Disclosure of Invention
The invention provides a probability evaluation method for fault tolerance online fault location of a complex active power distribution network, aiming at the technical problems that the existing power distribution network fault location method is easy to miss and misjudge and lacks strong adaptability to the complex active power distribution network feeder fault location problem.
In order to achieve the purpose, the technical scheme of the invention is realized as follows: a probability evaluation method for fault tolerance online fault location of a complex active power distribution network comprises the following steps:
the method comprises the following steps: the method comprises the following steps of performing partition decoupling on a complex active power distribution network, and dividing the complex active power distribution network into two area divisions of a simple active power distribution network and a single-power-supply radial power distribution network containing T-type coupling nodes by taking a power supply as a mark;
step two: quantifying the fault probability of the feeder line based on the alarm information received by the control master station;
step three: aiming at a radial power distribution network containing T-shaped coupling nodes, according to the independent area and coupling area division theory, causal equipment of automatic switch equipment and fault probability description thereof are established;
step four: the method comprises the steps that a simple active power distribution network is split into a plurality of single-power-supply radial power distribution networks, and cause-effect equipment of automatic switching equipment and fault probability description of the cause-effect equipment are established on the basis of all split single-power-supply radial power distribution networks;
step five: aiming at a radial power distribution network containing T-shaped coupling nodes, establishing a feeder fault probability accumulation characteristic calculation function of an independent area and a coupling area by taking the feeder fault probability as an internal variable based on algebraic modeling and parallel superposition characteristics according to the electrical characteristics and topological connectivity of the power distribution network and the coupling characteristics among the feeder fault probabilities of causal equipment in the independent area and the coupling area;
step six: aiming at a simple active power distribution network, establishing a feeder fault probability accumulation characteristic calculation function taking the feeder fault probability as an internal variable aiming at each radial power distribution network belonging to the simple power distribution network based on algebraic modeling according to the electrical characteristics of the power distribution network, topological connectivity and the coupling characteristics among the feeder fault probabilities of causal equipment, and establishing the feeder fault probability accumulation characteristic calculation function of the simple active power distribution network under the action of a plurality of power supply sources based on an overlapping principle;
step seven: aiming at a radial power distribution network containing T-shaped coupling nodes, current alarm information is collected and a probability approximation switch function set is established: collecting overcurrent alarm information of each feeder switch of the simultaneous distribution network by using a control main station, if a certain switch uploads the overcurrent alarm information, defining the feeder fault probability accumulation expected value to the section switch to be 1, otherwise, defining the feeder fault probability accumulation expected value to the section switch to be 0, and storing the feeder fault probability accumulation expected value based on the incidence relation and the sequence of the causal equipment; 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 eight: aiming at a simple active power distribution network, collecting current alarm information and establishing a switch function set with approximate probability: one power supply is taken as a main power supply, a fault current reference direction is given, a control main station is utilized to collect overcurrent alarm information of each feeder switch of the distribution network, if a section switch uploads the overcurrent alarm information and the direction of the section switch is the same as the reference direction, the feeder fault probability accumulation expected value of the section switch is defined to be 1, if a section switch uploads the overcurrent alarm information and the direction of the section switch is opposite to the reference direction, the feeder fault probability accumulation expected value of the section switch is defined to be-1, and if a section switch does not have the overcurrent alarm information, the feeder fault probability accumulation expected value of the section switch is defined to be 0; 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 nine: the feeder fault probability is taken as a constraint condition, the minimum square sum of deviation of a switching function set approximated by the probability is taken as an optimization target, and a probability evaluation optimization model of power distribution network feeder fault location equivalent to the feeder fault section fault probability is established;
step ten: 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 a nonlinear programming interior point method according to overcurrent alarm information uploaded by a feeder switch;
step eleven: and the control master station sends a brake-off command to an adjacent automatic switch of the feeder line section with possible faults according to the feeder line fault probability calculated in the step ten, so that the isolation of the feeder line fault section is realized.
The basic method for the partition decoupling in the step one is as follows: if the most upstream feeder line and the most downstream feeder line which are electrically coupled with the i-section feeder line are directly connected with a power supply, the i-section feeder line is divided into an active power distribution network, and other feeder lines are divided into a radial power distribution network.
