CN111044847A - Complex power distribution network fault tolerance online fault positioning method based on probability evaluation - Google Patents
Complex power distribution network fault tolerance online fault positioning method based on probability evaluation Download PDFInfo
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Abstract
本发明提出了一种基于概率评估的复杂配电网容错性在线故障定位方法，其步骤为：基于接收到的告警信息对馈线故障概率进行量化；建立自动化开关设备的因果设备；建立独立区域及耦合区域以馈线故障概率为内生变量的馈线故障概率累加特性计算函数；收集电流告警信息并建立概率逼近的开关函数集；基于并联叠加特性极值比较理论建立与馈线区段的故障概率等价的配电网馈线故障定位的概率评估优化模型；基于绝对值等价转换理论建立连续空间的配电网馈线故障定位的概率评估优化模型；控制主站依据馈线故障概率向可能故障馈线区段的紧邻自动化开关发送分闸命令。本发明实现便捷、可靠性高、容错性能力强、故障定位效率高、可应用于大规模配电网的在线定位。
The present invention proposes a fault-tolerant online fault location method for complex distribution network based on probability evaluation. In the coupling area, the feeder fault probability accumulation characteristic calculation function takes the feeder fault probability as the endogenous variable; the current alarm information is collected and the switch function set of probability approximation is established; based on the parallel superposition characteristic extreme value comparison theory, the equivalence of the fault probability of the feeder section is established The probability evaluation optimization model of the distribution network feeder fault location based on the absolute value equivalent transformation theory is established; the probability evaluation optimization model of the distribution network feeder fault location in continuous space is established based on the absolute value equivalence transformation theory; the main station is controlled according to the feeder fault probability to the possible faulty feeder section. The opening command is sent next to the automation switch. The invention is convenient to implement, high in reliability, strong in fault tolerance, and high in fault location efficiency, and can be applied to online location of large-scale distribution networks.
Description
Technical Field
The invention relates to the technical field of intelligent power distribution networks, in particular to a complex power distribution network fault tolerance online fault locating method based on probability evaluation, which can effectively quantize and isolate single fault or multiple fault probabilities when alarm information is not reported or is not reported for a complex power distribution network feeder fault section containing T-shaped coupling nodes.
Background
The operation and management experience of the power distribution network shows that: the automation and the intelligent level of the power distribution network are improved, the economical efficiency of the operation of the power distribution network can be obviously improved, and the safety and the reliability of the operation of the power distribution network can be effectively improved. The fault section positioning of the power distribution network is an important component of intelligent power distribution network construction, is an important technical means for reducing fault power failure time and improving the safety and reliability of power distribution network operation, and is a research hotspot in the field all the time.
The manual line patrol method is adopted for positioning the fault section for a long time, so that the labor intensity of workers of the power system is high, the fault positioning time is long, and the further improvement of the power supply reliability is influenced. With the wide application of power automation Terminal equipment such as Feeder Terminal Units (FTUs) in a power distribution network, the power flow information of the power distribution network can be dynamically acquired, particularly overcurrent alarm information can be directly acquired, the direct coupling action relationship between a Feeder short-circuit fault section and the overcurrent alarm information can be known according to a circuit theory, and the power distribution network fault positioning method based on information acquired by the FTUs can not only avoid the manual participation in the fault positioning process, but also obviously improve the positioning efficiency of the power distribution network fault section.
To date, a great deal of research has been carried out in academic circles on a power distribution network fault location method based on information acquired by an FTU (fiber to the next round) device, and the modeling theory adopted by the power distribution network fault section location method based on fault current information mainly comprises the following steps: artificial intelligence techniques, graph theory algorithms, optimization methods, and the like. But the artificial intelligence technology has weak adaptability to new fault types; the fault tolerance of the graph theory algorithm is generally weak. The power distribution network fault positioning method based on the optimization technology has strong fault tolerance and universality, and attracts a plurality of scholars to conduct research on the method.
Hitherto, the power distribution network fault section positioning method based on the optimization technology mainly comprises a power distribution network fault positioning group intelligent method based on logic optimization and a power distribution network fault section positioning nonlinear programming method based on algebraic modeling. The power distribution network fault positioning group intelligent method based on logic optimization has the advantages that the solving process has dependency on a random group intelligent algorithm, the positioning efficiency is low, the numerical stability is poor, and the fault range can be indirectly enlarged. The power distribution network fault location technology based on algebraic modeling is researched by a system, has good numerical stability and high fault decision efficiency, can be applied to the online fault location problem of large-scale power distribution network faults, has more advantages compared with a power distribution network fault location group intelligent method, but the fault location principle is realized on the basis of feeder line faults or normal two determined states, realizes the identification of feeder line fault section positions based on a deterministic theory framework, but the situations of missing report and false report of power distribution network alarm information are difficult to avoid, has strong uncertainty, solves the power distribution network fault location problem with strong uncertainty by utilizing the deterministic theory, and faces the following difficulties: (1) when the alarm information received by the power distribution network data acquisition system is deviated, the fault result given by an approximation relation model under a fault or normal two-state coding mechanism may be wrong due to the influence of uncertain distortion information, so that the reliability of the method is directly reduced, and wrong judgment and missing judgment of the fault are generated; (2) under a fault or normal two-state coding mechanism, an optimization model contains 0/1 discrete variables, complexity of a decision solving process is increased, and identification efficiency of a fault section is influenced. In addition, the power distribution network fault section positioning nonlinear programming method based on algebraic modeling lacks multiple fault positioning capability with strong adaptability to a complex power distribution network containing T-shaped coupling nodes.
