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Power system control using distributed and hierarchical problem solving
Power system control using distributed and hierarchical
problem solving Naoki Kobayashi, Hiroshi Okamoto, Akihiko Yokoyama and Yasuji Sekine Department of Electrical Engineering, The University of Tokyo, 7-3-1. Hongo, Bunkyo-ku. Tokyo. 113 Japan
This paper proposes an expert system which is designed to relieve transmission line overloads in electric power systems using two kinds of heuristic approaches: cooperative distributed problem solving (CDPS) and hierarchical problem solving (HPS). CDPS is a problem-solving technique using distributed, divided and roughly connected knowledge bases. H P S uses hierarchically divided knowledge bases. Both techniques start with local problem solving in each knowledge base followed by the expansion of the problem-solving area by incorporating the knowledge bases. Abilities of three kinds of systems, namely CDPS, H P S and the conventional approach using centralized problem solving, are evaluated using the IEEE 30-bus test system and the New England 39-bus test system. As a result, the two-level hierarchical system is proved to be the most adequate for the New England 39-bus test system. Keywords: expert system, cooperative distributed problem solving, hierarchical problem solving, transmission line overload relief, switching operation, generator redispatching, object-oriented language, system evaluation
I. I n t r o d u c t i o n Recently there have been many applications of knowledgebased technology such as expert systems to various kinds of industries. In contemporary electric power systems too, many prototype expert systems have been developed and some of them have been put into practical use. In general, the application of expert systems to power systems is becoming very popular. This is partly because the processing time to solve a problem is expected to become shorter and partly because the quality of the solution is expected to become better than that obtained by human experts. In practice, however, it is not easy to realize the above expectations. To solve the difficulty, Received 30 October 1991 ; revised 13 January 1992
Vol 14 No 213 April/June 1992
many new knowledge-based techniques have been proposed for improving the processing time and the quality of the solution utilizing the experience of expert system development. Electric power systems are becoming so large and so complex that conventional control schemes, which process all the components of the system by a single processor, are not always adequate in the light of control efficiency and the reliability of the control procedure. To solve this kind of problem, a feasibility study of distributed and/or parallel processing using multiple processors for distributed and/or hierarchical control is currently attracting considerable attention 1. From these two viewpoints, two kinds of heuristics, cooperative distributed problem solving (CDPS) 2 and hierarchical problem solving (HPS) 3, have been applied to the expert systems of this paper aiming at improving the processing time and the quality of the solution. The transmission line overload relief problem is adopted as a specific problem in this paper. This is because the problem has so far been formulated into a mathematical programming problem like linear programming in the conventional method 4'5 and it has been difficult to reduce the processing time. The expert system with CDPS or HPS makes it possible to solve the overload relief problem by using parallel and/or distributed processing. The next section of this paper gives a general description of the overload relief problem and of the two heuristics adopted. Sections III and IV describe the proposed system precisely. In Section V, the proposed system is compared with the conventional approach using centralized problem solving. II. O v e r l o a d
relief problem
I1.1 Conventional approach Transmission line overload relief is considered as a means of either preventive control, such as contingency analysis in a sound state, or emergency control in an emergency
0142-0615/92/2/30189-10 © 1992 Butterworth-Heinemann Ltd
189
state, or restoration control in a restoration state. In the conventional mathematical programming approach, different objective functions are used depending upon the system states 4'5. For example, the sum of the fuel costs of generators is minimized at the stage of monitoring and preventive control of transmission line overload while the control strategy is set up to minimize the time to restore the system to a normal state in emergency control. In contrast, the sum of loads not restored is usually minimized in restoration control. There are two typical operations to remove overload without interrupting supply. One is generator redispatching with continuous variables such as the output powers from the generators; the other is switching operation of lines or busbars with discrete variables such as the on-off state of the transmission lines. In the mathematical programming approach, it is not easy to deal with continuous variables and discrete variables simultaneously, though it is not theoretically impossible. A different approach using expert system techniques 5~ does not usually ensure optimal operation to relieve overload. However, it often gives intuitively reasonable operations by using the knowledge of expert operators in control centres. Moreover, it is not difficult to deal with continuous variables and discrete variables simultaneously. In the proposed system, the switching operation is executed in advance of generator redispatching when transmission lines are overloaded. This is because the switching operation does not make the sum of the fuel costs of generators higher than generator redispatching 6. In the emergency state, the goal is not to find the optimal solution but to find the most feasible solution fast, especially if the system is used on a real-time basis. This is why the proposed system focuses on emergency control in a real-time environment. 11.2 Proposed approaches Cooperative distributed problem solving (CDPS) is a problem-solving technique using roughly connected knowledge bases as shown in Figure 1. Most of the processing time is spent not in communication inside the knowledge bases but for computer processing in each knowledge base. In the proposed approach, the distributed subsystems of a large-scale power system are considered as distributed knowledge bases. Each subsystem can relieve overload by operating control equipment in its own subsystem and can request cooperation from other subsystems, if the overload relief problem cannot be solved in its own subsystem. Each subsystem tends to be so independent of other subsystems that this problem-solving technique is suited to distributed and parallel processing. Another proposed idea, hierarchical problem solving (HPS) uses hierarchically-divided subsystems. As shown in Figure 2, each subsystem is regarded as a problemsolving area. Each low-level subsystem is under control of a high-level subsystem when cooperation among low-level ones is requested. Therefore the subsystems in the upper levels have higher abilities than those in the lower levels. This technique is also suited for distributed and parallel processing of the operation inside each lowest-level subsystem. Both these problem-solving techniques take the same actions when the control procedure is restricted to only one subsystem. However, when the problem-solving area has to be expanded beyond one subsystem, cooperation
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Total system
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among the low-level subsystems is carried out through the high-level subsystem in HPS.
