Intelligent switch optimization configuration method to improve the fault recovery capability of distribution network

Abstract

The present invention provides an intelligent switch optimization configuration method for improving the fault recovery capability of a distribution network, and relates to the field of power distribution technology. The evaluation indicators of economy and reliability are increased, the fault load recovery rate, the number of intelligent switch actions, the self-rescue rate of important loads, the load supply interruption cost and the fault load recovery rate are increased, the initialization method is optimized, the inertia weight coefficient of the fault power outage time is added, and a nonlinear function about the fault recovery index is added to the learning factor to make the learning factor more efficient. This intelligent switch optimization configuration method can effectively improve the fault recovery capability of the distribution network.

Description

Technical Field

[0001] The present invention relates to the field of power distribution technology, and in particular to an intelligent switch optimization configuration method for improving the fault recovery capability of a distribution network. Background Art

[0002] Nowadays, in my country's power system, distribution network failures account for the majority of power grid failures. Distribution network failures will cause power outages for user loads, bring immeasurable economic losses, and damage the power company's own benefits.

[0003] The optimal configuration of switches in distribution networks is a nonlinear, non-differentiable optimization problem that has been widely studied and applied. Determine the location and number of intelligent switches on the distribution network feeder to achieve the optimal solution for system reliability while minimizing the number of switches used (intelligent switches are expensive) to ensure economy. This is the problem of optimal configuration of switches in distribution networks. The optimal configuration method of intelligent switches for load recovery in distribution networks should meet the following conditions:

[0004] (1) It can enable the distribution network to quickly restore load, fully guarantee the uninterrupted supply of the primary load of the power system, and take into account the secondary load. It can restore as many fault areas as possible.

[0005] (2) When a fault occurs, the number of operations of the intelligent switch should be reduced as much as possible, taking into account the life of the intelligent switch.

[0006] (3) Fully consider the operability and economy of the optimized configuration of intelligent switches.

[0007] (4) The system current and voltage limits are met, and the power flow constraints are met. No safety overload can occur.

[0008] The traditional distribution network intelligent switch optimization algorithm based on particle swarm algorithm, fault recovery index and economic objective function cannot fully guarantee economy and reliability, which reduces the credibility of the optimization results. Moreover, changes in factors such as power grid operation mode and load will affect the configuration plan. The constraints established by the penalty function method will make the augmented objective function worse and worse as the penalty factor increases, reducing the stability of the calculation. The selection of initialization and inertia weights in the traditional intelligent switch optimization configuration scheme is often obtained by relying on a large number of experiments, professional knowledge and experience of the staff, and lacks factors for economy and reliability.

[0009] In order to solve the above problems, the fault load recovery rate, the number of intelligent switch actions, and the self-rescue rate of important loads are added to the fault load recovery index. When establishing the economic objective function of the intelligent switch optimization configuration, the load supply interruption cost is added. When establishing the inequality constraint conditions for the distribution network intelligent switch optimization configuration, the fault load recovery rate is added, which reflects the constraint on reliability. The multiplier method is used to add penalties to the Lagrange function of the constraint conditions, which well guarantees the stability of numerical calculations. The triangular golden cut method is used to improve initialization and quickly find the initial particles that meet the required number of objective functions. The inertia weight coefficient of the fault power outage time is added to fully guarantee the economy of the scheme, improve the convergence speed, and quickly iterate to find the optimal solution. Improve the learning factor and add a nonlinear function about the fault recovery index to make the learning factor more efficient. This intelligent switch optimization configuration method can effectively improve the fault recovery capability of the distribution network.

[0010] Therefore, the proposal of an optimal configuration method for intelligent switches to improve the fault recovery capability of distribution networks has a certain theoretical basis and practical significance. Summary of the invention

[0011] In view of the deficiencies in the prior art, the present invention provides an intelligent switch optimization configuration method for improving the fault recovery capability of a distribution network.

[0012] A method for optimizing the configuration of intelligent switches for improving the fault recovery capability of a distribution network comprises the following steps:

[0013] Step 1: Establish distribution network fault recovery indicators, which include: fault load recovery rate, number of intelligent switch actions, load transfer amount, and self-rescue rate of important loads;

[0014] The fault load recovery rate is set to S1, that is, the proportion of the restored load to the total fault load. Where: H r Indicates the fault load recovery amount; H out Indicates the total amount of fault load;

[0015] The number of intelligent switch actions includes the number of section switch actions and the number of contact switch actions. If it is a section switch, Then S2 is the number of times the sectionalizing switch operates, and N is the number of intelligent switches installed in the distribution network; a i and b i is the state of the i-th intelligent switch before and after failure and recovery. i =1 or b i =1 indicates that the intelligent switch is in the closed state. i =0 or b i =0 indicates that the intelligent switch is disconnected. If it is a contact switch, Sjmax is the maximum number of actions of a single intelligent switch; S max is the maximum number of actions of all intelligent switches, M is the total number of branches in the regional power distribution system, N is the total number of trunks, i is the number of branches, and j is the number of trunks;

[0016] The load transfer amount is set to S3, that is, the load power transfer amount restored by scheduling during the process of handling the fault and restoring the load power supply;

[0017] The self-rescue rate of the important load is set to S4, where the important load is the primary load and the secondary load. The ratio of the capacity of the primary load and the secondary load restored within the power outage setting time to the total capacity of the primary load and the secondary load of the entire distribution network line is called the self-rescue rate of the important load, which is: Where: H 1i,j is the restoration capacity of the primary load on the jth branch of the ith trunk line; H 2i,j is the restoration capacity of the secondary load on the jth branch of the ith trunk line; L i is the number of main lines; L j is the number of branches; H 1,2 It is the total capacity of primary and secondary loads of the entire distribution system;

