Urban power grid reactive bilevel planning model and method based on layering and partitioning

Abstract

The invention relates to the field of reactive power compensation equipment optimal configuration, in particular to an urban power grid reactive power bilevel planning model and method based on layering and partitioning. The method comprises the following steps: (1) setting initialization parameters, layering a power grid by using different voltage levels, and partitioning different voltage levels by a voltage control partitioning method considering reactive power balance modularity; (2) calculating a voltage reactive power sensitivity index and a local power grid stability index, constructing a comprehensive index, selecting a middle and low voltage side configuration point to configure a reactor, evaluating system inertia distribution by node inertia, identifying a system frequency support weak area, and selecting a high voltage side configuration point to configure a phase modifier; and (3) constructing an upper-layer optimization model by taking the total equiannual value cost as an objective function, and constructing a lower-layer optimization model by taking the network loss and the voltage deviation as objective functions and introducing a penalty function to be added into a lower-layer objective function, and performing iterative optimization by using an improved arithmetic optimization algorithm, thereby solving the problem of optimal configuration after partitioning of the reactor and the phase modifier under different voltage levels.

Description

Technical Field

[0001] The invention relates to a double-layer reactive power planning model and method for an urban power grid based on hierarchical partitioning, and belongs to the technical field of power systems. Background Art

[0002] With the expansion of the scale and complexity of the power system, how to effectively configure reactive power compensation devices to improve the stability and voltage quality of the system has become a key issue. Traditional reactive power compensation configuration methods often lack detailed consideration of grid stratification and voltage control. The present invention proposes a configuration method that takes into account urban grid stratification and zoning and a two-layer model planning, which aims to achieve the optimal configuration of reactors and phase regulators at different voltage levels by comprehensively considering voltage reactive power sensitivity indicators, local grid stability indicators, and system inertia distribution. This method can not only improve the operating efficiency of the power grid, but also reduce network losses and voltage deviations. At the same time, considering cost-effectiveness, iterative optimization is performed by improving the arithmetic optimization algorithm, taking the total cost of equal annual value as the objective function, constructing an upper optimization model, and constructing a lower optimization model with network losses and voltage deviations as the objective function, thereby achieving dual optimization of the power system in terms of economy and reliability. Summary of the invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a model and method for reactive power double-layer planning of urban power grid based on hierarchical partitioning. After the power grid is hierarchically partitioned, different indicators are used to select the configuration points of reactive compensation equipment, and a double-layer planning model is established. Simulation is performed by improving the arithmetic optimization algorithm to achieve dual optimization of the power system in terms of economy and reliability.

[0004] Technical solution: The specific steps of the present invention are as follows: S1: Layer and partition the power grid, initialize parameter settings, use different voltage levels to layer the power grid, and partition different voltage levels using a voltage control partitioning method that considers reactive power balance modularity.

[0005] S2: On the medium and low voltage sides, the grid parameters are used to calculate the voltage sensitivity index and the local voltage index, and the reactor is configured by constructing a comprehensive voltage stability index with reasonable weights.

[0006] S3: Considering the frequency stability constraint on the high-voltage side, the node inertia is used to evaluate the system inertia distribution and identify the weak areas of system frequency support to configure the phase regulator.

[0007] S4: The upper optimization model is constructed with the equal annual value cost as the objective function, the installation location and installation capacity of the phase-shifting device and the reactor as the decision conditions, and the upper and lower limits of the installation capacity of the reactive compensation equipment and the upper and lower limits of the number of constraint groups as the constraint conditions.

[0008] S5: The lower optimization model is constructed with system network loss and voltage deviation as the objective function, adjustable transformer gear, phase regulator and reactor compensation capacity as decision variables, and upper and lower limits of reactive compensation equipment installation capacity and the number of constraint groups as upper and lower limits as constraints.

[0009] S6: In the objective function of the lower optimization model, a penalty function is introduced to construct a lower objective function that takes into account the node voltage exceeding the limit, so as to transform the constrained problem into an unconstrained problem.

[0010] S7: The improved arithmetic optimization algorithm is used to iterate the model and the optimal configuration of reactors and phase regulators at different voltage levels is obtained after stratification and partitioning.