The method for quantifying the fault probability of the feeder line in the second step comprises the following steps: based on the distortion and non-distortion condition of the alarm information, a direct calculation model for quantitative evaluation of the fault probability of the feeder line is provided: 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 third 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 method for dividing the independent area comprises the following steps: 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 method for dividing the coupling area comprises the following steps: at least two independent areas with power flow coupling exist at the downstream of the independent area of the power distribution network, and the independent areas are coupling areas; in the fourth step, the method for establishing causal equipment of the automatic switch equipment based on all the cracked single-power-supply radial power distribution networks comprises the following steps: the method is characterized in that automatic switches and feeders in the radial distribution network are taken as objects, and according to the topological connectivity of the distribution network and a power flow transmission mechanism, if fault overcurrent of one automatic switch L in a radial distribution network graph is directly related to short-circuit fault of a feeder section i, the feeder section i is causal equipment of the automatic switch L in the radial distribution network.
The method for describing the fault probability in the third step comprises the following steps: 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 failure; the method for describing the fault probability in the fourth step comprises the following steps: the fault probability of a feeder section i in a simple active power distribution network is p (i), 0 ≦ p (i) ≦ 1, and p (i) ≦ 0 indicates no fault, and p (i) ≦ 1 indicates a fault.
The method for constructing the fault probability accumulation characteristic calculation function of the feeder line in the independent area in the fifth step comprises the following steps: 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, whether the downstream feeder line has faults 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 the probability-based feeder line fault accumulation characteristic calculation function of each independent area is as follows:
wherein n isK,iNumber of causal feeders downstream of feeder i for independent area K, NKTotal number of feeders, P, for an individual zone KKA feeder fault probability set which is composed of single feeder fault probabilities of K distribution networks in independent areas is represented, p (l) is the feeder fault probability of the number l, FK,i(PK) A feeder fault probability cumulative characteristic calculation function corresponding to the ith feeder section switch of the independent area K;
the method for constructing the feeder fault probability accumulation characteristic calculation function of the coupling area in the step five comprises the following steps: 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 reflected 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, and the extreme value comparison theory of the parallel superposition characteristics is adopted, wherein the coupling area is based on a probability-described feeder fault probability accumulation characteristic calculation function FM,j(P) is:
wherein, KZTotal number of independent areas coupled to the coupling area, mM,jNumber of causal feeds downstream of feed i of coupling region M, MMTotal number of feeders for individual areas, PMRepresenting a feeder fault probability set, F, consisting of single feeder fault probabilities of M power distribution networks in a coupling areaK,1(P) represents a feeder fault probability accumulation characteristic calculation function of the most upstream feeder section switch in the independent area K, wherein K represents an independent area number, M represents a coupling area number, and FM,j(PM) Calculating the feeder fault probability accumulation characteristics corresponding to the jth feeder section switch of the coupling region MA function.
In the sixth step, the method for establishing the feeder fault probability cumulative characteristic calculation function of each radial distribution network of the simple distribution network comprises the following steps: whether the upstream feeder line of the single-power-supply radial distribution network 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 single-power-supply radial distribution network on the upstream feeder line after being cracked is reflected by algebraic addition operation, and the feeder line fault probability accumulation characteristic calculation function F of each single-power-supply radial distribution network after being cracked is described on the basis of the probabilityD,x,y(PD) Is composed of
Wherein, FD,x,y(PD) Representing the fault probability cumulative distribution function, n, corresponding to the feeder line y in the x single-power radial distribution network after the splittingD,yThe number of causal feeders at the downstream of the feeder y of the single-power radial distribution network x after the splitting is NDThe total number of the feeders of the single-power radial distribution network after the splitting is represented by P (h), and the failure probability description of the feeder h is represented by PDRepresenting a feeder fault probability set consisting of single feeder fault probabilities of the single power distribution network after the single active power distribution network is cracked corresponding to the simple active power distribution network;
in the sixth step, the mathematical model of the simple active power distribution network feeder fault probability accumulation characteristic calculation function under the action of multiple power supplies is established based on the superposition principle, and the mathematical model comprises the following steps:
FD,y(PD)=FD,1,y(PD)(1-FD,2,y(PD))-(1-FD,1,y(PD))FD,2,y(PD)y=1,2,…,ND,
wherein, FD,1,y(PD) Representing the fault probability cumulative distribution function F corresponding to the feeder line y in the single-power radial distribution network 1 after the splittingD,2,y(PD) And (3) accumulating the distribution function of the fault probability corresponding to the feeder line y in the single-power radial distribution network 2 after the splitting.
