Method for configuring reactive power dynamic resources taking into account network characteristics and voltage stability constraints

Abstract

The application discloses a reactive power dynamic resource configuration method considering network characteristics and voltage stability constraints, and belongs to the technical field of reactive power resource configuration of power systems. Based on the voltage stability demand of a new type of power system and the operation characteristics of network type equipment, a double-target function system is constructed, in which the minimum total configuration cost is taken as an economic target, and the minimum sum of square deviations of post-fault voltage is taken as a safety target. Three types of constraints, i.e. static operation, equipment physical limitation and network control characteristics, are set, and a reactive power dynamic resource configuration model is established. A convex optimization method of second-order cone relaxation is used to linearly solve non-convex items of the model, and a non-convex optimization method of a multi-objective particle swarm is combined to search for a Pareto front solution set, so that an optimized configuration scheme considering economy and safety is obtained. The application overcomes the shortcoming that a traditional reactive power optimization model does not consider network characteristics and voltage stability constraints, and effectively improves the voltage stability level and resource configuration efficiency of the new type of power system.

Description

Technical Field

[0001] This invention relates to the field of reactive power dynamic resource allocation technology in power systems, and specifically to a reactive power dynamic resource allocation method that takes into account network characteristics and voltage stability constraints. Background Technology

[0002] along with" "With the advancement of the goals, the penetration rate of new energy sources such as wind power and photovoltaics in the power system continues to increase. The access method based on inverter power supply has broken the traditional operation mechanism of the power system, making the system exhibit low inertia, weak damping, and strong fluctuation characteristics. Voltage stability issues are becoming increasingly prominent. The widespread deployment of grid-type power sources has also made the reactive power regulation method of traditional synchronous generators gradually ineffective. Therefore, it is urgent to achieve efficient allocation and dynamic regulation of reactive power resources to ensure the safe and stable operation of the new power system."

[0003] Currently, power electronic devices such as SVG / STATCOM and new energy converters have become the core of dynamic reactive power compensation in new power systems. However, their grid control characteristics significantly affect the steady-state power flow and transient voltage recovery of the system. Traditional reactive power optimization models only consider steady-state power balance, which cannot adapt to the operating characteristics of grid-connected equipment and is also difficult to balance the economy and safety of system operation. By constructing a dynamic reactive power resource optimization configuration model that considers grid characteristics and voltage stability constraints, with the dual objectives of minimizing the total cost of equipment configuration and minimizing the sum of squares of voltage deviations after a fault, and incorporating three types of constraints—static operation, equipment physical limitations, and grid control characteristics—and combining convex optimization with second-order cone relaxation and non-convex optimization with multi-objective particle swarm optimization, a dynamic reactive power resource optimization configuration scheme that balances economy and safety can be obtained. This model adapts to the operating characteristics of grid-connected equipment and effectively improves the voltage stability level and resource allocation efficiency of new power systems. Summary of the Invention

[0004] To address the aforementioned problems in the prior art, this invention provides a method for dynamic reactive power resource allocation that considers network characteristics and voltage stability constraints, comprising:

[0005] Based on the voltage stability requirements of the new power system and the operating characteristics of grid-type equipment, a dual objective function system is constructed with the goal of minimizing the total configuration cost as the economic objective and minimizing the sum of squared voltage deviations after a fault as the safety objective.

[0006] Based on the safety operation specifications of the power system, three types of constraints are set: static operation, equipment physical limitations, and grid control characteristics. A reactive power dynamic resource allocation model that takes into account grid characteristics and voltage stability constraints is established.

[0007] Solve the reactive power dynamic resource allocation model to obtain the optimal reactive power dynamic resource allocation scheme that takes into account network characteristics and voltage stability constraints.

[0008] As an improvement to the present invention, the economic objective includes at least the investment and maintenance costs of grid-type equipment, traditional dynamic equipment, and capacitor banks, calculated using the following formula:

[0009]

[0010] in, For economic purposes, It is the set of all buses or nodes in a new type of power system. For the unit investment of node i, The capacity of the network-type equipment allocated to node i. The maintenance cost of node i. Let i be the switching cost. The number of times the capacitor bank at node i is switched on and off; the unit investment and maintenance cost of the node includes the investment and maintenance costs of traditional dynamic equipment.

[0011] As an improvement to the present invention, the safety target is used to evaluate the voltage recovery capability and voltage stability of the new power system after a fault, and the calculation formula is as follows:

[0012]

[0013] in, For security purposes, This refers to a set of pre-defined fault conditions or disturbance scenarios in the power grid. It is the set of all buses or nodes in a new type of power system. Let be the voltage value at node i after fault k. Let be the reference voltage for node i.

[0014] As an improvement of the present invention, the static operating constraints include power flow balance constraints and system power balance constraints;

[0015] The physical constraints on the equipment include capacity circle constraints and reactive power ramp rate constraints.

