A method and system for site selection and capacity determination analysis of reactive devices in high-cable-rate urban power grids

Abstract

The present invention belongs to the technical field of reactive device site selection and capacity determination, and specifically relates to a method and system for site selection and capacity determination analysis of reactive devices in high-cable-rate urban power grids, the method comprising establishing a mathematical model for calculating the voltage sensitivity and loss sensitivity of the power grid, and converting the voltage sensitivity and loss sensitivity into a standard form by normalization; using an entropy weight adaptive decision method to evaluate the multi-objective weights involved in the mathematical model, forming a multi-objective site selection model based on voltage and loss sensitivity as an upper model; establishing a capacity planning model for reactive compensation devices based on minimizing economic costs considering power quality as a lower model; combining the upper model and the lower model to form a double-layer iterative model for site selection and capacity determination of reactive compensation devices in high-cable-rate urban power grids based on voltage and loss sensitivity; based on the double-layer iterative model, obtaining a reactive device site selection and capacity determination plan. The present invention can effectively improve the power quality and economy of the power grid.

Description

Technical Field

[0001] The invention belongs to the technical field of reactive device site selection and capacity determination, and in particular relates to a method and system for site selection and capacity determination analysis of reactive devices in a high-cable-rate urban power grid. Background Art

[0002] With the acceleration of urbanization, the demand for electricity in cities continues to increase. As the infrastructure for the operation of modern cities, the stability and efficiency of electricity directly affect the economic development of cities and the quality of life of residents. However, in cities with high cable rates, the problem of reactive power is particularly prominent due to the electrical characteristics of cables. The flow of reactive power may increase the loss of the power grid, reduce the quality of power supply, and even cause the voltage collapse of the power grid. This puts higher demands on the stability and efficiency of the power system. In order to ensure the stability and efficiency of urban power supply, reduce the flow of reactive power in the power grid, reduce power grid losses, and improve power supply quality, it is particularly important to study reactive power compensation technology in cities with high cable rates. Through reactive compensation, the reactive power in the power grid can be balanced, the power factor of the power grid can be improved, and the operation of the power grid can be improved.

[0003] The site selection of reactive power compensation devices directly affects their compensation effect and economy. Reasonable site selection can maximize the role of reactive power compensation devices, improve the power factor of the power grid, reduce power grid losses, and improve power quality. However, unreasonable site selection may lead to poor compensation effects and even waste of resources. Through reasonable site selection and configuration of reactive power compensation devices, the reactive power in the power grid can be balanced, voltage fluctuations and harmonic pollution can be reduced, and the stability and reliability of the power system can be improved. This is of great significance for ensuring urban power supply and preventing power grid failures.

[0004] At present, there are many comprehensive evaluation methods for multiple objectives, such as fuzzy analytic hierarchy process, superior and inferior solution distance method, data envelopment analysis method, entropy weight method, grey correlation analysis method, etc. Among them, entropy weight method belongs to objective weighting method, which can objectively and accurately evaluate the weights of various indicators of multi-objective optimization problems. This is a multi-factor decision analysis method, which determines the weights of each factor by calculating the information entropy of each factor, thereby solving the multi-factor decision problem. Adaptive decision emphasizes that the system can adjust the decision in real time according to the changes in the actual situation. In entropy weight adaptive decision, since the weights of each factor are dynamically calculated according to its information entropy, when the amount of information or importance of certain factors changes, the system can automatically adjust the weights of these factors, so as to make decisions that are more in line with the current situation. However, in existing research, these methods have not been well combined with the site selection and capacity determination of reactive power devices. Summary of the invention

[0005] In view of the above deficiencies in the prior art, the present invention provides a method and system for site selection and capacity determination analysis of reactive devices in a high-cable-rate urban power grid, which can effectively improve the power quality and economy of the power grid.

[0006] To achieve the above purpose, the technical solution adopted by the present invention is a method for site selection and capacity determination of reactive power devices in a high cable rate urban power grid, comprising the following steps:

[0007] S1. Establish a mathematical model for calculating the voltage sensitivity and loss sensitivity of the power grid, and convert the voltage sensitivity and loss sensitivity into a standard form through normalization;

[0008] S2, using the entropy weight adaptive decision method to evaluate the multi-objective weights involved in the mathematical model of S1, forming a multi-objective site selection model based on voltage and loss sensitivity as the upper model;

[0009] S3. Establishing a capacity planning model of reactive power compensation device based on minimizing economic cost considering power quality as a lower model;

[0010] S4, combining the upper model and the lower model to form a double-layer iterative model for site selection and capacity determination of reactive power compensation devices in high-cable-rate urban power grids based on voltage and loss sensitivity;

[0011] S5. Based on the double-layer iterative model, obtain the reactive power device site selection and capacity determination plan.

[0012] As a preferred solution of the present invention, in S1, the process of establishing a mathematical model for calculating the voltage sensitivity and loss sensitivity of the power grid is:

[0013] S11. Line loss of power grid It is expressed as:

[0014] (1);

[0015] In the formula, , , are the active power, reactive power and voltage amplitude at the sending end of the sth line respectively; is the resistance of the sth line, is the set of all lines;

[0016] S12, Ignore the influence of line loss changes caused by changes in load active and reactive power on branch power, assume that the node voltage is the rated voltage, and assume that the number of lines and nodes is the same, and the line number is consistent with its terminal node number; when the active power of the load at node i changes with and When the amount changes, the line loss changes It is expressed as:

[0017] (2);

[0018] In the formula, , Respectively represent the changes in active power and reactive power of the power grid at node i; is the set of lines from node i to the grid source node; n is the number of lines;

[0019] S13, when the active power of the load at node i changes with and When the amount changes, the voltage change at node m It is expressed as:

[0020] (3);

[0021] (4);

[0022] (5);

[0023] In the formula, is the voltage obtained from the initial power flow calculation of node m; is the node set from node m to the grid source node; It is the first node with a horizontal direction in the node set from node m to the grid source node; is the voltage change at node i; Is a node The voltage change at is the set of lines from node m to the grid source node; is the reactance of the sth line;

[0024] S14. For radial power grid, when the active power and reactive power of the load at node i change with and When the amount changes, the voltage at node m changes It is expressed as:

[0025] (6);

[0026] In the formula, , They are , The multiplication factors are expressed as:

[0027] (7);

[0028] (8);

[0029] In the formula, , Is a node The set of nodes that are connected to the grid source node.