From the above discussion, it can be seen that the power distribution network fault location algebraic modeling method based on the optimization technology in the existing power distribution network fault location method based on the information acquired by the automatic terminal has technical advantages, but still faces the difficult problem of missed judgment and wrong judgment when distortion positions of adjacent points and undistorted phases are equal and the technical problem of lack of strong identification capability of multiple faults for a complex power distribution network due to the adoption of a modeling mechanism of a deterministic theoretical framework. Therefore, a new power distribution network fault location optimization technology with strong alarm information distortion resistance and multiple fault location capability based on an uncertainty theory framework needs to be provided.
Disclosure of Invention
The invention provides a complex power distribution network fault tolerance online fault positioning method based on probability evaluation, aiming at the technical problems that the existing power distribution network fault positioning method still has the missed judgment and the wrong judgment when distortion positions and non-distortion positions of adjacent points are equal and the complex power distribution network lacks the strong identification capability of multiple faults.
In order to achieve the purpose, the technical scheme of the invention is realized as follows: a complex power distribution network fault tolerance online fault positioning method based on probability evaluation comprises the following steps:
the method comprises the following steps: quantifying the fault probability of the feeder line based on the alarm information received by the control master station;
step two: establishing causal equipment of the automatic switch equipment and fault probability description thereof according to the independent area and coupling area division theory of the power distribution network containing the T-shaped coupling node;
step three: according to the electrical characteristics and topological connectivity of the power distribution network and the coupling characteristics among the fault probabilities of causal equipment feeder lines of the independent area and the coupling area, based on algebraic modeling and parallel superposition characteristics, a feeder line fault probability accumulation characteristic calculation function with the fault probabilities of the feeder lines as internal variables in the independent area and the coupling area is established;
step four: collecting current alarm information and establishing a probability approximated switching function set: collecting overcurrent alarm information of feeder switches of the distribution network by using a control main station, and establishing a feeder fault probability accumulation expected value set; establishing a probability approximated switching function set on the basis of the deviation between the feeder fault probability accumulated expected value and the feeder fault probability accumulated characteristic calculation function value;
step five: the method comprises the steps of taking feeder line fault probability as a constraint condition, taking the minimum sum of squared deviations of a switch function set approximated by the probability as an optimization target, and establishing a probability evaluation optimization model of power distribution network feeder line fault location equivalent to the feeder line fault probability based on a parallel superposition characteristic extremum comparison theory;
step six: establishing a probability evaluation optimization model of power distribution network feeder fault location in a continuous space based on an absolute value equivalence conversion theory, and calculating and quantifying the fault probability of a feeder section by an interior point method of nonlinear programming according to overcurrent alarm information uploaded by a feeder switch;
step seven: and the control master station sends a switching-off command to the automatic switch which is close to the feeder line section with possible faults according to the feeder line fault probability, so that the isolation of the feeder line fault section is realized.
The method for quantifying the fault probability of the feeder line comprises the following steps: obtaining a direct calculation model of probability quantitative evaluation of the feeder line fault section based on distortion and non-distortion conditions of the alarm information: p (i) ═ Di/max(Di+di1), wherein p (i) represents the probability of the i-th feeder line failing, diAnd DiAnd respectively representing the distortion number and the non-distortion number of the alarm information associated with the ith feeder line relative to the alarm information of other feeder lines.
The method for establishing causal equipment of the automatic switch equipment in the second step comprises the following steps: taking the automatic switches and the feeders in the independent area and the coupling area as objects, and according to the topological connectivity of a power distribution network and a power flow transmission mechanism, if the fault overcurrent of one automatic switch L in the independent area and the coupling area is directly related to the short-circuit fault of a feeder section i, the feeder section i is a causal device of the automatic switches L in the independent area and the coupling area; the independent areas are divided into: taking a T-shaped coupling node of the power distribution network as a mark, if the other end of a feeder line branch is directly connected with a power supply, all the branches between the T-shaped coupling node and the power supply form an independent area; if the other end of the branch is directly connected with the T-shaped coupling node, all the feeders between the two T-shaped coupling nodes form an independent area; if the other end of the branch circuit has no power supply point or T-shaped coupling node, all feeder circuit branches between the T-shaped coupling node and the branch circuit tail end node form an independent area; the coupling area is divided into: and if no less than two independent areas with power flow coupling exist at the downstream of the independent area of the power distribution network, the independent area is the coupling area of the power distribution network.
The failure probability of the feeder line section i in the independent area and the coupling area is p (i), 0 ≦ p (i) ≦ 1, and p (i) ≦ 0 indicates no failure, and p (i) ≦ 1 indicates a failure.
The method for constructing the fault probability accumulation characteristic calculation function of the feeder line in the independent area comprises the following steps: whether the upstream feeder line of the power distribution network in the independent area fails or not has no influence on the fault accumulation probability of the downstream feeder line, whether the downstream feeder line fails or not can influence the fault accumulation probability of the upstream feeder line, the fault probability accumulation characteristic of the downstream feeder line to the upstream feeder line in the independent area is reflected by algebraic addition operation, and a feeder line fault probability accumulation characteristic calculation function F described by each independent area based on the probabilityK,i(P) is:
wherein n isK,iNumber of causal feeders i downstream of feeder K in independent area, NKThe total number of the feeders of the independent area K, P (l) is the fault probability of the ith feeder, N is the total number of the feeders of the complex distribution network, and P is [ P (1) P (2) … P (N)]Representing a feeder fault probability set.
