Voltage control method for distributed photovoltaic power generation based on HELM stability criterion

Abstract

The invention discloses a voltage control method for distributed photovoltaic power generation based on HELM stability criterion, comprising the following steps: step 1, establishing a voltage control model of distributed photovoltaic power generation in a distribution network; step 2, using the HELM method to calculate the distribution network flow including distributed photovoltaic power generation as a flow constraint condition of the voltage control optimization model of distributed photovoltaic power generation; step 3, using the HELM method to calculate the sensitivity of each order of node voltage as an inequality constraint condition and voltage stability judgment index of the voltage control model of distributed photovoltaic power generation; step 4, using a genetic algorithm to solve and determine the active power reduction amount, network loss and voltage stability judgment index of distributed photovoltaic power generation according to the objective function and constraint conditions. The method of the invention can be used for voltage control of distributed photovoltaic power sources in distribution networks, has fast calculation speed, better voltage control effect, can consider the influence of distributed photovoltaic power generation on voltage stability, 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 voltage control method for distributed photovoltaic power generation based on HELM stability criterion. Background Art

[0002] With the continuous expansion of the scale of distributed photovoltaic power generation grid connection, the problem of voltage over-limit caused by the reverse flow caused by the imbalance between photovoltaic power generation and load has received increasing attention. Distributed photovoltaic access to the distribution network can avoid the construction investment and power loss of traditional long-distance power transmission, and can realize the local consumption of energy. However, after a large number of distributed photovoltaics are connected to the grid, the entire distribution system will change from a traditional one-way radial network to a multi-power network, which will cause changes in the system flow and voltage distribution. At the same time, since the peak hours of typical residential loads and photovoltaic output are often mismatched, the distribution network is prone to power reverse transmission during strong light periods, causing the risk of voltage over-limit, and the risk of voltage over-limit during peak load periods, which will also increase line network losses and affect the normal operation of photovoltaic and distribution network systems. Therefore, the distribution network voltage control problem is an urgent problem to be solved for distributed photovoltaic grid connection.

[0003] In order to control the voltage of photovoltaic distributed generation (DG) after grid connection, it is necessary to optimize the configuration of photovoltaic DG. At present, there are two methods for DG optimization configuration: traditional mathematical optimization algorithm and artificial intelligence optimization algorithm. The former mainly includes linear programming, nonlinear programming, dynamic programming, etc. Artificial intelligence optimization algorithm is an algorithm established by imitating a certain law in nature. Compared with classical mathematical optimization methods, it can handle more complex problems in the optimization configuration of DG. Intelligent optimization algorithm has the advantages of fast convergence and strong adaptability. It mainly includes taboo search algorithm, genetic algorithm, particle swarm algorithm, simulated annealing algorithm, etc.

[0004] In order to consider the impact of DG on the voltage stability of the distribution network when controlling and optimizing the configuration of DG in the distribution network, it is necessary to introduce the voltage stability margin into 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, fewer voltage stability indicators are considered when optimizing the configuration of DG in the distribution network, so it is impossible to consider the impact of DG on the voltage stability of the distribution network when optimizing the configuration of DG in the distribution network.

[0005] In the past two years, a power flow calculation method based on the embedding of holomorphic functions (Holomorphic embedding method, HELM) has been proposed. This power flow method completely subverts the traditional Newton method. It can clarify whether the power flow solution exists without relying on the initial value of the node. The present invention is based on the voltage sensitivity stability criterion embedded in the holomorphic function, and proposes a voltage control method for distributed photovoltaic power generation. It can solve the problem of solving power flow and voltage sensitivity under pathological conditions, and does not need to calculate the maximum load margin. It can consider various operating conditions of DG, and can consider the voltage stability index when controlling the DG voltage. The calculation of this stability index is simple and fast, which is suitable for voltage control and optimization configuration problems involving DG. At present, there is no relevant literature research in this regard. Summary of the invention

[0006] In view of the shortcomings of the prior art, the present invention proposes a voltage control method for distributed photovoltaic power generation 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 voltage control of distributed photovoltaic power generation in the distribution network. The calculation speed is fast and the calculation is simple.

