CN106655155B - Power distribution network fault recovery method considering uncertainty of fault recovery time - Google Patents
Power distribution network fault recovery method considering uncertainty of fault recovery time Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/001—Methods to deal with contingencies, e.g. abnormalities, faults or failures
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
- Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
- Y04S10/00—Systems supporting electrical power generation, transmission or distribution
- Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
- Y04S10/52—Outage or fault management, e.g. fault detection or location
Abstract
The invention relates to a power distribution network fault recovery method considering uncertainty of fault recovery time, which comprises the following steps: according to the probability density function of the fault recovery time of the power distribution network, respectively acquiring two optimal power distribution network fault recovery times and probabilities of the two optimal power distribution network fault recovery times of the probability density function, namely the first power distribution network fault recovery time and the probability thereof, and the second power distribution network fault recovery time and the probability thereof; establishing a power distribution network fault recovery model by utilizing the first power distribution network fault recovery time, and taking the optimal solution of the power distribution network fault recovery model as a power distribution network fault recovery scheme; optimizing a power distribution network fault recovery scheme by using the second power distribution network fault recovery time; according to the method provided by the invention, the Wasserstein distance method is adopted to determine the fault recovery time, the fault recovery scheme is reasonably adjusted by using the fault recovery time, the best power supply recovery effect on the power failure area is realized, and the economical efficiency and the safety of the operation of the power distribution network are improved.
Description
Technical Field
The invention relates to the technical field of power distribution network operation, in particular to a power distribution network fault recovery method considering uncertainty of fault recovery time.
Background
The power distribution network fault recovery means that after a power distribution network fault occurs, the optimal switch combination scheme is determined, so that the aims of recovering the maximum power loss load, the minimum switch operation frequency, the minimum network loss and the like are achieved, and meanwhile, the conditions of connectivity, radiation and the like of the power distribution network after recovery are met.
In recent years, fault recovery of a power distribution network with distributed power supplies is also one of research hotspots, when the power distribution network fails and is isolated, the distributed power supplies in a power loss area independently supply power to important loads in the area to form an island operation mode, and power supply reliability can be improved. However, the output of uncontrollable DGs such as wind power, photovoltaic and the like has uncertainty, and the fault recovery time of the power distribution network also has uncertainty, so that the fault recovery schemes are different, and after the power distribution network fails, the power supply recovery effect on the power distribution network is different, so that the best power supply recovery effect on a power loss area cannot be achieved by using the traditional fault recovery method.
Disclosure of Invention
The invention provides a power distribution network fault recovery method considering uncertainty of fault recovery time, and aims to determine the fault recovery time by adopting a Wasserstein distance method, reasonably adjust a fault recovery scheme by utilizing the fault recovery time, realize the best power supply recovery effect on a power loss area, and improve the economical efficiency and the safety of power distribution network operation.
The purpose of the invention is realized by adopting the following technical scheme:
in a power distribution network fault recovery method that accounts for uncertainty in time to recover from a fault, the improvement comprising:
according to a probability density function of the fault recovery time of the power distribution network, respectively acquiring two optimal power distribution network fault recovery times of the probability density function and the probabilities of the two optimal power distribution network fault recovery times, namely the fault recovery time and the probability of a first power distribution network and the fault recovery time and the probability of a second power distribution network, wherein the probability of the fault recovery time of the first power distribution network is greater than the probability of the fault recovery time of the second power distribution network;
establishing a power distribution network fault recovery model by utilizing the first power distribution network fault recovery time, and taking the optimal solution of the power distribution network fault recovery model as a power distribution network fault recovery scheme;
and optimizing the power distribution network fault recovery scheme by utilizing the second power distribution network fault recovery time.
Preferably, the fault recovery time and the probability of the first power distribution network and the fault recovery time and the probability of the second power distribution network are determined by using the Wasserstein distance.
Further, the distribution network is made to failThe number of quantile points of the probability density function of the recovery time is S =2, and the following formula (1) is solved to respectively obtain the fault recovery time z of the first power distribution network 1 And a second distribution network fault recovery time z 2 ：
In the formula (1), g (t) is a probability density function of the fault recovery time of the power distribution network, s belongs to [1, S ], and r is an order.
Respectively acquiring the fault recovery time z of the first power distribution network according to the following formula (2) 1 Probability p of 1 And said second distribution network fault recovery time z 2 Probability p of 2 ：
Preferably, the establishing a power distribution network fault recovery model by using the first power distribution network fault recovery time includes:
the maximum of the total electric quantity of important loads recovered by a recovery power distribution network is an objective function, and the formula is as follows:
in the formula (3), F main Important load total electric quantity, z, for main network to recover to non-fault power loss area in fault period 1 For the time of fault recovery, n is the total number of system nodes, lambda i To the importance of the load on node i, L i,t For the load size of node i in time period t, y i,t As a state change parameter, y i,t =1 denotes that node i resumes power supply during time period t, y i,t =0 indicates that the node i does not recover power supply in the period t;
the constraint conditions include:
node voltage constraint, the formula is:
U min ≤U i.t ≤U max (4)
in the formula (4), U i,t For the voltage value of node i during time period t, U min Is the lower voltage limit, U, of node i max Is the upper voltage limit of node i;
a power balance constraint, the formula being:
in the formula (5), P i,t Active power, Q, injected for node i during time period t i,t Reactive power, G, injected for node i during time period t ij Is the conductance between nodes i, j, B ij Is susceptance, delta, between nodes i, j ij,t Is the voltage phase angle difference of the nodes i and j in the time period t, n is the total number of the system nodes, U i,t For the voltage amplitude of node i during time period t, U j,t Is the voltage amplitude of node j during time period t;
branch power constraint, the formula is:
P ij.t ≤P ijmax (6)
in the formula (6), P ij,t For the active power value, P, of the branch between node i and node j in time period t ij max The maximum value of the active power of the branch between the node i and the node j is allowed;
the radiation operation constraint of the power distribution network has the formula:
g∈G (7)
in the formula (7), G is a reconstructed network topology, and G is a set of network radial topologies.