The method for establishing the probability approximated switching function set in the seventh step and the eighth step comprises the following steps: 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 FK,i(PK)、FM,j(PM) And FD,y(PD) Respectively accumulating expected values I with the failure probability of the alarm information uploaded by the automatic terminal equipmenti、Ij、IyShould be completely approximated, i.e. the difference is 0, when the total number of feeders is N ═ NK+MM+NDProbability description switch function M of algebraic modeling with constraintsj、KiAnd DyThe analytical model of (2) is:
the method for establishing the probability evaluation optimization model in the ninth step comprises the following steps: based on the fault diagnosis minimum set theory and the overall optimal consistent approximation principle, the switching function M based on probability approximationj、Ki、KlAnd DyMeasuring the total approximation degree of the probability accumulation characteristic by using the deviation sum of squares minimization, and when the total number of feeders is NK+MMIn time, the probability evaluation optimization model for the fault location of the feeder line of the power distribution network is expressed as follows:
wherein f (P) represents the sum of squares of residual errors between alarm information fault probability accumulation expected values and feeder line section switch causal feeder line fault probability accumulation characteristic calculation functions;
feeder fault probability accumulation characteristic calculation function F based on probability description in coupling areaM,j(P) the equivalent mathematical model established based on the absolute value equivalent transformation theory is as follows:
in the step ten, the probability evaluation optimization model for the fault location of the feeder line of the power distribution network in the continuous space is established based on the absolute value equivalence conversion theory and comprises the following steps:
the probability evaluation optimization model for the fault location of the feeder line of the power distribution network in the continuous space has a convex optimization characteristic, and the fault probability of all feeder lines is directly calculated by adopting a nonlinear programming interior point method for decision solution; and in the eleventh step, the fault feeder line of the feeder line is cut off according to the sequence of the fault probability of the feeder line from large to small until the fault alarm information is not monitored, which indicates that the fault feeder line is successfully isolated.
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 possibly faulted of a complex active power distribution network, 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 of the fault probability, preferentially test removal of the feeder with large fault probability, and try removal of the feeder with small fault probability when overcurrent alarm information still exists after removal of the feeder, which indicates that the feeder sections are not faulted, and can not effectively remove the fault at the moment, and carry out fault isolation depending on the feeder sections with small fault probability, thereby being in conformity with the fault positioning of the feeder sections of the complex active power distribution network, and the constructed multi-fault probability evaluation model does not contain a least square model of discrete variables, the method meets the convex optimization characteristic, can directly adopt an interior point method to make a decision and solve, has strong numerical stability, and is more suitable for online fault location of large-scale complex active power distribution networks.
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 active power distribution network according to the present invention may be adopted, and the steps are as follows:
the method comprises the following steps: the method comprises the steps of conducting partition decoupling on a complex active power distribution network, and dividing the complex active power distribution network into two area divisions of a simple active power distribution network and a single-power-supply radial power distribution network with T-shaped coupling nodes by taking a power supply as a mark.
The basic method comprises the following steps: if the most upstream feeder line and the most downstream feeder line which are electrically coupled with the i-section feeder line are directly connected with a power supply, the i-section feeder line is divided into an active power distribution network, and other feeder lines are divided into a radial power distribution network.
As shown in FIG. 2(a), S1、S11For the inlet line breakers of substations S2、S3、……、S10Is a section switch of the feeder line. As shown in FIG. 2, the most upstream feeder line and the incoming breaker S which are electrically coupled with the feeder lines 1-51And when the most downstream feeder lines which are electrically coupled with the feeder lines 1-5 are connected with the distributed power supply, the feeder lines 1-5 form a simple active power distribution network, as shown in fig. 2(b), and other feeder lines 6-10 form a radial power distribution network containing T-shaped coupling nodes, as shown in fig. 2 (c).
