CN117335384A - Power distribution network fault recovery reconstruction method based on ant colony algorithm - Google Patents

Power distribution network fault recovery reconstruction method based on ant colony algorithm Download PDF

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CN117335384A
CN117335384A CN202311074398.9A CN202311074398A CN117335384A CN 117335384 A CN117335384 A CN 117335384A CN 202311074398 A CN202311074398 A CN 202311074398A CN 117335384 A CN117335384 A CN 117335384A
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王强
薛昊南
于永鑫
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Dengzhou Power Supply Co Of State Grid Henan Electric Power Co
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Dengzhou Power Supply Co Of State Grid Henan Electric Power Co
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Abstract

The invention relates to a power distribution network fault recovery reconstruction method based on an ant colony algorithm, which comprises the following steps: step 1: constructing a power distribution network fault recovery mathematical model; step 2: introducing an ant colony algorithm in the fault recovery of the power distribution network; step 3: recovering faults of the power distribution network based on an ant colony algorithm; step 4: constructing a power distribution network recovery reconstruction mathematical model; step 5: carrying out model solving by adopting an ICQPSO algorithm based on an integer type coding mode; step 6: analyzing an example; the method has the advantages of establishing a multi-target model, having global searching capability, being capable of being converted into single-target optimization, reducing searching space and avoiding reconstructing dimension disasters.

Description

Power distribution network fault recovery reconstruction method based on ant colony algorithm
Technical Field
The invention belongs to the technical field of power distribution network faults, and particularly relates to a power distribution network fault recovery reconstruction method based on an ant colony algorithm.
Background
The power distribution network recovery reconstruction and the network optimization reconstruction are network reconstruction realized based on different side reconstruction planes of the topology structure adjustment of the power distribution network; the distribution network generally has the characteristics of most sectionalizers, few tie switches, closed-loop design and open-loop operation; the network reconstruction is that a dispatcher optimizes the operation parameters by changing the states of the sectionalizing switch and the final-connection switch so as to enable the operation parameters to reach the power supply requirement; in order to reduce power failure loss and improve power supply quality of a power grid when a certain line of the power distribution network has permanent faults, the faults cannot be simply isolated, and a power loss load of a fault area is transferred to a non-fault area by changing states of a sectionalizing switch and a connecting switch, so that recovery of the power loss load is realized; the existing power distribution network fault recovery algorithm mainly comprises a traditional optimization algorithm, a heuristic algorithm and an artificial intelligence algorithm, but as the power grid structure and the running mode become more complex, the limitation of the existing method is increased, and the existing method is easy to sink into local optimum, but cannot be globally optimized; in addition, because the network loss before and after the reconstruction is different, the recovery reconstruction cannot simply assume that the network loss is unchanged; therefore, it is very necessary to provide a power distribution network fault recovery reconstruction method based on an ant colony algorithm, which builds a multi-objective model, has global searching capability, can be converted into single-objective optimization, reduces searching space, and avoids reconstruction dimension disaster.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a power distribution network fault recovery reconstruction method based on an ant colony algorithm, which is used for establishing a multi-target model, has global searching capability, can be converted into single-target optimization, reduces searching space and avoids reconstruction dimension disaster.
The purpose of the invention is realized in the following way: a power distribution network fault recovery reconstruction method based on an ant colony algorithm comprises the following steps:
step 1: constructing a power distribution network fault recovery mathematical model;
step 2: introducing an ant colony algorithm in the fault recovery of the power distribution network;
step 3: recovering faults of the power distribution network based on an ant colony algorithm;
step 4: constructing a power distribution network recovery reconstruction mathematical model;
step 5: carrying out model solving by adopting an ICQPSO algorithm based on an integer type coding mode;
step 6: and (5) analyzing an example.
The construction of the power distribution network fault recovery mathematical model in the step 1 specifically comprises the following steps: the fault recovery of the power distribution network is a multi-objective, multi-stage and multi-constraint nonlinear optimization problem, and an objective function is established according to the recovered objective and constraint: minw=p+t (1), where W is the loss suffered by the utility company after the failure; p is the system network loss; t is the operation cost of the switch; besides ensuring that a user can timely recover power supply and reduce loss and ensuring benefits, the network loss during operation of the power distribution network after recovery is ensured to be the minimum in the network structure after recovery, so that the loss of an electric company after a fault occurs is reduced to the minimum, the benefits of the electric company are ensured, and the network loss during operation after the fault recovery of the power distribution network is ensured to be the minimum, namely:S i ≤S i,max ，U i,min ≤U i ≤U i,max wherein P is loss The network loss of the power distribution network; n is the branch number of the power distribution network; r is R i The branch resistance of the ith branch; p (P) i 、Q i Active power and reactive power of branch i respectively; u (U) i The node voltage at the tail end of the branch i; k (K) i A state variable of a switch on a branch, wherein 0 represents opening and 1 represents closing; s is S i 、S i,max Calculating the power flowing through each branch i and the maximum allowable value thereof; u (U) i,min 、U i,max Upper voltage limits of nodes i, respectivelyAnd a lower limit value; switches in a power distribution network are generally classified into two types according to the operation conditions: a sectionalizer switch and a tie switch; as a device that is operated frequently for power restoration, the lifetime is affected by the operation, so that each fault restoration should operate the switch as little as possible, minimizing losses, so that losses of switch wear are added to the objective function, namely: />Wherein T is a Loss of wear for the switch; s is S sec,i The switch is a sectional switch, and the action sign is 1; s is S con,j The action sign is 1 for the contact switch; the summation operation means that 1 is added once each time the switch acts; m and n are respectively the number of switches of each section counted according to the section of the feeder terminal unit; k (K) sec 、K con The loss conversion coefficients of the sectionalizing and tie-switch actions, respectively.