[0011] In step S1: the power grid is divided into layers and zones. First, the power grid voltage is divided into layers according to 220kV on the high voltage side, 110kV and 35kV on the medium and low voltage sides. The initialization parameters are used to establish the initial state of the power network for subsequent power flow calculations. The voltage control partitioning method of reactive balance module is used to partition different voltage levels. The above method is as follows.

[0012] From the Newton-Raphson flow equation, we know that: (1) In the above formula, is the change in active power injection, is the change in reactive power injection, is the change in node phase angle, is the change in node voltage, is the Jacobian matrix. The relationship between reactive power and voltage is obtained by inverse derivation of equation (1): (2) In the above formula: is the inverse matrix of the Jacobian matrix, The sensitivity matrices constructed for voltage and reactive power represent the sensitivity between voltage amplitude changes and reactive power changes.

[0013] The mathematical expression of modularity index is as follows: (3) In the above formula: Represents modularity, with values ​​ranging from between, Represents a connected partition in the network and partitions The ratio of the number of edges to all edges, Representative Matrix The sum of the elements in each row (or column) is the sum of the elements in the The ratio of the number of edges connecting nodes in a partition to all edges, Representative Matrix The sum of the elements on the diagonal, that is, the ratio of the number of edges connecting the internal nodes of the partition to all the edges in the network.

[0014] In order to describe the reactive coupling degree of two nodes, the voltage reactive sensitivity between nodes is used. To weight, Elements in the matrix The specific expression is as follows: (4) In the above formula, is the symmetric matrix Row, No. Column elements, representing nodes With Node The voltage reactive sensitivity between and Representative Row, No. The sensitivity matrix constructed by columns.

[0015] The reactive power balance index is used to measure the balance between reactive power output and reactive load in the defined area. The specific formula is shown in formula (5).

[0016] (5) In the above formula, For the Total reactive load in a zone; For the The maximum output of reactive power source in each partition. The smaller the value, the The more balanced the reactive power of each partition is.

[0017] Will Sensitivity is incorporated into modularization, so that each partition meets reactive power balance and the voltage is kept within the normal range. The traditional modularity is improved, and the expression is shown in formula (6): (6) In the above formula, For the improved modularity, is the weight coefficient, between. The value of is positively correlated with the reactive voltage sensitivity, and the improved modularity can meet the reactive power demand within the power grid.

[0018] In step S2: on the medium and low voltage sides, the voltage sensitivity index and the local voltage index are calculated using the grid parameters, and the voltage stability comprehensive index is constructed with reasonable weights to configure the reactor. The above method is as follows.

[0019] The voltage reactive power sensitivity index method is: decompose the power flow Jacobian matrix by singular value to obtain the relationship between the node voltage and reactive power, and use its minimum singular value and its corresponding left and right singular vectors as the basis for judging the voltage stability index. Decomposing the Jacobian matrix in formula (1) by singular value can obtain: (7) In the above formula, , are the left and right singular vectors respectively; are the corresponding singular values; and is a unitary matrix. By equivalently replacing equation (7), the power flow constraint equation (1) can be expressed as (8) Under normal working conditions, Not strange, ; When the system reaches the voltage stability limit, Strange, , that is, when the singular value in the system is sufficiently small and infinitely close to 0, the corresponding state variable will change greatly, and the voltage will fluctuate greatly with a small change in reactive power. When the system is in a critical state, , , is the minimum singular value The corresponding left and right singular vectors. Take the power change of the system equal to the left singular vector corresponding to the minimum singular value, that is, , according to the orthogonal vector property , we can get: (9) The larger value of the right singular vector corresponding to the minimum singular value can be used as the node voltage-reactive sensitivity index. The larger the value, the higher the voltage sensitivity of the node, and the weak nodes in the system where the voltage is relatively sensitive to reactive power changes can be identified. is the voltage-reactive power sensitivity index obtained by singular value decomposition: (10) Voltage-reactive sensitivity index It is an indicator that reflects the "global type" of system voltage.

[0020] The local voltage stability of the load node The calculation formula for obtaining the indicator is: (11) In the above formula, express Node collection; express Node collection; To meet the participation factor matrix Line Column elements; represents the node voltage vector, Indicates that the node meets , The mutual impedance between For Node The system corresponds to the power; * is the conjugate symbol.

