CN110596531A - Power distribution network fault dynamic planning and positioning method - Google Patents
Power distribution network fault dynamic planning and positioning method Download PDFInfo
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- CN110596531A CN110596531A CN201910840781.8A CN201910840781A CN110596531A CN 110596531 A CN110596531 A CN 110596531A CN 201910840781 A CN201910840781 A CN 201910840781A CN 110596531 A CN110596531 A CN 110596531A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/08—Locating faults in cables, transmission lines, or networks
- G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
- G01R31/086—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution networks, i.e. with interconnected conductors
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/08—Locating faults in cables, transmission lines, or networks
- G01R31/088—Aspects of digital computing
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
- Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
- Y04S10/00—Systems supporting electrical power generation, transmission or distribution
- Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
- Y04S10/52—Outage or fault management, e.g. fault detection or location
Abstract
The invention provides a power distribution network fault dynamic planning and positioning method, which adopts causal analysis to establish an incidence relation model between automation equipment monitoring information and feeder line states and construct a power distribution network fault positioning mathematical model; the state of the combined optimization problem is simplified by combining a repulsion principle; and performing fault positioning through evaluation function calculation and non-fault section search. The invention solves the problem of complex fault location space of the power distribution network, simplifies the state of the combined optimization problem by combining the repulsion principle, reduces the overlapping of sub-problems, reduces the repeated calculation and improves the calculation speed.
Description
Technical Field
The invention relates to the technical field of power systems, in particular to a power distribution network fault dynamic planning and positioning method.
Background
With the continuous improvement of the living standard of people, the requirements of users on the power supply quality and the power supply reliability are higher and higher. In the event of a power distribution system fault, rapid and accurate analysis, location and isolation of the fault plays an extremely important role in minimizing power interruption for users, and improving power supply safety and reliability. Distribution network fault location is one of the important functions of distribution automation. When the power distribution network actually breaks down, the fault area can be quickly found out through the fault positioning function, effective guidance is provided for isolating the fault and quickly restoring the power supply of the user, and the method has important significance for improving the power supply reliability. The fault location of the power distribution network generally comprises 3 steps of fault warning, fault correlation analysis and fault accurate location.
Meanwhile, with the continuous development of smart power grids, Feeder Terminal Units (FTUs) And Data Acquisition And monitoring Control Systems (SCADA) are equipped in power distribution networks. The main method for positioning the fault section of the power distribution network is to position the fault section by using fault information uploaded to a control center by a Feeder Terminal Unit (FTU). As the distribution network is divided into different sections by each section switch, and the FTU is additionally arranged at the section switch, when the FTU monitors that the current is greater than a setting value, the fault of the power grid is considered to occur. The FTU uploads the fault information to a data acquisition and monitoring System (SCADA), and then fault location is carried out on the power grid.
However, when the method is used for fault location, due to the fact that the fault location space of the power distribution network is quite complex, overlapping and crossing are easily caused by individual problems in fault information combination, a large amount of repeated calculation is needed in the combination optimization process, the calculation amount is quite large, and the processing time is quite long. Therefore, how to simplify the state of the combinatorial optimization problem, reduce the overlap between sub-problems, reduce the repeated computation, and increase the computation speed is an urgent problem to be solved.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a power distribution network fault dynamic planning and positioning method to solve the problem of complex power distribution network fault positioning space, simplify the state of a combined optimization problem by combining a repulsion principle, reduce the overlapping of sub-problems, reduce repeated calculation and improve the calculation speed.
In order to achieve the purpose, the invention is realized by the following technical scheme: a power distribution network fault dynamic planning and positioning method comprises the following steps:
step 1: establishing an incidence relation model between the monitoring information of the automation equipment and the feeder line state by adopting causal analysis, and establishing a power distribution network fault positioning mathematical model;
step 2: optimizing fault data combination by combining a repulsion principle;
and step 3: and (4) completing fault positioning by calculating an evaluation function of each node of the power distribution network and searching a non-fault interval.
