CN111159922A - Key line identification method and device for cascading failure of power system - Google Patents

Key line identification method and device for cascading failure of power system Download PDF

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CN111159922A
CN111159922A CN202010064554.3A CN202010064554A CN111159922A CN 111159922 A CN111159922 A CN 111159922A CN 202010064554 A CN202010064554 A CN 202010064554A CN 111159922 A CN111159922 A CN 111159922A
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吴浩
柳璐
李林芝
戴飞
熊浩清
饶宇飞
崔惟
周宁
张振安
高昆
方舟
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Zhejiang University ZJU
State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Henan Electric Power Co Ltd
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Henan Electric Power Co Ltd
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Abstract

The invention provides a method and a device for identifying a key line of cascading failures of a power system, belonging to the field of cascading failure risk analysis and stability research of the power system, wherein the method comprises the following steps: performing cascading failure direct current power flow simulation on the power system to acquire failure chain data required by identification; decomposing the fault chain data into states at different moments to form a state network; based on a state network, solving a line risk value of a line fault in the state of the cascading faults at different moments by using an SARSA algorithm; and determining the line corresponding to the line risk value exceeding the given threshold value as the critical line of the cascading failure. The method can realize high-risk fault line identification based on cascading fault data, and carry out risk mitigation, prevention and control on cascading faults at different moments so as to guarantee safe and stable operation of the power system.

Description

Key line identification method and device for cascading failure of power system
Technical Field
The embodiment of the invention relates to the technical field of power systems, in particular to a method and a device for identifying a key line of cascading failures of a power system.
Background
Cascading failures of a power system often cause large-area power failure, and can cause the safe and stable operation threat of a power grid and serious social and economic losses. Typically, a cascading failure blackout is triggered by one or more initial disturbances and consists of many subsequent failures, which are directly due to the failure and decommissioning of components within the system. From the perspective of preventing and planning cascading failures of a power system, upgrading all lines which can cause the cascading failures and the major power failure consequences can eliminate most power failure accidents, but the upgrading is not economical and practical in practice. Considering that the overload of the power transmission line is a main inducing factor of cascading failure and blackout in actual operation, the fault line most relevant to serious blackout is identified, and the blackout risk can be effectively reduced by upgrading and modifying the key lines.
The conventional cascading failure research of a traditional power system comprises a dynamic process of simulating cascading failure blackout, fault process traversal and system risk analysis; or analyzing the key link of the cascading failure by using angles such as a topological structure, parameters and the like based on a complex network theory. According to the existing analysis method, in order to ensure the ergodicity of simulation, the simulation time is increased along with the system scale; and the complex network analysis method based on the topology ignores the physical characteristics of the power system, and errors exist in key link identification.
Disclosure of Invention
In view of this, embodiments of the present invention provide a method and an apparatus for identifying a critical line of a cascading failure of an electrical power system, so as to solve the problem of identifying the critical failure line.
In order to solve the technical problem, the embodiment of the invention adopts the following technical scheme:
in a first aspect, an embodiment of the present application provides a method for identifying a critical line of a cascading failure of an electrical power system, including:
performing cascading failure direct current power flow simulation on the power system to acquire failure chain data required by identification;
decomposing the fault chain data into states of the cascading faults at different moments to form a state network;
based on a state network, solving a line risk value of a line fault in the state of the cascading faults at different moments by using an SARSA algorithm;
and determining the line corresponding to the line risk value exceeding the given threshold value as the critical line of the cascading failure.
Further, the method for implementing cascading failure direct current power flow simulation of the power system comprises the following steps:
1) inputting initial operation parameters of a power grid;
2) setting a random initial disturbance event to trigger cascading failure;
3) carrying out island detection, and regulating the generator climbing influence parameters in each island to realize the balance of the generator and the load again; when the generator climbing cannot meet the power matching, the generator is cut off or load shedding operation is carried out;
4) calculating direct current power flow, and detecting whether the direct current power flow of a line exceeds a line capacity threshold value; if the threshold value is exceeded, entering 5); otherwise, go to 6);
5) selecting a line to simulate fault tripping based on a line fault probability model, and adding the tripping line into a fault chain; when a plurality of lines meet the condition of possible tripping, randomly selecting one line fault; if a line fault occurs, entering 3); otherwise go to 6);
6) and (5) ending the single cascading failure simulation process, recording a failure chain, and calculating the power failure accumulated load loss caused by the failure chain.