[0016] The network control characteristic constraints include voltage-reactive droop control characteristic constraints and virtual inertia characteristic constraints.

[0017] As an improvement of the present invention, the power flow balance constraint includes:

[0018] In a static scenario, power balance and node voltage upper and lower limits must be satisfied. The calculation formula is as follows:

[0019]

[0020]

[0021]

[0022] in, It is the set of all buses or nodes in a new type of power system. Let i be the electrical conductance between node i and node j. Let be the real part of the voltage phasor at node i. Let be the real part of the voltage phasor at node j. Let i be the imaginary part of the voltage phasor at node i. Let be the imaginary part of the voltage phasor at node j. Let be the susceptance between node i and node j. For the active power output of network-type devices at node i, Let be the active load of node i. For the reactive power output of network-type devices at node i, This is the reactive power compensation amount of the parallel capacitor bank installed at node i. For the reactive load of node i, This represents the lower limit of the allowable voltage at node i. This represents the upper limit of the allowable voltage at node i. The voltage amplitude at node i;

[0023] For a wired structure, the current in each line does not exceed the thermal stability limit, expressed as:

[0024]

[0025] in, Let be the current amplitude of line ij. The maximum allowable current for line ij is given. It is the set of all branches in the power grid;

[0026] The formula for calculating the system power balance constraint is:

[0027]

[0028] .

[0029] As an improvement to the present invention, the expression for the capacity circle constraint is:

[0030]

[0031] in, For network-type devices, the rated apparent power capacity at node i, For the active power output of network-type devices at node i, For the reactive power output of network-type devices at node i;

[0032] The expression for the reactive ramp rate constraint is:

[0033]

[0034] in, The reactive power output of the network-type device at node i at time t. For network-type equipment The reactive power output at node i at all times To control the time step, The maximum reactive power regulation rate of the network-type equipment at node i.

[0035] As an improvement of the present invention, the calculation formula for the voltage-reactive power droop control characteristic constraint is as follows:

[0036]

[0037] in, For the reactive power output of network-type devices at node i, The reference reactive power output of the network-type device at node i. This is the voltage-reactive droop factor. Let i be the voltage reference value at node i. Let be the voltage amplitude at node i;

[0038] The formula for calculating the virtual inertia characteristic constraint is as follows:

[0039]

[0040] in, For virtual inertia constant, Let i be the virtual angular velocity of the second-order network device. Let be the mechanical power of the second-order network-type equipment at node i. Let be the electromagnetic power of the second-order network device at node i.

[0041] As an improvement of the present invention, the solution of the reactive power dynamic resource allocation model includes:

[0042] A second-order cone relaxation convex optimization method is used to relax and linearize the non-convex terms of the reactive power dynamic resource allocation model to obtain a feasible solution and feasible domain boundary that satisfy the basic operating constraints of the new power system.

[0043] Using the feasible solutions as the original population, a Pareto front solution set is searched within the search space defined by the feasible domain boundary using a non-convex optimization method of multi-objective particle swarm optimization.

[0044] During the iteration process, the optimal solution of the new multi-objective particle swarm search is fed back to the second-order cone relaxation stage to dynamically update the feasible region boundary.

[0045] As an improvement of the present invention, the method of using a second-order cone relaxation convex optimization method to relax and linearize the non-convex terms of the reactive power dynamic resource allocation model includes:

[0046] To address the nonlinear characteristics of the power flow equations, auxiliary variables are introduced, and the calculation formula is as follows:

[0047]

[0048]

[0049]

[0050] in, Let be the voltage magnitude at node i. Let J be the voltage magnitude at node j. The voltage phase angle difference between node i and node j. , , For intermediate calculations, Let be the real part of the voltage phasor at node i. The imaginary part of the voltage phasor at node i;

[0051] Based on auxiliary variables, the nonlinear terms in the power flow equations are transformed into a linear representation, and the calculation formula is as follows:

[0052]

[0053]

[0054] in, Inject active power into node i. Let i be the self-conductance of node i. Let i be the electrical conductance between node i and node j. Let be the susceptance between node i and node j. For the active power output of network-type devices at node i, Let be the active load of node i. Inject reactive power into node i. Let be the self-susceptance of node i. For the reactive load of node i, For the reactive power output of network-type devices at node i, This is the reactive power compensation amount of the parallel capacitor bank installed at node i;

[0055] To ensure geometric consistency between auxiliary variables and branch power, a second-order cone constraint is introduced to restrict their product relationship, expressed as:

[0056]

[0057] in, As an auxiliary variable, For the set of all branches, It is the Euclidean norm;

[0058] The voltage upper and lower limit constraints are transformed into linear inequalities with respect to auxiliary variables, expressed as:

[0059]

[0060] in, This is the lower limit of the allowable voltage amplitude at node i; This represents the upper limit of the allowable voltage amplitude at node i;

[0061] For the capacity circle constraint, the apparent power limit of network-type equipment is transformed into a cone form, expressed as:

[0062]

[0063] in, The rated apparent power capacity of the network-type equipment at node i;

[0064] By introducing a weighted method, the biobjective function is transformed into a single-objective optimization function solvable by a convex optimization method with second-order cone relaxation. The calculation formula is as follows:

[0065]

[0066] in, The value of the comprehensive objective function after weighted transformation. The weighting coefficients for economic objectives. The normalized economic objective function value. The weighting coefficients for security objectives. This represents the normalized security objective function value.

