Active power distribution network multi-target planning method based on reliability explicit analytic expression

Abstract

The invention relates to an active power distribution network multi-target planning method based on reliability explicit analytic expression, and the method comprises the steps: building a reliability evaluation-oriented matrix calculation model, and building an ADN multi-target collaborative planning model which gives consideration to the power supply reliability, DG absorption capability and economical efficiency; carrying out linear reconstruction and optimization solution on the multi-target collaborative planning model; and outputting a multi-target collaborative planning result, and analyzing resource configuration characteristics and cost structure evolution characteristics of the ADN under multi-target collaborative optimization. According to the method, a matrix analytic calculation system oriented to reliability evaluation is established, an explicit analytic calculation method of the ADN reliability index considering SOP and ESS is provided, the reliability cost obtained through conversion of the reliability index is embedded into an ADN multi-objective optimization model, and coordination and balance among ADN power supply reliability, DG absorption capacity and economical efficiency are achieved through reasonable configuration of the SOP and the ESS.

Description

Technical Field

[0001] This invention belongs to the field of power grid control technology, and in particular to an active distribution network multi-objective planning method based on a reliability explicit analytical expression. Background Technology

[0002] Driven by the "dual-carbon" strategy, building a new power system with new energy sources as the mainstay has become the core path for global energy transformation. As a key technological means for low-carbon transformation, distributed generation (DG) is seeing a continuous increase in its penetration rate in distribution networks, propelling the evolution of distribution systems towards active distribution networks (ADNs) that support a high proportion of DG. However, while high-proportion DG integration improves the system's low-carbon efficiency, it also faces new challenges in resource optimization: 1) The strong fluctuations in DG output and load require distribution networks to have more flexible spatiotemporal power regulation capabilities to alleviate the constraints of source-load imbalance on DG absorption; 2) End-users' demands for power supply reliability are increasing, necessitating a breakthrough from the traditional extensive model of relying on redundant and flexible resource stacking to improve reliability, and avoiding a surge in investment and operation and maintenance costs that weakens system economics. Therefore, how to coordinate and optimize multiple resources to achieve a balance between ensuring power supply reliability, improving DG absorption levels, and maintaining system economics has become a key issue in the construction of new power systems.

[0003] Current research on ADN planning mainly focuses on economic-oriented resource synergistic optimization, which can be summarized into two typical paths: 1) Economic-DG absorption synergistic planning: constructing an optimization model based on network topology and source-load time-series characteristics to reduce the total system cost while improving DG absorption capacity; 2) Economic-reliability synergistic planning: incorporating distribution network investment costs, operation and maintenance costs, and reliability costs into the optimization framework to achieve a coordinated balance among these costs. However, the above research has insufficient consideration for the synergistic optimization of multiple objectives in ADN, that is, it has failed to establish a synergistic optimization model for ADN power supply reliability, DG absorption, and economics to reveal the trade-offs among multiple objectives.

[0004] ADN planning methods considering reliability improvement can be categorized into three types: post-planning reliability assessment and correction, heuristic optimization planning, and explicit analytical reliability embedding planning. For the first two types, the ADN planning model needs to be solved multiple times and a post-reliability assessment needs to be performed. These two types of planning methods can employ reliability assessment methods including analytical methods (AM) and Monte Carlo simulation (MCS). However, for complex mixed-integer programming problems such as multi-objective collaborative planning in ADN, traditional reliability assessment methods rely on topological traversal or probabilistic simulation, making it difficult to explicitly express ADN reliability indices. Consequently, the calculation results cannot be directly embedded into the optimization model, forcing the planning process to employ iterative correction or heuristic search. Furthermore, the above methods are essentially suboptimal solution approximation mechanisms, making it difficult to guarantee the optimality of the planning scheme after considering reliability constraints / objectives.

[0005] To address these challenges, existing research has proposed explicit reliability assessment methods applicable to traditional passive radial distribution networks and embedded them into distribution network expansion planning. Currently, with the high proportion of distributed generation (DG) access driving the evolution of distribution networks from passive unidirectional radial networks to active bidirectional interactive systems, their topology is undergoing a profound transformation from rigid constraints to flexible controllability. In this process, smart soft switches (SOPs), as core enabling devices supporting flexible networking, can significantly enhance system operational resilience and DG absorption capacity by providing continuous power flow regulation and rapid fault isolation capabilities. However, current research lacks explicit calculation methods for ADN reliability indices that take into account the rapid fault transfer capability of SOPs; that is, it is impossible to quantify the fault support capability of SOPs into a reliability index expression that can be embedded in the planning model, thus severely restricting the synergistic optimization design of high-reliability, high-penetration ADNs. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of existing technologies and propose an active distribution network multi-objective planning method based on explicit analytical expression of reliability. By establishing a matrix analytical calculation system oriented towards reliability assessment, an explicit analytical calculation method for ADN reliability index considering SOP and ESS is proposed. The reliability cost obtained by converting the reliability index is embedded into the ADN multi-objective optimization model. By rationally configuring SOP and ESS, a coordinated balance between ADN power supply reliability, DG absorption capacity and economy can be achieved.