III. Expert system configuration The proposed system is implemented by Symbolics Common LISP and Flavors (object-oriented language) on the Macintosh computer. The system uses an object-oriented knowledge representation model of the power system to make development of the system easy. II1.1 Object-oriented representation of power system Object-oriented knowledge representation is suited for modelling of a power system network and for simulation of switching operations or generator redispatching of the power system 8. Figure 3 shows a class hierarchy in an object-oriented model of the power system network. The network consists of three kinds of components. One is a source which represents generators and loads; the second is a node representing buses; the third is a branch which represents line groups defined as a set of lines connecting the common two buses to each other. In addition to the objects representing the real equipment of the network shown in Figure 3, which are called equipment objects, the following objects are introduced in order to control the equipment objects in Figure 3. These control objects are shown in Figure 4. II1.1.1 Block. A block is part of a network. It consists of subsets of buses, lines (line groups), generators and
Electrical Power & Energy Systems
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operations inside the subsystem, does it begin cooperation among the subsystems. This means an expansion of the problem-solving area. Load flow calculation of the whole system is also necessary for determining the flow through each transmission line. Therefore we perform a load flow calculation routine without using the knowledge-based system represented by objects. Both of them are connected through a load flow calculation interface which gathers the information from each object system and transfers the results of the load flow calculation to the object systems. The results of the load flow calculation are used to decide the marginal flow of line groups or the amount of generator output change. The process of the objects representing subsystems begins with the receiving of a message.
IV. Solving procedure I (~-)
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This section describes how to determine the operation of the proposed system to relieve transmission line overload. Before the precise description, 'job' is defined as a unit of process created by the request for overload relief. A job is divided into two parts: operation inside the subsystem and cooperation among subsystems. The execution of the jobs results in the operations needed for overload relief. All the jobs are executed independently of each other and often in parallel,
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loads connected to buses in the block. The proposed system uses two kinds of block: the power supply block and the load block. Blocks are created dynamically when they are needed and are thrown away when no longer needed.
II1.1.2 Subsystem and total system. A subsystem is not only a part of the network but also shows a knowledge base for problem solving. As shown in Section II, the whole power system is divided distributively or hierarchically for using CDPS or HPS respectively. In addition, the subsystems are supposed to be handled in parallel. In this paper, one distributed processor is assumed to be allocated to each subsystem. At present, however, all of the subsystems are implemented in a single processor with object-oriented knowledge representation. The total system is not only the total network but also shows a knowledge base used for HPS and centralized problem solving. It does not have the function of cooperation among subsystems. 111.2 System configuration Figure 5 shows the system configuration for CDPS and Figure 6 shows the data flow in HPS system. When each subsystem has a transmission line overload in itself, it begins the operation inside the subsystem independently. Only when it cannot relieve the overload by the
Vol 14 No 2/3 April/June 1992
system
Knowledge base represented as object Figure 5. System configuration Total
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191
IV.1 Operation inside subsystem The operation inside each subsystem is determined independently of other subsystems and is divided into three parts:
1 Operation within line-group (L1 job) energizes a de-energized line in the line group including the overloaded line. 2 Switching operation (GI job) connects the power supply block and load block by new paths. 3 Generator redispatching (G3 job or G4 job) reduces the generator loads in the power supply block (G3 job) or increases generator loads in the load block (G4 job). Figure 7 shows examples of an L1 job and a G1 job. A precise algorithm to search an effective line to be energized by a G1 job is described in Appendix I. The method to determine the changes of generator output powers in a power supply block by a G3 job is described in Appendix 2.
2
3 4
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IV.2 Cooperation among subsystems in CDPS A cooperative operation is divided into six parts as follows.
1 Request to neighbouring subsystems for generator load reduction (B1 job) is the request from the overloaded subsystem to the neighbouring subsystems connected
X Fault ~, Overload I-1 Open • Close
IV.3 Cooperation among subsystems in HPS As for the CDPS system, a cooperative operation is divided into six parts as follows.
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Figure 7. Examples of an L1 job and a G1 job
192
6
to the overloaded one for reducing the generator loads in the neighbouring ones and for transmitting the answer to the overloaded subsystem. Request to neighbouring subsystems for generator load increase (B2 job) is the request from the overloaded subsystem to the neighbouring subsystems for increasing the generator loads in the neighbouring ones and for transmitting the answer to the overloaded subsystem. Report means to report the results of operations inside the subsystem to the other subsystems. Interruption is a function such that if a new line is overloaded in another subsystem because of the results of the operation informed by report, the newly overloaded subsystem cancels the operation of the subsystem which has reported its results. Request to non-neighbouring subsystems.for generator load reduction (RS1 job) is the request from the overloaded subsystem to the other subsystems, which are not connected to the overloaded one directly but are connected to the neighbouring subsystems next to the overloaded one, for reducing the generator loads in the disconnected subsystems and for transmitting the answer to the overloaded subsystem. This operation is taken after the failure of a B1 job. Request to non-neighbourin9 subsystems.for generator load increase (RS2 job) is the request from the overloaded subsystem to the other subsystems, which are not connected to the overloaded one directly but are connected to the neighbouring subsystems next to the overloaded one, for generator load increase in the disconnected subsystems and for transmitting the answer to the overloaded subsystem. This operation is taken after the failure of a B2 job.
