A hierarchical planning method for dynamic reactive power resources in distribution network considering dynamic response characteristics and multi-resource coordination

Abstract

The application relates to a power distribution network dynamic reactive resource hierarchical planning method considering dynamic response characteristics and multi-resource coordination, which comprises the following steps: the PI controller proportional coefficient and integral coefficient of a dynamic reactive compensation device are included in planning layer decision variables, and joint optimization is realized with device site selection and rated capacity; a load-photovoltaic output correlation model is constructed to generate typical operation scenes, a model predictive control strategy is introduced to simulate real-time adjustment behavior of the device, accurate description of operation time sequence uncertainty and physical driving evaluation of operation cost are realized; the safety requirements of transient voltage drop depth and recovery time are quantified by using an opportunity constraint, and a penalty function is integrated into the optimization framework to replace an empirical dynamic penalty cost, and a quantifiable safety margin is provided. Compared with the prior art, the application provides a complete and reliable technical solution for dynamic reactive resource planning of a high photovoltaic penetration power distribution network.

Description

Technical Field

[0001] This invention relates to the field of distribution network planning technology, and in particular to a hierarchical planning method for dynamic reactive resources of distribution networks that considers dynamic response characteristics and multi-resource coordination. Background Technology

[0002] As a crucial link connecting users in the power system, the voltage stability of the distribution network directly affects power supply quality and operational safety. With the continuous increase in the penetration rate of distributed photovoltaic (PV) power, the power characteristics of the distribution network have undergone fundamental changes: from traditional unidirectional, deterministic power flow to bidirectional, highly volatile power flow. The intermittent and random nature of PV output leads to frequent voltage limit exceedances, especially during periods of high generation under light load, where voltage rise is prominent. Furthermore, during transient processes such as faults, the weak inertia of PV power and the risk of grid disconnection may exacerbate voltage drops, threatening the dynamic safety of the system.

[0003] To address these challenges, dynamic reactive power compensation devices (such as Static Var Compensators (SVCs) and Static Synchronous Compensators (STATCOMs) have become core resources for voltage regulation in distribution networks due to their fast response and strong regulation capabilities. Meanwhile, photovoltaic inverters themselves possess rapid reactive power regulation capabilities and can participate in system support as a dynamic reactive power source with near-zero marginal cost. How to rationally plan the installation location, capacity, and control parameters of dynamic reactive power equipment, and coordinate the utilization of the reactive power potential of photovoltaic inverters, is a key issue that urgently needs to be addressed in the current field of distribution network planning.

[0004] In recent years, scholars both domestically and internationally have conducted extensive research on reactive power planning for distribution networks, forming a planning methodology system based on the "site selection-capacity determination" approach. However, existing research still has significant shortcomings in handling dynamic response characteristics, multi-timescale coordination, and the integration of multiple resource types, specifically manifested in the following four challenges: First, the planning decision-making dimension is singular, and controller parameters and equipment capacity are optimized separately. Traditional dynamic reactive power planning methods generally treat equipment location and rated capacity as the only decision variables, while the proportional-integral (PI) parameters of the equipment controller are usually determined empirically or through post-optimization independent of the planning stage. This separation of "hardware capacity" and "software parameters" leads to two serious consequences: on the one hand, equipment capacity and response speed cannot be coordinated and matched, potentially resulting in contradictions such as sufficient capacity but insufficient dynamic support, or excessively fast response but idle capacity; on the other hand, the decisive influence of controller parameters on the transient voltage recovery process is completely ignored, and the dynamic performance of the planned scheme under real fault scenarios cannot be guaranteed. Existing research has not yet established a mathematical model that incorporates controller parameters into the decision variables of the planning level, and lacks a theoretical framework for joint optimization of capacity and parameters.

[0005] Second, the uncertainties during the operational phase are not accurately characterized, leading to distorted simulations of equipment regulation behavior. Distribution network operation is affected by the dual randomness of load fluctuations and photovoltaic output, with a significant correlation between the two (e.g., air conditioning load increases synchronously when photovoltaic output is high on sunny days). Existing planning methods often use independent sampling or typical daily curves to handle uncertainties, neglecting the joint probability distribution characteristics of load and photovoltaic power, resulting in systematic deviations between the generated operational scenarios and actual conditions. Furthermore, when assessing operating costs, most studies use heuristic rules (such as voltage threshold-based switching strategies) to simulate the reactive power regulation behavior of equipment, rather than realistically reflecting the dynamic response process of the controller on a continuous time scale. This simplification fails to transfer the controller parameters determined at the planning level to the operating cost assessment, leaving the economic evaluation of the planning scheme lacking a physical basis.

[0006] Third, the quantification methods for dynamic voltage safety have shortcomings and are difficult to integrate with planning optimization. Transient voltage safety is a key indicator for distribution network recovery after faults, but existing planning methods handle this issue rather crudely. A common approach is to introduce an empirical dynamic penalty cost term into the objective function, indirectly constraining the dynamic performance of equipment by setting a penalty coefficient. However, this coefficient lacks a physical or economic basis for calibration, and its value often depends on numerical simulations, making the planning results highly sensitive to human parameters. More importantly, the penalty cost method cannot provide a quantifiable safety margin, i.e., it cannot guarantee the probability that the planned scheme will meet the dynamic safety indicators under preset fault scenarios. Chance-constrained planning has mature applications in handling power system uncertainties, but it has not yet been introduced into distribution network dynamic reactive power planning to quantify the safety requirements for transient voltage drop depth and recovery time.

[0007] Fourth, the reactive power support capability of photovoltaic (PV) inverters has not been incorporated into the collaborative planning system. Although PV inverters possess millisecond-level reactive power response capabilities, and their capacity is fixed at the time of PV installation, resulting in near-zero marginal operating costs, existing dynamic reactive power planning studies generally treat them as fixed factors or passive resources, failing to include the inverter's available reactive power range as an adjustable constraint in the joint optimization of equipment location and capacity setting. This leads to a disconnect between the two resources: on the one hand, planning schemes may over-rely on dynamic compensation devices, resulting in investment redundancy; on the other hand, the rapid response advantage of PV inverters cannot be utilized during fault transients, weakening the system's dynamic voltage recovery capability. Establishing a joint optimization model for dynamic reactive power equipment and PV inverters, ensuring that their capacity configurations and control parameters are matched, is crucial for improving resource utilization efficiency.

[0008] In summary, existing dynamic reactive power planning methods for distribution networks have significant shortcomings in four aspects: decision-making dimensions, uncertainty modeling, dynamic security quantification, and multi-resource coordination. There is an urgent need to establish an optimization method that can coordinate planning, operation, and dynamic full-time scale, and integrate multiple types of reactive power resources. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a hierarchical planning method for dynamic reactive resources of distribution networks that can comprehensively plan, operate, and dynamically manage across the entire time scale, and integrate multiple types of reactive resources, taking into account dynamic response characteristics and multi-resource coordination.

[0010] The objective of this invention can be achieved through the following technical solutions: A hierarchical planning method for dynamic reactive power resources in distribution networks, considering dynamic response characteristics and multi-resource coordination, includes the following steps: Planning layer optimization steps: Obtain the equipment parameters of each node device in the distribution network. These equipment parameters include binary addressing variables, continuous capacity variables, and continuous controller parameter variables. These parameters are used as decision variables for the equipment layer planning optimization objective and optimized to obtain the optimized equipment parameters. Operational layer optimization steps: First, estimate the load multiplier and photovoltaic multiplier based on historical data of the distribution network. Then, construct multiple typical operating scenarios and their probabilities based on the joint probability distribution of the load multiplier and photovoltaic multiplier. For each typical operating scenario, calculate the corresponding scenario operation optimization objective based on the optimized equipment parameters. The actual reactive power output considered in this operation planning optimization objective is calculated using a discrete PI control law based on the continuous controller parameter variables. Finally, synthesize the calculated scenario operation optimization objective values ​​of each typical operating scenario and sum them with corresponding probabilities to construct the operational layer planning optimization objective, thereby solving for the operation adjustment strategy of each device. Dynamic layer optimization steps: For the preset typical fault scenarios, establish a time-domain simulation model that considers the differences in device response speed. Record the voltage trajectory of each node in each simulation step of the time-domain simulation model, and extract the corresponding voltage drop depth and voltage recovery time indicators to determine whether they meet the corresponding transient safety opportunity constraints. Then, it is required that the probability of all nodes meeting the transient safety opportunity constraints in all typical fault scenarios is not lower than the given confidence level. Collaborative optimization steps: Based on the equipment-level planning optimization objectives and the operation-level planning optimization objectives, construct a collaborative optimization overall objective, and use the transient security opportunity constraints as penalty terms to form a collaborative optimization model for solution, thereby obtaining the optimal reactive power resource planning scheme for the distribution network.