[0007] The technical problem solved by this invention is achieved through the following technical solution: The active distribution network multi-objective programming method based on explicit analytical expression of reliability includes the following steps: Step 1: Establish a matrix calculation model for reliability assessment to achieve an explicit analytical expression of the ADN reliability index that takes into account SOP and ESS. Step 2: Construct an ADN multi-objective collaborative planning model that takes into account power supply reliability, DG absorption capacity, and economy; Step 3: Perform linear reconstruction and optimization solution for the multi-objective collaborative programming model; Step 4: Output the results of multi-objective collaborative planning and analyze the resource allocation characteristics and cost structure evolution features of ADN under multi-objective collaborative optimization.

[0008] Furthermore, the specific implementation method of step 1 is as follows: Step 1.1: Based on the impact of distribution network branch faults on load nodes, they are divided into four types of impact; Step 1.2: Construct fault discrimination matrices for the four types of impacts respectively. FEIM ; Step 1.3: Construct the ESS islanded recovery matrix LRM ESS ; Step 1.4: Construct the SOP (Standard Operating Procedure) supply matrix LRM SOP ; Step 1.5: Based on the above construction FEIM ESS Island Recovery Matrix LRM ESS and SOP transfer matrix LRM SOP Explicit analytical calculation of ADN reliability indices taking into account SOP and ESS is performed.

[0009] Furthermore, the specific implementation method of step 1.5 is as follows: in the distribution network N The failure rate row vector of the branch is , N The row vector of the branch fault repair time is , N The row vector composed of the load demands of each node is , t ss This represents the operation time of the segmented switch. t ts Represents the operating time of the handshake switch. t ESS The switching operation time required to form an island t SOP The method for calculating the ADN reliability index, which takes into account both SOP and ESS, for SOP operation time is as follows: in, This represents the outage frequency vector for each load node. This represents a vector indicating the duration of power outages at each load node. n Indicates to be in numerical order N A row vector consisting of the number of users on each load node. N total The total number of users in the distribution system is represented by SAIFI, the System Average Interruption Frequency Index (SAIDI), the System Average Interruption Duration Index (EENS), and L is the load demand vector of each load node in the distribution network. Fault detection matrix. FEIM Each includes FEIM A , FEIM B and FEIM C .

[0010] Furthermore, the specific implementation method of step 2 is as follows: Step 2.1: The established active distribution network multi-objective programming model will be used in conjunction with investment and construction costs. Operation and maintenance costs Network loss cost Power supply reliability cost and DG's consumption costs The sum is minimized as the objective function: Step 2.2: Set the constraints for the multi-objective collaborative planning model; The constraints include: distribution network operation constraints, SOP operation constraints, ESS operation constraints, power supply restoration constraints, and system reliability level constraints.

[0011] Moreover, the specific implementation method of step 3 is as follows: the distribution network operation constraints and SOP operation constraints are equivalently reconstructed by the second-order cone optimization algorithm; at the same time, linearization modeling is performed on the power supply restoration constraints, and the optimized multi-objective collaborative planning model is transformed into a MISOCP problem, which is solved by calling the commercial solver CPLEX.

[0012] The advantages and positive effects of this invention are: This invention establishes a matrix analytical calculation system for reliability assessment, enabling the explicit expression of ADN reliability indices that consider SOP and ESS. This allows reliability costs to be uniformly embedded into a multi-objective programming framework, overcoming the limitation of heuristic algorithms in obtaining optimal planning solutions. Furthermore, this invention reveals the impact of reliability improvement on the marginal gain of distributed generation (DG) absorption and the total system cost structure. The planning results can also provide important decision-making references for power supply companies to coordinate the investment benefits of distribution networks and DG absorption capacity based on setting reasonable reliability levels. Attached Figure Description

[0013] Figure 1 This is a flowchart of the active distribution network multi-objective planning method based on explicit analytical expression of reliability, as described in this invention. Figure 2 This is a schematic diagram illustrating the operational logic of the circuit breaker and sectionalizing switch after a fault in this invention. Figure 3 This is a schematic diagram of the ESS islanded power restoration method of the present invention; Figure 4 This is a schematic diagram of the SOP power supply restoration of the present invention; Figure 5 This is a diagram of the Portuguese 54-node topology according to an embodiment of the present invention; Figure 6 This is a three-dimensional correlation diagram between power supply reliability, PV absorption rate, and total system cost in an embodiment of the present invention. Figure 7 This is a schematic diagram of the system node voltage distribution when SAIDI is 1.0 h / year according to an embodiment of the present invention; Figure 8 This is a diagram showing the relationship between SAIDI and the total system cost and PV absorption rate in an embodiment of the present invention. Detailed Implementation

[0014] The present invention will be further described in detail below with reference to the accompanying drawings.