[0030] As a preferred solution of the present invention, in S1, the Min-Max normalization is used to convert the voltage sensitivity of each node into a standard form through quantization, which is expressed as:

[0031] (9);

[0032] In the formula, is the voltage change at node m caused by the power change of the load at node i at time t; T is the number of moments; The number of nodes that can be addressed as grid coupling points; is the number of grid nodes; A set of addressable nodes for coupling points; It is the normalized value of the sum of all node voltage changes caused by the power change of the load at node i; It is the maximum value of the sum of all node voltage changes caused by the power of the load at each node changing sequentially; It is the minimum value of the sum of all node voltage changes caused by the power of the load at each node changing sequentially.

[0033] As a preferred solution of the present invention, in S1, the Min-Max normalization is used to convert the loss sensitivity of each node into a standard form by quantization, which is expressed as:

[0034] (10);

[0035] In the formula, is the normalized value of all line losses caused by the power change of the load at node i; is the magnitude of all line losses caused by the power change of the load at node i; It is the minimum value of the sum of all line losses caused by the power of the load at each node changing sequentially; It is the maximum value of the sum of all line losses caused by the sequential changes in the load power at each node.

[0036] As a preferred embodiment of the present invention, in S2, the process of evaluating the multi-objective weights involved in the mathematical model of S1 by using the entropy weight adaptive decision method is as follows:

[0037] S21. Based on the entropy weight adaptive decision-making method, the voltage sensitivity weight is expressed as:

[0038] (11);

[0039] In the formula, is the node voltage sensitivity weight; is the information entropy of the voltage sensitivity index; K is the number of evaluation objects, that is, the number of addressable nodes; is the information entropy of the dth evaluation index; D is the number of evaluation indicators; is an intermediate variable in the process of calculating voltage sensitivity weights. If ,So ;

[0040] S22, loss sensitivity weight is expressed as:

[0041] (12);

[0042] In the formula, is the line loss sensitivity weight; is the information entropy of the line loss sensitivity indicator; is an intermediate variable in the process of calculating the loss sensitivity weight. If ,So ;

[0043] S23, the multi-objective site selection model based on voltage and loss sensitivity is expressed as:

[0044] (13).

[0045] As a preferred solution of the present invention, in S3, the objective function of the capacity planning model is expressed as:

[0046] (14);

[0047] In the formula, is the unit cost coefficient of electricity purchase; is the power purchased by the power grid during period t; is the unit power cost coefficient of line loss; is the power loss of the power grid line during period t; is the voltage over-limit cost coefficient; It is the voltage off-line deviation; is the unit capacity reactive power compensation cost of the static reactive power compensator SVC, expressed as:

[0048] (15);

[0049] In the formula, is the capacity of the SVC; , , , is the cost coefficient of SVC.

[0050] As a preferred embodiment of the present invention, , , , The values ​​are 6.38, 0.003, -0.3051, and 127.38 respectively.

[0051] As a preferred solution of the present invention, the constraints of the capacity planning model are:

[0052] The active power balance constraint of the node is expressed as:

[0053] (16);

[0054] In the formula, is the node at time t Active power of Represents the set of all nodes in the power network; Indicates that at time t, Active power of represents the resistance of line ki; It represents the square of the current flowing through line ki at time t; represents the active load at node i at time t; represents the set of upper-level power grid nodes connected to node i; represents the set of wind turbines connected to node i; represents the set of PVs connected to node i; represents the active power injected or utilized by the upper grid node x at time t; represents the active power injected by wind turbine wt at time t; Represents the active power injected by photovoltaic pv at time t;

[0055] The reactive power balance constraint of the node is expressed as:

[0056] (17);

[0057] In the formula, is the node at time t Reactive power; Indicates that at time t, Reactive power; represents the reactive load at node i at time t; represents the reactive power injected or absorbed by the upper grid node x at time t; represents the set of SVCs connected to node i; represents the reactive power generated by SVC at time t, represents the reactive power injected by wt at time t, represents the reactive power injected by pv at time t;

[0058] The node voltage limit constraint is expressed as:

[0059] (18);

[0060] In the formula, is the voltage amplitude of node j at time t; is the voltage amplitude of node i at time t; is the voltage amplitude of the root node at time t; is the reactance of line ij; represents the resistance of line ij;

[0061] The inequality constraints of the capacity planning model are expressed as:

[0062] (19);

[0063] In the formula, , are the upper and lower limits of the voltage at node j at time t respectively;

[0064] The power transfer limit constraint is expressed as:

[0065] (20);

[0066] (twenty one);

[0067] In the formula, , are the maximum and minimum limits of active power transmitted by the upper power grid at time t respectively; , They are the maximum and minimum limits of reactive power transmitted by the upper power grid at time t;

[0068] The SVC issues a reactive power limit constraint, expressed as:

[0069] (twenty two);

[0070] In the formula, , They are the minimum and maximum limits of reactive power that can be generated by SVC;

[0071] The power limit constraint issued by wt is expressed as:

[0072] (twenty three);

[0073] (twenty four);

[0074] In the formula, , They are the maximum and minimum limits of the active power wt at time t respectively; , They are the maximum and minimum limits of reactive power wt at time t respectively;

[0075] The power limit constraint issued by pv is expressed as:

[0076] (25);

[0077] (26);

[0078] In the formula, , They are the maximum and minimum limits of the active power of pv at time t respectively; , They are the maximum and minimum limits of the reactive power of pv at time t respectively.

