming components (transformers).
A substation switching network (SSN) can be described by a model organized in a tri-level hierarchical structure. Thus, the knowledge base of the expert system is constructed according to the model. The switching configuration shown in Fig. 2 is used as an example [3,10].
2.
3.
Nodes Input nodes---nodes at the ends of each supply components. Examples are nodes 1, 2, 15 and 16. Output nodes---nodes at the ends of each load components. Examples are nodes 3, 8, 9 and 14. Branching nodes---joining nodes of circuit sections containing switching components. Examples are nodes 4,5 , 6,7,10,11,12 and 13. Branches Input branches---branches between two input nodes. SI
S2
s3
s4
""*~ OPENC.B.
7-
CLOSED ISOLATOR
-0-
OPEN ISOLATOR
-
TRANSFORMER
Fig. 2. A Substation Switching Configuration
Fig. 3. A Topologic Graph of the Switching Configuration.
224
Examples are s l-s4.
(2)
If a dead node (N) has several adjacent live nodes (NI, ... , Ni), its estimate E(N) is
(3)
Generally, if a dead node (N) has several adjacent nodes (Ni, ... , Ni), its estimate E(N) is
Output branches---branches between two output nodes.
E(N)=min(cost(N,Ni))
Examples are fl- f4. loint branches---branches between two branching nodes. Examples are branches 4, 5, 6, 8, 9, 11, 12 and 13. Obviously, in the TG of a SSN, nodes which are at connected status with branches between them at connected status form a sub-graph. This is called a connecLed distribution (CD) of the TG. Also, nodes at live status and branches between them which are at connected status fom1 a subgraph. This is called a live distribution (LD) of the TG. For example, nodes (I , 2, 5, 6, 7, 8, 12, 13, 14 and 16) and branches (I, 2, 5, 6, 7, 9, 13, 14 and 16) form a CD and also a LD of the TG in Fig. 3. PROBLEM SOLVING METHODS
E (N) = min ( cost (N, Ni ) + E (Ni) ) (2) where E(Ni) is the estimate of the ith adjacent node, as shown in Fig. 4. For example, E(5) = 0, E(l2) = 0, E(4) = 1, E(ll) = 1, E(l0)=2 in Fig. 3. Sorting Based on Rules
After the devices used for sequence switching have been selected, an ordering relation in their operations must be determined. For this, a hierarchical tri-Ievel sort is followed according to safety operation rules and human operator's experience. Some examples of the rules are:
Problem solving techniques used in the expert system include task decomposition, determination of branch costs and heuristic estimates, sorting based on rules, and determination of minimum spanning tree. Task Decomposition Switching operation tasks are to place into or remove from service one or several load components, supply components, switching devices, bus-bars, or other facilities, and to connect two live components with each other in a SSN, or disconnect them from each other. In a TG of SSN, these tasks can be classified as follows: TYPE I: connect a dead node. TYPE II: connect a group of dead nodes having interconnecting branches. TYPE Ill: disconnect a live node. TYPE IV: disconnect a group of live nodes. Connecting or disconnecting rwo live parts in the TG is similar to TYPE II or IV. A synchrocheck must be made at fixed breakers for the connection. Obviously, these tasks can be described by two cases: energization and deenergization. Branch Cost The operation cost of sequence switching is calculated on the basis of branch cost. The number of switching operations is used. The cost of switching operations must be attached to all branches in the TG of the SSN. The two subclassifications used are connection and disconnection cost. Based on a given existing switching configuration, the branch costs of the TG are deduced according to the following principles: (1)
(2)
(1)
The costs used for switching-on/off of a switching device may be chosen by the users. (In this example these costs are assumed equal.)
1. (a)
Sorting branches In the implementation of the energization task for two branches in an optimal path, the branch nearest to the live goal node is selected before the other.
(b)
In the implementation of the deenergization task, branches with lower voltage levels are selected before those at higher voltage levels.
2. (a)
Sorting switching components In the implementation of the energization task, switching devices in a branch must be closed in the following sequence: isolators nearest to the live goal node, isolators farthest from the goal node, and then the circuit breaker.
(b)
In the implementation of the deenergization task, switching devices in a branch must be opened in the following sequence: the circuit breaker, isolators nearest to the branch node to be deenergized, then isolators farthest from the node.
3. (a)
Insertion sort In the implementation of the energization task, all branches on both sides of the optimal path must be disconnected first to avoid changing the electrical status of components unrelated to the intended goal.
(b)
In the implementation of the deenergization task, all live nodes immediately connected with nodes to be deenergized and unrelated to the task must be first reconnected and energized through some transition branches.
(c)
In the implementation of the energization task, the last branch energized must not consist of a single isolator only. Its operation sequence mu st precede the nearest branch containing a circuit breaker. Minimum Spanning Tree
The branch connection cost is the sum of switching-on costs of all devices in the branch.
The branch disconnection cost is the sum of switchingoff costs of all devices in the branch. Heuristic Estimates
(3)
Consider the complex task of connecting a group of dead nodes to a LD. The best approach is to first connect one of the nodes to the LD, and then to connect each node through branches such that the sum of the branch costs is minimum. An approach to this implementation is a minimum spanning tree (MST) consisting of the group of dead nodes and these branches. A spanning tree of a graph is a subgraph of the graph such that: (1) it contains all nodes of the graph ,
Finding optimal sequence switching in a TG is a kind of graph search. This typically leads to the problem of combinatorial complexity due to the proliferation of alternatives. Against this problem, a heuristic searching method---Best-First search is used [11]. Information used in the method is represented by numerical heuristic estimates for the nodes in the TG. Such an estimate indicates how promising the node is with respect to reaching a goal node. Thus, the search continues from the most promising node.