[0015] Active distribution network multi-objective programming method based on explicit analytical expression of reliability, such as Figure 1 As shown, it includes the following steps: Step 1: Establish a matrix calculation model for reliability assessment to achieve an explicit analytical expression of the ADN reliability index that takes into account SOP and ESS.

[0016] Step 1 transforms reliability indicators into reliability costs, providing a quantitative basis for subsequent multi-objective collaborative planning. This cost is then embedded into the objective function of the multi-objective collaborative planning model in subsequent steps, ensuring that the coordination and balance between power supply reliability, DG absorption capacity, and economy are reasonably considered in multi-objective optimization.

[0017] The indicators for assessing the reliability of power distribution networks typically include the system average interruption frequency index (SAIFI), the system average interruption duration index (SAIDI), and the expected energy not supplied (EENS). To ensure the solvability of the explicit calculation model for reliability indicators, this invention sets the following assumptions.

[0018] 1) Feeders and ESS outlets directly connected to the distribution substation are equipped with circuit breakers, and sectionalizing switches are installed at both ends of each branch line.

[0019] 2) Only permanent faults of a single branch line in the distribution network are considered, and no reclosing device is configured in the system.

[0020] The operating logic of each circuit breaker and sectionalizing switch after a fault is as follows: Figure 2 As shown. After the fault occurred ( Figure 2 (a) The circuit breaker at the feeder outlet where the fault point is located and the ESS grid-connected circuit breaker tripped to clear the fault, resulting in a power outage at all load nodes on this feeder. Figure 2 (b) Then, the fault is isolated by disconnecting the sectionalizing switches at both ends of the branch line where the fault point is located, and the power supply to the load in the non-faulty feeder is restored by reclosing the circuit breaker in the non-faulty area. Figure 2 (c) Finally, after the fault repair is completed, the sectionalizing switch of the faulty branch is closed, restoring reliable power supply to all loads in the system. Figure 2 (d)).

[0021] Step 1.1: Based on the impact of distribution network branch faults on load nodes, the impact is divided into four types.

[0022] Step 1.2: Construct fault discrimination matrices for the four types of impacts respectively. FEIM.

[0023] 1) Impact Type a: After fault isolation, the affected load nodes cannot be powered back by the main power source until the fault is repaired, and the power outage time is the time required for fault repair. To characterize this type of impact, this invention constructs... FEIM A Its matrix elements FEIM A i,j The definition is as follows: (1) 2) Impact Type b: After fault isolation, the affected load nodes can only be restored to power from the main power supply after the sectionalizing switch isolates the fault; the power outage time is the sectionalizing switch operation time. To characterize this type of impact, this invention constructs... FEIM B Its matrix elements FEIM B i,j The definition is as follows: (2) 3) Impact Type c: After fault isolation, the affected load nodes can regain power through tie lines from other feeders, with the outage time equal to the time required for tie line resupply. To characterize this type of impact, this invention constructs... FEIM C Its matrix elements FEIM C i,j The definition is as follows: (3) 4) Impact type d: Distribution network branch faults have no impact on load nodes. This type of fault does not cause load loss, therefore this invention does not establish a corresponding fault impact correlation matrix.

[0024] Step 1.3: Construct the ESS islanded recovery matrix LRM ESS .