[0018] Step 2: Establish the economic objective function of the optimal configuration of the smart switch, which specifically includes the basic investment cost of the smart switch, operation and maintenance cost, failure loss cost, and load supply interruption cost;

[0019] The basic investment of the intelligent switch is set as C S , is the number of smart switches used multiplied by the unit price, Where: A k is the number of intelligent switches; B s is the unit price of the smart switch; α and r are the return on investment and the service life of the smart switch respectively;

[0020] The operation and maintenance cost is set as C B , is the annual maintenance cost of the installed smart switches, C B =A k C M B s , where: A k is the number of intelligent switches, C M is the maintenance rate, B s The unit price of the smart switch;

[0021] The failure loss cost is set as C L , according to the type of faults in the distribution network and the load loss corresponding to each type of fault, Where: n mkis the total number of fault types occurring in the distribution network; K i is the annual arithmetic square root number of the i-th fault; n i is the classification number of the load outage time caused by the i-th fault; T ij is the duration of the jth power outage corresponding to the i-th fault; P LPij is the load loss corresponding to the jth power outage duration of the i-th fault; C Lij is the power outage loss for users corresponding to the j-th power outage duration of the i-th fault;

[0022] The load supply interruption cost is set as C N , Where: C r Cost of production interruption caused by failure;

[0023] The economic objective function is set as:

[0024] f(x)=min(C S +C B +C L +C N )

[0025] Step 3: Optimize the configuration of the intelligent switches of the distribution network, establish inequality constraints, and add the constraint of the minimum fault recovery capability to the inequality constraints, that is, use the multiplier method to add a penalty to the Lagrange function of the constraint;

[0026] Step 3.1: Establish inequality constraints;

[0027] The inequality constraint conditions specifically include: the node voltage U i (t), branch apparent power S l(t) , branch current I j , load self-healing rate S1; then the inequality constraint condition expression is:

[0028]

[0029] Where: U imin (t), U imax (t) represent the maximum and minimum node voltage of node i respectively; t is the time when the fault occurs, S lmax is the capacity value of the line or transformer; I j is the actual current of branch j, I jmax is the maximum current carrying capacity of branch j; S 1min is the minimum value of fault load recovery rate;

[0030] Step 3.2: Add the constraint of minimum fault recovery capability to the inequality constraint, that is, use the multiplier method to add penalty to the Lagrange function of the constraint and establish the particle penalty function, as shown in the following formula:

[0031]

[0032] Where: f(x) is the economic objective function; h(x) is the equality constraint; g i (x) is converted to g i (x)≥0; λ is the Lagrangian factor; μ is the penalty factor; v i is the Lagrange multiplier corresponding to the i-th inequality constraint, j is the number of inequality constraints;

[0033] Step 4: Establish an intelligent switch optimization configuration algorithm to improve the fault recovery capability of the distribution network:

[0034] Step 4.1: Establish an improved particle swarm algorithm. The improved particle swarm algorithm regards the intelligent switch as a particle and uses binary to represent the state of the particle. Suppose a particle swarm has M particles, the search space is j-dimensional, and the position and speed of the i-th particle in the search space are x and i,j , v i,j , the optimal position of the i-th particle obtained by the iterative formula is p i,j ; The optimal position of the entire particle swarm is p g,j ;

[0035] The iteration formula is as follows:

[0036] v i,j (t+1)=ωv i,j (t)+c1r1[p i.j -x i,j (t)]+c2r2[p i.j -x i,j (t)] (3)

[0037] x i,j (t+1)=x i,j (t)+v i,j (t+1)

[0038] Where: t is the number of current iterations of the particle; ω is the inertia weight; c1, c2 are learning factors, c1, c2 are both greater than 0, r1, r2 are random numbers uniformly distributed in [0,1].

[0039] At each iteration, the particle position x i,j and the optimal position p i,j 、p g,j Set to 1 or 0, use vi.j represents the position x of the particle i,j The probability of v being 1. i.j Maintain the update rules. When using v i.j To update the position, the sig function is used to update v i.j The activity range is limited to [0,1], as shown in the following formula:

[0040] Sig[v i,j (t)] = 1 / {1 + exp[-v i,j (t)]} (4)

[0041] Step 4.2: Use the triangle golden cutting method to improve the initialization of the smart switch particle swarm;

[0042] Assume L1, L2, L3 are the three vertices of the triangle generated by three random particles in the particle swarm graph, y1, y2, y3 are the function values ​​corresponding to the vertices of the triangle, y max =max{y i},y min =min{y i},y max is the maximum value of the vertex function, y min is the minimum value of the vertex function, i=1,2,3;

[0043] Step 4.2.1: Generate random particles and calculate their economic objective function value y i ;

[0044] Step 4.2.2: Set y max and min The corresponding vertex particles are set as the initial vertices of the initial triangle;

[0045] Step 4.2.3: Use the triangular golden cut method to iterate and generate a new y max or min Particles are used as supplementary particles to generate the initial particles required by the objective function.

[0046] Step 4.2.3.1: Let the position vectors of the triangle vertices obtained by the search be v1, v2, v3:

[0047] f i =f(v i ),i=1,2,3

[0048] f i is the economic objective function value of triangle vertex i, and we have:

[0049]

[0050] Let v land v h They are the best vertex and the worst vertex of the triangle respectively. The worst vertex v h Remove it, leaving two vertices, and find their center points as follows:

[0051]

[0052] Step 4.2.3.2: Perform reflection, v r Reflection h , we have the following formula:

[0053] v r =v0+γ(v0-v h )

[0054] v r Yes h The reflection point, γ is the reflection constant;

[0055] Step 4.2.3.3: Calculate the extension point: After reflection, we have the following formula:

[0056] f(v r ) <f(v l )

[0057] Indicates v r -v0 also has a descending direction, calculate

[0058] v e =v0+e(v r -v0)

[0059] v e That is v r The extension point, e is the extension coefficient;

[0060] Step 4.3: Use the constraints in step 3 as the criteria for screening qualified particles, and add the inertia weight coefficient ω of the fault outage time t;

[0061]

[0062] Where: tav is the inertia weight corresponding to the annual average power outage time; ω tmax is the inertia weight corresponding to the peak value of the annual average power outage time; ω tmin is the inertia weight corresponding to the peak and valley value of the annual average power outage time; k is the control factor; t max is the annual average power outage time peak value; d is the current iteration number; D is the maximum allowed iteration number;

[0063] During the iteration process, the inertia weight will gradually decrease with the formula, and the particle swarm algorithm will gradually search from a large area to a small area for precise search.