[0067] Call the convex optimization solver to solve the single-objective optimization function and obtain the initial feasible solution and the feasible region boundary.

[0068] As an improvement to the present invention, the search for the Pareto front solution set using the nonconvex optimization method of the multi-objective particle swarm optimization includes:

[0069] Initialize the position and velocity of the particle swarm, with each particle representing a set of reactive dynamic resource allocation decision variables;

[0070] Calculate the dual-objective fitness of particles based on a dual-objective function;

[0071] Determine whether a particle is non-dominated by the external elite solution set, maintain the external elite solution set based on the non-domination relationship, and select the current Pareto optimal solution;

[0072] Update the individual historical best position of each particle and the group optimal solution of the entire particle swarm;

[0073] The position and velocity of the particles are updated based on the inertia weight and the learning factor;

[0074] The loop iterates until the preset termination condition is met;

[0075] A penalty is introduced to adjust the fitness of particles that violate the constraints. The calculation formula is as follows:

[0076]

[0077] in, The corrected fitness function. The original objective function includes both the economic objective function and the safety objective function. As a penalty weighting coefficient, This is a function that measures the degree to which a particle violates various constraints.

[0078] The beneficial effects of this invention are as follows: Compared with the traditional reactive power optimization model that only considers steady-state power balance, the reactive power dynamic resource allocation method proposed in this invention, which takes into account network characteristics and voltage stability constraints, fully considers the control characteristics of network-type equipment and the voltage stability requirements of new power systems. It constructs a dual-objective optimization model of economy and safety, and solves it by combining second-order cone relaxation convex optimization and multi-objective particle swarm optimization. Under the premise of ensuring the safe and stable operation of the system, it achieves efficient allocation of reactive power dynamic resources and accurate guarantee of voltage stability. Attached Figure Description

[0079] Figure 1 This is a flowchart of the steps of the reactive power dynamic resource allocation method of the present invention, which takes into account network characteristics and voltage stability constraints. Figure 2 This is a schematic diagram of the daily load curve of the IEEE 30-node system in an embodiment of the present invention; Figure 3 This is a schematic diagram of reactive power planning for network-type equipment in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the utilization level of network-type equipment in an embodiment of the present invention; Figure 5 This is a schematic diagram of load tracking performance in an embodiment of the present invention. Detailed Implementation

[0080] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0081] Please see Figure 1 The reactive power dynamic resource allocation method considering network characteristics and voltage stability constraints provided by this invention includes:

[0082] Step A: Based on the voltage stability requirements of the new power system and the operating characteristics of grid-type equipment, a dual objective function system is constructed with the goal of minimizing the total configuration cost as the economic objective and minimizing the sum of squared voltage deviations after a fault as the safety objective.

[0083] In embodiments of the present invention, the economic objective includes at least the investment and maintenance costs of grid-type equipment, traditional dynamic equipment, and capacitor banks, calculated using the following formula:

[0084]

[0085] in, For economic purposes, It is the set of all buses or nodes in a new type of power system. For the unit investment of node i, The capacity of the network-type equipment allocated to node i. The maintenance cost of node i. Let i be the switching cost. The number of times the capacitor bank at node i is switched on and off; the unit investment and maintenance cost of the node includes the investment and maintenance costs of traditional dynamic equipment.

[0086] The safety objective aims to minimize the sum of squared voltage deviations after a fault, reducing the deviation of the system voltage from the reference value after a fault. It seeks to assess the system's voltage recovery capability and voltage stability after a fault from an operational perspective. The calculation formula is as follows:

[0087]

[0088] in, For security purposes, This refers to a set of pre-defined fault conditions or disturbance scenarios in the power grid. It is the set of all buses or nodes in a new type of power system. Let be the voltage value at node i after fault k. Let be the reference voltage for node i.

[0089] In one specific embodiment of the present invention, the preset set of fault conditions or disturbance scenarios includes:

[0090] Key equipment N-1 fault condition; power output disturbance condition of new energy power station; power disturbance condition on the load side; short circuit fault and transient recovery condition.