Preferably, an ant colony algorithm is adopted to obtain an optimal solution of the power distribution network fault recovery model, and the optimal solution of the power distribution network fault recovery model is used as a power distribution network fault recovery scheme.
Preferably, the optimizing the power distribution network fault recovery scheme by using the second power distribution network fault recovery time includes:
if the first distribution network fault recovery time z 1 And a second distribution network fault recovery time z 2 Satisfies the following conditions: z is a radical of 1 ＞z 2 If not, the power distribution network is not adjustedA barrier recovery scheme;
if the first distribution network has a fault recovery time z 1 And a second distribution network fault recovery time z 2 Satisfies the following conditions: z is a radical of 1 ＜z 2 Then the fault recovery time z of the second power distribution network is used 2 For the fault recovery time of the power distribution network, the fault recovery time z of the second power distribution network 2 The constraint condition of the power distribution network fault recovery model is verified at each time interval, and if the second power distribution network fault recovery time z is up 2 If each period of time meets the constraint condition of the power distribution network fault recovery model, adjusting the power distribution network fault recovery time of the power distribution network fault recovery scheme to be the second power distribution network fault recovery time z 2 If the second distribution network fault recovery time z 2 If the time period does not meet the constraint condition of the power distribution network fault recovery model exists, load shedding is carried out on the power distribution network structure of the power distribution network fault recovery scheme until the second power distribution network fault recovery time z 2 Meets the constraint condition of a power distribution network fault recovery model in each time period, and adjusts the power distribution network fault recovery time of the power distribution network fault recovery scheme to be the second power distribution network fault recovery time z 2 。
In a power distribution network fault recovery apparatus that accounts for uncertainty in time to recover from a fault, the improvement comprising:
the acquisition module is used for respectively acquiring two optimal power distribution network fault recovery times of the probability density function and the probabilities of the two optimal power distribution network fault recovery times, namely a first power distribution network fault recovery time and the probability thereof and a second power distribution network fault recovery time and the probability thereof according to the probability density function of the power distribution network fault recovery time, wherein the probability of the first power distribution network fault recovery time is greater than the probability of the second power distribution network fault recovery time;
the creating module is used for creating a power distribution network fault recovery model by utilizing the first power distribution network fault recovery time, and taking the optimal solution of the power distribution network fault recovery model as a power distribution network fault recovery scheme;
and the optimization module is used for optimizing the power distribution network fault recovery scheme by utilizing the second power distribution network fault recovery time.
Preferably, the fault recovery time and the probability of the first power distribution network and the fault recovery time and the probability of the second power distribution network are determined by using the Wasserstein distance.
Further, the acquiring module includes:
a first obtaining unit, configured to enable the number of sub-sites of the probability density function of the power distribution network fault recovery time S =2, and solve the following equation (1) to obtain the first power distribution network fault recovery time z respectively 1 And a second distribution network fault recovery time z 2 ：
In the formula (1), g (t) is a probability density function of the fault recovery time of the power distribution network, s belongs to [1, S ], and r is an order.
A second obtaining unit, configured to obtain the failure recovery time z of the first power distribution network according to the following formula (2) 1 Probability p of 1 And said second distribution network fault recovery time z 2 Probability p of 2 ：
Preferably, the creating module includes:
the creating unit is used for maximizing the maximum important load total electric quantity for restoring the power distribution network as an objective function, and the formula is as follows:
in the formula (3), F main Important load total electric quantity, z, for main network to recover to non-fault power loss area in fault period 1 For the time of fault recovery, n is the total number of system nodes, lambda i To the importance of the load on node i, L i,t For the load size of node i in time period t, y i,t Is a state change parameter, y i,t =1 denotes that node i resumes power supply during time period t, y i,t =0 indicates that the node i does not recover power supply in the period t;
the constraint conditions include:
node voltage constraints are formulated as:
U min ≤U i.t ≤U max (4)
in formula (4), U i,t For the voltage value of node i in time period t, U min Lower voltage limit, U, of node i max Is the upper voltage limit of node i;
a power balance constraint, the formula being:
in the formula (5), P i,t Active power, Q, injected for node i during time period t i,t Reactive power, G, injected for node i during time period t ij Is the conductance between nodes i, j, B ij Is susceptance, delta, between nodes i, j ij,t The voltage phase angle difference of the nodes i and j in the time period t, n is the total number of the system nodes, U i,t For the voltage amplitude of node i in time period t, U j,t The voltage amplitude of node j in time period t;
branch power constraint, the formula is:
P ij.t ≤P ijmax (6)
in formula (6), P ij,t Active power value, P, for the branch between node i and node j in time period t ij max The maximum value of the active power allowed by the branch between the node i and the node j is obtained;
the radiation operation constraint of the power distribution network has the formula:
g∈G (7)
in the formula (7), G is a reconstructed network topology structure, and G is a set of network radial topology structures.