[0007] A voltage control method for distributed photovoltaic power generation based on HELM stability criterion comprises the following steps:

[0008] Step 1: Establish a voltage control model for distributed photovoltaic power generation in the distribution network, including objective functions and constraints. The objective function considers the active power reduction of distributed photovoltaic power generation, network loss and voltage stability index based on the holomorphic function embedding method; the constraints include power flow equation constraints, node voltage constraints and voltage stability index constraints;

[0009] Step 2: Use the HELM method to calculate the power flow of the distribution network including distributed photovoltaic power generation as the power flow constraint condition of the voltage control optimization model of distributed photovoltaic power generation;

[0010] Step 3: Use the HELM method to calculate the sensitivity of each order of node voltage as the inequality constraint condition and voltage stability index of the voltage control model of distributed photovoltaic power generation;

[0011] Step 4: Use genetic algorithm to solve and determine the active power reduction, network loss and voltage stability index of distributed photovoltaic power generation according to the objective function and constraints.

[0012] Preferably, the distributed photovoltaic power generation is connected to the distribution network at the maximum active output power, which will cause the voltage of the distribution network to exceed the limit and reduce the voltage stability. In order to control the voltage within the allowable range, the active output power of the distributed photovoltaic power generation needs to be reduced to control the voltage of the distribution network within the allowable range. In step 1, the minimum active reduction amount of distributed photovoltaic power generation is selected as the optimization objective function, and the expression is:

[0013]

[0014] Where N PV is the node set connected to distributed photovoltaic in the distribution network, P cut is the active reduction of distributed photovoltaic power generation, and P PV，n They are the maximum active output power of distributed photovoltaic power generation and the actual active output power of distributed photovoltaic power generation at node n respectively.

[0015] Preferably, for active network loss, the minimum network loss after reducing the distributed photovoltaic output is selected as the optimization objective function, and the expression is:

[0016]

[0017] 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 jis the reactive power at node j at the end of the impedance branch.

[0018] Preferably, for the HELM voltage stability judgment index, after the distributed photovoltaic is connected to the distribution network, it will affect the voltage stability of the distribution network. Reasonable reduction of the active power of distributed photovoltaic power generation can improve the voltage stability of the distribution network. The voltage stability after connecting to the distributed photovoltaic is the best as the optimization objective function, and the expression is:

[0019]

[0020] In the above formula, VSI HELM 1i is the voltage stability index of node i, is the sensitivity of the second-order component of the voltage s at node i to the reactive power injected into node j, is the sensitivity of the third-order component of the voltage at node i to the reactive power injected into node j, and real is the real part of the corresponding vector.

[0021] The smaller the stability judgment index is, the better the voltage stability of the distribution network is.

[0022] Preferably, the power flow equation constraint is

[0023]

[0024] 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, where 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 the nodes in the network.

[0025] Preferably, the node voltage constraint is

[0026] V i，min ≤V i ≤V i，max (5)

[0027] Where V i，min , V i，max are the lower and upper limits of the voltage at node i respectively;

[0028] Preferably, the voltage stability constraint is:

[0029]

[0030] Where: VSI HELM 2i is the HELM voltage stability collapse indicator of node i, is the sensitivity of the third-order component of the voltage s at node i to the reactive power injected into node j, is the sensitivity of the fifth-order component of the voltage at node i to the reactive power injected into node j, and real is the real part of the corresponding vector.

[0031] 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:

[0032]

[0033] 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;

[0034] After the sub-goals are dimensionlessly normalized, multiple goals are subjectively weighted, the weights of each sub-goal are determined, and the objective function is unified.

[0035] f=ω1f1+ω2f2+ω3f3 (8)

[0036] In the formula, ω i is the weight coefficient, ω1+ω2+ω3=1;

[0037] 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.

[0038]

[0039] 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;

[0040] Voltage over-limit penalty factor

[0041]

[0042] Voltage stability over-limit penalty factor

[0043]

[0044] 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 conditions and voltage stability judgment index of the voltage control optimization model of distributed photovoltaic power generation, including:

[0045] 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;

[0046] 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.

[0047] 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 determine the active power reduction of distributed photovoltaic power generation, the system's active network loss and voltage stability indicators.