[0021] The voltage stabilization comprehensive configuration: The following optimal compensation point is obtained Description: (12) In the above formula, , are the corresponding weights of the global stability index and the local stability index respectively. The optimal reactive power compensation point constraint condition is: (13) In the above formula, is the candidate node set; is the best compensation point; represents the set of compensation configuration points to be set; is the given number of reactive power compensation points. and In order to consider the corresponding weights of different global stability characteristics and local stability characteristics, the local stability ratio can be reduced when the node load levels in the system are relatively balanced. When there are nodes with heavy loads and large power fluctuation components and their local areas, the local stability index can be increased to obtain a better compensation position.

[0022] In step S3: considering the frequency stability constraint on the high voltage side, the node inertia is used to evaluate the system inertia distribution and identify the weak area of ​​system frequency support to configure the phase regulator. The above method is as follows: Defining Nodes The inertia is the disturbance power size and the node The ratio of the initial frequency change rate at , that is: (14) In the above formula, Representation Node Inertia; For Node Disturbance power; For Node At frequency.

[0023] According to the power system parameters, the correlation matrix between the potential nodes and node voltages in the generator is obtained, and the node frequency is expressed as the generator terminal frequency to obtain the generator The frequency changes to: (15) In the above formula, is the inertia time constant of the generator, For generator The synchronous power factor. For generator According to equation (15) and equation (14), we can get the node Calculate the inertia.

[0024] (16) In the above formula, The disturbance node and generator Susceptance between internal potential nodes, is the corresponding node in the association matrix and generator Elements of voltage relationships. Node The inertia depends on the inertia size of the inertia source such as the phase regulator and its electrical distance from it.

[0025] The calculation of power system frequency stability indicators mainly includes: system minimum inertia and critical inertia.

[0026] (17) In the above formula, is the minimum inertia of the power grid system, is the value of the maximum disturbance rate, is the maximum rate of change of frequency.

[0027] (18) In the above formula, is the critical inertia, is the reference frequency, is the moment when the frequency is the lowest, is the frequency drop amplitude. In summary, the boundary inertia level that satisfies these two indicators within the safety range after the disturbance is the critical inertia considering the frequency stability constraint.

[0028] In step S4: an upper optimization model is constructed with the equal annual cost as the objective function, the installation location and installation capacity of the phase regulator and reactor as the decision conditions, and the upper and lower limits of the installation capacity of the reactive compensation equipment and the upper and lower limits of the number of constraint groups as the constraint conditions. The model is constructed as follows: Equivalent annual total cost of the upper-level planning scheme Equivalent annual investment cost of equipment , annual maintenance cost , Decommissioning and disposal costs and system operating costs The relevant objective function is constructed as follows: (19) (20) (twenty one) (twenty two) (twenty three) (twenty four) In the above formula, , is the equivalent conversion factor of phase regulator and reactor; is a collection of reactive devices, and The total number of phase regulators and reactors put into use is: , The installation cost per unit capacity of phase regulator and reactor; , For the The first camera and the The configuration capacity of each reactor; is the unit reactor capacity; , and The labor cost for daily maintenance of equipment, the cost of regular testing and the cost of failure; Annual value coefficient of funds, is the discount rate, For equipment life.

[0029] The constraints include: (25) In the above formula, , They represent the upper and lower limits of the phase-shifting capacity of the node respectively; Indicates The capacity of the camera. Indicates the maximum capacity of the connected phase regulator; , Indicates the upper and lower limits of the number of reactor groups that can be put into the node; Indicates the upper limit of the total capacity of the reactor configuration.

[0030] In step S5: the lower optimization model is constructed with the system network loss and voltage deviation as the objective function, the adjustable transformer gear, phase regulator and reactor compensation capacity as the decision variables, and the upper and lower limits of the reactive compensation equipment installation capacity and the number of constraint groups as the upper and lower limits as the constraint conditions. The model shown is constructed as follows: Objective function: (26) In the above formula, is the number of branches, is the node voltage, is the phase angle; , Node With Node The conductance and phase difference between them; and is the actual node voltage and the ideal node voltage.