[0025] With the integration of ESS (Emerging Power Supply), the power distribution system gains islanding capability under fault conditions, maintaining power supply to specific areas after fault isolation, thereby improving the system's power supply reliability. To characterize the islanding recovery power supply range of ESS under different fault conditions, this invention constructs an ESS islanding recovery matrix. LRM ESS (load restoration matrix of ESS), LRM ESS The row number represents the branch number. LRM ESS The column number represents the load node number. LRM ESS The element is defined as follows: (4) This invention analyzes the power restoration process of an ESS island after a fault using a 7-node system. When a fault occurs in branch ④ of the power distribution system ( Figure 3 (a) The circuit breaker at the feeder outlet and the ESS grid-connected circuit breaker trip, and the sectionalizing switches on both sides of the faulty branch disconnect to isolate the fault. After the fault is isolated, the power-loss load node (4-7) can be restored to power through the ESS islanding. Figure 3(b)). For example, after considering both load demand and ESS capacity, node 7 is reduced, while nodes 4, 5, and 6 are restored to power through ESS islanding. Therefore, matrix elements , , The value is 1, and The value is 0. Figure 3 In the matrix, all elements marked by gray boxes are 1, representing the potential range of load nodes that can be restored to power supply under ideal conditions where the ESS has islanding operation capability and no capacity limit in the scenario of the corresponding fault branch.

[0026] Step 1.4: Construct the SOP (Standard Operating Procedure) supply matrix LRM SOP .

[0027] As a power electronic device that replaces traditional tie switches, the System Operating Panel (SOP) can quickly and accurately control its own power flow, change the power distribution of the system, and thus improve the operating status of the entire power distribution system. After a fault occurs in the power distribution network and is isolated, the SOP can not only achieve rapid power transfer of the lost load by dynamically adjusting the power flow between feeders, but also provide effective voltage support for the lost area, improving the power supply recovery capability of the power distribution system. To characterize the rapid power transfer capability of the SOP under different fault scenarios, this invention establishes an SOP power transfer matrix. LRM SOP (Load Restoration Matrix of SOP), the matrix elements are defined as follows: (5) This invention analyzes the power restoration process via SOP (Standard Operating Procedure) transfer after a fault using a 9-node system. Assuming a fault occurs in branch ⑥, to prevent the impact of the fault from spreading throughout the system, the SOP is first blocked. Then, the circuit breaker at the feeder outlet of the faulty branch ⑥ trips, the sectionalizing switches on both sides of the faulty branch disconnect to isolate the fault, and the SOP returns to its connected state. After fault isolation, load nodes 6, 7, 8, and 9 lose power and can be restored to power from other feeders via SOP transfer. In this example, considering both the power demand of the de-energized load nodes and the SOP port capacity, load nodes 8 and 9 are reduced, while nodes 7 and 8 achieve power restoration. Therefore, the corresponding matrix elements... and The value is 1, and and The value is 0. Figure 4 In the matrix, all elements marked by gray boxes are 1, representing the theoretical range of load nodes that can be restored to power supply under ideal conditions where the SOP has sufficient transfer capability in the corresponding fault branch scenario.

[0028] Step 1.5: Based on the above construction FEIM ESS Island Recovery Matrix LRM ESS and SOP transfer matrix LRM SOP Explicit analytical calculation of ADN reliability indices taking into account SOP and ESS is performed.

[0029] Set up distribution network N The failure rate row vector of the branch is , N The row vector of the branch fault repair time is , N The row vector composed of the load demands of each node is , t ss This represents the operation time of the segmented switch. t ts Represents the operating time of the handshake switch. t ESS The switching operation time required to form an island t SOP This refers to the SOP (Start of Production) operation time. The ADN (Advanced Depth Navigation) reliability index, taking into account both SOP and ESS (Effective Service Requirement), is calculated as follows: (6) (7) (8) in, This represents the outage frequency vector for each load node. This represents the vector of outage duration for each load node. n Indicates to be in numerical order N A row vector consisting of the number of users on each load node. N total This represents the total number of users in the power distribution system. Formula (6-8) enables the explicit analytical calculation of the ADN reliability index, taking into account both SOP and ESS, laying the foundation for the quantitative expression of reliability cost in the ADN multi-objective collaborative planning model.

[0030] Step 2: Construct an ADN multi-objective collaborative planning model that takes into account power supply reliability, DG absorption capacity, and economy.

[0031] Step 2.1: The established active distribution network multi-objective programming model will be used in conjunction with investment and construction costs. Operation and maintenance costs Network loss cost Power supply reliability cost and DG's consumption costs The sum is minimized as the objective function: (9) (a) Investment and construction costs The investment and construction costs include SOP (Standard Operating Procedure) investment costs and ESS (Essential Operating Procedure) investment costs. These costs need to be converted to annual equivalents using the Capital Recovery Factor (CRF).

[0032] (10) (11) Wherein, CRF is the capital recovery factor for the equipment. CRF SOP This is the capital recovery factor for SOP (Standard Operating Procedure) equipment. The discount rate is LT, and the useful life of the equipment is in years. , and These are the investment and construction costs per unit capacity of SOP, per unit capacity of ESS, and per unit power of ESS, respectively. , and These are the SOP capacity, the ESS rated capacity, and the ESS rated power, respectively. and These are the sets of nodes that connect the ADN to the SOP and ESS, respectively.

