CN106655155A - Power distribution network fault recovery method with consideration of the uncertainty of fault recovery time - Google Patents

Abstract

The invention relates to a power distribution network fault recovery method with consideration of the uncertainty of fault recovery time. The method comprises the following steps: according to the probability density function of the fault recovery time of the distribution network, obtaining two best power distribution network fault recovery times and the probabilities for the two best power distribution network fault recovery times respectively, or rather a first power distribution network fault recovery time and its probability and a second power distribution network fault recovery time and its probability; using the first power distribution network fault recovery time to establish a power distribution network fault recovery model and using the best solution of the power distribution network fault recovery model as the power distribution network fault recovery scheme; and using the second power distribution network fault recovery time to optimize the power distribution network fault recovery scheme. The method proposed by the invention adopts a Wasserstein distance method to determine the fault recovery times and through the utilization of the fault recovery times, proper adjustment can be made to the fault recovery scheme so as to realize the best power supply recovery to an area out of power and to increase the economy and security for power grid operations.

Description

One kind considers the probabilistic distribution network failure restoration methods of failure recovery time

Technical field

The present invention relates to power distribution network running technology field, and in particular to one kind considers that failure recovery time is probabilistic and matches somebody with somebody Electric network fault restoration methods.

Background technology

After distribution network failure recovers to refer to that distribution network failure occurs, by determining optimum switch combination scheme, realize extensive The targets such as multiple dead electricity load most, switching manipulation least number of times, loss minimization, while meeting power distribution network connectedness, spoke after recovery Penetrate the conditions such as shape.

It is also one of study hotspot that in recent years the distribution network failure containing distributed power source recovers, when power distribution network breaks down simultaneously After being isolated, the distributed power source in dead electricity area is independently-powered to the important load in the region, forms islet operation pattern, Power supply reliability can be improved.But exerting oneself for the uncontrollable DG such as wind-force, photovoltaic has uncertainty, and the failure of power distribution network is extensive The multiple time equally exists uncertainty, and causing trouble recovery scheme is different, and after power distribution network breaks down, the power supply to electrical network is extensive Effect difference is answered, it is thus impossible to best service restoration effect is reached to dead electricity region using conventional failure restoration methods.

The content of the invention

The present invention provides a kind of consideration failure recovery time probabilistic distribution network failure restoration methods, its objective is to adopt Determine the time of fault recovery with the method for Wasserstein distances, fault recovery scheme is entered using the failure recovery time Row Reasonable adjustment, realizes the service restoration effect best to dead electricity region, and improves the economy and security of distribution network operation.

The purpose of the present invention is realized using following technical proposals：

One kind considers the probabilistic distribution network failure restoration methods of failure recovery time, and it is theed improvement is that, including：

According to the probability density function of distribution network failure recovery time, two of the probability density function are obtained respectively most Excellent distribution network failure recovery time and the probability of described two optimum distribution network failure recovery times, i.e. the first distribution network failure is extensive Multiple time and its probability and the second distribution network failure recovery time and its probability, wherein, when first distribution network failure recovers Between probability more than the second distribution network failure recovery time probability；

Distribution network failure Restoration model is set up using the first distribution network failure recovery time, and the power distribution network is former The optimal solution of barrier Restoration model is used as distribution network failure recovery scheme；

Optimize the distribution network failure recovery scheme using the second distribution network failure recovery time.

Preferably, the first distribution network failure recovery time and its probability and the are determined using Wasserstein distances Two distribution network failure recovery times and its probability.

Further, the quantile S=2 of the probability density function of the distribution network failure recovery time is made, under solution Formula (1) obtains respectively the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂：

In formula (1), g (t) for distribution network failure recovery time probability density function, s ∈ [1, S], r is exponent number.

As the following formula (2) obtain respectively the first distribution network failure recovery time z₁Probability p₁With second power distribution network Failure recovery time z₂Probability p₂：

Preferably, it is described to set up distribution network failure Restoration model using the first distribution network failure recovery time, including：

It is object function to the maximum to recover distribution network restoration important load total electricity, formula is：

In formula (3), F_mainFor the important load total electricity that major network recovers in the failure period to non-faulting dead electricity region, z₁For Fault correction time, n is that system node is total, λ_iFor the significance level of load in node i, L_i,tIt is node i bearing in period t Lotus size, y_i,tFor state change parameter, y_i,t=1 expression node i restores electricity in period t, y_i,t=0 represents node i in the period T does not restore electricity；

Constraints includes：

Node voltage is constrained, and formula is：

U_min≤U_i.t≤U_max (4)

In formula (4), U_i,tFor node i period t magnitude of voltage, U_minFor the lower voltage limit of node i, U_maxFor the electricity of node i The pressure upper limit；

Power-balance constraint, formula is：

In formula (5), P_i,tFor the active power that node i is injected in period t, Q_i,tFor the idle work(that node i is injected in period t Rate, G_ijFor the conductance between node i, j, B_ijFor the susceptance between node i, j, δ_ij,tIt is node i, j in period t voltage phase angle Difference, n is that system node is total, U_i,tFor node i period t voltage magnitude, U_j,tFor node j period t voltage magnitude；

Branch power is constrained, and formula is：

P_ij.t≤P_ijmax (6)

In formula (6), P_ij,tFor branch road between node i and node j period t active power value, P_ij ^maxFor node i and node The active power of branch road allows maximum between j；

Power distribution network radiation operation is constrained, and formula is：

g∈G (7)

In formula (7), g is the network topology structure after reconstruct, and G is the set of the radial topological structure of network.