[0031] Constraints: (27) In the above formula, and Indicates compensation point The upper and lower limits of reactive power compensation capacity; and Indicates generator Upper and lower limits of the voltage at the machine end; and Indicates adjustable transformer The upper and lower limits of the tap position, , and Indicates the corresponding largest reactive power compensation device number, generator number and transformer number; (28) In the above formula, and Indicates generator The upper and lower limits of reactive power output; and Represents load node Voltage amplitude upper and lower limits; and Indicates branch The upper and lower limits of reactive power flow; , and Indicates the corresponding largest generator number, load node number and branch number.

[0032] In step S6: in the objective function of the lower optimization model, a penalty function is introduced to construct a lower objective function that takes into account the node voltage limit violation, with respect to the constraints of the system node voltage. This includes: By adding a penalty term to the objective function to penalize solutions that violate the constraints, the constrained problem is transformed into an unconstrained problem. The underlying optimization model is as follows: (29) (30) In the above formula, As penalty function, set , is the voltage limit function, and Represent the maximum and minimum voltage respectively; and Represents nodes The upper and lower limits for voltage out of limit.

[0033] In step S7: the model is optimized and iterated using an improved arithmetic optimization algorithm to obtain the optimal configuration of reactors and phase regulators at different voltage levels after stratification and partitioning. The arithmetic optimization algorithm is improved as follows: The improved arithmetic optimization algorithm is used to optimize the model iteratively, and a coordination strategy is adopted for the arithmetic optimization algorithm to simultaneously take into account or coordinate the "multiplication search", "division search", "addition search" and "subtraction search" to carry out searches, including: (31) (32) (33) (34) (35) (36) In the above formula, For the The iteration The first dimensional variables, for The optimal solution obtained in the first iteration dimensional variables, is an integer, is the sensitivity coefficient. When , the division operator is used for updating, otherwise the multiplication operator is used, mathematically optimizing the probability for The adaptive coefficient of Indicates The function value at the iteration, To adjust the control parameters of the search process, and They represent the upper and lower bounds of the search space respectively, represents the lower bound of the optimal solution, for A random angle in . is the symbolic function, It means the fitness value of the best individual in the population minus the fitness value of the current individual. , represents the current optimal individual fitness value, represents the average fitness value of the current population, Expressed as an inertia weight based on fitness value feedback.

[0034] Design new , which enhances the local development capability of the algorithm in the later stage and is beneficial to the optimization speed and accuracy of the algorithm.

[0035] (37) in, , , is an exponential function, Represents the maximum number of iterations, the new is a is a nonlinear monotonically decreasing function of .

[0036] The crossover mutation strategy is adopted to implement crossover mutation on the current optimal individual, so that the diversity of the population is effectively maintained: A new discriminant coefficient is designed, and its mathematical expression is shown in formula (38).

[0037] (38) (39) In the above formula, where: For the The iteration The optimal fitness value of an individual, If the fitness value of an individual does not change for two consecutive iterations, the individual may fall into a local optimum. is the population size, Indicates the identification Iteration No. Whether the individual is trapped in a local optimum, It means the The population as a whole falls into the local optimum at the iteration. From formula (39), we can see that The larger the value of , the greater the possibility that the algorithm will fall into a local optimum. , then crossover mutation is performed on the optimal individuals. The size of The larger the value, the greater the probability of mutation, and the greater the probability of the algorithm escaping the local optimum. The steps of crossover mutation are as follows: Assume that the current best individual in the group is , the randomly selected individuals are , which are respectively expressed as shown in formula (40), Represents the dimension of an individual.

[0038] (40) Generate a Dimensional cross template ,in , ,0 means crossing, 1 means no crossing; generate a value in the range [0,1] Number of dimensions ; Generate an outcast coefficient in [1,1] ,Right now The best individual With random individuals After the crossover operation, the individual positions are obtained as shown in formula (41).

[0039] (41) In the above formula, the coefficient Represents the crossover coefficient. The optimal individual adjusts the search step length of the optimal individual by exchanging cross information with random individuals. To control whether to perform dimension crossing and which dimension needs to be crossed; Represents the out-throw coefficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The present invention is a schematic diagram of the steps of a two-layer reactive power planning model and method for an urban power grid based on hierarchical partitioning according to an embodiment of the present invention.