Preferably, an ant colony algorithm is adopted to obtain an optimal solution of the power distribution network fault recovery model, and the optimal solution of the power distribution network fault recovery model is used as a power distribution network fault recovery scheme.
Preferably, the optimization module includes:
a first optimization unit for the time z for recovery of the first distribution network failure if 1 And a second distribution network fault recovery time z 2 Satisfies the following conditions: z is a radical of 1 ＞z 2 If so, not adjusting the power distribution network fault recovery scheme;
a second optimization unit for the time z for recovery of the first distribution network failure if 1 And a second distribution network fault recovery time z 2 Satisfies the following conditions: z is a radical of 1 ＜z 2 Then the fault recovery time z of the second power distribution network is used 2 For the fault recovery time of the power distribution network, the fault recovery time z of the second power distribution network 2 The constraint condition of the power distribution network fault recovery model is verified at each time interval, and if the second power distribution network fault recovery time z is up 2 If each period of time meets the constraint condition of the power distribution network fault recovery model, adjusting the power distribution network fault recovery time of the power distribution network fault recovery scheme to be the second power distribution network fault recovery time z 2 If the second distribution network fault recovery time z 2 If the time period does not meet the constraint condition of the power distribution network fault recovery model exists, load shedding is carried out on the power distribution network structure of the power distribution network fault recovery scheme until the second power distribution network fault recovery time z 2 Meets the constraint condition of a power distribution network fault recovery model in each time period, and adjusts the power distribution network fault recovery time of the power distribution network fault recovery scheme to be the second power distribution network fault recovery time z 2 。
The invention has the beneficial effects that:
in the prior art, the uncertainty exists in the fault recovery time of the power distribution network, the probability function is accurately dispersed under the condition that the probability density function of the fault recovery time is known, two fault recovery times with the maximum probability can be obtained, a fault recovery scheme can be conveniently formulated according to the actual fault condition of the power distribution network, meanwhile, an optimization scheme and a correction scheme are formulated respectively according to the two fault recovery times with different probabilities, after the power distribution network breaks down, the optimization scheme is executed firstly, the fault recovery time is judged by tracking fault information, the fault recovery scheme is adjusted in time, the action times of switching can be reduced, the service life of the switching is prolonged, the fault recovery with the maximum degree is realized, and the economical efficiency and the reliability of the operation of the power distribution network are improved.
Drawings
FIG. 1 is a flow chart of a method of fault recovery for a power distribution network in accordance with the present invention that takes into account uncertainty in the time to fault recovery;
fig. 2 is a schematic diagram of an application scenario of a power distribution network fault recovery method considering uncertainty of fault recovery time in an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a fault recovery device for a power distribution network, which considers uncertainty of fault recovery time according to the invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The invention provides a power distribution network fault recovery method considering uncertainty of fault recovery time, as shown in fig. 1, comprising the following steps:
101. according to a probability density function of power distribution network fault recovery time, respectively obtaining two optimal power distribution network fault recovery times of the probability density function and probabilities of the two optimal power distribution network fault recovery times, namely first power distribution network fault recovery time and the probability thereof and second power distribution network fault recovery time and the probability thereof, wherein the probability of the first power distribution network fault recovery time is greater than the probability of the second power distribution network fault recovery time;
the probability density function of the fault recovery time of the power distribution network can be obtained according to the average repair time of the power distribution system;
102. establishing a power distribution network fault recovery model by utilizing the first power distribution network fault recovery time, and taking the optimal solution of the power distribution network fault recovery model as a power distribution network fault recovery scheme;
103. and optimizing the power distribution network fault recovery scheme by using the second power distribution network fault recovery time.
Specifically, in step 101, the fault recovery time and the probability of the first power distribution network and the fault recovery time and the probability of the second power distribution network are determined by using the Wasserstein distance.
The method specifically comprises the following steps: enabling the number of quantile points of the probability density function of the power distribution network fault recovery time to be S =2, and solving the following formula (1) to respectively obtain the first power distribution network fault recovery time z 1 And a second distribution network fault recovery time z 2 ：
In the formula (1), g (t) is a probability density function of the fault recovery time of the power distribution network, s belongs to [1, S ], and r is an order.
