Table region modeling method, device and system for power distribution system, and storage medium

Abstract

The embodiment of the invention provides a feasible region modeling method, device and system for a power distribution system and a storage medium, and relates to the technical field of feasible region modeling of the power distribution system. The method comprises the following steps: constructing a power distribution system autonomous optimization model, performing decision optimization by taking economy as a target, and solving to obtain an energy state reference value of energy storage equipment in a scheduling time domain; on the basis of the energy state reference value, energy decoupling constraints are supplemented in the original feasible region, a time decoupling feasible region of the original feasible region is constructed, and high-dimensional dimensionality reduction of the original feasible region is achieved; and for the time decoupling feasible region after decoupling and dimensionality reduction, carrying out parallel calculation on vertexes of all the sub-feasible regions by adopting a vertex search method, and carrying out aggregation to obtain an aggregation equivalent feasible region of the power distribution system. Through cooperation of reference obtaining, decoupling dimension reduction and parallel solving, on the premise that feasibility is maintained, calculation efficiency and feasibility of feasible region characterization of the power distribution system containing the time coupling constraint are improved.

Description

Technical Field

[0001] This application relates to the field of feasible domain modeling technology for power distribution systems, and more specifically, to a feasible domain modeling method, apparatus, system, and storage medium for power distribution systems. Background Technology

[0002] Currently, with the rapid development of renewable energy, a large number of distributed photovoltaic and energy storage resources have been connected to the power distribution system, significantly enhancing the system's flexibility and adjustment potential. However, the dramatic increase in the number of distributed resources has also brought severe challenges to the operation and management of the power distribution system. In particular, how to accurately characterize the feasible operating domain of the system to support optimized scheduling decisions has become a fundamental problem that urgently needs to be solved.

[0003] To address this challenge, relevant technologies primarily employ two types of methods for characterizing feasible regions. One type is the vertex search algorithm based on exact solutions, which obtains the convex hull representation of a convex polyhedron by solving for its vertices. The other type is the approximate solution-based method, which uses a pre-defined geometric structure of the aggregated feasible region, such as a hypercube or a fixed convex polyhedron, to fit its parameters to achieve an approximate representation.

[0004] In the process of implementing the embodiments of this application, at least the following problems were found in the related technology:

[0005] With the integration of time-coupled devices such as energy storage, the feasible region of power distribution systems exhibits high-dimensional time-coupled characteristics. This makes exact vertex search-based methods susceptible to the curse of dimensionality, struggling to solve feasible regions with dimensions greater than 6. While approximate solution-based methods can handle time-coupled constraints, they introduce numerous approximations, resulting in limited accuracy and often overly conservative results, making it difficult to simultaneously guarantee computational feasibility and accuracy. Summary of the Invention

[0006] This application provides a feasible domain modeling method, apparatus, system, and storage medium for power distribution systems.

[0007] A first aspect of this application provides a feasible domain modeling method for a power distribution system, comprising:

[0008] An autonomous optimization model for the power distribution system is constructed, and decision optimization is carried out with economic efficiency as the objective. The energy state reference value of the energy storage device in the scheduling time domain is obtained by solving the model.

[0009] Based on the energy state reference value, energy decoupling constraints are added to the original feasible region to construct the time-decoupled feasible region of the original feasible region, thereby achieving high-dimensional reduction of the original feasible region.

[0010] For the decoupled and dimensionality-reduced time-decoupled feasible region, the vertex search method is used to calculate the vertices of each sub-feasible region in parallel, and the aggregated equivalent feasible region of the power distribution system is obtained.

[0011] In an optional embodiment of this application, an autonomous optimization model for the power distribution system is constructed to perform decision optimization with economic efficiency as the objective, and the energy state reference value of the energy storage device in the scheduling time domain is obtained by solving the model, including:

[0012] Construct an autonomous optimization model with the objective function of minimizing the total operating cost of the power distribution system;

[0013] Set constraints for the autonomous optimization model; among which, the constraints include operational constraints of all distributed resources in the power distribution system, network security constraints based on the linearized AC power flow model, and / or system power balance constraints.

[0014] Solve the autonomous optimization model and output the optimal state of charge value of the energy storage device in each scheduling period as the energy state reference value.

[0015] In an optional embodiment of this application, the total operating cost of the power distribution system includes the electricity purchase cost from the upstream power grid; the calculation of the electricity purchase cost from the upstream power grid includes:

[0016] Obtain the active power input at the common coupling node connecting the power distribution system and the upstream power grid;

[0017] The active power is multiplied by the preset unit electricity purchase cost to obtain the electricity purchase cost of the upper-level power grid.

[0018] In an optional embodiment of this application, the total operating cost of the power distribution system includes the curtailment penalty cost of distributed photovoltaic power generation; the calculation of the curtailment penalty cost of distributed photovoltaic power generation includes:

[0019] Obtain the day-ahead predicted power and actual output power of distributed photovoltaic power;

[0020] Calculate the difference between the predicted power and the actual output power before the day;

[0021] Multiply the difference by the preset unit curtailment penalty cost to obtain the curtailment penalty cost of distributed photovoltaic power.

[0022] In an optional embodiment of this application, the total operating cost of the power distribution system includes the operating cost of the energy storage device; the calculation of the operating cost of the energy storage device includes:

[0023] Obtain the charging and discharging power of energy storage devices;

[0024] Calculate the sum of the absolute values ​​of the charging power and the discharging power;

[0025] The sum of the absolute values ​​is multiplied by the preset unit charge / discharge cost to obtain the operating cost of the energy storage device.

[0026] In an optional embodiment of this application, the operational constraints of all distributed resources in the power distribution system include the operational constraints of distributed photovoltaic (PV) systems; the operational constraints of distributed PV systems include:

[0027] The actual output power of distributed photovoltaic power does not exceed its day-ahead forecast power.

[0028] In an optional embodiment of this application, the operational constraints of all distributed resources in the power distribution system include the operational constraints of energy storage devices; the operational constraints of energy storage devices include:

[0029] The charging power of the energy storage device does not exceed its maximum charging power limit; and / or,

[0030] The discharge power of the energy storage device does not exceed its upper limit; and / or,

[0031] The state of charge (SOC) of an energy storage device is between its lower SOC limit and upper SOC limit; and / or,

[0032] The energy evolution of energy storage devices between adjacent scheduling periods satisfies the energy conservation relationship determined by charging efficiency, discharging efficiency, charging power and / or discharging power.

[0033] In an optional embodiment of this application, based on the energy state reference value, energy decoupling constraints are supplemented in the original feasible region to construct a time-decoupled feasible region of the original feasible region, thereby achieving high-dimensional dimensionality reduction of the original feasible region, including:

[0034] The entire scheduling time domain is divided into multiple consecutive time windows;

[0035] For each time window, energy decoupling constraints are added to the original feasible region to construct a low-dimensional time decoupling feasible region corresponding to that time window; wherein, the energy decoupling constraints fix the state of charge of the energy storage device at the beginning of the time window to the value of the energy state reference value at that time.

[0036] The low-dimensional temporal decoupling feasible region corresponding to all time windows is taken as the temporal decoupling feasible region.

[0037] In an optional embodiment of this application, for each time window, energy decoupling constraints are supplemented in the original feasible region to construct a low-dimensional temporal decoupling feasible region corresponding to that time window, including:

[0038] Inherit all constraints belonging to the current time window from the original feasible domain;

[0039] Add an energy decoupling constraint at the start of the time window, whereby the energy storage device's state of charge at that moment equals the energy state reference value.

[0040] The inherited constraints and the added energy decoupling constraints together constitute the low-dimensional temporal decoupling feasible region corresponding to this time window.

[0041] In an optional embodiment of this application, based on the energy state reference value, energy decoupling constraints are added to the original feasible region to construct a time-decoupled feasible region of the original feasible region, thereby achieving high-dimensional dimensionality reduction of the original feasible region. The embodiment further includes:

[0042] By performing a union operation on the low-dimensional time decoupling feasible regions corresponding to all time windows, we obtain the equivalent approximate feasible region within the entire scheduling time domain.

[0043] In an optional embodiment of this application, for the decoupled and dimensionality-reduced temporally decoupled feasible region, the vertices of each sub-feasible region are computed in parallel using a vertex search method, including:

[0044] For each low-dimensional feasible region in the time-decoupled feasible region, a vertex search algorithm is executed in parallel to identify all vertices of that low-dimensional feasible region.

[0045] In an optional embodiment of this application, the vertex search algorithm includes an initialization phase, an inner loop optimization phase, and a convergence judgment phase.

[0046] In an optional embodiment of this application, the aggregation yields the aggregated equivalent feasible region of the power distribution system, including:

[0047] Project the set of vertices of each low-dimensional feasible region onto its boundary variable space. The boundary variables include the active power injection and reactive power injection at the common coupling node.

[0048] The projection results are aggregated to form a set describing the feasible range of boundary variables, which serves as the aggregated equivalent feasible region.

[0049] A second aspect of the present application provides a feasible domain modeling apparatus for a power distribution system, including a processor and a memory storing program instructions. The processor is configured to execute the feasible domain modeling method for a power distribution system as described in the first aspect of the present application when running the program instructions.