Further, in the step 5), the mathematical expression of the line fault probability model is as follows:
Figure BDA0002375558890000021
wherein, Fi,maxDenotes the upper limit of the line capacity of the ith line, Fi,cIndicating a set capacity threshold of the ith line, FiRepresenting line flow of the ith line, pi,tripIndicating the probability of failure of the ith line.
Further, the state specifically includes:
by stThe method represents a certain state at the time t, the physical meaning of the state is a state vector of a line in the system, and the specific formula is as follows:
Figure BDA0002375558890000022
wherein t represents the time of the fault, and the length N of the vector is equal to the number of lines in the system; the line states are represented by 0 and 1, with 1 representing a line in a fault state and 0 representing a line in a normal state.
Further, based on the state network, the circuit risk value of the line fault occurring in the state of the cascading faults at different moments is solved by using the SARSA algorithm, which includes:
the solving formula of the line risk value Q is as follows:
Figure BDA0002375558890000023
wherein Q (s, a) represents a line risk value Q at fault state s and selected faulty line a; e represents a mathematical expectation; t is the number of fault moments of the fault chain; a istIs shown in a fault state stThe next faulty line down; r ist+1Called line reward value, whose value is equal to the fault state s at time ttBy line fault atTransition to Fault State s at time t +1t+1Time, corresponding fault state st+1State prize value Rt
Figure BDA0002375558890000031
With A(s)t) Indicating the current fault state stOptional set of next faulty lines under, at∈A(st) (ii) a Line atThe selection of the faults uses a transition probability function, and the transition probability function adopts an epsilon-greedy line selection strategy:
Figure BDA0002375558890000032
wherein ε ∈ [0,1]]Representing an exploration probability for ensuring that all fault states in the fault chain can be searched; selecting a current fault state StThe probability of the fault line corresponding to the lower highest line risk value Q is 1-epsilon, and the current fault state StThe probability of the next randomly selected faulty line is s.
Further, the algorithm SARSA is based on Markov property, and the line risk value Q can be updated iteratively through a Bellman function; the iterative update formula of the line risk value Q is as follows:
Qk+1(st,at)←Qk(st,at)+α(rt+1+E{Qk+1(st+1,at+1)}-Qk(st,at))
wherein k is the iteration number, α is the control learning efficiency;
and circularly performing the iteration process until a convergence condition is met: | Qk+1(s,a)-QkAnd (s, a) | is less than or equal to sigma, namely the line risk values Q under all the states are converged, and the iteration process is finished to obtain the final line risk value Q'.
In a second aspect, an embodiment of the present invention provides an apparatus for identifying a critical line of a cascading failure of an electrical power system based on an SARSA algorithm, including:
the simulation acquisition module is used for performing cascading failure direct current power flow simulation on the power system and acquiring fault chain data required by identification;
the fault state acquisition module is used for decomposing the fault chain data into states of cascading faults at different moments to form a state network;
the line risk value solving module is used for solving the line risk value of the line fault in the states of different moments of the cascading failure by utilizing an SARSA algorithm based on the state network;
and the critical line identification module is used for determining the line corresponding to the line risk value exceeding the given threshold value as the critical line of the cascading failure.
By adopting the technical scheme provided by the embodiment of the application, the method has the following beneficial effects:
according to the key line identification method for the cascading failure of the power system, cascading failure simulation data are obtained, the line risk value of the line failure in the states of the cascading failure at different moments is solved through the SARSA algorithm, so that the risk degree of each line in different failure states is determined, the key line and the corresponding state of the key line are identified, cascading failure simulation of a large sample is avoided, and the effectiveness and the identification efficiency of the cascading failure key line identification are guaranteed.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments will be briefly described below.
FIG. 1 is a flowchart of a method for identifying a critical line of a cascading failure of a power system according to an embodiment of the present invention;
fig. 2 is an electrical wiring diagram based on an IEEE14 node system;
fig. 3 is a structural diagram of a critical line identification apparatus for cascading failures of an electrical power system according to an embodiment of the present invention.
Detailed Description
The present invention is further illustrated in the following description in conjunction with the drawings in specific embodiments, which are to be understood as merely illustrative of the present invention and not as limiting the scope of the invention. After reading this disclosure, all other embodiments that can be obtained by one of ordinary skill in the art without any creative effort based on the embodiments of the present disclosure belong to the protection scope of the present disclosure.