[0048] This method is used to control the voltage of the distribution network including distributed photovoltaic power generation. It not only takes into account the nonlinear factors of sensitivity, but also considers the impact of distributed photovoltaics on the voltage stability of the distribution network in the objective function and constraints. It has fast calculation speed and better voltage control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of a voltage control method for distributed photovoltaic power generation based on HELM stability criterion according to an embodiment of the present invention;

[0050] Figure 2 This is a schematic diagram of a 33-node power grid;

[0051] 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 are shown in Figure 3(a) which 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;

[0052] Figure 4 The curves of the total sensitivity and the real part of each order sensitivity of the voltage at node 17 when the DG capacity added to node 17 gradually increases in the IEEE 33-node system;

[0053] 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 changes in

[0054] Figure 6 It is a schematic diagram of a two-machine system;

[0055] 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 HELM 2i changes in

[0056] Figure 8 It is the system's 24h distributed photovoltaic power generation output and load curve;

[0057] Fig. 9 The voltage variation curve of the photovoltaic access point of the system for 24 hours before the control strategy is adopted;

[0058] Fig.10 The voltage variation curve of the photovoltaic access point of the system for 24 hours after the control strategy is adopted;

[0059] Fig.11 The comparison curve of the distributed photovoltaic active output of the system for 24 hours before and after the voltage control strategy is adopted;

[0060] Fig.12 The comparison curve of active network loss of the system for 24 hours before and after the voltage control strategy is adopted;

[0061] Fig.13 The comparison curve of HELM1 voltage stability index of the system for 24 hours before and after adopting the voltage control strategy. DETAILED DESCRIPTION

[0062] The present invention will be further described below in conjunction with the accompanying drawings.

[0063] refer to Figure 1 A voltage control method for distributed photovoltaic power generation based on HELM stability criterion in an embodiment of the present invention comprises the following steps:

[0064] Step 1: Establish a voltage control model for distributed photovoltaic power generation in the distribution network, including objective functions and constraints. The objective function considers the active power reduction of distributed photovoltaic power generation, network loss and voltage stability index based on the holomorphic function embedding method; the constraints include power flow equation constraints, node voltage constraints and voltage stability index constraints;

[0065] Step 2: Use the HELM method to calculate the power flow of the distribution network including distributed photovoltaic power generation as the power flow constraint condition of the voltage control optimization model of distributed photovoltaic power generation;

[0066] Step 3: Use the HELM method to calculate the sensitivity of each order of node voltage as the inequality constraint condition and voltage stability index of the voltage control model of distributed photovoltaic power generation;

[0067] Step 4: Use genetic algorithm to solve and determine the active power reduction, network loss and voltage stability index of distributed photovoltaic power generation according to the objective function and constraints.

[0068] In one embodiment of the present invention, the objective function of step 1 considers the active reduction of distributed photovoltaic power generation, active network loss and voltage stability index based on the holomorphic function embedding method. The constraints include power flow equation constraints, node voltage constraints and voltage stability index constraints.

[0069] 1. Objective Function

[0070] (1) Active power reduction of distributed photovoltaic power generation

[0071] Distributed photovoltaic power generation is connected to the distribution network at the maximum active output power, which will cause the voltage of the distribution network to exceed the limit and reduce the voltage stability. In order to control the voltage within the allowable range, it is necessary to reduce the active output power of distributed photovoltaic power generation to control the voltage of the distribution network within the allowable range. The minimum active reduction amount of distributed photovoltaic power generation is selected as the optimization objective function, and the expression is:

[0072]

[0073] Where N PV is the node set connected to distributed photovoltaic in the distribution network, P cut is the active reduction of distributed photovoltaic power generation, and P PV，n They are the maximum active output power of distributed photovoltaic power generation and the actual active output power of distributed photovoltaic power generation at node n respectively.

[0074] (2) Active network loss

[0075] Distributed photovoltaic 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 distributed photovoltaic is too large, it will cause reverse power flow in the distribution network and may also increase network losses. Reasonable reduction of the active power of distributed photovoltaic power generation can effectively reduce network losses, improve power generation utilization, and save energy. The minimum network loss after reducing the output of distributed photovoltaic power generation is selected as the optimization objective function, and the expression is:

[0076]

[0077] 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.