Preferably, the optimal solution of the distribution network failure Restoration model is obtained using ant group algorithm, and by the power distribution network The optimal solution of fault recovery model is used as distribution network failure recovery scheme.

It is preferably, described to optimize the distribution network failure recovery scheme using the second distribution network failure recovery time, Including：

If the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂Meet：z₁＞ z₂, then it is uncomfortable The whole distribution network failure recovery scheme；

If the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂Meet：z₁＜ z₂, then with institute State the second distribution network failure recovery time z₂For distribution network failure recovery time, to the second distribution network failure recovery time z₂ Each period carry out distribution network failure Restoration model constraints checking, if the second distribution network failure recovery time z₂ Each period be satisfied by the constraints of distribution network failure Restoration model, then by the electrical network of the distribution network failure recovery scheme Failure recovery time is adjusted to the second distribution network failure recovery time z₂If, the second distribution network failure recovery time z₂ Presence is unsatisfactory for the time period of the constraints of distribution network failure Restoration model, then to the electricity of the distribution network failure recovery scheme Web frame carries out cutting load, until the second distribution network failure recovery time z₂To be satisfied by distribution network failure extensive each period Answer the constraints of model and the electric network fault recovery time of the distribution network failure recovery scheme is adjusted into described second and match somebody with somebody Electric network fault recovery time z₂。

One kind considers the probabilistic distribution network failure recovery device of failure recovery time, and it is theed improvement is that, described Device includes：

Acquisition module, for according to the probability density function of distribution network failure recovery time, the probability being obtained respectively close The optimum distribution network failure recovery times of degree two of function and the probability of described two optimum distribution network failure recovery times, i.e., the One distribution network failure recovery time and its probability and the second distribution network failure recovery time and its probability, wherein, described first matches somebody with somebody Probability of the probability of electric network fault recovery time more than the second distribution network failure recovery time；

Creation module, for setting up distribution network failure Restoration model using the first distribution network failure recovery time, and Using the optimal solution of the distribution network failure Restoration model as distribution network failure recovery scheme；

Optimization module, for optimizing the distribution network failure recovery side using the second distribution network failure recovery time Case.

Preferably, the first distribution network failure recovery time and its probability and the are determined using Wasserstein distances Two distribution network failure recovery times and its probability.

Further, the acquisition module includes：

First acquisition unit, for making the quantile S=of the probability density function of the distribution network failure recovery time 2, solve following formula (1) and obtain the first distribution network failure recovery time z respectively₁With the second distribution network failure recovery time z₂：

In formula (1), g (t) for distribution network failure recovery time probability density function, s ∈ [1, S], r is exponent number.

Second acquisition unit, for (2) as the following formula the first distribution network failure recovery time z is obtained respectively₁Probability p₁ With the second distribution network failure recovery time z₂Probability p₂：

Preferably, in the creation module, including：

Creating unit, for being object function to the maximum to recover distribution network restoration important load total electricity, formula is：

In formula (3), F_mainFor the important load total electricity that major network recovers in the failure period to non-faulting dead electricity region, z₁For Fault correction time, n is that system node is total, λ_iFor the significance level of load in node i, L_i,tIt is node i bearing in period t Lotus size, y_i,tFor state change parameter, y_i,t=1 expression node i restores electricity in period t, y_i,t=0 represents node i in the period T does not restore electricity；

Constraints includes：

Node voltage is constrained, and formula is：

U_min≤U_i.t≤U_max (4)

In formula (4), U_i,tFor node i period t magnitude of voltage, U_minFor the lower voltage limit of node i, U_maxFor the electricity of node i The pressure upper limit；

Power-balance constraint, formula is：

In formula (5), P_i,tFor the active power that node i is injected in period t, Q_i,tFor the idle work(that node i is injected in period t Rate, G_ijFor the conductance between node i, j, B_ijFor the susceptance between node i, j, δ_ij,tIt is node i, j in period t voltage phase angle Difference, n is that system node is total, U_i,tFor node i period t voltage magnitude, U_j,tFor node j period t voltage magnitude；

Branch power is constrained, and formula is：

P_ij.t≤P_ijmax (6)

In formula (6), P_ij,tFor branch road between node i and node j period t active power value, P_ij ^maxFor node i and node The active power of branch road allows maximum between j；

Power distribution network radiation operation is constrained, and formula is：

g∈G (7)

In formula (7), g is the network topology structure after reconstruct, and G is the set of the radial topological structure of network.

Preferably, the optimal solution of the distribution network failure Restoration model is obtained using ant group algorithm, and by the power distribution network The optimal solution of fault recovery model is used as distribution network failure recovery scheme.