The ant colony algorithm introduced in the fault recovery of the power distribution network in the step 2 specifically comprises the following steps: the ant colony algorithm is a learning algorithm with positive feedback, through learning, the knowledge of the ant is continuously corrected, each ant carries out communication through pheromones, the amount of the pheromones on each side is continuously regulated so as to realize learning, the searching strategy of the ant colony algorithm is practically given in the form of probability, when the algorithm selects the searching direction, the algorithm is more likely to face to the found better solution domain, and meanwhile, the algorithm is likely to select other directions, so that the algorithm is not easy to fall into local optimum, which side of the ant k selected from a set at the moment t is determined by the conversion probability, and the probability that the ant k at the node b is selected to move to the node c is as follows:wherein F is t k = {0,1,..} is a set of possible paths for ant k next step; />The amount of pheromone on the sides (b, c) at the moment t; η (eta) bc For the visibility of the sides (b, c), in the reconstruction of the distribution network, it is set as the reciprocal of the impedance of each side; alpha, beta are two parameters, namely, alpha, beta is two parameters,reflecting the relative importance of the accumulated information and heuristic information of ants in the motion process in the ant selection path, the more sides of the pheromone are easy to be selected.
The power distribution network fault recovery process based on the ant colony algorithm in the step 3 specifically comprises the following steps:
step 3.1: and (3) a power distribution network fault recovery flow: firstly, analyzing a power failure area, and judging all power supply paths of a non-failure area searching power failure area, namely a contact switch adjacent to a power supply area to be recovered; through analysis of network shape and operation requirements during failure, after failure sections are cut off, failure section branches are deleted from original data, and the number of open switches is set to be the total number of tie switches minus the number of failure branches, so that the recovered network shape is finally a radiation network;
step 3.2: fault recovery algorithm: the ant colony algorithm is introduced into the reconstruction of the power distribution network, and the method has the advantages that ants can automatically form a radiation network in the process of traversing each node, namely each solution is a feasible solution, a power supply transformer substation and a load are called nodes, and one side represents the electrical connection between a pair of nodes; at the initial time t=0, the ant is positioned at the power supply point 1; the definition is as follows:connecting the kth ant t time to a node set of the tree; w (W) t k The node set is a node set which is not connected to the tree at the moment of the kth ant t; />A set of all selectable paths between two node sets at time t; />For t time->A set of new optional edges entered; />The probability of pheromone on each path at the time t.
The process of traversing the spanning tree by ants of the fault recovery algorithm in the step 3.2 specifically comprises the following steps:
step 3.21: t=0, starting from ant k,
step 3.22: ant k first at time t with probabilityRandom Slave set->Side l (s, w);
step 3.23: inspection ofIf the W is contained, disconnecting the L and returning to the previous step; otherwise, executing the next step;
step 3.24: updating the set of two nodes to makeAnd W is E W t k ；
Step 3.25: w (W) t k If the load node is empty, ending, and if the load node is empty, connecting all load nodes into a tree; otherwise, executing the next step;
step 3.26: updating a collectionLet->
The construction of the power distribution network recovery reconstruction mathematical model in the step 4 specifically comprises the following steps:
step 4.1: reconstructing a mathematical model of the power distribution network;
step 4.2: constraint conditions.
The reconstruction mathematical model of the power distribution network in the step 4.1 specifically comprises the following steps: the network loss of the power distribution network is an important index with excellent fault recovery reconstruction, and the minimum network loss of the power distribution network is selected as an objective function, specifically:wherein f is network loss; n is the branch number; k (k) i = (0, 1) represents the line state, k i =0 is line open, whereas line closed; r is R i The resistance value of the line i; p (P) i 、Q i Active power and reactive power for branch i; u (U) i Is the node i voltage.
The constraint conditions in the step 4.2 are specifically as follows: in the recovery and reconstruction process of the power distribution network, the constraints of power flow, node voltage, current, line capacity and network topology structure need to be met, and the specific constraints are as follows: (1) equation constraint of power flow:wherein, in the formula, P i Is active power; q (Q) i Is reactive power; p (P) Li Active power for the load node; q (Q) Li Reactive power for the load node; u (U) i Is the voltage of node i; u (U) j The voltage at node j; g i,j 、B i,j Respectively, electrical conductance and susceptance; θ i,j Is a phase difference;
(2) inequality constraint of voltage current and capacity:wherein V is i Is the voltage of node i; v (V) i_min 、V i_max The lower limit voltage and the upper limit voltage of the node i are respectively; i i For the current flowing through branch i; i i_max Maximum current allowed to flow for branch i; s is S i The actual power of branch i; s is S i_max Is the power limit of branch i;
(3) topology constraints of the power distribution network: in the recovery reconstruction, no islands and loops are present.
In the step 5, the model solving by adopting the quantum particle swarm algorithm ICQPSO algorithm based on the integer type coding mode specifically comprises the following steps:
step 5.1: basic particle swarm algorithm PSO: in the basic particle swarm algorithm, the potential solution of each problem can be imagined as a point in the multidimensional search space, called a particle, which represents the potential solution of the problem, the fitness value represents the quality of the particle, and the selection of the optimal particle is completed according to the position and the speed update, specifically: (1) and (5) updating the speed: v (t+1) =ωv (t) +c 1 r 1 (x pbest (t)-x(t))+c 2 r 2 (x gbest (t) -x (t)) (8), wherein ω is an inertial factor; v (t) is the speed of the particle at the t-th generation; x (t) is the position of the particle after t generations; c 1 、c 2 Representing a learning factor; r is (r) 1 、r 2 Is a random number between (0, 1); v (t+1) represents the speed of the t+1st iteration; x is x pbest Indicating individual optimality of the particles; x is x gbest Indicating global optimum of the particles; (2) and (3) position updating: x (t+1) =x (t) +v (t+1) (9), where x (t+1) is the position of the particle at the t+1th iteration;
step 5.2: introducing a quantum particle swarm algorithm QPSO: the quantum particle swarm algorithm is a new PSO algorithm model based on a global level parameter control method, namely a quantum particle swarm optimization QPSO algorithm, and a particle evolution equation of the QPSO is as follows: wherein, in the formula, P i A local attractor; mbest is the average optimal position of the particle iteration; m is population scale; beta is the contraction and expansion factor.