[0041] Figure 2 The present invention is a zoning flow chart of a two-layer reactive power planning model and method for an urban power grid based on hierarchical zoning according to an embodiment of the present invention.

[0042] Figure 3 The present invention is a flowchart of calculating comprehensive index configuration points of a two-layer reactive power planning model and method for an urban power grid based on hierarchical partitioning according to an embodiment of the present invention.

[0043] Figure 4The present invention is a flowchart of calculating phase-shifting configuration points of a two-layer reactive power planning model and method for an urban power grid based on hierarchical partitioning according to an embodiment of the present invention.

[0044] Figure 5 Configure the model structure diagram for bi-level programming.

[0045] Figure 6 The overall flow chart of the model configuration for bi-level planning. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0047] A two-layer reactive power planning model and method for urban power grid based on hierarchical partitioning, comprising the following steps: S1: Layer and partition the power grid, initialize parameter settings, use different voltage levels to layer the power grid, and partition different voltage levels using a voltage control partitioning method that considers reactive power balance modularity.

[0048] S2: On the medium and low voltage sides, the grid parameters are used to calculate the voltage sensitivity index and the local voltage index, and the reactor is configured by constructing a comprehensive voltage stability index with reasonable weights.

[0049] S3: Considering the frequency stability constraint on the high-voltage side, the node inertia is used to evaluate the system inertia distribution and identify the weak areas of system frequency support to configure the phase regulator.

[0050] S4: The upper optimization model is constructed with the equal annual value cost as the objective function, the installation location and installation capacity of the phase-shifting device and the reactor as the decision conditions, and the upper and lower limits of the installation capacity of the reactive compensation equipment and the upper and lower limits of the number of constraint groups as the constraint conditions.

[0051] S5: The lower optimization model is constructed with system network loss and voltage deviation as the objective function, adjustable transformer gear, phase regulator and reactor compensation capacity as decision variables, and upper and lower limits of reactive compensation equipment installation capacity and the number of constraint groups as upper and lower limits as constraints.

[0052] S6: In the objective function of the lower optimization model, a penalty function is introduced to construct a lower objective function that takes into account the node voltage exceeding the limit, so as to transform the constrained problem into an unconstrained problem.

[0053] S7: The improved arithmetic optimization algorithm is used to iterate the model and the optimal configuration of reactors and phase regulators at different voltage levels is obtained after stratification and partitioning.

[0054] Finally, it should be noted that the above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A two-level reactive power planning model and method for urban power grid based on hierarchical partitioning is characterized by The following steps are involved: S1: stratify and partition the power grid, initialize parameter settings, stratify the power grid using different voltage levels, and partition different voltage levels using a voltage control partitioning method that considers reactive power balance modularity; S2: On the medium and low voltage sides, the voltage sensitivity index and local voltage index are calculated using the grid parameters, and the voltage stability comprehensive index is constructed with reasonable weights to configure the reactor; S3: Considering the frequency stability constraint on the high-voltage side, the node inertia is used to evaluate the system inertia distribution and identify the weak frequency support area of ​​the system to configure the phase regulator; S4: Construct an upper optimization model with equal annual cost as the objective function, the installation location and installation capacity of the phase shifter and reactor as the decision conditions, and the upper and lower limits of the installation capacity of the reactive compensation equipment and the upper and lower limits of the number of constraint groups as the constraint conditions; S5: The lower optimization model is constructed with the system network loss and voltage deviation as the objective function, the adjustable transformer gear, phase regulator and reactor compensation capacity as the decision variables, and the upper and lower limits of the reactive compensation equipment installation capacity and the number of constraint groups as the upper and lower limits as the constraint conditions; S6: In the objective function of the lower optimization model, a penalty function is introduced to construct a lower objective function that takes into account the node voltage limit violation, thereby transforming the constrained problem into an unconstrained problem. S7: The improved arithmetic optimization algorithm is used to iterate the model and the optimal configuration of reactors and phase regulators at different voltage levels is obtained after stratification and partitioning.