[0033] (ii) Operation and maintenance costs Operation and maintenance costs include the costs of operating and maintenance of SOPs and ESS.

[0034] (12) in, and These are the maintenance costs per unit capacity for SOP and per unit capacity for ESS, respectively.

[0035] (iii) Network loss cost Network loss cost is the active power loss cost incurred during ADN operation.

[0036] (13) Where M represents the number of typical operating scenarios. For the first h The number of days represented by each scene. The unit price of electricity For branch roads ( i , j The resistance value of ) For the scene h Lower branch road ( i , j)exist t The current amplitude at a given time.

[0037] (iv) Reliability Costs This invention defines reliability cost as the cost of power loss caused by power outages to users during a fault.

[0038] (14) in, The unit electricity price is the cost of the unit power outage loss. For the scene h The EENS of the lower system can be calculated using formula (8).

[0039] (v) DG disposal costs It should be noted that in this invention, DG mainly refers to distributed photovoltaic (PV). To reflect the impact of PV curtailment on the system's economics, this invention converts the curtailed PV power into equivalent costs and incorporates them into the objective function.

[0040] (15) in, The set of nodes that connect to the PV in the ADN. The unit cost of solar power curtailment For the scene h Down t Photovoltaic power generation that is constantly being abandoned by the system.

[0041] Step 2.2: Set the constraints for the multi-objective collaborative planning model.

[0042] (a) Constraints on the operation of the distribution network (16) (17) (18) (19) in, and The first h In each scenario t Time branch ( i, j The active and reactive power transmitted on the network. For the first h In each scenario t The current in the branch at any given time. and The first h In each scenario t Time Node j The net active and reactive loads, and Representative node j The active and reactive loads, , , , and They represent the first h In each scenario t At every moment j The PV active power output, SOP active power output, SOP reactive power output, ESS discharge power and charging power. For node voltage, For the set of branches. , and A boolean variable indicating whether a node is connected to SOP, PV, and ESS.

[0043] (20) (twenty one) in, and For nodes i The allowable minimum voltage amplitude and the square of the maximum voltage amplitude, This represents the square of the maximum branch current.

[0044] (ii) SOP operational constraints This invention takes a back-to-back voltage source converter as an example, selecting... PQ - V dc Q As the steady-state control mode of SOP, one converter realizes the stable control of DC voltage, and another converter realizes the flexible control of transmission power. The active power constraints and capacity constraints at both ends are as follows.

[0045] (twenty two) (twenty three) in, and The first h In each scenario t Time Node i Active and reactive power of the port.

[0046] (III) ESS Operational Constraints (twenty four) (25) (26) (27) (28) (29) in, For ESS in the h In each scenario t Capacity of time, and These are the charging efficiency and discharging efficiency of ESS, respectively. and These are the minimum and maximum states (SOC) of ESS, respectively. and These represent ESS in the first... h In each scenario t The charging and discharging status at all times (binary variable, with a value of 1 or 0).

[0047] (iv) Power restoration constraints (30) (31) (32) (33) (34) (35) (36) (37) in, and Each is a matrix LRM SOP and LRM ESS In the h In each scenario t Time of the first i Line 1 j The element values ​​of the column, and They were respectively in the second h In each scenario t Time-based load nodes j The demand for active and reactive power, Indicates access node s The set of nodes in the feeder where the SOP is located. Indicates access node p The set of nodes in the feeder where the ESS is located. Indicates SOP to load node j The set of nodes on the power supply path, Indicates the distance from the ESS to the load node. j The set of nodes on the power supply path.

[0048] Constraints (30-33) state that the sum of active and reactive power of the transferred load must not exceed the capacity limit of the corresponding SOP and ESS equipment. Constraints (34-35) are connectivity constraints of the transfer path; if the branch... i During a fault, the load node j If power can be restored by SOP or ESS, then all nodes on its power supply path can also be restored by SOP or ESS. Constraint (36) indicates that the load node that is restored by transfer based on SOP must be a node with fault impact type C, that is, a node that needs to be transferred through tie line to restore power. Constraint (37) indicates that the load node that is restored by islanded operation of ESS must be a node with fault impact type A, that is, a node that can only be restored by main power supply after the fault is repaired.

[0049] (v) System reliability level constraints To ensure that the planning scheme achieves both economic objectives and a controllable level of power supply reliability, this model uses SAIDI as a constraint, setting it to not exceed a preset reliability upper limit, as detailed below: (38) in, This indicates the maximum average outage duration allowed by the ADN during its operating cycle.