[0064] Step 4.4: Introduce the learning factors c1 and c2 based on the reliability of the optimized configuration of the smart switch, as shown in the following formula:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] Where: c1 is the individual learning factor of the particle, that is, the individual acceleration factor, c2 is the social learning factor of the particle, that is, the social acceleration factor; c 1min 、c 2min are the minimum values ​​of individual learning factor and social learning factor, c 1max 、c 2max are the maximum values ​​of individual learning factor and social learning factor respectively; g imin (S1+S2+S3+S4) is S i (i=1,2,3,4) is the nonlinear constraint function for the minimum reliability requirement of the learning factor, g imax (S1+S2+S3+S4) is S i (i=1,2,3,4) Nonlinear constraint function for the maximum reliability requirement of the learning factor; α 1min ,β 2min ,x 3min ,γ 4min are the proportional coefficients of S1, S2, S3, and S4 under the minimum reliability requirement, α 1max ,β 2max ,x 3max ,γ 4max are the proportional coefficients of S1, S2, S3, and S4 under the maximum reliability requirement; S1-S4 are the fault load recovery rate, the number of intelligent switch actions, the load transfer amount, and the self-rescue rate of important loads; D is the maximum number of iterations allowed;

[0071] Step 4.5: Assuming that the total number of smart switches to be used is M, the improved particle swarm algorithm is used to search for the optimal solution in the M-dimensional space; the optimal state of a single particle is screened with the overall state to obtain the optimal configuration solution of the smart switch that improves the fault recovery capability of the distribution network;

[0072] Step 4.5.1: Initialize the position and state of the intelligent switch in the distribution network and determine the range of the learning factors c1 and c2 in the improved binary particle swarm algorithm [c 1min,c 1max ] and [c 2min ,c 2max ], the value range of inertia weight [ω min ,ω max ], maximum number of iterations D and speed parameters;

[0073] Step 4.5.2: The economic objective function of the intelligent switch optimization configuration in step 2 is combined with the inequality constraint of the switch optimization configuration, and the multiplier method is used to transform it, and the Lagrange multiplier is introduced to establish the particle penalty function F, that is, formula (2);

[0074] Step 4.5.3: Evaluate the state of a single particle, compare the current position of a single particle through the fitness function, calculate their fitness value, and compare it with the historical optimal value of the entire particle swarm. If the fitness value of a single particle is less than the historical optimal value of the particle swarm, go to step 4.5.4; otherwise, update the historical optimal value.

[0075] Step 4.5.4: Iterate the inertia weight coefficient ω and the learning factor according to (5) and (6);

[0076] Step 4.5.5: Update the state of the particle, including the velocity and displacement of the particle, and obtain the particle in the optimal position;

[0077] Step 4.5.6: Check whether the obtained optimal particle is an admissible solution to the switch optimization configuration inequality constraint; if it meets the requirements, the iteration ends and the optimal switch configuration solution is output. Otherwise, jump to step 4.5.3.

[0078] The beneficial effects of adopting the above technical solution are:

[0079] The present invention proposes an intelligent switch optimization configuration method for improving the fault recovery capability of a distribution network, adds economic and reliability assessment indicators, adds fault load recovery rate, intelligent switch action times, self-rescue rate of important loads, load supply interruption cost and fault load recovery rate, optimizes the initialization method, adds the inertia weight coefficient of the fault power outage time (improves the convergence speed, and can quickly iterate to find the optimal solution), and adds a nonlinear function about the fault recovery index to the learning factor (makes the learning factor more efficient). The present invention adds the fault load recovery rate, the intelligent switch action times, and the self-rescue rate of important loads to the fault load recovery index, and adds the load supply interruption cost when establishing the economic objective function of the intelligent switch optimization configuration. When establishing the inequality constraint condition for the distribution network intelligent switch optimization configuration, the fault load recovery rate is added, which reflects the constraint on reliability. The multiplier method is used to add a penalty to the Lagrange function of the constraint condition, which well guarantees the stability of the numerical calculation. The triangular golden cut method is used to improve the initialization, and the initial particles that meet the required number of the objective function are quickly found. Adding the inertia weight coefficient of the fault outage time can fully ensure the economy of the solution, improve the convergence speed, and quickly iterate to find the optimal solution. Improving the learning factor and adding a nonlinear function about the fault recovery index make the learning factor more efficient. This intelligent switch optimization configuration method can effectively improve the fault recovery capability of the distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is the overall flow chart of the present invention.