(2) (3)
it is connected,
it does not contain a loop. Among all spanning trees in the graph, a MST has minimal sum of connection costs for all its branches. KNOWLEDGE BASE A knowledge base in the expert system is a source of domain knowledge used in decision making of the substation sequence switching problem.
Heuristic estimates are called "estimates for energization (EE)". The estimates, E, for all dead nodes in the TG can be determined in the following manner. (I) Assume the EE of a live node equals zero, and the EE of a dead end-node (or leaf node) is infinite (in fact, a large positive integer).
225
Information in knowledge base has two forms---facts and rules. 1. Fact base It is a collection of FACf statements. Knowledge relates to the problem domain, and provides dynamic modeling of structure and status of the SSN in a hierarchical structure. The following are stored in the fact base: (a) factual knowledge on structure at the component level, branch level,
by actively using the knowledge base to decide (a) how to apply the facts and rules in the knowledge base to infer new knowledge and (b) how to interact with the user. Structure The inference engine consists of modular procedures in PROLOG, as shown in Fig. 5. By data-driven and forward chain methods, the following modular procedures are directly or recursively called according to implementation requirements in a problem-solving reasoning process: (1) Task Scheduler (TS)---determine different reasoning courses according to given switching operation task.
(b)
factual knowledge on connected status and electrical live/dead status,
(2)
(c)
factual knowledge on the TG,
Knowledge Organization
Optimal Path Search (OPS)---search for an optimal path from a starting node to a goal node in the TG. (3) Branches List Form-I (BLF- I)---a branch sorting procedure to form an available branches sequence for the energization task.
(d)
factual heuristic knowledge on branch costs and estimates for cnergization. Some examples of the FACT statements in Prolog are: (1) "isolator(i3, il03, open, normal)" means: an isolator called "i103" has a serial number "i3", is open and closed in normal operation. (2)
"branch(bran7, [n7, n8J, [b5, i6J, connected, joint-b)" means: a joint branch called "bran7" which is at connected status has two end-nodes "n7" and "n8", contains a breaker "b5" and an isolator "i6".
Branches List Form-I! (BLF-II)---a branch sorting procedure to form an available branches sequence for the deenergization task.
(5)
Components List Form (CLF)---a sorting procedure to present a sequence of switching operations (SO).
(6)
Minimum Spanning Tree Determination (MSTD).
(7) Task Driving-Type I (TD-TI). (8)
"branch-cost(bran15, 2, 0)" means: branch 15 has a connection cost of "2" and a disconnection cost of "0". 2. Rule base A rule base consists of IF-THEN statements. Knowledge in the rule base is used to describe relations of status in the SSN and basic reasoning, such as: (a) rules to deduce connected status and live/dead status at the branch level and network level, (b) rules to determine the CD and LD, (3)
Task Driving-Type IT (TD-TII).
(9) Task Driving-Type III (TD-TIII). (10) Task Driving-Type IV (ID-TIV). Basic Strategies I.
Task detennination The TS procedure is called to implement a given task of SO, and it performs the following items in sequence: (1) determine a (or group of) keyword(s) from the name(s) of main component(s) in the task, (2) determine by search a branch containing the component, or a group of the branches,
(c)
rules to calculate branch costs and determine estimates for energization. Some examples of the IF-THEN rules in Prolog are: (1) "branch-state(X, disconnected) branch(X,Switchlist,_,_), member(Y, Switchlist), switch-state(Y, open)." means: a branch X is at disconnected status if examination of the list of switches for branch X has a switch Y which is open.
determine an end node of the branch as a starting node for the task, or a group of starting nodes. 2. Search for a Path The OPS procedure searches [or an optimal path from the starting node to a live goal node in the TG of the SSN, and it performs the following items in sequence. (a) From the starting node, the adjacent node which is on an optimal path and nearest to a live goal node can be determined by use of the starting node's estimate. (3)
"branch-con-cost(X,N) :- branch-state(X,disconnected), branch(X,_, Switchlist,_,J, Length(Switchlist, N)." means: the connection cost of a branch X is N if the branch is at disconnected status and the list of switches for branch X includes N switches. (3) "node-state(X,live) connected(X,Y), node(Y,_,.:.., input-n)." means: a node X is live if X is connected to an input node Y. Features The knowledge base has the following features: (2)
(1)
(4)
(b) The branch between the starting node and the adjacent node is put onto a list "Branches List of Optimal Path"(BLOP). (c)
The search proceeds from the found adjacent node toward the goal node using the found node's estimate. (d) The goal node is reached. The BLOP is generated in this process. It is completed at the end of the search because the branch immediately connected to the goal node is the last member of the list. 3. Sorting Sorting is used to generate a list of switching devices into tasks of TYPE I, 1I after an optimal path has been found. A. Forming "Sequential Branches List"(SBL) All branches between the dead nodes and the optimal path have to be disconnected first to avoid connecting adjacent dead nodes. For this, the BLF-I procedure is called to perform the following steps in sequence: (1) Invert the BLOP, so the branch connected to the goal node on the path occupies the first position on the inverted list.
It is easy to extend or modify the contents of the knowledge base when the SSN is expanded, its configUJation or equipment status changed. In this way, the knowledge base can track the status of the SSN.
(2) The knowledge base is modularized, and independent of other parts of the expert system. Thus, it is easy to build. Its contents can be accessed and used by other substation software. (3) The knowledge base is easy to understand because the statements in it are written in PROLOG, a naturallanguage-like, artificial intelligence language based on predicate calculus. INFERENCE ENGINE The inference engine is used to run the expert system
(2) Check the first node nearest the goal node in the path
226
I;' rt
CD
"...
. n
starting node ............
et
disconnected.............. branch
"
'--'
Fig. 6. Insertion of Branches 1,2,3 and 4 Fig.