The invention aims to provide a key line identification method for cascading failures of a power system, which is characterized in that cascading failure simulation data are obtained, a line risk value of the line failures in the states of the cascading failures at different moments is solved through an SARSA algorithm, so that the risk degree of each line in different failure states is determined, the key line and the corresponding key failure state are identified, cascading failure simulation of a large sample is avoided, and the effectiveness and the identification efficiency of the cascading failure key line identification are guaranteed.
In order that the above objects and features of the present invention will become more apparent, the following examples will illustrate the present invention in further detail.
As shown in fig. 1, an embodiment of the present invention provides a method for identifying a critical line of a cascading failure of an electrical power system, where the method includes:
s100, performing cascading failure direct current power flow simulation on the power system to obtain failure chain data required by identification. The step 1 of the embodiment specifically realizes the following substeps:
1.1 inputting initial operation parameters of the power grid.
1.2 setting N-1 random initial disturbance event to trigger cascading failure.
1.3, carrying out island detection, and regulating the generator climbing influence parameters in each island to realize the balance of the generator and the load again; and when the generator climbing cannot meet the power matching, the generator is cut off or the load shedding operation is carried out.
1.4 calculating the direct current load flow, and according to a line fault probability model:
Figure BDA0002375558890000051
take Fi,max=1.4Fi,c。Fi,maxDenotes the upper limit of the line capacity of the ith line, Fi,cIndicating a set capacity threshold of the ith line, FiRepresenting line flow of the ith line, pi,tripIndicating the probability of failure of the ith line. Detecting whether the power flow of the line exceeds a line capacity threshold, and if so, entering 1.5; otherwise, 1.6 is entered.
1.5 selecting a line to simulate fault tripping based on a line fault probability model, and adding the tripping line into a fault chain; when a plurality of lines meet the condition of possible tripping, randomly selecting one line fault; if a line fault occurs, entering 1.3; otherwise go to 1.6.
1.6, ending the single cascading failure simulation process, recording a failure chain, and calculating the power failure accumulated load loss caused by the failure chain.
And S200, inputting fault chain data of cascading fault simulation, and decomposing the fault chain data into states of the cascading faults at different moments to form a state network. By stThe method represents a certain state at the time t, the physical meaning of the state is a state vector of a line in the system, and the specific formula is as follows:
Figure BDA0002375558890000052
wherein t represents the time of the fault, and the length N of the vector is equal to the number of lines in the system; the line states are represented by 0 and 1, with 1 representing a line in a fault state and 0 representing a line in a normal state.
Assuming that the same N-k preamble failure, a failure in a different order will result in the same system failure state; where k is the number of failed lines.
And S300, based on the state network, utilizing an SARSA algorithm to generate line risk values of line faults (namely, executing corresponding line faults) in the states of the cascading faults at different moments.
In the process of utilizing the SARSA algorithm, each fault state-line pair (s, a) is distributed with a line risk value Q for evaluating the quality of the fault of the line a adopted in a certain fault state s; the solving formula of the line risk value Q is as follows:
Figure BDA0002375558890000053
the solution of the line risk value Q is based on the reward value r. Wherein Q (s, a) represents a line risk value Q at fault state s and selected faulty line a; e represents a mathematical expectation; t is the number of fault moments of the fault chain; a istIs shown in a fault state stThe next faulty line down; r ist+1Called line reward value, whose value is equal to the fault state s at time ttBy line fault atTransition to Fault State s at time t +1t+1Time, corresponding fault state st+1State prize value Rt
Figure BDA0002375558890000061
With A(s)t) Indicating the current fault state stOptional set of next faulty lines under, at∈A(st) (ii) a Line atThe selection of the faults uses a transition probability function, and the transition probability function adopts an epsilon-greedy line selection strategy:
Figure BDA0002375558890000062
wherein ε ∈ [0,1]]Representing an exploration probability for ensuring that all fault states in the fault chain can be searched; selecting a current fault state StThe probability of the fault line corresponding to the lower highest line risk value Q is 1-epsilon, and the current fault state StThe probability of the next randomly selected faulty line is s. Take ε 1 and focus on exploring to traverse all fault states.