[0078] (3) HELM voltage stability determination index

[0079] After distributed photovoltaics are connected to the distribution network, the voltage stability of the distribution network will be affected. Reasonable reduction of the active power of distributed photovoltaic power generation can improve the voltage stability of the distribution network. The voltage stability after reducing the output of distributed photovoltaics is the best as the optimization objective function, and the expression is:

[0080]

[0081] Stability judgment index max(VSI HELM 1i ) is smaller, the better the voltage stability of the distribution network is.

[0082] 2. Constraints

[0083] (1) Power flow equation constraints

[0084]

[0085] 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, where 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 the nodes in the network.

[0086] (2) Node voltage constraints

[0087] V i，min ≤V i ≤Vi，max (5)

[0088] Where U i，min , U i，max are the lower and upper limits of the voltage at node i respectively.

[0089] (3) Voltage stability constraints

[0090]

[0091] Where: VSI HELM 2i is the HELM voltage stability collapse indicator of node i.

[0092] 3. Normalization

[0093] 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:

[0094]

[0095] 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.

[0096] 4. Convert multiple objective functions into a single objective function

[0097] 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.

[0098] f=ω1f1+ω2f2+ω3f3 (8)

[0099] In the formula, ω i is the weight coefficient, ω1+ω2+ω3=1.

[0100] 5. Comprehensive objective function

[0101] 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.

[0102]

[0103] In the formula, λ V is the node voltage over-limit penalty factor, λH 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.

[0104] Voltage over-limit penalty factor

[0105]

[0106] Voltage stability over-limit penalty factor

[0107]

[0108] In one embodiment of the present invention, in step 2, the HELM method is used to calculate the power flow of the distribution network including distributed photovoltaic power generation, and the power flow constraint conditions of the voltage control optimization model of distributed photovoltaic power generation include:

[0109] 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:

[0110] If the node is a PQ node, the node power equation is:

[0111]

[0112] 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, where 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.

[0113] Use the holopure function method to construct the node's embedded pure virtual function:

[0114]

[0115] 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 term of the frequency domain operator s;

[0116] If the node is a PQ node, substituting equation (13) into equation (12) yields:

[0117]

[0118] Where: Y ii is the self-admittance of node i in the node admittance matrix; Yik 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:

[0119]

[0120] Depend on

[0121]

[0122] According to the equality of coefficients of the s series, we can obtain:

[0123]

[0124] If the node is a PQ node, substitute equation (13) into equation (14) to obtain:

[0125]

[0126] Substituting formula (15) into formula (18), we get:

[0127]

[0128] According to formula (19), the coefficients of the s series are equal, so we can get:

[0129]

[0130] Assuming there is no grounding branch in the distribution network, Y i，shunt =0, Y ik，tran =Y ik .

[0131] When s=0, substituting into formula (20), or according to formula (20), the 0th order coefficients of the s series are equal, we can get:

[0132]

[0133] From this formula (17), we can get:

[0134] d k [0] = 1 / V k [0] (22)

[0135] When the order of s is 1

[0136]

[0137] V can be calculated k [1].

[0138] According to the equality of coefficients of S series, we can get:

[0139]

[0140] According to formula (22)

[0141]

[0142] Thus we can get:

[0143]

[0144] When s=1, the solution of the power flow can be obtained.

[0145] On this basis, the network loss in the objective function is calculated.

[0146] 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.

[0147] To find the sensitivity of voltage to active power and reactive power injected into the node, we need

[0148]

[0149] Where P j represents the active power injected by node j, Q j represents the reactive power injected by node j.

[0150] From the calculation process of formula (21), we can know that V i [0] is independent of the injected power at node i, so Both are 0.

[0151] In formula (23), both sides of P j , Q j Taking partial derivatives, we can get

[0152] When j = i:

[0153]

[0154] When j≠i:

[0155]

[0156] Combining equations (28) and (29), 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.