[0081] Figure 2 It is a result diagram of the intelligent switch optimization configuration scheme according to a specific implementation mode of the present invention. DETAILED DESCRIPTION

[0082] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0083] An intelligent switch optimization configuration method for improving the fault recovery capability of distribution network, such as Figure 1 As shown, the following steps are included:

[0084] Step 1: Establish distribution network fault recovery indicators, which include: fault load recovery rate, number of intelligent switch actions, load transfer amount, and self-rescue rate of important loads; optimize the reliability indicators of the optimal configuration of distribution network intelligent switches, including load recovery, number of switch actions, and protection of important loads;

[0085] The fault load recovery rate is set to S1, that is, the proportion of the recovered load to the total fault load. The main goal of the optimal configuration of the intelligent switch is to recover as much load as possible from the fault area. Where: H r Indicates the fault load recovery amount; H out Indicates the total amount of fault load;

[0086] The number of intelligent switch actions includes the number of sectional switch actions and the number of contact switch actions. The fewer the number of actions, the longer the service life of the switch, which reduces the operating cost and time consumption, and can effectively ensure the economic efficiency of the distribution network operation. Then S2 is the number of times the sectionalizing switch operates, and N is the number of intelligent switches installed in the distribution network; a i and b i is the state of the i-th intelligent switch before and after failure and recovery. i =1 or b i =1 indicates that the intelligent switch is in the closed state. i =0 or b i =0 indicates that the intelligent switch is disconnected. If it is a contact switch, S jmax is the maximum number of actions of a single intelligent switch; S max is the maximum number of actions of all intelligent switches, M is the total number of branches in the regional power distribution system, N is the total number of trunks, i is the number of branches, and j is the number of trunks;

[0087] The load transfer amount is set to S3, that is, the load power transfer amount restored by scheduling during the process of handling the fault to restoring the load power supply; the load transfer amount of the distribution network will affect the stability of the power grid system.

[0088] The self-rescue rate of the important load is set to S4, where the important load is the primary load and the secondary load. The primary load is the load that must be guaranteed to be safe. The flexible use of intelligent switches and distributed power sources can basically ensure that the primary load can take immediate action to avoid power outages when a failure occurs. The secondary load still has a very important protection status, and the power grid needs to have a higher fault recovery capability. The ratio of the capacity of the primary load and the secondary load recovered within 5 seconds of the power outage to the total capacity of the primary load and the secondary load of the entire distribution network line is called the self-rescue rate of the important load, which is Where: H 1i,j is the restoration capacity of the primary load on the jth branch of the ith trunk line; H 2i,j is the restoration capacity of the secondary load on the jth branch of the ith trunk line; L i is the number of main lines; L j is the number of branches; H 1,2 It is the total capacity of primary and secondary loads of the entire distribution system;

[0089] In this embodiment, the intelligent switches of the distribution network are optimally configured on the 3rd and 4th main feeders of the IEEERBTS-BUS3 system.

[0090] Calculating the stability of the system requires the system load and line parameters, as shown in Tables 1 and 2.

[0091] Table 1 Load user data

[0092]

[0093] Table 2 Lines and their lengths

[0094]

[0095] All other loads except residential loads are included, the proportion of load recovery rate is increased, and the minimum load recovery rate of the algorithm is set to 85%.

[0096] Step 2: Establish the economic objective function of the optimal configuration of the smart switch, which fully considers the economic efficiency of the optimal configuration scheme of the smart switch of the distribution network, including the basic investment cost of the smart switch, operation and maintenance cost, failure loss cost, and load supply interruption cost;

[0097] The basic investment of the intelligent switch is set as C S , which is the number of smart switches used multiplied by the unit price. Because the aging problem of the switches needs to be considered, the basic investment in smart switches needs to be converted into an equivalent annual value. Where: A k is the number of intelligent switches; B s is the unit price of the smart switch; α and r are the return on investment and the service life of the smart switch respectively;

[0098] The operation and maintenance cost is set as C B , is the annual maintenance cost of the installed smart switches, which is related to the initial investment. B =A k C M B s , where: A k is the number of intelligent switches, C M is the maintenance rate, B s The unit price of the smart switch;

[0099] The failure loss cost is set as C L , according to the type of faults in the distribution network and the load loss corresponding to each type of fault, Where: n mk is the total number of fault types occurring in the distribution network; K i is the annual arithmetic square root number of the i-th fault; n i is the classification number of the load outage time caused by the i-th fault; T ij is the duration of the jth power outage corresponding to the i-th fault; PLPij is the load loss corresponding to the jth power outage duration of the i-th fault; C Lij is the power outage loss for users corresponding to the j-th power outage duration of the i-th fault;

[0100] The load supply interruption cost is set as C N ,The traditional fault loss cost only calculates the loss of power outage for more than 2 minutes. ,In order to more strictly meet the requirements of fault recovery ,capacity, the fault loss within 2 minutes is also added to the ,objective function, mainly the short power outage loss. Where: C r Cost of production interruption caused by failure;

[0101] The economy and reliability of the optimal configuration of the intelligent switch of the integrated distribution network, as well as the requirements for meeting the fault recovery capability, are set as follows:

[0102] f(x)=min(C S +C B +C L +C N )

[0103] In this embodiment, all other loads except the residential load are included, the proportion of the load recovery rate is increased, and the minimum load recovery rate of the algorithm is set to 85%. When calculating the economic indicators, the parameters are shown in Table 3:

[0104] Table 3 Economic calculation parameters

[0105]

[0106] Step 3: Optimize the configuration of the intelligent switches of the distribution network, fully consider the economy and reliability, establish inequality constraints, and directly reflect the impact of the distribution network fault recovery capability requirements on the optimization configuration method of the intelligent switches. Add the constraint of the minimum fault recovery capability to the inequality constraint, that is, use the multiplier method to add a penalty to the Lagrange function of the constraint, which can greatly improve the stability.

[0107] Step 3.1: Establish inequality constraints;

[0108] The inequality constraint conditions specifically include: the node voltage U i (t), branch apparent power S l(t) , branch current I j , load self-healing rate S1; then the inequality constraint condition expression is:

[0109]

[0110] Where: U imin(t), U imax (t) represent the maximum and minimum node voltage of node i respectively; t is the time when the fault occurs, S lmax is the capacity value of the line or transformer; I j is the actual current of branch j, I jmax is the maximum current carrying capacity of branch j; S 1min It is the minimum value of the fault load recovery rate; it can directly reflect the impact of the distribution network fault recovery capability requirements on the optimal configuration method of the intelligent switch.