Step two: and quantifying the fault probability of the feeder line based on the alarm information received by the control main station.
The basic method comprises the following steps: based on the distortion and non-distortion condition of the alarm information, a direct calculation model for quantitative evaluation of the fault probability of the feeder line is provided: p (i) ═ Di/max(Di+di1), wherein p (i) represents the probability of the fault of the ith feeder section, namely the uncertainty probability assessment value of the feeder fault section, 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.
When the feeder section switch i has fault overcurrent, the alarm value is 1, otherwise the value is 0, and the alarm set [ 1110100000 ] in fig. 5 is aimed at according to the principle]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 p (i) ═ Di/max(Di+di1) and therefore the failure probability estimates for feeder 3 and feeder 5 are both 0.5.
Step three: aiming at a radial power distribution network containing T-shaped coupling nodes, causal equipment of automatic switch equipment and fault probability description thereof are established according to the independent area and coupling area division theory.
As shown in fig. 2(b), the distribution network is divided into independent areas: 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. Fig. 3 shows a section switch S8And a coupling node D1The feeder lines 8 between them form an independent area 1; coupling node D1And a section switch S10The feeder lines 9 and 10 between the two form an independent area 1; coupling node D1And a section switch S6The feed lines 6, 7 between constitute the separate areas 3.
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 a power distribution network coupling area. 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.
Establishing a causal device: 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. 3, 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 region 3, when the section switch S6When the alarm information of the monitoring point is uploaded, according to network topology connectivity and a power flow transmission mechanism, the situation that the feeder lines 6-7 are caused by short-circuit faults, which is the cause of the section switch S, can be known6A cause and effect device for current alarm information; when section switch S7When the monitoring point has alarm information to upload, the monitoring point is connected according to the network topologyThe communication and power flow transmission mechanism is known, and may be caused by short-circuit fault of the feeder 7, which causes the section switch S7Causal equipment for current alarm information. Independent area 1, 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. For independent area 2, when the switch S is segmented9When 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 9-10 may cause the section switch S9A cause and effect device for current alarm information; when section switch S10When 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 10, which is caused by the sectional switch S10Cause and effect of the 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. 3 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, 0 < p (i) < 1 indicates that the failure probability is p (i), and i indicates the feeder line number.
Step four: the method comprises the steps of splitting a simple active power distribution network into a plurality of single-power-supply radial power distribution networks, and establishing causal equipment of automatic switch equipment and fault probability description of the causal equipment based on all split single-power-supply radial power distribution networks.
The simple active distribution network of fig. 4(a) comprises two power sources S1And a distributed power source G represented as a power source S alone as shown in FIG. 4(b)1Single power supply radial distribution network and method of operationA single power radial distribution network powered by a distributed power supply G, as shown in fig. 4 (c).
A causal device is established for fig. 4(b), 4 (c): by taking the automatic switches and feeders in the radial distribution networks 4(b) and 4(c) as objects, according to the network topology connectivity of the distribution network and the transmission mechanism of power flow, if a fault overcurrent occurs in a certain automatic switch L in fig. 4(b) or 4(c) of the radial distribution network and a short-circuit fault occurs in a feeder section i and is directly related, the feeder section i is a causal device of the automatic switch L in fig. 4(b) or 4(c) of the radial distribution network.
As shown in fig. 4(b), 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. 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 1-5 is possibly caused, and the short-circuit fault is caused to 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 2-5 is possibly caused, and the fault is a section 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 network topology connectivity and a power flow transmission mechanism, the situation that the short-circuit fault occurs to the feeder lines 3-5, which is the cause of the section switch S, can be known3A cause and effect device for current alarm information; when section switch S4When 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 S5Cause and effect of the current alarm information. In the same way, the causal equipment of FIG. 4(c) is obtained. For FIGS. 4(b) andthe failure probability description of the causal equipment set and the failed feeder established in fig. 4(c) is shown in table 2.