Preferably, the optimization module, including：

First optimization unit, if for the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂ Meet：z₁＞ z₂, then the distribution network failure recovery scheme is not adjusted；

Second optimization unit, if for the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂ Meet：z₁＜ z₂, then with the second distribution network failure recovery time z₂For distribution network failure recovery time, match somebody with somebody to described second Electric network fault recovery time z₂Each period carry out distribution network failure Restoration model constraints checking, if described second matches somebody with somebody Electric network fault recovery time z₂Each period be satisfied by the constraints of distribution network failure Restoration model, then by the power distribution network The electric network fault recovery time of fault recovery scheme is adjusted to the second distribution network failure recovery time z₂If described second matches somebody with somebody Electric network fault recovery time z₂Presence is unsatisfactory for the time period of the constraints of distribution network failure Restoration model, then to the distribution The electric network composition of net fault recovery scheme carries out cutting load, until the second distribution network failure recovery time z₂Each period When being satisfied by the constraints of distribution network failure Restoration model and recovering the electric network fault of the distribution network failure recovery scheme Between be adjusted to the second distribution network failure recovery time z₂。

Beneficial effects of the present invention：

In prior art, there is uncertainty in the failure recovery time of power distribution network, one kind that the present invention is provided considers failure Recovery time probabilistic distribution network failure restoration methods, in the case of known fault repair time probability density function, By probability function carry out precision it is discrete, the failure recovery time of two kinds of maximum probabilities can be obtained, be easy to according to power distribution network Physical fault situation, formulates fault recovery scheme, meanwhile, according to the failure recovery time of two kinds of different probabilities, formulate respectively excellent Change scheme and amendment scheme, after power distribution network breaks down, are first carried out prioritization scheme, by being tracked to fault message, The length of failure judgement recovery time, and fault recovery scheme is adjusted in time, it is possible to reduce the action frequency of switch, extend switch Life-span, and maximum fault recovery is realized, improve the economy and reliability of distribution network operation.

Description of the drawings

Fig. 1 is a kind of flow chart for considering the probabilistic distribution network failure restoration methods of failure recovery time of the present invention；

Fig. 2 is that one kind considers that the probabilistic distribution network failure restoration methods of failure recovery time should in the embodiment of the present invention Use schematic diagram of a scenario；

Fig. 3 is a kind of structural representation for considering the probabilistic distribution network failure recovery device of failure recovery time of the present invention Figure.

Specific embodiment

The specific embodiment of the present invention is elaborated below in conjunction with the accompanying drawings.

To make purpose, technical scheme and the advantage of the embodiment of the present invention clearer, below in conjunction with the embodiment of the present invention In accompanying drawing, the technical scheme in the embodiment of the present invention is clearly and completely described, it is clear that described embodiment is The a part of embodiment of the present invention, rather than the embodiment of whole.Based on the embodiment in the present invention, those of ordinary skill in the art The all other embodiment obtained under the premise of creative work is not made, belongs to the scope of protection of the invention.

The probabilistic distribution network failure restoration methods of a kind of consideration failure recovery time that the present invention is provided, such as Fig. 1 institutes Show, including：

101., according to the probability density function of distribution network failure recovery time, obtain respectively the two of the probability density function Individual optimum distribution network failure recovery time and the probability of described two optimum distribution network failure recovery times, i.e. the first power distribution network event Barrier recovery time and its probability and the second distribution network failure recovery time and its probability, wherein, first distribution network failure is extensive Probability of the probability of multiple time more than the second distribution network failure recovery time；

Wherein it is possible to the probability according to the mean repair time of the distribution system acquisition distribution network failure recovery time is close Degree function；

102. set up distribution network failure Restoration model using the first distribution network failure recovery time, and by the distribution The optimal solution of net fault recovery model is used as distribution network failure recovery scheme；

103. optimize the distribution network failure recovery scheme using the second distribution network failure recovery time.

Specifically, in the step 101, when determining that first distribution network failure recovers using Wasserstein distances Between and its probability and the second distribution network failure recovery time and its probability.

Specifically include：The quantile S=2 of the probability density function of the distribution network failure recovery time is made, under solution Formula (1) obtains respectively the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂：

In formula (1), g (t) for distribution network failure recovery time probability density function, s ∈ [1, S], r is exponent number.

As the following formula (2) obtain respectively the first distribution network failure recovery time z₁Probability p₁With second power distribution network Failure recovery time z₂Probability p₂：

It is described to set up distribution network failure recovery mould using the first distribution network failure recovery time in the step 102 Type, including：

It is object function to the maximum to recover distribution network restoration important load total electricity, formula is：

In formula (3), F_mainFor the important load total electricity that major network recovers in the failure period to non-faulting dead electricity region, z₁For Fault correction time, n is that system node is total, λ_iFor the significance level of load in node i, L_i,tIt is node i bearing in period t Lotus size, y_i,tFor state change parameter, y_i,t=1 expression node i restores electricity in period t, y_i,t=0 represents node i in the period T does not restore electricity；

Constraints includes：

Node voltage is constrained, and formula is：

U_min≤U_i.t≤U_max (4)

In formula (4), U_i,tFor node i period t magnitude of voltage, U_minFor the lower voltage limit of node i, U_maxFor the electricity of node i The pressure upper limit；

Power-balance constraint, formula is：

In formula (5), P_i,tFor the active power that node i is injected in period t, Q_i,tFor the idle work(that node i is injected in period t Rate, G_ijFor the conductance between node i, j, B_ijFor the susceptance between node i, j, δ_ij,tIt is node i, j in period t voltage phase angle Difference, n is that system node is total, U_i,tFor node i period t voltage magnitude, U_j,tFor node j period t voltage magnitude；

Branch power is constrained, and formula is：

P_ij.t≤P_ijmax (6)

In formula (6), P_ij,tFor branch road between node i and node j period t active power value, P_ij ^maxFor node i and node The active power of branch road allows maximum between j；

Power distribution network radiation operation is constrained, and formula is：

g∈G (7)

In formula (7), g is the network topology structure after reconstruct, and G is the set of the radial topological structure of network.