[0050] A third aspect of this application provides a system comprising:

[0051] The system itself; and,

[0052] The feasible domain modeling device for a power distribution system, as described in the second aspect of this application, is installed on the system body.

[0053] A fourth aspect of the embodiments of this application provides a computer-readable storage medium storing program instructions that, when executed, cause a computer to perform a feasible domain modeling method for a power distribution system as described in the first aspect of the embodiments of this application.

[0054] The feasible domain modeling method, apparatus, system, and storage medium for power distribution systems provided in the embodiments of this application have the following beneficial effects:

[0055] This application's embodiments solve for the energy state reference value of energy storage devices by constructing an autonomous optimization model of the power distribution system, providing a benchmark close to optimized operation for subsequent processing. Based on this reference value, energy decoupling constraints are added to the original feasible domain, fixing the state of charge of the energy storage devices at the start of each time period, thereby cutting off energy coupling between different time periods. This achieves dimensionality reduction and decomposition of the original feasible domain with high-dimensional time coupling into multiple independent low-dimensional time-decoupled feasible domains. On this basis, the vertex search method is used to compute the vertices of each low-dimensional time-decoupled feasible domain in parallel. Due to the reduction in dimensionality, the computational complexity of the vertex search method is controlled, and parallel computation further improves the solution efficiency. Finally, the results of each sub-feasible domain are aggregated to obtain an aggregated equivalent feasible domain. By synergistically obtaining the reference, decoupling and dimensionality reduction, and parallel solution, the computational efficiency and feasibility of representing the feasible domain of the power distribution system with time coupling constraints are improved while maintaining feasibility. Attached Figure Description

[0056] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0057] Figure 1 This is a schematic diagram of a feasible domain modeling method for a power distribution system provided in an embodiment of this application;

[0058] Figure 2 This is a schematic diagram illustrating an application of a feasible domain modeling method for a power distribution system provided in an embodiment of this application.

[0059] Figure 3 This is a schematic diagram of the network topology of a power distribution system for verification provided in an embodiment of this application;

[0060] Figure 4 This is a schematic diagram of a feasible domain modeling device for a power distribution system provided in an embodiment of this application.

[0061] Figure label:

[0062] 800: Feasible domain modeling device for power distribution systems; 801: Processor; 802: Memory; 803: Communication interface; 804: Bus. Detailed Implementation

[0063] To make the technical solutions and advantages of the embodiments of this application clearer, the exemplary embodiments of this application will be described in further detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not an exhaustive list of all embodiments. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other.

[0064] Figure 1 This is a schematic diagram of a feasible domain modeling method for a power distribution system provided in an embodiment of this application. Any of the following methods can be executed in the system or in a server or terminal device that is connected to the system.

[0065] Combination Figure 1 As shown in the figure, this application provides a feasible domain modeling method for a power distribution system, including:

[0066] S01, construct an autonomous optimization model for the power distribution system, make decisions and optimize with economic efficiency as the objective, and solve to obtain the energy state reference value of the energy storage device in the scheduling time domain.

[0067] S02, based on the energy state reference value, adds energy decoupling constraints to the original feasible region to construct the time-decoupled feasible region of the original feasible region, thereby achieving high-dimensional reduction of the original feasible region.

[0068] S03. For the decoupled and dimensionality-reduced time-decoupled feasible region, the vertex search method is used to calculate the vertices of each sub-feasible region in parallel, and the aggregated equivalent feasible region of the power distribution system is obtained.

[0069] The feasible domain modeling method for power distribution systems provided in this application constructs an autonomous optimization model of the power distribution system to solve for the energy state reference value of the energy storage device, providing a benchmark for subsequent processing that closely approximates optimized operation. Based on this reference value, energy decoupling constraints are added to the original feasible domain, fixing the state of charge of the energy storage device at the start of each time period, thereby cutting off the energy coupling between different time periods. This achieves dimensionality reduction and decomposition of the high-dimensional time-coupled original feasible domain into multiple independent low-dimensional time-decoupled feasible domains. Furthermore, a vertex search method is used to compute the vertices of each low-dimensional time-decoupled feasible domain in parallel. Due to the reduced dimensionality, the computational complexity of the vertex search method is controlled, and parallel computation further improves the solution efficiency. Finally, the results of each sub-feasible domain are aggregated to obtain an aggregated equivalent feasible domain. By synergistically obtaining the reference, decoupling and dimensionality reduction, and parallel solving, the computational efficiency and feasibility of representing the feasible domain of a power distribution system with time-coupled constraints are improved while maintaining feasibility.

[0070] Optionally, an autonomous optimization model for the power distribution system is constructed to optimize decisions with economic efficiency as the objective, and the energy state reference value of the energy storage device in the scheduling time domain is obtained by solving the model. This includes: constructing an autonomous optimization model with the objective function of minimizing the total operating cost of the power distribution system; setting constraints on the autonomous optimization model, including operational constraints of all distributed resources in the power distribution system, network security constraints based on the linearized AC power flow model, and system power balance constraints; solving the autonomous optimization model and outputting the optimal state of charge value of the energy storage device in each scheduling period as the energy state reference value.

[0071] In this way, the objective function focuses on minimizing the total operating cost, aligning with the core economic demands of power distribution system operation. This ensures that the solved energy storage state reference value reflects the energy storage energy change pattern under optimized system operation, providing practical application guidance. Among the constraints, the distributed resource operation constraints clearly define the operating boundaries of resources such as photovoltaics and energy storage, such as ensuring that the actual output of photovoltaics does not exceed the day-ahead predicted power, and that the energy storage charging and discharging power and state of charge are within a reasonable range. This ensures that the reference value does not deviate from the actual operating capacity of the resources. The network security constraints, through a linearized AC power flow model, balance system security and model solvability, avoiding difficulties in solving the model due to complex power flow calculations. The system power balance constraints guarantee that the energy storage state corresponding to the reference value can maintain the power supply and demand balance of each node in the system, meeting the basic stability requirements of system operation. Through the above methods, the optimal state of charge value of the energy storage device obtained satisfies both the economic optimization objective and the resource operation constraints and system safety and stability requirements. This provides a reliable basis for subsequently supplementing energy decoupling constraints in the original feasible region, offering an accurate and realistic reference standard for achieving high-dimensional reduction of the original feasible region, and preventing subsequent decoupling operations from deviating from the actual operating range of the system.

[0072] Optionally, the total operating cost of the power distribution system includes the power purchase cost of the upstream power grid. The calculation of the power purchase cost of the upstream power grid includes: obtaining the active power input at the common coupling node connecting the power distribution system and the upstream power grid; multiplying the active power by the preset unit power purchase cost to obtain the power purchase cost of the upstream power grid.

[0073] Thus, the common coupling node is the core node for power exchange between the distribution system and the upper-level power grid. The active power input here directly reflects the actual scale of electricity purchased by the distribution system from the upper-level power grid. Using this parameter as the basis for calculating the electricity purchase cost can accurately capture the core quantitative indicators of the electricity purchase process and avoid calculation deviations caused by selecting power data from non-critical nodes. The preset unit electricity purchase cost is determined by combining actual grid pricing rules, time-of-use pricing policies, and other realistic factors. It conforms to the cost accounting logic in the actual economic operation of the distribution system. Multiplying the actual purchased electricity (i.e., the active power of the common coupling node) by this unit cost is a simple calculation method that closely matches the actual economic transaction scenario and can truly reflect the economic expenditure in the electricity purchase process. Since the cost of purchasing electricity from the upstream power grid is an important component of the total operating cost of the distribution system, and the total operating cost is the core of the objective function of the autonomous optimization model to "minimize the total operating cost", accurate calculation of the cost of purchasing electricity from the upstream power grid can enable the objective function to more accurately match the actual economic operating needs of the distribution system, avoid the model optimization direction from deviating from reality due to the distortion of cost data, and thus enable the subsequent solution of the autonomous optimization model to obtain a reference value of energy state of energy storage equipment that is more in line with the actual operating scenario based on a reasonable economic objective.

[0074] Optionally, the total operating cost of the power distribution system includes the curtailment penalty cost of distributed photovoltaic power. The calculation of the curtailment penalty cost of distributed photovoltaic power includes: obtaining the day-ahead predicted power and the actual output power of distributed photovoltaic power; calculating the difference between the day-ahead predicted power and the actual output power; and multiplying the difference by a preset unit curtailment penalty cost to obtain the curtailment penalty cost of distributed photovoltaic power.