[0011] Furthermore, the binary addressing variable represents a dynamic reactive power device of type t installed at node i, satisfying the addressing variable constraint, the expression of which is: In the formula, Install a dynamic reactive power device of type t on node i. It is a binary variable. A value of 1 indicates that a device of type t is installed on node i, and a value of 0 indicates that a device of type t is not installed on node i. For the set of candidate nodes; A set of device types; The continuous capacity variable This indicates the rated capacity of the type t device installed at node i; The continuous controller parameter variables include and , where represent the proportional coefficient and integral coefficient of the type t device installed at node i, respectively.

[0012] Furthermore, the constraints in the process of solving the equipment layer planning optimization objective include equipment capacity limits, total number of equipment limits, and investment budget constraints; The expression for the device capacity limit is: In the formula, , These are the minimum and maximum rated capacities of equipment of type t, respectively. The expression for the limit on the total number of devices is: In the formula, , These are the minimum and maximum allowed number of units to be installed, respectively. The expression for the investment budget constraint is: In the formula, Let be the present value of the initial investment in the device of type t installed at node i. This is the upper limit of the budget.

[0013] Furthermore, in the operation layer optimization step, the expression for calculating the actual reactive power output is: In the formula, Let t be the actual reactive power output of device of type i in scenario s during time period h. and The optimized continuous controller parameter variables, This is the voltage reference value. This is the voltage measurement value from the previous time period. This is a limiting function that restricts the output to the continuously variable capacity obtained after optimization. Within the range, This represents the interval between adjacent time periods.

[0014] Furthermore, the constraints in the process of solving the operational layer planning optimization objective include power flow equations, equipment output constraints, and photovoltaic inverter reactive power output constraints. The photovoltaic inverter reactive power output constraints consider that the reactive power output of the photovoltaic inverter is limited by the photovoltaic inverter's capacity and power factor. The expression for the photovoltaic inverter reactive power output constraints is as follows: In the formula, For the reactive power output of photovoltaic inverter node j during time period h in scenario s, Let J be the capacity of the photovoltaic inverter at node j. Let h be the active load of photovoltaic inverter node j in scenario s during time period h. This is the minimum permissible power factor.

[0015] Furthermore, the typical fault scenarios include fault types such as three-phase short circuit, two-phase short circuit, and single-phase grounding of the line. The faults in the typical fault scenarios are described by fault location, type, duration, and probability of occurrence. The time-domain simulation model is constructed based on the device differential equations described by a first-order inertial element and a PI controller. During the simulation process of the time-domain simulation model, the device differential equations are updated using the Euler method within each simulation step. The power flow equations considering the load ZIP model and fault admittance correction are solved, and the voltage trajectories of each node are recorded.

[0016] Furthermore, the expression for the device's differential equation is: In the formula, For the reactive power output of device type t at node i, Let be the intrinsic time constant of node i. and The optimized continuous controller parameter variables, Let i be the voltage reference value at node i. Let be the voltage of device i.

[0017] Furthermore, the calculation expression for the voltage drop depth is as follows: In the formula, Let be the voltage drop depth of node j under a typical fault scenario f. Let be the voltage at node j at time t. The fault start time. Duration of the fault; The expression for calculating the voltage recovery time is as follows: In the formula, Let be the voltage recovery time of node j under typical fault scenario f. This is the recovery threshold.

[0018] Furthermore, the expression for the transient security opportunity constraint is: In the formula, The lower limit of the permissible voltage drop depth, It is a positive number. The first binary variable represents whether node j meets the voltage drop index under fault f; The maximum allowable recovery time, The second binary variable represents whether node j meets the recovery time metric under fault f; Let f be the probability of occurrence of a typical failure scenario. The first level of risk. This is the second level of risk.

[0019] Furthermore, the calculation expression for the overall collaborative optimization objective is as follows: In the formula, To collaboratively optimize the overall goal, To optimize the planning objectives at the equipment level, To optimize the goals of the runtime layer, The amount of violation of the transient security opportunity constraint. As a penalty factor; The equipment layer planning optimization objective is the degree to which the dynamic equipment requirements of the distribution network system are met or the annual value of the total investment cost of the entire distribution network system. The optimization objective of the operation layer planning is the operational stability of the distribution network system or the expected value of the annual operating cost of the distribution network system.

[0020] Compared with the prior art, the present invention has the following advantages: (1) This invention uses the proportional and integral coefficients of the PI controller of the dynamic reactive power compensation device as continuous decision variables in the planning layer, which together with the binary variables of equipment location and the continuous variables of rated capacity constitute a complete decision space. By establishing a mathematical correlation model between controller parameters and equipment transient response characteristics, capacity configuration and response speed are deeply coupled in the optimization process. This method breaks through the traditional serial mode of determining capacity first and then setting parameters in planning, and can adaptively match equipment capacity and controller parameters according to the dynamic needs of the system, avoiding performance redundancy or insufficient support caused by improper parameters.

[0021] (2) This invention constructs a data-model hybrid-driven operation layer evaluation method at the operation layer. First, a Copula function is used to describe the joint probability distribution of load multipliers and photovoltaic multipliers. By generating a typical scenario set with a consistent dependency structure, the temporal uncertainty of the operation phase is accurately characterized. Second, a model predictive control strategy is introduced to simulate the real-time adjustment behavior of the equipment during daily operation. The controller parameters determined at the planning layer are directly used for discrete PI control laws, so that the operation cost calculation can truly reflect the dynamic response process of the equipment. This evaluation method incorporates network loss cost, equipment operation and maintenance cost, voltage over-limit penalty, and distributed power generation revenue into the objective function, realizing the accurate quantification of the economic performance of the planning scheme.

[0022] (3) This invention establishes a transient voltage safety assessment model at the dynamic layer that considers the differences in device response speed. Time-domain simulations are performed for preset typical fault scenarios to extract the voltage drop depth and recovery time indicators for each node. Unlike the traditional penalty cost method, this invention introduces opportunity constraints to quantify dynamic safety requirements, requiring that the probability of all nodes meeting the indicators in all fault scenarios is not less than a given confidence level. This opportunity constraint is integrated into the optimization framework through a penalty function. This method provides a quantifiable safety margin for the planning scheme without calibrating empirical penalty coefficients, while ensuring the solvability of the optimization problem.