[0091] Step B: Based on the safety operation specifications of the power system, set three types of constraints: static operation, equipment physical limitations, and grid control characteristics, and establish a reactive power dynamic resource allocation model that takes into account grid characteristics and voltage stability constraints.

[0092] In embodiments of the present invention, static operating constraints include power flow balance constraints and system power balance constraints; equipment physical limitation constraints include capacity circle constraints and reactive power ramp rate constraints; and network control characteristic constraints include voltage-reactive power droop control characteristic constraints and virtual inertia characteristic constraints.

[0093] Specifically, power flow balance constraints include: in static scenarios, power balance and node voltage upper and lower limits must be satisfied, and the calculation formula is as follows:

[0094]

[0095]

[0096]

[0097] in, It is the set of all buses or nodes in a new type of power system. Let i be the electrical conductance between node i and node j. Let be the real part of the voltage phasor at node i. Let be the real part of the voltage phasor at node j. Let i be the imaginary part of the voltage phasor at node i. Let be the imaginary part of the voltage phasor at node j. Let be the susceptance between node i and node j. For the active power output of network-type devices at node i, Let be the active load of node i. For the reactive power output of network-type devices at node i, This is the reactive power compensation amount of the parallel capacitor bank installed at node i. For the reactive load of node i, This represents the lower limit of the allowable voltage at node i. This represents the upper limit of the allowable voltage at node i. Let be the voltage amplitude at node i.

[0098] In one specific embodiment of the present invention, the lower limit of the allowed voltage of node i is 0.95 pu, and the upper limit of the allowed voltage of node i is 1.05 pu.

[0099] For a wired structure, the current in each line does not exceed the thermal stability limit, expressed as:

[0100]

[0101] in, Let be the current amplitude of line ij. Let be the maximum allowable current of line ij, i.e., the thermal stability limit. It is the set of all branches in the power grid.

[0102] To ensure the basic feasibility of the new power system operating in all time periods, the overall active and reactive power balance condition must be met. The formula for calculating the system power balance constraint is as follows:

[0103]

[0104]

[0105] This constraint means that the active and reactive power provided by the network-type equipment and capacitor banks in the system should be able to meet the load demand during that period and be maintained within a reasonable margin.

[0106] Considering the physical limitations of network-type equipment during operation, its output capacity is affected by factors such as the equipment's capacity, dynamic response speed, and thermal performance, physical constraints are set for the equipment.

[0107] Specifically, the capacity circle constraint limits the apparent power output of network-type equipment to not exceed its rated capacity, expressed as:

[0108]

[0109] in, For network-type devices, the rated apparent power capacity at node i, For the active power output of network-type devices at node i, The reactive power output of the network-type device at node i.

[0110] The reactive power ramp rate constraint considers the reactive power regulation speed limit of the equipment, and the equipment cannot have a sudden response in a short time. The expression is:

[0111]

[0112] in, The reactive power output of the network-type device at node i at time t. For network-type equipment The reactive power output at node i at all times To control the time step, The maximum reactive power regulation rate of the network-type equipment at node i.

[0113] Considering that grid-type equipment in a low short-circuit ratio grid can achieve a dynamic response relationship between voltage and reactive power through voltage-reactive power droop control, thereby improving the system voltage regulation performance, grid-type control characteristic constraints are set.

[0114] Specifically, the calculation formula for the voltage-reactive power droop control characteristic constraint is as follows:

[0115]

[0116] in, For the reactive power output of network-type devices at node i, The reference reactive power output of the network-type device at node i. This is the voltage-reactive droop factor. Let i be the voltage reference value at node i. Let be the voltage amplitude at node i.

[0117] Meanwhile, second-order grid-type equipment possesses virtual inertia characteristics that simulate the inertia of synchronous generators, used to suppress frequency fluctuations. This characteristic introduces an inertial transient effect through its response to the rate of change of active power, causing dynamic frequency support due to power differences. The calculation formula for the virtual inertia characteristic constraint is as follows:

[0118]

[0119] in, For virtual inertia constant, Let be the virtual angular velocity of the second-order network-type device at node i, and its derivative be the rate of frequency change. This indicates that the network-type device provides virtual inertia support during dynamic power changes, thereby reducing the system power change rate. Let be the mechanical power of the second-order network-type equipment at node i. Let be the electromagnetic power of the second-order network device at node i.

[0120] Step C: Solve the reactive power dynamic resource allocation model to obtain the optimal reactive power dynamic resource allocation scheme that takes into account network characteristics and voltage stability constraints.

[0121] In an embodiment of the present invention, a convex optimization method with second-order cone relaxation is used to relax and linearize the non-convex terms of the reactive power dynamic resource allocation model to obtain feasible solutions and feasible domain boundaries that satisfy the basic operating constraints of the new power system. The feasible solutions are used as the original population, and a non-convex optimization method with multi-objective particle swarm optimization is used to search for Pareto front solutions within the search space defined by the feasible domain boundary. During the iteration process, the optimal solutions newly searched by multi-objective particle swarm optimization are fed back to the second-order cone relaxation stage to dynamically update the feasible domain boundary.