Further, the step 1 comprises: establishing an approximation relation model between fault current out-of-limit information uploaded by an FTU (fiber to the Unit) and an endogenous variable by using state information of a feeder line branch as the endogenous variable; and constructing a nonlinear programming model containing absolute values for the approximation relation model and converting the nonlinear programming model into a power distribution network fault positioning mathematical model.
Further, the step 1 specifically comprises:
when the approximation relation model is established, the state information of the feeder branch circuit is required to approximate the current out-of-limit information of the automation device acquired by the FTU, so that an incoming line breaker, a section switch and a tie switch are taken as nodes, the state information of the feeder branch circuit is taken as an internal variable, a 0-1 coding mode is adopted during coding, a number 1 is adopted to represent the fault of a feeder section, and a number 0 represents the normal of the feeder section;
the approximation relation model is an incidence relation model established between automation equipment monitoring information and feeder line states by adopting causal analysis, the power distribution network is a 6-node single-power-supply radial power distribution network, and x (1) -x (6) are assumed to be respectively fed linesInformation on the operating states of the lines 1-6,respectively representing the current out-of-limit information values of the circuit breaker and the section switch, and taking the value as 1 when overcurrent exists; if the FTU of the circuit breaker S1 acquires fault current out-of-limit information, connectivity and power flow distribution characteristics of a power system are known easily according to graph theory, and the current out-of-limit signal may be caused by short-circuit faults of the feeder lines 1-6; therefore, the device status information and S of the feeder lines 1-61The FTU current out-of-limit states are directly related, namely x (1) -x (6) are direct reasons for the IS1 value being 1, and the feeder lines 1-6 are calledThe cause and effect device of (1);
according to the state associated information of the causal equipment, on the premise of single fault assumption, the state information of the causal equipment and the current out-of-limit information of the circuit breaker and the section switch can be established and described on the basis of the fault minimum set theoryThe associated information between the two approaches to a relational model; x is a feeder line state vector and,an approximation function for the corresponding automation device; the symbol V represents the logic "OR", and the built approach relation model is as follows:
analysis can obtain: the switch model can correctly and effectively reflect the association relation between causal equipment, but does not meet the fault diagnosis minimum set theory. Therefore, a false determination will occur because there is a "many-to-one" relationship. The method is improved, although the one-to-one state approximation is realized, the model construction is complex due to the construction based on the logic value theory, the decision calculation cannot be carried out by using a conventional optimization method based on good numerical stability, and the application in a large-scale power distribution network is limited due to the existence of the solving efficiency and the unstable numerical value.
According to the above formula, the logic operation V in the model is changed into subtraction operation, and a new approximation relation model can be obtained as follows:
in the formula, the symbol "-" directly represents algebraic subtraction operation and directly contains the parallel superposition characteristic of the coupling effect of the running state information of the causal association equipment on the uploaded alarm information; as can be seen from the comparison of the established approximation relationship model and the logic model, the model not only meets the causal association relationship between the devices, but also avoids the logic relationship operation.
X is a feeder state vector, and when N automation devices are provided, the distribution network fault location non-logical relation model containing absolute values can be expressed as follows:
s.t.X＝[x(1),x(2),…,x(n)]
x(i)＝0/1,X∈Rn
in the formula: sj0Automation equipment S for distribution networkjA node position of a first downstream causal association feeder line;is SjThe number of causally related devices;
different from a radial power distribution network, the ring network open-loop operation power distribution network is provided with a plurality of power distribution areas, no electrical contact exists between different areas, and multiple times of positioning is needed when the areas break down simultaneously. In order to avoid the situation, when fault location is carried out on the power distribution network, a fault diagnosis minimum set theory, a unified labeling idea of the power distribution region and independent power distribution region division are adopted to form the power distribution network into a plurality of single-power-supply radiation type power distribution networks, and then a fault location unified mathematical model of the looped network open-loop operation power distribution network is established in 3 steps of determination of causal equipment association information, establishment of an approximation relation model and conversion of a linear programming model of a target function and a constraint condition. The feeders 1-m belong to an independent power distribution area 1; the feeders m + 1-n belong to the independent power distribution area 2;
according to theoretical analysis and causal association equipment information, a new mathematical model for fault location of the dual-power-supply looped network open-loop operation power distribution network is established as follows:
x(i)＝0/1。
further, the step 2 combines the repulsion principle to simplify the state of the combined optimization problem. And in the dynamic planning subproblem division process by adopting a repulsion principle, the overlapping of subproblems is reduced, the repeated calculation is reduced, and the calculation speed is improved.