[0023] (4) This invention tightly couples the planning layer, operation layer and dynamic layer through data flow and constraints: the decision variables (equipment type, capacity, controller parameters) of the planning layer are input to the operation layer and the dynamic layer; the annual operating cost calculated by the operation layer and the opportunity constraint violation situation evaluated by the dynamic layer are fed back to the upper layer, which together constitute the total cost target and form a full-time-scale collaborative optimization framework of planning-operation-dynamic, providing a complete technical solution for dynamic reactive power resource planning of high photovoltaic penetration distribution networks. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating a hierarchical planning method for dynamic reactive resources in a distribution network that considers dynamic response characteristics and multi-resource coordination, provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of a three-layer collaborative optimization framework provided in an embodiment of the present invention; Figure 3 This is a flowchart of an improved genetic simulated annealing algorithm provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of an inner-layer simulation process provided in an embodiment of the present invention; Figure 5 This is a structural diagram of an IEEE 33-node standard distribution network provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the convergence curve of an IGSA algorithm provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of the equipment installation location and capacity distribution corresponding to an optimal solution provided in an embodiment of the present invention; Figure 8 This is a schematic diagram of a typical node voltage distribution provided in an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0026] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0027] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0028] Example 1 like Figure 1 and Figure 2 As shown, this embodiment provides a hierarchical planning method for dynamic reactive power resources in distribution networks that considers dynamic response characteristics and multi-resource coordination, including the following steps: Planning layer optimization step S1: Obtain the equipment parameters of each node device in the distribution network. These equipment parameters include binary addressing variables, continuous capacity variables, and continuous controller parameter variables. They are used as decision variables for the equipment layer planning optimization objective to optimize and solve for the optimized equipment parameters. Operational layer optimization step S2: Estimate the load multiplier and photovoltaic multiplier based on historical data of the distribution network. Based on the joint probability distribution of the load multiplier and photovoltaic multiplier, construct multiple typical operating scenarios and their probabilities. For each typical operating scenario, calculate the corresponding scenario operation optimization objective based on the optimized equipment parameters. The actual reactive power output considered in this operation planning optimization objective is calculated using a discrete PI control law based on the continuous controller parameter variables. Combine the calculated values ​​of the scenario operation optimization objectives of each typical operating scenario with corresponding probabilities and perform a weighted summation to construct the operational layer planning optimization objective, so as to solve for the operation adjustment strategy of each device. Dynamic layer optimization step S3: For the preset typical fault scenarios, establish a time-domain simulation model that considers the differences in equipment response speed. Record the voltage trajectory of each node in each simulation step of the time-domain simulation model, extract the corresponding voltage drop depth and voltage recovery time index to determine whether it meets the corresponding transient safety opportunity constraint. Then, it is required that the probability of all nodes meeting the transient safety opportunity constraint in all typical fault scenarios is not lower than the given confidence level. Collaborative optimization step S4: Based on the planning and optimization objectives of the equipment layer and the planning and optimization objectives of the operation layer, construct the overall collaborative optimization objective, and use the transient security opportunity constraint as a penalty term to form a collaborative optimization model for solving, so as to obtain the optimal reactive power resource planning scheme for the distribution network.

[0029] The overall approach of this method is to deeply couple planning decisions with operational performance and dynamic safety, aiming to minimize the total annual cost over the entire life cycle. The planning layer not only determines the installation location and rated capacity of the equipment but also uses the equipment's PI controller parameters as decision variables, achieving coordinated optimization of "hardware capacity" and "software parameters." This ensures that the equipment's dynamic response capability matches its capacity, avoiding performance redundancy or inadequacy due to improper parameter settings. The operation layer employs load-PV output correlation modeling based on Copula functions to generate typical operating scenarios with probabilistic consistency. A model predictive control strategy is introduced to simulate the real-time adjustment behavior of the equipment during daily operation, accurately assessing annual operating costs (including grid losses, equipment maintenance, voltage over-limit penalties, and distributed generation revenue). The dynamic layer performs time-domain simulations for preset typical fault scenarios, establishing a transient voltage safety assessment model that considers differences in equipment response speed. Voltage drop depth and recovery time are transformed into opportunity constraints, ensuring that the probability of the system meeting dynamic safety indicators under various fault conditions is not lower than a given confidence level, replacing traditional, difficult-to-calibrate penalty cost methods. In addition, the reactive power support capability of photovoltaic inverters is incorporated into the coordinated adjustment of the operation layer and the dynamic layer to achieve joint optimization of multiple types of reactive power resources.

[0030] The three layers are tightly coupled through data flow and constraints: decision variables (equipment type, capacity, controller parameters) from the planning layer are input to the operation and dynamic layers; the annual operating cost calculated by the operation layer and the opportunity constraint violations evaluated by the dynamic layer are fed back to the upper layer, together constituting the total cost objective. This problem is a mixed-integer nonlinear programming problem, characterized by multiple constraints and high nonlinearity. This embodiment proposes an improved genetic simulated annealing algorithm for solving the problem, integrating the global search capability of the genetic algorithm and the local escape capability of simulated annealing, effectively avoiding getting trapped in local optima. The entire framework has been implemented on the IEEE 33-bus distribution system (corresponding to the program example in this embodiment), and the effectiveness and superiority of the method have been verified through actual simulation.

[0031] The core innovations of this method are reflected in four aspects: First, it incorporates controller parameters into planning decisions to achieve coordinated optimization of capacity and parameters; second, it combines Copula functions with model predictive control to accurately characterize operational uncertainties; third, it quantifies dynamic safety requirements with opportunity constraints, giving the planning scheme a quantifiable safety margin; and fourth, it achieves multi-resource coordination between dynamic reactive power equipment and photovoltaic inverters, improving investment efficiency. The overall framework is as follows: Figure 1 As shown, subsequent chapters will elaborate on each layer of the model, the solution algorithm, and the verification results of the examples.

[0032] I. Planning Layer Model: Co-optimization of Equipment Location and Capacity Determination with Controller Parameters Traditional dynamic reactive power planning methods often focus only on the installation location and rated capacity of equipment, neglecting the crucial impact of controller parameters on dynamic performance. This leads to a mismatch between equipment response speed and system demand during actual operation, or a contradiction between capacity redundancy and insufficient dynamic support capability. To address this issue, this section proposes incorporating the proportional and integral coefficients of the equipment's PI controller into the planning decision variables, achieving synergistic optimization of "hardware capacity" and "software parameters." The core idea is to simultaneously optimize equipment capacity and control parameters to ensure a coordinated match between the reactive power response speed and capacity under fault conditions, meeting both steady-state voltage regulation requirements and guaranteeing rapid and effective reactive power support during transient processes. This step first defines decision variables, including binary addressing variables, continuous capacity variables, and continuous controller parameter variables, and establishes an annual value model for investment costs, discounting equipment purchase, installation, land, and connection costs to annual rates. Simultaneously, practical engineering constraints such as equipment capacity limits, installation quantity restrictions, and investment budgets are considered. To heuristically generate initial solutions, a voltage sensitivity index based on electrical distance is also introduced. By using controller parameters as the optimization object, this section lays the foundation for more accurately characterizing the device response behavior in subsequent operational and dynamic layer simulations, reflecting the planning concept of deep coupling between capacity and parameters.

[0033] 2.1 Decision Variables Assume the power distribution system has a total of There are nodes, and the candidate node set is... Define binary variables This indicates that a dynamic reactive power device of type t is installed at node i, where the set of device types is... Continuous variables This represents the rated capacity (Mvar) of the type t device installed at node i. (Continuous variable) and These represent the proportional gain and integral gain of the device, respectively. To avoid installing multiple devices at the same node, constraints are introduced: (1) In the formula: This is a binary variable; a value of 1 indicates that a device of type t is installed at node i. For the set of candidate nodes; This is a set of device types.

[0034] The controller parameters must be within the feasible range for the project: (2) (3) In the formula: , For type t device ratio 2.2 Investment Cost Annual Value Model Investment costs consist of equipment purchase costs, installation costs, land costs, and access fees. Optimizing controller parameters does not increase hardware costs and therefore does not affect the investment. The initial investment for device type t on node i is: (4) In the formula: Fixed installation cost (in yuan) for type t equipment; Cost per unit capacity (RMB / Mvar); Land cost (RMB / unit); Cost of accessing the system (RMB / unit).

[0035] The residual value of the equipment at the end of its planned lifespan of n years is calculated based on the initial investment. calculate: (5) In the formula: This refers to the residual value rate.