[0122] Specifically, the reactive power dynamic resource allocation model exhibits typical non-convex characteristics. First, the active / reactive power balance term in the AC power flow equations includes product terms between variables and trigonometric function terms, creating nonlinear and bilinear coupling, resulting in an inherently non-convex model. Second, the capacity constraints of grid-type equipment are expressed as a quadratic function of apparent power, forming a non-convex conical boundary condition, essentially a non-convex quadratic cone constraint. Third, the voltage stability margin constraint depends on the minimum singular value of the reactive power-voltage Jacobian matrix, involving eigenvalue extraction and nonlinear matrix inequality constraints, increasing the complexity of the solution. These non-convex structures limit the feasibility of directly solving the model using traditional convex optimization methods. Therefore, this invention employs a second-order cone relaxation convex optimization method to relax and linearize the non-convex terms of the reactive power dynamic resource allocation model.

[0123] To address the nonlinear characteristics of the power flow equations, auxiliary variables are introduced, and the calculation formula is as follows:

[0124]

[0125]

[0126]

[0127] in, Let be the voltage magnitude at node i. Let J be the voltage magnitude at node j. The voltage phase angle difference between node i and node j. , , For intermediate calculations, Let be the real part of the voltage phasor at node i. Let i be the imaginary part of the voltage phasor at node i.

[0128] After introducing the above variables, the nonlinear terms in the original power flow equations can be transformed into a linearized representation, as shown in the following expression:

[0129]

[0130]

[0131] in, Inject active power into node i. Let i be the self-conductance of node i. Let i be the electrical conductance between node i and node j. Let be the susceptance between node i and node j. For the active power output of network-type devices at node i, Let be the active load of node i. Inject reactive power into node i. Let be the self-susceptance of node i. For the reactive load of node i, For the reactive power output of network-type devices at node i, This is the reactive power compensation amount of the parallel capacitor bank installed at node i.

[0132] To ensure the geometric consistency between auxiliary variables and branch power, a second-order cone constraint is introduced to restrict their product relationship. This equation represents the standard second-order cone constraint:

[0133]

[0134] in, As an auxiliary variable, For the set of all branches, It is the Euclidean norm.

[0135] The voltage upper and lower limit constraints are transformed into linear inequalities with respect to auxiliary variables, expressed as:

[0136]

[0137] in, This is the lower limit of the allowable voltage amplitude at node i; This represents the upper limit of the allowable voltage amplitude at node i.

[0138] For the capacity circle constraint, the apparent power limit of network-type equipment is transformed into a cone form, expressed as:

[0139]

[0140] in, The rated apparent power capacity of the network-type device at node i.

[0141] The economic objective function is to minimize the investment and maintenance costs of dynamic reactive resources, while the safety objective function is to minimize the system voltage deviation. By introducing a weighted method, the dual objective functions are transformed into a single objective function solvable by a second-order cone relaxation convex optimization method. The calculation formula is as follows:

[0142]

[0143] in, The value of the comprehensive objective function after weighted transformation. The weighting coefficients for economic objectives. The normalized economic objective function value. The weighting coefficients for security objectives. This represents the normalized security objective function value.

[0144] After completing the above variable substitution, constraint transformation, and objective function linearization, the convex optimization solver is called to solve the single-objective optimization function to obtain the initial feasible solution and the feasible region boundary. The initial feasible solution will serve as the initial population source for the next step of the non-convex optimization method of multi-objective particle swarm optimization, and the feasible region boundary will be used to limit the search space of the non-convex optimization method of multi-objective particle swarm optimization.

[0145] The above methods offer fast solution speed, clear model structure, and high optimization accuracy. However, due to the introduction of relaxation processing, the feasible region of the reactive power dynamic resource allocation model may expand, posing a certain risk of solution bias. Auxiliary constraints such as the McCormick Envelope can be introduced to further shrink the variable space, thereby improving the accuracy of the relaxed solution.

[0146] Specifically, the non-convex optimization method of multi-objective particle swarm optimization uses particles as basic individuals. Each particle represents a set of reactive resource allocation decision variables, and its position can be composed of equipment capacity, dynamic reactive power output, capacitor bank switching actions, etc. The fitness of a particle consists of an economic objective function and a safety objective function. A non-dominated sorting mechanism is used to maintain an external elite solution set and select the current Pareto optimal solution.

[0147] The process of the nonconvex optimization method for multi-objective particle swarm optimization includes:

[0148] Initialize the position and velocity of the particle swarm. Each particle represents a set of reactive resource allocation decision variables, and the position of the particle is randomly generated within the feasible region boundary.