[0111] Step 3.2: Add the constraint of minimum fault recovery capability to the inequality constraint, that is, use the multiplier method to add a penalty to the Lagrange function of the constraint, so that when solving the unconstrained problem, the penalty factor does not need to tend to infinity to find the optimal solution, and the stability of the numerical calculation can also be well guaranteed. Establish a particle penalty function, as shown in the following formula:

[0112]

[0113] Where: f(x) is the economic objective function; h(x) is the equality constraint; g i (x) is converted to g i (x)≥0; λ is the Lagrangian factor; μ is the penalty factor; v i is the Lagrange multiplier corresponding to the i-th inequality constraint, j is the number of inequality constraints;

[0114] Step 4: Establish an intelligent switch optimization configuration algorithm to improve the fault recovery capability of the distribution network:

[0115] Step 4.1: Particle Swarm Optimization (PSO) is a common intelligent algorithm that uses "particles" to imitate the foraging behavior of bird flocks, and solves optimization problems by sharing information between individual particles and the whole. Each admissible solution in the search range space can be regarded as a "particle". The state of the particle has position and speed. The current position of the particle is a potential solution, and its flight process is the individual particle search process. PSO uses the target function as a fitness function to measure the fitness value of the particle state and evaluate the quality of the particle. Each iteration will change the state (position and speed) of the particle, thereby changing the fitness value of the particle. The best position found by a single particle during flight "foraging" is the optimal solution for the particle itself, while the best position found by the particle swarm is the optimal solution for the entire particle swarm.

[0116] An improved particle swarm algorithm is established. The improved particle swarm algorithm regards the intelligent switch as a particle and uses binary to represent the state of the particle, so as to better apply it to the particle swarm algorithm. Assume that a particle swarm has M particles, the search space is j-dimensional, and the position and speed of the i-th particle in the search space are x i,j , v i,j , the optimal position of the i-th particle obtained by the iterative formula is p i,j ; The optimal position of the entire particle swarm is p g,j ;

[0117] The iteration formula is as follows:

[0118] v i,j (t+1)=ωv i,j (t)+c1r1[p i.j -x i,j (t)]+c2r2[p i.j -x i,j (t)] (3)

[0119] x i,j (t+1)=x i,j (t)+v i,j (t+1)

[0120] Where: t is the number of current iterations of the particle; ω is the inertia weight; c1, c2 are learning factors, c1, c2 are both greater than 0, r1, r2 are random numbers uniformly distributed in [0,1].

[0121] This particle swarm algorithm has better optimization ability when used in binary coding. In each iteration, the particle position x i,j and the optimal position p i,j 、p g,j Set to 1 or 0, use v i.j represents the position x of the particle i,j The probability of v being 1. i.j Maintain the update rules. When using v i.j To update the position, the sig function is used to update v i.j The activity range is limited to [0,1], as shown in the following formula:

[0122] Sig[v i,j (t)] = 1 / {1 + exp[-v i,j (t)]} (4)

[0123] Step 4.2: Use the triangle golden cutting method to improve the initialization of the smart switch particle swarm;

[0124] The initialization position and speed of the particle swarm in the particle swarm algorithm PSO are randomly generated. When the dimension of the particle swarm is large, the convergence performance will decrease. The triangular golden cutting method is based on the characteristics of the triangle. It compares the size of the function value of the three vertices of the triangle with the change of the position prediction function. After folding, expanding and shrinking, it approaches the optimal solution, which can greatly improve the search speed for the minimum point. By introducing the triangular golden cutting method to initialize the particle swarm, it is necessary to randomly generate some points, and then compare the function values ​​to determine the state. Let L1, L2, L3 be the three vertices of the triangle generated by three random particles in the particle swarm graph, y1, y2, y3 are the function values ​​corresponding to the vertices of the triangle, y max =max{y i},y min =min{y i},y max is the maximum value of the vertex function, y min is the minimum value of the vertex function, i=1,2,3;

[0125] Step 4.2.1: Generate random particles and calculate their economic objective function value y i ;

[0126] Step 4.2.2: Set y max and min The corresponding vertex particles are set as the initial vertices of the initial triangle;

[0127] Step 4.2.3: Use the triangular golden cut method to iterate and generate a new y max or min Particles are used as supplementary particles to generate the initial particles required by the objective function.

[0128] Step 4.2.3.1: Let the position vectors of the triangle vertices obtained by the search be v1, v2, v3:

[0129] f i =f(v i ),i=1,2,3

[0130] f i is the economic objective function value of triangle vertex i, and we have:

[0131]

[0132] Let v l and v h They are the best vertex and the worst vertex of the triangle respectively. The worst vertex v h Remove it, leaving two vertices, and find their center points as follows:

[0133]

[0134] Step 4.2.3.2: Perform reflection, v r Reflection h , we have the following formula:

[0135] v r =v0+γ(v0-v h )

[0136] v r Yes h The reflection point, γ is the reflection constant, usually 1. Because it is the worst vertex of reflection, the probability v r Will be better than v h better.

[0137] Step 4.2.3.3: Calculate the extension point: After reflection, we have the following formula:

[0138] f(v r ) <f(v l )

[0139] Indicates v r -v0 also has a descending direction, calculate

[0140] v e =v0+e(v r -v0)

[0141] v e That is v r The extension point, e is the extension coefficient, usually taken as 2.

[0142] Step 4.3: Use the constraints in step 3 as the criteria for screening qualified particles, and add the inertia weight coefficient ω of the fault outage time t;

[0143] The traditional standard particle swarm algorithm has defects (it is difficult to jump out of the local optimal error, the search accuracy is not enough to find the optimal solution in the later stage, the convergence speed is not enough, etc.). The inertia weight is the fitness of the particle to maintain the state of the previous iteration. Finding the appropriate inertia weight can quickly iterate to find the optimal solution.