[0036] Considering the time value of money, the discount rate *r* is used to equalize the investment and residual value in annualized terms. The equalization factor is: (6) After the residual value is discounted to present value, its equivalent value deduction can be expressed as: (7) Therefore, the annualized investment value for device type t at node i is: (8) The total annual investment cost of the entire system is: (9) 2.3 Technical Constraints 2.3.1 Equipment Capacity Limitations Different types of equipment are subject to product specifications, and their rated capacity should be within the allowable range: (10) In the formula: , These are the minimum and maximum rated capacities (Mvar) for device type t, respectively.

[0037] 2.3.2. Limitation on the total number of devices Considering factors such as site resources and operation and maintenance capabilities, the total number of dynamic reactive power devices installed in the entire system must meet the following requirements: (11) In the formula: , These represent the minimum and maximum allowed number of units to be installed, respectively.

[0038] 2.3.3 Investment Budget Constraints The sum of the present value of the initial investment in all equipment must not exceed the budget ceiling B: (12) 2.4 Sensitivity Indicators To heuristically generate an initial solution, the voltage-reactive power sensitivity of each candidate node is calculated. i The electrical distance to the root node is defined as: (13) In the formula: , Let K be the resistance and reactance (per unit value) of branch k on the path. Sensitivity scoring is taken as... After normalization, it is used for initialization.

[0039] II. Runtime Layer Model: Scene Generation and Model Predictive Control Simulation Based on Copula The operation layer serves as a bridge connecting planning decisions and actual operational performance. Its core task is to accurately assess the annual operating cost of the system throughout its entire lifecycle, given a planning scheme. Traditional methods typically employ simple typical daily curves or random sampling, which struggle to reflect the correlation between load and photovoltaic output. Furthermore, equipment regulation behavior often relies on heuristic rules, leading to deviations from actual conditions. This section proposes a data-model hybrid-driven operation cost assessment method: First, a Copula function is used to describe the joint probability distribution of load multipliers and photovoltaic multipliers, generating typical operating scenarios with a consistent dependency structure, making the scenario set closer to actual statistical characteristics. Second, a Model Predictive Control (MPC) strategy is introduced to simulate the real-time regulation process of equipment during daily operation. The optimized controller parameters are directly used for discrete PI control laws, accurately reflecting the dynamic response of equipment based on voltage deviations. Through scenario-by-scenario and hourly power flow calculations, network loss costs, equipment maintenance costs, voltage over-limit penalties, and distributed power generation revenue are accumulated, ultimately weighted to obtain the expected annual operating cost. This layer not only provides a key component for the total cost target but also transmits the impact of controller parameters to the operating cost through MPC simulation, achieving closed-loop coupling between planning and operation.

[0040] 2.1 Load-PV Output Correlation Modeling Based on Copula The marginal distributions of the load multiplier L and the photovoltaic multiplier P can be estimated from historical data, and are denoted as follows: and Clayton Copula was chosen to describe its lower-tail correlation: (14) In the formula: , ; The Copula parameter can be obtained by maximum likelihood estimation.

[0041] The steps to generate S typical scenarios based on Copula are as follows: 1. Generate random samples that follow a Copula. , ; 2. Obtain the load multiplier and photovoltaic multiplier through inverse transformation: , ; 3. Perform K-means clustering on the multipliers to obtain typical scenarios and their probabilities. ( ).

[0042] 2.2 Objective function of the runtime layer For a given planning scheme (including equipment type, capacity, and controller parameters), what is the operating cost for each time period h in each scenario s? It consists of network loss costs, equipment operation and maintenance costs, voltage over-limit penalties, and DG generation revenue: (15) In the formula: Unit network loss cost (RMB / kWh); The total active power loss (MW) of the system in scenario s during time period h. h represents the duration of the time period; The unit reactive power output maintenance cost of equipment of type t (RMB / Mvarh); Mvar represents the actual reactive power output (Mvar) of device type t on node i. , Voltage over-limit penalty coefficient (yuan / pu) 2 ); Let be the voltage amplitude (pu) at node j; , These are the upper and lower limits of the allowable voltage. The distributed generation revenue coefficient (RMB / MWh). Let be the active power output (MW) of DG at node j.

[0043] 2.3 Simulation of Model Predictive Control Strategy To accurately reflect the equipment's regulation behavior during actual operation, an MPC strategy in the form of a discrete PI controller is adopted. The reactive power reference value of the equipment during time period h is determined by the following formula: (16) In the formula: , To optimize the obtained controller parameters; This is a voltage reference value (usually taken as 1.02 pu). The voltage measurement value is from the previous time period; the integral term represents the accumulated historical deviation. This is a limiting function that restricts the output to within the device's capacity. Actual reactive power output. This is the reference value after the amplitude is limited.

[0044] 2.4 Power Flow Equations and Operating Constraints 2.4.1 Power Flow Equations Using polar coordinates for the power flow equations, for each node j: (17) (18) In the formula: , The active and reactive loads of node j are obtained by multiplying the base load by the load multiplier. , Let be the real and imaginary parts of the nodal admittance matrix; This represents the phase angle difference of the node voltage.

[0045] 2.4.2 Equipment Output Constraints The actual reactive power output of the equipment is limited by its rated capacity: (19) 2.4.3 Reactive Power Constraints of DG Photovoltaic inverters can provide reactive power support, but their reactive power output is limited by the inverter's capacity and power factor. (20) In the formula: The capacity of the photovoltaic inverter at node j; This is the minimum allowable power factor (0.85 in this embodiment).

[0046] 2.5 Annual operating costs The expected annual operating cost is the weighted sum of the daily operating costs for each scenario multiplied by 365 days. (twenty one) III. Dynamic Layer Model: Transient Safety Opportunity Constraints Considering Differences in Response Speed Dynamic voltage safety is a crucial indicator for distribution network operation, especially during post-fault transient processes, where the rapid response capability of dynamic reactive power equipment directly impacts voltage sag depth and recovery time. Existing planning methods often quantify dynamic performance by introducing penalty costs, but the penalty coefficient is difficult to calibrate reasonably and cannot guarantee that dynamic safety meets probabilistic requirements. This section innovatively employs chance constraints to characterize transient safety requirements: for preset typical fault scenarios (such as three-phase short circuits and single-phase grounding), a time-domain simulation model considering differences in equipment response speed is established, where equipment dynamics are described by a first-order inertial element and a PI controller, with the controller parameters serving as optimization variables for the planning layer. The voltage sag depth and recovery time of each node are extracted through simulation and compared with allowable limits. Binary variables are introduced to indicate whether the indicators are met, thus requiring that the probability of all nodes meeting the indicators under all fault scenarios is not less than a given confidence level. This chance constraint, integrated into the optimization framework through a penalty function, provides a quantifiable safety margin for the planning scheme, replacing the traditional empirical penalty costs. The model in this section directly utilizes the controller parameters provided by the planning layer, achieving deep coupling between dynamic performance and planning decisions, and ensuring the robustness of the planning scheme under real-world fault scenarios.

[0047] 3.1 Fault Scenario Set Consider N-1 possible faults in the system, including three-phase short circuits, two-phase short circuits, and single-phase grounding. Fault scenario set. It contains F faults, each fault f is determined by its location. ,type Duration and probability of occurrence describe( This embodiment presupposes three types of faults: three-phase short circuit at node 18 (probability 0.6), single-phase grounding at node 25 (probability 0.3), and two-phase short circuit at node 30 (probability 0.1).

[0048] 3.2 Equipment Transient Model The transient response of a dynamic reactive power device is described by a first-order inertial element and a PI controller, with controller parameters... To optimize variables, which directly affect response speed. The device's differential equation is: (twenty two) In the formula: The device's inherent time constant (s) is set to 0.05 for SVC and 0.02 for STATCOM. The voltage reference value is set to 1.0 pu. The integrator is initialized to 0, and anti-saturation limiting is set.