Respectively acquiring the fault recovery time z of the first power distribution network according to the following formula (2) 1 Probability p of 1 And said second distribution network fault recovery time z 2 Probability p of 2 ：
In the step 102, establishing a power distribution network fault recovery model by using the first power distribution network fault recovery time includes:
the maximum of the total electric quantity of important loads recovered by recovering the power distribution network is an objective function, and the formula is as follows:
in formula (3), F main Important load total electric quantity, z, for main network to recover to non-fault power loss area in fault period 1 For the fault repair time, n is the total number of system nodes, λ i To the importance of the load on node i, L i,t For the load size of node i in time period t, y i,t As a state change parameter, y i,t =1 denotes that node i resumes power supply during time period t, y i,t =0 indicates that the node i is not powered back for the time period t;
the constraint conditions include:
node voltage constraints are formulated as:
U min ≤U i.t ≤U max (4)
in formula (4), U i,t For the voltage value of node i in time period t, U min Lower voltage limit, U, of node i max Is the upper voltage limit of node i;
a power balance constraint, formulated as:
in formula (5), P i,t Active power, Q, injected for node i during time period t i,t Reactive power, G, injected for node i during time period t ij Is the conductance between nodes i, j, B ij Is susceptance, delta, between nodes i, j ij,t The voltage phase angle difference of the nodes i and j in the time period t, n is the total number of the system nodes, U i,t For the voltage amplitude of node i in time period t, U j,t The voltage amplitude of node j in time period t;
branch power constraint, the formula is:
P ij.t ≤P ijmax (6)
in formula (6), P ij,t For the active power value, P, of the branch between node i and node j in time period t ij max The maximum value of the active power allowed by the branch between the node i and the node j is obtained;
the radiation operation constraint of the power distribution network has the formula:
g∈G (7)
in the formula (7), G is a reconstructed network topology structure, and G is a set of network radial topology structures.
Further, in the step 102, an ant colony algorithm is adopted to obtain an optimal solution of the power distribution network fault recovery model, and the optimal solution of the power distribution network fault recovery model is used as a power distribution network fault recovery scheme.
At present, the technology for formulating the power distribution network fault recovery scheme by adopting the ant colony algorithm is mature, the invention aims to effectively solve the problem of network reconstruction optimization for recovering power supply after the power distribution network fault, avoid a large number of infeasible solutions in the searching process, complete the fault recovery of a main network by adopting the ant colony algorithm based on a spanning tree, and optimize the switch state combination of a non-fault area according to the power supply recovery capability.
The ant colony algorithm is an optimized searching method similar to population evolution, and is essentially characterized in that ants can release pheromones to identify paths and exchange information on the paths passed by the ants, the higher the concentration of pheromones reserved on the paths with shorter paths in the same time is, the ants can search the shorter paths according to the concentration of the pheromones on the paths, and by applying the positive feedback mechanism, the ant colony can quickly search the optimal paths, and the concentration of the pheromones on the paths is also the highest.
For example: the invention provides a specific implementation process for acquiring an optimal solution of a power distribution network fault recovery model by adopting an ant colony algorithm and taking the optimal solution of the power distribution network fault recovery model as a power distribution network fault recovery scheme, which comprises the following steps:
ants generate a feasible radial network by using a spanning tree strategy;
carrying out load flow calculation on the current network;
if the calculation result does not meet the constraint condition of the power distribution network fault recovery model, performing load shedding operation;
and repeating the iteration until a termination condition is met.
Specifically, aiming at the radiation characteristic of the power distribution network, when the ant colony algorithm is used for solving the problem of reconstruction after network faults of the power distribution network, the network topology after the faults corresponding to each run completed by ants is radiation type by adopting the spanning tree strategy, the radiation type checking and repairing process is avoided, each generation is guaranteed to be a feasible solution, the searching efficiency of the algorithm is improved, the routing rule of the ant colony algorithm and the pheromone updating strategy are improved, and the convergence speed is accelerated.
Using section switch and interconnection switch of distribution network as non-directional edge e of graph i (i =1,2 \8230m), the load on the line constitutes the node v of the graph j (j =1,2 \8230n), power supply point as root node v 0 The distribution network can be described as an undirected graph G, and the numbering of the nodes of the undirected graph G is denoted by v j (j =1,2 8230n). Describing the undirected graph G by using a net-based structure matrix abrach with n rows and n columns, wherein n is the number of system nodes, namely
Wherein if the nodes i and j are connected by a switch, a ij ＝a ji =1, and the remaining elements are 0.
As another example, as shown in fig. 2, taking the network shown in fig. 2 as an example, the solid line represents a closed section switch, and the dotted line represents an open tie switch, then:
after a network base structure matrix of the power distribution network is obtained, according to the principle of a spanning tree, taking an ant k as an example, the following three sets and two sequences are defined for an undirected graph G which is equivalent to the power distribution network:
(1) Each branch corresponds to an adjacent node set Anode = { b = v And each row element is a node number adjacent to the row node number, taking the network shown in fig. 2 as an example, where the adjacent node matrix is:
(2) Ant k selected node set Endnode = { b = { (b) } i Recording the node numbers that have been selected so far, where v i ∈G；
(3) Ant k optional node set Choosensode = { b = { (b) } w And in the current state, the node set which can be selected as the next path in the unselected nodes.
(4) Branch selection sequence L ij (i, j =1,2, \8230;, n), record the selected leg 0.
(5) Node marker sequence M i (i =1,2, \8230;, n), marking whether the node is already used as the end node of a certain branch, if so, marking 1, and otherwise, marking 0.
By adopting a search strategy of a random spanning tree, taking the power distribution network shown in fig. 2 as an example, the three sets and the two sequences are combined to guide ants to generate a feasible solution meeting topological constraints, and the steps are as follows:
(1) Initial network topology description: and numbering all nodes and switches to generate an undirected graph G after numbering to obtain an abrach matrix.
(2) Initialization: set the set Anode, endnode, choosenode and sequence M used by the algorithm i If ants are placed at the head end power node, then Endnode = {1}, choosensode = {2}, M k The element is (1, 0).