[0050] Step 3: Perform linear reconstruction and optimization solution of the multi-objective collaborative programming model.

[0051] The distribution network operation constraints (19), SOP operation constraints (23), and network connectivity constraints (34) and (35) all contain quadratic terms, resulting in nonlinearity and strong nonconvexity of the model, making it difficult to solve directly. Therefore, this invention uses a second-order cone optimization algorithm to equivalently reconstruct constraints (19) and (23). The reconstructed constraint forms are (39) and (40), respectively.

[0052] (39) (40) For network connectivity constraints (34) and (35), this invention performs linearization modeling on these constraints. For any load node j It can be based on a known set of paths. and Using graph traversal algorithms (breadth-first search or depth-first search) combined with a shortest path strategy based on node numbering, nodes are identified. j The set of preceding nodes on the power supply path can be linearized by constraints as follows: (41) (42) Here, "\" represents the set difference operation. Indicates SOP to node j In the power supply path, except for the nodes j The set of preceding nodes other than itself. Indicates ESS to node j In the power supply path, except for the nodes j The set of preceding nodes other than itself. Thus, the multi-objective coordination programming model proposed in this invention can be transformed into a MISOCP problem, which can then be solved directly using the commercial solver CPLEX.

[0053] Step 4: Output the results of multi-objective collaborative planning and analyze the resource allocation characteristics and cost structure evolution features of ADN under multi-objective collaborative optimization.

[0054] Based on the above-mentioned active distribution network multi-objective planning method based on explicit analytical expression of reliability, this invention is verified in the Portugal 54-node distribution system. The network topology of the 54-node distribution system is as follows: Figure 5 As shown. The system comprises 4 substations, 10 feeders, and 5 tie switches. The five tie switches are located at the following nodes: 8-33, 9-22, 13-43, 38-39, and 46-47. The SOP installation locations selected in this invention are the nodes where these five tie switches are located. The ESS installation locations are nodes 8, 13, 25, 38, and 50. Additionally, the load data comes from the distribution network of a city in northern China, covering the period from September 2022 to October 2023, totaling 8760 hours, with a maximum system load of 30.67MW. To achieve detailed PV modeling, the PV data in this example is generated using the detailed physical model chain PVlib, and the required meteorological and load data are from the same region, with a maximum PV penetration rate of 50%.

[0055] Table 1. SOP and ESS operating parameters, investment cost coefficients, and various reliability parameters

[0056] This invention is based on the annual historical operation data of a power distribution network in a city in northern China, and uses an improved Gaussian mixture model (GMM) for typical day clustering. The clustering results show that the BIC index is minimized when the number of typical days is 3. The three selected typical days correspond to the operation characteristics of the transition season, summer, and winter, respectively. Table 1 shows the SOP and ESS operating parameters, investment cost coefficients, and various reliability parameters.

[0057] To explore the synergistic optimization effect of Standard Operating Procedures (SOPs) and Energy Saving Streams (ESS) in improving ADN reliability, DG absorption capacity, and economy, this invention uses SAIDI as the core indicator for measuring ADN power supply reliability. Typical scenarios are constructed and analyzed by setting five constraint levels (1.6 h / year, 1.4 h / year, 1.2 h / year, 1.0 h / year, and 0.8 h / year). Table 2 compares in detail the investment and construction costs, operation and maintenance costs, network loss costs, reliability costs, PV absorption costs, total system costs, and PV absorption rates under the five scenarios. Table 3 shows the configuration results of SOPs and ESSs under different reliability levels.

[0058] Table 2: Economic Costs and PV Absorption Rate in Various Scenarios

[0059] Table 3: Planning Results of SOP and ESS

[0060] As shown in Table 3, the SOP capacity configured in the system shows a continuous increasing trend with the improvement of reliability. When SAIDI decreases from 1.6 h / year to 1.2 h / year, the total SOP capacity increases from 2.83 MVA to 6.95 MVA. At this stage, the newly added SOP capacity can meet the fault transfer needs of most load nodes in the ADN, the SOP configuration efficiency is high, and the marginal benefit of reliability improvement is significant. When SAIDI further decreases from 1.2 h / year to 1.0 h / year and 0.8 h / year, the total SOP capacity jumps to 13.65 MVA and 18.89 MVA, respectively. This trend indicates that under higher reliability requirements, in order to ensure the rapid restoration of power supply to nodes with large power demand in the ADN under fault conditions or to cope with extreme fault conditions, the ADN needs to significantly increase the SOP configuration capacity. The required SOP investment and operation and maintenance costs rise rapidly, while the marginal benefit of reliability improvement gradually decreases, showing a typical "high reliability - high cost" characteristic.