[0075] Thus, the predicted power output is based on the expected output level of distributed photovoltaic (PV) power determined in the previous planning, while the actual output power is the real output of PV power during operation. The difference between the two directly corresponds to the unutilized PV power, i.e., the curtailed power. Obtaining this difference can accurately capture the actual scale of curtailment and avoid cost calculation errors caused by estimating curtailment using indirect data. The preset unit curtailment penalty cost is set in combination with the actual situation such as PV resource utilization efficiency requirements and energy waste losses caused by curtailment. It conforms to the practical logic of the distribution system to economically constrain curtailment. Multiplying the actual curtailment by the unit curtailment penalty cost can truly reflect the degree of impact of curtailment on the total operating cost. The curtailment penalty cost of distributed photovoltaic power is a component of the total operating cost of the power distribution system. Accurate calculation of the curtailment penalty cost allows the objective function of the autonomous optimization model to more comprehensively cover the economic expenditure items in the system operation, avoiding the model optimization direction from deviating from actual needs due to omission or miscalculation of curtailment costs. As a result, when solving the model, it will focus more on coordinating the matching of resources such as energy storage and load with photovoltaic output in the process of pursuing the minimum total operating cost, thereby reducing curtailment. The final energy state reference value of the energy storage equipment will also better meet the dual requirements of efficient resource utilization and economic operation.

[0076] Optionally, the total operating cost of the power distribution system includes the operating cost of the energy storage device. The calculation of the operating cost of the energy storage device includes: obtaining the charging power and discharging power of the energy storage device; calculating the sum of the absolute values ​​of the charging power and discharging power; and multiplying the sum of the absolute values ​​by a preset unit charging and discharging cost to obtain the operating cost of the energy storage device.

[0077] Thus, charging and discharging are the core energy-consuming and loss-generating processes in the operation of energy storage devices, both of which incur actual costs. Calculating the sum of the absolute values ​​of charging and discharging power avoids numerical cancellation caused by opposite charging and discharging power directions, accurately capturing the total actual charging and discharging activity of the energy storage device, and ensuring that the basic data for cost calculation truly reflects the operating load. The preset unit charging and discharging cost is determined by combining actual operating factors such as charging and discharging losses and maintenance requirements of the energy storage device, which conforms to the actual composition logic of the energy storage device's operating cost. Multiplying the total charging and discharging activity by the unit charging and discharging cost can accurately reflect the economic expenditure of energy storage operation. The operating cost of energy storage devices is an important component of the total operating cost of the power distribution system. Accurate operating cost calculation allows the objective function of the autonomous optimization model to fully cover the key economic expenditures of system operation, avoiding deviations in the model's optimization of energy storage charging and discharging strategies from actual needs due to cost quantification biases. Therefore, when solving the model, it prompts the model to reasonably balance the regulatory role of energy storage and operating costs in the process of pursuing the minimum total operating cost. The resulting optimal state of charge (i.e., energy state reference value) of the energy storage device in each scheduling period is also more consistent with the actual operating scenario.

[0078] Optionally, the operational constraints of all distributed resources in the power distribution system include the operational constraints of distributed photovoltaic (PV) systems, which include: the actual output power of distributed PV systems does not exceed their day-ahead forecast power.

[0079] Thus, the predicted power output is the maximum output level that photovoltaic (PV) power can potentially reach within the dispatch cycle, determined based on prior analysis of factors such as sunlight conditions and equipment performance. This value reflects the actual usable potential of PV resources. Limiting the actual output power to not exceeding this value can prevent PV output from exceeding the pre-planned output range of the system, preventing system power imbalances or dispatch plan disruptions caused by sudden increases in output, and meeting the basic requirements for stable operation of the distribution system. The operational constraints of distributed PV are part of the operational constraints of all distributed resources in the distribution system and are also an important component of the constraints of the autonomous optimization model. By clearly defining the upper limit boundary of PV output, the model can perform calculations based on real and feasible PV output data when solving for the goal of minimizing total operating costs. This avoids the model's solution results deviating from the actual operating scenario due to PV output exceeding expectations, thereby ensuring that the final output energy storage device's optimal state of charge (i.e., energy state reference value) in each dispatch period is more in line with the actual operating requirements of the system.

[0080] Optionally, the operational constraints of all distributed resources in the power distribution system include the operational constraints of energy storage devices. The operational constraints of energy storage devices include: the charging power of the energy storage device does not exceed its upper limit of charging power; the discharging power of the energy storage device does not exceed its upper limit of discharging power; the state of charge of the energy storage device is between its lower limit of state of charge and its upper limit of state of charge; and the energy evolution of the energy storage device between adjacent scheduling periods satisfies the energy conservation relationship determined by charging efficiency, discharging efficiency, charging power, and discharging power.

[0081] Thus, the upper limits of charging and discharging power are safety operating thresholds determined based on the hardware performance of the energy storage device. Limiting the charging and discharging power within these ranges prevents damage due to overload and ensures the safe operation of the energy storage device. The upper and lower limits of the state of charge (SOC) are set in conjunction with battery life protection and energy regulation requirements. This prevents excessively low SOC from affecting battery cycle life or excessively high SOC from causing safety hazards, while ensuring that the energy storage device always retains a certain energy regulation margin to meet system power balance requirements. The energy conservation relationship between adjacent scheduling periods takes into account energy losses during the charging and discharging process of the energy storage device. Since energy storage charging and discharging is not a complete energy conversion in actual applications, charging efficiency and discharging efficiency directly affect the energy transfer effect. Therefore, the operating constraints of the energy storage device can accurately reflect the evolution of stored energy in different time periods, avoiding energy calculation deviations that are unrealistic under ideal conditions. These constraints, as an important component of the distributed resource operation constraints of the power distribution system, can provide the model with limiting boundaries that closely resemble the actual operation of energy storage devices after being integrated into the constraints of the autonomous optimization model. This avoids the generation of solutions that exceed the energy storage capacity or violate energy laws during model solving, thereby ensuring that the optimal state of charge (i.e., the energy state reference value) output by the model for each scheduling period conforms to the actual operating scenario of the energy storage device.

[0082] Optionally, the operating constraints of all distributed resources in the power distribution system include the operating constraints of the static var compensator (SVC). The operating constraints of the SVC include: the reactive power output of the SVC is between its lower reactive power limit and its upper reactive power limit.

[0083] Thus, the lower and upper limits of reactive power of the static var compensator (SVC) are determined based on the device's own hardware performance (such as maximum reactive power output capacity and minimum operating threshold) and the power distribution system's reactive power regulation requirements (such as maintaining node voltage stability and satisfying power balance). Limiting its output reactive power within this range can prevent the device from being damaged due to operation beyond its capacity, and at the same time prevent problems such as system voltage fluctuations and power imbalances caused by excessive or insufficient reactive power regulation, which meets the basic requirements for the safe operation of the power distribution system. The operating constraints of the SVC are part of the operating constraints of all distributed resources in the power distribution system and are a component of the constraints of the autonomous optimization model. By clarifying the reactive power regulation boundary of the SVC, the model can perform calculations based on the actual regulation capacity of the SVC when solving for the goal of minimizing total operating cost. This avoids the model's solution results from deviating from the actual scenario due to ignoring the device's operating limitations, and thus makes the final output energy state reference value of the energy storage device more consistent with the actual operating needs of the entire power distribution system.

[0084] Optionally, the network security constraints based on the linearized AC power flow model include node voltage security constraints, which include: the voltage squared value of each node is between a preset lower limit and an upper limit of the voltage squared value.

[0085] Thus, node voltage is one of the core indicators for the safe operation of a power distribution system, directly related to the normal operation of electrical equipment and system stability. The preset lower and upper limits of the voltage square are determined based on actual needs such as the voltage tolerance range of electrical equipment and power supply quality standards, accurately defining the voltage safety range. The use of voltage square values ​​for constraints is because, in a linearized AC power flow model, the voltage square value avoids interference from nonlinear terms of voltage variables in the model solution, better adapts to the solution logic of the linearized model, reduces the model's computational complexity, and ensures efficient model solving. Node voltage safety constraints are an important component of network security constraints. Integrating them into the constraints of the autonomous optimization model prevents the model from ignoring voltage safety when pursuing the minimization of total operating costs, and avoids the calculated energy storage device operating strategies leading to node voltages exceeding the safe range. This ensures that the optimal state of charge (i.e., energy state reference value) of the energy storage device output for each scheduling period is obtained under the premise of system voltage safety, meeting the actual safety requirements of the power distribution system operation.

[0086] Optionally, the network security constraints based on the linearized AC power flow model include branch current security constraints, which include: the current amplitude of each branch does not exceed a preset current upper limit.

[0087] In this way, the branch current amplitude directly reflects the actual current carrying capacity of the branch. The preset upper limit of the current is determined by combining the hardware characteristics of the branch conductor, such as material, cross-sectional area, and heat dissipation conditions, as well as the safety operation standards of the power distribution system. This upper limit accurately corresponds to the maximum current that the branch can safely carry. Limiting the branch current amplitude to not exceeding this upper limit can effectively prevent problems such as overheating and insulation damage caused by overcurrent in the branch, and avoid causing line faults or safety accidents. The branch current safety constraint is an important component of network security constraints. By relying on the constraints of the autonomous optimization model integrated into the linearized AC power flow model, it can prevent the model from excessively pursuing economic optimization and ignoring branch current safety when solving with the goal of minimizing the total operating cost. This avoids the branch current exceeding the limit due to the solved energy storage charging and discharging strategy or power allocation scheme. As a result, the optimal value of the state of charge of the energy storage device (i.e., the energy state reference value) output by the model for each scheduling period is obtained under the premise of safe operation of the branch, which meets the hardware safety operation requirements of the power distribution system.

