A method for site selection and capacity determination of distributed generation based on HELM stability criterion

Abstract

The invention discloses a method for siting and sizing distributed power sources based on the HELM stability criterion, which includes the following steps: Step 1, establish a siting and sizing model of distributed power sources in the distribution network, including an objective function and constraint conditions, where the objective function considers the comprehensive cost of distributed power sources, network loss, and a voltage stability criterion based on the holomorphic function embedding method; Step 2, use the HELM method to calculate the power flow of the distribution network containing distributed power sources as the power flow constraint condition of the siting and sizing optimization model of distributed power sources; Step 3, use the HELM method to calculate the sensitivities of each order of node voltage as the inequality constraint condition and voltage stability criterion of the siting and sizing model of distributed power sources; Step 4, use the genetic algorithm to solve and determine the installation location and installation capacity P of distributed power sources according to the objective function and constraint conditions DGi The method of the invention can be used for siting and sizing distributed power flow in the distribution network, has a fast calculation speed, better voltage control effect, and has high theoretical significance and application value.

Description

Technical Field

[0001] The invention belongs to the field of electric power information technology, and in particular relates to a distributed power source site selection and capacity determination method based on HELM stability criterion. Background Art

[0002] With the development of power electronics and control technology and other related technologies, it has become possible to connect a large number of distributed generation (DG) to the distribution network, which also brings a series of problems to the distribution system. Distributed generation plays a vital role in the operation and planning of the distribution network. After the DG is connected, the distribution system changes from a radial structure to an active structure and causes changes in its internal flow, which in turn affects the voltage and changes it, which will have a significant impact on all aspects of the distribution network. In addition, the access location and capacity of the DG will have a certain impact on the network loss of the distribution network system, the voltage level and stability of the distribution network, the power quality, and relay protection. If the distribution and scale of the distributed generation are inappropriate, it may cause a significant increase in power loss and cause voltage drops at some nodes in the power system. In addition, it will also cause changes in the duration, direction, and size of the fault current.

[0003] The site selection and capacity determination of distributed generation is a multi-objective optimization problem, and the possible mutual constraints and contradictions between the sub-objectives will also affect its own optimization. It can be seen that it is necessary to accurately evaluate the impact of distributed generation in order to make correct decisions. The solution to the multi-objective optimization problem should be able to accurately determine the impact of distributed generation on the power grid and give its optimal distribution and capacity. In this way, the safety and economy of the power grid operation will not be seriously damaged by the gradual penetration of distributed generation in the power grid.

[0004] At present, there are two methods for optimizing the site selection and capacity of distributed power generation: traditional mathematical optimization algorithms and artificial intelligence optimization algorithms. The former mainly includes linear programming, nonlinear programming, dynamic programming, etc. Artificial intelligence optimization algorithms are algorithms that imitate a certain law in nature. Compared with classical mathematical optimization methods, they can handle more complex problems in the site selection and capacity of DG. Intelligent optimization algorithms have the advantages of fast convergence and strong adaptability. They mainly include taboo search algorithms, genetic algorithms, particle swarm algorithms, simulated annealing algorithms, etc.

[0005] In order to consider the impact of DG on the voltage stability of the distribution network when selecting the site and sizing the DG in the distribution network, it is necessary to introduce the voltage stability margin in the objective function. The conventional method for analyzing and judging the static voltage stability of the distribution network is to calculate the maximum load that causes voltage instability based on the continuous power flow method, compare the current power flow with the maximum load, and if the current power flow is less than the maximum load, the voltage is considered stable. This analysis method has the following problems: 1) The continuous calculation has a large amount of calculation and a long calculation time, which does not meet the real-time requirements of online voltage stability judgment and control; 2) With the access of DG or FACT, and the non-proportional increase of node load, the maximum load will change, and the maximum load calculated using the continuous power flow method is not accurate. There are also some other indicators proposed in the literature to judge whether the distribution network voltage is stable, such as line collapse index, line voltage stability L index, etc., but these indicators are derived based on the two-machine system, and cannot consider the complex distribution network load model connected to DG or FACT equipment, or ignore the line resistance or grounding capacitance, etc., and the evaluation is not accurate enough. Therefore, when selecting the site and sizing the DG in the distribution network, few voltage stability indicators are considered, so it is impossible to consider the impact of DG on the voltage stability of the distribution network when selecting the site and sizing the DG in the distribution network.

[0006] In the past two years, a power flow calculation method based on the embedding of a holomorphic function (HELM) has been proposed. This power flow method completely subverts the traditional Newton method and can clarify whether a power flow solution exists without relying on the initial value of the node. The present invention is based on the embedding of a holomorphic function into the voltage sensitivity stability criterion, which can solve the problem of solving power flow and voltage sensitivity under pathological conditions, does not need to calculate the maximum load margin, can consider various operating conditions of DG, and can consider the voltage stability index when selecting the site and sizing the DG. The calculation of this stability index is simple and fast, and is suitable for the site selection and sizing problem involving DG. At present, there is no relevant literature research in this regard. Summary of the invention

[0007] In view of the shortcomings of the prior art, the present invention proposes a distributed power generation site selection and sizing method based on the HELM stability criterion. The present invention uses the HELM method to calculate the voltage sensitivity and voltage stability criterion, and uses it for the site selection and sizing of distributed power sources in the distribution network. It is suitable for various DG load models, has fast calculation speed and simple calculation.