Step 5.3: improvement of particle encoding;
step 5.4: an integer encoded quantum particle swarm algorithm.
The integer type encoded quantum particle swarm algorithm in the step 5.4 specifically comprises the following steps:
step 5.41: the method is improved in the particle updating process, adopts an integer coding mode, avoids the situation of dimension disaster, and specifically comprises the following steps:wherein, the round (·) function integers the particles;
step 5.42: after the switches in the 'circles' are subjected to integer type coding, the sizes of all the circles are inconsistent, and the circles cannot run out of boundaries in the particle updating process, so that the switches are subjected to standard constraint in the following specific standard constraint modes:in U A 、L A Representing the initial upper and lower limits of the corresponding particle at each individual "circle"; the control particle update non-out-of-limit pseudocode is: if { (X) ij ＞U Aj )(X ij ＜L Aj )}，X ij ＝Randint(1,1,[L Aj ,U Aj ]) (15) wherein the Randint (-) function randomly generates integer particles within the range of the out-of-limit particles.
The invention has the beneficial effects that: the invention is a power distribution network fault recovery reconstruction method based on ant colony algorithm, in use, the invention builds a mathematical model with minimum network loss and minimum operation switch number as multiple targets based on the condition of voltage stabilization based on the ant colony algorithm, has global searching capability without depending on the setting of initial parameters, converts the multi-target optimization problem into single-target optimization by changing weight coefficients, avoids the radiation type inspection process, improves algorithm efficiency, adopts the ant colony algorithm to carry out the post-fault recovery reconstruction, has good robustness, flexibility and universality, and is suitable for combining the optimization problem; according to the invention, the minimum network loss is taken as an objective function, and an integer type coding quantum particle swarm algorithm is adopted, so that when a permanent fault occurs in a certain line of the power distribution network, the power distribution network after the permanent fault is isolated is recovered and reconstructed, and the dimension disaster problem in the recovery reconstruction of the power distribution network is avoided; the method has the advantages of establishing a multi-target model, having global searching capability, being capable of being converted into single-target optimization, reducing searching space and avoiding reconstructing dimension disasters.
Drawings
FIG. 1 is a fault recovery flow chart of the present invention.
Fig. 2 is a schematic diagram of a 33 node power distribution system of a company according to the present invention.
Fig. 3 is a schematic diagram of a 33-node power distribution system of a company after fault recovery according to the present invention.
Fig. 4 is a schematic diagram of an IEEE16 node system of the present invention.
Fig. 5 is a flowchart of an algorithm of the present invention.
Fig. 6 is a schematic diagram of an IEEE33 node power distribution system of the present invention.
Fig. 7 is a schematic diagram of a network topology after fault recovery reconstruction according to the present invention.
FIG. 8 is a schematic diagram showing the node voltage comparison before and after the fault recovery according to the present invention.
FIG. 9 is a schematic diagram of an algorithm fitness curve according to the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Example 1
As shown in fig. 1-9, a method for reconstructing power distribution network fault recovery based on an ant colony algorithm comprises the following steps:
step 1: constructing a power distribution network fault recovery mathematical model;
step 2: introducing an ant colony algorithm in the fault recovery of the power distribution network;
step 3: recovering faults of the power distribution network based on an ant colony algorithm;
step 4: constructing a power distribution network recovery reconstruction mathematical model;
step 5: carrying out model solving by adopting an ICQPSO algorithm based on an integer type coding mode;
step 6: and (5) analyzing an example.
In the step 1The construction of the power distribution network fault recovery mathematical model specifically comprises the following steps: the fault recovery of the power distribution network is a multi-objective, multi-stage and multi-constraint nonlinear optimization problem, and an objective function is established according to the recovered objective and constraint: minw=p+t (1), where W is the loss suffered by the utility company after the failure; p is the system network loss; t is the operation cost of the switch; besides ensuring that a user can timely recover power supply and reduce loss and ensuring benefits, the network loss during operation of the power distribution network after recovery is ensured to be the minimum in the network structure after recovery, so that the loss of an electric company after a fault occurs is reduced to the minimum, the benefits of the electric company are ensured, and the network loss during operation after the fault recovery of the power distribution network is ensured to be the minimum, namely:S i ≤S i,max ，U i,min ≤U i ≤U i,max wherein P is loss The network loss of the power distribution network; n is the branch number of the power distribution network; r is R i The branch resistance of the ith branch; p (P) i 、Q i Active power and reactive power of branch i respectively; u (U) i The node voltage at the tail end of the branch i; k (K) i A state variable of a switch on a branch, wherein 0 represents opening and 1 represents closing; s is S i 、S i,max Calculating the power flowing through each branch i and the maximum allowable value thereof; u (U) i,min 、U i,max The upper limit value and the lower limit value of the voltage of the node i are respectively; switches in a power distribution network are generally classified into two types according to the operation conditions: a sectionalizer switch and a tie switch; as a device that is operated frequently for power restoration, the lifetime is affected by the operation, so that each fault restoration should operate the switch as little as possible, minimizing losses, so that losses of switch wear are added to the objective function, namely: />Wherein T is a Loss of wear for the switch; s is S sec,i The motor is a sectionalizing switch (normally closed), and the action sign is 1; s is S con,j The contact switch (normally open) is adopted, and the action sign is 1; the summation operation means that 1 is added once each time the switch acts; m is mN is the number of switches of each section counted according to the Feeder Terminal Unit (FTU) section; k (K) sec 、K con The loss conversion coefficients of the actions of the sectionalizer switch and the tie switch can be set correspondingly according to parameters such as the type and the like of the switch; because metrics of indexes such as the switching operation times and the power supply quantity are not consistent, the indexes can be converted into loss indexes according to respective conversion relations in order to establish a unified metric model.