[0079] As a preferred solution of the present invention, in S5, the process of obtaining the reactive power device site selection and capacity determination plan is as follows:

[0080] S51, inputting grid parameters, and importing new energy output and load data;

[0081] S52, optimize the grid load, use the Gurobi solver to solve with an error of 0.01%, and obtain the grid loss data when the grid is in normal operation voltage;

[0082] S53, randomly selecting a grid node, connecting it to the SVC, and increasing the grid load proportionally, and optimizing the capacity of the SVC based on the lower layer model;

[0083] S54, set the number of iterations z=1, and the location node when the number of iterations is z is expressed as ;

[0084] S55, when When the node voltage sensitivity and line loss sensitivity are calculated, the SVC operation scheme is connected to each node in turn based on the upper model;

[0085] S56, based on the upper model, the target weight is calculated using the entropy weight adaptive decision method to obtain the current optimal node;

[0086] S57, again based on the lower layer model, perform capacity optimization of the SVC to obtain the current optimal operation plan;

[0087] S58, the number of iterations z=z+1, iterative calculation is performed again until the iteration termination condition is met, and the final optimal operation plan is output, which is the reactive power device site selection and capacity determination plan.

[0088] A high cable rate urban power grid reactive device site selection and capacity analysis system, used to implement the above method, is characterized by comprising:

[0089] A sensitivity calculation module is used to establish a mathematical model for calculating the voltage sensitivity and loss sensitivity of the power grid, and convert the voltage sensitivity and loss sensitivity into a standard form through normalization;

[0090] The double-layer iterative model building module uses the entropy weight adaptive decision-making method to evaluate the multi-objective weights involved in the mathematical model of S1, and forms a multi-objective site selection model based on voltage and loss sensitivity as the upper model; a capacity planning model for reactive power compensation devices based on minimizing economic costs considering power quality is established as the lower model; the upper model and the lower model are combined to form a double-layer iterative model based on voltage and loss sensitivity for site selection and capacity determination of reactive power compensation devices in high-cable-rate urban power grids;

[0091] The scheme acquisition module obtains the reactive power device site selection and sizing scheme based on a two-layer iterative model.

[0092] The algorithm involved in the present invention can be executed by an electronic device. The electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. The algorithm is implemented by executing the program by the processor.

[0093] The beneficial effects of the present invention are:

[0094] The present invention effectively improves the power quality and economy of the power grid by constructing a double-layer iterative model. The method first uses an entropy weight adaptive decision-making method to evaluate the weights of multiple objectives, ensuring the objectivity and accuracy of the decision-making process. Then, by optimizing the site selection and capacity of the reactive power compensation device, the economic cost is minimized while ensuring the power quality. These improvements not only improve the stability and power supply quality of the power system, but also have a positive impact on the energy supply and economic development of the city. It has been verified that the present invention can significantly reduce the voltage fluctuation and line loss of the power grid, with the voltage fluctuation reduced by 21.652% and the line loss reduced by 14.216%. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 It is a schematic diagram of the process of the method of the present invention;

[0096] Figure 2 It is a schematic diagram of the structure of a high-cable-rate urban power grid during the verification process of the present invention;

[0097] Figure 3It is a schematic diagram of the site selection results of the high cable rate urban power grid reactive compensation device based on the single objectives of voltage sensitivity and loss sensitivity in the verification process of the present invention;

[0098] Figure 4 It is a schematic diagram of site selection of reactive power compensation device for high cable rate urban power grid based on voltage and loss sensitivity in the verification process of the present invention;

[0099] Figure 5 It is a schematic diagram of the grid voltage without reactive power compensation device under the initial load state during the verification process of the present invention;

[0100] Figure 6 It is a schematic diagram of the grid voltage after the site selection and capacity determination of the reactive power compensation device based on voltage sensitivity in the verification process of the present invention;

[0101] Figure 7 It is a schematic diagram of the grid voltage after the site selection and capacity determination of the reactive power compensation device based on loss sensitivity in the verification process of the present invention;

[0102] Figure 8 It is a schematic diagram of the grid voltage after the site selection and capacity determination of the reactive power compensation device based on the voltage-loss sensitivity in the verification process of the present invention;

[0103] Fig. 9 It is a schematic diagram of the compensation power of the reactive compensator during the verification process of the present invention;

[0104] Fig.10 It is a module schematic diagram of the system of the present invention. DETAILED DESCRIPTION

[0105] The embodiments of the present invention are further described below in conjunction with the accompanying drawings:

[0106] Example 1

[0107] like Figure 1 As shown, a method for site selection and capacity determination analysis of reactive power devices in a high-cable-rate urban power grid includes the following steps:

[0108] S1. Establish a mathematical model for calculating the voltage sensitivity and loss sensitivity of the power grid, and convert the voltage sensitivity and loss sensitivity into a standard form through normalization;

[0109] S2, using the entropy weight adaptive decision method to evaluate the multi-objective weights involved in the mathematical model of S1, forming a multi-objective site selection model based on voltage and loss sensitivity as the upper model;

[0110] S3. Establishing a capacity planning model of reactive power compensation device based on minimizing economic cost considering power quality as a lower model;

[0111] S4, combining the upper model and the lower model to form a double-layer iterative model for site selection and capacity determination of reactive power compensation devices in high-cable-rate urban power grids based on voltage and loss sensitivity;

[0112] S5. Based on the double-layer iterative model, obtain the reactive power device site selection and capacity determination plan.