[0008] A method for site selection and capacity determination of distributed power generation based on HELM stability criterion includes the following steps:

[0009] Step 1: Establish a site selection and capacity determination model for distributed generation in the distribution network, including objective functions and constraints. The objective function considers the comprehensive cost of distributed generation, network loss and voltage stability index based on the holomorphic function embedding method; the constraints include power flow equation constraints, node voltage constraints, DG capacity constraints and voltage stability index constraints;

[0010] Step 2: Use the HELM method to calculate the power flow of the distribution network including distributed generation as the power flow constraint condition of the distributed generation site selection and sizing optimization model;

[0011] Step 3: Use the HELM method to calculate the sensitivity of each order of node voltage, which is used as the inequality constraint condition and voltage stability index of the distributed generation site selection and capacity determination model;

[0012] Step 4: Use genetic algorithm to solve and determine the installation location and installation quantity P of distributed generation according to the objective function and constraint conditions. DGi .

[0013] Preferably, the comprehensive cost of distributed power generation comprehensively considers the investment cost, operation and maintenance cost, network loss cost and power purchase cost of distributed power generation access, and selects the minimum comprehensive cost after connecting to DG to establish the objective function, which is expressed as:

[0014] f1=min(C DG +C OM +C L +C G ) (1)

[0015] In the formula, C DG is the DG investment cost, C OM is the DG operation and maintenance cost, C L is the network loss cost, C G The cost of purchasing electricity;

[0016] The investment cost is

[0017]

[0018] Where N DG is the total number of DGs in the distribution network; r is the discount rate, k is the useful life of DGs; C tou_i is the unit capacity investment cost of the i-th DG; P DG_i is the active capacity of the i-th DG;

[0019] The operation and maintenance cost is

[0020]

[0021] In the formula, C yum_i is the operation and maintenance cost of the i-th DG.

[0022] The network loss cost is

[0023] C L =C p *T max *P loss (4)

[0024] In the formula, C p is the unit electricity price, T max is the annual maximum load loss hours, P loss is the active network loss of the distribution network;

[0025] The cost of purchasing electricity is that after the distributed power generation is connected to the distribution system, it can directly supply power to the load, thereby reducing the cost of purchasing electricity from the power generation enterprise;

[0026]

[0027] Where N is the node number, T max is the annual maximum load utilization hours, P load_i is the load of the ith node.

[0028] Preferably, for active network loss, the minimum network loss after connecting to DG is selected as the optimization objective function, and the expression is:

[0029]

[0030] In the above formula, P loss is the active network loss of the distribution network; N is the total number of nodes in the distribution network; i and j are the node numbers at both ends of branch k respectively; U j is the voltage amplitude at node j; R ij is the resistance between nodes i and j; P j is the active power of node j at the end of the impedance branch; Q j is the reactive power at node j at the end of the impedance branch.

[0031] Preferably, for the HELM voltage stability judgment index, after DG is connected to the distribution network, it will affect the voltage stability of the distribution network. Reasonable configuration of DG can improve the voltage stability of the distribution network. The voltage stability after connecting DG is selected as the optimization objective function, and the expression is:

[0032]

[0033] Stability judgment index max(VSI HELM1i ) is smaller, the better the voltage stability of the distribution network is.

[0034] Preferably, the power flow equation constraint is

[0035]

[0036] Where Y ik represents the mutual admittance between nodes i and j in the node admittance matrix, V k represents the injected voltage at node k, and the value of k ranges from 1 to N. represents the conjugate of the apparent power injected into node i, represents the conjugate of the voltage injected into node i, and N represents all nodes of the network;

[0037] The node voltage constraint is

[0038] U i，min ≤U i ≤U i，max (9)

[0039] Where U i，min , U i，max are the lower and upper limits of the voltage at node i respectively;

[0040] The DG capacity constraint is:

[0041]

[0042] Where: P DGi is the active power of the DG connected to node i; P DGimax is the maximum DG active power allowed to be connected to node i; Ω is the set of DG installation nodes; μ is the penetration rate; P Ltital is the total active load of the system.

[0043] The voltage stability constraint is:

[0044]

[0045]

[0046] Where: VSI HELM 2i is the HELM voltage stability collapse indicator of node i.

[0047] Preferably, since each sub-objective function has different dimensions and conflicts with each other, it is necessary to normalize them. The normalized fitness function value is between 0 and 1, specifically:

[0048]

[0049] Where i is the number of iterations, j is the population of the optimization algorithm; F(i) min is the minimum value of the objective function fitness value of the i-th iteration, F(i) max is the maximum value of the objective function adaptation value of the i-th iteration; F(ij ) is the fitness value of the jth value of the objective function in the i-th iteration population, F N (i j ) is the normalized fitness value of the jth value of the objective function in the i-th iteration population;

[0050] After the sub-goals are dimensionless, multiple goals are subjectively weighted, the weights of each sub-goal are determined, and the objective function is unified.

[0051] f=ω 1 f1+ω 2 f2+ω 3 f3 (13)

[0052] In the formula, ω i is the weight coefficient, ω 1 +ω 2 +ω 3 =1;

[0053] The penalty term of node voltage and the penalty term of voltage stability are incorporated into the objective function to obtain a comprehensive objective function.

[0054]

[0055] In the formula, λ V is the node voltage over-limit penalty factor, λ H is the voltage stability over-limit penalty factor, V ilim 、V imin 、V imax They represent the maximum or minimum value, minimum value, and maximum value that the voltage of node i can take respectively;

[0056] Voltage over-limit penalty factor

[0057]

[0058] Voltage stability over-limit penalty factor

[0059]

[0060] Preferably, in step 3, the HELM method is used to calculate the sensitivity of each order of node voltage, which is used as the inequality constraint condition and voltage stability judgment index of the distributed generation site selection and capacity optimization model, including:

[0061] Through theoretical derivation, simulation analysis and comparison with the L index, a stability judgment index is added Assuming that node j is connected to DG, i corresponds to the electrical network node, each time node j is connected to a different DG capacity, N-1 The voltage stability change of the distribution network system with DG added is determined based on this value. Here real refers to the real part of the corresponding complex number. Add the optimization objective function;

[0062] Add an indicator Assuming that point j is connected to DG, i corresponds to the electrical network node, each time a different DG capacity is connected, N-1 To determine whether the voltage stability of the distribution network system with DG added has reached the voltage stability collapse point. Add constraints.