1 Request to an upper-level subsystem for generator load reduction (B1 job) is the request from the overloaded lowest-level subsystem to the closest upper-level subsystem connected to the overloaded one for generator load reduction in the upper-level subsystem and for transmitting the answer to the overloaded subsystem. 2 Request to an upper-level subsystem .for generator load increase (B2 job) is the request from the overloaded lowest-level subsystem to the closest upperlevel subsystem connected to the overloaded one for generator load increase in the upper-level subsystem and for transmitting the answer to the overloaded subsystem. 3 Report means to report the results of operations inside the subsystem to the upper-level subsystem. 4 Interruption is the same operation as that of the CDPS system. 5 Cooperation among upper-level subsystemsjbr generator load reduction (RS1 job) means to request from the overloaded lowest-level subsystem to the closest upperlevel subsystem connected to the overloaded one for cooperation among the upper-level subsystems. It aims at reducing the generator load in the closest upper-level subsystems which are not connected to the overloaded one, by coordinating the subsystems under the control of the upper-level subsystem. It also transmits the answer to the overloaded subsystem on request. This
Electrical Power & Energy Systems
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operation is taken after the failure of a B1 job. This operation is similar to a B1 job. However, the area of operation is not in the lowest-level subsystems but in the closest upper-level subsystems. Figure 8 shows the difference between a B1 job and a RS1 job. 6 Cooperation among upper-level subsystemsfor generator load increase (RS2 job) is the request from the overloaded lowest-level subsystem to the closest upperlevel subsystem connected to the overloaded one for cooperation among the upper-level subsystems. It aims at increasing the generator load in the closest upperlevel subsystems which are not connected to the overloaded one by coordinating the subsystems under the control of the upper-level subsystem. It also transmits the answer to the overloaded subsystem on request. This operation is taken after the failure of a B2 job. IV.4 Control strategy Control strategy 6 indicates how to decide the order of executing jobs. Figure 9 shows the control strategy which is constructed in the proposed system. Each box denotes a job. The numerical superscript on the box denotes the priority of the jobs to be executed when multiple jobs are feasible inside one subsystem at the same time. The arrow denotes the transition of feasible jobs for each overloaded transmission line. When multiple feasible operations are available in one job, the local optimal operation among these candidates is selected. For example, when multiple switching operations are available in one subsystem, the most effective line or line group is selected. The 'most effective' line is the one which when energized results in the largest reduction of overload current. For effective search, a heuristic value called 'node value' is used in searching the network (see Appendix 2).
Vol 14 No 2/3 April/June 1992
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evaluation
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As statedin SectionI, the processingtime and quality of the solution are important factors in evaluating the ability of the proposed system. It is also important to compare the conventional system with the newly developed system.
193
V.1 Effect of the number of subsystems on inference
be solved only by the operation inside a subsystem; and cooperative, solved by cooperation between subsystems in the CDPS or HPS system.
time This section compares inference times of control systems using CDPS, HPS and centralized problem solving. The IEEE 30-bus test system shown in Figure 10 is chosen as an example. The system is divided into two or three subsystems for CDPS or HPS. In this case, both parallel and sequential processing schemes are taken into account. Figure 11 shows the inference time from the input of transmission line trip data to the end of the relief operation without load flow calculation time. In this study, load flow calculation time is 0.72s in both sequential and parallel processing. Two kinds of contingencies are simulated: non-cooperative, that can
V.2 Effect of the depth of hierarchy on inference time
This section describes the effect of the depth of hierarchy in the HPS system, and the number of subsystems in the CDPS system, on the inference time. The New England 39-bus test system is chosen as an example, As shown in Figure 12, the system is divided into three subsystems for HPS with a hierarchy of two levels. The corresponding CDPS system is divided into subsystems 1, 2 and 3. For HPS with a hierarchy of three levels, the system consists of three middle-level sub-
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Figure 11. Inference times for I EE E 30- bus system (load flow calculation time excluded): (a) sequential processing; (b) parallel processing. ©, hierarchical, non-cooperative; • , distributed, non-cooperative; [ ] , hierarchical, cooperative; I , distributed, cooperative. 0 and • are almost overlaid in the figure
194
Electrical Power & Energy Systems
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in Figure 12. Figure 13 shows the inference time without load flow calculation time. The severity of fault on the horizontal axis is defined as follows.
Middle
High
Severity of foult
Figure 13. Inference times for New England 39-bus test system (load flow calculation time excluded). A, centralized; O, two-level hierarchical; 0, threelevel hierarchical; I-], distributed (divided into three); I , distributed (divided into six). 0 and [] are almost overlaid in the figure
systems and six end-level subsystem, la, lb, 2a, 2b, 3a and 3b. The CDPS system corresponding to the threelevel HPS system is divided into six subsystems. In this case, parallel processing at each level is taken into account. An example of the problem to be solved is shown
Vol 14 No 2/3 April/June 1992
• An overload of 'low severity' is one which is relieved only by the operation inside an end-level subsystem of the three-level HPS system or inside a subsystem of the CDPS system consisting of six subsystems. • An overload of'middle severity' is one which is relieved by the cooperative control of the end-level subsystems in the three-level HPS system or of the overloaded subsystem and its adjacent subsystems in the CDPS system consisting of six subsystems: in other words, an overload relieved by the operation inside a subsystem in the two-level HPS system or in the CDPS system consisting of three subsystems. • An overload of 'high severity' is one which is relieved by the cooperative control of the end-level subsystems in the two-level HPS system or of the overloaded subsystem and its adjacent subsystems in the CDPS system consisting of three subsystems. V.2 Comparison of solution In this section, the New England 39-bus test system is selected as an example. Twelve cases of single contingency and 105 cases of double contingency are simulated and the solutions obtained by CDPS, HPS and the centralized problem-solving systems are compared in Table 1. In the proposed expert systems, neither the fuel cost of generators nor the restriction on the load increase or decrease rate of the generator is taken into account. The quality
195
Table 1. Comparison of solutions
Same operation Same change of generator output power Smaller change of generator output power Greater change of generator output power Total cases
Two-level hierarchical system
Three-level hierarchical system
Distributed system divided into three
Distributed system divided into six
99 l0 6 2 117
81 17 6 13 117
71 14 9 23 117
27 29 8 61 117
of the solution is evaluated in the light of the amount of changes in generator output powers: the solution minimizing the total change of generator output power is considered to be the best solution. The meanings of the terms in Table 1 are as follows:
Table 2. Evaluation of performance
• Same operation means that the operations obtained by the CDPS or the HPS system are exactly the same as that obtained by the centralized problem-solving system. • Same change of generator output power means that the total change of generator output power obtained by the CDPS or HPS system is equal to that by the centralized problem-solving system, but the number or kind of generators to change the output power is different. • Smaller change of generator output power or Greater change of generator output power means that the total change of generator output power obtained by the CDPS or HPS system is less or more than that by the centralized problem-solving system.
Centralized system
It is seen from Table 1 that the two-level hierarchical system is superior to the other systems in the light of the quality of the solution. Table 2 shows the results of an evaluation of each problem-solving system from two aspects: processing time and quality of solution. It can be seen that the two-level hierarchical problem-solving system seems to be the best one for the New England 39-bus test system.