[0113] In S1, the process of establishing a mathematical model for calculating the voltage sensitivity and loss sensitivity of the power grid is:

[0114] S11. Line loss of power grid It is expressed as:

[0115] (1);

[0116] In the formula, , , are the active power, reactive power and voltage amplitude at the sending end of the sth line respectively; is the resistance of the sth line, is the set of all lines;

[0117] S12. Considering that the proportion of line loss in branch power is very small, the influence of line loss change caused by load active and reactive power change on branch power is ignored. Assuming that the node voltage is the rated voltage, and assuming that the number of lines and nodes is the same, the line number is consistent with its terminal node number; when the active power of the load at node i changes with and When the amount changes, the line loss changes It is expressed as:

[0118] (2);

[0119] In the formula, , Respectively represent the changes in active power and reactive power of the power grid at node i; is the set of lines from node i to the grid source node; n is the number of lines;

[0120] S13, when the active power of the load at node i changes with and When the amount changes, the voltage change at node m It is expressed as:

[0121] (3);

[0122] (4);

[0123] (5);

[0124] In the formula, is the voltage obtained from the initial power flow calculation of node m; is the node set from node m to the grid source node; It is the first node with a horizontal direction in the node set from node m to the grid source node; is the voltage change at node i; Is a node The voltage change at is the set of lines from node m to the grid source node; is the reactance of the sth line;

[0125] S14. For radial power grid, when the active power and reactive power of the load at node i change with and When the amount changes, the voltage at node m changes It is expressed as:

[0126] (6);

[0127] In the formula, , They are , The multiplication factors are expressed as:

[0128] (7);

[0129] (8);

[0130] In the formula, , Is a node The set of nodes that are connected to the grid source node.

[0131] The voltage and loss sensitivity of the load connected to any node can be calculated by equations (1) to (8). In the specific calculation, the historical operation data set of the high cable rate power grid and the predicted operation data set of the high cable rate power grid can be obtained to calculate the voltage sensitivity and loss sensitivity of each node of the power grid. The node voltage and distribution network flow can be obtained by an initial flow calculation.

[0132] In S1, Min-Max normalization is used to convert the voltage sensitivity of each node into a standard form through quantization, which is expressed as:

[0133] (9);

[0134] In the formula, is the voltage change at node m caused by the power change of the load at node i at time t; T is the number of moments; The number of nodes that can be addressed as grid coupling points; is the number of grid nodes; A set of addressable nodes for coupling points; It is the normalized value of the sum of all node voltage changes caused by the power change of the load at node i; It is the maximum value of the sum of all node voltage changes caused by the power of the load at each node changing sequentially; It is the minimum value of the sum of all node voltage changes caused by the power of the load at each node changing sequentially.

[0135] In S1, Min-Max normalization is used to convert the loss sensitivity of each node into a standard form through quantization, which is expressed as:

[0136] (10);

[0137] In the formula, is the normalized value of all line losses caused by the power change of the load at node i; is the magnitude of all line losses caused by the power change of the load at node i; It is the minimum value of the sum of all line losses caused by the power of the load at each node changing sequentially; It is the maximum value of the sum of all line losses caused by the sequential changes in the load power at each node.

[0138] For the multi-objective problem of voltage-loss sensitivity in the upper-level planning, the system model cannot be solved directly. The entropy weight method can objectively and accurately evaluate the weights of each indicator of the multi-objective optimization problem. This is a multi-factor decision analysis method. It determines the weight of each factor by calculating the information entropy of each factor, thereby solving the multi-factor decision problem. In entropy weight adaptive decision-making, the entropy value of each indicator reflects the size and importance of its information. The larger the entropy value of the indicator, the smaller its weight, indicating that the indicator has less influence in the decision. Adaptive decision-making emphasizes that the system can adjust the decision in real time according to changes in actual conditions. In entropy weight adaptive decision-making, since the weights of each factor are dynamically calculated based on its information entropy, when the information amount or importance of certain factors changes, the system can automatically adjust the weights of these factors, thereby making decisions that are more in line with the current situation.

[0139] In S2, the process of using the entropy weight adaptive decision-making method to evaluate the multi-objective weights involved in the mathematical model of S1 is:

[0140] S21. Based on the entropy weight adaptive decision-making method, the voltage sensitivity weight is expressed as:

[0141] (11);

[0142] In the formula, is the node voltage sensitivity weight; is the information entropy of the voltage sensitivity index; K is the number of evaluation objects, that is, the number of addressable nodes; is the information entropy of the dth evaluation index; D is the number of evaluation indicators; is an intermediate variable in the process of calculating voltage sensitivity weights. If ,So ;

[0143] S22, loss sensitivity weight is expressed as:

[0144] (12);

[0145] In the formula, is the line loss sensitivity weight; is the information entropy of the line loss sensitivity indicator; is an intermediate variable in the process of calculating the loss sensitivity weight. If ,So ;

[0146] S23, the multi-objective site selection model based on voltage and loss sensitivity is expressed as:

[0147] (13).

[0148] The load forecast data is used to optimize the hourly comprehensive dispatch for the next day, taking the comprehensive cost of power quality as the control target, considering the power purchase cost of the power grid, line power loss cost, node voltage over-limit penalty cost, and static VAR compensator construction cost.