The SARSA algorithm is based on Markov property, and the line risk value Q can be updated iteratively through a Bellman function; the iterative update formula of the line risk value Q is as follows:
Qk+1(st,at)←Qk(st,at)+α(rt+1+E{Qk+1(st+1,at+1)}-Qk(st,at))
the method comprises the steps of obtaining a fault state evolution path with a high reward value, controlling learning efficiency, wherein k is iteration times, α is controlling learning efficiency and represents the speed of learning the fault state evolution path with the high reward value, the aggressiveness is strong when α is 1, and the α is conservative when the α is 0, namely the learning speed of the system to experience is higher when the α is larger, generally, α belongs to [0,1], and α is 0.75, so that reasonable learning efficiency is guaranteed.
And circularly performing the iteration process until all the line risk values Q in the fault state network are converged, and taking the sigma as 0.1:
|Qk+1(s,a)-Qk(s,a)|≤σ
namely, the line risk values Q under all fault states are converged, and the iteration process is ended to obtain the final line risk value Q'.
And S400, determining the line corresponding to the line risk value exceeding the given threshold value as a key line of the cascading failure.
According to the method for identifying the key line of the cascading failure of the power system, cascading failure simulation data are obtained, the line risk value Q of the failure state transfer is obtained through the Bellman function in an iterative updating mode, the convergence value of the line risk value Q is accurately calculated, the risk degree of each line in different failure states is determined, and therefore the key line and the corresponding pre-critical failure state of the key line are identified. The problems of overlong consumed time, low calculation efficiency and the like caused by performing cascading failure simulation on a large sample are solved. In addition, experiments verify that the method can effectively identify the key line and the fault state causing the key line, obviously reduce the system load loss of the cascading failure blackout of the line aiming at the upgrading and modifying measures of the key line, and provide an assistant decision suggestion for the upgrading and modifying of the key line of the power grid, the path prediction of the cascading failure and the blackout risk prevention.
Specifically, the present embodiment takes the IEEE14 node standard test system as an example to verify the critical line identification method for cascading failures provided in the present embodiment.
First, a line risk value Q of the example power grid at an initial time is calculated, and the calculation result is shown in fig. 2.
It can be seen that as an initial fault, the line risk values Q for lines 1, 2 are 78.3, 49.6 respectively, with the highest Q value among all initially faulty lines. From the grid topology, lines 1, 2 are critical lines connecting the generator of node 1 with the rest of the network, any disconnection of one of them will cause the other line to be heavily overloaded and tripped, causing a severe power shortage and more likely causing a blackout accident.
Furthermore, a line fault criticality calculation of the line in different fault states is performed, i.e. a line risk value Q of the line in different fault states is calculated. As the cascading failure process progresses, the line risk value Q of the line may change with the failure condition, resulting in increased line criticality. For the transmission lines with the same transmission section, such as the lines 3, 4 and 7, after any two lines are tripped due to faults, the line risk value Q of the other line is increased to 99.5. This is because the lines 3, 4, 7 are the critical transmission paths between the generator nodes (1, 2) and the load nodes (3, 4, 9), and if all of the 3 lines are disconnected, the load flow transmission pressure of the rest of the lines will be caused, and the lines may be tripped by overload, so that the risk of cascading failures is increased sharply. Taking line 7 as an example, the following table lists the line risk values Q of line 7 under different fault conditions:
Figure BDA0002375558890000071
it can be seen that line 7 is sensitive to fault conditions 3, 4 and in addition to the presence of line 1. In contrast, line 7 is less sensitive to fault conditions that include line faults in areas of concentrated load. Therefore, cascading failure prevention and control measures can be provided in a targeted manner, and upgrading and transformation of key lines with high line risk values Q at the initial moment are enhanced; and recording the identified key fault propagation paths with the line risk value Q increased after certain fault states so as to deploy a relay protection scheme in a targeted manner.
It can be seen that the method for identifying the critical line of the cascading failure of the power system provided by the embodiment verifies the feasibility and effectiveness of the method through the application of the IEEE14 node power grid.
The invention provides a device for identifying a critical line of cascading failure of a power system based on an SARSA algorithm, which can execute any method for identifying the critical line of cascading failure of the power system provided by any embodiment of the invention and has corresponding functional modules and beneficial effects for executing the method. As shown in fig. 3, includes:
the simulation acquisition module 100 is configured to perform cascading failure direct current power flow simulation on the power system, and acquire fault chain data required for identification;
a fault state obtaining module 200, configured to decompose the fault chain data into states of cascading faults at different times, so as to form a state network;
a line risk value solving module 300, configured to solve, based on the state network, a line risk value of a line fault (i.e., an execution corresponding line fault) occurring in a state of a cascading failure at different times by using an SARSA algorithm;
and the critical line identification module 400 is used for determining the line corresponding to the line risk value exceeding the given threshold value as the critical line of the cascading failure.