In order to reduce the space complexity, the state of the combined optimization problem is simplified by combining a repulsion theory, so that the problem can be completed in polynomial time and can be O (2)k) Time and polynomial space solution, and calculation speed is improved.
The adopted repulsion principle is specifically as follows:
refers to a given set U andwherein U is called the corpus, A1,…AnCalled a demand, then
This is true.
Further, in the step 3, the division of the non-fault section by using dynamic programming mainly includes two stages: the evaluation function calculation and the optimal non-fault section search specifically comprise the following steps:
step 31: calculating an evaluation function value of each node of the power distribution network according to a depth-first traversal sequence;
step 32: and judging whether each node is selected to the optimal non-fault section one by one according to the inverse process of depth-first traversal by utilizing the evaluation function values of each node.
Further, the evaluation functionComprises the following steps:
wherein L isk0,1, …, k is a subset of nodes of V.Are subtrees of T generated by these nodes,is the set of this subtree arc.
Node avWhether or not to be selected into the power restoration region depends on whether or not the following expression holds:
in the formula (I), the compound is shown in the specification,wherein, T (a)v) Represented by node avIs the root subtree and H is the maximum number of nodes.
Further, the establishing process of the non-fault section comprises the following steps: the method comprises the steps of forming root trees by different root nodes respectively, then utilizing DPA to solve TKPs corresponding to the root trees one by one to form a plurality of independent non-fault sections, namely decomposing the problem of dividing the non-fault sections of the power distribution system into a plurality of TKPs, and then solving one by one.
Further, the establishing process of the non-fault section specifically includes:
first, an evaluation function is initialized,here, L0＝{0}；
Then, forward calculation is carried out; the method specifically comprises the following steps:
computing an evaluation of a currently traversed nodeA function. Traversing nodes in the tree, and recording the traversed nodes into a set LkWhere k is the node currently traversed, compute for k ≠ 0 and all H ≠ 0,1,2, …, HThe following were used:
the forward pushing process calculates at LkCorresponding tree in case of {0,1,2, …, k }An objective function value of the TKP containing the node k and taking h as a requirement constraint;
finally, backtracking calculation is carried out; the method specifically comprises the following steps:
calculating the parent node a of the currently traversed node kkCorresponding to J ═ Lk-1Evaluation function F of U.T (k)J(akH). If the current node k encountered in the traversal process is a leaf node or all child nodes of k have been traversed, backtracking to the parent node a of kk. (otherwise, continue the forward calculation starting with the first non-traversed child node of k.) for all H0, 1,2, …, H, calculate FJ(akH) is as follows:
when all the nodes have been traversed at least once, backtracking from the node n to the root node to obtainWherein L isn＝{0,1,2,…,n}；
Merging non-fault sections: set variableAndcorrespondingly: if it isRepresentation treeThe optimal subtree under the h constraint comprises a v node; otherwise, explainThe optimal subtree under the h constraint does not contain the v node; as for the root node, it is,the values of (A) are as follows:
for non-root node v, let J ═ L according to equation (10)v-1U.T (v), corresponding to IJ(v, h) takes the following values:
assuming initial v-n and H-H, all v are subject to connectivity constraintsk∈l0,v，Is formed in whichThe node v is marked while letting v-1 and h-dv(ii) a Otherwise, v-1; until v is less than or equal to 0 or h is less than or equal to 0, the marked node generates an optimal non-fault interval.