[0144] The larger the inertia weight ω, the higher the ability of the particle swarm algorithm to search the global allowed set; the smaller ω, the more convergent the particle swarm algorithm can be to perform precise search in the search interval. Finding the right ω is extremely important.

[0145] Adding the inertia weight of the fault outage time t can directly reflect the guiding role of the outage time in finding the optimal value of the objective function, and adjust the inertia weight through the decision factor k to increase the flexibility of the algorithm. Fully consider the application of economic benefits in the optimal configuration of intelligent switches in distribution networks.

[0146]

[0147] Where: tav is the inertia weight corresponding to the annual average power outage time; ω tmax is the inertia weight corresponding to the peak value of the annual average power outage time; ω tmin is the inertia weight corresponding to the peak and valley value of the annual average power outage time; k is the control factor; t max is the annual average power outage time peak value; d is the current iteration number; D is the maximum allowed iteration number;

[0148] During the iteration process, the inertia weight will gradually decrease with the formula, and the particle swarm algorithm will gradually search from a large area to a small area for precise search.

[0149] Step 4.4: Introduce the learning factors c1 and c2 based on the reliability of the optimized configuration of the smart switch, as shown in the following formula:

[0150]

[0151]

[0152]

[0153]

[0154]

[0155] Where: c1 is the individual learning factor of the particle, that is, the individual acceleration factor, c2 is the social learning factor of the particle, that is, the social acceleration factor; c 1min 、c 2min are the minimum values ​​of individual learning factor and social learning factor, c 1max 、c 2max are the maximum values ​​of individual learning factor and social learning factor respectively; g imin (S1+S2+S3+S4) is S i (i=1,2,3,4) is the nonlinear constraint function for the minimum reliability requirement of the learning factor, g imax (S1+S2+S3+S4) is S i (i=1,2,3,4) Nonlinear constraint function for the maximum reliability requirement of the learning factor; α 1min ,β 2min ,x 3min ,γ 4min are the proportional coefficients of S1, S2, S3, and S4 under the minimum reliability requirement, α 1max ,β 2max ,x 3max ,γ 4maxare the proportional coefficients of S1, S2, S3, and S4 under the maximum reliability requirement; S1-S4 are the fault load recovery rate, the number of intelligent switch actions, the load transfer amount, and the self-rescue rate of important loads; D is the maximum number of iterations allowed;

[0156] c 2min 、c 2max Obtained from experience with power grid fault examples.

[0157] In the early stage of iteration: c1 should be large and c2 should be small, so that a large area can be searched quickly and the search radius can be expanded.

[0158] In the later stage of iteration: c1 should be small and c2 should be large, so that accurate search can be performed in a smaller area to find the optimal value that meets the accuracy.

[0159] In this embodiment, the number of particles c=15, the range of the learning factor c1 is [0.7-1.3], and the range of the learning factor c2 is [0.8-1.4]. The speed range of the particles in different dimensions is [-1, 1]. Then the algorithm iterative calculation is started.

[0160] Step 4.5: Assuming that the total number of smart switches to be used is M, the improved particle swarm algorithm is used to search for the optimal solution in the M-dimensional space; the optimal state of a single particle is screened with the overall state to obtain the optimal configuration solution of the smart switch that improves the fault recovery capability of the distribution network;

[0161] Step 4.5.1: Initialize the position and state of the intelligent switch in the distribution network and determine the range of the learning factors c1 and c2 in the improved binary particle swarm algorithm [c 1min ,c 1max ] and [c 2min ,c 2max ], the value range of inertia weight [ω min ,ω max ], maximum number of iterations D and speed parameters;

[0162] Step 4.5.2: The economic objective function of the intelligent switch optimization configuration in step 2 is combined with the inequality constraint of the switch optimization configuration, and the multiplier method is used to transform it, and the Lagrange multiplier is introduced to establish an efficient and simple particle penalty function F, that is, formula (2);

[0163] Step 4.5.3: Evaluate the state of a single particle, compare the current position of a single particle through the fitness function, calculate their fitness value, and compare it with the historical optimal value of the entire particle swarm. If the fitness value of a single particle is less than the historical optimal value of the particle swarm, go to step 4.5.4; otherwise, update the historical optimal value.

[0164] Step 4.5.4: Iterate the inertia weight coefficient ω and the learning factor according to (5) and (6);

[0165] Step 4.5.5: Update the state of the particle, including the velocity and displacement of the particle, and obtain the particle in the optimal position;

[0166] Step 4.5.6: Check whether the obtained optimal particle is an admissible solution to the switch optimization configuration inequality constraint; if it meets the requirements, the iteration ends and the optimal switch configuration solution is output. Otherwise, jump to step 4.5.3.

[0167] The optimal configuration scheme of the intelligent switch obtained in this embodiment is as follows: Figure 2 As shown in the figure, since important loads must fully ensure the reliability of power supply, smart switches are configured on their first and second sides; for non-important loads with lower load stability requirements, in order to ensure the economy of the solution, only smart switches are configured on their first side or even no switches are configured.

[0168] The economic performance, reliability and fault recovery index of the optimal configuration scheme of the intelligent switch are compared with the unconstrained configuration scheme and the comprehensive configuration scheme as shown in Table 4.

[0169] Table 4 Comparison of configuration schemes

[0170]

[0171] Compared with the comprehensive configuration plan of intelligent switches in the distribution network, the optimal configuration has slightly higher power outage loss costs, but the switch investment and operation and maintenance costs are greatly reduced, which greatly improves the economy of the scheme configuration; and the addition of self-rescue rate constraints on important loads allows the configuration scheme results to better ensure reliability, especially the key protection of a type of load.