Further, in the step 102, the optimum of the distribution network failure Restoration model is obtained using ant group algorithm Solution, and using the optimal solution of the distribution network failure Restoration model as distribution network failure recovery scheme.

At present, the technology using ant group algorithm formulation distribution network failure recovery scheme is more ripe, and the present invention is effective Solve the network reconfiguration optimization problem restored electricity after distribution network failure, it is to avoid occur a large amount of infeasible solutions in search procedure, adopt The fault recovery of major network, and the switch shape according to service restoration ability to non-faulting area are completed with the ant group algorithm for being based on spanning tree State combination carries out optimizing.

Ant group algorithm is a kind of optimizing search method similar to Evolution of Population, and its essence is that ant can be in the path passed through Upper release pheromone comes identification path, exchange information, and the pheromone concentration retained on the shorter path in path in same time is got over Height, ant finds shorter path further according to pheromone concentration on path, by the way that with such a positive feedback mechanism, ant colony can Soon to search for the path of optimum, the pheromone concentration in the path also can highest.

For example：The present invention provides the optimal solution that a kind of employing ant group algorithm obtains the distribution network failure Restoration model, and Using the optimal solution of the distribution network failure Restoration model as distribution network failure recovery scheme specific implementation process, including：

Ant utilizes spanning tree strategy, generates a kind of feasible radial networks；

Load flow calculation is carried out to current network；

If result of calculation is unsatisfactory for the constraints of distribution network failure Restoration model, cutting load operation is carried out；

Iteration, until meeting end condition.

Specifically, for the radiativity feature of power distribution network, the weight after power distribution network network failure is solved using ant group algorithm All it is radiation using network topology after the failure corresponding to " distance of swimming " each time that spanning tree strategy completes ant during structure problem Type, it is to avoid radiation type checking and repair process, it is ensured that per generation be feasible solution, improve the search efficiency of algorithm, and to ant The routing rule of group's algorithm and pheromone update strategy are improved, and accelerate convergence rate.

Using the block switch and interconnection switch of power distribution network as figure nonoriented edge e_i(i=1,2 ... m), the load on circuit The node v of pie graph_j(j=1,2 ... n), and power supply point is used as root node v₀, then power distribution network can be described as a non-directed graph G, nothing Numbering to figure G nodes is expressed as v_j(j=1,2 ... n).Should using the net based structures matrix A branch description of a n rows n row Non-directed graph G, wherein n are the number of system node, i.e.,

Wherein, if there is switch to be connected between node i and j, a_ij=a_ji=1, and remaining element is 0.

Again for example, as shown in Fig. 2 by taking the network shown in Fig. 2 as an example, solid line represents the block switch of closure, dotted line is represented The interconnection switch of disconnection, then：

It is equivalent to power distribution network by taking ant k as an example according to the principle of spanning tree after obtaining the net based structures matrix of power distribution network Into non-directed graph G define three below set and two sequences：

(1) each branch road correspondence adjacent node set Anode={ b_v, it is the section adjacent with the row node serial number per row element Period, wherein adjacent node matrix is by taking network shown in Fig. 2 as an example：

(2) ant k has selected node set Endnode={ b_i, the node serial number being up to the present selected into is recorded, its Middle v_i∈G；

(3) the optional node set Choosenode={ b of ant k_w, under current state, can be with selected in unselected node For the node set of next paths.

(4) branch road selects sequence L_ij(i, j=1,2 ..., n), record has selected branch road 0.

(5) vertex ticks sequence M_i(i=1,2 ..., n), whether flag node is as the minor details of a certain bar branch road Point, is to remember 1, otherwise remembers 0.

Using the search strategy of random spanning tree, by taking power distribution network shown in Fig. 2 as an example, with reference to above three set and two sequences Row, instruct ant to generate the feasible solution for meeting topological constraints, and step is as follows：

(1) initial network topology description：All nodes and switch are numbered, the non-directed graph G after numbering is generated, are obtained Abranch matrixes.

(2) initialize：Set Anode, Endnode, Choosenode and sequence M that algorithm is used are set_i, ant is put In head end power supply node, then Endnode={ 1 }, Choosenode={ 2 }, M_kElement for (1,0,0,0,0).

(3) Path selection：Every ant selects a node y according to certain rule from Choosenode set.

(4) record branch road and select sequence L_ij：Record current procedures under branch road first and last node i be Endnode in y phases The point of association, end-node j is the point y selected from Choosenode.

(5) set and sequence amendment：(a).Endnode：Newly-increased selected node y；(b).Choosenode：New set element Element corresponding to y rows in Anode matrixes, and node has been selected in deletion.Network amendment to generating：First and last node to branch road Check and correction, has selected interstitial content plus 1, by M_iIn the node correspondence position mark 1 this time chosen, by the branch road minor details in initial network The corresponding load of point is added in the branch road end-node.If now Choosenode=Φ and M_iIn have been labeled as 1 node total number Less than number of network node, then M is now found_iIn for 0 node serial number X as selected node, and in Endnode select and X First node of the associated point as branch road.

(6) until selecting circuitry number to reach till node keeps count of, being so far generated as one can for circulation step (3)-(5) Row solution.Then load is added into respective nodes, obtains a kind of feasible radial net in new network structure, i.e. above-mentioned steps Network.The route searching of current ant terminates.