The method for constructing the fault probability accumulation characteristic calculation function of the feeder line in the coupling area comprises the following steps: whether feeder line on upstream of power distribution network in coupling area is in fault pairThe fault accumulation probability of a downstream feeder line is not influenced, the fault accumulation probability of an upstream feeder line is influenced by whether the downstream feeder line is in fault or not, the fault probability parallel superposition characteristics of all feeder lines in a downstream power coupling independent area are reflected, the fault probability accumulation characteristics of the downstream feeder line to the upstream feeder line in the coupling area are coupled back by algebraic addition, the parallel superposition characteristics of the independent area to the coupling area are described by the extreme value 1 value characteristics of algebraic addition and fault probability parallel accumulation, the extreme value comparison theory of the parallel superposition characteristics is adopted, and the coupling area M is based on a probability-described feeder fault probability accumulation characteristic calculation function FM,j(P) is:
wherein n isM,jNumber of causal feeds, K, downstream of feed j for coupling region MZTotal number of independent areas coupled to the coupling area, mM,jThe number of causal feeds downstream of the feed j of the coupling region M.
The method for establishing the feeder line fault probability accumulation expected value set comprises the following steps: if a section switch uploads overcurrent alarm information, the feeder line fault probability accumulated expected value to the section switch is defined to be 1, otherwise, the feeder line fault probability accumulated expected value to the section switch is defined to be 0, and the feeder line fault probability accumulated expected value is stored based on the incidence relation and the sequence of the causal equipment; the method for establishing the probability approximated switching function set in the fourth step comprises the following steps: when the feeder line fault probability which is most likely to have faults is determined under the scene of no alarm information distortion, the fault probability accumulated value F is usedK,i(P) or FM,j(P) building a switching function with the fault probability accumulation expected value of the alarm information uploaded by the automatic terminal equipment, and when the total number of the feeder lines is N-NK+NMProbabilistic approximation of temporal, algebraic descriptions to switching function MjAnd KiThe constrained mathematical model is:
wherein I represents the feeder number of the independent area K, j represents the feeder number of the coupling area M, and IjAccumulating expected values, I, for feeder fault probabilities to sectionalizers j within an independent area MiAccumulating expected values for feeder fault probabilities to sectionalizers i in independent zones K [ P (1) P (2) … P (N)]Representing a set of feeder fault probabilities, FK,i(P) a probability-based feeder i fault probability accumulation characteristic calculation function for the independent area K, FM,j(P) calculating a function for the coupling region M based on the probability-described feeder j fault probability accumulation characteristics.
The method for establishing the probability evaluation optimization model for the fault location of the feeder line of the power distribution network in the fifth step comprises the following steps: the analytical model describing the switching function according to the probability can know that: under the condition of no alarm information distortion, the probability description switch function analysis model represented by the alarm information distortion has a unique solution, and the probability value of each feeder line fault can be obtained by solving the unique solution; for the condition of missing report or false report of alarm information, due to the non-negative limitation of the fault probability p (i) of the feeder line, according to the fault diagnosis minimum set theory and the overall optimal consistent approximation principle, the switch function M based on probability approximationjAnd KiThe total approximation degree of the probability accumulation characteristic is measured by adopting the sum of squares of deviation and minimization, and the probability evaluation optimization model of the feeder line fault location of the power distribution network is expressed as
Wherein f (P) represents the sum of squares of residual errors between alarm information fault probability accumulated expected values and feeder line section switch causal feeder line fault probability accumulated characteristic calculation functions, NK+MMIs the total number of feeders.
The probability evaluation optimization model for the fault location of the feeder line of the power distribution network in the continuous space, which is established based on the absolute value equivalence conversion theory in the sixth step, is as follows:
wherein, FM,j(P) is a coupling region M groupIn a fault probability accumulation characteristic calculation function of the feeder line j described by the probability, an equivalent mathematical model established based on an absolute value equivalent transformation theory is as follows:
aiming at solving the convex optimization characteristic of the probability evaluation optimization model of the fault location of the feeder line of the power distribution network in the continuous space, directly adopting a nonlinear programming interior point method to make a decision and calculating the fault probability of all the feeder lines; and the control main station carries out fault feeder isolation according to the feeder fault probability, and carries out feeder fault feeder removal according to the sequence of the feeder fault probability from large to small until overcurrent alarm information is not monitored, indicating that the fault feeder isolation is successfully realized.
The invention has the beneficial effects that: compared with the prior art, the method is realized under the framework based on the uncertainty theory, has higher credibility and stronger fault tolerance compared with an algebraic modeling fault section positioning method under the deterministic theory framework, can directly obtain the fault probability of all feeder sections which are possible to have faults, can provide a maximum possible fault removal scheme for a decision maker, can carry out fault removal according to a sequential heuristic method from large to small in fault probability, preferentially tries to remove the feeder with large fault probability, still has overcurrent alarm information after removal to indicate that the feeder sections do not have faults, needs to try to remove the feeder with small fault probability when the fault cannot be effectively removed, carries out fault isolation depending on the feeder sections with small fault probability, is in accordance with multiple fault positioning of the feeder sections of the power distribution network, and the constructed fault probability evaluation model does not contain a least square model of a discrete variable, the method meets the convex optimization characteristic, can directly adopt an interior point method to decide and solve, has strong numerical stability, and is more suitable for online fault location of a large-scale complex radial distribution network.
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 some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a circuit diagram of a radial distribution network with T-coupling in normal operation of the present invention.
Fig. 3 is a diagram of an independent area of a circuit of a radial distribution network with T-coupling according to the present invention.