[0149] In S3, the objective function of the capacity planning model is expressed as:

[0150] (14);

[0151] In the formula, is the unit cost coefficient of electricity purchase; is the power purchased by the power grid during period t; is the unit power cost coefficient of line loss; is the power loss of the power grid line during period t; It is the voltage over-limit cost coefficient, which can adjust the node voltage over-limit penalty level according to the actual grid needs; It is the voltage off-line deviation; is the unit capacity reactive power compensation cost of the static reactive power compensator SVC, expressed as:

[0152] (15);

[0153] In the formula, is the capacity of the SVC; , , , is the cost coefficient of SVC. Different types of reactive power compensation equipment correspond to different coefficients. In this embodiment, , , , The values ​​are 6.38, 0.003, -0.3051, and 127.38 respectively.

[0154] The constraints of the capacity planning model are:

[0155] The active power balance constraint of the node is expressed as:

[0156] (16);

[0157] In the formula, is the node at time t Active power of Represents the set of all nodes in the power network; Indicates that at time t, Active power of represents the resistance of line ki; It represents the square of the current flowing through line ki at time t; represents the active load at node i at time t; represents the set of upper-level power grid nodes connected to node i; represents the set of wind turbines connected to node i; represents the set of PVs connected to node i; represents the active power injected or utilized by the upper grid node x at time t; represents the active power injected by wind turbine wt at time t; Represents the active power injected by photovoltaic pv at time t;

[0158] The reactive power balance constraint of the node is expressed as:

[0159] (17);

[0160] In the formula, is the node at time t Reactive power; Indicates that at time t, Reactive power; represents the reactive load at node i at time t; represents the reactive power injected or absorbed by the upper grid node x at time t; represents the set of SVCs connected to node i; represents the reactive power generated by SVC at time t, represents the reactive power injected by wt at time t, represents the reactive power injected by pv at time t;

[0161] The node voltage limit constraint is expressed as:

[0162] (18);

[0163] In the formula, is the voltage amplitude of node j at time t; is the voltage amplitude of node i at time t; is the voltage amplitude of the root node at time t; is the reactance of line ij; represents the resistance of line ij;

[0164] The inequality constraints of the capacity planning model are expressed as:

[0165] (19);

[0166] In the formula, , are the upper and lower limits of the voltage at node j at time t respectively;

[0167] The power transfer limit constraint is expressed as:

[0168] (20);

[0169] (twenty one);

[0170] In the formula, , are the maximum and minimum limits of active power transmitted by the upper power grid at time t respectively; , They are the maximum and minimum limits of reactive power transmitted by the upper power grid at time t;

[0171] The SVC issues a reactive power limit constraint, expressed as:

[0172] (twenty two);

[0173] In the formula, , They are the minimum and maximum limits of reactive power that can be generated by SVC;

[0174] The power limit constraint issued by wt is expressed as:

[0175] (twenty three);

[0176] (twenty four);

[0177] In the formula, , They are the maximum and minimum limits of the active power wt at time t respectively; , They are the maximum and minimum limits of reactive power wt at time t respectively;

[0178] The power limit constraint issued by pv is expressed as:

[0179] (25);

[0180] (26);

[0181] In the formula, , They are the maximum and minimum limits of the active power of pv at time t respectively; , They are the maximum and minimum limits of the reactive power of pv at time t respectively.

[0182] The reactive compensation device is sited in the high-cable-rate urban power grid based on voltage and loss sensitivity, and is installed at the optimal node. The capacity of the reactive compensation device is optimized with the goal of minimizing the economic cost of power quality. The optimal operating capacity and plan of the device are obtained and passed back to the upper-level model. The upper-level model selects a site again based on the operating plan, and iterates until the two site selection nodes are the same, and the iteration is exited.

[0183] In S5, the process of obtaining the reactive power device site selection and capacity determination plan is as follows:

[0184] S51, inputting grid parameters, and importing new energy output and load data;

[0185] S52, optimize the grid load, use the Gurobi solver to solve with an error of 0.01%, and obtain the grid loss data when the grid is in normal operation voltage;

[0186] S53, randomly selecting a grid node, connecting it to the SVC, and increasing the grid load proportionally, and optimizing the capacity of the SVC based on the lower layer model;

[0187] S54, set the number of iterations z=1, and the location node when the number of iterations is z is expressed as ;

[0188] S55, when When the node voltage sensitivity and line loss sensitivity are calculated, the SVC operation scheme is connected to each node in turn based on the upper model;

[0189] S56, based on the upper model, the target weight is calculated using the entropy weight adaptive decision method to obtain the current optimal node;

[0190] S57, again based on the lower layer model, perform capacity optimization of the SVC to obtain the current optimal operation plan;

[0191] S58, the number of iterations z=z+1, iterative calculation is performed again until the iteration termination condition is met, and the final optimal operation plan is output, which is the reactive power device site selection and capacity determination plan.

[0192] The verification process is:

[0193] This verification example simulates the feasibility of the proposed method for site selection and sizing of reactive power compensation devices in high-cable-rate urban power grids based on voltage and loss sensitivity. The simulations in this verification example are all implemented on an experimental computer using the MATLAB platform. The computer is equipped with an Intel Core i9-14900K processor, 96GB of RAM, and a clock frequency of 3.20GHz.

[0194] This verification example uses the IEEE14-node network to verify the feasibility of the method proposed in the present invention. Figure 2 As shown in Figure 1, the base voltage of the system is 12.66 kV, and the safe operating voltage range allowed by the PDN is set to [0.95 pu, 1.05 pu]. PV is connected to nodes 9 and 12, and wind turbines are connected to nodes 4 and 14. The simulation verification is carried out using a 24-hour time node. The power generation data of the photovoltaic wind turbine on a typical day is shown in Figure 1. Figure 6 The peak electricity price of 10:00-14:00 and 17:00-21:00 is set at 0.956 yuan / KWh, the flat electricity price of 7:00-9:00, 15:00-16:00 and 22:00-24:00 is set at 0.703 yuan / KWh, and the valley electricity price of 1:00-6:00 is set at 0.494 yuan / KWh.