[0061] Overall, the total configured capacity and power of the five ESS units in the system gradually increase with the improvement of power supply reliability. Specifically, the ESS units at nodes 25 and 50 are located at the ends of feeders, and their respective end-of-line areas lack Standard Operating Procedures (SOPs). When a fault occurs on a branch of the feeder, the ESS can switch to islanded operation to restore power to the non-faulty loads, reducing the outage time at the load nodes from the original fault repair time to the islanding response time tESS. When SAIDI decreased from 1.6 h / year to 0.8 h / year, the ESS capacity at node 25 increased from 1.02 MWh to 3.63 MWh, an increase of 256%, and the ESS capacity at node 50 increased from 2.01 MWh to 6.86 MWh, an increase of 241%. These two ESS units played a crucial role in improving the system's power supply reliability.

[0062] In contrast, although the ESS at nodes 8, 13, and 38 are located at the end of the feeders, there is a SOP (Standard Operating Procedure) at the end of the feeder. When a branch on the feeder fails, the power-loss load node can quickly restore power through the SOP. Therefore, the ESS at nodes 8, 13, and 38 are mainly used for peak shaving and valley filling, as well as multi-period energy regulation, to achieve spatiotemporal balance of PV output and improve PV absorption capacity. Therefore, the capacity of the ESS at nodes 8, 13, and 38 increases relatively slowly with the improvement of reliability.

[0063] Based on the various economic costs and PV absorption rates under different reliability levels in Table 2, this invention constructs a three-dimensional correlation diagram between ADN power supply reliability, total system cost, and PV absorption rate, as shown below. Figure 6 As shown. By Figure 6 It can be seen that as SAIDI decreases, the system effectively improves its ability to quickly transfer loads after a fault and its spatiotemporal power regulation capabilities by configuring SOPs and ESSs, while simultaneously improving PV absorption. During this stage, the reduction in reliability and absorption costs exceeds the increase in investment and maintenance costs, resulting in a downward trend in the total system cost. As reliability further improves, although PV absorption capacity slightly increases, the required flexibility resources increase significantly. At this point, the cost increase from configuring SOPs and ESSs exceeds the benefits from improved reliability and PV absorption, the marginal benefit of new investment tends to diminish, and the overall economic efficiency of the system decreases. In summary, the total system cost shows a trend of first decreasing and then increasing. The results show that when SAIDI is 1.0 h / year, the total cost is lowest at 13.6346 million yuan, corresponding to a PV absorption rate of 90.44%. At this point, ADN achieves the optimal balance between power supply reliability, economic efficiency, and PV absorption capacity, demonstrating the optimal configuration characteristics under multi-objective collaborative optimization.

[0064] Figure 7The figure shows the node voltage distribution of the entire system when SAIDI is 1.0 h / year. The voltage of each node remains within the safe operating range. Flexible power regulation across feeders based on SOP and energy allocation of ESS over time effectively solve the local voltage exceedance problem of ADN under PV access. The results show that the proposed collaborative optimization configuration model achieves multi-objective equilibrium while ensuring the safe and stable operation of the ADN.

[0065] To further clarify the dual impact of power supply reliability on system economy and PV absorption capacity, this invention constructs a two-dimensional sensitivity relationship curve between SAIDI and total system cost and PV absorption rate, as shown below. Figure 8 As shown. From Figure 8 As can be seen, when SAIDI decreases from 1.6 h / year to 1.0 h / year, the total system cost continues to decrease. Configuring SOPs and ESSs during this stage not only effectively improves the system's power supply reliability and PV absorption capacity but also enhances system economics while controlling investment and maintenance costs. However, when SAIDI further decreases from 1.0 h / year to 0.7 h / year, to cope with power restoration needs under extreme fault conditions, the system requires more flexible resources, leading to a significant increase in investment and maintenance costs, and the total system cost actually rises. Therefore, the total system cost exhibits a U-shaped trend of first decreasing and then increasing.