(3) Path selection: each ant selects a node y from the Choosensode set according to a certain rule.
(4) Recording branch selection sequence L ij : and recording a head node i of the branch in the current step as a point associated with y in the Endnode, and recording a tail node j as a point y selected from the Choosensode.
(5) Collection and sequence correction: (a), endnode: newly adding the selected node y; (b) choosensode: and the new set elements are elements corresponding to the y rows in the Anode matrix, and the selected nodes are deleted. And (3) correcting the generated network: checking the first and last nodes of the branch, adding 1 to the number of the selected nodes, and adding M to the number of the selected nodes i Marking the corresponding position of the node selected at this time with 1, and corresponding to the tail node of the branch in the initial networkA load is placed on the branch end node. If Choosensode = Φ and M i The total number of the nodes marked as 1 in the network is less than the number of the network nodes, and M is found at the moment i Node number X of 0 in as the selected node, and the point associated with X in the Endnode is selected as the head node of the branch.
(6) And (5) circulating the steps (3) to (5) until the number of the selected branches reaches the number of the nodes, so that a feasible solution is generated. And then adding the load into the corresponding node to obtain a new network structure, namely a feasible radial network in the steps. The path search of the current ant ends.
At the initial time in the above step, the trend of the ants k (k =1, 2.. The number of Nant, and Nant is the number of ants in each generation) is determined according to the pheromone concentration on each path during the movement process, so that the probability of selecting a path is determined by adopting the pheromone concentration, and the probability of selecting the path is higher as the pheromone accumulation on a certain path is more. The probability that the ant k is transferred from the branch i to the branch j is as follows:
in the formula: all of the same k Representing the set of next selectable paths of ants; tau. ij Pheromone concentration, eta, for ants transferred from branch i to branch j ij Representing the visibility (eta) of the transition to path (i, j) ij ＝1/z ij )，z ij Representing the impedance of the line; alpha and beta are pheromone importance degree factors and visibility importance degree factors, and alpha reflects the function of pheromone accumulated in the moving process of ants in the moving process of the ants; beta represents the relative importance of visibility.
Branch selection rules: each ant employs roulette rules in selecting a diversion path from the choosensode collection. First, a comparison sequence was constructed: x is the number of 1 ＝p(1)，x 2 ＝x 1 +p(2)，…，x m ＝x m-1 + p (m), p (i) is the branch transition probability calculated according to the formula (3-10), m is the number of selectable paths, and all the adjacent alternatives of the current selected pathPer unit processing is carried out on the transition probability on the path by x m As a reference value, guarantee x after treatment 1 ＜x 2 ＜…＜x m E (0, 1), and finally generating a random number rand e (0, 1), selecting a rule:
wherein, next is the selected branch of this ant.
At the initial time, the pheromone concentration on each path is assumed to be the same, and τ is used ij (0) = C initializes each path pheromone (C is a small constant). Tau is ij For the pheromone concentration of ants transferred from branch i to branch j, when j = i, tau ii Representing the pheromone concentration on branch i when the branch i starts to search for a path (the branch i is necessarily connected with a power supply point).
And after one ant colony iteration is completed, the pheromone on the branch is required to be updated. If the pheromones left by all ants passing through the branches are accumulated to be used as correction quantity, the pheromones tend to be averaged and fall into random search, and the positive effect of the optimal solution in the colony on the pheromones is not facilitated. Therefore, through path search of a generation of Nant ants, nant paths are contrastively analyzed to obtain an optimal path (optimal network configuration structure) therein, all paths in the optimal path, namely the optimal distribution network structure, are recorded after a generation of circulation is completed, pheromones on the corresponding paths are sequentially updated according to the sequence of the paths, and the method mainly comprises the following two aspects: volatilization of pheromones and pheromone regulation. When ants search a path and release pheromones, the pheromones on the path slowly volatilize along with the time, the process is simulated by the first half part of the following formula, and rho (0 < rho < 1) is the volatilization degree of the pheromones and reflects the concentration of the pheromones remaining on the path after volatilization:
τ ij (t+1)＝(1-ρ)τ ij (t)+Δτ ij (t)
in the formula: delta tau ij For the pheromone concentration increment of ants transferred from branch i to branch j in the optimal path in each generation, the optimal path isContinuously accumulating pheromones on the path, and improving the convergence speed of the algorithm, wherein:
wherein Q is a constant, reflecting the pheromone enhancement degree, f best Maximum value of objective function in all network structures generated for a generation of Nant ants, B best Is a set of legs in the optimal network structure.
After one ant colony iteration is completed, the following global optimal optimization mode is adopted: and storing the optimal solution obtained by each iteration as Best1, comparing the optimal solution with the optimal solution Best0 obtained last time, and storing the better one as Best0. And repeating each iteration, and obtaining the optimal solution when the convergence condition is met. And after the pheromone updating and the optimal solution storage are finished, the next ant colony iteration is carried out until the convergence condition is met, and the optimal fault recovery result is obtained.