(3 )
s.
nodes have to be disconnected. and the live adjacent nodes must remain live after the disconnection. The TD- TIll procedure is called to perfom1 the following steps:
Structure of the Inference Engine
shown in Fig. 6. Insert branches between the node and its adjacent nodes. which are not in the path. after the first branch in the inverted list. Check the next node.
Repeat steps (2) and (3) until the starting node is checked. In thi s way. a complete SBL used for sequence switc hin g is completed. B. Forming "Sequential Component s Li st (SCLl" The CLF procedure is called to sort th e switching-on order for devices in each branch in the SBL according to the rules used for sorting. The completed SCL presents the output res ult of the sequence switching to the task.
(a)
the BLF-II procedure is called to form a "Neighbouring Branches List (NBL)" including all branches between the starting and all live adjacent nodes.
(b)
check the adjacent nodes under the assumption that all branches in the NBL are disconnected. and determine all nodes which become dead. the OPS procedure searches for an optimal path from the determined nodes.
(4)
(c) (d)
form a "Transition Branches List (TBL)" from the branches between the determined and the starting nodes.
Task Reasoning
(e)
append the TBL to the NBL and form a SBL.
After completion of ta sk determination. reasoning is continued until an available sequence of SO is presented in the form of SCL.
(t)
the CLF procedure is called to form a SCL.
I.
4.
Reasoning steps for ta sks of TYPE IV The reasoning used to disconnect a group of live starting nodes is similar to TYPE III tasks except that the SCL mayor may not contain the switching for connected branches between all nodes in the group because of different operational requirement s. MAN-MACHINE INTERACTION
Reasoning steps for tasks of TYPE I The TO-TI procedure performs the following steps:
(a)
the OPS procedure searches for an optimal path.
(b)
the BLF-I procedure forms a SBL.
(c)
the CLF procedure forms a SCL.
Reasonin g ste ps for task s of TYPE [[ The TO-Tll procedure is called to followin g steps:
The expert system includes a friendly user interface for smooth interaction between the expert system and the user. It also provides the user with an insight into the problemsolving process used by the inference engine.
2.
(a)
perform
the
compare the estimate s of the nodes in the starting node group. and select the node with the minimal estimate. for example. node N2 in Fig . 7.
(b)
the OPS. BLF-I and CLF procedures fom1 a "Part Sequ ential Component Li st (PS CL)" .
(c)
the MSTO procedure form s a "Minimum Spanning Tree Component List (MSTCLl" for switching devices in the branches between the starting nodes.
(d) 3.
This man-machine interaction includes the functions:
1.
Handling keyboard and screen input and output.
2.
Supporting smooth dialogue between the user and the expert sys tem. Recognizing errors or cognitive mi smatch between the user and the system.
3.
append the PSCL to the MSTCL in the selected node. and form a SCL. Reasoning steps for tasks of TYPE III
4.
Incorporating new knowledge or new problem-solving skills into the system.
5.
Providing user-friendly features by easy interaction in PROLOG.
To di sconnect a live startin g node from a LO. all branches b( ~ ween the nod e and each of its all live adjacent E(N)
E(NI)
@ E(N2)
Fig. 4. Heuristic estimates
Fig. 7. Selection of a starting node '2.27
As an assistant in decision making, the expert system presents a sequence of switching operations as a proposal to operators. The expert system is capable of answering the user's question in the following way: user's question: How did you reach this conclusion?
CONCLUSIONS
Application of expert system technology to a computerbased integrated control and protective system will benefit substation automation. Sequence switching based on expert systems is a promising way to improve its implementation because of its logicality and dependency on experience.
system' answer: This conclusion is deduced from rule A that is deduced from rule B that is deduced from rule C .... With some insight into the system's reasoning process, operators are able to compare the system's proposed sequence switching against their experience. APPLICATION EXAMPLES
The paper formulates the optimal sequence switching problem, presents the knowledge-based modeling of a substation switching network and a set of intelligent problem solving methods for sequence switching, and develops an expert system used to assist operators in sequence switching decisions. The expert system consists of three parts: (1) a knowledge base for a tri-Ievel hierarchical model of substation switching network which features ease of construction, modification and comprehension; (2) an inference engine based on intelligent problem solving methods, such as task decomposition, determination of branch cost and heuristic estimates, sorting using rules, and a minimum spanning tree;
Examples are presented to illustrate the application of the developed expert system. The examples are based on a substation switching network in Fig. 2 and its topologic graph in Fig. 3. Their sequences of switching operations are given by the expert system. Each example is based on an existing switching configuration, or a switching configuration determined by switching operations in the former example. Example l. Task:
(3) put feeder fl in service
Starting node: node 3 Live dis. nodes: 1,2,5,6,7,8,12,13,14,16 Sequence:
a user interface which caters to smooth man-machine interaction and provides the user with an insight into the problem solving process.
The application examples of the expert system show encouraging results in determining operations required to accomplish engineering tasks.
1126,1103, B120
Example 2. Task:
REFERENCES
put supply s3 in service
[1]
G. S. Hope and B. J. Cory, "Development of Digital Computer Programs for the Automatic Switching of Power Systems Networks", IEEE Trans. on PAS, V.87, N.7, July 1968, pp. 1587-1599.
[2]
G. H. Couch, I. F. Morrison, "Substation SwitchingAn Approach to the Determination of Optimal Sequence", PSCC Proc. V.I!, Grenoble, Sept. 11-16, 1972, Paper No. :2.1/l.
[3]
A. Traca-de-Almeida, "Substation Interlocking and Sequence Switching Using a Digital Computer", IEEE Trans. on PAS, V.loo, N.6, July 1981, pp. 3002-3007.