2. According to the hierarchical and partitioned urban power grid reactive power two-layer planning model and method described in claim 1, it is characterized by: In step S1, the power grid is divided into layers and zones. First, the power grid voltage is divided into layers according to 220 kV on the high voltage side and 110 kV and 35 kV on the medium and low voltage sides. Initialization parameters are used to establish the initial state of the power network for subsequent power flow calculations. The voltage control partitioning method of reactive balance module is used to partition different voltage levels, including: From the Newton-Raphson flow equation, we know that: （1） In the above formula, is the change in active power injection, is the change in reactive power injection, is the change in node phase angle, is the change in node voltage, is the Jacobian matrix. The relationship between reactive power and voltage is obtained by inverse derivation of equation (1): （2） In the above formula: is the inverse matrix of the Jacobian matrix, The sensitivity matrix constructed for voltage and reactive power represents the sensitivity between voltage amplitude change and reactive power change; The mathematical expression of modularity index is as follows: （3） In the above formula: Represents modularity, with values ​​ranging from between, Represents a connected partition in the network and partitions The ratio of the number of edges to all edges, Representative Matrix The sum of the elements in each row (or column) is the sum of the elements in the The ratio of the number of edges connecting nodes in a partition to all edges, Representative Matrix The sum of the elements on the diagonal, that is, the ratio of the number of edges connecting the internal nodes of the partition to all the edges in the network; In order to describe the reactive coupling degree of two nodes, the voltage reactive sensitivity between nodes is used. To weight, Elements in the matrix The specific expression is as follows: （4） In the above formula, is the symmetric matrix Row, No. Column elements, representing nodes With Node The voltage reactive sensitivity between and Representative Row, No. Column constructed sensitivity matrix; The reactive power balance index is used to measure the balance between reactive power output and reactive load in the defined area. The specific formula is shown in formula (5). （5） In the above formula, For the Total reactive load in a zone; For the The maximum output of reactive power source in each partition. The smaller the value, the The more balanced the reactive power of each partition is; Will Sensitivity is incorporated into modularization, so that each partition meets reactive power balance and the voltage is kept within the normal range. The traditional modularity is improved, and the expression is shown in formula (6): （6） In the above formula, For the improved modularity, is the weight coefficient, between, The value of is positively correlated with the reactive voltage sensitivity, and the improved modularity can meet the reactive power demand within the power grid.

3. According to the hierarchical and partitioned urban power grid reactive power two-layer planning model and method described in claim 1, it is characterized by: On the medium and low voltage side, the voltage sensitivity index and local voltage index are calculated using the grid parameters, and the comprehensive index is constructed to configure the reactor, including: voltage-reactive sensitivity configuration point analysis: The power flow Jacobian matrix is ​​subjected to singular value decomposition to obtain the relationship between the node voltage and the reactive power. Its minimum singular value and its corresponding left and right singular vectors are used as the basis for judging the voltage stability index. The Jacobian matrix in formula (1) is subjected to singular value decomposition to obtain: （7） In the above formula, , are the left and right singular vectors respectively; are the corresponding singular values; and is a unitary matrix, and by equivalently replacing equation (7), the power flow constraint equation (1) can be expressed as （8） Under normal working conditions, Not strange, ; When the system reaches the voltage stability limit, Strange, That is, when the singular value in the system is sufficiently small and infinitely close to 0, the corresponding state variable will change greatly, and the voltage will fluctuate greatly with a small change in reactive power. When the system is in a critical state, , , is the minimum singular value The corresponding left and right singular vectors are equal to the power change of the system and the left singular vector corresponding to the minimum singular value, that is, , according to the orthogonal vector property , we can get: （9） The larger value of the right singular vector corresponding to the minimum singular value can be used as the node voltage-reactive sensitivity index. The larger the value, the higher the voltage sensitivity of the node, and the weak nodes in the system where the voltage is relatively sensitive to the reactive power change can be identified. is the voltage-reactive power sensitivity index obtained by singular value decomposition: （10） Voltage-reactive sensitivity index It is an indicator that reflects the "global type" of system voltage; The local voltage stability of the load node The calculation formula for obtaining the indicator is: (11) In the above formula, express Node collection; express Node collection; To meet the participation factor matrix Line Column elements; represents the node voltage vector, Indicates that the node meets , The mutual impedance between For Node The system conforms to the power; * is the conjugate symbol; The voltage stabilization comprehensive configuration: The following optimal compensation point is obtained Description: （12） In the above formula, , are the corresponding proportions of the global stability index and the local stability index respectively. The optimal reactive power compensation point constraint is: （13） In the above formula, is the candidate node set; is the best compensation point; represents the set of compensation configuration points to be set; is the given number of reactive power compensation points; and In order to consider the corresponding weights of different global stability characteristics and local stability characteristics, the local stability ratio can be reduced when the node load levels in the system are relatively balanced. When there are nodes with heavy loads and large power fluctuation components and their local areas, the local stability index can be increased to obtain a better compensation position.