Fig. 4 is a circuit diagram of a radial distribution network with T-type coupling when the dual feeder line of the present invention is in fault operation.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
As shown in fig. 1, when a line of a power distribution network fails, the probability evaluation method for fault tolerance online fault location of a complex radial power distribution network of the present invention may be adopted, and the method includes the following steps:
the method comprises the following steps: based on the alarm information received by the control main station, the feeder line fault probability is quantized firstly, and an uncertainty probability evaluation value of a feeder line fault section is obtained.
The basic invention is as follows: obtaining a direct calculation model of the quantitative evaluation of the fault probability of the feeder line based on the distortion and non-distortion conditions of the alarm information, wherein the uncertainty probability evaluation value of the fault section of the feeder line is as follows: p (i) ═ Di/max(Di+di1), wherein p (i) represents the probability of the i-th feeder line failing, diAnd DiAnd respectively representing the distortion number and the non-distortion number of the alarm information associated with the ith feeder line relative to the alarm information of other feeder lines.
As in FIGS. 2, 3, and 4, S1For the inlet line breakers of substations S2、S3、……、S8Being section switches, circuit breakers S of the feeder1And a section switch S2-S8The rear sides are their respective feeders 1-8. When the feeder line section switch I has fault overcurrent, the alarm value is 1, otherwise, the value is 0, and for the alarm set I in fig. 2, 3 and 4, [ 11101000 ]]Of the distortion number d of the feeder 3i＝I5And a non-distortion number Di＝I3All of which are 1, the distortion number d of the feed line 5i＝I4And a non-distortion number Di＝I5All have a value of 1, according to the calculation model p (i) ═ Di/max(Di+di1) and therefore the failure probability estimates for feeder 3 and feeder 5 are both 0.5.
Step two: according to the theory of dividing the independent area and the coupling area of the power distribution network containing the T-shaped coupling node, causal equipment of the automatic switch equipment and the fault probability description of the causal equipment are established.
Independent regional division of distribution network: taking a T-shaped coupling node of the power distribution network as a mark, if the other end of a feeder line branch is directly connected with a power supply, all the branches between the T-shaped coupling node and the power supply form an independent area; if the other end of the branch is directly connected with the T-shaped coupling node, all the feeders between the two T-shaped coupling nodes form an independent area; if the other end of the branch circuit has no power supply point or T-shaped coupling node, all feeder circuit branches between the T-shaped coupling node and the branch circuit tail end node form an independent area. Circuit breaker S in FIG. 21And T-type coupling node D1The feeder lines 1, 2 and 3 among the feeder lines form an independent area 3; t-type coupling node D1And a section switch S5The feeder lines 4 and 5 between the two form an independent area 1; t-type coupling node D1And a section switch S8The feed lines 6, 7, 8 between constitute the individual areas 2.
Dividing a coupling area of a power distribution network: and if no less than two independent areas with power flow coupling exist at the downstream of the independent area of the power distribution network, the independent area is the coupling area of the power distribution network. There are two power flow coupling independent areas, independent area 1 and independent area 2, downstream of independent area 3, and therefore independent area 3 is coupling area 3.
The method for establishing a causal device of an automatic switchgear comprises the following steps: the method is characterized in that automatic switches and feeders in an independent area and a coupling area are taken as objects, and according to the topological connectivity of a power distribution network and a power flow transmission mechanism, if fault overcurrent of one automatic switch L in the independent area and the coupling area is directly related to short-circuit fault of a feeder section i, the feeder section i is causal equipment of the automatic switches L in the independent area and the coupling area.
As shown in fig. 2, according to the topology connectivity theory and the power flow direction, if the fault overcurrent of a certain automatic switch S is directly related to the fault short-circuited in the feeder line section i, the feeder line section i is a causal device of the automatic switch S. In the coupling zone 3, when the circuit breaker S1When the alarm information of the monitoring point is uploaded, according to network topology connectivity and a power flow transmission mechanism, the monitoring point can know that the short-circuit fault of the feeder lines 1-3 possibly causes the breaker S1A cause and effect device for current alarm information; when section switch S2When the alarm information of the monitoring point is uploaded, according to network topology connectivity and a power flow transmission mechanism, it can be known that the short-circuit fault of the feeder lines 2-3 may cause the sectional switch S2A cause and effect device for current alarm information; when section switch S3When the alarm information of the monitoring point is uploaded, according to the network topology connectivity and the transmission mechanism of the power flow, it is known that the short-circuit fault possibly occurs to the feeder line 3, which causes the section switch S3Causal equipment for current alarm information. In the independent area 1, when the switch S is segmented4When the alarm information of the monitoring point is uploaded, according to the network topology connectivity and the power flow transmission mechanism, it can be known that the short-circuit fault of the feeder lines 4-5 may cause the section switch S4A cause and effect device for current alarm information; when section switch S5When the alarm information of the monitoring point is uploaded, according to the network topology connectivity and the transmission mechanism of the power flow, it is known that the short-circuit fault possibly occurs to the feeder 5, which causes the section switch S5Causal equipment for current alarm information. Independent area 2, when section switch S6When the alarm information of the monitoring point is uploaded, according to network topology connectivity and a power flow transmission mechanism, the monitoring point can know that the short-circuit fault possibly occurs to the feeder lines 6-8, which causes the short-circuit faultSection switch S6A cause and effect device for current alarm information; when section switch S7When the monitoring point has alarm information to upload, according to the network topology connectivity and the transmission mechanism of the power flow, it is known that the short-circuit fault may occur in the feeders 7 and 8, which is the cause of the section switch S7Cause and effect of current alarm information; when section switch S8When the alarm information of the monitoring point is uploaded, according to the network topology connectivity and the transmission mechanism of the power flow, it is known that the short-circuit fault possibly occurs to the feeder line 8, which causes the section switch S8Causal equipment for current alarm information. The fault probability description of the causal equipment set and faulty feeder established for the coupling zone 3, the independent zone 1 and the independent zone 2 in fig. 2 is shown in table 1.