The step 103 includes:
if the first distribution network has a fault recovery time z 1 And a second distribution network fault recovery time z 2 Satisfies the following conditions: z is a radical of 1 ＞z 2 If so, not adjusting the power distribution network fault recovery scheme;
if the first distribution network has a fault recovery time z 1 And a second distribution network fault recovery time z 2 Satisfies the following conditions: z is a radical of 1 ＜z 2 Then the fault recovery time z of the second power distribution network is used 2 For the fault recovery time of the power distribution network, the fault recovery time z of the second power distribution network 2 The constraint condition of the power distribution network fault recovery model is verified at each time interval, and if the second power distribution network fault recovery time z is up 2 Each time interval of the power distribution network fault recovery model meets the constraint condition of the power distribution network fault recovery model, and the power distribution network fault recovery time of the power distribution network fault recovery scheme is adjusted to be the second power distribution network fault recovery time z 2 If the second distribution network fault recovery time z 2 If the time period does not meet the constraint condition of the power distribution network fault recovery model exists, the power distribution network is subjected toThe power grid structure of the fault recovery scheme carries out load shedding until the fault recovery time z of the second power distribution network 2 Meets the constraint condition of a power distribution network fault recovery model in each time period, and adjusts the power distribution network fault recovery time of the power distribution network fault recovery scheme to be the second power distribution network fault recovery time z 2 。
A fault recovery apparatus for a power distribution network that accounts for uncertainty in time to recover from a fault, as shown in fig. 3, the apparatus comprising:
the acquisition module is used for respectively acquiring two optimal power distribution network fault recovery times of the probability density function and the probabilities of the two optimal power distribution network fault recovery times, namely a first power distribution network fault recovery time and the probability thereof and a second power distribution network fault recovery time and the probability thereof according to the probability density function of the power distribution network fault recovery time, wherein the probability of the first power distribution network fault recovery time is greater than the probability of the second power distribution network fault recovery time;
and determining the fault recovery time and the probability of the first power distribution network and the fault recovery time and the probability of the second power distribution network by using the Wasserstein distance.
The creating module is used for creating a power distribution network fault recovery model by utilizing the first power distribution network fault recovery time, and taking the optimal solution of the power distribution network fault recovery model as a power distribution network fault recovery scheme;
and obtaining an optimal solution of the power distribution network fault recovery model by adopting an ant colony algorithm, and taking the optimal solution of the power distribution network fault recovery model as a power distribution network fault recovery scheme.
And the optimization module is used for optimizing the power distribution network fault recovery scheme by utilizing the second power distribution network fault recovery time.
Further, the obtaining module includes:
a first obtaining unit, configured to enable the number of sub-sites of the probability density function of the power distribution network fault recovery time S =2, and solve the following equation (1) to obtain the first power distribution network fault recovery time z respectively 1 And a second distribution network fault recovery time z 2 ：
In the formula (1), g (t) is a probability density function of the fault recovery time of the power distribution network, s belongs to [1, S ], and r is an order.
A second obtaining unit, configured to obtain the fault recovery time z of the first power distribution network according to the following formula (2) 1 Probability p of 1 And the second distribution network fault recovery time z 2 Probability p of 2 ：
Preferably, the creating module includes:
the creating unit is used for maximizing the maximum important load total electric quantity for restoring the power distribution network as an objective function, and the formula is as follows:
in the formula (3), F main Important load total electric quantity, z, for main network to recover to non-fault power loss area in fault period 1 For the time of fault recovery, n is the total number of system nodes, lambda i To the importance of the load on node i, L i,t For the load size of node i in time period t, y i,t Is a state change parameter, y i,t =1 denotes that node i resumes power supply during time period t, y i,t =0 indicates that the node i is not powered back for the time period t;
the constraint conditions include:
node voltage constraint, the formula is:
U min ≤U i.t ≤U max (4)
in the formula (4), U i,t For the voltage value of node i during time period t, U min Lower voltage limit, U, of node i max Is the upper voltage limit of node i;
a power balance constraint, formulated as:
in the formula (5), P i,t Active power, Q, injected for node i during time period t i,t Reactive power, G, injected for node i during time period t ij Is the conductance between nodes i, j, B ij Is susceptance, delta, between nodes i, j ij,t Is the voltage phase angle difference of the nodes i and j in the time period t, n is the total number of the system nodes, U i,t For the voltage amplitude of node i during time period t, U j,t Is the voltage amplitude of node j during time period t;
branch power constraint, the formula is:
P ij.t ≤P ijmax (6)
in the formula (6), P ij,t Active power value, P, for the branch between node i and node j in time period t ij max The maximum value of the active power of the branch between the node i and the node j is allowed;
the radiation operation of the power distribution network is restricted by the following formula:
g∈G (7)
in the formula (7), G is a reconstructed network topology, and G is a set of network radial topologies.