4. According to the hierarchical and partitioned urban power grid reactive power two-layer planning model and method described in claim 1, it is characterized by: Considering the frequency stability constraint on the high voltage side, the node inertia is used to evaluate the system inertia distribution and identify the weak area of ​​system frequency support to configure the phase regulator, including: Defining Nodes The inertia is the disturbance power size and the node The ratio of the initial frequency change rate at , that is: （14） In the above formula, Representation Node Inertia; For Node Disturbance power; For Node Frequency; According to the power system parameters, the correlation matrix between the potential nodes and node voltages in the generator is obtained, and the node frequency is expressed as the generator terminal frequency to obtain the generator The frequency changes to: （15） In the above formula, is the inertia time constant of the generator, For generator The synchronous power factor, For generator According to equation (15) and equation (14), we can get the node Calculation of inertia; （16） In the above formula, The disturbance node and generator Susceptance between internal potential nodes, is the corresponding node in the association matrix and generator Elements of voltage relationships. Node The inertia depends on the inertia of the inertia source such as the phase regulator and its electrical distance from it; The calculation of power system frequency stability indicators mainly includes: system minimum inertia and critical inertia, （17） In the above formula, is the minimum inertia of the power grid system, is the value of the maximum disturbance rate, is the maximum rate of change of frequency; （18） In the above formula, is the critical inertia, is the reference frequency, is the moment when the frequency is the lowest, is the frequency drop amplitude. In summary, the boundary inertia level that satisfies these two indicators within the safety range after the disturbance is the critical inertia considering the frequency stability constraint.

5. According to the hierarchical and partitioned urban power grid reactive power two-layer planning model and method described in claim 1, it is characterized by: The upper optimization model is constructed with the equal annual value cost as the objective function, the installation location and installation capacity of the phase regulator and reactor as the decision conditions, and the upper and lower limits of the installation capacity of the reactive compensation equipment and the upper and lower limits of the number of constraint groups as the constraint conditions; Equivalent annual total cost of the upper-level planning scheme Equivalent annual investment cost of equipment , annual maintenance cost , Decommissioning and disposal costs and system operating costs The relevant objective function is constructed as follows: （19） （20） （21） （22） （23） （24） In the above formula, , is the equivalent conversion factor of phase regulator and reactor; is a collection of reactive devices, and The total number of phase regulators and reactors put into use is: , The installation cost per unit capacity of phase regulator and reactor; , For the The first camera and the The configuration capacity of each reactor; is the unit reactor capacity; , and The labor cost for daily maintenance of equipment, the cost of regular testing and the cost of failure; Annual value coefficient of funds, is the discount rate, For equipment life; The upper-level constraints include: （25） In the above formula, , They represent the upper and lower limits of the phase-shifting capacity of the node respectively; Indicates The capacity of the camera. Indicates the maximum capacity of the connected phase regulator; , Indicates the upper and lower limits of the number of reactor groups that can be put into the node; Indicates the upper limit of the total capacity of the reactor configuration.