[0063] Genetic algorithm uses the idea of ​​natural selection and genetic inheritance to solve complex optimization problems in real life. It compares binary strings to chromosome genes and simulates the crossover and mutation process of chromosome genes to search for the installation location and installation amount P of distributed power sources. DGi Optimal solution.

[0064] The method of the present invention can be used for the site selection and sizing of distributed power flow in the distribution network. The influence of distributed power sources on the voltage stability of the distribution network is considered in the objective function and constraint conditions, which solves the problem that it is difficult to consider the influence of DG on voltage stability when selecting the site and sizing the distribution network. The method has fast calculation speed, better voltage control effect, and high theoretical significance and application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a flow chart of the method for site selection and capacity determination of distributed generation based on HELM voltage stability criterion;

[0066] Figure 2 It is a schematic diagram of a 33-node power grid;

[0067] Figure 3(a) to Figure 3(c) The changes of various voltage stability indicators when adding PQ type DGs of different capacities to 17 nodes in the IEEE 33-node system. Figure 3(a) is the voltage stability L indicator considering reverse power flow; Figure 3(b) is the voltage stability VSI indicator; Figure 3(c) is the λV curve of 17 nodes in the IEEE 33-node system drawn by Matpower.

[0068] Figure 4 This is the change curve of the total sensitivity and the real part of each order sensitivity on the voltage at node 17 when the DG capacity added to node 17 gradually increases in the IEEE 33-node system.

[0069] Figure 5 To determine the voltage stability index VSI for voltage sensitivity by adding PQ type DG with different capacities to 17 nodes in the IEEE 33-node system HELM 1i of changes.

[0070] Figure 6 This is a schematic diagram of a two-machine system.

[0071] Figure 7 To determine the voltage stability index VSI for voltage sensitivity by adding PQ type DG with different capacities to 17 nodes in the IEEE 33-node system HELM2i of changes.

[0072] Figure 8 Comparison of node voltage before and after distributed generation is connected to the distribution network.

[0073] Fig. 9 Comparison of active power loss of lines before and after distributed power generation is connected to the distribution network.

[0074] Fig.10 Comparison of HELM1 voltage stability indicators before and after distributed generation is connected to the distribution network. DETAILED DESCRIPTION

[0075] The present invention will be further described below in conjunction with the accompanying drawings.

[0076] refer to Figure 1 , which shows a distributed power generation site selection and capacity determination method based on HELM stability criterion according to an embodiment of the present invention, comprising the following steps:

[0077] Step 1: Establish a site selection and capacity determination model for distributed generation in the distribution network, including objective functions and constraints. The objective function considers the comprehensive cost of distributed generation, network loss and voltage stability index based on the holomorphic function embedding method; the constraints include power flow equation constraints, node voltage constraints, DG capacity constraints and voltage stability index constraints;

[0078] Step 2: Use the HELM method to calculate the power flow of the distribution network including distributed generation as the power flow constraint condition of the distributed generation site selection and sizing optimization model;

[0079] Step 3: Use the HELM method to calculate the sensitivity of each order of node voltage, which is used as the inequality constraint condition and voltage stability index of the distributed generation site selection and capacity determination model;

[0080] Step 4: Use genetic algorithm to solve and determine the installation location and installation quantity P of distributed generation according to the objective function and constraint conditions. DGi .

[0081] In one embodiment of the present invention, the objective function of step 1 considers the comprehensive cost of distributed power sources, active network loss and voltage stability index based on the holomorphic function embedding method. The constraints include power flow equation constraints, node voltage constraints, branch current constraints, DG capacity constraints, and voltage stability index constraints.

[0082] 1. Objective Function

[0083] (1) Comprehensive expenses

[0084] Taking into account the investment cost, operation and maintenance cost, network loss cost and power purchase cost of distributed power generation access, the objective function is established by selecting the minimum comprehensive cost after access to DG. The expression is:

[0085] f1=min(C DG +C OM +C L +C G ) (1)

[0086] In the formula, C DG is the DG investment cost, C OM is the DG operation and maintenance cost, C L is the network loss cost, C G The cost of purchasing electricity.

[0087] 1) Investment cost

[0088]

[0089] Where N DG is the total number of DGs in the distribution network; r is the discount rate, k is the useful life of DGs; C tou_i is the unit capacity investment cost of the i-th DG; P DG_i is the active capacity of the i-th DG connected.

[0090] 2) Operation and maintenance costs

[0091]

[0092] In the formula, C yun_i is the operation and maintenance cost of the i-th DG.

[0093] 3) Network loss costs

[0094] C L =C p *T max *P loss (4)

[0095] In the formula, C p is the unit electricity price, T max is the annual maximum load loss hours, P loss is the active network loss of the distribution network.

[0096] 4) Electricity purchase cost

[0097] After the distributed power sources are connected to the distribution system, they can directly supply power to the load, thereby reducing the power grid's electricity purchase costs from power generation companies.

[0098]

[0099] Where N is the node number, T max is the annual maximum load utilization hours, P load_i is the load of the ith node.

[0100] (2) Active network loss

[0101] DG access to the distribution network can reduce the flow of power in the adjacent branches of the node and reduce network losses. However, if the capacity of the connected DG is too large, it will cause reverse power flow in the distribution network and may also increase network losses. Reasonable configuration of DG can effectively reduce network losses, improve power generation utilization, and save energy. The minimum network loss after connecting to DG is selected as the optimization objective function, and the expression is:

[0102]

[0103] In the above formula, P loss is the active power loss of the distribution network; N is the total number of nodes in the distribution network; i and j are the node numbers at both ends of branch k; U j is the voltage amplitude at node j; R ij is the resistance between nodes i and j; P j is the active power of node j at the end of the impedance branch; Q j Its reactive power.