[0157] From formula (25), we can know that:

[0158]

[0159] From this it follows that:

[0160]

[0161] Similarly, on both sides of formula (24), j , Q j Taking partial derivatives, we can get:

[0162] When j = i:

[0163]

[0164] When j≠i:

[0165]

[0166] Can be found

[0167] From formula (25), we can deduce

[0168]

[0169] By looping formulas (30)-(34), all

[0170] Then substitute into formula (27) to calculate the total nonlinear sensitivity of voltage to injected power.

[0171] 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 (32) 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.

[0172] Finally, the overall voltage sensitivity and It can be obtained by formula (27).

[0173] The traditional distribution network analysis shows that when the voltage is stable, the load increases in the same direction. The HELM is used to calculate the voltage sensitivity of each order, and then the high-order sensitivity is subtracted 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, the voltage is judged to be 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 started. 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.

[0174] 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.

[0175] 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.

[0176] Figure 6 It 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 (21), when n = 0, we can get:

[0177]

[0178] Y 11 =-Y 12 , so we can get:

[0179] V2[0]=V1[0] (36)

[0180] From formula (22), we can get:

[0181]

[0182] From formula (23) when n = 1, we get:

[0183]

[0184] Substituting formula (22) into formula (38), we can obtain the following solution:

[0185]

[0186] From formula (17), we can get:

[0187]

[0188] From formula (24) when n = 2, we get:

[0189]

[0190] Substituting equation (40) into equation (41), solving the equations yields

[0191]

[0192] From formula (17), we can get:

[0193]

[0194] From formula (24) when n=3, we get:

[0195]

[0196] Substituting equation (43) into equation (44), solving the equations yields

[0197]

[0198] Based on V2[0], V2[1], V2[2], and V2[3] derived above, the partial derivatives of the node load reactive power are calculated respectively, and the results are shown in Equations (46), (47), (48), and (49).

[0199]

[0200]

[0201]

[0202]

[0203] In order to simplify the operation appropriately, assume that R = 0, V2[0] = 1 and let

[0204]

[0205] From (50), we can get:

[0206] 4XQ 2 +Q+P 2 X=0 (51)

[0207] 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.

[0208] 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.

[0209] 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.

[0210] Step 4: Use genetic algorithm to solve and determine the results of distributed photovoltaic power generation, network loss and voltage stability index according to the objective function and constraints.

[0211] 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:

[0212] 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;

[0213] 2) Determine the access node of DG;

[0214] 3) The nodes connected to the DG are binary-encoded as individuals to generate the initial population;

[0215] 4) Calculate the fitness value of the individual;

[0216] 5) Generate new populations through crossover and mutation, calculate their fitness values, and select the best fitness value in each population;

[0217] 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).

[0218] The present invention has the following beneficial effects: it proposes a voltage control method for distributed photovoltaic power generation based on a holomorphic function embedded in a voltage sensitivity stability criterion, which can be used for voltage control of distributed photovoltaic power generation in a distribution network, and solves the problem that it is difficult to consider the impact of distributed photovoltaic power generation on voltage stability when controlling the voltage of a distribution network. The method has fast calculation speed and simple calculation, and has high theoretical significance and application value.

[0219] The present invention will be further explained below with reference to the accompanying drawings;

[0220] like Figure 1 As shown, the voltage control method containing distributed photovoltaic power generation based on the HELM stability criterion of the present invention is as follows:

[0221] Step 1: According to Figure 2 The data of the 33-node power grid shown in the figure establishes the voltage control model of distributed photovoltaic power generation in the distribution network:

[0222] 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:

[0223] 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.

[0224] Previously, the corresponding voltage stability index was derived using the two-machine system theory. Here, an example simulation is used to verify this index.

[0225] 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.

[0226] 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.

[0227] 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.

[0228] from Figure 4 It can be seen that with the increase of DG capacity, the real part of the even-order voltage sensitivity to reactive sensitivity gradually decreases, and the real part of the odd-order voltage sensitivity to reactive sensitivity first decreases and then increases. With the increase of DG capacity, 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; continue to increase the capacity, 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 intersection is very similar.

[0229] 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.

[0230] 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 5 The change curve of voltage sensitivity to determine the voltage collapse point index is shown in Figure 7 shown.