[0149] The dual-objective fitness of each particle is calculated based on the dual-objective function: the decision variables represented by the particle are substituted into the power flow equation to solve the system operating state, and the economic objective value and the safety objective value are calculated respectively.

[0150] To determine if the current particle is not dominated by any particle in the external elite solution set, maintain the external elite solution set based on the non-domination relationship and select the current Pareto optimal solution: Determine if the current particle's bi-objective fitness is dominated by any particle in the external elite solution set: If the current particle is not dominated by any particle in the external elite solution set, add it to the external elite solution set; if the current particle dominates some particles in the external elite solution set, replace the dominated particles with the current particle; if the current particle is dominated by any particle in the external elite solution set, discard the current particle. The particles in the maintained external elite solution set are the current Pareto optimal solution.

[0151] The individual historical best position of each particle is updated based on non-dominated relationships, and the swarm best is selected from the external elite solution set. The update rule for individual historical best is as follows: for each particle, the bi-objective fitness of the current position is non-dominated and compared with the bi-objective fitness of its own historical best position. If the bi-objective fitness of the current position dominates the bi-objective fitness of its own historical best position, the current position is directly updated as the best position. If the two do not dominate each other, the bi-objective fitness with higher crowding is retained to avoid individual best degradation. The update rule for swarm best is as follows: after adding the newly generated non-dominated particles to the external elite set, all particles in the external elite set are non-dominated and sorted to select the Pareto front solution for the current iteration. At the same time, the front solutions are sorted in descending order of crowding. When the size of the external elite set exceeds a set threshold, particles with low crowding are removed first to maintain population diversity and solution distribution.

[0152] The position and velocity of particles are updated based on inertia weights and learning factors: the inertia weights adopt a linear dynamic adjustment strategy, while the learning factors are configured with fixed values. In a specific embodiment of the present invention, the initial value of the inertia weights is set to 0.9, and it decreases linearly to 0.4 as the number of iterations increases; the cognitive learning factor and the social learning factor both range from 1.8 to 2.2, with a preferred value of 2.0.

[0153] The algorithm iterates until a preset termination condition is met. This termination condition employs a combination of criteria, including a maximum iteration count criterion, a convergence stability criterion, and a computation time criterion. In one specific embodiment, the maximum iteration count criterion includes setting the iteration count to a range of 100-200 times, preferably 150 times. When the iteration count reaches this upper limit, the algorithm automatically terminates to avoid unlimited iteration. The convergence stability criterion includes ensuring that the number of Pareto front solutions in the external elite set remains unchanged for 20 consecutive iterations and that the rate of change of the hypervolume index is less than 0.5%. The computation time criterion includes ensuring that the computation time for a single optimization exceeds 30 minutes. When the computation time exceeds this threshold, the algorithm is forcibly terminated to avoid excessively long computation times for large-scale examples. The iteration terminates when any one of the above conditions is met, and the algorithm outputs the complete set of Pareto optimal solutions in the current external elite set.

[0154] For the constraints in the reactive power dynamic resource allocation model, a strategy combining feasibility priority and penalty functions is adopted. A penalty term is introduced for each objective function value of a particle that violates the constraints, calculated as follows:

[0155]

[0156] in, The corrected fitness function. The original objective function includes both the economic objective function and the safety objective function. As a penalty weighting coefficient, This is a function that measures the degree to which a particle violates various constraints.

[0157] To verify the effectiveness of this invention, the IEEE 30-node system was selected as the test object to construct a typical computational example. The typical daily load curve selected in this invention is as follows: Figure 2 As shown, the system load forms two load peaks in the early morning and evening, respectively, exhibiting a typical "double-peak" load characteristic. This characteristic is representative and suitable as a typical example to support and verify the results of the optimization model proposed in this invention.

[0158] The system parameter settings used in the simulation process of this invention are shown in Table 1, including the number of nodes, number of stages, reference power, voltage limit, frequency reference value, and network-type equipment installation nodes, which provide data support for subsequent optimization result analysis.

[0159] Table 1 Parameter Setting Table

[0160]

[0161] To verify the dynamic control capability and operational rationality of the reactive power dynamic resource allocation method, this invention further analyzes the reactive power scheduling, equipment utilization level, and load tracking performance in the optimization results to verify the effectiveness and rationality of the reactive power dynamic resource allocation of this invention.

[0162] Daily reactive power planning for grid-type equipment, such as Figure 3 As shown, the network-type equipment exhibits clear time-series response characteristics over a 24-hour period. During high-load periods in the daytime, each device maintains a high output level, especially during the midday and evening peak load periods, with coordinated adjustments between devices to meet the needs of system voltage stability and load changes. In contrast, during the relatively low load periods in the early morning and midday, the device output appropriately decreases, achieving the dual goals of dynamic reactive power support and load adaptation, demonstrating excellent voltage-reactive power droop control characteristics.