[0104] (3) HELM voltage stability determination index

[0105] After DG is connected to the distribution network, it will affect the voltage stability of the distribution network. Reasonable configuration of DG can improve the voltage stability of the distribution network. The voltage stability after connecting DG is the best as the optimization objective function, and the expression is:

[0106]

[0107] Stability judgment index max(VSI HELM1i ) is smaller, the better the voltage stability of the distribution network is.

[0108] 2. Constraints

[0109] (1) Power flow equation constraints

[0110]

[0111] Where Y ik represents the mutual admittance between nodes i and j in the node admittance matrix, V k represents the injected voltage at node k, and the value of k ranges from 1 to N. represents the conjugate of the apparent power injected into node i, represents the conjugate of the voltage injected into node i, and N represents all the nodes in the network.

[0112] (2) Node voltage constraints

[0113] U i，min ≤U i ≤U i，max (9)

[0114] Where U i，min , U i，max are the lower and upper limits of the voltage at node i respectively.

[0115] (3) DG capacity constraints

[0116]

[0117] Where: P DGi is the active power of the DG connected to node i; P DGimax is the maximum DG active power allowed to be connected to node i; Ω is the set of DG installation nodes; μ is the penetration rate; P Ltotal is the total active load of the system.

[0118] (4) Voltage stability constraints

[0119]

[0120] Where: VSI HELM 2i is the HELM voltage stability collapse indicator of node i.

[0121] 3. Normalization

[0122] Since each sub-objective function has different dimensions and conflicts with each other, it is necessary to normalize them. The normalized fitness function value is between 0 and 1. Specifically:

[0123]

[0124] Where i is the number of iterations, j is the population of the optimization algorithm; F(i) min is the minimum value of the objective function fitness value of the i-th iteration, F(i) max is the maximum value of the objective function adaptation value of the i-th iteration; F(i j ) is the fitness value of the jth value of the objective function in the i-th iteration population, F N (i j ) is the normalized fitness value of the jth value of the population at the i-th iteration of the objective function.

[0125] 4. Convert multiple objective functions into a single objective function

[0126] After the sub-goals are dimensionless, multiple goals are subjectively weighted, the weights of each sub-goal are determined, and the objective function is unified.

[0127] f=ω 1 f1+ω 2 f2+ω 3 f3 (13)

[0128] In the formula, ω i is the weight coefficient, ω 1 +ω 2 +ω 3 =1.

[0129] 5. Comprehensive objective function

[0130] The penalty term of node voltage and the penalty term of voltage stability are incorporated into the objective function to obtain a comprehensive objective function.

[0131]

[0132] In the formula, λ V is the node voltage over-limit penalty factor, λ H is the voltage stability over-limit penalty factor, V ilim 、V imin 、V imax They represent the maximum or minimum value, minimum value, and maximum value that the voltage of node i can take respectively.

[0133] Voltage over-limit penalty factor

[0134]

[0135] Voltage stability over-limit penalty factor

[0136]

[0137] In one embodiment of the present invention, in step 2, the HELM method is used to calculate the sensitivity of each order of the node voltage, which is used as the inequality constraint condition and voltage stability judgment index of the voltage control optimization model, including:

[0138] Assume that there is no grounded branch in the distribution network, the root node is a balancing node, and the distributed generation is assumed to be a PQ node:

[0139] If the node is a PQ node, the node power equation is:

[0140]

[0141] where Y ik represents the mutual admittance between nodes i and j in the node admittance matrix, V k represents the injected voltage at node k, and the value of k ranges from 1 to N. represents the conjugate of the apparent power injected into node i, represents the conjugate of the voltage injected into the i-node, N represents all the nodes in the network, and m represents the number of PQ nodes.

[0142] Use the holopure function method to construct the node's embedded pure virtual function:

[0143]

[0144] Where V i [n] represents the nth voltage component of the voltage at node i in the HELM power flow calculation, s n represents the nth order term of the frequency domain operator s;

[0145] If the node is a PQ node, substituting equation (18) into equation (17) yields:

[0146]

[0147] Where: Y ii is the self-admittance of node i in the node admittance matrix; Y ik is the mutual admittance between nodes i and k in the node admittance matrix; Y i，shunt is the grounding admittance of node i. Assuming there is no grounding branch, Y i，shunt = 0. Assumption:

[0148]

[0149] Depend on

[0150]

[0151] According to the equality of coefficients of the s series, we can obtain:

[0152]

[0153] If the node is a PQ node, substitute equation (18) into equation (19) to obtain:

[0154]

[0155] Substituting formula (20) into formula (23), we can obtain:

[0156]

[0157] From formula (24), we can get the following equation based on the equality of the coefficients of the s series:

[0158]

[0159] Assuming there is no grounding branch in the distribution network, Y i，shunt =0, Y ik，tran =Y ik .

[0160] When s=0, substituting into equation (25), or according to equation (25), the 0th-order coefficients of the s series are equal, we can obtain:

[0161]

[0162] From this formula (22) we can get:

[0163] d k [0] = 1 / V k [0] (29)

[0164] When the order of s is 1

[0165]

[0166] V can be obtained k [1].

[0167] According to the equality of coefficients of S series, we can get:

[0168]

[0169] According to formula (11)

[0170]

[0171] Thus we can get:

[0172]

[0173] When s=1, the solution of the power flow can be obtained.

[0174] On this basis, the network loss in the objective function is calculated.

[0175] Step 3: Use the HELM method to calculate the sensitivity of each order of node voltage as the inequality constraint condition of the DG site selection and capacity determination model and the voltage stability judgment index.