TABLE 2 causal Equipment set and probability description for an Automation switch
The probability description method of the simple active power distribution network cause-effect equipment comprises the following steps: the fault probability of a feeder section i in a simple active power distribution network is p (i), 0 ≦ p (i) ≦ 1, p (i) ≦ 0 indicates no fault, p (i) ≦ 1 indicates a fault, 0 < p (i) < 1 indicates that the fault probability is p (i), and i indicates a feeder number.
Step five: aiming at a radial power distribution network containing T-shaped coupling nodes, a feeder fault probability accumulation characteristic calculation function with feeder fault probability p (i) as an internal variable in an independent area and a coupling area is established based on algebraic modeling and parallel superposition characteristics according to the electrical characteristics and topological connectivity of the power distribution network and the coupling characteristics among the feeder fault probabilities of causal equipment 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 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 mathematical model F of a feeder line fault probability accumulation characteristic calculation function based on probability description in each independent areaK,i(P) can be represented as:
wherein n isK,iNumber of causal feeders downstream of feeder i for independent area K, NKTotal number of feeders, P, for an individual zone KKA feeder fault probability set which represents the single feeder fault probability of the K distribution networks in the independent areas, and p (l) a feeder fault probability summary with the number lRate, FK,i(PK) And calculating a function for the feeder fault probability accumulation characteristic corresponding to the ith feeder section switch of the independent area K.
That is, the accumulated probability of the fault of the upstream feeder line should be equal to the algebraic sum of the fault probabilities of the feeder line and the downstream causal feeder line, and the accumulated characteristic calculation function of the fault probabilities of the feeder lines in the independent area 1 and the independent area 2 is as follows: ,
F1,8(PK)=p(8),
F2,9(PK)=p(9)+p(10),
F2,10(PK)=p(10)。
(2) constructing a calculation function of the probability accumulation characteristics of the feeder line fault in the coupling area
The coupled region feeder fault probability accumulation characteristic calculation function reflects whether the upstream feeder of the power distribution network in the coupled region has no influence on the downstream feeder fault accumulation probability, and whether the downstream feeder has a fault and 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 region, the fault probability accumulation characteristic of the downstream feeder to the upstream feeder in the coupled region is reversely coupled by algebraic addition, the parallel superposition characteristic of the independent region to the coupled region is described by the extreme value 1 value characteristic of algebraic addition and fault probability parallel accumulation, the extreme value comparison theory of the parallel superposition characteristic is adopted, and the coupled region is based on the probability-described feeder fault probability accumulation characteristic calculation function mathematical model FM,j(P) can be represented as:
wherein, KZTotal number of independent areas coupled to the coupling area, mM,jNumber of causal feeds downstream of feed i of coupling region M, MMTotal number of feeders for individual areas, PMRepresenting a feeder fault probability set, F, consisting of single feeder fault probabilities of M power distribution networks in a coupling areaK,1(P) feeder fault summary of the most upstream feeder section switch in the independent area KA rate accumulation characteristic calculation function, K represents an independent area number, M represents a coupling area number, FM,j(PM) And calculating a function for the feeder fault probability accumulation characteristic corresponding to the jth feeder section switch in the coupling region M.
The feeder fault probability accumulation characteristic calculation function of the coupling region 3 in fig. 3 is:
F3,6(PM)=p(6)+p(7)+min[F1,8(PK)+F2,9(PK),1],
F3,7(PM)=p(7)+min[F1,8(PK)+F2,9(PK),1]。
step six: aiming at a simple active power distribution network, according to the electrical characteristics of the power distribution network, topological connectivity and the coupling characteristics among the feeder fault probabilities of causal equipment, on the basis of algebraic modeling, a feeder fault probability accumulation characteristic calculation function taking the feeder fault probability p (i) as an internal variable is established for each radial power distribution network belonging to the simple power distribution network, and the simple active power distribution network feeder fault probability accumulation characteristic calculation function under the action of a multi-power supply is established on the basis of a superposition principle.