[0163] The daily utilization rate of network-type equipment is as follows Figure 4As shown, the utilization rate of the three grid-type reactive power units remained between 80% and 90% for most of the day, with no overload operation or prolonged idleness observed, indicating that their capacity configuration has good adaptability and redundancy design. Especially during periods of sudden load increases or voltage disturbances, the equipment can quickly increase its utilization rate to ensure voltage response capability, verifying the high adaptability and robustness of the optimized configuration.

[0164] The load tracking performance of the optimized scheme is as follows: Figure 5 As shown, the standardized total active power output curve is highly consistent with the actual load curve, and the tracking error is always controlled within a small range. This fully demonstrates that the grid-type equipment has good response accuracy and control sensitivity under optimized scheduling, and can effectively support the stable operation of the system.

[0165] In summary, the reactive power dynamic resource allocation method of the present invention achieves efficient resource scheduling and voltage control in actual operation, which not only meets the system safety requirements, but also takes into account economy and sustainability, demonstrating good engineering adaptability and promotion potential.

[0166] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A method for dynamic reactive power resource allocation considering network characteristics and voltage stability constraints, characterized in that, include: Based on the voltage stability requirements of the new power system and the operating characteristics of grid-type equipment, a dual objective function system is constructed with the goal of minimizing the total configuration cost as the economic objective and minimizing the sum of squared voltage deviations after a fault as the safety objective. Based on the safety operation specifications of the power system, three types of constraints are set: static operation, equipment physical limitations, and grid control characteristics. A reactive power dynamic resource allocation model that takes into account grid characteristics and voltage stability constraints is established. Solve the reactive power dynamic resource allocation model to obtain the optimal reactive power dynamic resource allocation scheme that takes into account network characteristics and voltage stability constraints.

2. The reactive power dynamic resource allocation method considering network characteristics and voltage stability constraints according to claim 1, characterized in that: The economic objectives include at least the investment and maintenance costs of grid-type equipment, traditional dynamic equipment, and capacitor banks, calculated using the following formula: ； in, For economic purposes, It is the set of all buses or nodes in a new type of power system. For the unit investment of node i, The capacity of the network-type equipment allocated to node i. Let i be the operation and maintenance cost. Let i be the switching cost. The number of times the capacitor bank at node i is switched on and off; the unit investment and maintenance cost of the node includes the investment and maintenance costs of traditional dynamic equipment.

3. The reactive power dynamic resource allocation method considering network characteristics and voltage stability constraints according to claim 1, characterized in that: The security objective is used to evaluate the voltage recovery capability and voltage stability of the new power system after a fault, and the calculation formula is as follows: ； in, For security purposes, This refers to a set of pre-defined fault conditions or disturbance scenarios in the power grid. It is the set of all buses or nodes in a new type of power system. Let be the voltage value at node i after fault k. Let be the reference voltage for node i.

4. The reactive power dynamic resource allocation method considering network characteristics and voltage stability constraints according to claim 1, characterized in that: The static operating constraints include power flow balance constraints and system power balance constraints; The physical constraints on the equipment include capacity circle constraints and reactive power ramp rate constraints. The network control characteristic constraints include voltage-reactive droop control characteristic constraints and virtual inertia characteristic constraints.

5. The reactive power dynamic resource allocation method considering network characteristics and voltage stability constraints according to claim 4, characterized in that: The power flow balance constraints include: In a static scenario, power balance and node voltage upper and lower limits must be satisfied. The calculation formula is as follows: ； ； ； in, It is the set of all buses or nodes in a new type of power system. Let i be the electrical conductance between node i and node j. Let be the real part of the voltage phasor at node i. Let be the real part of the voltage phasor at node j. Let i be the imaginary part of the voltage phasor at node i. Let be the imaginary part of the voltage phasor at node j. Let be the susceptance between node i and node j. For the active power output of network-type devices at node i, Let be the active load of node i. For the reactive power output of network-type devices at node i, This is the reactive power compensation amount of the parallel capacitor bank installed at node i. For the reactive load of node i, This represents the lower limit of the allowable voltage at node i. This represents the upper limit of the allowable voltage at node i. The voltage amplitude at node i; For a wired structure, the current in each line does not exceed the thermal stability limit, expressed as: ； in, Let be the current amplitude of line ij. The maximum allowable current for line ij is given. It is the set of all branches in the power grid; The formula for calculating the system power balance constraint is: ； 。 6. The reactive power dynamic resource allocation method considering network characteristics and voltage stability constraints according to claim 4, characterized in that: The expression for the capacity circle constraint is: ； in, For network-type devices, the rated apparent power capacity at node i, For the active power output of network-type devices at node i, For the reactive power output of network-type devices at node i; The expression for the reactive ramp rate constraint is: ； in, The reactive power output of the network-type device at node i at time t. For network-type equipment The reactive power output at node i at all times To control the time step, The maximum reactive power regulation rate of the network-type equipment at node i.