[0176] To find the sensitivity of voltage to active power and reactive power injected into the node, we need

[0177]

[0178] Where P j represents the active power injected by node j, Q j represents the reactive power injected by node j.

[0179] From the calculation process of formula (28), we can know that V i [0] is independent of the injected power at node i, so Both are 0.

[0180] On both sides of formula (30), j , Q j Taking partial derivatives, we can get

[0181] When j = i:

[0182]

[0183] When j≠i:

[0184]

[0185] Combining equations (35) and (36), we can solve It can be seen from the solution process that and It has nothing to do with the system power flow distribution, but only with the network structure and electrical distance, which is called voltage structure sensitivity.

[0186] From formula (32), we can know

[0187]

[0188] From this it follows that:

[0189]

[0190] Similarly, on both sides of formula (31), j , Q j Taking partial derivatives, we can get:

[0191] When j = i:

[0192]

[0193] When j≠i:

[0194]

[0195] Can be found

[0196] From formula (32), we can deduce

[0197]

[0198] By looping formulas (37)-(41), all

[0199] Then substitute into formula (34) to calculate the total nonlinear sensitivity of voltage to injected power.

[0200] The analysis found that It is proportional to the load to the first power, because when n = 2, the first term on the right side of formula (39) is a constant, and the second term is proportional to the load; It is proportional to the square of the load, and so on. Here they are defined as the voltage sensitivity. and It gets smaller and smaller as the value of n increases.

[0201] Finally, the overall voltage sensitivity and It can be obtained by formula (34).

[0202] In traditional distribution network analysis, when the voltage is stable, the load increases in the same direction. Previous literature

[12] proposed using HELM to calculate the voltage sensitivity of each order, and then subtract the high-order sensitivity from the low-order sensitivity. Under normal circumstances, the low-order sensitivity is greater than the high-order sensitivity, that is, the difference is positive; when the load increases, if the difference is negative, it is judged that the voltage is unstable; during voltage stability prevention control, a threshold is set for the difference. If the value of the low-order sensitivity minus the high-order sensitivity exceeds this threshold, it is considered that the voltage is about to become unstable, and voltage prevention control is initiated. As a preferred method, after calculating the 6th-order voltage sensitivity, the low-order voltage sensitivity is subtracted from the high-order voltage sensitivity to determine whether the voltage is unstable.

[0203] However, when analyzing the voltage stability of a distribution network containing DG, the growth direction of DG and load may be opposite, and a reverse flow may occur. The real and imaginary parts of the even-order voltage reactive sensitivity and odd-order voltage reactive sensitivity show different change trends. At this time, taking the amplitude of the voltage sensitivity can only determine whether the voltage is unstable, but cannot determine the change in voltage stability.

[0204] Taking a two-node system model as an example, the method of determining the voltage collapse point based on the HELM voltage sensitivity index is deduced and analyzed.

[0205] Figure 6 is a schematic diagram of a two-node system, that is, the system has only two nodes, node 1 is the balance node, and node 2 is the only load node. According to the HELM power flow construction method (28), when n = 0, we can get:

[0206]

[0207] Y 11 =-Y 12 , so we can get:

[0208] V 2 [0] = V 1 [0] (43)

[0209] From formula (29), we can get:

[0210]

[0211] From formula (31) when n = 1, we get:

[0212]

[0213] Substituting formula (29) into formula (45), we can obtain the following solution:

[0214]

[0215] From formula (22), we can get:

[0216]

[0217] From formula (31) when n = 2, we get:

[0218]

[0219] Substituting equation (47) into equation (48), solving the equations yields

[0220]

[0221] From formula (22), we can get:

[0222]

[0223] From formula (31) when n=3, we get:

[0224]

[0225] Substituting equation (50) into equation (51), solving the equations yields

[0226]

[0227] According to the above derivation, V 2 [0], V 2 [1] V 2 [2] V 2 [3], the partial derivatives of the reactive power of the node load are calculated respectively, and the results are shown in Equations (67), (68), and (69).

[0228]

[0229]

[0230]

[0231]

[0232]

[0233] In order to simplify the calculation appropriately, assume that R = 0, V 2 [0] = 1 and set

[0234]

[0235] From (57), we can get:

[0236] 4XQ 2 +Q+P 2 X=0 (58)

[0237] The condition for the equation Q to have a solution is 1-16P 2 X 2 ≥0, that is This condition is completely consistent with the power transfer limit of a pure impedance load circuit, indicating that the real part of the odd-order voltage sensitivity and the real part of the even-order voltage sensitivity correspond to an inflection point or extreme value of voltage stability.

[0238] Through theoretical derivation, simulation analysis and comparison with the L index, a stability judgment index is added Assuming that node j is connected to DG, i corresponds to the electrical network node, each time node j is connected to a different DG capacity, N-1 The voltage stability change of the distribution network system with DG added is determined based on the value. Here real refers to the real part of the corresponding complex number. Add the optimization objective function.

[0239] Add an indicator Assuming that point j is connected to DG, i corresponds to the electrical network node, each time a different DG capacity is connected, N-1 To determine whether the voltage stability of the distribution network system with DG added has reached the voltage stability collapse point. Add constraints.

[0240] Step 4: Use genetic algorithm to solve and determine the installation location and installation capacity P of distributed generation according to the objective function and constraints. DGi , and can obtain results such as comprehensive costs, network losses and voltage stability indicators.