[0049] 3.3 Transient Simulation and Dynamic Indicators For each fault scenario f, a time-domain simulation is performed, with a time step of [missing information]. s, total duration The fault originated from... s, continuing After clearing, within each step, the device dynamic equations are first updated using the Euler method, and then the power flow equations considering the load ZIP model and fault admittance correction are solved. The voltage trajectories of each node are recorded. Extract the following metrics: Voltage sag depth ; Voltage recovery time , In the formula: The recovery threshold is set to 0.95 pu.

[0050] 3.4 Transient Security Opportunity Constraints The requirement is that the probability of all nodes satisfying the dynamic safety metric under all failure scenarios is not less than a given confidence level. This chance constraint can be expressed as: (twenty three) (twenty four) In the formula: The lower limit of the allowable voltage drop depth (taken as 0.75 pu); The maximum allowable recovery time (taken as 2.0s); , The risk level is set to 0.05 in this embodiment.

[0051] Since the number of failure scenarios is limited, chance constraints can be transformed into deterministic constraints. Binary variables are introduced. , Indicate whether the indicators are met: (25) (26) In the formula: M is a sufficiently large positive number. It is also required that the weighted average probability does not exceed the risk level. (27) 3.5 Dynamic penalty cost substitution If opportunity constraints are used, the dynamic layer does not incur direct costs, but it must satisfy the aforementioned constraints. During optimization, violations of opportunity constraints are handled through a penalty function, unifying the process within the overall cost minimization framework.

[0052] IV. Collaborative Planning of Multiple Types of Reactive Resources With the large-scale integration of distributed photovoltaic (PV) power, PV inverters have become an important reactive power regulation resource in distribution networks. Their fast response and flexible adjustment effectively assist dynamic reactive power compensation devices. However, existing planning studies typically treat PV inverters as fixed factors, failing to incorporate their reactive power capacity into optimization decisions, leading to resource waste or redundant investment. This section proposes treating the reactive power support capacity of PV inverters as an adjustable resource in both the operational and dynamic layers, enabling collaborative planning between dynamic reactive power equipment and PV inverters. Specifically, in the operational layer power flow calculation, the reactive power output of PV inverters is limited by inverter capacity and power factor, and can participate in regulation as a continuous variable. In the dynamic layer transient simulation, PV inverters also adopt a fast response model, jointly providing reactive power support with dynamic equipment. Through this collaboration, the capacity requirements and controller parameters of dynamic equipment can be matched with the reactive power capacity of PV, fully leveraging the fast response advantage of PV inverters and reducing the investment cost of dynamic equipment. This section also provides a precise expression for the available reactive power range of PV inverters and uses it as a constraint condition in both the operational and dynamic layers. This collaborative planning approach not only improves resource utilization efficiency but also enhances the system's dynamic voltage recovery capability under fault conditions.

[0053] 4.1 Modeling of the non-functional capacity of photovoltaic inverters Photovoltaic inverters can provide reactive power, but are limited by inverter capacity and active power output. The photovoltaic inverter capacity at node j is... Contribute your efforts Determined by the scenario multiplier. The maximum available reactive power capacity is: (28) Considering power factor limitations, the actual available reactive power capacity is: (29) 4.2 Optimization of Photovoltaic Reactive Power Inverter capacity is determined by photovoltaic investment and is not considered an optimization variable, but its reactive power output... As a variable at the operational level, it is constrained by equation (29). In the operational MPC, the reactive power output of photovoltaic power and the reactive power output of dynamic equipment are coordinated and adjusted, and are uniformly driven by voltage deviation.

[0054] 4.3 Advantages of Collaborative Planning The rapid response capability of photovoltaic inverters can provide instantaneous reactive power support during faults, compensating for the insufficient response time of dynamic equipment. Through collaborative optimization, the capacity requirements and controller parameters of dynamic equipment can be matched with the photovoltaic reactive power capacity, achieving optimal resource allocation.

[0055] V. Three-layer collaborative optimization model and solution method The first three sections established mathematical models for the planning, operation, and dynamic layers, respectively. However, these three layers are tightly coupled through decision and state variables, requiring a unified solution to obtain the globally optimal solution. This section first presents the overall objective function for the three-layer collaborative optimization—minimizing the total cost over the entire lifecycle (equal annual values), including the equal annual value of investment costs and the expected annual operating costs. The opportunity constraints of the dynamic layer are treated as penalty terms, forming a complete optimization model. This model is a mixed-integer nonlinear programming problem, characterized by high dimensionality, nonlinearity, and multiple constraints, making it difficult to solve using traditional mathematical optimization methods. Therefore, this embodiment proposes an improved genetic simulated annealing algorithm (IGSA), integrating the global search capability of genetic algorithms with the local escape capability of simulated annealing. The algorithm design includes: chromosome encoding (simultaneously encoding device type, capacity, and controller parameters), heuristic and random initial population generation, tournament selection, single-point crossover, adaptive mutation, elite retention, and simulated annealing local search for the optimal individual in each generation. The inner simulation module is responsible for calculating the operating cost and dynamic constraint violation for each individual, forming a complete fitness evaluation. Through iterative evolution, the final output is a planning scheme that satisfies dynamic safety constraints and minimizes the total cost. This section elaborates on each step of the algorithm and its interface with the three-layer model, reflecting the integrated design concept of model and algorithm.

[0056] 5.1 Collaborative Optimization Objective Function The goal of the three-layer collaborative optimization is to minimize the total annual cost over the entire lifecycle, while satisfying planning, operational, and dynamic safety constraints. The total cost consists of the annual cost of investment. Expected annual operating costs The opportunity constraints of the dynamic layer are handled through a penalty function. The objective function expression is: (30) In the formula: Given by equation (9); Given by equation (21); The violation of dynamic opportunity constraints is specifically defined as: (31) In the formula: , Defined by equations (25)-(26), it indicates whether node j meets the voltage drop and recovery time index under fault f; , Given a risk level (0.05 in this example); As a penalty factor, take This is to ensure that schemes that violate the constraints are effectively eliminated.

[0057] 5.2 Constraints Collaborative optimization must meet the following constraints: 1. Planning-level constraints: Equipment type uniqueness constraint: Equation (1) Controller parameter range constraints: Equations (2)-(3) Equipment capacity limit: Equation (10) Total number of devices limited: Equation (11) Investment budget constraint: Equation (12) 2. Runtime layer constraints: Power flow equations: Equations (17)-(18) Equipment output limit: Formula (19) DG reactive power output limitation: Equation (20) 3. Opportunity constraints at the dynamic layer: Definition of voltage sag and recovery time indicator variables: Equations (25)-(26) The probability satisfies the condition: Equation (27) Of the constraints mentioned above, the planning layer constraints are hard constraints, which are directly handled in the chromosome encoding and repair operations of the genetic algorithm; the running layer constraints are automatically satisfied in the power flow calculation; and the dynamic layer chance constraints are incorporated into the objective function through the penalty function.

[0058] 5.3 Improved Genetic Simulated Annealing Algorithm (IGSA) The IGSA algorithm proposed in this embodiment combines the global search capability of genetic algorithms with the local escape capability of simulated annealing, effectively solving high-dimensional mixed-integer nonlinear programming problems. The algorithm flow is as follows: Figure 3 As shown, the specific design is as follows.

[0059] 5.3.1 Chromosome coding Chromosomes use real number encoding and have a length of [missing information]. It is divided into four sections: Type of gene segment (length) ): Values ​​for each gene , respectively, represent not installing, installing SVC, and installing STATCOM.

[0060] Capacity gene segment (length) Each gene takes a value of [0,1], and during decoding, it is mapped to the actual capacity based on its type. (32) Proportional coefficient gene segment (length) ): Values ​​[0,1], decoded as .

[0061] Integral coefficient gene segment (length) ): Values ​​[0,1], decoded as .

[0062] For nodes without installed devices, their capacity and controller parameters are invalid, but they still need to participate in crossover and mutation during evolution. The repair operation will set them to 0 or a reasonable value.