TABLE 1 causal Equipment set and probability description for an Automation switch
The failure probability of the feeder line section i in the independent area and the coupling area is p (i), 0 ≦ p (i ≦ 1), p (i) ≦ 0 indicates no failure, p (i) ≦ 1 indicates a failure, and 0 < p (i) < 1 indicates that the failure probability thereof is p (i).
Step three: according to the electrical characteristics and topological connectivity of the power distribution network and the coupling characteristics among the fault probabilities of causal equipment feeder lines of the independent area and the coupling area, on the basis of algebraic modeling and parallel superposition characteristics, a feeder line fault probability cumulative characteristic calculation function with the feeder line fault probability p (i) as an internal variable is established in the independent area and the coupling area.
(1) Constructing a calculation function of the probability accumulation characteristics of the feeder line faults in the independent area
Whether the upstream feeder line of the power distribution network in the independent area fails or not has no influence on the fault accumulation probability of the downstream feeder line, whether the downstream feeder line fails or not influences the fault accumulation probability of the upstream feeder line, the fault probability accumulation characteristic of the downstream feeder line of the independent area to the upstream feeder line is reflected by algebraic addition operation, and n is assumedK,iThe number of causal feeders downstream of the feeder i in the independent area K is N, and the total number of feeders in the independent area K is NKWhen each independent area is based onProbability-described mathematical model F of feeder fault probability accumulation characteristic calculation functionK,i(P) can be represented as:
where P (l) is the fault probability of the ith feeder, and P ═ P (1) P (2) … P (n) ] represents the feeder fault probability set.
For the distribution network in fig. 2, the cumulative probability of failure of the upstream feeder line should be equal to the algebraic sum of the probabilities of failure of the feeder line and the downstream causal feeder line, and the cumulative characteristic calculation function of the feeder line failure probabilities of the independent area 1 and the independent area 2 is:
F1,4(P)＝p(4)+p(5)，
F1,5(P)＝p(5)，
F2,6(P)＝p(6)+p(7)+p(8)，
F2,7(P)＝p(7)+p(8)，
F2,8(P)＝p(8)。
(2) constructing a calculation function of the probability accumulation characteristics of the feeder line fault in the coupling area
The feeder fault probability accumulation characteristic calculation function of the coupling area reflects whether the upstream feeder of the power distribution network in the coupling area has a fault or not and has no influence on the fault accumulation probability of the downstream feeder, and whether the downstream feeder has a fault or not can influence the fault accumulation probability of the upstream feeder, and simultaneously reflects the fault probability parallel superposition characteristic of all the feeders in the downstream power coupling independent area, the fault probability accumulation characteristic of the downstream feeder in the coupling area to the upstream feeder is reversely coupled by algebraic addition, and the parallel superposition characteristic of the independent area to the coupling area is described by the extreme value 1 value characteristic of algebraic addition and fault probability parallel accumulation. KZFor the total number of independent regions coupled to the coupling region, assume mM,jNumber of causal feeds downstream of feed j for coupling zone M, MMThe total number of the feeders in the independent area adopts the extreme value comparison theory of the parallel superposition characteristics, and the coupling area M adopts a mathematical model F of a feeder fault probability accumulation characteristic calculation function based on probability descriptionM,j(P) can be represented as:
wherein n isM,jNumber of causal feeds, K, downstream of feed j for coupling region MZTotal number of independent areas coupled to the coupling area, mM,jThe number of causal feeds downstream of the feed j of the coupling region M.
The feeder fault probability accumulation characteristic calculation function of the coupling region 3 in fig. 2 is:
F3,1(P)＝p(1)+p(2)+p(3)+min[F1,4(P)+F2,6(P),1]，
F3,2(P)＝p(2)+p(3)+min[F1,4(P)+F2,6(P),1]，
F3,3(P)＝p(3)+min[F1,4(P)+F2,6(P),1]。
step four: collecting current alarm information and establishing a probability approximated switching function set: the method comprises the steps that overcurrent alarm information of feeder switches of a uniform distribution network is collected by a control main station, if a section switch uploads the overcurrent alarm information, a feeder fault probability accumulation expected value to the section switch is defined to be 1, otherwise, the feeder fault probability accumulation expected value to the section switch is defined to be 0, and storage is carried out based on the incidence relation and the sequence of causal equipment; and then, establishing a switch function set with probability approximation based on the deviation between the feeder fault probability accumulation expected value and the feeder fault probability accumulation characteristic calculation function value.