Compared with the prior art, the invention has the following beneficial effects: the invention provides a power distribution network fault dynamic planning and positioning method, which adopts causal analysis to establish an incidence relation model between automation equipment monitoring information and feeder line states and construct a power distribution network fault positioning mathematical model; the state of the combined optimization problem is simplified by combining a repulsion principle; and performing fault positioning through evaluation function calculation and non-fault section search. The invention divides the fault location division of the power distribution network containing a plurality of DGs into a plurality of knapsack problems based on the repulsion theorem and the dynamic planning theory, effectively reduces the overlapping intersection among the problems, and locates the fault section through the merging process of the non-fault sections. The method solves the problem that the fault location space of the power distribution network is complex, simplifies the state of the combined optimization problem by combining the repulsion principle, reduces the overlapping of sub-problems, reduces the repeated calculation and improves the calculation speed.
Therefore, compared with the prior art, the invention has prominent substantive features and remarkable progress, and the beneficial effects of the implementation are also obvious.
Drawings
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 description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a structural diagram of the open-loop operation of the dual power grid according to the embodiment of the invention.
Fig. 3 is a simplified model diagram of an IEEE69 node distribution network according to an embodiment of the present invention.
Fig. 4 is a table of the results of the fault location simulation of the dynamic programming method according to the embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings.
As shown in fig. 1, a method for dynamically planning and positioning a power distribution network fault includes the following steps:
step 1: and establishing an incidence relation model between the monitoring information of the automation equipment and the feeder line state by adopting causal analysis, and establishing a power distribution network fault positioning mathematical model.
Step 2: and optimizing fault data combination by combining a repulsion principle.
And step 3: and (4) completing fault positioning by calculating an evaluation function of each node of the power distribution network and searching a non-fault interval.
And (3) establishing an incidence relation model between the monitoring information of the automation equipment and the feeder line state by adopting causal analysis in the step (1) and establishing a power distribution network fault positioning mathematical model. The method comprises the steps of adopting state information of a feeder line branch as an internal variable, establishing an approximation relation model between fault current out-of-limit information uploaded by an FTU and the internal variable by using a causal analysis and an analog-to-digital method, constructing a nonlinear programming model containing absolute values on the basis of a fault diagnosis minimum set theory, obtaining characteristics of a time approximation relation model through model extreme values, converting the model extreme values into a linear integer programming model, and accordingly optimizing and solving by adopting a capacitance and repulsion principle and dynamic programming.
(1) First model parameter determination and encoding are performed.
During modeling, the state information of the feeder line branch circuit is required to approach the current out-of-limit information of the automation device collected by the FTU, so that the incoming line breaker, the section switch and the interconnection switch are used as nodes, and the state information of the feeder line branch circuit is used as an internal variable. And still adopting a 0-1 coding mode during coding, wherein the number 1 is adopted to represent the fault of the feeder line section, and the number 0 represents the normal of the feeder line section.
(2) The fault is then located to the best approximated non-logical relationship model.
The approximation relation model is the basis of constructing a fault positioning optimization model, an incidence relation model between automation equipment monitoring information and feeder line states is established by adopting causal analysis, and analysis is carried out by adopting a 6-node single-power-supply radial distribution network as an example. Assuming that x (1) -x (6) are respectively the operation status information of the feeder lines 1-6,respectively representing the current out-of-limit information values of the circuit breaker and the section switch, and taking the value as 1 when overcurrent exists. If circuit breaker S1 in FIG. 2The FTU acquires fault current out-of-limit information, connectivity and power system power flow distribution characteristics are known easily according to graph theory, and current out-of-limit signals are possibly caused by short circuit faults of the feeder lines 1-6. Therefore, the device status information and S of the feeder lines 1-61The FTU current out-of-limit states are directly related, namely x (1) -x (6) are direct reasons for the IS1 value being 1, and the feeder lines 1-6 are calledThe cause and effect device of (1). In the same way, it can be seen that FIG. 2 showsCause and effect feeder devices, cause and effect device ordering and number.