[0063] 5.3.2 Fitness Function The fitness function is defined as the reciprocal of the total cost, so that maximizing the fitness corresponds to minimizing the cost: (33) In the formula: The amount of violation of hard constraints at the planning level, including exceeding limits on the number of equipment, capacity, and budget, is linearly summed according to the proportion of the exceedance. As a planning constraint penalty factor, take .

[0064] 5.3.3 Initial Population Generation The initial population was generated using a combination of heuristic and random methods, with the heuristic proportion set at 50%. Heuristic solutions were sorted based on voltage sensitivity: the solution with the highest sensitivity was selected. to Several nodes were selected as candidates, and device types were randomly assigned (for the top 30% of high-sensitivity nodes, STATCOM was selected with a 70% probability and SVC with a 30% probability; for the remaining nodes, the selection was equal in probability). Capacity was uniformly randomized within allowable limits, and controller parameters were randomly perturbed around typical values ​​(typical values: SVC...). STATCOM (The perturbation amplitude is 20%). The remaining individuals are generated completely randomly to ensure population diversity.

[0065] 5.3.4 Genetic manipulation Selection: A tournament selection method is used, where three individuals are randomly selected each time, and the one with the highest fitness is selected to enter the mating pool. This process is repeated until the parent population is full.

[0066] Crossover: Single-point crossover is used, and the crossover probability is... Randomly select a crossover point, swap all gene segments after the crossover point between the two parent individuals, and generate two offspring individuals.

[0067] Mutation: For each gene, a mutation probability is given. Initiate mutation. When a gene of a certain type mutates, if the current value is -1, it will randomly change to 0 or 1; if the current value is 0 or 1, it will change to -1 with a 0.5 probability and to another type with a 0.5 probability. For continuous gene mutations, add a Gaussian perturbation. And truncated to [0,1].

[0068] Repair procedure: After mutation, check the total number of devices for each individual. If the number of installations exceeds... Randomly remove redundant devices (set type genes to -1, and corresponding capacity and parameter genes to 0); if less than Randomly select an uninstalled node to add a device (random type, random capacity, random parameters). Simultaneously ensure that the capacity and parameter values ​​are non-zero at the installation node.

[0069] 5.3.5 Simulated Annealing Local Search After each generation of genetic operations, simulated annealing local search is performed on the current best individual to enhance local discovery capabilities. The steps are as follows: 1. Using the current best individual As the initial solution, initialize the current temperature. .

[0070] 2. For L=10 iterations: right Generate new solutions by performing random perturbations Perturbation strategy: Randomly select 1 to 3 gene loci, randomly change the type of gene, and add Gaussian noise (the amplitude decreases as the temperature decreases) to continuous genes.

[0071] Calculate the fitness of the new solution fitness of the original solution .

[0072] like Then accept the new solution. Otherwise, based on probability. accept.

[0073] 3. Temperature update: ,in This is the cooling coefficient.

[0074] 4. If the termination temperature is reached If there is no improvement after several consecutive attempts, then the process should be terminated.

[0075] 5.3.6 Elite Retention Each generation retains the three individuals with the highest fitness (E=3) to directly enter the next generation, preventing the loss of the optimal solution.

[0076] 5.3.7 Termination Conditions Reaching the maximum number of generations Or the optimal fitness has not improved for 10 consecutive generations (relative change is less than 10%). The algorithm terminates when ( ).

[0077] 5.4 Inner Layer Simulation Process For each individual (i.e., each planning scheme), its annual operating cost needs to be calculated through inner-layer simulation. and dynamic constraint violation The simulation process is as follows: 5.4.1 Runtime Layer Simulation like Figure 4 As shown, it includes the following steps: 1. Input the device type, rated capacity, and controller parameters obtained from the individual decoding.

[0078] 2. For each typical scenario (S=4): Obtain the probability of this scene and 24-hour load multiplier and photovoltaic multipliers .

[0079] For each time period : Calculate the load on each node: , .

[0080] Calculate the active power output of each photovoltaic node: .

[0081] The reactive power reference value of each dynamic reactive power device is determined according to formula (16). And the actual output is limited.

[0082] The available reactive power range of the photovoltaic inverter is determined according to formula (20), and the photovoltaic reactive power output is set (this embodiment adopts local voltage control, that is, to absorb or generate reactive power as much as possible to support the voltage).

[0083] The node voltages are obtained by using the forward-backward substitution method for power flow calculation. Network loss and the actual reactive power of the equipment .

[0084] Calculate the operating cost for this period according to formula (15). This adds up to the daily operating costs.

[0085] The daily operating cost for this scenario is: .

[0086] 3. Calculate annual operating costs: .

[0087] 5.4.2 Dynamic Layer Simulation 1. Obtain the steady-state operating point before the fault: Use the power flow result at 12 noon in scenario 1 (winter peak) as the initial steady state.

[0088] 2. For each fault scenario : Initialize device state: The integrator is initialized to 0.

[0089] Set simulation parameters: Total duration s, step size s, fault initiation s, duration of failure Set according to the scenario.

[0090] For each simulation step : Determine if the current time is within the fault range. If so, modify the node admittance matrix (simulate a short circuit by connecting a small impedance in parallel at the fault node).

[0091] The device dynamic equations are updated using the Euler method (Equation (22)) to obtain the current time. .

[0092] Consider the load ZIP model (Equations (23)-(24)) to update the node injection power.

[0093] Solve the power flow equations to obtain the voltages at each node. .

[0094] Record the voltage trajectory at each node and calculate: Voltage sag depth Recovery time Determine whether equations (25)-(26) are satisfied, and record the results. , .

[0095] 3. Calculate the dynamic constraint violation amount according to formula (31). .

[0096] VI. Case Analysis 6.1 Testing System and Basic Data Using an IEEE 33-node distribution network as the test object, the system has a rated voltage of 12.66kV, a base capacity of 10MVA, and a topology containing 32 branches and 33 nodes, with node 1 being the slack node. The overall system structure is as follows: Figure 5As shown. Photovoltaic access nodes 12, 22, and 29 each have a single inverter capacity of 200kVA. The candidate nodes for dynamic reactive power equipment are all 32 nodes except the root node, allowing the installation of SVC or STATCOM, with a single unit capacity ranging from 0.5 to 3.0 Mvar. The total number of installed units is 2 to 5, with a total investment budget of 1.5 million yuan. Controller parameter optimization range: proportional coefficient and integral coefficient. The planning period is 20 years, with a discount rate of 6% and a residual value rate of 5%. Four typical operating scenarios are generated using Clayton Copula, with probabilities of 0.32, 0.28, 0.22, and 0.18, respectively. Three fault scenarios are preset: three-phase short circuit at node 18 (probability 0.6), single-phase grounding at node 25 (probability 0.3), and two-phase short circuit at node 30 (probability 0.1). Transient safety requirements are a voltage drop depth of no less than 0.75 pu, a recovery time of no more than 2.0 seconds, and a risk level of 0.05.

[0097] 6.2 Optimization of Convergence and Algorithm Performance Analysis An improved genetic simulated annealing algorithm is used to solve the three-layer co-optimization model. The convergence process is as follows: Figure 6 As shown. Figure 6 The optimal fitness curve was plotted as a function of generations. Fitness is defined as the reciprocal of the total annual cost; a higher value indicates a better solution. The initial fitness of the population was approximately 0.015. After the first five generations of rapid search, the fitness quickly climbed to 0.032, indicating that the algorithm effectively identified high-quality solution regions early in the evolutionary process. After the 10th generation, the fitness curve stabilized with only minor fluctuations, mainly due to the continuous perturbation and optimization of the optimal individual by the simulated annealing local search. By the 20th generation, the optimal fitness reached 0.0386, an improvement of approximately 157% compared to the initial population. The entire evolutionary process did not exhibit significant oscillations or prolonged stagnation, verifying the effectiveness of the combined mechanism of global search in the genetic algorithm and local escape in simulated annealing.