[4]
K.
[5]
E. N. Dialynas, A. V. Machias, "Interactive Modeling of Substation Switching Operations Following a Failure Event", lEE Proc. V.134, Pt.C, No. 2, March 1987, pp. 153-16l.
[6]
B. F. Wollenberg, Tochiaki Sajaguchi, "Artificial Intelligence in Power System Operations", Proc. of the IEEE, V. 75, N. 12, December 1987, pp. 1678-1685.
[7J
Z. Z. Zhang, G. S. Hope and O. P. Malik, "Expert Systems in Electric Power Systems: A Bibliographic Survey", IEEE Power Engineering Society Winter Meeting, New York, Jan. 29 - Feb. 3, 1989, Paper No.: 89 WM 212-2 PWRS.
Task: take transformer S6T2 out of service Starting node: node 6
[8]
Intelligent, Expandable Program for Power System Trouble Analysis", IEEE Trans. on Power Systems, V. PWRS-I, n.3, August 1986, pp. 182-187.
live dis. nodes: 1,2,3,4,5,6,7,9,10,11,12,13,15,16.
[9]
W. F. Clocksin, C. S. Mellish, "Programming in Prolog", Springer-Verlag, Berlin, 1984.
Starting node:
node 15
Live dis. nodes: 1,2,3,4,5,6,7,8,12,13,14,16. Sequence:
B380, 1313, B340(synchrochecking)
Example 3. Task:
put feeder f3 in service
Starting node: node 9 Live dis. nodes: 1,2,3,4,5,6,7,8,11,12,13,14,15,16. Sequence:
1326, B130, 1303, B320
Example 4. Task: take feeder f2 out of service Starting node: node 8 live dis. nodes: 1,2,3,4,5,6,7,8,11,12,13,14,15,16. Sequence:
B220,1203
Example 5. Task: take feeder f4 out of service Starting node: node 14 live dis. nodes: 1,2,3,4,5,6,7,9, 10,11, 12, 13, 14, 15, 16. Sequence: B420, 1403 Example 6.
Sequence:
B120, B240, B280, 1213, 1226
P. Brand, J. Kopainsky and W. Wimmer, "Topology-Based Interlocking of Electrical Substations", IEEE Trans. on Power Delivery, V.PWRD-1, N.3, July 1986, pp. 118-126.
[10] G. P. Hutchinson, "Interlocking in Large Electricity Supply Substations---A Fundamental Approach", Proc. lEE, Vol. 113, No. 6, June 1966, pp. 1063-1074. [11] Judea Pearl, "Heuristics: Intelligent Search Strategies for Computer Problem Solving", Addison-Wesley Publishing Company, California, 1984.
228
AN EXPERT SYSTEM FOR SWITCHING DECISIONS IN SUBSTATIONS Z. Z. Zhang, G. S. Hope and O. P. Malik Dept.
(lI Eleetrim/
ElIg ill enillg, U lliven'it\,
Abstract
PROBLEM SPECIFICATION AND EXPERT SYSTEM
Automatic sequence switching has been an important pursuit in the field of substation automation since the introduction of computers to substations in the 1960s. Computer-based methods for substation switching have been presented previously. Early work used Boolean algebra to express the relationship between substation switches [1]. Dynamic programming [2] and substation information matrix [3] were used to search for the optimal sequence of switching operations. Computer aided interlocking of substations is attractive because it decreases cost and increases capabilities [4]. Also attention has been given to automatic restoration and rearrangement of substations following an abnormality [5] . In recent years expert systems have captured the interest of power system engineers [6,7]. Operation assistance proved to be one of the most valuable applications of expert systems [8]. Substation Switching operations have two obvious features :
(b)
Problem Specification In a substation switching decisions are made by operators or computers. The following three considerations are basic. 1.
2.
(a)
Human safety must be ensured and device operational limitations must not be overreached. (b) Normal conditions (for example, continuity of supply to loads) in parts of the substation unrelated to the task must not be affected. Safety requirements lead to the following mandatory constraints:
These features indicate that expert system technology can make a contribution to solving the above-mentioned problems. The following problems must be solved to improve the functioning of current sequence switching: (I) reduce the burden of numerical processing,
All operational interlocking rules must be followed. All power sources unrelated to the task must not be interrupted, even temporarily.
(2) improve software flexibility for ease of substation modification or extension, and
Status of components unrelated to the task must not be changed, even temporarily.
(3) provide a detailed explanation of switching operations sequence selected to fit the severity of events. 3.
An expert system used for sequence switching has three possible application benefits:
(2)
support automatic switching functions microprocessor-based protection and control,
(3)
provide the energy management system(EMS) with a tool to rapidly restore supply in emergencies.
Safety Substation switching operations must be safe in the following sense:
Experience of human operators plays an important role in decision making.
provide operators of substations with an intelligent assistant,
Functionality The objective of switching operations is to meet requirements of power transmission, transformation and distribution by opening and closing switching devices. In these tasks equipment which maintains the supply to other loads is placed in or removed from service. Fulfillment of the tasks depends upon sequence switching operations and leads to the necessity of determining the sequence.
Decision making is based on deductive inference following a definite logical sequence from some current switching pattern.
(I)
Callada
This paper presents an expert system used to help operators make decisions for sequence switching in substations. Its intelligent problem solving method is also presented. The organization of the paper is as follows. The sequence switching problem is formulated first. Then a model of substation switching network and problems solving methods are discussed. Next, a knowledge base, an inference engine, and a user interface in the expert system are described. At the end, simulation results in a substation are given in the form of application examples.