[0088] Optionally, the system power balance constraint includes: at each node, the sum of the active and reactive power input from the line and the active and reactive power injected by distributed resources is equal to the active and reactive loads of that node.

[0089] Thus, nodes are the basic units for power transmission, conversion, and consumption in a power distribution system. The power supply and demand relationship of each node directly affects the stable operation of the entire system. Line input power is the energy that a node obtains from the outside, while distributed resource injection power is the regulating energy generated locally by the node. Together, they constitute the power supply of the node. The active and reactive loads of a node represent its energy demand. Ensuring that supply and demand are equal can fundamentally avoid power shortages caused by power gaps at nodes, or energy waste and system disturbances caused by power surpluses, which conforms to the basic laws of stable operation of a power distribution system. System power balance constraints are an important component of the constraints of the autonomous optimization model. By clarifying the power balance relationship of each node, the model, when solving with the goal of minimizing total operating costs, will not only pursue economic benefits but also avoid ignoring the basic balance of power supply and demand. This prevents the solved energy storage charging and discharging strategies or distributed resource scheduling schemes from violating the power balance law. Consequently, the optimal state of charge (i.e., energy state reference value) of the energy storage devices output by the model for each scheduling period is obtained under the premise of satisfying the power balance of each node, and fully conforms to the actual operating needs of the power distribution system.

[0090] Optionally, based on the energy state reference value, energy decoupling constraints are added to the original feasible domain to construct a time-decoupling feasible domain of the original feasible domain, thereby achieving high-dimensional dimensionality reduction of the original feasible domain. This includes: dividing the entire scheduling time domain into multiple consecutive time windows; for each time window, adding energy decoupling constraints to the original feasible domain to construct a low-dimensional time-decoupling feasible domain corresponding to that time window, wherein the energy decoupling constraints fix the state of charge of the energy storage device at the beginning of the time window to the value of the energy state reference value at that time; and using the low-dimensional time-decoupling feasible domains corresponding to all time windows as the time-decoupling feasible domain.

[0091] Thus, the original feasible region exhibits high-dimensionality due to the continuous coupling of the state of charge (SOC) of the energy storage devices across the entire scheduling time domain (the SOC of the previous time period affects the SOC of the next time period), making it difficult for traditional computational methods such as vertex search to handle. By dividing the problem into continuous time-domain windows, the high-dimensional problem across the entire time domain can be decomposed into multiple short-time sub-problems, reducing the time dimension of each sub-problem. The supplementary energy decoupling constraints, using the energy state reference values ​​obtained through the autonomous optimization model that closely match the economic optimization of the system, fix the SOC at the start of each time-domain window. This severs the coupling relationship of SOC between different time-domain windows, making the feasible region corresponding to each time-domain window an independent low-dimensional space. Integrating these low-dimensional feasible regions into a time-decoupled feasible region retains the constraint information in the original feasible region that meets the actual operational requirements (due to the reasonableness of the energy state reference values) while avoiding the computational obstacles caused by high-dimensional coupling. The above method transforms the original high-dimensional feasible region into a low-dimensional subdomain that can be processed separately. When using the vertex search method, there is no need to deal with the high-dimensional computation problem, thereby improving the efficiency and feasibility of solving the feasible region, while ensuring that the decoupled feasible region does not deviate from the actual operating range of the system.

[0092] Optionally, the entire scheduling time domain can be divided into multiple consecutive time windows, including: for a 24-hour scheduling time domain, it can be divided into 12 consecutive 2-hour time windows.

[0093] Thus, without dividing the 24-hour scheduling time domain, the continuous coupling of the energy storage device's state of charge across the entire time domain would create a high-dimensional feasible region, leading to an exponential increase in computational complexity with increasing dimensionality for the vertex search method, making it difficult to solve efficiently. Dividing it into continuous 2-hour time windows offers several advantages. First, the 2-hour duration avoids both situations where the energy storage's state of charge is too short (deviating from actual operating patterns) and situations where the duration is too long (preventing effective dimensionality reduction). This ensures that the state of charge changes within each time window align with the actual operating scenario, while significantly reducing the dimensionality of the feasible region corresponding to a single time window. Second, 12 consecutive windows completely cover the 24-hour scheduling time domain, ensuring no scheduling periods are missed and guaranteeing that the subsequently constructed time-decoupled feasible region reflects the overall operational situation across the entire time domain. By dividing the time into sub-time windows as described above, the feasible domain dimension of each sub-time window is within the range that the vertex search method can efficiently process (such as the previously mentioned decoupled projection dimension of 4, avoiding the computational difficulties of more than 6 dimensions). This lays the foundation for subsequent addition of energy decoupling constraints for each window, construction of low-dimensional time decoupled feasible domains, and parallel computation of vertices in each sub-domain. It effectively reduces the computational difficulty of solving the overall feasible domain and improves the solution efficiency.

[0094] Optionally, for each time window, energy decoupling constraints are added to the original feasible domain to construct a low-dimensional time decoupling feasible domain corresponding to that time window. This includes: inheriting all constraints belonging to that time window from the original feasible domain; adding energy decoupling constraints at the start of that time window, where the energy decoupling constraint is that the state of charge of the energy storage device at that moment is equal to the energy state reference value; and the inherited constraints and the added energy decoupling constraints together constitute the low-dimensional time decoupling feasible domain corresponding to that time window.

[0095] Thus, the constraints in the original feasible region (such as distributed resource operation constraints, network security constraints, and system power balance constraints) are the core of ensuring the safe and stable operation of the power distribution system. Inheriting these constraints belonging to the current time window ensures that the constructed low-dimensional feasible region does not deviate from the basic requirements of actual system operation, avoiding distortion of the feasible region due to the loss of key constraints. The added energy decoupling constraint, relying on the energy state reference value obtained through the autonomous optimization model that conforms to economic and system constraints, fixes the state of charge at the beginning of the time window, which can directly sever the continuous coupling relationship of the state of charge between the current time window and the previous time window, breaking the high-dimensional characteristics of the original feasible region caused by the correlation of the state of charge in the entire time domain. The low-dimensional time-decoupled feasible region constructed by the combination of the two not only retains the feasibility basis of the original feasible region, but also decomposes the high-dimensional problem into independent low-dimensional sub-problems, avoiding the complexity problem brought by high-dimensional coupling to subsequent calculations (such as vertex search method), making the solution of each sub-domain easier to implement, while ensuring that the results of the decoupled feasible region fit the actual operating scenario of the system.

[0096] Optionally, based on the energy state reference value, energy decoupling constraints are added to the original feasible region to construct the time-decoupled feasible region of the original feasible region, thereby achieving high-dimensional dimensionality reduction of the original feasible region. It also includes: performing a union operation on the low-dimensional time-decoupled feasible regions corresponding to all time windows to obtain the equivalent approximate feasible region of the entire scheduling time domain.

[0097] Thus, the low-dimensional temporal decoupling feasible region corresponding to each time window is constructed based on the energy state reference value to supplement the decoupling constraints. Essentially, it is a subset (internal approximation) of the original feasible region, which can only reflect the feasible operating range of the system within the corresponding time window and cannot independently cover the entire scheduling time domain. Without union operation, the scattered low-dimensional feasible regions will lead to fragmentation of the feasible region representation in the entire time domain, making it difficult to support the analysis of the system's operating characteristics throughout the entire time domain. However, through union operation, the feasible spaces of each time window can be integrated and pieced together, so that the equivalent feasible region can completely cover all feasible operating scenarios in the entire scheduling time domain. At the same time, since each low-dimensional feasible region does not exceed the boundary of the original feasible region (internal approximation attribute), their union is always within the range of the original feasible region, and will not introduce infeasibility points beyond the original feasible region, ensuring that every operating state of the equivalent internal approximation feasible region conforms to the actual operating constraints of the system. The above method retains the computational advantages of low-dimensional decoupling and solves the problem of incomplete temporal coverage of a single low-dimensional feasible region. It provides a complete and reliable foundation for subsequent parallel computation of vertex search on the full temporal feasible region and obtaining the aggregated equivalent feasible region, ensuring that the final feasible region representation is both efficient and in line with the actual operating requirements of the system.

[0098] Optionally, the low-dimensional temporal decoupling feasible region corresponding to each time window is a subset of the original feasible region.

[0099] Thus, the low-dimensional time-decoupling feasible region is constructed by inheriting all constraints belonging to the corresponding time window from the original feasible region (including distributed resource operation constraints, network security constraints based on the linearized AC power flow model, system power balance constraints, etc.) and additionally supplementing energy decoupling constraints (fixing the state of charge of the energy storage device at the beginning of the time window to the energy state reference value). The constraints of the original feasible region are the core boundaries that ensure the safe and stable operation of the power distribution system. Inheriting these constraints means that the low-dimensional time-decoupling feasible region has met the basic operational limitations of the original feasible region. The supplementary energy decoupling constraints are additional restrictions added on the basis of the original constraints, further narrowing the scope of the feasible region without relaxing or breaking any constraint boundaries of the original feasible region. Therefore, the operating range of each low-dimensional time-decoupling feasible region will inevitably not exceed the original feasible region, becoming a subset of the original feasible region. This subset property ensures that the equivalent approximate feasible region obtained by performing a union operation on the low-dimensional feasible region, as well as the aggregated equivalent feasible region obtained by parallel computation based on the low-dimensional feasible region, are always within the safety constraints of the original feasible region. This ensures that all solution results meet the actual operating requirements of the system and avoids the safety and feasibility of scheduling decisions being affected by the distortion of the feasible region caused by decoupling operations.