According to the state associated information of the causal equipment, on the premise of single fault assumption, the state information of the causal equipment and the current out-of-limit information of the circuit breaker and the section switch can be established and described on the basis of the fault minimum set theoryThe associated information between them approximates to the relational model. X is a feeder line state vector and,is an approximation function of the corresponding automation device. The symbol V represents the logic "OR", and the built approach relation model is as follows:
analysis can obtain: the switch model can correctly and effectively reflect the association relation between causal equipment, but does not meet the fault diagnosis minimum set theory. Therefore, a false determination will occur because there is a "many-to-one" relationship. The method is improved, although the one-to-one state approximation is realized, the model construction is complex due to the construction based on the logic value theory, the decision calculation cannot be carried out by using a conventional optimization method based on good numerical stability, and the application in a large-scale power distribution network is limited due to the existence of the solving efficiency and the unstable numerical value.
According to the above formula, the logic operation V in the model is changed into subtraction operation, and a new approximation relation model can be obtained as follows:
in the formula, the symbol "-" directly represents the algebraic subtraction operation and also directly contains the parallel superposition characteristic of the coupling effect of the running state information of the causal association equipment on the uploaded alarm information. As can be seen from the comparison of the established approximation relationship model and the logic model, the model not only meets the causal association relationship between the devices, but also avoids the logic relationship operation.
By taking a radial distribution network as an example, the new model is verified to have the advantages of simultaneously meeting the minimum set theory of fault diagnosis and making up the defects of the existing model.
The distribution network fault location indirect method is essentially to find fault current alarm information which can explain most all automatic switches such as FTUs and the like, namely, the difference between all over-current state information caused by feeder line faults and fault current out-of-limit state information uploaded by each monitoring point is supposed to be minimized, the difference is 0 under the most ideal condition, the algebraic sum of the formula is zero, the non-negativity of the value of the formula is considered, and the minimum difference value of 0 is met only when the values of the formula are respectively 0. And analyzing the single feeder fault without information distortion, and if the values of the formula are all 0, accurately finding the preset fault position, which indicates that the new approximation relation model meets the minimum set theory of fault diagnosis.
It is assumed that the FTUs of both the circuit breaker and the sectionalizer obtain fault current out-of-limit information, i.e., it is assumed that the short-circuit fault occurs on the feeder 5, at which timeIs1, and when the value of x (5) is1,the minimum value of 0 can be reached. Fusing the value of x (5), only if the value of x (4) is 0,a minimum value of 0 is reached. In the same way, the method for preparing the composite material, when the value of (2) reaches the minimum value of 0, the values of x (1) to x (3) can only be 0, and the short-circuit fault of the feeder 5 can be identified and is consistent with the assumed fault position. The established approximation relation model meets the fault diagnosis minimum set theory, and a feeder fault section can be accurately positioned.
X is a feeder state vector, and according to the optimal approximation idea of indirect fault location of the power distribution network, a mathematical model of a target function for fault location in the diagram 1 can be expressed as follows:
when there are N automation devices, the distribution network fault location non-logical relationship model with absolute values can be expressed as:
s.t.X＝[x(1),x(2),…,x(n)]
x(i)＝0/1,X∈Rn
in the formula: sj0Automation equipment S for distribution networkjA node position of a first downstream causal association feeder line;is SjNumber of causally related devices.
Different from a radial power distribution network, the ring network open-loop operation power distribution network is provided with a plurality of power distribution areas, no electrical contact exists between different areas, and multiple times of positioning is needed when the areas break down simultaneously. In order to avoid the situation, when fault location is carried out on the power distribution network, a fault diagnosis minimum set theory, a unified labeling idea of the power distribution region and independent power distribution region division are adopted to form the power distribution network into a plurality of single-power-supply radiation type power distribution networks, and then a fault location unified mathematical model of the looped network open-loop operation power distribution network is established in 3 steps of determination of causal equipment association information, establishment of an approximation relation model and conversion of a linear programming model of a target function and a constraint condition. The feeders 1-m belong to an independent power distribution area 1; the feeders m +1 to n belong to the independent power distribution area 2.
According to theoretical analysis and causal association equipment information, a new mathematical model for fault location of the dual-power-supply looped network open-loop operation power distribution network is established as follows:
x(i)＝0/1
and the state of the combined optimization problem is simplified by the aid of the combined repulsion principle in the step 2. And in the dynamic planning subproblem division process by adopting a repulsion principle, the overlapping of subproblems is reduced, the repeated calculation is reduced, and the calculation speed is improved.