The ant colony algorithm introduced in the fault recovery of the power distribution network in the step 2 specifically comprises the following steps: in the reconstruction of the power distribution network, the loss on each branch can change along with the change of the whole network shape, namely the weight value of each side is continuously changed, and the construction of a tree with the minimum weight value (namely the minimum line loss) is far insufficient, the power distribution network with the minimum weight value often cannot meet other constraint conditions, such as equipment capacity constraint and voltage drop constraint, an ant colony algorithm is introduced, the algorithm can learn the weight value of each side and reflect the preference degree of the side, namely the influence of the side selected on the reliability of the network, and the algorithm is dynamically evaluated according to the obtained scheme so as to continuously correct self knowledge; the ant colony algorithm is a learning algorithm with positive feedback, through learning, the knowledge of the ant is continuously corrected, each ant carries out communication through pheromones, the amount of the pheromones on each side is continuously regulated so as to realize learning, the searching strategy of the ant colony algorithm is practically given in the form of probability, when the algorithm selects the searching direction, the algorithm is more likely to face to the found better solution domain, and meanwhile, the algorithm is likely to select other directions, so that the algorithm is not easy to fall into local optimum, which side of the ant k selected from a set at the moment t is determined by the conversion probability, and the probability that the ant k at the node b is selected to move to the node c is as follows:wherein F is t k = {0,1,..} is a set of possible paths for ant k next step; />The amount of pheromone on the sides (b, c) at the moment t; η (eta) bc For the visibility of the sides (b, c), in the reconstruction of the distribution network, it is set as the reciprocal of the impedance of each side; alpha and beta are two parameters, which respectively reflect the relative importance of the accumulated information and heuristic information of ants in the motion process in the ant selection path, and the more sides of the pheromone are easier to select.
The power distribution network fault recovery process based on the ant colony algorithm in the step 3 specifically comprises the following steps:
step 3.1: and (3) a power distribution network fault recovery flow: firstly, analyzing a power failure area, and judging all power supply paths of a non-failure area searching power failure area, namely a contact switch adjacent to a power supply area to be recovered; through analysis of network shape and operation requirements during failure, after failure sections are cut off, failure section branches are deleted from original data, and the number of open switches is set to be the total number of tie switches minus the number of failure branches, so that the recovered network shape is finally a radiation network; the recovery flow is shown in FIG. 1;
step 3.2: fault recovery algorithm: the ant colony algorithm is introduced into the reconstruction of the power distribution network, and the method has the advantages that ants can automatically form a radiation network in the process of traversing each node, namely, each solution is a feasible solution, compared with the coding form of the traditional genetic algorithm, the space for understanding is reduced, the power supply transformer substation and the load are both called nodes, and one side represents the electrical connection between a pair of nodes; at the initial time t=0, the ant is positioned at the power supply point 1; the definition is as follows:connecting the kth ant t time to a node set of the tree; w (W) t k The node set is a node set which is not connected to the tree at the moment of the kth ant t; />A set of all selectable paths between two node sets at time t; />For t time->A set of new optional edges entered; />The probability of pheromone on each path at the time t.
The process of traversing the spanning tree by ants of the fault recovery algorithm in the step 3.2 specifically comprises the following steps:
step 3.21: t=0, starting from ant k,
step 3.22: ant k first at time t with probabilityRandom Slave set->Side l (s, w);
step 3.23: inspection ofIf the W is contained, disconnecting the L and returning to the previous step; otherwise, executing the next step;
step 3.24: updating the set of two nodes to makeAnd W is E W t k ；
Step 3.25: w (W) t k If the load node is empty, ending, and if the load node is empty, connecting all load nodes into a tree; otherwise, executing the next step;
step 3.26: updating a collectionLet->
In this embodiment, when the pheromone is selected for updating, a central control ant is set as a path updating basis, and the function of the central control ant is to find out the current optimal solution; the optimal solution obtained by the ant colony algorithm is the combination of each feeder line and the corresponding switch in the power restoration area, the algorithm finally directly outputs and executes the result, instructs the corresponding switch to act, and quickly restores the normal power supply of the non-fault power failure area.
In this embodiment, the calculation analysis: taking a 33-node distribution system of a certain company as an example, as shown in fig. 2, assuming that 7-8 branches are failed and cut off, deleting the branches 7-8 in original data, comparing with reconstruction under normal conditions, changing the number of operable switches from (32+5) to (32+4), opening 4 switches, taking the minimum network loss into consideration, programming a fault recovery system by matlab to obtain a reconstruction result, as shown in fig. 3, after fault recovery, when only the minimum network loss is considered, closing 4 final-connected switches (8-21, 12-22, 9-15 and 18-33), opening 3 sectional switches (9-10, 14-15 and 32-33), switching operation number is 7, and total network loss is 138.039kW, which indicates that the network shape after fault recovery can be ensured to be optimized after the fault is cleared.
The invention is a power distribution network fault recovery reconstruction method based on ant colony algorithm, in use, the invention builds a mathematical model with minimum network loss and minimum operation switch number as multiple targets based on the ant colony algorithm on the premise of voltage stabilization, has global searching capability without depending on the setting of initial parameters, converts the multi-target optimization problem into single-target optimization by changing weight coefficients, avoids the radiation type inspection process, improves algorithm efficiency, adopts the ant colony algorithm to carry out post-fault recovery reconstruction, has good robustness, flexibility and universality, is suitable for combining optimization problems, can obtain good effect when applied to the power distribution network fault recovery reconstruction problem through example analysis verification, and can accurately obtain the optimal scheme of power distribution network post-fault power distribution network reconstruction; according to the invention, the minimum network loss is taken as an objective function, and an integer type coding quantum particle swarm algorithm is adopted, so that when a permanent fault occurs in a certain line of the power distribution network, the power distribution network after the permanent fault is isolated is recovered and reconstructed, and the dimension disaster problem in the recovery reconstruction of the power distribution network is avoided; the method has the advantages of establishing a multi-target model, having global searching capability, being capable of being converted into single-target optimization, reducing searching space and avoiding reconstructing dimension disasters.