The fault probability accumulation characteristic calculation function (relation with each radial distribution network feeder fault probability accumulation characteristic calculation function of the simple distribution network) of the single-power-supply radial distribution network after the splitting reflects whether the upstream feeder of the single-power-supply radial distribution network has no influence on the fault accumulation probability of the downstream feeder thereof due to the fault or not, and the fault accumulation probability of the upstream feeder is influenced due to the fault or not of the downstream feeder, the fault probability accumulation characteristic of the downstream feeder of the single-power-supply radial distribution network to the upstream feeder after the splitting is reflected by algebraic addition operation, and the feeder fault probability accumulation characteristic calculation function mathematical model F of each single-power-supply radial distribution network after the splitting is described based on the probabilityD,x,y(PD) Comprises the following steps:
wherein, FD,x,y(PD) For radiation of a single power supply after cleavingCumulative distribution function of fault probability, n, corresponding to feeder line y in x-shaped distribution networkD,yThe number of causal feeders at the downstream of the feeder y of the single-power radial distribution network x after the splitting is NDThe total number of the feeders of the single-power radial distribution network after the splitting is represented by P (h), and the failure probability description of the feeder h is represented by PDAnd (4) a feeder line fault probability set consisting of single feeder line fault probabilities of the single power distribution network after the single active power distribution network is cracked corresponding to the simple active power distribution network is represented.
In the figure 4(a), the total number of the simple active power distribution network feeders is equal to 5, and in the figure 4(b) of the single-power radial power distribution network after the splitting, a mathematical model F of a feeder fault probability accumulation characteristic calculation function based on probability descriptionD,1,y(PD) Can be expressed as:
FD,1,1(PD)=p(1)+p(2)+p(3)+p(4)+p(5),
FD,1,2(PD)=p(2)+p(3)+p(4)+p(5),
FD,1,3(PD)=p(3)+p(4)+p(5),
FD,1,4(PD)=p(4)+p(5),
FD,1,5(PD)=p(5)。
probability description-based mathematical model F of feeder fault probability accumulation characteristic calculation function in fig. 4(c) of single-power radial distribution network after splittingD,2,y(PD) Can be expressed as:
FD,2,1(PD)=0,
FD,2,2(PD)=p(1),
FD,2,3(PD)=p(1)+p(2),
FD,2,4(PD)=p(1)+p(2)+p(3),
FD,2,5(PD)=p(1)+p(1)+p(3)+p(4),
the method comprises the following steps of establishing a mathematical model of a simple active power distribution network feeder fault probability accumulation characteristic calculation function under the action of multiple power supply sources based on the superposition principle:
FD,y(PD)=FD,1,y(PD)(1-FD,2,y(PD))-(1-FD,1,y(PD))FD,2,y(PD)y=1,2,…,ND,
wherein, FD,1,y(PD) Representing the fault probability cumulative distribution function F corresponding to the feeder line y in the single-power radial distribution network 1 after the splittingD,2,y(PD) And representing a fault probability cumulative distribution function corresponding to the feeder line y in the single-power supply radial distribution network 2 after the splitting.
The method comprises the following steps of establishing a mathematical model of a simple active power distribution network feeder fault probability accumulation characteristic calculation function under the action of multiple power supply sources based on the superposition principle:
FD,1(PD)=FD,1,1(PD)(1-FD,2,1(PD))-(1-FD,1,1(PD))FD,2,1(PD),
FD,2(PD)=FD,1,2(PD)(1-FD,2,2(PD))-(1-FD,1,2(PD))FD,2,2(PD),
FD,3(PD)=FD,1,3(PD)(1-FD,2,3(PD))-(1-FD,1,3(PD))FD,2,3(PD),
FD,4(PD)=FD,1,4(PD)(1-FD,2,4(PD))-(1-FD,1,4(PD))FD,2,4(PD),
FD,5(PD)=FD,1,5(PD)(1-FD,2,5(PD))-(1-FD,1,5(PD))FD,2,5(PD)。
step seven: aiming at a radial power distribution network containing T-shaped coupling nodes, current alarm information is collected and a probability approximation switch function set is established: collecting overcurrent alarm information of each feeder switch of the simultaneous distribution network by using a control main station, if a certain switch uploads the overcurrent alarm information, defining the feeder fault probability accumulation expected value to the section switch to be 1, otherwise, defining the feeder fault probability accumulation expected value to the section switch to be 0, and storing the feeder fault probability accumulation expected value based on the incidence relation and the sequence of the causal equipment; and establishing a switch function set with approximate probability on the basis of the deviation between the feeder fault probability accumulation expected value and the feeder fault probability accumulation characteristic calculation function value.