The optimization module comprises:
a first optimization unit for the recovery time z if the first distribution network failure 1 And a second distribution network fault recovery time z 2 Satisfies the following conditions: z is a radical of 1 ＞z 2 If so, not adjusting the power distribution network fault recovery scheme;
a second optimization unit for the time z for recovery of the first distribution network failure if 1 And a second distribution network fault recovery time z 2 Satisfies the following conditions: z is a radical of formula 1 ＜z 2 Then the fault recovery time z of the second power distribution network is used 2 For the fault recovery time of the power distribution network, the fault recovery time z of the second power distribution network 2 The constraint condition of the power distribution network fault recovery model is verified at each time interval, and if the second power distribution network fault recovery time z is up 2 If each period of time meets the constraint condition of the power distribution network fault recovery model, adjusting the power distribution network fault recovery time of the power distribution network fault recovery scheme to be the second power distribution network fault recovery time z 2 If the second distribution network fault recovery time z 2 If the time period does not meet the constraint condition of the power distribution network fault recovery model exists, load shedding is carried out on the power distribution network structure of the power distribution network fault recovery scheme until the second power distribution network fault recovery time z 2 Meets the constraint condition of a power distribution network fault recovery model in each period of time, and adjusts the power distribution network fault recovery time of the power distribution network fault recovery scheme to be the second power distribution network fault recovery time z 2 。
Finally, it should be noted that: although the present invention has been described in detail with reference to the above embodiments, it should be understood by those skilled in the art that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (8)
1. A method for fault recovery in a power distribution network that accounts for uncertainty in time to recover from a fault, the method comprising:
according to a probability density function of power distribution network fault recovery time, respectively obtaining two optimal power distribution network fault recovery times of the probability density function and probabilities of the two optimal power distribution network fault recovery times, namely first power distribution network fault recovery time and the probability thereof and second power distribution network fault recovery time and the probability thereof, wherein the probability of the first power distribution network fault recovery time is greater than the probability of the second power distribution network fault recovery time;
establishing a power distribution network fault recovery model by utilizing the first power distribution network fault recovery time, and taking the optimal solution of the power distribution network fault recovery model as a power distribution network fault recovery scheme;
optimizing the power distribution network fault recovery scheme by utilizing the second power distribution network fault recovery time;
the fault recovery time and the probability of the first power distribution network and the fault recovery time and the probability of the second power distribution network are determined by using Wasserstein distance;
the method for optimizing the power distribution network fault recovery scheme by using the second power distribution network fault recovery time comprises the following steps:
if the first distribution network fault recovery time z 1 And a second distribution network fault recovery time z 2 Satisfies the following conditions: z is a radical of 1 ＞z 2 If so, not adjusting the power distribution network fault recovery scheme;
if the first distribution network has a fault recovery time z 1 And a second distribution network fault recovery time z 2 Satisfies the following conditions: z is a radical of formula 1 ＜z 2 Then the fault recovery time z of the second power distribution network is used 2 For the fault recovery time of the power distribution network, the fault recovery time z of the second power distribution network 2 The constraint condition of the power distribution network fault recovery model is verified at each time interval, and if the second power distribution network fault recovery time z is up 2 Each time interval of the power distribution network fault recovery model meets the constraint condition of the power distribution network fault recovery model, and the power distribution network fault recovery time of the power distribution network fault recovery scheme is adjusted to be the second power distribution network fault recovery time z 2 If the second distribution network fault recovery time z 2 If the time period does not meet the constraint condition of the power distribution network fault recovery model exists, load shedding is carried out on the power distribution network structure of the power distribution network fault recovery scheme until the second power distribution network fault recovery time z 2 Meets the constraint condition of a power distribution network fault recovery model in each time period, and adjusts the power distribution network fault recovery time of the power distribution network fault recovery scheme to be the second power distribution network fault recovery time z 2 。
2. The method according to claim 1, characterized in that the first distribution network fault recovery time z is obtained by solving the following formula (1) by letting the number of quantile points of the probability density function of the distribution network fault recovery time S =2 1 And a second distribution network fault recovery time z 2 ：
In the formula (1), g (t) is a probability density function of the fault recovery time of the power distribution network, s belongs to [1, S ], and r is an order;
respectively acquiring the fault recovery time z of the first power distribution network according to the following formula (2) 1 Probability p of 1 And the second distribution network fault recovery time z 2 Probability p of 2 ：
3. The method according to claim 1, wherein said utilizing said first power distribution network fault recovery time to build a power distribution network fault recovery model comprises:
the maximum of the total electric quantity of important loads recovered by a recovery power distribution network is an objective function, and the formula is as follows:
in the formula (3), F main Important load total electric quantity, z, for main network to recover to non-fault power loss area in fault period 1 For the time of fault recovery, n is the total number of system nodes, lambda i To the importance of the load on node i, L i,t For node i load size, y, in time period t i,t Is a state change parameter, y i,t =1 denotes that node i resumes power supply during time period t, y i,t =0 indicates that the node i does not recover power supply in the period t;
the constraint conditions include:
node voltage constraints are formulated as:
U min ≤U i.t ≤U max (4)
in the formula (4), U i,t For the voltage value of node i in time period t, U min Lower voltage limit, U, of node i max Is the upper voltage limit of node i;
a power balance constraint, the formula being:
in formula (5), P i,t Active power, Q, injected for node i during time period t i,t Reactive power, G, injected for node i during time period t ij Is the conductance between nodes i, j, B ij Is susceptance, delta, between nodes i, j ij,t The voltage phase angle difference of the nodes i and j in the time period t, n is the total number of the system nodes, U i,t For the voltage amplitude of node i during time period t, U j,t Is the voltage amplitude of node j during time period t;
branch power constraint, the formula is:
P ij.t ≤P ijmax (6)
in the formula (6), P ij,t Active power value, P, for the branch between node i and node j in time period t ij max The maximum value of the active power allowed by the branch between the node i and the node j is obtained;
the radiation operation of the power distribution network is restricted by the following formula:
g∈G (7)
in the formula (7), G is a reconstructed network topology structure, and G is a set of network radial topology structures.