VII. Acknowledgement The authors acknowledge the financial support for this research from the Ministry of Education of Japan. Support and encouragement by Professor L. L. Grigsby of Auburn University in Alabama are highly appreciated.
Inference time Long (~0.6s) Two-level Short hierarchical system (~0.1 s) Three-level Short hierarchical system (~0.1 s) Distributed system Short divided into three (~0.1 s) Distributed system Intermediate divided into six ( ~ 0.2 s)
+ 4 cases - 5 to - 15 cases - 5 to - 15 cases - 5 3 cases
VIII. References 1 2
196
0 case
* Quality of solution=number of cases of 'smaller change of generation output power' - number of cases of "greater change of generation output power"
VI. Conclusions This paper has presented two kinds of new expert system technique, cooperative distributed problem solving and hierarchical problem solving. These techniques have been applied to a transmission line overload relief problem. Using the IEEE 30-bus test system and the New England 39-bus test system, they have been proved to reduce inference time by using distributed multiple processors in parallel as compared with conventional centralized problem solving. In addition, it has been made clear that the two-level hierarchical problem-solving system seems to be the most suitable for the New England 39-bus test system. Moreover it should be noted that the use of object-oriented representation and object-oriented language in this research makes it easy to develop the proposed expert system, to change or add data on the power system and to simulate distributed or parallel processing.
Quality of solution*
3 4
5 6
7
8
Wager, W R, Keyhani, A, Hao, S and Wong, T C 'A rulebased approach to decentralized voltage control' IEEE Trans. on PWRS Vol 5 No 2 (1990) pp643-651 Filman, R E and Friedman, D P Coordinated Computing McGraw-Hill Inc. (1984) M e s a r o v i c , M D, M a c k o , D and Takahara, Y Theory of Hierarchical Multilevel Systems Academic Press Inc. (1970) Van Amerongen, R A i and Van a e e t e r e n , H P "Security control by real power rescheduling, network switching and load shedding', CIGRE SC 32-02 (1980) Delfino, B e t al. 'Evaluating artificial intelligence applications for electric power systems: knowledge-based approaches to l i ne overload alleviation', CIGRE SC 38/39-07 (1990) Paillet, O and Dubost, L 'AMPERE: a knowledge-based system for network reconfiguration" Proc. First Syrup. on Expert System Applications to Power Systems, Stockholm, Helsinki (1988) pp 8 - 3 2 - 8 - 3 8 Y o k o y a m a , R, M a t s u m o t o , T, Niimura, T and Ueki, Y 'An expert system for interactive operation guidance in power system emergency control" Proc. Second Syrup. on Expert System Applications to Power Systems, Seattle, Washington, USA (1989) pp 348-353 Sekine, Y, Kato, M, Sakaguchi, T and Fukui, C 'An object-oriented approach to four applications', Expert System Applications in Power Systems, Prentice Hall (1990) pp 258 342
Electrical Power & Energy Systems
Appendix 1 The power supply block and load block are dynamically generated when job, except L1 job, is executed. The power supply block is generated from the starting node which lies upstream of the overloaded transmission line. It consists of a set of nodes which receive no load flow from nodes in the overloaded subsystem except generator nodes. However, the power supply block is able to receive a load flow from a node belonging to the other subsystem. Figure A 1 shows an example of a power supply block and a load block. The load block is generated from the starting node lying downstream of the overloaded line. No load flow is delivered from the load block to nodes in the overloaded subsystem except load nodes, but the load block is able to deliver a load flow to a node belonging to the other subsystem. An index called node value is introduced to indicate to what extent each node is responsible for the overload• This index is used to search a new path in a G1 job. The node value of a node in the power supply block indicates the ratio of the flow coming out of the node to the flow through the overloaded line. First, the node value of the upstream node of the overloaded transmission line is set at the amount of the flow of the overloaded transmission line. Second, the node value of each node belonging to the power supply block is calculated from Figure A2 and the following equation:
t ,oo.
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where V(no) is the node value of no,flOWo,t(nk)is the flow coming out of nk, and fog is the flow from no to nk.
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After obtaining the node values in the power block, a network search to find a new path in the G1 job begins. The algorithm is as follows. 1 Let n 1 be a node in the power supply block which has the biggest node value. 2 Let n o be a node, not belonging to the power supply block, which is connected to n 1 directly by one line group. 3 Let n 1 to nk be nodes in the power supply block connected to no by one line group. 4 Let the node value of no be vo. The value of vo is obtained from Figure A3 and Equation (2):
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The overloaded subsystem Figure A1. Power supply block and load block Vol 14 No 2/3 April/June 1992
vo=max{min{vj, v ~ } }
(A1.2)
where f j is the flow capacity of line group j, lj is the flow through line group j, Af is the overloaded flow, and v~ is the node value of node j. 5 Add node n o into power supply block. 6 If node n o belongs to the load block, both of the blocks are connected by the most effective path to alleviate the overload. If a de-energized line is included in the new path, the line is energized. If node n o does not belong to the load block, operations 1-6 are iterated until no no is found.
Appendix 2 After the failure of a G1 job, a G3 job to reduce the generator output power in the power supply block begins. To determine the amount of each generator output power
197
change in the power supply block, the overload relief coefficient of each generator in the power supply block is used. This is the ratio of the change of flow of the overloaded transmission line to the output change of the generators. It is obtained from the DC load flow calculation (see Equation (A2.1)):
F °''
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where Apu is the load flow change of line group i, Apbj
198
is the change of injection power to node j, and aij is the overload relief coefficient of node j to line group i. Using this coefficient, the changes of generator output powers are given by Equation (A2.2).
AGj=
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~=l[(a.--atd)2"Gj]
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where a~a is the overload relief coefficient of the downstream node of the overloaded line, Gj is the generator output power of node j in the power supply block, AG~ is the generator output power change of node j in the power supply block, Afis the overload flow, and is a loss factor (..~0.05-0.1).