As shown in fig. 1 and 2, S1The feeder sections 1-8 are the incoming breakers S of substation SUB11SUB1 of the substation S2-S8The feeder line section switch is a feeder line automatic switch. Assume that feeders 5 and 7 are malfunctioning and that two conditions are set: (1) if the FTU information distortion does not exist, fault overcurrent occurs in the feeder line section switches 1-8, and the fault overcurrent is detected according to the serial number S of the section switches1、S2、……、S8The feeder fault probability accumulation expected value set formed at this time is as follows: [111111110](ii) a (2) Presence of section switch S3Or S6One-bit information missing report and sectional switch S3And a section switch S6And if two bits of information are missed, the feeder fault probability accumulation expected value sets formed at the moment are respectively as follows: [110111110]、[1 1 1 11 0 11 0]、[1 1 0 1 1 0 1 1 0]。
The invention aims to find out the corresponding equipment with faults by using the switching function, so that the equipment can explain the feeder fault probability accumulated expected value obtained by the control main station. Therefore, when a probability description switch function analysis model is constructed, the following requirements are met: when the feeder fault probability which is most likely to have faults is determined under the scene of no alarm information distortion, the fault probability accumulated value F quantized by the associated characteristic analytical model is obtainedK,i(P) or FM,j(P) and alarm information fault probability accumulated expected value I uploaded by automatic terminal equipmentiThe switching function is constructed by completely approximating the total number of the feeders, i.e. the difference is 0, and when the total number of the feeders is N, the total number of the feeders is NK+MMProbabilistic approximation of temporal, algebraic descriptions to switching function MjAnd KiThe constrained mathematical model is:
wherein I represents the feeder number of the independent area K, j represents the feeder number of the coupling area M, and IjAccumulating expected values, I, for feeder fault probabilities to feeder j within independent region MiAccumulating expected values for feeder fault probabilities to feeder i within independent region K [ P (1) P (2) … P (N)]Representing a set of feeder fault probabilities, FK,i(P) a probability-based feeder i fault probability accumulation characteristic calculation function for the independent area K, FM,j(P) calculating a function for the coupling region M based on the probability-described feeder j fault probability accumulation characteristics.
Based on a differentiated approximation relationship representation method in a calculation method, in the power distribution network shown in fig. 2, an analytic model of a probability description switching function with constrained algebraic modeling is as follows:
step five: and establishing a probability evaluation optimization model of the power distribution network feeder fault location equivalent to the feeder fault section uncertainty probability evaluation value p (i) based on a parallel superposition characteristic extremum comparison theory by taking the feeder fault probability 0 not more than p (i) not more than 1 as a constraint condition and taking the probability approximated switch function set deviation square sum minimum as an optimization target.
The analytical model describing the switching function according to the probability can know that: the probability description switch function analysis model represented by the probability description switch function analysis model has a unique solution under the condition of no alarm information distortion, the probability value of each feeder line fault can be obtained by solving the unique solution, however, for the condition that alarm information is not reported or is false reported, the probability description switch function analysis model has the characteristic of incompatibility among equations due to the non-negativity limitation of the feeder line fault probability p (i), and at the moment, the total approximation degree is measured by adopting the residual error square sum minimization in the calculation method according to the fault diagnosis minimum set theory and the total optimal consistent approximation principle. A probability evaluation optimization model for power distribution network feeder fault location is based on a probability approximation switching function M according to a fault diagnosis minimum set theory and an overall optimal consistent approximation principlej、KiAnd KlAnd measuring the total approximation degree of the probability accumulation characteristic by using the deviation square sum minimization in a calculation method so as to calculate the probability of the fault of the feeder line. When the total number of the feeder lines is NK+MMIn time, the probability evaluation optimization model for the fault location of the feeder line of the power distribution network can be expressed as
Wherein f (P) represents the sum of squares of residual errors between alarm information fault probability accumulated expected values and feeder line section switch causal feeder line fault probability accumulated characteristic calculation functions, NK+MMIs the total number of feeders.
The probability evaluation optimization model for the fault location of the feeder line of the power distribution network shown in FIG. 2 can be expressed as
Step six: a probability evaluation optimization model of power distribution network feeder fault location in a continuous space is established based on an absolute value equivalence conversion theory, and fault probability p (i) of a feeder line section is calculated and quantized through an interior point method of nonlinear programming according to overcurrent alarm information uploaded by a feeder line switch.
The coupling region is based on a mathematical model F of a probability description feeder fault probability accumulation characteristic calculation functionM,j(P), the equivalent mathematical model established based on the absolute value equivalent transformation theory is as follows:
wherein, FM,j(P) calculating a function for the coupling region M based on the probability-described fault probability accumulation characteristic of the feeder j.
Probability description-based feeder fault probability accumulation characteristic calculation function mathematical model F of coupling region 3 in FIG. 23,1(P)、F3,2(P)、F3,3(P), the equivalent mathematical model established based on the absolute value equivalent transformation theory is as follows:
the probability evaluation optimization model of the feeder line fault location of the power distribution network, which is equivalently established based on the absolute value equivalence conversion theory, of the continuous space is as follows:
the probability evaluation optimization model for the fault location of the feeder line of the power distribution network in the continuous space in fig. 2 is as follows:
and (3) aiming at the convex optimization characteristic of the fault section positioning probability evaluation optimization model of the continuous space, directly adopting a nonlinear programming interior point method to carry out decision solving, and calculating the fault probability of all the feeder lines. The results of fault location without information distortion and with information distortion for the specific examples of fig. 1, 2 and 3 are shown in table 2:
TABLE 2 Fault location simulation results
Note: "-" indicates that the formula p (i) ═ D cannot be used directlyi/max(Di+diAnd 1) calculating a probability evaluation value.
Step seven: and the control master station sends a switching-off command to the automatic switch which is close to the feeder line section with possible faults according to the feeder line fault probability, so that the isolation of the feeder line fault section is realized.
And the control main station carries out fault feeder isolation according to the feeder fault probability, and carries out feeder fault feeder removal according to the sequence of the feeder fault probability from large to small until overcurrent alarm information is not monitored, which indicates that the fault feeder isolation is successfully realized. And according to the fault probability result of the number 4 of the feeder fault section location completed in the step seven, the fault probability of the feeder 5 is 1, and the calculation probability of the feeder 7 is 0.5. At this time, because the fault probability of the feeder line 5 is high, the control master station preferentially sends a brake-off command to the automatic switches at the two ends of the feeder line 5, and deletes the probability corresponding to the brake-off command, so that the isolation of the feeder line fault section 5 is realized, the fault of the feeder line 7 is 0.5, at this time, the feeder lines 5 and 7 belong to different feeder line independent areas, at this time, the control master station sends a brake-off command to the automatic switches at the two ends of the feeder line 7, so that the isolation of the feeder line fault section 7 is realized, and the fault is successfully removed. At this time, if the method under the deterministic framework is adopted, only the feeder 5 can be isolated, and the fault of the feeder 7 cannot be isolated successfully, so that the method has obvious high fault tolerance, high reliability and multiple fault section positioning capability.