[0098] Figure 7The optimal planning scheme for equipment installation location and capacity distribution is presented. The optimized scheme involves installing four dynamic reactive power devices, specifically configured as follows: 1.2 Mvar STATCOM at node 15, 2.5 Mvar SVC at node 25, 1.8 Mvar STATCOM at node 30, and 1.5 Mvar SVC at node 33. The total equipment capacity is 7.0 Mvar, with an initial investment of 1.426 million yuan, meeting both quantity and budget constraints. From the spatial distribution of equipment selection, STATCOM, due to its faster dynamic response capability (time constant 0.02s), is preferentially placed at the electrically distant end nodes 15 and 30 to handle deeper voltage drops and more urgent rapid support requirements during faults; while SVC (time constant 0.05s) is installed at the heavier-loaded, slightly more distant middle nodes 25 and 33, focusing on steady-state voltage maintenance and long-term reactive power support. Regarding controller parameters, the proportional gain of STATCOM is relatively large (3.2~4.0), which enhances the ability to quickly inject power in the early stages of a fault; the integral gain of SVC is relatively high (1.0~1.2), which is beneficial to improving steady-state voltage regulation accuracy. This differentiated configuration fully reflects the technical advantages brought about by the joint optimization of "hardware capacity" and "software parameters".

[0099] 6.3 Evaluation of Steady-State Operating Performance and Voltage Distribution To accurately characterize the uncertainty and interdependence of load and photovoltaic output, this embodiment uses the ClaytonCopula function to generate 24-hour time-series curves for four typical operating scenarios. Scenario 1 (probability 0.32) represents a high-load, low-PV scenario, where the load multiplier peaks above 1.15, while the PV multiplier is only around 0.25, exhibiting a clear lower-tail dependency characteristic, corresponding to winter heating or cloudy / rainy weather. Scenario 2 (probability 0.28) represents a low-load, high-PV scenario, where the load multiplier drops to as low as 0.55 at night, while the PV multiplier remains between 0.85 and 0.95, accompanied by high-frequency fluctuations caused by cloud disturbances, realistically reproducing the stochastic characteristics of PV power generation on sunny days. Scenarios 3 and 4 represent medium-load, medium-PV, and low-load, medium-PV operating conditions, respectively, with the multiplier curves showing a transitional state, both retaining the bi-peak characteristics of daily load and the diurnal distribution pattern of PV power generation.

[0100] Under the optimal planning scheme, a typical operating point (load multiplier 1.0, photovoltaic multiplier 0.8) is selected for power flow calculation. Figure 8The comparison shows the node voltage distribution under uncompensated and coordinated planning schemes. Without compensation, due to the long line impedance, the voltages at the terminal nodes 17, 18, 32, and 33 drop below 0.92 pu, severely exceeding the limit. Although the voltage at the photovoltaic access point rises slightly, it is insufficient to eliminate the overall low voltage problem. After installing dynamic reactive power equipment and coordinating with photovoltaic reactive power regulation, the overall system voltage level significantly improves: all node voltages recover to above 0.95 pu, with the highest voltage around 1.04 pu, occurring near node 8; the lowest voltage is 0.962 pu at node 33, achieving a 100% voltage compliance rate, and no exceeding the upper limit occurs. At node 25, the 2.5 Mvar SVC generates approximately 1.8 Mvar reactive power, restoring the voltage from 0.91 pu to 0.98 pu; at node 30, the STATCOM generates 1.2 Mvar reactive power, effectively supporting the voltage at the terminal nodes 31-33.

[0101] Table 1 summarizes the voltage statistics for four typical scenarios. In Scenario 1 (high load, low PV), due to the heaviest load, the lowest voltage drops to 0.958 pu, but is still within the safe range. In Scenario 2 (low load, high PV), the highest voltage reaches 1.038 pu, but does not reach the upper limit of 1.07 pu. The annual voltage exceedance penalty cost drops sharply from approximately 52,000 yuan / year before planning to 1,400 yuan / year, a reduction of 97.3%. This indicates that the proposed planning scheme has excellent voltage regulation capabilities under time-series uncertainties in multiple scenarios, and the reactive power coordination of the PV inverter effectively improves the voltage suppression effect during periods of high low load.

[0102] Table 1. Voltage Statistical Indicators for Typical Scenarios 6.4 Verification of Dynamic Transient Security and Response Characteristics At the moment of the fault, the voltage at node 18 dropped sharply to approximately 0.42 pu, significantly below the allowable drop depth limit of 0.75 pu; the lowest voltages at nodes 25 and 33 were 0.68 pu and 0.71 pu, respectively, also close to or below the safety limits. After the fault was cleared, thanks to the coordinated and rapid support from the dynamic reactive power equipment and the photovoltaic inverter, the voltages at each node quickly recovered: node 18 recovered to above 0.95 pu in approximately 0.38 seconds after the fault was cleared, with a total recovery time of approximately 0.58 seconds, far less than the allowable upper limit of 2.0 seconds; the recovery times for nodes 25 and 33 were 0.72 seconds and 0.65 seconds, respectively. During the recovery process, due to the superposition effect of the second-order system damping characteristics and the rapid reactive power injection from the photovoltaic system, the voltage curve exhibited brief, small oscillations, but quickly converged to the steady-state value, without affecting the system recovery quality.

[0103] Table 2 summarizes the dynamic safety indicators of key nodes under three preset fault scenarios. Node 18, a three-phase short circuit, causes the most severe voltage drop (minimum 0.42 pu), but thanks to the fast response brought by the large proportional coefficient of STATCOM, its recovery time is the shortest (0.58 s). Node 25, a single-phase ground fault, has a relatively concentrated impact range, with a minimum voltage of 0.68 pu and a recovery time of 0.72 s. Node 30, a two-phase short circuit, has characteristics between the two, with a minimum voltage of 0.63 pu and a maximum recovery time of 0.85 s. The calculated value of the violation of the dynamic opportunity constraint is 0.032, which is lower than the risk level of 0.05, indicating that the system meets the dynamic safety requirements in more than 90% of fault scenarios. Compared with the traditional non-cooperative planning scheme (without photovoltaic reactive power participation), the voltage recovery time of this scheme is shortened by an average of 0.25 s, and the dynamic penalty cost is reduced by approximately 82%. This advantage stems from the rapid coordination between the photovoltaic inverter and the STATCOM / SVC: the photovoltaic reactive power response has almost no inertial delay, and can provide instantaneous reactive power injection in the early stages of a fault; the STATCOM then establishes continuous large-capacity reactive power support, and the two complement each other effectively in terms of time scale and capacity dimension.

[0104] Table 2 Dynamic Indicators of Key Nodes under Various Failure Scenarios 6.5 Life Cycle Economic Analysis Table 3 compares the annual cost composition of the three schemes over their entire lifecycle. The total annual cost of the collaborative planning scheme in this embodiment is RMB 873,500, including an annual investment cost of RMB 421,500, an expected annual operating cost of RMB 438,000, and a dynamic penalty of only RMB 14,000. Within the annual operating cost, network loss costs are RMB 186,000, equipment maintenance costs are RMB 125,000, voltage exceedance penalties are RMB 1,400, and DG generation revenue is -RMB 124,400. Network losses are reduced from an average of 148.3 MWh per year without planning to 92.1 MWh, a decrease of 37.9%, saving approximately RMB 74,000 in electricity costs annually.

[0105] The photovoltaic-independent scheme relies solely on dynamic reactive power equipment and fails to utilize the reactive power potential of the photovoltaic inverter. The optimized result requires the installation of 5 devices, increasing the total capacity to 9.2 Mvar, raising the annual investment to 563,000 yuan / year, operating costs to 512,000 yuan / year, and the total cost to 1,125,800 yuan / year, which is 28.9% higher than the scheme in this embodiment. While the scheme without a planning baseline has no equipment investment costs, the grid loss cost is as high as 296,600 yuan / year, the voltage over-limit penalty is 52,000 yuan / year, and the dynamic penalty is 185,000 yuan / year, totaling 533,600 yuan / year. Furthermore, it cannot meet transient safety constraints and is not feasible in practical engineering. Regarding the dynamic penalty cost, the scheme in this embodiment is only 14,000 yuan / year, indicating that using an opportunity-constrained penalty function instead of empirical penalty coefficients can achieve a quantifiable transient safety margin at a very low economic cost, avoiding the problems of manual adjustment and over-penalty of penalty coefficients in traditional methods.