[0195] The impact of access point site selection methods on system operation:

[0196] In order to verify the impact of the voltage-loss sensitivity site selection method on the operation of urban power grids with high cable rates, the voltage sensitivity site selection, loss sensitivity site selection and voltage-loss sensitivity multi-objective site selection are analyzed respectively. In the voltage sensitivity site selection and loss sensitivity site selection, the connection location of the coupling point is selected with the minimum sum of the voltage fluctuation amplitudes of each node and the minimum sum of the loss fluctuations of each line at 24 moments after the coupling point load is connected to the power grid as the goals. The voltage-loss sensitivity multi-objective site selection method uses the entropy weight method to determine the respective weights of the voltage sensitivity and loss sensitivity after the coupling point load is connected, and selects the node with the minimum target value to determine the connection location of the coupling point. In order to save resources, such as Figure 3-Figure 4 Shown are the sensitivity fluctuation curves of the voltage sensitivity site selection method and the loss sensitivity site selection method, and the sensitivity scatter plot of the voltage-loss sensitivity site selection method.

[0197] Figure 3 The blue curve in the middle is the sensitivity amplitude of each node under the site selection method based on voltage sensitivity. It can be seen from the figure that the node with the smallest voltage sensitivity is node 2. This is because node 2 is close to the source node, and the change of its injected power has little effect on the system voltage. This type of node has little effect on the voltage. It can be found from the figure that the farther away from the source node, the higher the voltage sensitivity of the node, so under the voltage sensitivity site selection method, node 2 is the best choice.

[0198] Figure 3 The yellow curve in the middle is the sensitivity amplitude of each node under the site selection method based on loss sensitivity. For the site selection method based on loss sensitivity, it can be seen from the figure that node 7 is the node with the smallest loss sensitivity after the reactive power compensator is connected to the power grid. This is because the reactive power output of the new energy at node 9 is large, resulting in reactive power reverse transmission, forming a situation where the reactive power of lines 4, 5, and 6 is forwarded, and the reactive power of lines 7 and 8 is reversed, making node 7 in a reactive valley state. Therefore, installing the reactive compensator at node 7 can reduce the transmission of line reactive power, thereby reducing line losses. The new energy output of nodes 12 and 14 causes the power of lines 4, 9, 11 and lines 4, 12, and 13 to be reversed. Installing a reactive compensation device near this node will only increase the reactive transmission power and lead to increased losses.

[0199] For the above voltage sensitivity site selection method and loss sensitivity site selection method, their site selection results are targeted at voltage / loss, and it is inevitable that they will lose sight of one while focusing on the power quality of the power grid. As shown in Table 1, although the voltage sensitivity site selection ensures the optimality of voltage fluctuation, the maximum voltage fluctuation of each node is 0.01014 (unit value), the minimum is 0.00041, and the average is 0.004. Although the optimality of voltage quality is guaranteed among the three site selection methods, the cost is that the PDN loss is 29.0% higher than that of the loss sensitivity site selection scheme. Similarly, although the loss sensitivity site selection scheme ensures the lowest overall power grid loss, its maximum and average node voltage fluctuations are 211.1% and 212.6% higher than those of the voltage sensitivity site selection scheme, respectively.

[0200] Table 1 Comparison of optimization results of different site selection methods

[0201]

[0202] Compared with voltage sensitivity site selection and loss sensitivity site selection, the voltage and loss sensitivity multi-objective site selection scheme based on entropy weight adaptive decision-making balances the characteristics of the two. The scatter plot of the site selection results is shown in Figure 2. Figure 4 As shown in the figure, the entropy weight adaptive decision method is used to determine the weights of voltage sensitivity and loss sensitivity, which are decomposed into 4.367 and 5.633. Finally, node 5 is determined to be the node with the smallest loss sensitivity after the reactive compensator is connected to the PDN. This result makes a compromise between the voltage sensitivity and loss sensitivity site selection results. It is closer to the source node than the loss sensitivity site selection result, thereby ensuring the stability of the grid voltage, and is selected near the reactive power valley node to reduce the line reactive power transmission and line loss. The specific results are shown in Table 1. The average voltage fluctuation of each node is 0.00691, which is 44.73% lower than that of the loss sensitivity site selection scheme; and the grid loss is 0.00678, which is 9.2% lower than that of the voltage sensitivity site selection scheme.

[0203] Figure 5 It is a schematic diagram of the grid voltage without reactive power compensation device under the initial load state; Figure 6 This is a schematic diagram of the grid voltage after the site selection and capacity determination of the reactive power compensation device based on voltage sensitivity. Figure 7 This is a schematic diagram of the grid voltage after the site selection and capacity determination of the reactive power compensation device based on loss sensitivity. Figure 8This is a schematic diagram of the grid voltage after the reactive compensation device is sited and capped based on voltage-loss sensitivity. It can be seen from the figure that under the voltage sensitivity site selection strategy, although the load is larger than the original state, the reactive compensator minimizes the grid voltage fluctuation, while under the loss sensitivity site selection strategy, the grid voltage fluctuates greatly. Although the loss sensitivity site selection strategy ensures the minimum grid loss, the cost is excessive voltage fluctuation. Relatively speaking, the water-electricity coupling state grid voltage under the voltage-loss sensitivity site selection strategy can not only maintain the stability of the grid voltage, but also reduce the grid loss to the optimum. The feasibility of this site selection method is verified.