The final purpose of the probability evaluation method for the positioning of the fault section of the power distribution network is to find out the corresponding equipment with the fault by using a switching function, so that the equipment can best explain the feeder fault probability accumulation expected value acquired by the control main station. Therefore, when a probability description switch function analysis model is constructed, the following requirements are met: when the feeder line fault probability which is most likely to have faults is determined in the scene without alarm information distortion, the fault probability accumulated value quantized by the associated characteristic analysis model and the alarm information fault probability accumulated expected value uploaded by the automatic terminal equipment are completely approximate, namely the difference is 0.
Based on the representation method of the approximation relationship of differentiation in the calculation method, the power distribution network containing T-shaped coupling nodes shown in figure 3 has an analytic model of probability description switch function with constraint algebraic modeling as
Step eight: aiming at a simple active power distribution network, collecting current alarm information and establishing a switch function set with approximate probability: the method comprises the steps of setting a fault current reference direction by taking one power supply as a main power supply, utilizing a control main station to collect overcurrent alarm information of feeder switches of a distribution network simultaneously, defining the feeder fault probability accumulation expected value of the switch to be 1 if a certain section switch uploads the overcurrent alarm information and the direction of the certain section switch is the same as the reference direction, defining the feeder fault probability accumulation expected value of the section switch to be-1 if a certain switch uploads the overcurrent alarm information and the direction of the certain switch is opposite to the reference direction, defining the feeder fault probability accumulation expected value of the section switch to be 0 if a certain section switch does not have the overcurrent alarm information, and then establishing a switch function set with probability approaching based on the deviation between the feeder fault probability accumulation expected value and a feeder fault probability accumulation characteristic calculation function value.
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 I quantized by the associated characteristic analytical model is obtainedyThe failure probability accumulation expected value of the alarm information uploaded by the automatic terminal equipment is completely approximate, namely the difference is 0. Based on the representation method of the approximation relationship of differentiation in the calculation method, the simple active power distribution network shown in FIG. 4(a) has an analytic model of probability description switch function with constraint algebraic modeling as
Using fault probability accumulations FK,i(P)、FM,j(P) and FD,y(P) and alarm information fault probability accumulated expected value I uploaded by automatic terminal equipmenti、Ij、IyConstructing a switching function by the difference, and when the total number of the feeder lines is N-NK+MM+NDProbabilistic approximation of temporal, algebraic descriptions to switching function Mj、KiAnd DyThe constrained mathematical model is:
step nine: and establishing a probability evaluation optimization model of the fault location of the feeder line of the power distribution network, which is equivalent to the fault probability p (i) of the feeder line fault section, by taking the feeder line fault probability 0 not more than p (i) not more than 1 as a constraint condition and taking the minimum square sum of the deviation of the switching function set approximated by the probability as an optimization target.
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, however, for the condition that alarm information is not reported or is misinformed, due to the non-negativity limitation of the feeder line fault probability p (i), the probability description switch function analysis model has the condition that the probability description switch function analysis model has faultsAnd (3) the incompatibility characteristic among the equations, and at the moment, the total approximation degree is measured by adopting the residual error sum of squares 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 complex active 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、Ki、KlAnd DyAnd 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 follows:
and f (P) represents the sum of squares of residuals between alarm information fault probability accumulation expected values and feeder line section switch causal feeder line fault probability accumulation characteristic calculation functions.
The probability evaluation optimization model for distribution network feeder fault location shown in fig. 5 can be expressed as:
step ten: 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 a nonlinear programming inner point method according to overcurrent alarm information uploaded by a feeder line switch.