The method comprises the steps that a control main station is used for collecting current alarm information of each feeder section switch of the power distribution network, feeder fault probability is quantized, and a feeder fault probability accumulation expected value set is established based on an independent area and a coupling area; establishing a probability approximated switching function set; establishing a probability evaluation optimization model of power distribution network feeder fault location equivalent to the feeder fault section uncertainty probability evaluation value p (i) based on a parallel superposition characteristic extreme value comparison theory; establishing a probability evaluation optimization model of power distribution network feeder fault location in a continuous space based on an absolute value equivalence conversion theory and calculating fault probabilities of all feeders by using a nonlinear programming interior point method; and realizing the positioning and isolation of the fault feeder line section according to the probability value. The method realizes high fault-tolerant positioning when alarm information is distorted in a single fault section or multiple fault sections of the feeder line of the power distribution network containing the T-shaped coupling node, and has the advantages of convenience in realization, high reliability, strong fault-tolerant capability, high fault positioning efficiency, applicability to online positioning of a large-scale power distribution network and the like.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (10)
1. A complex power distribution network fault tolerance online fault positioning method based on probability evaluation is characterized by comprising the following steps:
the method comprises the following steps: quantifying the fault probability of the feeder line based on the alarm information received by the control master station;
step two: establishing causal equipment of the automatic switch equipment and fault probability description thereof according to the independent area and coupling area division theory of the power distribution network containing the T-shaped coupling node;
step three: according to the electrical characteristics and topological connectivity of the power distribution network and the coupling characteristics among the fault probabilities of causal equipment feeder lines of the independent area and the coupling area, based on algebraic modeling and parallel superposition characteristics, a feeder line fault probability accumulation characteristic calculation function with the fault probabilities of the feeder lines as internal variables in the independent area and the coupling area is established;
step four: collecting current alarm information and establishing a probability approximated switching function set: collecting overcurrent alarm information of feeder switches of the distribution network by using a control main station, and establishing a feeder fault probability accumulation expected value set; establishing a probability approximated switching function set on the basis of the deviation between the feeder fault probability accumulated expected value and the feeder fault probability accumulated characteristic calculation function value;
step five: the method comprises the steps of taking feeder line fault probability as a constraint condition, taking the minimum sum of squared deviations of a switch function set approximated by the probability as an optimization target, and establishing a probability evaluation optimization model of power distribution network feeder line fault location equivalent to the feeder line fault probability based on a parallel superposition characteristic extremum comparison theory;
step six: establishing a probability evaluation optimization model of power distribution network feeder fault location in a continuous space based on an absolute value equivalence conversion theory, and calculating and quantifying the fault probability of a feeder section by an interior point method of nonlinear programming according to overcurrent alarm information uploaded by a feeder switch;
step seven: and the control master station sends a switching-off command to the automatic switch which is close to the feeder line section with possible faults according to the feeder line fault probability, so that the isolation of the feeder line fault section is realized.
2. The complex distribution network fault tolerance online fault location method based on probability evaluation as claimed in claim 1, wherein the quantification method of the feeder line fault probability is: obtaining a direct calculation model of probability quantitative evaluation of the feeder line fault section based on distortion and non-distortion conditions of the alarm information: p (i) ═ Di/max(Di+di1), wherein p (i) represents the probability of the i-th feeder line failing, diAnd DiRespectively representing alarm information associated with the ith feeder line relative to other feeder linesThe distortion number and the non-distortion number of the line alarm information.
3. The complex power distribution network fault tolerance online fault location method based on probability evaluation as claimed in claim 1 or 2, wherein the method for establishing the causal equipment of the automatic switch equipment in the second step is as follows: taking the automatic switches and the feeders in the independent area and the coupling area as objects, and according to the topological connectivity of a power distribution network and a power flow transmission mechanism, if the fault overcurrent of one automatic switch L in the independent area and the coupling area is directly related to the short-circuit fault of a feeder section i, the feeder section i is a causal device of the automatic switches L in the independent area and the coupling area; the independent areas are divided into: taking a T-shaped coupling node of the power distribution network as a mark, if the other end of a feeder line branch is directly connected with a power supply, all the branches between the T-shaped coupling node and the power supply form an independent area; if the other end of the branch is directly connected with the T-shaped coupling node, all the feeders between the two T-shaped coupling nodes form an independent area; if the other end of the branch circuit has no power supply point or T-shaped coupling node, all feeder circuit branches between the T-shaped coupling node and the branch circuit tail end node form an independent area; the coupling area is divided into: and if no less than two independent areas with power flow coupling exist at the downstream of the independent area of the power distribution network, the independent area is the coupling area of the power distribution network.
4. The complex distribution network fault tolerance online fault location method based on probability evaluation as claimed in claim 3, wherein the fault probability of feeder line section i in the independent area and the coupling area is p (i), 0 ≦ p (i) ≦ 1, and p (i) ≦ 0 represents no fault, and p (i) ≦ 1 represents fault.