6. According to the hierarchical and partitioned urban power grid reactive power two-layer planning model and method as described in claim 1, it is characterized by: The lower optimization model is constructed with the system network loss and voltage deviation as the objective function, the adjustable transformer gear, phase regulator and reactor compensation capacity as the decision variables, and the upper and lower limits of the reactive compensation equipment installation capacity and the number of constraint groups as the upper and lower limits as the constraints. The objective function is as follows: （26） In the above formula, is the number of branches, is the node voltage, is the phase angle; , Node With Node The conductance and phase difference between them; and is the actual voltage and ideal voltage of the node; The constraints are as follows: （27） In the above formula, and Indicates compensation point The upper and lower limits of reactive power compensation capacity; and Indicates generator Upper and lower limits of the voltage at the machine end; and Indicates adjustable transformer The upper and lower limits of the tap position, , and Indicates the corresponding largest reactive power compensation device number, generator number and transformer number; （28） In the above formula, and Indicates generator The upper and lower limits of reactive power output; and Represents load node Voltage amplitude upper and lower limits; and Indicates branch The upper and lower limits of reactive power flow; , and Indicates the corresponding largest generator number, load node number and branch number.

7. According to the hierarchical and partitioned urban power grid reactive power two-layer planning model and method as described in claim 1, it is characterized by: In the objective function of the lower optimization model, a penalty function is introduced to construct the lower objective function that takes into account the node voltage limit, according to the constraints of the system node voltage, including: By adding a penalty term to the objective function to penalize solutions that violate the constraints, the constrained problem is transformed into an unconstrained problem. The lower-level objective function model is built as follows: （29） （30） In the above formula, As penalty function, set , is the voltage limit function, and Represent the maximum and minimum voltage respectively; and Represents nodes The upper and lower limits for voltage out of limit.

8. According to the hierarchical and partitioned urban power grid reactive power two-layer planning model and method as described in claim 1, it is characterized by: The improved arithmetic optimization algorithm is used to optimize the model iteratively, and a coordination strategy is adopted for the arithmetic optimization algorithm to simultaneously take into account or coordinate the "multiplication search", "division search", "addition search" and "subtraction search" to carry out searches, including: (31) (32) (33) (34) (35) (36) In the above formula, For the The first iteration The first dimensional variables, for The optimal solution obtained in the first iteration dimensional variables, is an integer, is the sensitivity coefficient. When , the division operator is used for updating, otherwise the multiplication operator is used, mathematically optimizing the probability for The adaptive coefficient of Indicates The function value at the iteration, To adjust the control parameters of the search process, and They represent the upper and lower bounds of the search space respectively, represents the lower bound of the optimal solution, for A random angle in is the symbolic function, It means the fitness value of the best individual in the population minus the fitness value of the current individual. , represents the current optimal individual fitness value, Represents the average fitness value of the current population, Represented as an inertia weight based on fitness value feedback; Design new , which enhances the local development capability of the algorithm in the later stage, and is beneficial to the optimization speed and accuracy of the algorithm; (37) in, , , is an exponential function, Represents the maximum number of iterations, the new is a A nonlinear monotonically decreasing function of ; The crossover mutation strategy is adopted to implement crossover mutation on the current optimal individual, so that the diversity of the population is effectively maintained: A new discriminant coefficient is designed, and its mathematical expression is shown in formula (38): (38) (39) In the above formula, where: For the The iteration The optimal fitness value of an individual, If the fitness value of an individual does not change for two consecutive iterations, the individual may fall into a local optimum. is the population size, Indicates the identification Iteration No. Whether the individual is trapped in a local optimum, It means the The population as a whole falls into the local optimum at the iteration. From formula (39), we can see that The larger the value of , the greater the possibility that the algorithm will fall into the local optimum. , then the optimal individuals are cross-mutated, from The size of The larger the value, the greater the probability of mutation, and the greater the probability of the algorithm escaping the local optimum. The steps of crossover mutation are as follows: Assume that the current best individual in the group is , the randomly selected individuals are , which are respectively expressed as shown in formula (40), Represents the dimensions of an individual: (40) Generate a Dimensional cross template ,in , ,0 means crossing, 1 means no crossing; generates a value in the range [0,1] Number of dimensions ; Generate an outcast coefficient in [1,1] ,Right now ; The best individual With random individuals After the crossover operation, the individual positions are obtained as shown in formula (41): (41) In the above formula, the coefficient Represents the crossover coefficient. The optimal individual adjusts the search step length of the optimal individual by exchanging cross information with random individuals. To control whether to perform dimension crossing and which dimension needs to be crossed; Represents the out-throw coefficient.

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