[0066] PV absorption rate is positively correlated with system power supply reliability. As SAIDI gradually decreases from 1.6 h / year to 0.7 h / year, the system PV absorption rate increases from 83.89% to 91.40%, but the rate of increase gradually decreases, exhibiting a clear diminishing marginal return. The essence of this phenomenon lies in the fact that with the coordinated configuration of SOP and ESS, the system possesses stronger spatiotemporal power regulation capabilities. Specifically, SOP enhances cross-feeder power flow regulation capabilities, while ESS provides flexibility in the time dimension, coordinating the mismatch between PV generation and load demand, and improving PV absorption capacity to a certain extent. However, as shown in Table 3 regarding SOP and ESS configurations, the improvement in system reliability mainly relies on the SOP capacity and the ESS equipment at nodes 25 and 50, located at the end of the feeders and lacking interconnection capabilities, to enhance the ability to quickly restore power supply to lost loads. Once the SOP capacity reaches the point where it can cover the transfer capacity of the unabsorbed PV power along the entire feeder, its marginal contribution to PV absorption capacity tends to saturate. At this point, the improvement in PV absorption capacity relies more on the ESS at nodes 8, 13, and 38. These ESS mainly function as energy storage and peak shaving, and their capacity changes little as SAIDI continues to decrease, thus limiting the ability of ADN to further improve PV absorption capacity at higher reliability levels. Therefore, as system reliability continues to improve, the rate of increase in PV absorption rate tends to level off.

[0067] It should be emphasized that the embodiments described in this invention are illustrative and not limiting. Therefore, this invention includes, but is not limited to, the embodiments described in the specific implementation. Any other implementation methods derived by those skilled in the art based on the technical solutions of this invention also fall within the scope of protection of this invention.

Claims

1. A multi-objective programming method for active distribution networks based on explicit analytical expression of reliability, characterized in that: Includes the following steps: Step 1: Establish a matrix calculation model for reliability assessment to achieve an explicit analytical expression of the ADN reliability index that takes into account SOP and ESS. Step 2: Based on the matrix calculation model, construct an ADN multi-objective collaborative planning model that takes into account power supply reliability, DG absorption capacity, and economy; Step 3: Perform linear reconstruction and optimization solution for the multi-objective collaborative programming model; Step 4: Output the results of multi-objective collaborative planning and analyze the resource allocation characteristics and cost structure evolution features of ADN under multi-objective collaborative optimization.

2. The active distribution network multi-objective planning method based on explicit analytical expression of reliability according to claim 1, characterized in that: The specific implementation method of step 1 is as follows: Step 1.1: Based on the impact of distribution network branch faults on load nodes, they are divided into four types of impact; Step 1.2: Construct fault discrimination matrices for the four types of impacts respectively. FEIM ; Step 1.3: Construct the ESS islanded recovery matrix LRM ESS ; Step 1.4: Construct the SOP (Standard Operating Procedure) supply matrix LRM SOP ; Step 1.5: Based on the above construction FEIM ESS Island Recovery Matrix LRM ESS and SOP transfer matrix LRM SOP Explicit analytical calculation of ADN reliability indices taking into account SOP and ESS is performed.

3. The active distribution network multi-objective planning method based on explicit analytical expression of reliability according to claim 2, characterized in that: The specific implementation method of step 1.5 is as follows: in the distribution network N The failure rate row vector of the branch is , N The row vector of the branch fault repair time is , N The row vector composed of the load demands of each node is , t ss This represents the operation time of the sectionalizing switch. t ts Represents the operating time of the handshake switch. t ESS The switching operation time required to form an island t SOP The method for calculating the ADN reliability index, which takes into account both SOP and ESS, for SOP operation time is as follows: ； ； ； in, This represents the outage frequency vector for each load node. This represents a vector indicating the duration of power outages at each load node. n Indicates to be in numerical order N A row vector consisting of the number of users on each load node. N total The system represents the total number of users in the distribution system; SAIFI is the system average outage frequency index; SAIDI is the system average outage duration index; EENS is the expected power shortage in the system; and L is the load demand vector of each load node in the distribution network. (Fault detection matrix) FEIM Each includes FEIM A , FEIM B and FEIM C .

4. The active distribution network multi-objective planning method based on explicit analytical expression of reliability according to claim 1, characterized in that: The specific implementation method of step 2 is as follows: Step 2.1: The established active distribution network multi-objective programming model will be used in conjunction with investment and construction costs. Operation and maintenance costs Network loss cost Power supply reliability cost and DG's consumption costs The sum is minimized as the objective function: ； Step 2.2: Set the constraints for the multi-objective collaborative planning model; The constraints include: distribution network operation constraints, SOP operation constraints, ESS operation constraints, power supply restoration constraints, and system reliability level constraints.

5. The active distribution network multi-objective planning method based on explicit analytical expression of reliability according to claim 1, characterized in that: The specific implementation method of step 3 is as follows: the distribution network operation constraints and SOP operation constraints are equivalently reconstructed by the second-order cone optimization algorithm; at the same time, linearization modeling is performed on the power supply restoration constraints, and the optimized multi-objective collaborative programming model is transformed into a MISOCP problem, which is solved by calling the commercial solver CPLEX.

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