In order to reduce the space complexity, the state of the combined optimization problem is simplified by combining a repulsion theory, so that the problem can be completed in polynomial time and can be O (2)k) Time and polynomial space solution, and calculation speed is improved.
The principle of repulsion means that a given set U is given andwherein U is called the corpus, A1,…AnCalled a demand, then
This is true.
And 3, calculating an evaluation function and searching a non-fault section in the step 3 to locate the fault. The non-fault interval division by adopting dynamic planning mainly comprises two stages: evaluation function calculation and optimal non-fault interval search, namely:
(1) calculating the evaluation function value of each node according to the depth-first traversal sequence;
(2) and then judging whether each node is selected to the optimal non-fault section one by one according to the inverse process of depth-first traversal by utilizing the evaluation function values of each node.
Evaluation functionComprises the following steps:
wherein L isk0,1, …, k is a subset of nodes of V.Are subtrees of T generated by these nodes,is the set of this subtree arc.
Node avWhether or not to be selected into the power restoration region depends on whether or not the following expression holds:
in the formula (I), the compound is shown in the specification,wherein, T (a)v) Represented by node avIs the root subtree and H is the maximum number of nodes.
Establishing a non-fault interval: the method includes the steps that root trees are formed by taking different root nodes respectively, then DPA is used for solving TKPs corresponding to the root trees one by one to form a plurality of independent non-fault sections, namely, the problem of dividing the non-fault sections of the power distribution system is decomposed into a plurality of TKPs, and then the TKPs are solved one by one.
(1) And (5) initializing.
Here, L0＝{0}。
(2) And (5) forward calculation.
And calculating the evaluation function of the currently traversed node. Traversing nodes in the tree, and recording the traversed nodes into a set LkWhere k is the node currently traversed, compute for k ≠ 0 and all H ≠ 0,1,2, …, HThe following were used:
the forward pushing process calculates at LkCorresponding tree in case of {0,1,2, …, k }The objective function value of TKP containing node k and constrained by h as requirement.
(3) And (5) backtracking calculation. Calculating the parent node a of the currently traversed node kkCorresponding to J ═ Lk-1Evaluation function F of U.T (k)J(akH). If the current node k encountered in the traversal process is a leaf node or all child nodes of k have been traversed, backtracking to the parent node a of kk. (otherwise, continue the forward calculation starting with the first non-traversed child node of k.) for all H0, 1,2, …, H, calculate FJ(akH) is as follows:
when all the nodes have been traversed at least once, backtracking from the node n to the root node to obtainWherein L isn＝{0,1,2,…,n}。
Merging non-fault sections: set variableAndcorrespondingly: if it isRepresentation treeThe optimal subtree under the h constraint comprises a v node; otherwise, explainThe optimal subtree under the h constraint does not contain the v node. As for the root node, it is,the values of (A) are as follows:
for non-root node v, let J ═ L according to equation (10)v-1U.T (v), corresponding to IJ(v, h) takes the following values:
assuming initial v-n and H-H, all v are subject to connectivity constraintsk∈l0,v，Is formed in whichThe node v is marked while letting v-1 and h-dv(ii) a Otherwise, v-1. Until v is less than or equal to 0 or h is less than or equal to 0, the marked node generates an optimal non-fault interval.
On the basis of the method, the specific application examples are as follows:
an MATLAB/Simulink simulation tool box is utilized to carry out simulation verification on a power distribution network fault section positioning method of a dynamic programming method based on a repulsion principle. A radial distribution network system simulation model is built, each feeder line adopts an IEEE69 node system overhead line parameter model, as shown in figure 3, the length of each section is 3km, 1-69 are 69 measuring points on a feeder line III, and measuring point 1 is a measuring point at the beginning end of the feeder line III (at the outlet of a transformer).
As shown in fig. 4, it can be concluded from the simulation result that the fault location of the power distribution network including the distributed power supply can be well solved by using the dynamic planning method based on the repulsion principle. And when the information uploaded by the FTU is distorted, the work can still be carried out smoothly, so that the dynamic programming method based on the repulsion principle is proved to have good fault tolerance, is not influenced by interference, and can well carry out fault positioning work.