Probability description-based feeder fault probability accumulation characteristic calculation function mathematical model F for coupling regionM,j(PM) The equivalent mathematical model established based on the absolute value equivalent transformation theory is as follows:
probability description-based feeder fault probability accumulation characteristic calculation function mathematical model F of coupling region 3 in FIG. 33,6(PM)、F3,7(PM) An equivalent mathematical model established based on the absolute value equivalent transformation theory is
The probability evaluation optimization model for the fault location of the feeder line of the power distribution network is based on the absolute value equivalence conversion theory to establish a probability evaluation optimization model for the fault location of the feeder line of the power distribution network in a continuous space
The probability evaluation optimization model for power distribution network feeder line fault location in continuous space, which is equivalently established based on the absolute value equivalence transformation theory, of the probability evaluation optimization model for power distribution network feeder line fault location in fig. 5 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.
As shown in fig. 5, the simulation is performed for three cases of information distortion and no information distortion when a single feeder, a double feeder and a triple feeder fail. Considering that the fault situation is more, for a single fault, only the conditions of no information distortion (1111-, and only aiming at the condition that no information distortion (1111-. Table 3 shows the results of the fault location simulation of the complex active power distribution network.
TABLE 3 Fault location simulation results
Note: "-" indicates that the formula p (i) ═ D cannot be used directlyi/max(Di+di1) calculating a probability evaluation value; "N" indicates that the probability evaluation value does not need to be calculated.
Step eleven: and the control master station sends a brake-off command to an adjacent automatic switch of the feeder line section with possible faults according to the feeder line fault probability calculated in the step ten, so that the isolation of the feeder line fault section is realized.
And (4) cutting off the fault feeder line of the feeder line according to the sequence of the fault probability of the feeder line from large to small until the overcurrent alarm information is not monitored, indicating that the fault feeder line is successfully isolated. According to the fault probability result of the number 11 of the feeder fault section location completed in the step ten, the fault probability of the feeder 1 and the feeder 4 is 1, the calculation probability of the feeder 8 is 1, and the fault probability of the feeder 10 is 0.5. At this time, because the fault probability of the feeder line 8 is greater than 1, the control master station preferentially sends a brake-off command to the automatic switches at the two ends of the feeder line 8, and deletes the probability corresponding to the brake-off command, so that the isolation of the feeder line fault section 8 is realized, the fault of the feeder line 10 is 0.5, the feeder lines 10 and 8 belong to different feeder line independent areas, and at this time, the control master station sends the brake-off command to the automatic switches at the two ends of the feeder line 8, so that the isolation of the feeder line fault section 8 is realized, and the fault is successfully removed; at this time, the probability of the feeder line 1 and the probability of the feeder line 4 are both 0.5, but the feeder line 4 is positioned at the downstream, and the control master station sends a brake-off command to the automatic switches at the two ends of the feeder line 4 to successfully remove the fault. At this time, if the method under the deterministic framework is adopted, only the feeders 3 and 8 can be isolated, and misjudgment occur, so that the method has obvious high fault tolerance, high reliability and multiple fault section positioning capability.
According to the method, the complex active power distribution network is subjected to partition decoupling, and is divided into two area divisions, namely a simple active power distribution network and a single-power radial power distribution network with T-shaped coupling nodes by taking a power supply as a mark; collecting current alarm information of each feeder switch of the power distribution network by using a control main station, and quantifying the fault probability of the feeders; establishing a feeder fault probability accumulation expected value set based on an independent area and a coupling area of a single-power radial distribution network containing T-type coupling nodes; establishing a switching function set containing a T-shaped coupling node single-power-supply radial distribution network independent area and coupling area probability approximation; aiming at a simple active power distribution network, establishing a feeder fault probability accumulation characteristic calculation function taking the feeder fault probability as an internal variable aiming at each radial power distribution network belonging to the simple power distribution network based on algebraic modeling, and establishing the simple active power distribution network feeder fault probability accumulation characteristic calculation function under the action of multiple power supply sources based on a superposition principle; establishing a probability evaluation optimization model of power distribution network feeder fault location equivalent to the feeder fault section uncertainty probability evaluation value 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 for a single fault section or multiple fault sections of the feeder line of the complex active power distribution network, and has the advantages of convenience in realization, high reliability, strong fault-tolerant capability, high fault positioning efficiency, applicability to online positioning of the large-scale complex active 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.