Electrical Power & Energy Systems
problem solving Naoki Kobayashi, Hiroshi Okamoto, Akihiko Yokoyama and Yasuji Sekine Department of Electrical Engineering, The University of Tokyo, 7-3-1. Hongo, Bunkyo-ku. Tokyo. 113 Japan
This paper proposes an expert system which is designed to relieve transmission line overloads in electric power systems using two kinds of heuristic approaches: cooperative distributed problem solving (CDPS) and hierarchical problem solving (HPS). CDPS is a problem-solving technique using distributed, divided and roughly connected knowledge bases. H P S uses hierarchically divided knowledge bases. Both techniques start with local problem solving in each knowledge base followed by the expansion of the problem-solving area by incorporating the knowledge bases. Abilities of three kinds of systems, namely CDPS, H P S and the conventional approach using centralized problem solving, are evaluated using the IEEE 30-bus test system and the New England 39-bus test system. As a result, the two-level hierarchical system is proved to be the most adequate for the New England 39-bus test system. Keywords: expert system, cooperative distributed problem solving, hierarchical problem solving, transmission line overload relief, switching operation, generator redispatching, object-oriented language, system evaluation
I. I n t r o d u c t i o n Recently there have been many applications of knowledgebased technology such as expert systems to various kinds of industries. In contemporary electric power systems too, many prototype expert systems have been developed and some of them have been put into practical use. In general, the application of expert systems to power systems is becoming very popular. This is partly because the processing time to solve a problem is expected to become shorter and partly because the quality of the solution is expected to become better than that obtained by human experts. In practice, however, it is not easy to realize the above expectations. To solve the difficulty, Received 30 October 1991 ; revised 13 January 1992
Vol 14 No 213 April/June 1992
many new knowledge-based techniques have been proposed for improving the processing time and the quality of the solution utilizing the experience of expert system development. Electric power systems are becoming so large and so complex that conventional control schemes, which process all the components of the system by a single processor, are not always adequate in the light of control efficiency and the reliability of the control procedure. To solve this kind of problem, a feasibility study of distributed and/or parallel processing using multiple processors for distributed and/or hierarchical control is currently attracting considerable attention 1. From these two viewpoints, two kinds of heuristics, cooperative distributed problem solving (CDPS) 2 and hierarchical problem solving (HPS) 3, have been applied to the expert systems of this paper aiming at improving the processing time and the quality of the solution. The transmission line overload relief problem is adopted as a specific problem in this paper. This is because the problem has so far been formulated into a mathematical programming problem like linear programming in the conventional method 4'5 and it has been difficult to reduce the processing time. The expert system with CDPS or HPS makes it possible to solve the overload relief problem by using parallel and/or distributed processing. The next section of this paper gives a general description of the overload relief problem and of the two heuristics adopted. Sections III and IV describe the proposed system precisely. In Section V, the proposed system is compared with the conventional approach using centralized problem solving. II. O v e r l o a d
relief problem
I1.1 Conventional approach Transmission line overload relief is considered as a means of either preventive control, such as contingency analysis in a sound state, or emergency control in an emergency
0142-0615/92/2/30189-10 © 1992 Butterworth-Heinemann Ltd
189
state, or restoration control in a restoration state. In the conventional mathematical programming approach, different objective functions are used depending upon the system states 4'5. For example, the sum of the fuel costs of generators is minimized at the stage of monitoring and preventive control of transmission line overload while the control strategy is set up to minimize the time to restore the system to a normal state in emergency control. In contrast, the sum of loads not restored is usually minimized in restoration control. There are two typical operations to remove overload without interrupting supply. One is generator redispatching with continuous variables such as the output powers from the generators; the other is switching operation of lines or busbars with discrete variables such as the on-off state of the transmission lines. In the mathematical programming approach, it is not easy to deal with continuous variables and discrete variables simultaneously, though it is not theoretically impossible. A different approach using expert system techniques 5~ does not usually ensure optimal operation to relieve overload. However, it often gives intuitively reasonable operations by using the knowledge of expert operators in control centres. Moreover, it is not difficult to deal with continuous variables and discrete variables simultaneously. In the proposed system, the switching operation is executed in advance of generator redispatching when transmission lines are overloaded. This is because the switching operation does not make the sum of the fuel costs of generators higher than generator redispatching 6. In the emergency state, the goal is not to find the optimal solution but to find the most feasible solution fast, especially if the system is used on a real-time basis. This is why the proposed system focuses on emergency control in a real-time environment. 11.2 Proposed approaches Cooperative distributed problem solving (CDPS) is a problem-solving technique using roughly connected knowledge bases as shown in Figure 1. Most of the processing time is spent not in communication inside the knowledge bases but for computer processing in each knowledge base. In the proposed approach, the distributed subsystems of a large-scale power system are considered as distributed knowledge bases. Each subsystem can relieve overload by operating control equipment in its own subsystem and can request cooperation from other subsystems, if the overload relief problem cannot be solved in its own subsystem. Each subsystem tends to be so independent of other subsystems that this problem-solving technique is suited to distributed and parallel processing. Another proposed idea, hierarchical problem solving (HPS) uses hierarchically-divided subsystems. As shown in Figure 2, each subsystem is regarded as a problemsolving area. Each low-level subsystem is under control of a high-level subsystem when cooperation among low-level ones is requested. Therefore the subsystems in the upper levels have higher abilities than those in the lower levels. This technique is also suited for distributed and parallel processing of the operation inside each lowest-level subsystem. Both these problem-solving techniques take the same actions when the control procedure is restricted to only one subsystem. However, when the problem-solving area has to be expanded beyond one subsystem, cooperation
190
Total system
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among the low-level subsystems is carried out through the high-level subsystem in HPS.