[0204] Fig. 9 This is a schematic diagram of the reactive compensator compensation power. Affected by the 9-node photovoltaic output, the photovoltaic output is lost at night, and the reactive compensator compensation power is large. During the day, because the photovoltaic output is sufficient, the reactive compensator reduces the power output. It can be seen from the figure that the output of the reactive compensator is basically consistent with the output law of the photovoltaic.

[0205] Example 2

[0206] like Fig.10 As shown, a high cable rate urban power grid reactive device site selection and capacity analysis system is used to implement the method described in Example 1, including:

[0207] A sensitivity calculation module is used to establish a mathematical model for calculating the voltage sensitivity and loss sensitivity of the power grid, and convert the voltage sensitivity and loss sensitivity into a standard form through normalization;

[0208] The double-layer iterative model building module uses the entropy weight adaptive decision-making method to evaluate the multi-objective weights involved in the mathematical model of S1, and forms a multi-objective site selection model based on voltage and loss sensitivity as the upper model; a capacity planning model for reactive power compensation devices based on minimizing economic costs considering power quality is established as the lower model; the upper model and the lower model are combined to form a double-layer iterative model based on voltage and loss sensitivity for site selection and capacity determination of reactive power compensation devices in high-cable-rate urban power grids;

[0209] The scheme acquisition module obtains the reactive power device site selection and sizing scheme based on a two-layer iterative model.

Claims

1. A method for site selection and capacity determination of reactive power devices in high-cable-rate urban power grids, characterized in that The following steps are involved: S1. Establish a mathematical model for calculating the voltage sensitivity and loss sensitivity of the power grid, and convert the voltage sensitivity and loss sensitivity into a standard form through normalization; S2, using the entropy weight adaptive decision method to evaluate the multi-objective weights involved in the mathematical model of S1, forming a multi-objective site selection model based on voltage and loss sensitivity as the upper model; S3. Establishing a capacity planning model of reactive power compensation device based on minimizing economic cost considering power quality as a lower model; S4, combining the upper model and the lower model to form a double-layer iterative model for site selection and capacity determination of reactive power compensation devices in high-cable-rate urban power grids based on voltage and loss sensitivity; S5. Based on the double-layer iterative model, obtain the reactive power device site selection and capacity determination plan.

2. A method for site selection and capacity determination of reactive power devices in a high cable rate urban power grid according to claim 1, characterized in that: In the above S1, the process of establishing a mathematical model for calculating the voltage sensitivity and loss sensitivity of the power grid is as follows: S11. Line loss of power grid It is expressed as: （1）； In the formula, , , are the active power, reactive power and voltage amplitude at the sending end of the sth line respectively; is the resistance of the sth line, is the set of all lines; S12, Ignore the influence of line loss changes caused by changes in load active and reactive power on branch power, assume that the node voltage is the rated voltage, and assume that the number of lines and nodes is the same, and the line number is consistent with its terminal node number; When the active power of the load at node i changes with and When the amount changes, the line loss changes It is expressed as: （2）； In the formula, , Respectively represent the changes in active power and reactive power of the power grid at node i; is the set of lines from node i to the grid source node; n is the number of lines; S13, when the active power of the load at node i changes with and When the amount changes, the voltage change at node m It is expressed as: （3）； （4）； （5）； In the formula, is the voltage obtained from the initial power flow calculation of node m; is the node set from node m to the grid source node; It is the first node with a horizontal direction in the node set from node m to the grid source node; is the voltage change at node i; Is a node The voltage change at is the set of lines from node m to the grid source node; is the reactance of the sth line; S14. For radial power grid, when the active power and reactive power of the load at node i change with and When the amount changes, the voltage at node m changes It is expressed as: （6）； In the formula, , They are , The multiplication factors are expressed as: （7）； （8）； In the formula, , Is a node The set of nodes that are connected to the grid source node.

3. A method for site selection and capacity determination analysis of reactive devices in a high cable rate urban power grid according to claim 2, characterized in that: In S1, the Min-Max normalization is used to convert the voltage sensitivity of each node into a standard form through quantization, which is expressed as: （9）； In the formula, is the voltage change at node m caused by the power change of the load at node i at time t; T is the number of moments; The number of nodes that can be addressed as grid coupling points; is the number of grid nodes; A set of addressable nodes for coupling points; It is the normalized value of the sum of all node voltage changes caused by the power change of the load at node i; It is the maximum value of the sum of all node voltage changes caused by the power of the load at each node changing sequentially; It is the minimum value of the sum of all node voltage changes caused by the power of the load at each node changing sequentially.

4. A method for site selection and capacity determination of reactive power devices in a high cable rate urban power grid according to claim 3, characterized in that: In S1, Min-Max normalization is used to convert the loss sensitivity of each node into a standard form through quantization, which is expressed as: （10）； In the formula, is the normalized value of all line losses caused by the power change of the load at node i; is the magnitude of all line losses caused by the power change of the load at node i; It is the minimum value of the sum of all line losses caused by the power of the load at each node changing sequentially; It is the maximum value of the sum of all line losses caused by the sequential changes in the load power at each node.