It should be noted that, the embodiments of the detailed steps of the processing in each module have been described in the foregoing, and are not described again here; the above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The integrated unit, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a removable hard disk, a magnetic or optical disk, and other various media capable of storing program codes.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
The above description is only a preferred embodiment of the present invention, and is used to help understand the method and its core idea of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (12)

1. A method for identifying a critical line of a cascading failure of a power system is characterized by comprising the following steps:
performing cascading failure direct current power flow simulation on the power system to acquire failure chain data required by identification;
decomposing the fault chain data into states of the cascading faults at different moments to form a state network;
based on a state network, solving a line risk value of a line fault in the state of the cascading faults at different moments by using an SARSA algorithm;
and determining the line corresponding to the line risk value exceeding the given threshold value as the critical line of the cascading failure.
2. The method for identifying the critical line of the cascading failure of the power system according to claim 1, wherein the method for implementing the cascading failure direct current power flow simulation of the power system comprises the following steps:
1) inputting initial operation parameters of a power grid;
2) setting a random initial disturbance event to trigger cascading failure;
3) carrying out island detection, and regulating the generator climbing influence parameters in each island to realize the balance of the generator and the load again; when the generator climbing cannot meet the power matching, the generator is cut off or load shedding operation is carried out;
4) calculating direct current power flow, and detecting whether the direct current power flow of a line exceeds a line capacity threshold value; if the threshold value is exceeded, entering 5); otherwise, go to 6);
5) selecting a line to simulate fault tripping based on a line fault probability model, and adding the tripping line into a fault chain; when a plurality of lines meet the condition of possible tripping, randomly selecting one line fault; if a line fault occurs, entering 3); otherwise go to 6);
6) and (5) ending the single cascading failure simulation process, recording a failure chain, and calculating the power failure accumulated load loss caused by the failure chain.
3. The method as claimed in claim 2, wherein in the step 5), the mathematical expression of the line fault probability model is as follows:
Figure FDA0002375558880000011
wherein, Fi,maxDenotes the upper limit of the line capacity of the ith line, Fi,cIndicating a set capacity threshold of the ith line, FiRepresenting line flow of the ith line, pi,tripIndicating the probability of failure of the ith line.
4. The method according to claim 1, wherein the status specifically comprises:
by stThe method represents a certain state at the time t, the physical meaning of the state is a state vector of a line in the system, and the specific formula is as follows:
Figure FDA0002375558880000021
wherein t represents the time of the fault, and the length N of the vector is equal to the number of lines in the system; the line states are represented by 0 and 1, with 1 representing a line in a fault state and 0 representing a line in a normal state.
5. The method as claimed in claim 1, wherein the step of solving the line risk value of the line fault occurring in the states of the cascading faults at different times based on the state network by using the SARSA algorithm comprises:
the solving formula of the line risk value Q is as follows:
Figure FDA0002375558880000022
wherein Q (s, a) represents a line risk value Q at fault state s and selected faulty line a; e represents a mathematical expectation; t is the number of fault moments of the fault chain; a istIs shown in a fault state stThe next faulty line down; r ist+1 is called the line reward value, whose value is equal to the fault state s at time ttBy line fault atTransition to Fault State s at time t +1t+1When, toDue fault state st+1State prize value Rt
Figure FDA0002375558880000023
With A(s)t) Indicating the current fault state stOptional set of next faulty lines under, at∈A(st) (ii) a Line atThe selection of the faults uses a transition probability function, and the transition probability function adopts an epsilon-greedy line selection strategy:
Figure FDA0002375558880000024
wherein ε ∈ [0,1]]Representing an exploration probability for ensuring that all fault states in the fault chain can be searched; selecting a current fault state StThe probability of the fault line corresponding to the lower highest line risk value Q is 1-epsilon, and the current fault state StThe probability of the next randomly selected faulty line is s.
6. The method for identifying the key line of the cascading failure of the power system as claimed in claim 1, wherein the SARSA algorithm is based on Markov property, and the line risk value Q is updated by iteration of a Bellman function; the iterative update formula of the line risk value Q is as follows:
Qk+1(st,at)←Qk(st,at)+α(rt+1+E{Qk+1(st+1,at+1)}-Qk(st,at) α is the control learning efficiency;
and circularly performing the iteration process until a convergence condition is met: | Qk+1(s,a)-QkAnd (s, a) | is less than or equal to sigma, namely the line risk values Q under all the states are converged, and the iteration process is finished to obtain the final line risk value Q'.