[0172] The above description is only a preferred embodiment of the present disclosure and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but should also cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the above-mentioned inventive concept. For example, the above-mentioned features are replaced with the technical features with similar functions disclosed in the embodiments of the present disclosure (but not limited to) to form a technical solution.

Claims

1. A method for optimizing the configuration of intelligent switches for improving the fault recovery capability of a distribution network, characterized in that: The following steps are involved: Step 1: Establish distribution network fault recovery indicators, which include: fault load recovery rate, number of intelligent switch actions, load transfer amount, and self-rescue rate of important loads; Step 2: Establish the economic objective function of the optimal configuration of the smart switch, which specifically includes the basic investment cost of the smart switch, operation and maintenance cost, failure loss cost, and load supply interruption cost; Step 3: Optimize the configuration of the intelligent switches of the distribution network, establish inequality constraints, and add the constraint of the minimum fault recovery capability to the inequality constraints, that is, use the multiplier method to add a penalty to the Lagrange function of the constraint; Step 4: Establish an intelligent switch optimization configuration algorithm for improving the fault recovery capability of the distribution network, and obtain the optimal configuration solution of the intelligent switch for improving the fault recovery capability of the distribution network; Step 4.1: Establish an improved particle swarm algorithm. The improved particle swarm algorithm regards the intelligent switch as a particle and uses binary to represent the state of the particle. Suppose a particle swarm has M particles, the search space is j-dimensional, and the position and speed of the i-th particle in the search space are x and i,j , v i,j , the optimal position of the i-th particle obtained by the iterative formula is p i,j ; The optimal position of the entire particle swarm is p g,j ; The iteration formula is as follows: v i,j (t+1)=ωv i,j (t)+c1r1[p i.j -x i,j (t)]+c2r2[p i.j -x i,j (t)] (3) x i,j (t+1)=x i,j (t)+v i,j (t+1) Where: t is the number of current iterations of the particle; ω is the inertia weight; c1, c2 are learning factors, c1, c2 are both greater than 0, r1, r2 are random numbers uniformly distributed in [0,1]; At each iteration, the particle position x i,j and the optimal position p i,j 、p g,j Set to 1 or 0, use v i.j represents the position x of the particle i,j The probability of v being 1 i.j Maintain the update rule; when using v i.j To update the position, the sig function is used to update v i.j The activity range is limited to [0,1], as shown in the following formula: Sig[v i,j (t)]=1 / {1+exp[-v i,j (t)]} (4) Step 4.2: Use the triangle golden cutting method to improve the initialization of the smart switch particle swarm; Assume L1, L2, L3 are the three vertices of the triangle generated by three random particles in the particle swarm graph, y1, y2, y3 are the function values ​​corresponding to the vertices of the triangle, y max =max{y i },y min =min{y i }, ymax is the maximum value of the vertex function, ymin is the minimum value of the vertex function, i=1,2,3; Step 4.3: Use the constraints in step 3 as the criteria for screening qualified particles, and add the inertia weight coefficient ω of the fault outage time t; Where: tav is the inertia weight corresponding to the annual average power outage time; ω tmax is the inertia weight corresponding to the peak value of the annual average power outage time; ω tmin is the inertia weight corresponding to the peak and valley value of the annual average power outage time; k is the control factor; t max is the annual average power outage time peak value; d is the current iteration number; D is the maximum allowed iteration number; During the iteration process, the inertia weight will gradually decrease with the formula, and the particle swarm algorithm will gradually search from a large area to a small area for precise search; Step 4.4: Introduce the learning factors c1 and c2 based on the reliability of the optimized configuration of the smart switch, as shown in the following formula: Where: c1 is the individual learning factor of the particle, that is, the individual acceleration factor, c2 is the social learning factor of the particle, that is, the social acceleration factor; c 1min 、c 2min are the minimum values ​​of individual learning factor and social learning factor, c 1max 、c 2max are the maximum values ​​of individual learning factor and social learning factor respectively; g imin (S1+S2+S3+S4) is S i (i=1,2,3,4) is the nonlinear constraint function for the minimum reliability requirement of the learning factor, g imax (S1+S2+S3+S4) is S i (i=1,2,3,4) Nonlinear constraint function for the maximum reliability requirement of the learning factor; α 1min ,β 2min ,x 3min ,γ 4min are the proportional coefficients of S1, S2, S3, and S4 under the minimum reliability requirement, α 1max ,β 2max ,x 3max ,γ 4max are the proportional coefficients of S1, S2, S3, and S4 under the maximum reliability requirement; S1-S4 are the fault load recovery rate, the number of intelligent switch actions, the load transfer amount, and the self-rescue rate of important loads; D is the maximum number of iterations allowed; Step 4.5: Assume that the total number of smart switches to be used is M, and use the improved particle swarm algorithm to search for the optimal solution in the M-dimensional space; the optimal state of a single particle is screened with the overall state to obtain the optimal configuration solution of the smart switch that improves the fault recovery capability of the distribution network.

2. The intelligent switch optimization configuration method for improving the fault recovery capability of the distribution network according to claim 1 is characterized in that: The fault load recovery rate in step 1 is set to S1, that is, the proportion of the restored load to the total fault load. Where: H r Indicates the fault load recovery amount; H out Indicates the total amount of fault load; The number of intelligent switch actions includes the number of section switch actions and the number of contact switch actions. If it is a section switch, Then S2 is the number of times the sectionalizing switch operates, and N is the number of intelligent switches installed in the distribution network; a i and b i is the state of the i-th intelligent switch before and after failure and recovery. i =1 or b i =1 indicates that the intelligent switch is in the closed state. i =0 or b i =0 indicates that the intelligent switch is disconnected. If it is a contact switch, S jmax is the maximum number of actions of a single intelligent switch; S max is the maximum number of actions of all intelligent switches, M is the total number of branches in the regional power distribution system, N is the total number of trunks, i is the number of branches, and j is the number of trunks; The load transfer amount is set to S3, that is, the load power transfer amount restored by scheduling during the process of handling the fault and restoring the load power supply; The self-rescue rate of important loads is set to S4, where important loads are primary loads and secondary loads. The ratio of the capacity of primary loads and secondary loads restored within the set power outage time to the total capacity of primary loads and secondary loads of the entire distribution network is called the self-rescue rate of important loads. Where: H 1i,j is the restoration capacity of the primary load on the jth branch of the ith trunk line; H 2i,j is the restoration capacity of the secondary load on the jth branch of the ith trunk line; L i is the number of main lines; L j is the number of branches; H 1,2 It is the total capacity of the primary and secondary loads of the entire distribution system.