7. The reactive power dynamic resource allocation method considering network characteristics and voltage stability constraints according to claim 4, characterized in that: The calculation formula for the voltage-reactive droop control characteristic constraint is as follows: ； in, For the reactive power output of network-type devices at node i, The reference reactive power output of the network-type device at node i. This is the voltage-reactive droop factor. Let i be the voltage reference value at node i. Let be the voltage amplitude at node i; The formula for calculating the virtual inertia characteristic constraint is as follows: ； in, For virtual inertia constant, Let i be the virtual angular velocity of the second-order network device at node i. Let be the mechanical power of the second-order network-type equipment at node i. Let be the electromagnetic power of the second-order network device at node i.

8. The reactive power dynamic resource allocation method considering network characteristics and voltage stability constraints according to claim 1, characterized in that: Solving the reactive power dynamic resource allocation model includes: A second-order cone relaxation convex optimization method is used to relax and linearize the non-convex terms of the reactive power dynamic resource allocation model to obtain a feasible solution and feasible domain boundary that satisfy the basic operating constraints of the new power system. Using the feasible solutions as the original population, a Pareto front solution set is searched within the search space defined by the feasible domain boundary using a non-convex optimization method of multi-objective particle swarm optimization. During the iteration process, the optimal solution of the new multi-objective particle swarm search is fed back to the second-order cone relaxation stage to dynamically update the feasible region boundary.

9. The reactive power dynamic resource allocation method considering network characteristics and voltage stability constraints according to claim 8, characterized in that: The convex optimization method employing second-order cone relaxation to relax and linearize the non-convex terms of the reactive power dynamic resource allocation model includes: To address the nonlinear characteristics of the power flow equations, auxiliary variables are introduced, and the calculation formula is as follows: ； ； ； in, Let be the voltage amplitude at node i. Let J be the voltage magnitude at node j. The voltage phase angle difference between node i and node j. , , For intermediate calculations, Let be the real part of the voltage phasor at node i. The imaginary part of the voltage phasor at node i; Based on auxiliary variables, the nonlinear terms in the power flow equations are transformed into a linear representation, and the calculation formula is as follows: ； ； in, Inject active power into node i. Let i be the self-conductance of node i. Let i be the electrical conductance between node i and node j. Let be the susceptance between node i and node j. For the active power output of network-type devices at node i, Let be the active load of node i. Inject reactive power into node i. Let be the self-susceptance of node i. For the reactive load of node i, For the reactive power output of network-type devices at node i, This is the reactive power compensation amount of the parallel capacitor bank installed at node i; To ensure geometric consistency between auxiliary variables and branch power, a second-order cone constraint is introduced to restrict their product relationship, expressed as: ； in, As an auxiliary variable, For the set of all branches, It is the Euclidean norm; The voltage upper and lower limit constraints are transformed into linear inequalities with respect to auxiliary variables, expressed as: ； in, This is the lower limit of the allowable voltage amplitude at node i; This represents the upper limit of the allowable voltage amplitude at node i; For the capacity circle constraint, the apparent power limit of network-type equipment is transformed into a cone form, expressed as: ； in, The rated apparent power capacity of the network-type equipment at node i; By introducing a weighted method, the biobjective function is transformed into a single-objective optimization function solvable by a convex optimization method with second-order cone relaxation. The calculation formula is as follows: ； in, The value of the comprehensive objective function after weighted transformation. The weighting coefficients for economic objectives. The normalized economic objective function value. The weighting coefficients for security objectives. This represents the normalized security objective function value. Call the convex optimization solver to solve the single-objective optimization function and obtain the initial feasible solution and the feasible region boundary.

10. The reactive power dynamic resource allocation method considering network characteristics and voltage stability constraints according to claim 8, characterized in that: The search for the Pareto front solution set using the nonconvex optimization method of the multi-objective particle swarm optimization method includes: Initialize the position and velocity of the particle swarm, with each particle representing a set of reactive dynamic resource allocation decision variables; The dual-objective fitness of particles is calculated based on a dual-objective function; Determine whether a particle is non-dominated by the external elite solution set, maintain the external elite solution set based on the non-domination relationship, and select the current Pareto optimal solution; Update the individual historical best position of each particle and the group optimal solution of the entire particle swarm; The position and velocity of the particles are updated based on the inertia weight and the learning factor; The loop iterates until the preset termination condition is met; A penalty is introduced to adjust the fitness of particles that violate the constraints. The calculation formula is as follows: ； in, The corrected fitness function. The original objective function includes both the economic objective function and the safety objective function. As a penalty weighting coefficient, This is a function that measures the degree to which a particle violates various constraints.

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