Therefore, the fault location model constructed by the invention can simplify the state of the combined optimization problem by combining the repulsion principle, can make a decision by using a conventional optimization algorithm with good numerical stability and high solving efficiency, can be applied to fault location of a large-scale power distribution network, and has great engineering application value.
The invention is further described with reference to the accompanying drawings and specific embodiments. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and these equivalents also fall within the scope of the present application.
Claims (8)
1. A power distribution network fault dynamic planning and positioning method is characterized by comprising the following steps:
step 1: establishing an incidence relation model between the monitoring information of the automation equipment and the feeder line state by adopting causal analysis, and establishing a power distribution network fault positioning mathematical model;
step 2: optimizing fault data combination by combining a repulsion principle;
and step 3: and (4) completing fault positioning by calculating an evaluation function of each node of the power distribution network and searching a non-fault interval.
2. The power distribution network fault dynamic planning and positioning method according to claim 1, wherein the step 1 comprises: establishing an approximation relation model between fault current out-of-limit information uploaded by an FTU (fiber to the Unit) and an endogenous variable by using state information of a feeder line branch as the endogenous variable; and constructing a nonlinear programming model containing absolute values for the approximation relation model and converting the nonlinear programming model into a power distribution network fault positioning mathematical model.
3. The power distribution network fault dynamic planning and positioning method according to claim 1, wherein the step 1 specifically comprises:
when the approximation relation model is established, the state information of the feeder branch circuit is required to approximate the current out-of-limit information of the automation device acquired by the FTU, so that an incoming line breaker, a section switch and a tie switch are taken as nodes, the state information of the feeder branch circuit is taken as an internal variable, a 0-1 coding mode is adopted during coding, a number 1 is adopted to represent the fault of a feeder section, and a number 0 represents the normal of the feeder section;
the approximation relation model is an incidence relation model which is established between the monitoring information of the automation equipment and the feeder line state by adopting causal analysis, the power distribution network is a 6-node single-power-supply radial power distribution network, x (1) -x (6) are assumed to be the operation state information of the feeder lines 1-6 respectively,respectively representing the current out-of-limit information values of the circuit breaker and the section switch, and taking the value as 1 when overcurrent exists; if the FTU of the circuit breaker S1 acquires fault current out-of-limit information, connectivity and power flow distribution characteristics of a power system are known easily according to graph theory, and the current out-of-limit signal may be caused by short-circuit faults of the feeder lines 1-6; therefore, the device status information and S of the feeder lines 1-61The FTU current out-of-limit states are directly related, namely x (1) -x (6) are direct reasons for the IS1 value being 1, and the feeder lines 1-6 are calledThe cause and effect device of (1);
according to the state associated information of the causal equipment, on the premise of single fault assumption, the state information of the causal equipment and the current out-of-limit information of the circuit breaker and the section switch can be established and described on the basis of the fault minimum set theoryThe associated information between the two approaches to a relational model; x is a feeder line state vector and,an approximation function for the corresponding automation device; the symbol V represents the logic "OR", and the built approach relation model is as follows:
according to the above formula, the logic operation V in the model is changed into subtraction operation, and a new approximation relation model can be obtained as follows:
in the formula, the symbol "-" directly represents algebraic subtraction operation and directly contains the parallel superposition characteristic of the coupling effect of the running state information of the causal association equipment on the uploaded alarm information;
x is a feeder state vector, and when N automation devices are provided, the distribution network fault location non-logical relation model containing absolute values can be expressed as follows:
s.t.X＝[x(1),x(2),…,x(n)]
x(i)＝0/1,X∈Rn
in the formula: sj0Automation equipment S for distribution networkjA node position of a first downstream causal association feeder line;is SjThe number of causally related devices;