III. Expert system configuration The proposed system is implemented by Symbolics Common LISP and Flavors (object-oriented language) on the Macintosh computer. The system uses an object-oriented knowledge representation model of the power system to make development of the system easy. II1.1 Object-oriented representation of power system Object-oriented knowledge representation is suited for modelling of a power system network and for simulation of switching operations or generator redispatching of the power system 8. Figure 3 shows a class hierarchy in an object-oriented model of the power system network. The network consists of three kinds of components. One is a source which represents generators and loads; the second is a node representing buses; the third is a branch which represents line groups defined as a set of lines connecting the common two buses to each other. In addition to the objects representing the real equipment of the network shown in Figure 3, which are called equipment objects, the following objects are introduced in order to control the equipment objects in Figure 3. These control objects are shown in Figure 4. II1.1.1 Block. A block is part of a network. It consists of subsets of buses, lines (line groups), generators and
Electrical Power & Energy Systems
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operations inside the subsystem, does it begin cooperation among the subsystems. This means an expansion of the problem-solving area. Load flow calculation of the whole system is also necessary for determining the flow through each transmission line. Therefore we perform a load flow calculation routine without using the knowledge-based system represented by objects. Both of them are connected through a load flow calculation interface which gathers the information from each object system and transfers the results of the load flow calculation to the object systems. The results of the load flow calculation are used to decide the marginal flow of line groups or the amount of generator output change. The process of the objects representing subsystems begins with the receiving of a message.
IV. Solving procedure I (~-)
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This section describes how to determine the operation of the proposed system to relieve transmission line overload. Before the precise description, 'job' is defined as a unit of process created by the request for overload relief. A job is divided into two parts: operation inside the subsystem and cooperation among subsystems. The execution of the jobs results in the operations needed for overload relief. All the jobs are executed independently of each other and often in parallel,
calculatio~
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Figure 4. Control objects
Non-objectsystem
j
loads connected to buses in the block. The proposed system uses two kinds of block: the power supply block and the load block. Blocks are created dynamically when they are needed and are thrown away when no longer needed.
II1.1.2 Subsystem and total system. A subsystem is not only a part of the network but also shows a knowledge base for problem solving. As shown in Section II, the whole power system is divided distributively or hierarchically for using CDPS or HPS respectively. In addition, the subsystems are supposed to be handled in parallel. In this paper, one distributed processor is assumed to be allocated to each subsystem. At present, however, all of the subsystems are implemented in a single processor with object-oriented knowledge representation. The total system is not only the total network but also shows a knowledge base used for HPS and centralized problem solving. It does not have the function of cooperation among subsystems. 111.2 System configuration Figure 5 shows the system configuration for CDPS and Figure 6 shows the data flow in HPS system. When each subsystem has a transmission line overload in itself, it begins the operation inside the subsystem independently. Only when it cannot relieve the overload by the
Vol 14 No 2/3 April/June 1992
system
Knowledge base represented as object Figure 5. System configuration Total
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191
IV.1 Operation inside subsystem The operation inside each subsystem is determined independently of other subsystems and is divided into three parts:
1 Operation within line-group (L1 job) energizes a de-energized line in the line group including the overloaded line. 2 Switching operation (GI job) connects the power supply block and load block by new paths. 3 Generator redispatching (G3 job or G4 job) reduces the generator loads in the power supply block (G3 job) or increases generator loads in the load block (G4 job). Figure 7 shows examples of an L1 job and a G1 job. A precise algorithm to search an effective line to be energized by a G1 job is described in Appendix I. The method to determine the changes of generator output powers in a power supply block by a G3 job is described in Appendix 2.
2
3 4
5
IV.2 Cooperation among subsystems in CDPS A cooperative operation is divided into six parts as follows.
1 Request to neighbouring subsystems for generator load reduction (B1 job) is the request from the overloaded subsystem to the neighbouring subsystems connected
X Fault ~, Overload I-1 Open • Close
IV.3 Cooperation among subsystems in HPS As for the CDPS system, a cooperative operation is divided into six parts as follows.
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Figure 7. Examples of an L1 job and a G1 job
192
6
to the overloaded one for reducing the generator loads in the neighbouring ones and for transmitting the answer to the overloaded subsystem. Request to neighbouring subsystems for generator load increase (B2 job) is the request from the overloaded subsystem to the neighbouring subsystems for increasing the generator loads in the neighbouring ones and for transmitting the answer to the overloaded subsystem. Report means to report the results of operations inside the subsystem to the other subsystems. Interruption is a function such that if a new line is overloaded in another subsystem because of the results of the operation informed by report, the newly overloaded subsystem cancels the operation of the subsystem which has reported its results. Request to non-neighbouring subsystems.for generator load reduction (RS1 job) is the request from the overloaded subsystem to the other subsystems, which are not connected to the overloaded one directly but are connected to the neighbouring subsystems next to the overloaded one, for reducing the generator loads in the disconnected subsystems and for transmitting the answer to the overloaded subsystem. This operation is taken after the failure of a B1 job. Request to non-neighbourin9 subsystems.for generator load increase (RS2 job) is the request from the overloaded subsystem to the other subsystems, which are not connected to the overloaded one directly but are connected to the neighbouring subsystems next to the overloaded one, for generator load increase in the disconnected subsystems and for transmitting the answer to the overloaded subsystem. This operation is taken after the failure of a B2 job.