Example 2
As shown in fig. 1-9, a method for reconstructing power distribution network fault recovery based on an ant colony algorithm comprises the following steps:
step 1: constructing a power distribution network fault recovery mathematical model;
step 2: introducing an ant colony algorithm in the fault recovery of the power distribution network;
step 3: recovering faults of the power distribution network based on an ant colony algorithm;
step 4: constructing a power distribution network recovery reconstruction mathematical model;
step 5: carrying out model solving by adopting an ICQPSO algorithm based on an integer type coding mode;
step 6: and (5) analyzing an example.
The construction of the power distribution network recovery reconstruction mathematical model in the step 4 specifically comprises the following steps:
step 4.1: reconstructing a mathematical model of the power distribution network;
step 4.2: constraint conditions.
The reconstruction mathematical model of the power distribution network in the step 4.1 specifically comprises the following steps: the network loss of the power distribution network is an important index with excellent fault recovery reconstruction, and the minimum network loss of the power distribution network is selected as an objective function, specifically:wherein f is network loss; n is the branch number; k (k) i = (0, 1) represents the line state, k i =0 is line open, whereas line closed; r is R i The resistance value of the line i; p (P) i 、Q i Active power and reactive power for branch i; u (U) i Is the node i voltage.
The constraint conditions in the step 4.2 are specifically as follows: in the process of recovering and reconstructing a power distribution network, the tide needs to be satisfiedFlow constraints, node voltages, currents, line capacities and network topology constraints, the specific constraints are: (1) equation constraint of power flow:wherein, in the formula, P i Is active power; q (Q) i Is reactive power; p (P) Li Active power for the load node; q (Q) Li Reactive power for the load node; u (U) i Is the voltage of node i; u (U) j The voltage at node j; g i,j 、B i,j Respectively, electrical conductance and susceptance; θ i,j Is a phase difference;
(2) inequality constraint of voltage current and capacity:wherein V is i Is the voltage of node i; v (V) i_min 、V i_max The lower limit voltage and the upper limit voltage of the node i are respectively; i i For the current flowing through branch i; i i_max Maximum current allowed to flow for branch i; s is S i The actual power of branch i; s is S i_max Is the power limit of branch i;
(3) topology constraints of the power distribution network: in the recovery reconstruction, no islands and loops are present.
The model solving based on the ICQPSO algorithm in the step 5 specifically comprises the following steps:
step 5.1: basic particle swarm algorithm PSO: in the basic particle swarm algorithm, the potential solution of each problem can be imagined as a point in the multidimensional search space, called a particle, which represents the potential solution of the problem, the fitness value represents the quality of the particle, and the selection of the optimal particle is completed according to the position and the speed update, specifically: (1) and (5) updating the speed: v (t+1) =ωv (t) +c 1 r 1 (x pbest (t)-x(t))+c 2 r 2 (x gbest (t) -x (t)) (8), wherein ω is an inertial factor; v (t) is the speed of the particle at the t-th generation; x (t) is the position of the particle after t generations; c 1 、c 2 Representing a learning factor; r is (r) 1 、r 2 Is (0, 1)Random numbers between the two; v (t+1) represents the speed of the t+1st iteration; x is x pbest Indicating individual optimality of the particles; x is x gbest Indicating global optimum of the particles; (2) and (3) position updating: x (t+1) =x (t) +v (t+1) (9), where x (t+1) is the position of the particle at the t+1th iteration;
step 5.2: introducing a quantum particle swarm algorithm QPSO: when the basic sub-group algorithm is applied to fault recovery reconstruction of a complex power distribution network, the basic sub-group algorithm has the defects of lower calculation precision, difficulty in global convergence and the like, so that the quantum particle swarm algorithm QPSO is introduced to realize the optimization of the structure after the power distribution network faults, the quantum particle swarm algorithm is a new PSO algorithm model based on a global level parameter control method, namely the quantum particle swarm optimization QPSO algorithm, compared with the PSO algorithm, the QPSO algorithm simplifies the complexity, improves the global convergence of the algorithm, and the particle evolution equation of the QPSO is as follows: wherein, in the formula, P i A local attractor; mbest is the average optimal position of the particle iteration; m is population scale; beta is the contraction and expansion factor.
Step 5.3: improvement of particle encoding;
in the embodiment, the recovery reconstruction of the power distribution network is to open and close the rest switches (the tie switch and the sectionalizing switch) after the system isolation fault so as to realize the recovery of power supply, and aiming at the problem of the discreteness of the recovery reconstruction of the power distribution network, binary coding and integer coding are the most main 2 coding modes; in binary coding, because of the complexity of the power distribution network, the switches are relatively more, if a binary coding mode is adopted, 0 and 1 represent the opening and closing of the switches, the search space of the algorithm is greatly increased, the iteration speed of the whole algorithm is reduced, and a large number of infeasible solutions can be generated even; therefore, the invention selects the integer coding mode, and on the basis of not influencing the recovery reconstruction result, the following rules are made before coding:
1) The simulated permanent faults of the power distribution network are isolated, and the non-fault area operates normally;
2) All switches (including a sectionalizer and a tie switch) of the distribution network can normally operate;
3) The bypass switch not in any loop should be closed and not participate in the encoding; for the distribution network branch switch (8) in fig. 4, it must remain closed;
4) The branch switch directly connected with the power supply is closed, and the coding is not participated in; the branch switches (1), (2), (3) as in fig. 4;
in the power distribution network calculation example system, the power distribution system is subjected to circle drawing, one tie switch represents one circle, the tail end of the circle corresponds to one tie switch, and each circle is independently coded; the integer type encoding results of fig. 4 are shown in table 1;
TABLE 1IEEE16 node System coding results
Step 5.4: an integer encoded quantum particle swarm algorithm.