7. A key line identification device for cascading failure of a power system based on an SARSA algorithm is characterized by comprising:
the simulation acquisition module is used for performing cascading failure direct current power flow simulation on the power system and acquiring fault chain data required by identification;
the fault state acquisition module is used for decomposing the fault chain data into states of cascading faults at different moments to form a state network;
the line risk value solving module is used for solving the line risk value of the line fault in the states of different moments of the cascading failure by utilizing an SARSA algorithm based on the state network;
and the critical line identification module is used for determining the line corresponding to the line risk value exceeding the given threshold value as the critical line of the cascading failure.
8. The apparatus of claim 7, wherein the simulation obtaining module is specifically configured to:
1) inputting initial operation parameters of a power grid;
2) setting a random initial disturbance event to trigger cascading failure;
3) carrying out island detection, and regulating the generator climbing influence parameters in each island to realize the balance of the generator and the load again; when the generator climbing cannot meet the power matching, the generator is cut off or load shedding operation is carried out;
4) calculating direct current power flow, and detecting whether the direct current power flow of a line exceeds a line capacity threshold value; if the threshold value is exceeded, entering 5); otherwise, go to 6);
5) selecting a line to simulate fault tripping based on a line fault probability model, and adding the tripping line into a fault chain; when a plurality of lines meet the condition of possible tripping, randomly selecting one line fault; if a line fault occurs, entering 3); otherwise go to 6);
6) and (5) ending the single cascading failure simulation process, recording a failure chain, and calculating the power failure accumulated load loss caused by the failure chain.
9. The apparatus according to claim 8, wherein in the step 5), the mathematical expression of the line fault probability model is as follows:
Figure FDA0002375558880000031
wherein, Fi,maxDenotes the upper limit of the line capacity of the ith line, Fi,cIndicating a set capacity threshold of the ith line, FiRepresenting line flow of the ith line, pi,tripIndicating the probability of failure of the ith line.
10. The apparatus of claim 7, wherein the states are specifically:
by stThe method represents a certain state at the time t, the physical meaning of the state is a state vector of a line in the system, and the specific formula is as follows:
Figure FDA0002375558880000041
wherein t represents the time of the fault, and the length N of the vector is equal to the number of lines in the system; the line states are represented by 0 and 1, with 1 representing a line in a fault state and 0 representing a line in a normal state.
11. The apparatus of claim 7, wherein the apparatus for identifying critical lines of cascading failures of the power system based on the SARSA algorithm is used to solve the line risk values of the line failures occurring in the states of the cascading failures at different times based on the state network, and includes:
the solving formula of the line risk value Q is as follows:
Figure FDA0002375558880000042
wherein Q (s, a) represents a line risk value Q at fault state s and selected faulty line a; e represents a mathematical expectation; t is the number of fault moments of the fault chain; a istIs shown in a fault state stThe next faulty line down; r ist+1Called line reward value, whose value is equal to the fault state s at time ttBy line fault atTransition to Fault State s at time t +1t+1Time, corresponding fault state st+1State prize value Rt
Figure FDA0002375558880000043
With A(s)t) Indicating the current fault state stOptional set of next faulty lines under, at∈A(st) (ii) a Line atThe selection of the faults uses a transition probability function, and the transition probability function adopts an epsilon-greedy line selection strategy:
Figure FDA0002375558880000044
wherein ε ∈ [0,1]]Representing an exploration probability for ensuring that all fault states in the fault chain can be searched; selecting a current fault state StThe probability of the fault line corresponding to the lower highest line risk value Q is 1-epsilon, and the current fault state StThe probability of the next randomly selected faulty line is s.
12. The apparatus according to claim 7, wherein the SARSA algorithm is based on Markov property, and iteratively updates the line risk value Q through a Bellman function; the iterative update formula of the line risk value Q is as follows:
Qk+1(st,at)←Qk(st,at)+α(rt+1+E{Qk+1(st+1,at+1)}-Qk(st,at))
wherein k is the iteration number, α is the control learning efficiency;
and circularly performing the iteration process until a convergence condition is met: | Qk+1(s,a)-QkAnd (s, a) | is less than or equal to sigma, namely the line risk values Q under all the states are converged, and the iteration process is finished to obtain the final line risk value Q'.
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