1 Request to an upper-level subsystem for generator load reduction (B1 job) is the request from the overloaded lowest-level subsystem to the closest upper-level subsystem connected to the overloaded one for generator load reduction in the upper-level subsystem and for transmitting the answer to the overloaded subsystem. 2 Request to an upper-level subsystem .for generator load increase (B2 job) is the request from the overloaded lowest-level subsystem to the closest upperlevel subsystem connected to the overloaded one for generator load increase in the upper-level subsystem and for transmitting the answer to the overloaded subsystem. 3 Report means to report the results of operations inside the subsystem to the upper-level subsystem. 4 Interruption is the same operation as that of the CDPS system. 5 Cooperation among upper-level subsystemsjbr generator load reduction (RS1 job) means to request from the overloaded lowest-level subsystem to the closest upperlevel subsystem connected to the overloaded one for cooperation among the upper-level subsystems. It aims at reducing the generator load in the closest upper-level subsystems which are not connected to the overloaded one, by coordinating the subsystems under the control of the upper-level subsystem. It also transmits the answer to the overloaded subsystem on request. This
Electrical Power & Energy Systems
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Figure8. B1 job and RS1 job Ocurrence of overlood
operation is taken after the failure of a B1 job. This operation is similar to a B1 job. However, the area of operation is not in the lowest-level subsystems but in the closest upper-level subsystems. Figure 8 shows the difference between a B1 job and a RS1 job. 6 Cooperation among upper-level subsystemsfor generator load increase (RS2 job) is the request from the overloaded lowest-level subsystem to the closest upperlevel subsystem connected to the overloaded one for cooperation among the upper-level subsystems. It aims at increasing the generator load in the closest upperlevel subsystems which are not connected to the overloaded one by coordinating the subsystems under the control of the upper-level subsystem. It also transmits the answer to the overloaded subsystem on request. This operation is taken after the failure of a B2 job. IV.4 Control strategy Control strategy 6 indicates how to decide the order of executing jobs. Figure 9 shows the control strategy which is constructed in the proposed system. Each box denotes a job. The numerical superscript on the box denotes the priority of the jobs to be executed when multiple jobs are feasible inside one subsystem at the same time. The arrow denotes the transition of feasible jobs for each overloaded transmission line. When multiple feasible operations are available in one job, the local optimal operation among these candidates is selected. For example, when multiple switching operations are available in one subsystem, the most effective line or line group is selected. The 'most effective' line is the one which when energized results in the largest reduction of overload current. For effective search, a heuristic value called 'node value' is used in searching the network (see Appendix 2).
Vol 14 No 2/3 April/June 1992
I
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Figure 9. Controlstrategy V.
System
evaluation
- comparative
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As statedin SectionI, the processingtime and quality of the solution are important factors in evaluating the ability of the proposed system. It is also important to compare the conventional system with the newly developed system.
193
V.1 Effect of the number of subsystems on inference
be solved only by the operation inside a subsystem; and cooperative, solved by cooperation between subsystems in the CDPS or HPS system.
time This section compares inference times of control systems using CDPS, HPS and centralized problem solving. The IEEE 30-bus test system shown in Figure 10 is chosen as an example. The system is divided into two or three subsystems for CDPS or HPS. In this case, both parallel and sequential processing schemes are taken into account. Figure 11 shows the inference time from the input of transmission line trip data to the end of the relief operation without load flow calculation time. In this study, load flow calculation time is 0.72s in both sequential and parallel processing. Two kinds of contingencies are simulated: non-cooperative, that can
V.2 Effect of the depth of hierarchy on inference time
This section describes the effect of the depth of hierarchy in the HPS system, and the number of subsystems in the CDPS system, on the inference time. The New England 39-bus test system is chosen as an example, As shown in Figure 12, the system is divided into three subsystems for HPS with a hierarchy of two levels. The corresponding CDPS system is divided into subsystems 1, 2 and 3. For HPS with a hierarchy of three levels, the system consists of three middle-level sub-
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Figure 11. Inference times for I EE E 30- bus system (load flow calculation time excluded): (a) sequential processing; (b) parallel processing. ©, hierarchical, non-cooperative; • , distributed, non-cooperative; [ ] , hierarchical, cooperative; I , distributed, cooperative. 0 and • are almost overlaid in the figure
194
Electrical Power & Energy Systems
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in Figure 12. Figure 13 shows the inference time without load flow calculation time. The severity of fault on the horizontal axis is defined as follows.
Middle
High
Severity of foult
Figure 13. Inference times for New England 39-bus test system (load flow calculation time excluded). A, centralized; O, two-level hierarchical; 0, threelevel hierarchical; I-], distributed (divided into three); I , distributed (divided into six). 0 and [] are almost overlaid in the figure
systems and six end-level subsystem, la, lb, 2a, 2b, 3a and 3b. The CDPS system corresponding to the threelevel HPS system is divided into six subsystems. In this case, parallel processing at each level is taken into account. An example of the problem to be solved is shown
Vol 14 No 2/3 April/June 1992
• An overload of 'low severity' is one which is relieved only by the operation inside an end-level subsystem of the three-level HPS system or inside a subsystem of the CDPS system consisting of six subsystems. • An overload of'middle severity' is one which is relieved by the cooperative control of the end-level subsystems in the three-level HPS system or of the overloaded subsystem and its adjacent subsystems in the CDPS system consisting of six subsystems: in other words, an overload relieved by the operation inside a subsystem in the two-level HPS system or in the CDPS system consisting of three subsystems. • An overload of 'high severity' is one which is relieved by the cooperative control of the end-level subsystems in the two-level HPS system or of the overloaded subsystem and its adjacent subsystems in the CDPS system consisting of three subsystems. V.2 Comparison of solution In this section, the New England 39-bus test system is selected as an example. Twelve cases of single contingency and 105 cases of double contingency are simulated and the solutions obtained by CDPS, HPS and the centralized problem-solving systems are compared in Table 1. In the proposed expert systems, neither the fuel cost of generators nor the restriction on the load increase or decrease rate of the generator is taken into account. The quality
195
Table 1. Comparison of solutions
Same operation Same change of generator output power Smaller change of generator output power Greater change of generator output power Total cases
Two-level hierarchical system
Three-level hierarchical system
Distributed system divided into three
Distributed system divided into six
99 l0 6 2 117
81 17 6 13 117
71 14 9 23 117
27 29 8 61 117
of the solution is evaluated in the light of the amount of changes in generator output powers: the solution minimizing the total change of generator output power is considered to be the best solution. The meanings of the terms in Table 1 are as follows:
Table 2. Evaluation of performance
• Same operation means that the operations obtained by the CDPS or the HPS system are exactly the same as that obtained by the centralized problem-solving system. • Same change of generator output power means that the total change of generator output power obtained by the CDPS or HPS system is equal to that by the centralized problem-solving system, but the number or kind of generators to change the output power is different. • Smaller change of generator output power or Greater change of generator output power means that the total change of generator output power obtained by the CDPS or HPS system is less or more than that by the centralized problem-solving system.
Centralized system
It is seen from Table 1 that the two-level hierarchical system is superior to the other systems in the light of the quality of the solution. Table 2 shows the results of an evaluation of each problem-solving system from two aspects: processing time and quality of solution. It can be seen that the two-level hierarchical problem-solving system seems to be the best one for the New England 39-bus test system.