Computer-based sequence switching offers advantages of integration in substation automation. This paper presents an expert system, designed in PROLOG, for sequence switching of substations. A knowledge base for a hierarchical structure model of substation switching network, an inference engine based on suggested sequence switching strategy and a user interface with man-machine interaction are described. Also, application examples in a substation are given. INTRODUCTION
(a)
of Ca/gw )',
Switching operations must progress sequentially. Optimality
There are many switching sequences that satisfy the given goals. Selection of the minimal cost sequence is an approach to optimization. Under the assumption that individual devices' operation cost for opening or closing are equal, the total number of operations to perform the given task should be minimal. The goal is to determine a particular sequence of switching tasks which minimizes operating costs and meets the mandatory safety constraints.
with
223
r- -
-
-
-----,
i - I nference I engi ne I I
I
Component Level Fas t base Rule base
Each switching device in the SSN is described by the data: name, type, serial number, switch-on/off status, live/dead status, working conditions (normal, maintained, automatically operated). Links between switching devices in the SSN are described also. Branch Level
Knowl edge base
Shell
Branches and nodes at each end are described by the following data.
User
(a)
Fig. 1. Structure of the expert system Expert System
branch: name, type, serial number, included component names, names of end nodes, connected status, working conditions.
To deal with the sequence switching problem, an expert system designed in PROLOG [9] to assist operators to determine strategy is presented .. Fig. 1 shows the structure of the expert system. It consists of a knowledge base, an inference engine and a user interface. The latter two parts together are called an expert system shell.
node: name, type, serial number, linked branches names, live/dead status and heuristic search estimate. Connected status of a branch depends on switch-on/off status of all switching devices in the branch, and are described by corresponding logic relations. Network Level
The expert system provides the following three main functions.
The following three aspects of SSN are described at the network level. 1. Physical joint structure This gives the fixed connections between all branches and nodes of the SSN. 2. Connected status This gives the connectivity between different elements (nodes, branches) in the SSN. The current connected status in the SSN depends on the physical joint structure and the current connected status of all its branches, and are deduced through reasoning. 3. Live status This gives the description of live elements in the SSN. Current live status in electricity depends on the distribution of supplies and current connected status in the network, and can be deduced through reasoning. Topologic Graph
(b)
Knowledge acquisition Users are able to integrate new knowledge into the expert system. The model of a substation switching network can be modified according to current variations. Reasoning rules can be added or eliminated to improve implementation of the system. 1.
Problem solving Given a task of switching operations, the expert system does the following: 2.
analyses the task defines the problem in terms of switching operations suggests a sequence switching program of operations that deal with the task. 3.
Explanation The system is interactive and can answer user's question during and after the problem solving process. Thus, the reasoning and decision process as well as the switching strategy are available to the operalor. MODELING OF SUBSTATION SWITCHING NETWORK
The topologic graph (TG) of the SSN consists of a set of nodes and a set of edges. Each edge is a branch which consists of some basic components. Fig. 3 shows the TG for the SSN in Fig. 2. Concepts which are necessary to the reasoning in the TG are identified as follows. 1. Components Components in the TG are classified into the following types: st:pply components (transmission lines), load components (feeders to loads), switching components (circuit breakers and isolators), joint components (busbars) and transforming components (transformers).
A substation switching network (SSN) can be described by a model organized in a tri-level hierarchical structure. Thus, the knowledge base of the expert system is constructed according to the model. The switching configuration shown in Fig. 2 is used as an example [3,10].
2.
3.
Nodes Input nodes---nodes at the ends of each supply components. Examples are nodes 1, 2, 15 and 16. Output nodes---nodes at the ends of each load components. Examples are nodes 3, 8, 9 and 14. Branching nodes---joining nodes of circuit sections containing switching components. Examples are nodes 4,5 , 6,7,10,11,12 and 13. Branches Input branches---branches between two input nodes. SI
S2
s3
s4
""*~ OPENC.B.
7-
CLOSED ISOLATOR
-0-
OPEN ISOLATOR
-
TRANSFORMER
Fig. 2. A Substation Switching Configuration
Fig. 3. A Topologic Graph of the Switching Configuration.
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Examples are s l-s4.
(2)
If a dead node (N) has several adjacent live nodes (NI, ... , Ni), its estimate E(N) is
(3)
Generally, if a dead node (N) has several adjacent nodes (Ni, ... , Ni), its estimate E(N) is
Output branches---branches between two output nodes.
E(N)=min(cost(N,Ni))
Examples are fl- f4. loint branches---branches between two branching nodes. Examples are branches 4, 5, 6, 8, 9, 11, 12 and 13. Obviously, in the TG of a SSN, nodes which are at connected status with branches between them at connected status form a sub-graph. This is called a connecLed distribution (CD) of the TG. Also, nodes at live status and branches between them which are at connected status fom1 a subgraph. This is called a live distribution (LD) of the TG. For example, nodes (I , 2, 5, 6, 7, 8, 12, 13, 14 and 16) and branches (I, 2, 5, 6, 7, 9, 13, 14 and 16) form a CD and also a LD of the TG in Fig. 3. PROBLEM SOLVING METHODS
E (N) = min ( cost (N, Ni ) + E (Ni) ) (2) where E(Ni) is the estimate of the ith adjacent node, as shown in Fig. 4. For example, E(5) = 0, E(l2) = 0, E(4) = 1, E(ll) = 1, E(l0)=2 in Fig. 3. Sorting Based on Rules
After the devices used for sequence switching have been selected, an ordering relation in their operations must be determined. For this, a hierarchical tri-Ievel sort is followed according to safety operation rules and human operator's experience. Some examples of the rules are:
Problem solving techniques used in the expert system include task decomposition, determination of branch costs and heuristic estimates, sorting based on rules, and determination of minimum spanning tree. Task Decomposition Switching operation tasks are to place into or remove from service one or several load components, supply components, switching devices, bus-bars, or other facilities, and to connect two live components with each other in a SSN, or disconnect them from each other. In a TG of SSN, these tasks can be classified as follows: TYPE I: connect a dead node. TYPE II: connect a group of dead nodes having interconnecting branches. TYPE Ill: disconnect a live node. TYPE IV: disconnect a group of live nodes. Connecting or disconnecting rwo live parts in the TG is similar to TYPE II or IV. A synchrocheck must be made at fixed breakers for the connection. Obviously, these tasks can be described by two cases: energization and deenergization. Branch Cost The operation cost of sequence switching is calculated on the basis of branch cost. The number of switching operations is used. The cost of switching operations must be attached to all branches in the TG of the SSN. The two subclassifications used are connection and disconnection cost. Based on a given existing switching configuration, the branch costs of the TG are deduced according to the following principles: (1)
(2)
(1)
The costs used for switching-on/off of a switching device may be chosen by the users. (In this example these costs are assumed equal.)