[0241] Genetic algorithms use the ideas of natural selection and genetic inheritance to solve complex optimization problems in real life. They compare binary strings to chromosome genes and simulate the crossover and mutation process of chromosome genes to search for the optimal solution. The main process is as follows:

[0242] 1) Input the original node load, branch impedance and other system parameters, use the HELM method to calculate the initial power flow, voltage reactive power sensitivity and voltage stability judgment index, and obtain the voltage value of each node, system network loss and voltage stability judgment index;

[0243] 2) Determine the access node of DG;

[0244] 3) The nodes connected to the DG are binary-encoded as individuals to generate the initial population;

[0245] 4) Calculate the fitness value of the individual;

[0246] 5) Generate new populations through crossover and mutation, calculate their fitness values, and select the best fitness value in each population;

[0247] 6) If the convergence condition is met, output the solution corresponding to the optimal fitness value; otherwise, change the crossover rate and mutation rate and return to step 5).

[0248] The present invention has the following beneficial effects:

[0249] A distributed generation site selection and sizing method based on holomorphic function embedded in voltage sensitivity stability criterion is proposed, which can be used for site selection and sizing of distributed power flow in distribution network, solving the problem that it is difficult to consider the impact of DG on voltage stability when selecting site and sizing distribution network. It has fast calculation speed and simple calculation, and has high theoretical significance and application value.

[0250] The present invention will be further explained below with reference to the accompanying drawings;

[0251] like Figure 1 As shown, the distributed power generation site selection and capacity determination method based on the HELM voltage stability criterion of the present invention comprises the following steps:

[0252] Step 1: According to Figure 2 The data of the 33-node power grid shown in the figure establishes the site selection and capacity determination model of distributed generation in the distribution network:

[0253] Step 2: According to Figure 2 The data of the 33-node power grid shown in the figure is used to establish a mathematical model of the distribution network. The HELM method is used to calculate the power flow of the distribution network including distributed generation as the power flow constraint condition of the voltage control optimization model:

[0254] Step 3: Use the HELM method to calculate the sensitivity of each order of node voltage as the inequality constraint condition of the voltage control optimization model and the voltage stability judgment index.

[0255] Previously, the corresponding voltage stability index was derived using the two-machine system theory. Here, an example simulation is used to verify this index.

[0256] Figure 3(a) to Figure 3(c)The changes of various voltage stability indicators when adding PQ type DGs of different capacities to 17 nodes in the IEEE 33-node system. Figure 3(a) is the voltage stability L indicator diagram; Figure 3(b) is the voltage stability VSI indicator diagram; Figure 3(c) is the λV curve diagram of the 17-node IEEE 33-node system drawn by Matpower.

[0257] from Figure 3(a) to Figure 3(c) It can be seen that when the DG capacity connected to the distribution system is too large, it is not feasible to judge the voltage stability by the voltage stability VSI index and the voltage stability margin index λ based on the continuous power flow. It is more reliable to use the voltage stability L index to judge the voltage stability, but the L index can judge the change of voltage stability, but cannot judge the voltage collapse point. As can be seen from Figure 3(a), when considering the reverse power flow generated by excessive DG access capacity, when the PQ type DG is connected at a fixed position, when the access capacity of the distributed power source is within a certain range, it can be seen that the larger the connected DG capacity, the smaller the L index; as the connected DG capacity increases and exceeds a certain range, the DG capacity continues to increase. At this time, the reverse power flow generated by the DG capacity being greater than the total load at the lower end is getting larger and larger. At this time, the L index moves from the DG access point branch to the distribution network starting branch and gradually increases, and the voltage stability gradually decreases.

[0258] Figure 4 This is the change curve of the total sensitivity and the real part of each order sensitivity on the voltage at node 17 when the DG capacity added to node 17 gradually increases in the IEEE 33-node system.

[0259] from Figure 5 It can be seen that as the DG capacity increases, the real part of the even-order voltage sensitivity to reactive power sensitivity gradually decreases, and the real part of the odd-order voltage sensitivity to reactive power sensitivity first decreases and then increases. As the DG capacity increases, the absolute value of the difference between the real part of the even-order voltage sensitivity and the real part of the odd-order voltage sensitivity gradually decreases; when the DG increases to a certain capacity, the real part of the even-order voltage sensitivity and the real part of the odd-order voltage sensitivity will intersect; as the capacity continues to increase, the absolute value of the difference between the real part of the even-order voltage sensitivity and the real part of the odd-order voltage sensitivity increases; the real part curves of different even-order voltage sensitivities intersect, and the real part curves of different odd-order voltage sensitivities also intersect, and the DG capacity at the time of intersection is very similar.

[0260] By analyzing the changes in the absolute value of the difference between the real part of the even-order reactive sensitivity and the real part of the odd-order reactive sensitivity when adding DG of different capacities and the changes in the voltage stability L index considering reverse power flow, we can find that they have similarities. For the L index, as the capacity of the connected DG increases, the L index of the branch first decreases, and the voltage stability becomes better. After the connected capacity exceeds a certain range, the L index of the branch from the access point to the initial end slowly increases, and the voltage stability gradually deteriorates. For the real part of the voltage reactive sensitivity, as the capacity of the connected DG increases, the absolute value of the difference between the real part of the even-order voltage reactive sensitivity and the real part of the odd-order voltage reactive sensitivity first decreases and then increases; in addition, when the DG capacity is added to a certain extent, the real parts of different even-order voltage reactive sensitivities will intersect, and the real parts of different odd-order voltage reactive sensitivities will also intersect. The DG capacity corresponding to this intersection is the same as the capacity corresponding to the change in the L index. Therefore, it can be verified that VSI HELM 1i It is correct and feasible to judge the changes of voltage stability of distribution network containing DG.

[0261] 17 nodes are added with DG of different capacities, and the voltage stability index VSI is calculated using the sensitivity of each order of node voltage of HELM. HELM 1i and VSI HELM 2i , the voltage sensitivity determines the change curve of the voltage stability index, such as Figure 6 The change curve of voltage sensitivity to determine the voltage collapse point index is shown in Figure 8 shown.