Wherein, initial time in above-mentioned steps, ant k (k=1,2 ..., Nant, Nant be per generation ant number) fortune Trend is determined according to the pheromone concentration on each paths during dynamic, therefore the general of optional path is determined using pheromone concentration Rate, the probability in the pheromones accumulation more more options path is also bigger on a certain path.Ant k is transferred to branch road j's by branch road i Probability is：

In formula：allow^kRepresent the set of ant next step optional path；τ_ijIt is transferred to branch road j's by branch road i for ant Pheromone concentration, η_ijExpression is transferred to the visibility (η in path (i, j)_ij=1/z_ij), z_ijRepresent the impedance magnitude of the circuit；α It is the pheromones significance level factor and the visibility significance level factor with β, α reflects the pheromones that ant accumulates in motion process Effect played in ant motion；β represents the relative importance of visibility.

Branch road selects rule：Every ant is advised when transfer path is selected in gathering from Choosenode using roulette Then.First, comparative sequences are constructed：x₁=p (1), x₂=x₁+ p (2) ..., x_m=x_m-1+ p (m), p (i) are according to formula (3- 10) calculated branch road transition probability, m is optional path number, to currently on all of its neighbor alternative path in routing footpath Transition probability carry out standardization process, with x_mOn the basis of be worth, x is ensured after process₁＜ x₂＜ ... ＜ x_m∈ (0,1), finally produce Random number rand ∈ (0,1), select rule：

In formula, Next is the branch road that this ant is chosen.

Initial time, it is believed that pheromone concentration is identical on each paths, with τ_ij ⁽⁰⁾=C initializes each routing information element, and (C is One little constant).τ_ijFor the pheromone concentration that ant is transferred to branch road j by branch road i, as j=i, τ_iiRepresent initial by branch road i (branch road i must connect power supply point), pheromone concentration on i branch roads during searching route.

Complete to be needed to Pheromone update on branch road after an ant colony iteration.If all ants are stayed on branch road Pheromones have all added up and have been used as correction, then pheromones can tend to average and be absorbed in random search, be unfavorable in colony most Positive role of the excellent solution to pheromones.Therefore, through the route searching of generation Nant ant, comparative analysis Nant kind approach, Wherein optimal path (optimum network configuration structure) is obtained, completes to record all paths in optimal path after generation circulation, i.e., Pheromones on corresponding path, according to the sequencing of its travels along path, are updated successively by optimum distribution network structure, Mainly include two aspects：The volatilization of pheromones and pheromones are adjusted.While ant finds path, release pheromone, road Pheromones As time goes on slowly " can volatilize " on footpath, and following formula first halfs have imitated this process, ρ (0 ＜ ρ ＜ 1) it is pheromones degree of volatility, reflects the pheromone concentration retained in volatilization rear path：

τ_ij(t+1)=(1- ρ) τ_ij(t)+Δτ_ij(t)

In formula：Δτ_ijIt is that ant is transferred to the pheromone concentration increment of branch road j by branch road i in per generation in optimal path, Continuous accumulating information element, improves convergence of algorithm speed on preferred path, wherein：

In formula, Q is a constant, and reflecting pheromones strengthens degree, f_bestFor all nets that generation Nant ant generates Object function maximum, B in network structure_bestFor the set of fingers in the optimum network structure.

Complete after an ant colony iteration using the optimizing mode of following global optimum：The optimal solution that each iteration is obtained Best1 is saved as, it is compared with optimal solution Best0 that last time obtains, wherein will save as Best0 compared with the superior.Each iteration Repeat, required optimal solution is obtained when the condition of convergence is met.After Pheromone update and optimal solution preservation is completed, under entrance Ant colony iteration, until meeting the condition of convergence, that is, obtains the fault recovery result of optimum.

In the step 103, including：

If the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂Meet：z₁＞ z₂, then it is uncomfortable The whole distribution network failure recovery scheme；

If the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂Meet：z₁＜ z₂, then with institute State the second distribution network failure recovery time z₂For distribution network failure recovery time, to the second distribution network failure recovery time z₂ Each period carry out distribution network failure Restoration model constraints checking, if the second distribution network failure recovery time z₂ Each period be satisfied by the constraints of distribution network failure Restoration model, then by the electrical network of the distribution network failure recovery scheme Failure recovery time is adjusted to the second distribution network failure recovery time z₂If, the second distribution network failure recovery time z₂ Presence is unsatisfactory for the time period of the constraints of distribution network failure Restoration model, then to the electricity of the distribution network failure recovery scheme Web frame carries out cutting load, until the second distribution network failure recovery time z₂To be satisfied by distribution network failure extensive each period Answer the constraints of model and the electric network fault recovery time of the distribution network failure recovery scheme is adjusted into described second and match somebody with somebody Electric network fault recovery time z₂。

One kind considers the probabilistic distribution network failure recovery device of failure recovery time, as shown in figure 3, described device bag Include：

Acquisition module, for according to the probability density function of distribution network failure recovery time, the probability being obtained respectively close The optimum distribution network failure recovery times of degree two of function and the probability of described two optimum distribution network failure recovery times, i.e., the One distribution network failure recovery time and its probability and the second distribution network failure recovery time and its probability, wherein, described first matches somebody with somebody Probability of the probability of electric network fault recovery time more than the second distribution network failure recovery time；

Wherein, the first distribution network failure recovery time and its probability and second are determined using Wasserstein distances Distribution network failure recovery time and its probability.