[0100] Optionally, for the decoupled and dimensionality-reduced temporally decoupled feasible region, the vertex search method is used to compute the vertices of each sub-feasible region in parallel, including: for each low-dimensional feasible region in the temporally decoupled feasible region, the vertex search algorithm is executed in parallel to identify all vertices of that low-dimensional feasible region.

[0101] In this way, the original high-dimensional feasible region has been decomposed into multiple independent low-dimensional feasible regions by supplementing the energy decoupling constraint. These low-dimensional feasible regions, due to their reduced dimensionality (e.g., after dividing the 24-hour scheduling time domain into 12 two-hour time windows, the projection dimension is within the range that the vertex search method can efficiently handle), avoid the problem of exponential growth in computational complexity of the traditional vertex search method in high-dimensional scenarios. This makes vertex identification in a single low-dimensional feasible region highly efficient. Simultaneously, the energy decoupling constraint has severed the temporal coupling between the low-dimensional feasible regions, making them independent and without data dependencies. There are no constraints on the order of computation, which provides the premise for parallel execution of the vertex search algorithm. This allows for simultaneous vertex identification in multiple low-dimensional feasible regions, rather than sequential processing, thus significantly reducing the overall computation time. This method not only solves the problem of difficult vertex identification in high-dimensional feasible regions but also further improves computational efficiency through parallel computing, ensuring accurate acquisition of vertices in each low-dimensional feasible region within a reasonable timeframe.

[0102] Optionally, the vertex search algorithm includes an initialization phase, an inner loop optimization phase, and a convergence judgment phase.

[0103] Thus, the initialization phase, by setting the initial values ​​for the outer loop iterations, initializing the search direction vector, solving the vertex search model to obtain the initial vertex set, and constructing the initial convex hull, provides a reasonable starting foundation for the algorithm. This avoids search direction deviations caused by unordered initial states and ensures that the algorithm starts vertex recognition from a starting point that aligns with the characteristics of the low-dimensional feasible region. The inner loop optimization phase searches for the outward normal vector of each face of the current convex hull, solves the vertex search model to obtain new vertices, and updates the vertex set and convex hull. This continuously fills in vertices not covered by the initial convex hull, gradually improving the recognition of vertices in the low-dimensional feasible region, enhancing the completeness of vertex recognition, and avoiding the omission of key vertices. The convergence judgment phase terminates the algorithm by calculating the convex hull volume difference or determining whether the maximum number of iterations has been reached. This prevents the algorithm from getting stuck in meaningless repeated iterations, controlling computation time while ensuring vertex recognition accuracy (volume difference less than the preset tolerance), balancing computational efficiency and result accuracy. Through the aforementioned phased algorithm structure, the vertex search process has a clear starting direction, can be continuously optimized and improved, and can be terminated reasonably, which adapts to the needs of vertex recognition in low-dimensional feasible regions and ensures that the final output vertex set can accurately reflect the boundary features of the low-dimensional feasible region.

[0104] Optionally, the initialization phase includes: setting initial values ​​for the outer loop iteration; initializing a set of search direction vectors; solving a vertex search model for each search direction vector, the vertex search model aiming to maximize the inner product of the search direction vector and the decision variable, with the current low-dimensional feasible region as a constraint; gathering the solved vertices into an initial vertex set; and constructing an initial convex hull based on the initial vertex set.

[0105] Thus, setting initial values ​​for the outer loop iterations avoids iterative chaos caused by the lack of a clear starting state, defining an orderly beginning for the entire search process. Initializing a set of search direction vectors can cover different dimensional directions of the low-dimensional feasible region, preventing the search from being limited to a single direction and missing key boundary vertices. The vertex search model aims to maximize the inner product of the search direction vector and the decision variable because the value of the decision variable corresponding to maximizing the inner product is precisely the boundary vertex of the low-dimensional feasible region in that direction. Combined with the constraints of the current low-dimensional feasible region (such as distributed resource operation constraints, network security constraints, etc.), it can ensure that the solved vertices are both within the feasible range and accurately reflect the boundary characteristics of the feasible region in that direction. Gathering these vertices from different directions into an initial vertex set can provide sufficient and comprehensive boundary point support for subsequent convex hull construction, avoiding the inability of the convex hull to initially represent the shape of the feasible region due to insufficient initial points. Constructing an initial convex hull based on the initial vertex set transforms scattered vertices into an initial geometric representation with a clear boundary shape. This provides a clear object for further searching the convex hull surface during the inner loop optimization stage, eliminating the need for subsequent optimizations to explore the feasible region boundary from scratch. This lays the foundation for the entire vertex search algorithm to efficiently and accurately identify vertices in the low-dimensional feasible region.

[0106] Optionally, during the initialization phase, at least 2T different vertices are obtained by solving the vertex search model to form an initial vertex set, where T is the number of scheduling periods contained in the time window corresponding to the current low-dimensional feasible region.

[0107] Thus, the geometry of the current low-dimensional feasible region is related to the number of scheduling periods T in the time window. As a convex polyhedron, it requires a sufficient number of vertices to initially cover the boundary features in different directions. At least 2T different vertices can capture the boundary information of the feasible region from multiple key directions, avoiding the problem of oversimplification of the initial convex hull due to insufficient initial vertices, which fails to reflect the true boundary of the feasible region. If the number of initial vertices is less than 2T, the initial convex hull may miss some boundary directions, requiring frequent addition of new vertices in subsequent inner loop optimization, increasing computational load and easily introducing bias. Sufficient initial vertices allow the initial convex hull constructed based on it to be closer to the actual boundary of the low-dimensional feasible region, reducing the number of times vertices need to be added in the inner loop optimization stage, reducing the overall computational complexity of the algorithm, and avoiding significant shape deviations in the initial convex hull. This ensures that subsequent inner loop optimization is carried out from a more accurate foundation, guaranteeing that the final identified set of low-dimensional feasible region vertices can completely and accurately reflect the boundary of the feasible region.

[0108] Optionally, during the initialization phase, the Quickhull algorithm is used to construct the initial convex hull based on the initial vertex set.

[0109] In this way, the Quickhull algorithm exhibits high convex hull construction efficiency in low-dimensional spaces (such as the current low-dimensional feasible region, where the number of scheduling periods T in the corresponding time window is small and the dimension is low). It can quickly eliminate redundant vertices in the initial vertex set by iteratively partitioning the space and filtering key vertices, focusing on the core vertices that constitute the convex hull boundary, thus avoiding the problem of excessively long construction time caused by a large number of initial vertices (e.g., at least 2T). Simultaneously, the algorithm can accurately identify vertices in the initial vertex set that reflect the boundary characteristics of the low-dimensional feasible region, ensuring that the constructed initial convex hull fits the actual geometry of the low-dimensional feasible region, avoiding oversimplification or shape deviation. This efficient and accurate initial convex hull construction method not only shortens the computation time in the initialization phase but also eliminates the need for frequent corrections to the convex hull shape in subsequent inner loop optimization phases, reducing the number of iterations and the risk of deviation, and ensuring the overall efficiency and accuracy of the vertex search algorithm.

[0110] Optionally, the inner loop optimization stage includes: obtaining the external normal vector of each face of the current convex hull; using each external normal vector as a new search direction vector to solve the vertex search model; if a new vertex is obtained, adding the new vertex to the vertex set and updating the convex hull.

[0111] In this way, the current convex hull is constructed based on the initial vertices. Due to insufficient coverage of the initial vertices, there may be boundary gaps. The outward normal vector of each face of the convex hull points precisely to the outside of the convex hull, which corresponds exactly to the direction of the convex hull that may have missing vertices. Using the outward normal vector as the new search direction vector, combined with a vertex search model that aims to maximize the inner product of this vector and the decision variable, and constrained by the current low-dimensional feasible region, the new vertex obtained will necessarily be the boundary vertex of the low-dimensional feasible region in that direction (the value of the decision variable that maximizes the inner product is the boundary vertex in the corresponding direction), and can specifically fill the boundary gap of the current convex hull in that face direction. The addition of new vertices and the updating of the convex hull keep the shape of the convex hull close to the true boundary of the low-dimensional feasible region, avoiding the blindness of the search direction, reducing invalid iterations, and ensuring that the vertex recognition process is both efficient and covers the key boundaries.

[0112] Optionally, the convergence judgment stage includes: calculating the volume difference between the current convex hull and the previous convex hull; determining whether the volume difference is less than the preset tolerance, or determining whether the maximum number of iterations has been reached; if the volume difference is less than the preset tolerance or the maximum number of iterations has been reached, then terminating the iteration and outputting the current vertex set as the final result.