[0262] from Figure 6 It can be seen that when the access capacity of DG is within a certain range, the larger the access capacity of DG, the higher the VSI HELM 1i The smaller the index, the better the system voltage stability; as the connected DG capacity increases and exceeds a certain range, the DG capacity continues to increase. At this time, VSI HELM 1i The index increases, and the system voltage stability becomes worse. Figure 8 It can be seen that when the access capacity of 17 nodes DG is greater than 2500KW, VSI HELM 2i >0, the system is in voltage collapse, which cannot be determined by the CPF method and the L index method.

[0263] From the above simulation results, it can be seen that the voltage stability index VSI proposed in this patent HELM 1i and VSI HELM 2i , it is possible to simultaneously determine the voltage stability performance change of the distribution network containing DG and whether the voltage stability collapses, and the calculation speed is fast and simple.

[0264] Step 4: Use genetic algorithm to solve the configured model and determine the optimal access location and capacity of distributed generation.

[0265] Selected Figure 1 IEEE 33-node distribution network construction example. The base power of the distribution network is 10MVA, the base voltage is 12.66kV, the total active load of the system is 3715kW, and the total reactive load is 2300kvar. The rated capacity of a single DG is 20kW, and the maximum active capacity of each candidate node that can be installed is 300kW. Unit capacity investment cost C tou_i is 1500 yuan / kW, the annual return on investment r is 0.1, the planned period k is 20 years, and the unit operation and maintenance cost C yun_i The unit electricity price is 500 yuan / kW. p 0.5 yuan / (kW·h), the annual maximum power grid loss hour is T max The annual maximum grid utilization hours are T max is 5600h, the node voltage range is: 0.93-1.07 (unit value), DG penetration μ is 25%, and the weight coefficient The penalty factor K is set to 100.

[0266] The genetic algorithm parameters are set as follows: population size N = 50, maximum number of iterations M = 100, crossover probability Pc = 0.8, and mutation probability Pm = 0.08.

[0267] Table 1 shows the configuration of distributed power sources, with a total capacity of 820kw. Most distributed power sources are installed at the end of the distribution network line. This is because when the voltage at the beginning of the line is constant, it is difficult to ensure that the voltage at the end of the line reaches the lower limit of the voltage allowed by the distribution network voltage. However, when the end of the line is connected to DG, the power transmitted on the feeder will be greatly reduced, and the voltage difference between the beginning and the end of the line will also decrease accordingly, which will greatly increase the voltage level at the end of the line and meet the system voltage requirements.

[0268] Table 1 Distributed power supply configuration scheme

[0269]

[0270] Table 2 compares the cost, network loss, and HELM voltage stability judgment index before and after access to distributed power sources. It can be seen from Table 2 that before access to distributed power sources, the system does not need to consider investment and operation and maintenance costs, but the network loss cost and electricity purchase cost are high. After the distributed power source is connected, the network loss cost is reduced by 174,400 yuan and the electricity purchase cost is reduced by 2.296 million yuan by supplying power at the end of the radiation network. Although the investment and operation and maintenance costs are increased, the total cost is reduced by 1.9159 million yuan, bringing considerable economic benefits to the operation of the distribution network. The active network loss of the system before and after access to distributed power sources is reduced from the original 202.6kw to 93.53kw, which effectively promotes energy saving and loss reduction of the power grid. The HELM voltage stability judgment index is reduced from the original 0.4228 to 0.3078, which improves the safety and stability of the distribution network operation.

[0271] Table 2 Cost, network loss and HELM voltage stability judgment indicators before and after distributed generation access

[0272] No DG Access DG DG investment cost / 10,000 yuan 14.45 DG operation and maintenance cost / 10,000 yuan 41 Network loss cost / 10,000 yuan 32.4 14.96 Electricity purchase cost / 10,000 yuan 1040.2 810.6 Total cost / 10,000 yuan 1072.6 881.01 Active network loss / kW 202.6 93.53 HELM voltage stability determination index 0.4228 0.3078

[0273] In order to verify the optimization ability and advancement of the method of the present invention, the optimization results obtained by the method of the present invention and the method without adding voltage stability indicators and constraints are compared. Both are based on a 33-node distribution system as a model. The comparison results are shown in Table 3. As can be seen from Table 3, when the DG access capacity is the same, the cost saved by the method of the present invention is 1.9159 million yuan, and the network loss improvement rate is 53.84%. The cost saved by the method without adding voltage stability indicators and constraints is 1.6897 million yuan, and the network loss improvement rate is 52.46%. This shows that the method of the present invention is better in reducing network losses, has better economic benefits, and can consider the impact of DG on the voltage stability of the distribution network.

[0274] Table 3 Comparison of the results of the method of the present invention with those of other methods

[0275]

[0276]

[0277] Figure 8 This is a comparison of node voltages before and after the distributed generation is connected to the distribution network. It can be seen from the figure that the proposed configuration method can reasonably connect the distributed generation to the distribution network, which can effectively improve the voltage level of each node, especially the minimum voltage node, and greatly improve the safety and stability of the distribution network operation.

[0278] Fig. 9 This is a comparison of the active network loss of the line before and after the distributed power generation is connected to the distribution network. It can be seen from the figure that after the distributed power generation is connected to the distribution network, the active network loss of the overall line is reduced, which effectively promotes energy saving and loss reduction of the power grid.

[0279] Fig.10 The figure shows the comparison of HELM1 voltage stability index before and after the distributed generation is connected to the distribution network. It can be seen from the figure that after the distributed generation is connected to the distribution network, the overall HELM1 voltage stability index is reduced, which effectively improves the voltage stability of the system.