Creation module, for setting up distribution network failure Restoration model using the first distribution network failure recovery time, and Using the optimal solution of the distribution network failure Restoration model as distribution network failure recovery scheme；

Wherein, the optimal solution of the distribution network failure Restoration model is obtained using ant group algorithm, and the power distribution network is former The optimal solution of barrier Restoration model is used as distribution network failure recovery scheme.

Optimization module, for optimizing the distribution network failure recovery side using the second distribution network failure recovery time Case.

Further, the acquisition module includes：

First acquisition unit, for making the quantile S=of the probability density function of the distribution network failure recovery time 2, solve following formula (1) and obtain the first distribution network failure recovery time z respectively₁With the second distribution network failure recovery time z₂：

In formula (1), g (t) for distribution network failure recovery time probability density function, s ∈ [1, S], r is exponent number.

Second acquisition unit, for (2) as the following formula the first distribution network failure recovery time z is obtained respectively₁Probability p₁ With the second distribution network failure recovery time z₂Probability p₂：

Preferably, in the creation module, including：

Creating unit, for being object function to the maximum to recover distribution network restoration important load total electricity, formula is：

In formula (3), F_mainFor the important load total electricity that major network recovers in the failure period to non-faulting dead electricity region, z₁For Fault correction time, n is that system node is total, λ_iFor the significance level of load in node i, L_i,tIt is node i bearing in period t Lotus size, y_i,tFor state change parameter, y_i,t=1 expression node i restores electricity in period t, y_i,t=0 represents node i in the period T does not restore electricity；

Constraints includes：

Node voltage is constrained, and formula is：

U_min≤U_i.t≤U_max (4)

In formula (4), U_i,tFor node i period t magnitude of voltage, U_minFor the lower voltage limit of node i, U_maxFor the electricity of node i The pressure upper limit；

Power-balance constraint, formula is：

In formula (5), P_i,tFor the active power that node i is injected in period t, Q_i,tFor the idle work(that node i is injected in period t Rate, G_ijFor the conductance between node i, j, B_ijFor the susceptance between node i, j, δ_ij,tIt is node i, j in period t voltage phase angle Difference, n is that system node is total, U_i,tFor node i period t voltage magnitude, U_j,tFor node j period t voltage magnitude；

Branch power is constrained, and formula is：

P_ij.t≤P_ijmax (6)

In formula (6), P_ij,tFor branch road between node i and node j period t active power value, P_ij ^maxFor node i and node The active power of branch road allows maximum between j；

Power distribution network radiation operation is constrained, and formula is：

g∈G (7)

In formula (7), g is the network topology structure after reconstruct, and G is the set of the radial topological structure of network.

The optimization module, including：

First optimization unit, if for the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂ Meet：z₁＞ z₂, then the distribution network failure recovery scheme is not adjusted；

Second optimization unit, if for the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂ Meet：z₁＜ z₂, then with the second distribution network failure recovery time z₂For distribution network failure recovery time, match somebody with somebody to described second Electric network fault recovery time z₂Each period carry out distribution network failure Restoration model constraints checking, if described second matches somebody with somebody Electric network fault recovery time z₂Each period be satisfied by the constraints of distribution network failure Restoration model, then by the power distribution network The electric network fault recovery time of fault recovery scheme is adjusted to the second distribution network failure recovery time z₂If described second matches somebody with somebody Electric network fault recovery time z₂Presence is unsatisfactory for the time period of the constraints of distribution network failure Restoration model, then to the distribution The electric network composition of net fault recovery scheme carries out cutting load, until the second distribution network failure recovery time z₂Each period When being satisfied by the constraints of distribution network failure Restoration model and recovering the electric network fault of the distribution network failure recovery scheme Between be adjusted to the second distribution network failure recovery time z₂。

Finally it should be noted that：Above example is most only to illustrate technical scheme rather than a limitation Pipe has been described in detail with reference to above-described embodiment to the present invention, and those of ordinary skill in the art should be understood：Still The specific embodiment of the present invention can be modified or equivalent, and without departing from any of spirit and scope of the invention Modification or equivalent, it all should cover within the claims of the present invention.

Claims (12)

1. it is a kind of to consider the probabilistic distribution network failure restoration methods of failure recovery time, it is characterised in that methods described bag Include：

According to the probability density function of distribution network failure recovery time, two optimums that the probability density function is obtained respectively are matched somebody with somebody Electric network fault recovery time and the probability of described two optimum distribution network failure recovery times, i.e. when the first distribution network failure recovers Between and its probability and the second distribution network failure recovery time and its probability, wherein, the first distribution network failure recovery time Probability of the probability more than the second distribution network failure recovery time；

Distribution network failure Restoration model is set up using the first distribution network failure recovery time, and the distribution network failure is extensive The optimal solution of multiple model is used as distribution network failure recovery scheme；

Optimize the distribution network failure recovery scheme using the second distribution network failure recovery time.

2. the method for claim 1, it is characterised in that the first distribution network failure recovery time and its probability and Two distribution network failure recovery times and its probability are determined using Wasserstein distances.