5. The complex distribution network fault tolerance online fault location method based on probability evaluation as claimed in claim 4, wherein the method for constructing the independent area feeder fault probability accumulation characteristic calculation function is as follows: whether the upstream feeder line of the power distribution network in the independent area has faults or not has no influence on the fault accumulation probability of the downstream feeder line, and whether the downstream feeder line has faults or not can influence the fault accumulation probability of the upstream feeder lineThe fault probability accumulation characteristic of the downstream feeder line to the upstream feeder line in the independent areas is reflected by algebraic addition operation, and each independent area is based on a probability-described feeder line fault probability accumulation characteristic calculation function FK,i(P) is:
wherein n isK,iNumber of causal feeders i downstream of feeder K in independent area, NKThe total number of the feeders of the independent area K, P (l) is the fault probability of the ith feeder, N is the total number of the feeders of the complex distribution network, and P is [ P (1) P (2) … P (N)]Representing a feeder fault probability set.
6. The complex distribution network fault tolerance online fault location method based on probability evaluation as claimed in claim 3 or 4, wherein the method for constructing the coupled area feeder fault probability accumulation characteristic calculation function is as follows: whether an upstream feeder line of a power distribution network in a coupling area has a fault or not has no influence on the fault accumulation probability of a downstream feeder line, whether the downstream feeder line has the fault or not can influence the fault accumulation probability of the upstream feeder line, the fault probability parallel superposition characteristics of all feeder lines in a downstream power coupling independent area are reflected, the fault probability accumulation characteristics of the downstream feeder line in the coupling area to the upstream feeder line are coupled back by algebraic addition, the parallel superposition characteristics of the independent area to the coupling area are described by the aid of extreme value 1 value characteristics of algebraic addition and fault probability parallel accumulation, and a feeder line fault probability accumulation characteristic calculation function F based on probability description in the coupling area M is compared by adopting a parallel superposition characteristic extreme value comparison theoryM,j(P) is:
wherein n isM,jNumber of causal feeds, K, downstream of feed j for coupling region MZTotal number of independent areas coupled to the coupling area, mM,jThe number of causal feeds downstream of the feed j of the coupling region M.
7. The complex distribution network fault tolerance online fault location method based on probability evaluation as claimed in claim 6, wherein the establishment method of the feeder line fault probability accumulation expectation value set is as follows: if a section switch uploads overcurrent alarm information, the feeder line fault probability accumulated expected value to the section switch is defined to be 1, otherwise, the feeder line fault probability accumulated expected value to the section switch is defined to be 0, and the feeder line fault probability accumulated expected value is stored based on the incidence relation and the sequence of the causal equipment; the method for establishing the probability approximated switching function set in the fourth step comprises the following steps: when the feeder line fault probability which is most likely to have faults is determined under the scene of no alarm information distortion, the fault probability accumulated value F is usedK,i(P) or FM,j(P) building a switching function with the fault probability accumulation expected value of the alarm information uploaded by the automatic terminal equipment, and when the total number of the feeder lines is N-NK+NMProbabilistic approximation of temporal, algebraic descriptions to switching function MjAnd KiThe constrained mathematical model is:
wherein I represents the feeder number of the independent area K, j represents the feeder number of the coupling area M, and IjAccumulating expected values, I, for feeder fault probabilities to sectionalizers j within an independent area MiAccumulating expected values for feeder fault probabilities to sectionalizers i in independent zones K [ P (1) P (2) … P (N)]Representing a set of feeder fault probabilities, FK,i(P) a probability-based feeder i fault probability accumulation characteristic calculation function for the independent area K, FM,j(P) calculating a function for the coupling region M based on the probability-described feeder j fault probability accumulation characteristics.
8. The complex distribution network fault tolerance online fault location method based on probability evaluation as claimed in claim 7, wherein the establishment method of the probability evaluation optimization model for distribution network feeder line fault location in the fifth step is as follows: resolution of switching function by probability descriptionThe model can know that: under the condition of no alarm information distortion, the probability description switch function analysis model represented by the alarm information distortion has a unique solution, and the probability value of each feeder line fault can be obtained by solving the unique solution; for the condition of missing report or false report of alarm information, due to the non-negative limitation of the fault probability p (i) of the feeder line, according to the fault diagnosis minimum set theory and the overall optimal consistent approximation principle, the switch function M based on probability approximationjAnd KiThe total approximation degree of the probability accumulation characteristic is measured by adopting the sum of squares of deviation and minimization, and the probability evaluation optimization model of the feeder line fault location of the power distribution network is expressed as
Wherein f (P) represents the sum of squares of residual errors between alarm information fault probability accumulated expected values and feeder line section switch causal feeder line fault probability accumulated characteristic calculation functions, NK+MMIs the total number of feeders.
9. The complex distribution network fault tolerance online fault location method based on probability evaluation as claimed in claim 8, wherein the probability evaluation optimization model of distribution network feeder fault location of continuous space established based on the absolute value equivalence transformation theory in the sixth step is:
wherein, FM,j(P) a fault probability accumulation characteristic calculation function of the feeder line j based on probability description in the coupling region M, wherein an equivalent mathematical model established based on an absolute value equivalent transformation theory is as follows:
10. the complex power distribution network fault tolerance online fault location method based on probability evaluation as claimed in claim 9, wherein the fault probability of all the feeders is calculated by directly adopting a nonlinear programming interior point method for decision making aiming at the convex optimization characteristic of the probability evaluation optimization model for solving the fault location of the feeder line of the power distribution network in the continuous space; and the control main station carries out fault feeder isolation according to the feeder fault probability, and carries out feeder fault feeder removal according to the sequence of the feeder fault probability from large to small until overcurrent alarm information is not monitored, indicating that the fault feeder isolation is successfully realized.
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