[0113] Thus, the difference in convex hull volume directly reflects the completeness of the vertex set and the stability of the convex hull shape. When the volume difference is less than the preset tolerance, it indicates that the addition of vertices has minimal impact on the convex hull shape, the convex hull has essentially conformed to the true boundary of the low-dimensional feasible region, the vertex set is relatively complete, and further iterations offer limited gain. Setting a maximum number of iterations is to prevent the algorithm from getting stuck in infinite iterations due to special circumstances (such as an excessively small tolerance setting), providing a clear termination boundary for the computation process and controlling the overall computation time. Through the above dual judgment logic, the accuracy of vertex recognition is guaranteed through the tolerance standard (meeting the accuracy requirements of feasible region representation in actual operation), while the computational cost is controlled through the maximum number of iterations, enabling the algorithm to efficiently output a reliable vertex set.

[0114] Optionally, the aggregation to obtain the aggregated equivalent feasible region of the power distribution system includes: projecting the vertex set of each low-dimensional feasible region onto its boundary variable space, where the boundary variables include the active power injection and reactive power injection at the common coupling node; and aggregating the projection results to form a set describing the feasible range of the boundary variables, which serves as the aggregated equivalent feasible region.

[0115] Thus, each low-dimensional feasible region is an inner approximate subset obtained by decoupling and dimensionality reduction of the original feasible region. The vertex set of each low-dimensional feasible region has been accurately captured using a vertex search method to capture its corresponding boundary features. The common coupling node, as a key node for power interaction between the distribution system and the upper-level power grid, has active and reactive power injections as core boundary variables reflecting the distribution system's external power interaction capability. Selecting these two variables as the projection boundary variables allows us to focus on the key dimensions characterizing the aggregated feasible region of the distribution system, stripping away irrelevant internal variables in the low-dimensional feasible regions, and ensuring that the projection direction aligns with actual application requirements. Projecting the vertex set of each low-dimensional feasible region into this boundary variable space transforms the boundary features of each low-dimensional feasible region into the value range of the core boundary variables. By aggregating these projection results, we can integrate the feasible information of all low-dimensional feasible regions on the core boundary variables, forming a set that completely covers the feasible range of the distribution system's external power interaction within the entire scheduling time domain. This set is the aggregated equivalent feasible region. By leveraging the efficient computational foundation established by previous decoupling dimensionality reduction and parallel vertex search, the computational challenges brought about by high-dimensional variables are avoided. Furthermore, by focusing on core boundary variables and aggregated projection results, the aggregated equivalent feasible region can accurately reflect the actual operating boundary of the power distribution system, providing reliable feasible region support for the optimized scheduling decision of the power distribution system.

[0116] In this embodiment of the application, an autonomous optimization model for the power distribution system is constructed, and decision optimization is performed with economic efficiency as the objective. The energy state reference value of the energy storage device in the scheduling time domain is obtained by solving the model, including:

[0117] Construct an autonomous optimization model with the objective function of minimizing the total operating cost of the power distribution system. The objective function can be expressed as:

[0118] minC UP +C PV +C ES

[0119] Among them, C UP C represents the cost of electricity purchased by the superior authority. PV C represents the cost of solar power curtailment penalties. ES This represents the operating cost of energy storage.

[0120] The autonomous optimization model is constrained by a set of original operational constraints Ω1 of the distribution system, which defines the original feasible region of the system. Ω1 includes operational constraints for all distributed resources in the distribution system, network security constraints based on a linearized AC power flow model, and system power balance constraints. Specifically, Ω1 includes the following constraints:

[0121] 1. Power constraints of common coupling nodes:

[0122]

[0123] in, and These represent the active power and reactive power input at time t of the common coupling node connecting the distribution network and the upper-level power grid. and They represent The lower and upper limits; and They represent The lower and upper limits.

[0124] 2. Operational constraints of distributed photovoltaic power generation:

[0125]

[0126] in, This represents the actual output power of distributed photovoltaic power at time t. This represents its predicted power level.

[0127] 3. Operational constraints of energy storage devices:

[0128]

[0129]

[0130] in, and These represent the charging power and discharging power of the energy storage device at time t, respectively. and These represent the upper limits of its charging power and discharging power, respectively. This represents the state of charge of the energy storage device at time t. and These represent its lower and upper limits, respectively; η c and η d These represent the charging efficiency and discharging efficiency of the energy storage device, respectively; Q ES This represents the amount of electricity stored in the energy storage device.

[0131] 4. Operating constraints of static var compensators:

[0132]

[0133] in, This represents the reactive power output by the static var compensator at time t. and These represent its lower limit and upper limit, respectively.

[0134] 5. Network security constraints based on a linearized AC power flow model, specifically including node voltage security constraints and constraints reflecting power flow relationships:

[0135]

[0136] in, and These represent the active power and reactive power input to the nth node line at time t, respectively. and These represent the distributed resources accessed by node n at time t, as well as the sum of active and reactive power input from the upstream power grid; and These represent the active and reactive loads of node n at time t, respectively. This represents the squared voltage value of node n at time t. and These represent the lower and upper limits, respectively; r(n) and x(n) represent the line resistance and reactance, respectively.

[0137] The original set of operational constraints Ω1 described above can be represented in the following compact form:

[0138]

[0139] Where x represents the internal decision variable, and a1, a2, a3 and b1 represent the matrix coefficients.

[0140] Solve the above autonomous optimization model to output the optimal state of charge (SOC) value of the energy storage device in each scheduling period. As a reference value for energy state.

[0141] In this embodiment, the total operating cost of the power distribution system includes the cost of electricity purchased from the upstream power grid, the cost of curtailment penalties for distributed photovoltaic power, and the operating cost of energy storage devices. The formula for calculating the cost of electricity purchased from the upstream power grid is as follows:

[0142] C UP =c UP ·P UP

[0143] Among them, c UP P represents the upstream power purchase cost per unit of power, which is a preset economic parameter; UP This represents the sum of active power input to the common coupling node. The formula for calculating the curtailment penalty cost of distributed photovoltaic power is:

[0144]

[0145] Among them, c PV The unit power photovoltaic curtailment penalty cost is a preset economic parameter. P represents the total predicted photovoltaic power output. PV This represents the total actual output power of photovoltaic power. The formula for calculating the operating cost of energy storage equipment is:

[0146] C ES =c ES ·(P c,ES +P d,ES )

[0147] Among them, c ES P represents the unit power energy storage charging and discharging cost, which is a preset economic parameter; c,ES and P d,ES These represent the total charging power and the total discharging power of the energy storage device, respectively.

[0148] In this embodiment of the application, based on the energy state reference value, energy decoupling constraints are added to the original feasible region to construct a time-decoupled feasible region of the original feasible region, thereby achieving high-dimensional dimensionality reduction of the original feasible region, including:

[0149] First, the autonomous optimization model of the power distribution system is solved to obtain the optimal state of charge (SOC) value of the energy storage device at each moment in the scheduling time domain, which serves as the energy state reference value.

[0150] Next, to achieve decoupling in the time dimension, energy decoupling constraints are added to the original set of operational constraints Ω1, thereby constructing the feasible region for time decoupling. Mathematically, this process can be represented as adding a set of equality constraints to the original constraints:

[0151]

[0152] Wherein, τ represents the set of decoupling moments, which consists of a pre-defined series of time points; This is a supplementary energy decoupling constraint, whose function is to fix the state of charge of the energy storage device at the decoupling time t to the corresponding energy state reference value.

[0153] Then, the entire scheduling time domain is divided into multiple consecutive time period windows. Specifically, a complete scheduling cycle (e.g., 24 hours) can be divided into multiple consecutive time period windows of preset duration. For example, 24 scheduling periods can be divided into 12 consecutive 2-time period windows, i.e., the decoupling time set is τ = {2, 4, ..., 22}. Through this division, each time period window contains fewer time periods (e.g., 2 time periods), making the dimension of projection calculation for each window (e.g., active power injected to common coupling nodes) smaller. and reactive power injection When projecting, the dimension (4) is reduced, thus enabling efficient computation using vertex search.

[0154] For each time window obtained from the segmentation, the energy decoupling constraint at the start time of that window is added to the original feasible region, thereby constructing the low-dimensional temporal decoupling feasible region corresponding to that time window. The union of the low-dimensional temporal decoupling feasible regions corresponding to all time windows constitutes the temporal decoupling feasible region of the entire scheduling time domain. Its mathematical expression is:

[0155]

[0156] in, The low-dimensional temporal decoupling feasible region represents the time window corresponding to the coverage times t and t+1.

[0157] Since the supplementary energy decoupling constraints add restrictions to the original constraints, each low-dimensional time decoupling feasible region... and their union Both are subsets of the original feasible region Ω1, i.e., inner approximations.

[0158] Finally, for each low-dimensional time decoupling feasible region A projection operation is performed on its boundary variable space. The boundary variables include at least the active and reactive power inputs at each time step of the common coupling nodes connecting the distribution system to the upper-level power grid. After projection, the aggregated sub-feasibility region describing the feasible range of the boundary variables of this window is obtained. Its compact form can be expressed as:

[0159]

[0160] Where α1(t,t+1) and β1(t,t+1) are the matrix coefficient vector and constant term describing the projection of the convex polyhedron.