3. method as claimed in claim 2, it is characterised in that make the probability density function of the distribution network failure recovery time Quantile S=2, solve following formula (1) obtain the first distribution network failure recovery time z respectively₁With the event of the second power distribution network Barrier recovery time z₂：

${\∫}_{-\mathrm{\∞}}^{z_s}{g}^{1/(1+r)}\left(t\right)dt=\frac{2s-1}{2S}{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}{g}^{1/(1+r)}g\left(t\right)dt---\left(1\right)$

In formula (1), g (t) for distribution network failure recovery time probability density function, s ∈ [1, S], r is exponent number；

As the following formula (2) obtain respectively the first distribution network failure recovery time z₁Probability p₁With second distribution network failure Recovery time z₂Probability p₂：

$\left\{\begin{array}{cc}{p}_s={\∫}_{z_1}^{\frac{z_s+z_{s+1}}{2}}g\left(t\right)dt& s=1\\ p_s={\∫}_{\frac{z_s+z_{s-1}}{2}}^{z_{s+1}}g\left(t\right)dt& s=2\end{array}\right.---\left(2\right).$

4. the method for claim 1, it is characterised in that described to be set up using the first distribution network failure recovery time Distribution network failure Restoration model, including：

It is object function to the maximum to recover distribution network restoration important load total electricity, formula is：

$F_{main}=\underset{t=1}{\overset{z_1}{\Σ}}\underset{i\∈n}{\Σ}{\mathrm{\λ}}_i{L}_{i,t}{y}_{i,t}---\left(3\right)$

In formula (3), F_mainFor the important load total electricity that major network recovers in the failure period to non-faulting dead electricity region, z₁For failure Repair time, n is that system node is total, λ_iFor the significance level of load in node i, L_i,tIt is big in the load of period t for node i It is little, y_i,tFor state change parameter, y_i,t=1 expression node i restores electricity in period t, y_i,t=0 represents node i in period t not Restore electricity；

Constraints includes：

Node voltage is constrained, and formula is：

U_min≤U_i.t≤U_max (4)

In formula (4), U_i,tFor node i period t magnitude of voltage, U_minFor the lower voltage limit of node i, U_maxFor on the voltage of node i Limit；

Power-balance constraint, formula is：

$\left\{\begin{array}{c}{P}_{i.t}-U_{i.t}\underset{j=1}{\overset{n}{\Σ}}{U}_{j.t}(G_{ij}{\mathrm{cos\δ}}_{ij.t}+B_{ij}{\mathrm{sin\δ}}_{ij.t})=0\\ Q_{i.t}-U_{i.t}\underset{j=1}{\overset{n}{\Σ}}{U}_{j.t}(G_{ij}{\mathrm{cos\δ}}_{ij.t}+B_{ij}{\mathrm{sin\δ}}_{ij.t})=0\end{array}\right.---\left(5\right)$

In formula (5), P_i,tFor the active power that node i is injected in period t, Q_i,tFor the reactive power that node i is injected in period t, G_ijFor the conductance between node i, j, B_ijFor the susceptance between node i, j, δ_ij,tIt is node i, j in period t phase difference of voltage, n For system node sum, U_i,tFor node i period t voltage magnitude, U_j,tFor node j period t voltage magnitude；

Branch power is constrained, and formula is：

P_ij.t≤P_ijmax (6)

In formula (6), P_ij,tFor branch road between node i and node j period t active power value, P_ij ^maxFor between node i and node j The active power of branch road allows maximum；

Power distribution network radiation operation is constrained, and formula is：

g∈G (7)

In formula (7), g is the network topology structure after reconstruct, and G is the set of the radial topological structure of network.

5. the method for claim 1, it is characterised in that the distribution network failure Restoration model is obtained using ant group algorithm Optimal solution, and using the optimal solution of the distribution network failure Restoration model as distribution network failure recovery scheme.

6. the method for claim 1, it is characterised in that described to be optimized using the second distribution network failure recovery time The distribution network failure recovery scheme, including：

If the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂Meet：z₁＞ z₂, then institute is not adjusted State distribution network failure recovery scheme；

If the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂Meet：z₁＜ z₂, then with described Two distribution network failure recovery time z₂For distribution network failure recovery time, to the second distribution network failure recovery time z₂It is every The individual period carries out the constraints checking of distribution network failure Restoration model, if the second distribution network failure recovery time z₂It is every The individual period is satisfied by the constraints of distribution network failure Restoration model, then by the electric network fault of the distribution network failure recovery scheme Recovery time is adjusted to the second distribution network failure recovery time z₂If, the second distribution network failure recovery time z₂Exist The time period of the constraints of distribution network failure Restoration model is unsatisfactory for, then the electrical network of the distribution network failure recovery scheme is tied Structure carries out cutting load, until the second distribution network failure recovery time z₂Each period be satisfied by distribution network failure recover mould The electric network fault recovery time of the distribution network failure recovery scheme is simultaneously adjusted to second power distribution network by the constraints of type Failure recovery time z₂。

7. it is a kind of to consider the probabilistic distribution network failure recovery device of failure recovery time, it is characterised in that described device bag Include：

Acquisition module, for according to the probability density function of distribution network failure recovery time, the probability density letter being obtained respectively The optimum distribution network failure recovery time of several two and the probability of described two optimum distribution network failure recovery times, i.e., first matches somebody with somebody Electric network fault recovery time and its probability and the second distribution network failure recovery time and its probability, wherein, first power distribution network Probability of the probability of failure recovery time more than the second distribution network failure recovery time；

Creation module, for setting up distribution network failure Restoration model using the first distribution network failure recovery time, and by institute The optimal solution of distribution network failure Restoration model is stated as distribution network failure recovery scheme；

Optimization module, for optimizing the distribution network failure recovery scheme using the second distribution network failure recovery time.