1. (a)
Sorting branches In the implementation of the energization task for two branches in an optimal path, the branch nearest to the live goal node is selected before the other.
(b)
In the implementation of the deenergization task, branches with lower voltage levels are selected before those at higher voltage levels.
2. (a)
Sorting switching components In the implementation of the energization task, switching devices in a branch must be closed in the following sequence: isolators nearest to the live goal node, isolators farthest from the goal node, and then the circuit breaker.
(b)
In the implementation of the deenergization task, switching devices in a branch must be opened in the following sequence: the circuit breaker, isolators nearest to the branch node to be deenergized, then isolators farthest from the node.
3. (a)
Insertion sort In the implementation of the energization task, all branches on both sides of the optimal path must be disconnected first to avoid changing the electrical status of components unrelated to the intended goal.
(b)
In the implementation of the deenergization task, all live nodes immediately connected with nodes to be deenergized and unrelated to the task must be first reconnected and energized through some transition branches.
(c)
In the implementation of the energization task, the last branch energized must not consist of a single isolator only. Its operation sequence mu st precede the nearest branch containing a circuit breaker. Minimum Spanning Tree
The branch connection cost is the sum of switching-on costs of all devices in the branch.
The branch disconnection cost is the sum of switchingoff costs of all devices in the branch. Heuristic Estimates
(3)
Consider the complex task of connecting a group of dead nodes to a LD. The best approach is to first connect one of the nodes to the LD, and then to connect each node through branches such that the sum of the branch costs is minimum. An approach to this implementation is a minimum spanning tree (MST) consisting of the group of dead nodes and these branches. A spanning tree of a graph is a subgraph of the graph such that: (1) it contains all nodes of the graph ,
Finding optimal sequence switching in a TG is a kind of graph search. This typically leads to the problem of combinatorial complexity due to the proliferation of alternatives. Against this problem, a heuristic searching method---Best-First search is used [11]. Information used in the method is represented by numerical heuristic estimates for the nodes in the TG. Such an estimate indicates how promising the node is with respect to reaching a goal node. Thus, the search continues from the most promising node.
(2) (3)
it is connected,
it does not contain a loop. Among all spanning trees in the graph, a MST has minimal sum of connection costs for all its branches. KNOWLEDGE BASE A knowledge base in the expert system is a source of domain knowledge used in decision making of the substation sequence switching problem.
Heuristic estimates are called "estimates for energization (EE)". The estimates, E, for all dead nodes in the TG can be determined in the following manner. (I) Assume the EE of a live node equals zero, and the EE of a dead end-node (or leaf node) is infinite (in fact, a large positive integer).
225
Information in knowledge base has two forms---facts and rules. 1. Fact base It is a collection of FACf statements. Knowledge relates to the problem domain, and provides dynamic modeling of structure and status of the SSN in a hierarchical structure. The following are stored in the fact base: (a) factual knowledge on structure at the component level, branch level,
by actively using the knowledge base to decide (a) how to apply the facts and rules in the knowledge base to infer new knowledge and (b) how to interact with the user. Structure The inference engine consists of modular procedures in PROLOG, as shown in Fig. 5. By data-driven and forward chain methods, the following modular procedures are directly or recursively called according to implementation requirements in a problem-solving reasoning process: (1) Task Scheduler (TS)---determine different reasoning courses according to given switching operation task.
(b)
factual knowledge on connected status and electrical live/dead status,
(2)
(c)
factual knowledge on the TG,
Knowledge Organization
Optimal Path Search (OPS)---search for an optimal path from a starting node to a goal node in the TG. (3) Branches List Form-I (BLF- I)---a branch sorting procedure to form an available branches sequence for the energization task.
(d)
factual heuristic knowledge on branch costs and estimates for cnergization. Some examples of the FACT statements in Prolog are: (1) "isolator(i3, il03, open, normal)" means: an isolator called "i103" has a serial number "i3", is open and closed in normal operation. (2)
"branch(bran7, [n7, n8J, [b5, i6J, connected, joint-b)" means: a joint branch called "bran7" which is at connected status has two end-nodes "n7" and "n8", contains a breaker "b5" and an isolator "i6".
Branches List Form-I! (BLF-II)---a branch sorting procedure to form an available branches sequence for the deenergization task.
(5)
Components List Form (CLF)---a sorting procedure to present a sequence of switching operations (SO).
(6)
Minimum Spanning Tree Determination (MSTD).
(7) Task Driving-Type I (TD-TI). (8)
"branch-cost(bran15, 2, 0)" means: branch 15 has a connection cost of "2" and a disconnection cost of "0". 2. Rule base A rule base consists of IF-THEN statements. Knowledge in the rule base is used to describe relations of status in the SSN and basic reasoning, such as: (a) rules to deduce connected status and live/dead status at the branch level and network level, (b) rules to determine the CD and LD, (3)
Task Driving-Type IT (TD-TII).