[0231] from Figure 5 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 As the index increases, the system voltage stability deteriorates. From the figure, we can see that the voltage collapse point index VSI HELM 2i It is always less than 0, indicating that the voltage of the 17-node DG access capacity to the 1200KW system is stable. Figure 4 and Figure 7 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.

[0232] 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.

[0233] Step 4: Use genetic algorithm to solve the configured model and determine the active power reduction, network loss and voltage stability index of distributed photovoltaic power generation.

[0234] Selected Figure 1 IEEE 33-node distribution network construction example. The base power of the distribution network is 10MVA, and the base voltage is 12.66kV. The voltage range allowed for normal operation of the distribution network is: 0.93-1.07 (per unit value), the power factor of the distributed photovoltaic power source is 0.9, nodes 16, 18, 31, and 33 are set as access nodes for distributed photovoltaic power sources, and the total output power of the distributed photovoltaic power sources at a certain moment is evenly distributed to the nodes connected to the photovoltaic power source. The weight coefficients ω1=0.6, ω2=0.2, ω3=0.2, and the penalty factor K is set to 1000. Taking a typical summer day in a certain place in my country as an example, the changes in the total active output and total load of distributed photovoltaic power generation in the system within 24 hours of a day are shown as follows. Figure 8 shown.

[0235] 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.

[0236] Table 1 shows the voltage information of the photovoltaic access points when the voltage control strategy is not adopted. It can be seen from Table 1 that when the voltage control strategy is not adopted, the highest voltages of the photovoltaic access points 16, 18, 31, and 33 of the distribution network are 1.1411, 1.1584, 1.0946, and 1.1008 (per unit value), respectively, which all exceed the upper voltage limit of 1.07 allowed for the normal operation of the distribution network. The lowest voltages of the photovoltaic access points are 0.9337, 0.9316, 0.9353, and 0.9344 (per unit value), respectively, which do not exceed the lower voltage limit of 0.93 allowed for the normal operation of the distribution network. Therefore, it is necessary to reasonably reduce the capacity of distributed photovoltaic power generation so that the voltage of the distribution network exceeding the upper limit is controlled within the voltage range allowed for normal operation.

[0237] Table 1 Voltage information of photovoltaic access point when voltage control strategy is not adopted

[0238] node Maximum voltage / pu Minimum voltage / pu 16 1.1411 0.9337 18 1.1584 0.9316 31 1.0946 0.9353 33 1.1008 0.9344

[0239] Table 2 shows the voltage information of the photovoltaic access points when the voltage control strategy is adopted. It can be seen from the table that after the voltage control strategy is adopted, the highest voltages of the photovoltaic access points 16, 18, 31, and 33 of the distribution network are 1.0529, 1.0528, 1.0578, and 1.0627 (per unit value), respectively, which do not exceed the upper voltage limit of 1.07 allowed for the normal operation of the distribution network. The lowest voltages of the photovoltaic access points are 0.9337, 0.9316, 0.9353, and 0.9344 (per unit value), respectively, which do not exceed the lower voltage limit of 0.93 allowed for the normal operation of the distribution network. This shows that the control strategy of active power reduction of distributed photovoltaic power generation can control the voltage of the distribution network within the voltage range allowed for the normal operation of the distribution network.

[0240] Table 2 Voltage information of photovoltaic access point and photovoltaic output reduction information when voltage control strategy is adopted

[0241] node Maximum voltage / pu Minimum voltage / pu Cumulative reduction in photovoltaic output / kW 16 1.0529 0.9337 2101.67 18 1.0528 0.9316 7055 31 1.0578 0.9353 826.67 33 1.0627 0.9344 961.67

[0242] Fig. 9 The voltage change of the photovoltaic access point of the system for 24 hours before the control strategy is adopted. Fig.10 The voltage change of the photovoltaic access point of the system after adopting the control strategy for 24 hours is shown in Figure 2. Fig. 9 It can be seen that when the control strategy is not adopted, the voltage exceeds the limit at 9 to 17 o'clock within 24 hours; Fig.10 It can be seen that the voltage at 24 moments after the control strategy was adopted was within the voltage range allowed for normal operation of the distribution network.