[0106] Table 3 Comparison of Life Cycle Costs (Unit: RMB 10,000 / Year) In summary, the collaborative planning scheme proposed in this embodiment achieves the optimal balance in three dimensions: life cycle cost, steady-state voltage regulation, and fault transient safety. Compared with the traditional planning mode that relies solely on dynamic reactive power equipment, it not only significantly reduces investment and operating costs but also fully leverages the advantage of zero marginal cost reactive power support from photovoltaic inverters. Compared with no planning benchmark, it significantly suppresses grid losses and voltage overruns and provides a reliable transient safety guarantee.

[0107] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A hierarchical planning method for dynamic reactive power resources in distribution networks, considering dynamic response characteristics and multi-resource coordination, characterized in that, Includes the following steps: Planning layer optimization steps: Obtain the equipment parameters of each node device in the distribution network. These equipment parameters include binary addressing variables, continuous capacity variables, and continuous controller parameter variables. These parameters are used as decision variables for the equipment layer planning optimization objective and optimized to obtain the optimized equipment parameters. Operational layer optimization steps: Estimate the load multiplier and photovoltaic multiplier based on historical data of the distribution network, and construct multiple typical operating scenarios and their probabilities based on the joint probability distribution of the load multiplier and photovoltaic multiplier; For each typical operating scenario, the corresponding scenario operation optimization target is calculated based on the optimized equipment parameters. The actual reactive power output considered in the operation planning optimization target is calculated based on the continuous controller parameter variables through a discrete PI control law. The calculated values ​​of the scenario operation optimization objectives for various typical operating scenarios are weighted and summed with corresponding probabilities to construct the operation layer planning optimization objective, so as to obtain the operation adjustment strategy of each device; Dynamic layer optimization steps: For the preset typical fault scenarios, establish a time-domain simulation model that considers the differences in device response speed. Record the voltage trajectory of each node in each simulation step of the time-domain simulation model, and extract the corresponding voltage drop depth and voltage recovery time indicators to determine whether they meet the corresponding transient safety opportunity constraints. Then, it is required that the probability of all nodes meeting the transient safety opportunity constraints in all typical fault scenarios is not lower than the given confidence level. Collaborative optimization steps: Based on the equipment-level planning optimization objectives and the operation-level planning optimization objectives, construct a collaborative optimization overall objective, and use the transient security opportunity constraints as penalty terms to form a collaborative optimization model for solution, thereby obtaining the optimal reactive power resource planning scheme for the distribution network.

2. The hierarchical planning method for dynamic reactive power resources in a distribution network considering dynamic response characteristics and multi-resource coordination as described in claim 1, characterized in that, The binary addressing variable represents the dynamic reactive power device of type t installed at node i; The continuous capacity variable This indicates the rated capacity of the type t device installed at node i; The continuous controller parameter variables include and , where represent the proportional coefficient and integral coefficient of the type t device installed at node i, respectively.

3. The hierarchical planning method for dynamic reactive power resources in a distribution network considering dynamic response characteristics and multi-resource coordination as described in claim 2, characterized in that, The constraints in the process of solving the equipment layer planning optimization objective include equipment capacity limits, total number of equipment limits, and investment budget constraints. The expression for the device capacity limit is: In the formula, , These are the minimum and maximum rated capacities of equipment of type t, respectively. The expression for the limit on the total number of devices is: In the formula, , These are the minimum and maximum allowed number of units to be installed, respectively. The expression for the investment budget constraint is: In the formula, Let be the present value of the initial investment in the device of type t installed at node i. This is the budget ceiling.

4. The hierarchical planning method for dynamic reactive power resources in distribution networks considering dynamic response characteristics and multi-resource coordination as described in claim 1, characterized in that, In the operation layer optimization step, the expression for calculating the actual reactive power output is: In the formula, Let t be the actual reactive power output of device of type i in scenario s during time period h. and The optimized continuous controller parameter variables, This is the voltage reference value. This is the voltage measurement value from the previous time period. This is a limiting function that restricts the output to the continuously variable capacity obtained after optimization. Within the range, This represents the interval between adjacent time periods.

5. The hierarchical planning method for dynamic reactive power resources in a distribution network considering dynamic response characteristics and multi-resource coordination as described in claim 1, characterized in that, The constraints in the process of solving the operational layer planning optimization objective include power flow equations, equipment output constraints, and photovoltaic inverter reactive power output constraints. The photovoltaic inverter reactive power output constraints consider that the reactive power output of the photovoltaic inverter is limited by the photovoltaic inverter capacity and power factor. The expression for the photovoltaic inverter reactive power output constraints is as follows: In the formula, For the reactive power output of photovoltaic inverter node j during time period h in scenario s, Let J be the capacity of the photovoltaic inverter at node j. Let h be the active load of photovoltaic inverter node j in scenario s during time period h. This is the minimum permissible power factor.

6. The hierarchical planning method for dynamic reactive power resources in a distribution network considering dynamic response characteristics and multi-resource coordination as described in claim 1, characterized in that, The typical fault scenarios include three-phase short circuit, two-phase short circuit and single-phase grounding of the line. The faults in the typical fault scenarios are described by fault location, type, duration and probability of occurrence. The time-domain simulation model is constructed based on the device differential equations described by a first-order inertial element and a PI controller. During the simulation process of the time-domain simulation model, the device differential equations are updated using the Euler method within each simulation step. The power flow equations considering the load ZIP model and fault admittance correction are solved, and the voltage trajectories of each node are recorded.

7. A hierarchical planning method for dynamic reactive power resources in a distribution network considering dynamic response characteristics and multi-resource coordination, as described in claim 6, is characterized in that... The expression for the differential equation of the device is: In the formula, For the reactive power output of device type t at node i, Let be the intrinsic time constant of node i. and The optimized continuous controller parameter variables, Let i be the voltage reference value at node i. Let be the voltage of device i.

8. A hierarchical planning method for dynamic reactive power resources in a distribution network considering dynamic response characteristics and multi-resource coordination, as described in claim 7, is characterized in that... The formula for calculating the voltage drop depth is: In the formula, Let be the voltage drop depth of node j under a typical fault scenario f. Let be the voltage at node j at time t. The fault start time. Duration of the fault; The expression for calculating the voltage recovery time is as follows: In the formula, Let be the voltage recovery time of node j under typical fault scenario f. This is the recovery threshold.

9. A hierarchical planning method for dynamic reactive power resources in a distribution network considering dynamic response characteristics and multi-resource coordination, as described in claim 8, is characterized in that... The expression for the transient security opportunity constraint is: In the formula, The lower limit of the permissible voltage drop depth, It is a positive number. The first binary variable represents whether node j meets the voltage drop index under fault f; The maximum allowable recovery time, The second binary variable represents whether node j meets the recovery time metric under fault f; Let f be the probability of occurrence of a typical failure scenario. The first level of risk. This is the second level of risk.

10. A hierarchical planning method for dynamic reactive power resources in a distribution network considering dynamic response characteristics and multi-resource coordination, as described in claim 1, is characterized in that... The calculation expression for the overall collaborative optimization objective is as follows: In the formula, To collaboratively optimize the overall goal, To optimize the planning objectives at the equipment level, To optimize the goals of the runtime layer, The amount of violation of the transient security opportunity constraint. As a penalty factor; The equipment layer planning optimization objective is the degree to which the dynamic equipment requirements of the distribution network system are met or the annual value of the total investment cost of the entire distribution network system. The optimization objective of the operation layer planning is the operational stability of the distribution network system or the expected value of the annual operating cost of the distribution network system.

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