(9) Task Driving-Type III (TD-TIII). (10) Task Driving-Type IV (ID-TIV). Basic Strategies I.
Task detennination The TS procedure is called to implement a given task of SO, and it performs the following items in sequence: (1) determine a (or group of) keyword(s) from the name(s) of main component(s) in the task, (2) determine by search a branch containing the component, or a group of the branches,
(c)
rules to calculate branch costs and determine estimates for energization. Some examples of the IF-THEN rules in Prolog are: (1) "branch-state(X, disconnected) branch(X,Switchlist,_,_), member(Y, Switchlist), switch-state(Y, open)." means: a branch X is at disconnected status if examination of the list of switches for branch X has a switch Y which is open.
determine an end node of the branch as a starting node for the task, or a group of starting nodes. 2. Search for a Path The OPS procedure searches [or an optimal path from the starting node to a live goal node in the TG of the SSN, and it performs the following items in sequence. (a) From the starting node, the adjacent node which is on an optimal path and nearest to a live goal node can be determined by use of the starting node's estimate. (3)
"branch-con-cost(X,N) :- branch-state(X,disconnected), branch(X,_, Switchlist,_,J, Length(Switchlist, N)." means: the connection cost of a branch X is N if the branch is at disconnected status and the list of switches for branch X includes N switches. (3) "node-state(X,live) connected(X,Y), node(Y,_,.:.., input-n)." means: a node X is live if X is connected to an input node Y. Features The knowledge base has the following features: (2)
(1)
(4)
(b) The branch between the starting node and the adjacent node is put onto a list "Branches List of Optimal Path"(BLOP). (c)
The search proceeds from the found adjacent node toward the goal node using the found node's estimate. (d) The goal node is reached. The BLOP is generated in this process. It is completed at the end of the search because the branch immediately connected to the goal node is the last member of the list. 3. Sorting Sorting is used to generate a list of switching devices into tasks of TYPE I, 1I after an optimal path has been found. A. Forming "Sequential Branches List"(SBL) All branches between the dead nodes and the optimal path have to be disconnected first to avoid connecting adjacent dead nodes. For this, the BLF-I procedure is called to perform the following steps in sequence: (1) Invert the BLOP, so the branch connected to the goal node on the path occupies the first position on the inverted list.
It is easy to extend or modify the contents of the knowledge base when the SSN is expanded, its configUJation or equipment status changed. In this way, the knowledge base can track the status of the SSN.
(2) The knowledge base is modularized, and independent of other parts of the expert system. Thus, it is easy to build. Its contents can be accessed and used by other substation software. (3) The knowledge base is easy to understand because the statements in it are written in PROLOG, a naturallanguage-like, artificial intelligence language based on predicate calculus. INFERENCE ENGINE The inference engine is used to run the expert system
(2) Check the first node nearest the goal node in the path
226
I;' rt
CD
"...
. n
starting node ............
et
disconnected.............. branch
"
'--'
Fig. 6. Insertion of Branches 1,2,3 and 4 Fig.
(3 )
s.
nodes have to be disconnected. and the live adjacent nodes must remain live after the disconnection. The TD- TIll procedure is called to perfom1 the following steps:
Structure of the Inference Engine
shown in Fig. 6. Insert branches between the node and its adjacent nodes. which are not in the path. after the first branch in the inverted list. Check the next node.
Repeat steps (2) and (3) until the starting node is checked. In thi s way. a complete SBL used for sequence switc hin g is completed. B. Forming "Sequential Component s Li st (SCLl" The CLF procedure is called to sort th e switching-on order for devices in each branch in the SBL according to the rules used for sorting. The completed SCL presents the output res ult of the sequence switching to the task.
(a)
the BLF-II procedure is called to form a "Neighbouring Branches List (NBL)" including all branches between the starting and all live adjacent nodes.
(b)
check the adjacent nodes under the assumption that all branches in the NBL are disconnected. and determine all nodes which become dead. the OPS procedure searches for an optimal path from the determined nodes.
(4)
(c) (d)
form a "Transition Branches List (TBL)" from the branches between the determined and the starting nodes.
Task Reasoning
(e)
append the TBL to the NBL and form a SBL.
After completion of ta sk determination. reasoning is continued until an available sequence of SO is presented in the form of SCL.
(t)
the CLF procedure is called to form a SCL.
I.
4.
Reasoning steps for ta sks of TYPE IV The reasoning used to disconnect a group of live starting nodes is similar to TYPE III tasks except that the SCL mayor may not contain the switching for connected branches between all nodes in the group because of different operational requirement s. MAN-MACHINE INTERACTION
Reasoning steps for tasks of TYPE I The TO-TI procedure performs the following steps:
(a)
the OPS procedure searches for an optimal path.
(b)
the BLF-I procedure forms a SBL.
(c)
the CLF procedure forms a SCL.
Reasonin g ste ps for task s of TYPE [[ The TO-Tll procedure is called to followin g steps:
The expert system includes a friendly user interface for smooth interaction between the expert system and the user. It also provides the user with an insight into the problemsolving process used by the inference engine.
2.
(a)
perform
the
compare the estimate s of the nodes in the starting node group. and select the node with the minimal estimate. for example. node N2 in Fig . 7.
(b)
the OPS. BLF-I and CLF procedures fom1 a "Part Sequ ential Component Li st (PS CL)" .
(c)
the MSTO procedure form s a "Minimum Spanning Tree Component List (MSTCLl" for switching devices in the branches between the starting nodes.
(d) 3.
This man-machine interaction includes the functions:
1.
Handling keyboard and screen input and output.
2.