3. The intelligent switch optimization configuration method for improving the fault recovery capability of the distribution network according to claim 1 is characterized in that: The basic investment of the smart switch in step 2 is set to C S , is the number of smart switches used multiplied by the unit price, Where: A k is the number of intelligent switches; B s is the unit price of the smart switch; α and r are the return on investment and the service life of the smart switch respectively; The operation and maintenance cost is set as C B , is the annual maintenance cost of the installed smart switches, C B =A k C M B s , where: A k is the number of intelligent switches, C M is the maintenance rate, B s The unit price of the smart switch; The failure loss cost is set as C L , according to the type of faults in the distribution network and the load loss corresponding to each type of fault, Where: n mk is the total number of fault types occurring in the distribution network; K i is the annual arithmetic square root number of the i-th fault; n i is the classification number of the load outage time caused by the i-th fault; T ij is the duration of the jth power outage corresponding to the i-th fault; P LPij is the load loss corresponding to the jth power outage duration of the i-th fault; C Lij is the power outage loss for users corresponding to the j-th power outage duration of the i-th fault; The load supply interruption cost is set as C N , Where: C r Cost of production interruption caused by failure; The economic objective function is set as: f(x)=min(C S +C B +C L +C N )。 4. The intelligent switch optimization configuration method for improving the fault recovery capability of the distribution network according to claim 1 is characterized in that: The step 3 specifically comprises the following steps: Step 3.1: Establish inequality constraints; The inequality constraint conditions specifically include: the node voltage U i (t), branch apparent power S l(t) , branch current I j , load self-healing rate S1; then the inequality constraint condition expression is: Where: U imin (t), U imax (t) represent the maximum and minimum node voltage of node i respectively; t is the time when the fault occurs, S lmax is the capacity value of the line or transformer; I j is the actual current of branch j, I jmax is the maximum current carrying capacity of branch j; S 1min is the minimum value of fault load recovery rate; Step 3.2: Add the constraint of minimum fault recovery capability to the inequality constraint, that is, use the multiplier method to add penalty to the Lagrange function of the constraint and establish the particle penalty function, as shown in the following formula: Where: f(x) is the economic objective function; h(x) is the equality constraint; g i (x) is converted to g i (x)≥0; λ is the Lagrangian factor; μ is the penalty factor; v i is the Lagrange multiplier corresponding to the i-th inequality constraint, and j is the number of inequality constraints.

5. The intelligent switch optimization configuration method for improving the fault recovery capability of the distribution network according to claim 1 is characterized in that: The step 4.2 specifically includes the following steps: Step 4.2.1: Generate random particles and calculate their economic objective function value y i ; Step 4.2.2: Set y max and min The corresponding vertex particles are set as the initial vertices of the initial triangle; Step 4.2.3: Use the triangular golden cut method to iterate and generate a new y max or min Particles are used as supplementary particles to generate the initial particles required by the objective function; Step 4.2.3.1: Let the position vectors of the triangle vertices obtained by the search be v1, v2, v3: f i =f(v i ),i=1,2,3 f i is the economic objective function value of triangle vertex i, and we have: Let v l and v h They are the best vertex and the worst vertex of the triangle respectively. The worst vertex v h Remove it, leaving two vertices, and find their center points as follows: Step 4.2.3.2: Perform reflection, v r Reflection h , we have the following formula: v r =v0+γ(v0-v h ) v r Yes h The reflection point, γ is the reflection constant; Step 4.2.3.3: Calculate the extension point: After reflection, we have the following formula: f(v r )<f(v l ) Indicates v r -v0 also has a descending direction, calculate v e =v0+e(v r -v0) v e That is v r The extension point, e is the extension coefficient.

6. The intelligent switch optimization configuration method for improving the fault recovery capability of the distribution network according to claim 1, characterized in that: The step 4.5 specifically includes the following steps: Step 4.5.1: Initialize the position and state of the intelligent switch in the distribution network and determine the range of the learning factors c1 and c2 in the improved binary particle swarm algorithm [c 1min ,c 1max ] and [c 2min ,c 2max ], the value range of inertia weight [ω min ,ω max ], maximum number of iterations D and speed parameters; Step 4.5.2: The economic objective function of the intelligent switch optimization configuration in step 2 is combined with the inequality constraint of the switch optimization configuration, and the multiplier method is used to transform it, and the Lagrange multiplier is introduced to establish the particle penalty function F, that is, formula (2); Step 4.5.3: Evaluate the state of a single particle, compare the current position of a single particle through the fitness function, calculate their fitness value, and compare it with the historical optimal value of the entire particle group. If the fitness value of a single particle is less than the historical optimal value of the particle group, the optimality is poor, go to step 4.5.4; otherwise, update the historical optimal value; Step 4.5.4: Iterate the inertia weight coefficient ω and the learning factor according to (5) and (6); Step 4.5.5: Update the state of the particle, including the velocity and displacement of the particle, and obtain the particle in the optimal position; Step 4.5.6: Check whether the obtained optimal particle is an admissible solution to the switch optimization configuration inequality constraint; if it meets the requirements, end the iteration and output the optimal switch configuration solution; otherwise, jump to step 4.5.3.

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