[0161] By performing a union operation on the aggregated feasible regions obtained by projecting all time windows, the equivalent approximate feasible region within the entire scheduling time domain can be obtained.

[0162]

[0163] The equivalent approximate feasible region This is the aggregated equivalent feasible region that ultimately characterizes the power interaction capability of the power distribution system at the common coupling node.

[0164] In this embodiment of the application, for the decoupled and dimensionality-reduced temporally decoupled feasible region, the vertex search method is used to compute the vertices of each sub-feasible region in parallel, including:

[0165] For each low-dimensional temporal decoupling feasible region in the temporal decoupling feasible region, a vertex search algorithm is executed in parallel to identify all vertices of that low-dimensional temporal decoupling feasible region.

[0166] The vertex search algorithm includes an initialization phase, an inner loop optimization phase, and a convergence determination phase. The vertex search process is implemented by constructing and iteratively solving a vertex search model.

[0167] The mathematical representation of vertex search model OP1 is:

[0168]

[0169] Where δ represents a preset search direction vector; σ is the objective function value of the OP1 model; x is the internal decision variable; P UP and Q UP These are boundary variables, representing the active power injection and reactive power injection at the common coupling node, respectively. This represents the low-dimensional time-decoupling feasible region to be solved. The goal of this model is to find a set of decision variables that maximizes the projection of the boundary variable vector onto a given search direction δ, while satisfying all constraints of the low-dimensional time-decoupling feasible region. This optimal solution is a boundary vertex of the feasible region in that direction.

[0170] The initialization phase includes: setting the initial value of the outer loop iteration counter, for example, letting j = 0. Initializing a set of search direction vectors, which are used for preliminary exploration in different directions of the feasible region boundary space. Solving the vertex search model OP1 for each initialized search direction vector δ. Each successfully solved optimal solution corresponds to an extreme point of the low-dimensional time-decoupling feasible region in that search direction, i.e., a vertex. All the solved vertices are aggregated to form the initial vertex set V0. To ensure the representativeness of the constructed initial convex hull, at least 2T distinct vertices are needed, where T is the number of scheduling periods contained in the time window corresponding to the low-dimensional time-decoupling feasible region. A convex hull construction algorithm is used to calculate its convex hull based on the initial vertex set V0, obtaining the initial convex hull O0. The convex hull construction algorithm can be a fast convex hull algorithm.

[0171] The inner loop optimization phase includes: obtaining the current convex hull O in each outer loop iteration. j-1 The outer normal vector of each surface of the initial convex hull (O0) is used in the first iteration. Each outer normal vector is used as a new search direction vector δ. For each new search direction vector, the vertex search model OP1 is solved again. If a new vertex is obtained, and this vertex does not exist in the current vertex set V, then the search is considered complete. j-1 If the vertex is in the set, then add it to form the updated vertex set V. j Based on the updated vertex set V j Recalculate the convex hull to obtain the updated convex hull O. j .

[0172] The convergence determination phase includes: after each inner loop optimization and convex hull update, determining whether the algorithm meets the termination condition. The termination condition includes any of the following cases:

[0173] (1) The convex hull obtained by two consecutive outer loop iterations (e.g., O) j With O j-1 (1) The hypervolume difference is less than a preset tolerance threshold. (2) The number of iterations in the outer loop reaches a preset maximum allowed number of iterations. When any termination condition is met, the algorithm stops iterating and sets the current vertex set V. j The final vertex set output is the result of this low-dimensional time-decoupled feasible region.

[0174] In this application embodiment, a verification implementation of the proposed power distribution system feasible domain modeling method is provided.

[0175] First, a typical power distribution network test system is constructed as the verification environment. This test system can be a power distribution system improved based on a standard feeder model. In a specific example, an improved IEEE 33-node power distribution system is used as the test network, with the following topology: Figure 3 As shown, the system is connected to the upper-level power grid through a common coupling node. The network contains 33 nodes and multiple branches, forming a typical radial distribution network structure.

[0176] In this test power distribution system, various distributed resources are connected. Specifically, the connected devices may include multiple distributed photovoltaic (PV) units, multiple energy storage devices, multiple distributed generators, and multiple static var compensators (SVCs). For example, in one implementation scenario, the system includes 6 distributed PV units, 3 energy storage devices, 10 distributed generators, and 10 SVCs. The connection locations of each device are configured according to the system topology and requirements; specific connection nodes can be found in the appendix. Figure 3 The network topology diagram is shown. The safety boundary parameters for system operation are preset. For example, the allowable range of voltage at each node of the distribution network is set to 0.95 per unit to 1.05 per unit, and the upper limit of current for each branch is set to 150 amperes.

[0177] The verification process was conducted in a hardware and software environment with specific computing resources. For example, on a computer equipped with 16GB of memory and an Intel Core i7-12700H processor (2.70GHz), the MATLAB software environment was used, and the Gurobi mathematical programming solver was invoked using the Yalmip modeling toolkit to solve all optimization models.

[0178] To verify the accuracy and advantages of the method proposed in this application, it is compared and analyzed with at least two other feasible region representation methods. The first comparison method is the traditional vertex search method; the second comparison method is a feasible region characterization method based on decoupling algorithms; the third comparison method is the method proposed in this application, the overall process of which can be summarized as follows: Figure 2 The diagram illustrates a collaborative process based on priority decision-making, time decoupling, and parallel vertex search. Figure 2 The flowchart shown clearly illustrates the complete steps from building an autonomous optimization model of the power distribution system, to obtaining energy state reference values, then performing time decoupling and dimensionality reduction, and finally obtaining the equivalent feasible region through parallel vertex search and aggregation.

[0179] To quantify the accuracy of the aggregated equivalent feasible regions obtained by different methods, two error evaluation metrics are defined: average objective function error and average optimal solution error. A positive average objective function error indicates that the optimal operating cost obtained within the equivalent feasible region is lower than the optimal operating cost obtained within the original feasible region. This implies that the scope of the equivalent feasible region is expanded, potentially including infeasible points outside the original feasible region. Conversely, a negative average objective function error indicates that the equivalent feasible region is an inner approximate subset of the original feasible region, entirely located within the original feasible region, thus ensuring feasibility. The average optimal solution error directly measures the average deviation between the optimal solution obtained within the equivalent feasible region and the optimal solution obtained within the original feasible region.

[0180] The specific verification results are as follows:

[0181]

[0182] Verification results show that, due to the high-dimensional temporal coupling characteristics, traditional vertex search methods struggle to obtain effective results when solving the 6-dimensional and higher projection problems of this embodiment. While the second comparative method can solve the problem, its approximation process neglects some temporal coupling constraints, resulting in an equivalent feasible region larger than the original feasible region (average objective function error of 0.0918 pu), meaning it includes infeasible points outside the original feasible region. In contrast, the method proposed in this application calculates a negative average objective function error (-0.0823 pu), indicating that its equivalent feasible region is a strictly inner approximate subset of the original feasible region, completely within the original feasible region, thus ensuring that all represented running points are feasible. Furthermore, the average optimal solution error of the method in this application (0.0542 pu) is lower than that of the second comparative method (0.0567 pu), demonstrating higher computational accuracy. Therefore, the feasible domain modeling method proposed in this application can effectively handle the high-dimensional feasible domain representation problem of power distribution systems with time-coupled devices and network security constraints, and has better computational accuracy while ensuring the feasibility of the solution results.

[0183] Therefore, the feasible domain modeling method proposed in this application can effectively handle the high-dimensional feasible domain representation problem of power distribution systems with time-coupled devices and network security constraints, and has better computational accuracy while ensuring the feasibility of the solution results.

[0184] Combination Figure 4 As shown in the figure, this application provides a feasible domain modeling device 800 for a power distribution system, including a processor 801 and a memory 802. Optionally, the device may further include a communication interface 803 and a bus 804. The processor 801, communication interface 803, and memory 802 can communicate with each other via the bus 804. The communication interface 803 can be used for information transmission. The processor 801 can call logical instructions in the memory 802 to execute the feasible domain modeling method for a power distribution system described in the above embodiment.

[0185] Furthermore, the logic instructions in the aforementioned memory 802 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium.

[0186] The memory 802, as a computer-readable storage medium, can be used to store software programs and computer-executable programs, such as program instructions / modules corresponding to the methods in the embodiments of this application. The processor 801 executes functional applications and data processing by running the program instructions / modules stored in the memory 802, thereby implementing the feasible domain modeling method for power distribution systems described in the above embodiments.

[0187] The memory 802 may include a program storage area and a data storage area. The program storage area may store the operating system and application programs required for at least one function; the data storage area may store data created based on the use of the terminal device. Furthermore, the memory 802 may include high-speed random access memory and may also include non-volatile memory.