VII. Acknowledgement The authors acknowledge the financial support for this research from the Ministry of Education of Japan. Support and encouragement by Professor L. L. Grigsby of Auburn University in Alabama are highly appreciated.
Inference time Long (~0.6s) Two-level Short hierarchical system (~0.1 s) Three-level Short hierarchical system (~0.1 s) Distributed system Short divided into three (~0.1 s) Distributed system Intermediate divided into six ( ~ 0.2 s)
+ 4 cases - 5 to - 15 cases - 5 to - 15 cases - 5 3 cases
VIII. References 1 2
196
0 case
* Quality of solution=number of cases of 'smaller change of generation output power' - number of cases of "greater change of generation output power"
VI. Conclusions This paper has presented two kinds of new expert system technique, cooperative distributed problem solving and hierarchical problem solving. These techniques have been applied to a transmission line overload relief problem. Using the IEEE 30-bus test system and the New England 39-bus test system, they have been proved to reduce inference time by using distributed multiple processors in parallel as compared with conventional centralized problem solving. In addition, it has been made clear that the two-level hierarchical problem-solving system seems to be the most suitable for the New England 39-bus test system. Moreover it should be noted that the use of object-oriented representation and object-oriented language in this research makes it easy to develop the proposed expert system, to change or add data on the power system and to simulate distributed or parallel processing.
Quality of solution*
3 4
5 6
7
8
Wager, W R, Keyhani, A, Hao, S and Wong, T C 'A rulebased approach to decentralized voltage control' IEEE Trans. on PWRS Vol 5 No 2 (1990) pp643-651 Filman, R E and Friedman, D P Coordinated Computing McGraw-Hill Inc. (1984) M e s a r o v i c , M D, M a c k o , D and Takahara, Y Theory of Hierarchical Multilevel Systems Academic Press Inc. (1970) Van Amerongen, R A i and Van a e e t e r e n , H P "Security control by real power rescheduling, network switching and load shedding', CIGRE SC 32-02 (1980) Delfino, B e t al. 'Evaluating artificial intelligence applications for electric power systems: knowledge-based approaches to l i ne overload alleviation', CIGRE SC 38/39-07 (1990) Paillet, O and Dubost, L 'AMPERE: a knowledge-based system for network reconfiguration" Proc. First Syrup. on Expert System Applications to Power Systems, Stockholm, Helsinki (1988) pp 8 - 3 2 - 8 - 3 8 Y o k o y a m a , R, M a t s u m o t o , T, Niimura, T and Ueki, Y 'An expert system for interactive operation guidance in power system emergency control" Proc. Second Syrup. on Expert System Applications to Power Systems, Seattle, Washington, USA (1989) pp 348-353 Sekine, Y, Kato, M, Sakaguchi, T and Fukui, C 'An object-oriented approach to four applications', Expert System Applications in Power Systems, Prentice Hall (1990) pp 258 342
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Appendix 1 The power supply block and load block are dynamically generated when job, except L1 job, is executed. The power supply block is generated from the starting node which lies upstream of the overloaded transmission line. It consists of a set of nodes which receive no load flow from nodes in the overloaded subsystem except generator nodes. However, the power supply block is able to receive a load flow from a node belonging to the other subsystem. Figure A 1 shows an example of a power supply block and a load block. The load block is generated from the starting node lying downstream of the overloaded line. No load flow is delivered from the load block to nodes in the overloaded subsystem except load nodes, but the load block is able to deliver a load flow to a node belonging to the other subsystem. An index called node value is introduced to indicate to what extent each node is responsible for the overload• This index is used to search a new path in a G1 job. The node value of a node in the power supply block indicates the ratio of the flow coming out of the node to the flow through the overloaded line. First, the node value of the upstream node of the overloaded transmission line is set at the amount of the flow of the overloaded transmission line. Second, the node value of each node belonging to the power supply block is calculated from Figure A2 and the following equation:
t ,oo.
I,=1
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(AI.1)
where V(no) is the node value of no,flOWo,t(nk)is the flow coming out of nk, and fog is the flow from no to nk.
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of the overloaded line Figure A2. Calculation of node value nI n2
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After obtaining the node values in the power block, a network search to find a new path in the G1 job begins. The algorithm is as follows. 1 Let n 1 be a node in the power supply block which has the biggest node value. 2 Let n o be a node, not belonging to the power supply block, which is connected to n 1 directly by one line group. 3 Let n 1 to nk be nodes in the power supply block connected to no by one line group. 4 Let the node value of no be vo. The value of vo is obtained from Figure A3 and Equation (2):
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The overloaded subsystem Figure A1. Power supply block and load block Vol 14 No 2/3 April/June 1992
vo=max{min{vj, v ~ } }
(A1.2)
where f j is the flow capacity of line group j, lj is the flow through line group j, Af is the overloaded flow, and v~ is the node value of node j. 5 Add node n o into power supply block. 6 If node n o belongs to the load block, both of the blocks are connected by the most effective path to alleviate the overload. If a de-energized line is included in the new path, the line is energized. If node n o does not belong to the load block, operations 1-6 are iterated until no no is found.
Appendix 2 After the failure of a G1 job, a G3 job to reduce the generator output power in the power supply block begins. To determine the amount of each generator output power
197
change in the power supply block, the overload relief coefficient of each generator in the power supply block is used. This is the ratio of the change of flow of the overloaded transmission line to the output change of the generators. It is obtained from the DC load flow calculation (see Equation (A2.1)):
F °''
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where Apu is the load flow change of line group i, Apbj
198
is the change of injection power to node j, and aij is the overload relief coefficient of node j to line group i. Using this coefficient, the changes of generator output powers are given by Equation (A2.2).
AGj=
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~=l[(a.--atd)2"Gj]
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where a~a is the overload relief coefficient of the downstream node of the overloaded line, Gj is the generator output power of node j in the power supply block, AG~ is the generator output power change of node j in the power supply block, Afis the overload flow, and is a loss factor (..~0.05-0.1).
Electrical Power & Energy Systems