Supporting smooth dialogue between the user and the expert sys tem. Recognizing errors or cognitive mi smatch between the user and the system.
3.
append the PSCL to the MSTCL in the selected node. and form a SCL. Reasoning steps for tasks of TYPE III
4.
Incorporating new knowledge or new problem-solving skills into the system.
5.
Providing user-friendly features by easy interaction in PROLOG.
To di sconnect a live startin g node from a LO. all branches b( ~ ween the nod e and each of its all live adjacent E(N)
E(NI)
@ E(N2)
Fig. 4. Heuristic estimates
Fig. 7. Selection of a starting node '2.27
As an assistant in decision making, the expert system presents a sequence of switching operations as a proposal to operators. The expert system is capable of answering the user's question in the following way: user's question: How did you reach this conclusion?
CONCLUSIONS
Application of expert system technology to a computerbased integrated control and protective system will benefit substation automation. Sequence switching based on expert systems is a promising way to improve its implementation because of its logicality and dependency on experience.
system' answer: This conclusion is deduced from rule A that is deduced from rule B that is deduced from rule C .... With some insight into the system's reasoning process, operators are able to compare the system's proposed sequence switching against their experience. APPLICATION EXAMPLES
The paper formulates the optimal sequence switching problem, presents the knowledge-based modeling of a substation switching network and a set of intelligent problem solving methods for sequence switching, and develops an expert system used to assist operators in sequence switching decisions. The expert system consists of three parts: (1) a knowledge base for a tri-Ievel hierarchical model of substation switching network which features ease of construction, modification and comprehension; (2) an inference engine based on intelligent problem solving methods, such as task decomposition, determination of branch cost and heuristic estimates, sorting using rules, and a minimum spanning tree;
Examples are presented to illustrate the application of the developed expert system. The examples are based on a substation switching network in Fig. 2 and its topologic graph in Fig. 3. Their sequences of switching operations are given by the expert system. Each example is based on an existing switching configuration, or a switching configuration determined by switching operations in the former example. Example l. Task:
(3) put feeder fl in service
Starting node: node 3 Live dis. nodes: 1,2,5,6,7,8,12,13,14,16 Sequence:
a user interface which caters to smooth man-machine interaction and provides the user with an insight into the problem solving process.
The application examples of the expert system show encouraging results in determining operations required to accomplish engineering tasks.
1126,1103, B120
Example 2. Task:
REFERENCES
put supply s3 in service
[1]
G. S. Hope and B. J. Cory, "Development of Digital Computer Programs for the Automatic Switching of Power Systems Networks", IEEE Trans. on PAS, V.87, N.7, July 1968, pp. 1587-1599.
[2]
G. H. Couch, I. F. Morrison, "Substation SwitchingAn Approach to the Determination of Optimal Sequence", PSCC Proc. V.I!, Grenoble, Sept. 11-16, 1972, Paper No. :2.1/l.
[3]
A. Traca-de-Almeida, "Substation Interlocking and Sequence Switching Using a Digital Computer", IEEE Trans. on PAS, V.loo, N.6, July 1981, pp. 3002-3007.
[4]
K.
[5]
E. N. Dialynas, A. V. Machias, "Interactive Modeling of Substation Switching Operations Following a Failure Event", lEE Proc. V.134, Pt.C, No. 2, March 1987, pp. 153-16l.
[6]
B. F. Wollenberg, Tochiaki Sajaguchi, "Artificial Intelligence in Power System Operations", Proc. of the IEEE, V. 75, N. 12, December 1987, pp. 1678-1685.
[7J
Z. Z. Zhang, G. S. Hope and O. P. Malik, "Expert Systems in Electric Power Systems: A Bibliographic Survey", IEEE Power Engineering Society Winter Meeting, New York, Jan. 29 - Feb. 3, 1989, Paper No.: 89 WM 212-2 PWRS.
Task: take transformer S6T2 out of service Starting node: node 6
[8]
Intelligent, Expandable Program for Power System Trouble Analysis", IEEE Trans. on Power Systems, V. PWRS-I, n.3, August 1986, pp. 182-187.
live dis. nodes: 1,2,3,4,5,6,7,9,10,11,12,13,15,16.
[9]
W. F. Clocksin, C. S. Mellish, "Programming in Prolog", Springer-Verlag, Berlin, 1984.
Starting node:
node 15
Live dis. nodes: 1,2,3,4,5,6,7,8,12,13,14,16. Sequence:
B380, 1313, B340(synchrochecking)
Example 3. Task:
put feeder f3 in service
Starting node: node 9 Live dis. nodes: 1,2,3,4,5,6,7,8,11,12,13,14,15,16. Sequence:
1326, B130, 1303, B320
Example 4. Task: take feeder f2 out of service Starting node: node 8 live dis. nodes: 1,2,3,4,5,6,7,8,11,12,13,14,15,16. Sequence:
B220,1203
Example 5. Task: take feeder f4 out of service Starting node: node 14 live dis. nodes: 1,2,3,4,5,6,7,9, 10,11, 12, 13, 14, 15, 16. Sequence: B420, 1403 Example 6.
Sequence:
B120, B240, B280, 1213, 1226
P. Brand, J. Kopainsky and W. Wimmer, "Topology-Based Interlocking of Electrical Substations", IEEE Trans. on Power Delivery, V.PWRD-1, N.3, July 1986, pp. 118-126.
[10] G. P. Hutchinson, "Interlocking in Large Electricity Supply Substations---A Fundamental Approach", Proc. lEE, Vol. 113, No. 6, June 1966, pp. 1063-1074. [11] Judea Pearl, "Heuristics: Intelligent Search Strategies for Computer Problem Solving", Addison-Wesley Publishing Company, California, 1984.
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