5. A method for site selection and capacity determination of reactive power devices in a high cable rate urban power grid according to claim 4, characterized in that: In S2, the process of using the entropy weight adaptive decision method to evaluate the multi-objective weights involved in the mathematical model of S1 is as follows: S21. Based on the entropy weight adaptive decision-making method, the voltage sensitivity weight is expressed as: （11）； In the formula, is the node voltage sensitivity weight; is the information entropy of the voltage sensitivity index; K is the number of evaluation objects, that is, the number of addressable nodes; is the information entropy of the dth evaluation index; D is the number of evaluation indicators; is an intermediate variable in the process of calculating voltage sensitivity weights. If ,So ; S22, loss sensitivity weight is expressed as: （12）； In the formula, is the line loss sensitivity weight; is the information entropy of the line loss sensitivity indicator; is an intermediate variable in the process of calculating the loss sensitivity weight. If ,So ; S23, the multi-objective site selection model based on voltage and loss sensitivity is expressed as: （13）。 6. A method for site selection and capacity determination analysis of reactive devices in a high cable rate urban power grid according to claim 5, characterized in that: In the above-mentioned S3, the objective function of the capacity planning model is expressed as: （14）； In the formula, is the unit cost coefficient of electricity purchase; is the power purchased by the power grid during period t; is the unit power cost coefficient of line loss; is the power loss of the power grid line during period t; is the voltage over-limit cost coefficient; It is the voltage off-line deviation; is the unit capacity reactive power compensation cost of the static reactive power compensator SVC, expressed as: （15）； In the formula, is the capacity of the SVC; , , , is the cost coefficient of SVC.

7. A method for site selection and capacity determination analysis of reactive devices in a high cable rate urban power grid according to claim 6, characterized in that: , , , The values ​​are 6.38, 0.003, -0.3051, and 127.38 respectively.

8. A method for site selection and capacity determination analysis of reactive devices in a high cable rate urban power grid according to claim 6, characterized in that: The constraints of the capacity planning model are: The active power balance constraint of the node is expressed as: （16）； In the formula, is the node at time t Active power of Represents the set of all nodes in the power network; Indicates that at time t, the node Active power of Indicates the resistance of line ki; It represents the square of the current flowing through line ki at time t; represents the active load at node i at time t; represents the set of upper-level power grid nodes connected to node i; represents the set of wind turbines connected to node i; represents the set of PV connected to node i; represents the active power injected or utilized by the upper grid node x at time t; represents the active power injected by wind turbine wt at time t; Represents the active power injected by photovoltaic pv at time t; The reactive power balance constraint of the node is expressed as: （17）； In the formula, is the node at time t Reactive power; Indicates that at time t, the node Reactive power; represents the reactive load at node i at time t; represents the reactive power injected or absorbed by the upper grid node x at time t; represents the set of SVCs connected to node i; represents the reactive power generated by SVC at time t, represents the reactive power injected by wt at time t, represents the reactive power injected by pv at time t; The node voltage limit constraint is expressed as: （18）； In the formula, is the voltage amplitude of node j at time t; is the voltage amplitude of node i at time t; is the voltage amplitude of the root node at time t; is the reactance of line ij; represents the resistance of line ij; The inequality constraints of the capacity planning model are expressed as: （19）； In the formula, , are the upper and lower limits of the voltage at node j at time t respectively; The power transfer limit constraint is expressed as: （20）； （21）； In the formula, , are the maximum and minimum limits of active power transmitted by the upper power grid at time t respectively; , They are the maximum and minimum limits of reactive power transmitted by the upper power grid at time t; The SVC issues a reactive power limit constraint, expressed as: （22）； In the formula, , They are the minimum and maximum limits of reactive power that can be generated by SVC; The power limit constraint issued by wt is expressed as: （23）； （24）； In the formula, , They are the maximum and minimum limits of the active power wt at time t respectively; , They are the maximum and minimum limits of reactive power wt at time t respectively; The power limit constraint issued by pv is expressed as: （25）； （26）； In the formula, , They are the maximum and minimum limits of the active power of pv at time t respectively; , They are the maximum and minimum limits of the reactive power of pv at time t respectively.

9. A method for site selection and capacity determination analysis of reactive devices in a high cable rate urban power grid according to claim 8, characterized in that: In S5, the process of obtaining the reactive power device site selection and capacity determination plan is as follows: S51, inputting grid parameters, and importing new energy output and load data; S52, optimize the grid load, use the Gurobi solver to solve with an error of 0.01%, and obtain the grid loss data when the grid is in normal operation voltage; S53, randomly selecting a grid node, connecting it to the SVC, and increasing the grid load proportionally, and optimizing the capacity of the SVC based on the lower layer model; S54, set the number of iterations z=1, and the location node when the number of iterations is z is expressed as ; S55, when When the node voltage sensitivity and line loss sensitivity are calculated, the SVC operation scheme is connected to each node in turn based on the upper model; S56, based on the upper model, the target weight is calculated using the entropy weight adaptive decision method to obtain the current optimal node; S57, again based on the lower layer model, perform capacity optimization of the SVC to obtain the current optimal operation plan; S58, the number of iterations z=z+1, iterative calculation is performed again until the iteration termination condition is met, and the final optimal operation plan is output, which is the reactive power device site selection and capacity determination plan.

10. A high cable rate urban power grid reactive device site selection and capacity analysis system, used to implement the method according to any one of claims 1 to 9, characterized in that: include: A sensitivity calculation module is used to establish a mathematical model for calculating the voltage sensitivity and loss sensitivity of the power grid, and convert the voltage sensitivity and loss sensitivity into a standard form through normalization; The double-layer iterative model building module uses the entropy weight adaptive decision-making method to evaluate the multi-objective weights involved in the mathematical model of S1, and forms a multi-objective site selection model based on voltage and loss sensitivity as the upper model; a capacity planning model for reactive power compensation devices based on minimizing economic costs considering power quality is established as the lower model; the upper model and the lower model are combined to form a double-layer iterative model based on voltage and loss sensitivity for site selection and capacity determination of reactive power compensation devices in high-cable-rate urban power grids; The scheme acquisition module obtains the reactive power device site selection and sizing scheme based on a two-layer iterative model.

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