4. The method of claim 1, wherein an ant colony algorithm is used to obtain the optimal solution of the power distribution network fault recovery model, and the optimal solution of the power distribution network fault recovery model is used as a power distribution network fault recovery scheme.
5. A power distribution network fault recovery apparatus that accounts for uncertainty in time to recover from a fault, the apparatus comprising:
the acquisition module is used for respectively acquiring two optimal power distribution network fault recovery times of the probability density function and the probabilities of the two optimal power distribution network fault recovery times, namely first power distribution network fault recovery time and the probability thereof and second power distribution network fault recovery time and the probability thereof according to the probability density function of the power distribution network fault recovery time, wherein the probability of the first power distribution network fault recovery time is greater than the probability of the second power distribution network fault recovery time;
the creating module is used for creating a power distribution network fault recovery model by utilizing the first power distribution network fault recovery time, and taking the optimal solution of the power distribution network fault recovery model as a power distribution network fault recovery scheme;
the optimization module is used for optimizing the power distribution network fault recovery scheme by utilizing the second power distribution network fault recovery time;
determining the fault recovery time and the probability of the first power distribution network and the fault recovery time and the probability of the second power distribution network by using the Wasserstein distance;
the optimization module comprises:
a first optimization unit for the recovery time z if the first distribution network failure 1 And a second distribution network fault recovery time z 2 Satisfies the following conditions: z is a radical of 1 ＞z 2 If so, not adjusting the power distribution network fault recovery scheme;
a second optimization unit for the time z for recovery of the first distribution network failure if 1 And a second distribution network fault recovery time z 2 Satisfies the following conditions: z is a radical of formula 1 ＜z 2 Then with said second distribution network fault recovery time z 2 For the fault recovery time of the power distribution network, the fault recovery time z of the second power distribution network 2 The constraint condition of the power distribution network fault recovery model is verified at each time interval, and if the second power distribution network fault recovery time z is up 2 Each time interval of the power distribution network fault recovery model meets the constraint condition of the power distribution network fault recovery model, and the power distribution network fault recovery time of the power distribution network fault recovery scheme is adjusted to be the second power distribution network fault recovery time z 2 If the second distribution network has the fault recovery time z 2 If the time period does not meet the constraint condition of the power distribution network fault recovery model, the power distribution network fault recovery model is matchedThe power grid structure of the power grid fault recovery scheme carries out load shedding until the fault recovery time z of the second power distribution network 2 Meets the constraint condition of a power distribution network fault recovery model in each time period, and adjusts the power distribution network fault recovery time of the power distribution network fault recovery scheme to be the second power distribution network fault recovery time z 2 。
6. The apparatus of claim 5, wherein the obtaining module comprises:
a first obtaining unit, configured to make the number of sub-sites of the probability density function of the power distribution network fault recovery time S =2, and solve the following formula (1) to obtain the first power distribution network fault recovery time z respectively 1 And a second distribution network fault recovery time z 2 ：
In the formula (1), g (t) is a probability density function of the fault recovery time of the power distribution network, s belongs to [1, S ], and r is an order;
a second obtaining unit, configured to obtain the failure recovery time z of the first power distribution network according to the following formula (2) 1 Probability p of 1 And the second distribution network fault recovery time z 2 Probability p of 2 ：
7. The apparatus of claim 5, wherein the creating module comprises:
the creating unit is used for creating an objective function with the maximum of the total electric quantity of important loads recovered by the recovery power distribution network, and the formula is as follows:
in formula (3), F main Important load total electric quantity, z, for main network to restore to non-fault power loss area in fault period 1 For the fault repair time, n is the total number of system nodes, λ i To the importance of the load on node i, L i,t For node i load size, y, in time period t i,t As a state change parameter, y i,t =1 denotes that node i resumes power supply during time period t, y i,t =0 indicates that the node i does not recover power supply in the period t;
the constraint conditions include:
node voltage constraints are formulated as:
U min ≤U i.t ≤U max (4)
in the formula (4), U i,t For the voltage value of node i during time period t, U min Lower voltage limit, U, of node i max Is the upper voltage limit of node i;
a power balance constraint, the formula being:
in formula (5), P i,t Active power, Q, injected for node i during time period t i,t Reactive power, G, injected for node i during time period t ij Is the conductance between nodes i, j, B ij Is susceptance, delta, between nodes i, j ij,t Is the voltage phase angle difference of the nodes i and j in the time period t, n is the total number of the system nodes, U i,t For the voltage amplitude of node i in time period t, U j,t Is the voltage amplitude of node j during time period t;
branch power constraint, the formula is:
P ij.t ≤P ijmax (6)
in formula (6), P ij,t For the active power value, P, of the branch between node i and node j in time period t ij max The maximum value of the active power allowed by the branch between the node i and the node j is obtained;
the radiation operation constraint of the power distribution network has the formula:
g∈G (7)
in the formula (7), G is a reconstructed network topology structure, and G is a set of network radial topology structures.
8. The apparatus of claim 5, wherein an ant colony algorithm is used to obtain the optimal solution of the power distribution network fault recovery model, and the optimal solution of the power distribution network fault recovery model is used as a power distribution network fault recovery scheme.
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