The integer type encoded quantum particle swarm algorithm in the step 5.4 specifically comprises the following steps:
step 5.41: the method is improved in the particle updating process, adopts an integer coding mode, avoids the situation of dimension disaster, and specifically comprises the following steps:wherein, the round (·) function integers the particles;
step 5.42: after the switches in the 'circles' are subjected to integer type coding, the sizes of all the circles are inconsistent, and the circles cannot run out of boundaries in the particle updating process, so that the switches are subjected to standard constraint in the following specific standard constraint modes:in U A 、L A Representing the initial upper and lower limits of the corresponding particle at each individual "circle"; the control particle update non-out-of-limit pseudocode is: if { (X) ij ＞U Aj )(X ij ＜L Aj )}，X ij ＝Randint(1,1,[L Aj ,U Aj ]) (15) wherein the Randint (·) function randomly generates integer particles within the range of the out-of-limit particles; the flow of the ICQPSO algorithm is shown in FIG. 5.
In this embodiment, the calculation analysis: (1) parameter setting: simulation verification is carried out by adopting an IEEE33 node power distribution system shown in fig. 6, wherein the proposed branch 8 is a permanent fault, the reference power of the power distribution system is 10MVA, the first-stage reference voltage is 12.66kV, the total load is 3715kW+j2300kvar, and the initial parameters are set: the population size is swarmsize=50, the iteration number T is 100, and the minimum error is 10 -6 The method comprises the steps of carrying out a first treatment on the surface of the Carrying out circle coding on the power distribution network system by adopting the coding mode in the step 5.3, wherein the contact switch corresponds to the last code, and the specific coding result is shown in a table 2;
table 2IEEE33 node system encoding results
(2) And recovering reconstruction result analysis based on ICQPSO: the network is reconstructed by taking the minimum network loss as an objective function, and fig. 7 shows a network topology structure after the fault recovery reconstruction, and all power-loss loads realize power supply recovery by changing the states of the sectionalizing switch and the interconnecting switch and meet the radial operation requirement of the system; table 3 is the result of the fault resilient reconstruction;
table 3 fault resilient reconstruction results
As can be obtained by analysis in table 3, after the recovery and reconstruction of the IEEE33 node system, the network loss is reduced from 202.700kw to 145.885kw by about 28%, and the minimum voltage standard value of the node is also increased from 0.9133 to 0.9396; the voltages of the nodes before and after the restoration are shown in table 4, and in order to realize the restoration of the power supply of all loads, the tie switches 35 and 37 are switched from open to closed, so that the circuit is elongated, the voltage drop is increased, and the voltage nodes 19, 20, 21, 22, 23, 24 and 25 are slightly reduced; however, as shown in fig. 8, the voltage curve before and after the restorative reconstruction can be obtained, and the power supply voltage quality of the whole power distribution network is still greatly improved;
TABLE 4 recovery of the values of the post-reconstruction node voltages per unit
(3) Algorithm performance comparison: in order to better verify the feasibility of the method, the calculation results are compared, and the calculation results of the algorithm (ICOPSO algorithm) of the invention are compared with the calculation results of the genetic algorithm and the membrane algorithm, and as can be seen from the calculation results of the genetic algorithm and the membrane algorithm in Table 5, when the permanent fault occurs in the branch 8, the branch switches 14, 28 and 32 are opened, the tie switch 33 is closed, the switching action times are 8, and all the power loss loads in the network are recovered; although the invention also considers the switching action times in the objective function, the switching action times are 8 times which are the same as the action switching times of the genetic algorithm and the membrane algorithm in comparison, and the network loss after the algorithm is recovered and reconstructed is obviously lower, so the network topology switch combination obtained by the algorithm is better;
the results of the algorithm in Table 53
FIG. 9 is a graph of convergence of fitness values (network loss) using the algorithm of the present invention, resulting in a faster algorithm convergence rate for the algorithm of the present invention, when compared to the success of the algorithm of the present invention at iteration 16, the success of the algorithm of the present invention at 33, and the success of the algorithm of the present invention at film 22;
in summary, the algorithm of the invention is more feasible and effective when the power distribution network is restored and reconstructed.
The invention is a power distribution network fault recovery reconstruction method based on ant colony algorithm, in use, the invention builds a mathematical model with minimum network loss and minimum operation switch number as multiple targets based on the condition of voltage stabilization based on the ant colony algorithm, has global searching capability without depending on the setting of initial parameters, converts the multi-target optimization problem into single-target optimization by changing weight coefficients, avoids the radiation type inspection process, improves algorithm efficiency, adopts the ant colony algorithm to carry out the post-fault recovery reconstruction, has good robustness, flexibility and universality, and is suitable for combining the optimization problem; according to the invention, the minimum network loss is taken as an objective function, and an integer type coding quantum particle swarm algorithm is adopted, so that when a permanent fault occurs in a certain line of the power distribution network, the power distribution network after the permanent fault is isolated is recovered and reconstructed, and the dimension disaster problem in the recovery reconstruction of the power distribution network is avoided; the invention considers the economy and practicability of the fault recovery of the power distribution network, and firstly, a power distribution network fault recovery reconstruction model is established by taking the minimum network loss as an objective function; then, aiming at the problem of explosion of search space in a complex power distribution network by a binary quantum particle swarm algorithm (BOPSO), adopting a quantum particle swarm algorithm in an integer type coding mode, drawing a circle of the complex power distribution network, independently coding discrete switches in each circle, and establishing constraint conditions of a range and boundary specifications of the coded switches in the circle by considering that normally closed switches exist in the circle and the number of branch switches of each independent circle in the coding process; finally, an IEEE33 node system is selected for carrying out example analysis, and a fault recovery result is compared with recovery results of a genetic algorithm and a membrane algorithm, so that applicability and effectiveness of a quantum particle swarm algorithm in the recovery reconstruction of the power distribution network in an integer type coding mode are verified; the method has the advantages of establishing a multi-target model, having global searching capability, being capable of being converted into single-target optimization, reducing searching space and avoiding reconstructing dimension disasters.