different from a radial power distribution network, the ring network open-loop operation power distribution network is provided with a plurality of power distribution areas, no electrical contact exists between different areas, and multiple times of positioning is needed when the areas break down simultaneously. In order to avoid the situation, when fault location is carried out on the power distribution network, a fault diagnosis minimum set theory, a unified labeling idea of the power distribution region and independent power distribution region division are adopted to form the power distribution network into a plurality of single-power-supply radiation type power distribution networks, and then a fault location unified mathematical model of the looped network open-loop operation power distribution network is established in 3 steps of determination of causal equipment association information, establishment of an approximation relation model and conversion of a linear programming model of a target function and a constraint condition. The feeders 1-m belong to an independent power distribution area 1; the feeders m + 1-n belong to the independent power distribution area 2;
according to theoretical analysis and causal association equipment information, a new mathematical model for fault location of the dual-power-supply looped network open-loop operation power distribution network is established as follows:
x(i)＝0/1。
4. the power distribution network fault dynamic planning and positioning method according to claim 1, wherein the repulsion principle adopted in the step 2 specifically is:
refers to a given set U and wherein U is called the corpus, A1,…AnCalled a demand, then
Is established。
5. The power distribution network fault dynamic planning and positioning method according to claim 1, wherein the step 3 specifically includes:
step 31: calculating an evaluation function value of each node of the power distribution network according to a depth-first traversal sequence;
step 32: and judging whether each node is selected to the optimal non-fault section one by one according to the inverse process of depth-first traversal by utilizing the evaluation function values of each node.
6. The power distribution network fault dynamic planning and positioning method according to claim 1, wherein the evaluation functionComprises the following steps:
wherein L isk0,1, …, k is a subset of nodes of V.Are subtrees of T generated by these nodes,is the set of this subtree arc.
Node avWhether or not to be selected into the power restoration region depends on whether or not the following expression holds:
in the formula (I), the compound is shown in the specification,wherein, T (a)v) Represented by node avRoot of Siberian cockleburTree, H is the maximum number of nodes.
7. The method for dynamically planning and positioning the faults of the power distribution network according to claim 6, wherein the establishing process of the non-fault interval comprises the following steps: the method comprises the steps of forming root trees by different root nodes respectively, then utilizing DPA to solve TKPs corresponding to the root trees one by one to form a plurality of independent non-fault sections, namely decomposing the problem of dividing the non-fault sections of the power distribution system into a plurality of TKPs, and then solving one by one.
8. The power distribution network fault dynamic planning and positioning method according to claim 7, wherein the establishment process of the non-fault section specifically comprises:
first, an evaluation function is initialized,here, L0＝{0}；
Then, forward calculation is carried out; the method specifically comprises the following steps:
and calculating the evaluation function of the currently traversed node. Traversing nodes in the tree, and recording the traversed nodes into a set LkWhere k is the node currently traversed, compute for k ≠ 0 and all H ≠ 0,1,2, …, HThe following were used:
the forward pushing process calculates at LkCorresponding tree in case of {0,1,2, …, k }An objective function value of the TKP containing the node k and taking h as a requirement constraint;
finally, backtracking calculation is carried out; the method specifically comprises the following steps:
calculating the current positionTraverse parent node a of node kkCorresponding to J ═ Lk-1Evaluation function F of U.T (k)J(akH). If the current node k encountered in the traversal process is a leaf node or all child nodes of k have been traversed, backtracking to the parent node a of kk. (otherwise, continue the forward calculation starting with the first non-traversed child node of k.) for all H0, 1,2, …, H, calculate FJ(akH) is as follows:
when all the nodes have been traversed at least once, backtracking from the node n to the root node to obtainWherein L isn＝{0,1,2,…,n}；
Merging non-fault sections: set variableAndcorrespondingly: if it isRepresentation treeThe optimal subtree under the h constraint comprises a v node; otherwise, explainThe optimal subtree under the h constraint does not contain the v node; as for the root node, it is,the values of (A) are as follows:
for non-root node v, let J ═ L according to equation (10)v-1U.T (v), corresponding to IJ(v, h) takes the following values:
assuming initial v-n and H-H, all v are subject to connectivity constraintsk∈l0,v，Is formed in whichThe node v is marked while letting v-1 and h-dv(ii) a Otherwise, v-1; until v is less than or equal to 0 or h is less than or equal to 0, the marked node generates an optimal non-fault interval.
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