[0188] This application provides a system comprising: a system body and the aforementioned feasible domain modeling device 800 for a power distribution system. The feasible domain modeling device 800 for a power distribution system is installed on the system body. The installation relationship described herein is not limited to placement within the system, but also includes installation connections with other components of the system, including but not limited to physical connections, electrical connections, or signal transmission connections. Those skilled in the art will understand that the feasible domain modeling device 800 for a power distribution system can be adapted to feasible system bodies to achieve other feasible embodiments.

[0189] This application provides a computer-readable storage medium storing computer-executable instructions configured to execute the above-described feasible domain modeling method for power distribution systems.

[0190] The technical solutions of this application embodiment can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes one or more instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in this application embodiment. The aforementioned storage medium can be a non-transitory storage medium, including: USB flash drive, portable hard drive, read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk, and other media capable of storing program code.

[0191] The technical solutions of this application embodiment can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes one or more instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in this application embodiment. The aforementioned storage medium can be a non-transitory storage medium, including: USB flash drive, portable hard drive, read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk, and other media capable of storing program code.

[0192] The foregoing description and accompanying drawings fully illustrate embodiments of this application to enable those skilled in the art to practice them. Other embodiments may include structural, logical, electrical, procedural, and other changes. The embodiments represent only possible variations. Individual components and functions are optional unless explicitly required, and the order of operation may vary. Parts and features of some embodiments may be included in or replace parts and features of other embodiments. Moreover, the terminology used in this application is for describing embodiments only and is not intended to limit the claims. As used in the description of embodiments and claims, the singular forms “a,” “an,” and “the” are intended to equally include the plural forms unless the context clearly indicates otherwise. Similarly, the term “and / or,” as used herein, means including one or more of the associated listed items and all possible combinations thereof. Additionally, when used in this application, the term "comprise" and its variations "comprises" and / or "comprising" refer to the presence of stated features, integrals, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or groups thereof. Without further limitations, an element defined by the phrase "comprising a..." does not exclude the presence of other identical elements in the process, method, or apparatus that includes said element. In this document, each embodiment may focus on the differences from other embodiments, and similar or identical parts between embodiments can be referred to mutually. For methods, products, etc., of the embodiments claimed, if they correspond to the method section of the embodiments claimed, then the relevant parts can be referred to the description of the method section.

[0193] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments claimed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the embodiments of this application. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0194] The methods and products (including but not limited to devices and equipment) disclosed in the embodiments herein can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For instance, the division of units may be merely a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed may be through some interfaces, and the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to implement this embodiment according to actual needs. In addition, the functional units in the embodiments of this application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0195] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than that shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. In the descriptions corresponding to the flowcharts and block diagrams in the accompanying drawings, the operations or steps corresponding to different blocks may also occur in a different order than disclosed in the description; sometimes there is no specific order between different operations or steps. For example, two consecutive operations or steps may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. Each block in a block diagram and / or flowchart, and combinations of blocks in a block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

Claims

1. A feasible domain modeling method for power distribution systems, characterized in that, include: An autonomous optimization model for the power distribution system is constructed, and decision optimization is carried out with economic efficiency as the objective. The energy state reference value of the energy storage device in the scheduling time domain is obtained by solving the model. Based on the energy state reference value, energy decoupling constraints are added to the original feasible region to construct the time-decoupled feasible region of the original feasible region, thereby achieving high-dimensional reduction of the original feasible region. For the decoupled and dimensionality-reduced time-decoupled feasible region, the vertex search method is used to calculate the vertices of each sub-feasible region in parallel, and the aggregated equivalent feasible region of the power distribution system is obtained.

2. The method according to claim 1, characterized in that, An autonomous optimization model for the power distribution system is constructed, and decision optimization is performed with economic efficiency as the objective. The energy state reference value of the energy storage device in the scheduling time domain is obtained by solving the model, including: Construct an autonomous optimization model with the objective function of minimizing the total operating cost of the power distribution system; Set constraints for the autonomous optimization model; among which, the constraints include operational constraints of all distributed resources in the power distribution system, network security constraints based on the linearized AC power flow model, and / or system power balance constraints. Solve the autonomous optimization model and output the optimal state of charge value of the energy storage device in each scheduling period as the energy state reference value.

3. The method according to claim 2, characterized in that, The total operating cost of the power distribution system includes the cost of purchasing electricity from the upstream power grid; The calculation of the electricity purchase cost from the upstream power grid includes: Obtain the active power input at the common coupling node connecting the power distribution system and the upstream power grid; The active power is multiplied by the preset unit electricity purchase cost to obtain the electricity purchase cost of the upper-level power grid.

4. The method according to claim 2, characterized in that, The total operating cost of the power distribution system includes the curtailment penalty cost of distributed photovoltaic power; the calculation of the curtailment penalty cost of distributed photovoltaic power includes: Obtain the day-ahead predicted power and actual output power of distributed photovoltaic power; Calculate the difference between the predicted power and the actual output power before the day; Multiply the difference by the preset unit curtailment penalty cost to obtain the curtailment penalty cost of distributed photovoltaic power.

5. The method according to claim 2, characterized in that, The total operating cost of the power distribution system includes the operating cost of energy storage equipment; the calculation of the operating cost of energy storage equipment includes: Obtain the charging and discharging power of energy storage devices; Calculate the sum of the absolute values ​​of the charging power and the discharging power; The sum of the absolute values ​​is multiplied by the preset unit charge / discharge cost to obtain the operating cost of the energy storage device.

6. The method according to claim 2, characterized in that, The operational constraints of all distributed resources in the power distribution system include the operational constraints of distributed photovoltaic (PV) systems; the operational constraints of distributed PV systems include: The actual output power of distributed photovoltaic power does not exceed its day-ahead forecast power.

7. The method according to claim 2, characterized in that, The operational constraints of all distributed resources in the power distribution system include the operational constraints of energy storage devices; the operational constraints of energy storage devices include: The charging power of the energy storage device does not exceed its maximum charging power limit; and / or, The discharge power of the energy storage device does not exceed its upper limit; and / or, The state of charge (SOC) of an energy storage device is between its lower SOC limit and upper SOC limit; and / or, The energy evolution of energy storage devices between adjacent scheduling periods satisfies the energy conservation relationship determined by charging efficiency, discharging efficiency, charging power and / or discharging power.

8. The method according to any one of claims 1 to 7, characterized in that, Based on the energy state reference value, energy decoupling constraints are added to the original feasible region to construct a time-decoupled feasible region of the original feasible region, achieving high-dimensional reduction of the original feasible region, including: The entire scheduling time domain is divided into multiple consecutive time windows; For each time window, energy decoupling constraints are added to the original feasible region to construct a low-dimensional time decoupling feasible region corresponding to that time window; wherein, the energy decoupling constraints fix the state of charge of the energy storage device at the beginning of the time window to the value of the energy state reference value at that time. The low-dimensional temporal decoupling feasible region corresponding to all time windows is taken as the temporal decoupling feasible region.

9. The method according to claim 8, characterized in that, For each time window, energy decoupling constraints are added to the original feasible region to construct a low-dimensional temporal decoupling feasible region corresponding to that time window, including: Inherit all constraints belonging to the current time window from the original feasible domain; Add an energy decoupling constraint at the start of the time window, whereby the energy storage device's state of charge at that moment equals the energy state reference value. The inherited constraints and the added energy decoupling constraints together constitute the low-dimensional temporal decoupling feasible region corresponding to this time window.

10. The method according to claim 8, characterized in that, Based on energy state reference values, energy decoupling constraints are added to the original feasible region to construct a time-decoupled feasible region of the original feasible region, achieving high-dimensional reduction of the original feasible region. This also includes: By performing a union operation on the low-dimensional time decoupling feasible regions corresponding to all time windows, we obtain the equivalent approximate feasible region within the entire scheduling time domain.

11. The method according to any one of claims 1 to 7, characterized in that, For the decoupled and dimensionality-reduced temporally decoupled feasible region, a vertex search method is used to compute the vertices of each sub-feasible region in parallel, including: For each low-dimensional feasible region in the time-decoupled feasible region, a vertex search algorithm is executed in parallel to identify all vertices of that low-dimensional feasible region.

12. The method according to claim 11, characterized in that, The vertex search algorithm includes an initialization phase, an inner loop optimization phase, and a convergence judgment phase.

13. The method according to any one of claims 1 to 7, characterized in that, Aggregation yields the aggregated equivalent feasible region of the power distribution system, including: Project the set of vertices of each low-dimensional feasible region onto its boundary variable space. The boundary variables include the active power injection and reactive power injection at the common coupling node. The projection results are aggregated to form a set describing the feasible range of boundary variables, which serves as the aggregated equivalent feasible region.

14. A feasible domain modeling apparatus for a power distribution system, comprising a processor and a memory storing program instructions, characterized in that, The processor is configured to execute, when running the program instructions, the feasible domain modeling method for a power distribution system as described in any one of claims 1 to 13.

15. A system, characterized in that, include: System body; as well as, The feasible domain modeling device for a power distribution system as described in claim 14 is installed on the system body.

16. A computer-readable storage medium storing program instructions, characterized in that, When the program instructions are executed, they cause the computer to perform the feasible domain modeling method for a power distribution system as described in any one of claims 1 to 13.

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