Claims (10)

1. A power distribution network fault recovery reconstruction method based on an ant colony algorithm is characterized by comprising the following steps of: the method comprises the following steps:
step 1: constructing a power distribution network fault recovery mathematical model;
step 2: introducing an ant colony algorithm in the fault recovery of the power distribution network;
step 3: an ant colony algorithm-based power distribution network fault recovery flow;
step 4: constructing a power distribution network recovery reconstruction mathematical model;
step 5: carrying out model solving by adopting an ICQPSO algorithm based on an integer type coding mode;
step 6: and (5) analyzing an example.
2. The method for reconstructing the fault recovery of the power distribution network based on the ant colony algorithm as set forth in claim 1, wherein the method comprises the following steps: the construction of the power distribution network fault recovery mathematical model in the step 1 specifically comprises the following steps: the fault recovery of the power distribution network is a multi-objective, multi-stage and multi-constraint nonlinear optimization problem, and an objective function is established according to the recovered objective and constraint: minw=p+t (1), where W is the loss suffered by the utility company after the failure; p is the system network loss; t is the operation cost of the switch; besides ensuring that a user can timely recover power supply and reduce loss and ensuring benefits, the network loss during operation of the power distribution network after recovery is ensured to be the minimum in the network structure after recovery, so that the loss of an electric company after a fault occurs is reduced to the minimum, the benefits of the electric company are ensured, and the network loss during operation after the fault recovery of the power distribution network is ensured to be the minimum, namely:S i ≤S i,max ，U i,min ≤U i ≤U i,max wherein P is loss The network loss of the power distribution network; n is the branch number of the power distribution network; r is R i The branch resistance of the ith branch; p (P) i 、Q i Active power and reactive power of branch i respectively; u (U) i The node voltage at the tail end of the branch i; k (K) i Is a state variable of a switch on a branch, 0 represents open, 1 represents closed；S i 、S i,max Calculating the power flowing through each branch i and the maximum allowable value thereof; u (U) i,min 、U i,max The upper limit value and the lower limit value of the voltage of the node i are respectively; switches in a power distribution network are generally classified into two types according to the operation conditions: a sectionalizer switch and a tie switch; as a device that is operated frequently for power restoration, the lifetime is affected by the operation, so that each fault restoration should operate the switch as little as possible, minimizing losses, so that losses of switch wear are added to the objective function, namely: />Wherein T is a Loss of wear for the switch; s is S sec,i The switch is a sectional switch, and the action sign is 1; s is S con,j The action sign is 1 for the contact switch; the summation operation means that 1 is added once each time the switch acts; m and n are respectively the number of switches of each section counted according to the section of the feeder terminal unit; k (K) sec 、K con The loss conversion coefficients of the sectionalizing and tie-switch actions, respectively.
3. The method for reconstructing the fault recovery of the power distribution network based on the ant colony algorithm as set forth in claim 1, wherein the method comprises the following steps: the ant colony algorithm introduced in the fault recovery of the power distribution network in the step 2 specifically comprises the following steps: the ant colony algorithm is a learning algorithm with positive feedback, through learning, the knowledge of the ant is continuously corrected, each ant carries out communication through pheromones, the amount of the pheromones on each side is continuously regulated so as to realize learning, the searching strategy of the ant colony algorithm is practically given in the form of probability, when the algorithm selects the searching direction, the algorithm is more likely to face to the found better solution domain, and meanwhile, the algorithm is likely to select other directions, so that the algorithm is not easy to fall into local optimum, which side of the ant k selected from a set at the moment t is determined by the conversion probability, and the probability that the ant k at the node b is selected to move to the node c is as follows:wherein F is t k = {0,1,..} is a set of possible paths for ant k next step; />The amount of pheromone on the sides (b, c) at the moment t; η (eta) bc For the visibility of the sides (b, c), in the reconstruction of the distribution network, it is set as the reciprocal of the impedance of each side; alpha and beta are two parameters, which respectively reflect the relative importance of the accumulated information and heuristic information of ants in the motion process in the ant selection path, and the more sides of the pheromone are easier to select.
4. The method for reconstructing the fault recovery of the power distribution network based on the ant colony algorithm as set forth in claim 1, wherein the method comprises the following steps: the power distribution network fault recovery process based on the ant colony algorithm in the step 3 specifically comprises the following steps:
step 3.1: and (3) a power distribution network fault recovery flow: firstly, analyzing a power failure area, and judging all power supply paths of a non-failure area searching power failure area, namely a contact switch adjacent to a power supply area to be recovered; through analysis of network shape and operation requirements during failure, after failure sections are cut off, failure section branches are deleted from original data, and the number of open switches is set to be the total number of tie switches minus the number of failure branches, so that the recovered network shape is finally a radiation network;
step 3.2: fault recovery algorithm: the ant colony algorithm is introduced into the reconstruction of the power distribution network, and the method has the advantages that ants can automatically form a radiation network in the process of traversing each node, namely each solution is a feasible solution, a power supply transformer substation and a load are called nodes, and one side represents the electrical connection between a pair of nodes; at the initial time t=0, the ant is positioned at the power supply point 1; the definition is as follows:connecting the kth ant t time to a node set of the tree; w (W) t k The node set is a node set which is not connected to the tree at the moment of the kth ant t; />A set of all selectable paths between two node sets at time t; />For t time->A set of new optional edges entered; />The probability of pheromone on each path at the time t.