8. device as claimed in claim 7, it is characterised in that determine first power distribution network using Wasserstein distances Failure recovery time and its probability and the second distribution network failure recovery time and its probability.

9. device as claimed in claim 8, it is characterised in that the acquisition module includes：

First acquisition unit, for making the quantile S=2 of the probability density function of the distribution network failure recovery time, asks Solution following formula (1) obtains respectively the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂：

${\∫}_{-\mathrm{\∞}}^{z_s}{g}^{1/(1+r)}\left(t\right)dt=\frac{2s-1}{2S}{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}{g}^{1/(1+r)}g\left(t\right)dt---\left(1\right)$

In formula (1), g (t) for distribution network failure recovery time probability density function, s ∈ [1, S], r is exponent number；

Second acquisition unit, for (2) as the following formula the first distribution network failure recovery time z is obtained respectively₁Probability p₁And institute State the second distribution network failure recovery time z₂Probability p₂：

$\left\{\begin{array}{cc}{p}_s={\∫}_{z_1}^{\frac{z_s+z_{s+1}}{2}}g\left(t\right)dt& s=1\\ p_s={\∫}_{\frac{z_s+z_{s-1}}{2}}^{z_{s+1}}g\left(t\right)dt& s=2\end{array}\right.---\left(2\right).$

10. device as claimed in claim 7, it is characterised in that in the creation module, including：

Creating unit, for being object function to the maximum to recover distribution network restoration important load total electricity, formula is：

$F_{main}=\underset{t=1}{\overset{z_1}{\Σ}}\underset{i\∈n}{\Σ}{\mathrm{\λ}}_i{L}_{i,t}{y}_{i,t}---\left(3\right)$

In formula (3), F_mainFor the important load total electricity that major network recovers in the failure period to non-faulting dead electricity region, z₁For failure Repair time, n is that system node is total, λ_iFor the significance level of load in node i, L_i,tIt is big in the load of period t for node i It is little, y_i,tFor state change parameter, y_i,t=1 expression node i restores electricity in period t, y_i,t=0 represents node i in period t not Restore electricity；

Constraints includes：

Node voltage is constrained, and formula is：

U_min≤U_i.t≤U_max (4)

In formula (4), U_i,tFor node i period t magnitude of voltage, U_minFor the lower voltage limit of node i, U_maxFor on the voltage of node i Limit；

Power-balance constraint, formula is：

$\left\{\begin{array}{c}{P}_{i.t}-U_{i.t}\underset{j=1}{\overset{n}{\Σ}}{U}_{j.t}(G_{ij}{\mathrm{cos\δ}}_{ij.t}+B_{ij}{\mathrm{sin\δ}}_{ij.t})=0\\ Q_{i.t}-U_{i.t}\underset{j=1}{\overset{n}{\Σ}}{U}_{j.t}(G_{ij}{\mathrm{cos\δ}}_{ij.t}+B_{ij}{\mathrm{sin\δ}}_{ij.t})=0\end{array}\right.---\left(5\right)$

In formula (5), P_i,tFor the active power that node i is injected in period t, Q_i,tFor the reactive power that node i is injected in period t, G_ijFor the conductance between node i, j, B_ijFor the susceptance between node i, j, δ_ij,tIt is node i, j in period t phase difference of voltage, n For system node sum, U_i,tFor node i period t voltage magnitude, U_j,tFor node j period t voltage magnitude；

Branch power is constrained, and formula is：

P_ij.t≤P_ijmax (6)

In formula (6), P_ij,tFor branch road between node i and node j period t active power value, P_ij ^maxFor between node i and node j The active power of branch road allows maximum；

Power distribution network radiation operation is constrained, and formula is：

g∈G (7)

In formula (7), g is the network topology structure after reconstruct, and G is the set of the radial topological structure of network.

11. devices as claimed in claim 7, it is characterised in that the distribution network failure is obtained using ant group algorithm and recovers mould The optimal solution of type, and using the optimal solution of the distribution network failure Restoration model as distribution network failure recovery scheme.

12. devices as claimed in claim 7, it is characterised in that the optimization module, including：

First optimization unit, if for the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂Meet： z₁＞ z₂, then the distribution network failure recovery scheme is not adjusted；

Second optimization unit, if for the first distribution network failure recovery time z₁With the second distribution network failure recovery time z₂Meet： z₁＜ z₂, then with the second distribution network failure recovery time z₂For distribution network failure recovery time, to second power distribution network therefore Barrier recovery time z₂Each period carry out distribution network failure Restoration model constraints checking, if second power distribution network therefore Barrier recovery time z₂Each period be satisfied by the constraints of distribution network failure Restoration model, then it is the distribution network failure is extensive The electric network fault recovery time of compound case is adjusted to the second distribution network failure recovery time z₂If, the second power distribution network event Barrier recovery time z₂Presence is unsatisfactory for the time period of the constraints of distribution network failure Restoration model, then to the distribution network failure The electric network composition of recovery scheme carries out cutting load, until the second distribution network failure recovery time z₂Each period be satisfied by The constraints of distribution network failure Restoration model simultaneously adjusts the electric network fault recovery time of the distribution network failure recovery scheme For the second distribution network failure recovery time z₂。