Claims

1. A method for site selection and capacity determination of distributed generation based on HELM stability criterion. It is characterized in that The following steps are involved: Step 1: Establish a site selection and capacity determination model for distributed generation in the distribution network, including objective function and constraints. The objective function considers the comprehensive cost of distributed generation, active network loss and HELM voltage stability judgment index; the constraints include power flow equation constraints, node voltage constraints, DG capacity constraints, and voltage stability index constraints; Step 2: Use the HELM method to calculate the power flow of the distribution network including distributed generation as the power flow constraint condition of the distributed generation site selection and sizing optimization model; Step 3: Use the HELM method to calculate the sensitivity of each order of node voltage, which is used as the inequality constraint condition and voltage stability index of the distributed generation site selection and capacity determination model; Step 4: Use genetic algorithm to solve and determine the installation location and installation quantity P of distributed generation according to the objective function and constraint conditions. DGi ; The comprehensive cost of distributed power generation comprehensively considers the investment cost, operation and maintenance cost, network loss cost and power purchase cost of distributed power generation access, and selects the minimum comprehensive cost after access to DG to establish the objective function, which is expressed as: f1=min(C DG +C OM +C L +C G ) (1) In the formula, C DG is the DG investment cost, C OM is the DG operation and maintenance cost, C L is the network loss cost, C G The cost of purchasing electricity; The investment cost is: Where N DG is the total number of DGs in the distribution network; r is the discount rate, k is the useful life of DGs; C tou_i is the unit capacity investment cost of the i-th DG; P DG_i is the active capacity of the i-th DG; The operation and maintenance cost is In the formula, C yun_i is the operation and maintenance cost of the i-th DG; The network loss cost is C L =C p *t max *P loss (4) In the formula, C p is the unit electricity price, t max is the annual maximum load loss hours, P loss is the active network loss of the distribution network; The cost of purchasing electricity is that after the distributed power generation is connected to the distribution system, it can directly supply power to the load, thereby reducing the cost of purchasing electricity from the power generation enterprise; Where N is the node number, T max is the annual maximum load utilization hours, P load_i is the load of the ith node; For active network loss, the minimum network loss after connecting DG is selected as the optimization objective function, and the expression is: In the above formula, P loss is the active network loss of the distribution network; N is the total number of nodes in the distribution network; i and j are the node numbers at both ends of branch k respectively; U j is the voltage amplitude at node j; R ij is the resistance between nodes i and j; P j is the active power of node j at the end of the impedance branch; Q j is the reactive power of node j at the end of the impedance branch; For the HELM voltage stability judgment index, after DG is connected to the distribution network, it will affect the voltage stability of the distribution network. Reasonable configuration of DG can improve the voltage stability of the distribution network. The best voltage stability after connecting DG is selected as the optimization objective function, and the expression is: Stability judgment index max(VSI HELM1i ) is smaller, the better the voltage stability of the distribution network is; Step 3: Use the HELM method to calculate the sensitivity of each order of node voltage, which is used as the inequality constraint conditions and voltage stability judgment index of the distributed generation site selection and capacity optimization model, including: Through theoretical derivation, simulation analysis and comparison with the L index, a stability judgment index is added Assume that node j is connected to DG, i corresponds to the electrical network node, and each time node j is connected to a different DG capacity, calculate N-1 The voltage stability change of the distribution network system with DG added is determined based on the value. Here, real refers to the real part of the corresponding complex number. Add the optimization objective function; Add an indicator Assume that point j is connected to DG, i corresponds to the electrical network node, and each time a different DG capacity is connected, calculate N-1 To determine whether the voltage stability of the distribution network system with DG added has reached the voltage stability collapse point. Add constraints.

2. The method for site selection and capacity determination of distributed power generation based on HELM stability criterion according to claim 1, It is characterized in that The power flow equation constraint is: Where Y ik represents the mutual admittance between nodes i and j in the node admittance matrix, V k represents the injected voltage at node k, and the value of k ranges from 1 to N. represents the conjugate of the apparent power injected into node i, represents the conjugate of the voltage injected into the i-node, and N represents all nodes of the network; The node voltage constraint is: U i,min Ui Ui,max(9) In the formula, U i,min , U i,max are the lower and upper limits of the voltage at node i respectively; The DG capacity constraint is: Where: P DGi is the active power of the DG connected to node i; P DGimax is the maximum DG active power allowed to be connected to node i; W is the set of DG installation nodes; μ is the penetration rate; P Ltotal is the total active load of the system; The voltage stability constraint is: Where: VSI HELM2i is the HELM voltage stability collapse indicator of node i.

3. The method for site selection and capacity determination of distributed power generation based on HELM stability criterion as claimed in claim 2, It is characterized in that Since each sub-objective function has different dimensions and conflicts with each other, it is necessary to normalize them. The normalized fitness function value is between 0 and 1, specifically: Where i is the number of iterations, j is the population of the optimization algorithm; F(i) min is the minimum value of the objective function fitness value of the i-th iteration, F(i) max is the maximum value of the objective function adaptation value of the i-th iteration; F(i j ) is the fitness value of the jth value of the objective function in the i-th iteration population, F N (i j ) is the normalized fitness value of the jth value of the objective function in the i-th iteration population; After the sub-goals are dimensionless, the multiple goals are subjectively weighted, the weights of each sub-goal are determined, and the objective function is unified: <h2 style=";text-align:left;direction:ltr">f=w<h2 style=";text-align:left;direction:ltr"> 1 <h2 style=";text-align:left;direction:ltr"> f1+w<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> f2+w<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> f3 (13) In the formula, w i is the weight coefficient, w 1 +w 2 +w 3 =1; The penalty term of node voltage and the penalty term of voltage stability are incorporated into the objective function to obtain a comprehensive objective function: In the formula, λ V is the node voltage over-limit penalty factor, λ H is the voltage stability over-limit penalty factor, V ilim 、V imin 、V imax They represent the maximum or minimum value, minimum value, and maximum value that the voltage of node i can take respectively; Voltage over-limit penalty factor: Voltage stability over-limit penalty factor:

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