5. The method for reconstructing the fault recovery of the power distribution network based on the ant colony algorithm as set forth in claim 4, wherein the method comprises the following steps: the process of traversing the spanning tree by ants of the fault recovery algorithm in the step 3.2 specifically comprises the following steps:
step 3.21: t=0, starting from ant k,
step 3.22: ant k first at time t with probabilityRandom Slave set->Side l (s, w);
step 3.23: inspection ofIf the W is contained, disconnecting the L and returning to the previous step; otherwise, executing the next step;
step 3.24: updating the set of two nodes to makeAnd W is E W t k ；
Step 3.25: w (W) t k If the load node is empty, ending, and if the load node is empty, connecting all load nodes into a tree; otherwise, executing the next step;
step 3.26: updating a collectionLet->
6. The method for reconstructing the fault recovery of the power distribution network based on the ant colony algorithm as set forth in claim 1, wherein the method comprises the following steps: the construction of the power distribution network recovery reconstruction mathematical model in the step 4 specifically comprises the following steps:
step 4.1: reconstructing a mathematical model of the power distribution network;
step 4.2: constraint conditions.
7. The method for reconstructing the fault recovery of the power distribution network based on the ant colony algorithm as set forth in claim 6, wherein the method comprises the following steps: the reconstruction mathematical model of the power distribution network in the step 4.1 specifically comprises the following steps: the network loss of the power distribution network is an important index with excellent fault recovery reconstruction, and the minimum network loss of the power distribution network is selected as an objective function, specifically:wherein f is network loss; n is the branch number; k (k) i = (0, 1) represents the line state, k i =0 is line open, whereas line closed; r is R i The resistance value of the line i; p (P) i 、Q i Active power and reactive power for branch i; u (U) i Is the node i voltage.
8. The method for reconstructing the fault recovery of the power distribution network based on the ant colony algorithm as set forth in claim 6, wherein the method comprises the following steps: in said step 4.2The constraint conditions are specifically as follows: in the recovery and reconstruction process of the power distribution network, the constraints of power flow, node voltage, current, line capacity and network topology structure need to be met, and the specific constraints are as follows: (1) equation constraint of power flow:wherein, in the formula, P i Is active power; q (Q) i Is reactive power; p (P) Li Active power for the load node; q (Q) Li Reactive power for the load node; u (U) i Is the voltage of node i; u (U) j The voltage at node j; g i,j 、B i,j Respectively, electrical conductance and susceptance; θ i,j Is a phase difference;
(2) inequality constraint of voltage current and capacity:wherein V is i Is the voltage of node i; v (V) i_min 、V i_max The lower limit voltage and the upper limit voltage of the node i are respectively; i i For the current flowing through branch i; i i_max Maximum current allowed to flow for branch i; s is S i The actual power of branch i; s is S i_max Is the power limit of branch i;
(3) topology constraints of the power distribution network: in the recovery reconstruction, no islands and loops are present.
9. The method for reconstructing the fault recovery of the power distribution network based on the ant colony algorithm as set forth in claim 1, wherein the method comprises the following steps: in the step 5, the model solving by adopting the quantum particle swarm algorithm ICQPSO algorithm based on the integer type coding mode specifically comprises the following steps:
step 5.1: basic particle swarm algorithm PSO: in the basic particle swarm algorithm, the potential solution of each problem can be imagined as a point in the multidimensional search space, called a particle, which represents the potential solution of the problem, the fitness value represents the quality of the particle, and the selection of the optimal particle is completed according to the position and the speed update, specifically: (1) and (5) updating the speed: v (t+1) =ωv (t) +c 1 r 1 (x pbest (t)-x(t))+c 2 r 2 (x gbest (t) -x (t)) (8), wherein ω is an inertial factor; v (t) is the speed of the particle at the t-th generation; x (t) is the position of the particle after t generations; c 1 、c 2 Representing a learning factor; r is (r) 1 、r 2 Is a random number between (0, 1); v (t+1) represents the speed of the t+1st iteration; x is x pbest Indicating individual optimality of the particles; x is x gbest Indicating global optimum of the particles; (2) and (3) position updating: x (t+1) =x (t) +v (t+1) (9), where x (t+1) is the position of the particle at the t+1th iteration;
step 5.2: introducing a quantum particle swarm algorithm QPSO: the quantum particle swarm algorithm is a new PSO algorithm model based on a global level parameter control method, namely a quantum particle swarm optimization QPSO algorithm, and a particle evolution equation of the QPSO is as follows: wherein, in the formula, P i A local attractor; mbest is the average optimal position of the particle iteration; m is population scale; beta is the contraction and expansion factor.
Step 5.3: improvement of particle encoding;
step 5.4: an integer encoded quantum particle swarm algorithm.
10. The method for reconstructing the fault recovery of the power distribution network based on the ant colony algorithm as set forth in claim 9, wherein the method comprises the following steps: the integer type encoded quantum particle swarm algorithm in the step 5.4 specifically comprises the following steps:
step 5.41: the method is improved in the particle updating process, adopts an integer coding mode, avoids the situation of dimension disaster, and specifically comprises the following steps:wherein, the round (·) function integers the particles;
step 5.42: after the switches in the 'circles' are subjected to integer type coding, the sizes of all the circles are inconsistent, and the circles cannot run out of boundaries in the particle updating process, so that the switches are subjected to standard constraint in the following specific standard constraint modes:in U A 、L A Representing the initial upper and lower limits of the corresponding particle at each individual "circle"; the control particle update non-out-of-limit pseudocode is: if { (X) ij ＞U Aj )(X ij ＜L Aj )}，X ij ＝Randint(1,1,[L Aj ,U Aj ]) (15) wherein the Randint (-) function randomly generates integer particles within the range of the out-of-limit particles.
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CN117937476A (en) * 2024-03-22 2024-04-26 国网湖北省电力有限公司经济技术研究院 Active power distribution network partition optimizing and reconstructing method and system based on early warning state
CN117937476B (en) * 2024-03-22 2024-06-11 国网湖北省电力有限公司经济技术研究院 Active power distribution network partition optimizing and reconstructing method and system based on early warning state

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