[0243] Fig.11 This is a comparison of the distributed photovoltaic output of the system for 24 hours before and after the voltage control strategy is adopted. It can be seen from the figure that the distributed photovoltaic output is significantly reduced from 9:00 to 17:00.

[0244] Fig.12 This figure compares the system's 24-hour active network loss before and after the voltage control strategy is adopted. It can be seen from the figure that after the voltage control strategy is adopted, the active network loss from 9 to 17 o'clock is significantly reduced, which effectively promotes energy saving and loss reduction of the power grid.

[0245] Fig.13 The figure shows the comparison of the HELM1 voltage stability index of the system for 24 hours before and after the voltage control strategy is adopted. It can be seen from the figure that the HELM1 voltage stability index at 9 to 17 hours is significantly reduced after the voltage control strategy is adopted, which effectively improves the voltage stability of the system.

[0246] from Figures 9 to 13It can be seen that for the voltage control problem after distributed photovoltaics are connected to the distribution network, the voltage control method of the patented invention can be used to ensure that the voltage is controlled within the limit range, and to reduce the reduction of photovoltaics as much as possible, improve the absorption of photovoltaics, reduce network losses, and improve voltage stability.

Claims

1. A voltage control method for distributed photovoltaic power generation based on HELM stability criterion, characterized in that: The following steps are involved: Step 1: Establish a voltage control model for distributed photovoltaic power generation in the distribution network, including objective functions and constraints. The objective function includes the active power reduction of distributed photovoltaic power generation, active network loss and voltage stability index based on the holomorphic function embedding method; the constraints include power flow equation constraints, node voltage constraints and voltage stability index constraints; Step 2: Use the HELM method to calculate the power flow of the distribution network including distributed photovoltaic power generation as the power flow constraint condition of the voltage control optimization model of distributed photovoltaic power generation; Step 3: Use the HELM method to calculate the sensitivity of each order of node voltage as the inequality constraint condition and voltage stability index of the voltage control model of distributed photovoltaic power generation; Step 4: Using genetic algorithm to solve and determine the active power reduction amount, network loss and voltage stability index of distributed photovoltaic power generation according to the objective function and constraint conditions; In step 1, the minimum active reduction of distributed photovoltaic power generation is selected as the optimization objective function, and the expression is: Where N PV is the node set connected to distributed photovoltaic in the distribution network, P cut is the active power reduction of distributed photovoltaic power generation, and P PV,n are the maximum active output power of distributed photovoltaic power generation and the actual active output power of distributed photovoltaic power generation at node n respectively; In step 1, for active network loss, the minimum network loss after reducing the distributed photovoltaic output 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 Its reactive power; The best voltage stability after reducing the output of distributed photovoltaic power 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. In the formula, VSI HELM1i is the voltage stability index of node i, is the sensitivity of the second-order component of the voltage s at node i to the reactive power injected into node j, is the sensitivity of the third-order component of the voltage at node i to the reactive power injected into node j, and real is the real part of the corresponding vector; 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, multiple goals are subjectively weighted, the weights of each sub-goal are determined, and the objective function is unified; f=w1f1+w2f2+w3f3 (8) In the formula, w i is the weight coefficient, w1+w2+w3=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: 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 voltage control model of distributed photovoltaic power generation: 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 is determined based on the value. 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 voltage control method for distributed photovoltaic power generation based on HELM stability criterion according to claim 1, 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 the nodes in the network.

3. The voltage control method for distributed photovoltaic power generation based on HELM stability criterion according to claim 1, characterized in that: The node voltage constraint is: U i,min U i U i,max (5) In the formula, U i,min , U i,max are the lower and upper limits of the voltage at node i respectively.

4. The voltage control method for distributed photovoltaic power generation based on HELM stability criterion according to claim 1, characterized in that: The voltage stability constraint is: Where VSI HELM2i is the HELM voltage stability collapse indicator of node i, is the sensitivity of the third-order component of the voltage s at node i to the reactive power injected into node j, is the sensitivity of the fifth-order component of the voltage at node i to the reactive power injected into node j, and real is the real part of the corresponding vector.

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