Optimal configuration method of retired battery energy storage system in heavy overload management of power distribution network

Abstract

An optimal configuration method for a decommissioned battery energy storage system in power distribution network heavy overload treatment comprises the steps that a life loss model of current-carrying equipment is established, and the severity of power distribution network heavy overload is measured through a current-carrying equipment life loss fluctuation quantity sum index; constructing an energy storage system ESS economic evaluation model considering battery capacity attenuation and compensation, and quantifying the annual net cost of the energy storage system ESS; establishing a dual-objective optimization model based on the total life loss fluctuation quantity of the current-carrying equipment and the annual net cost of the energy storage system ESS; an improved fuzzy membership function is adopted to convert double targets into a single target optimization problem, and an energy storage system ESS optimal configuration and output strategy is solved based on an adaptive inertia weight particle swarm optimization algorithm. According to the method, a more accurate and economic scheme is provided for energy storage optimization configuration in a power distribution network heavy overload treatment scene.

Description

Technical Field

[0001] This invention relates to the field of distribution network overload mitigation, specifically to an optimized configuration method for retired battery energy storage systems in distribution network overload mitigation. Background Technology

[0002] With regional economic development, load growth, and the large-scale integration of electric vehicles (EVs), distribution networks are prone to forward overload problems of current-carrying equipment. Simultaneously, the high proportion of distributed photovoltaic (DPV) installations can easily induce reverse overload problems in the distribution network during periods of relatively low load. Energy storage, as a crucial support for source-load balance, can address these issues by deploying Energy Storage Systems (ESS) in the distribution network. However, the rational and effective configuration of ESS systems becomes extremely critical.

[0003] Existing research on energy storage optimization configuration merely treats heavy overload problems as constraints based on the power or current limitations of current-carrying equipment. No comprehensive evaluation method has been proposed for addressing bidirectional heavy overload problems occurring in transformers and lines within the distribution network, using this as the optimization objective. Furthermore, with the large-scale integration of electric vehicles (EVs) into the distribution network, their power batteries are undergoing a generational shift and are being retired. Many of these batteries, after diagnosis, sorting, and reconfiguration, can still be reused in other scenarios. If retired batteries are used to replace new batteries in an energy storage system (ESS), it can significantly reduce purchase costs while also reducing resource waste and environmental pollution, lowering carbon emission intensity, and achieving both economic and environmental benefits. Summary of the Invention

[0004] This invention provides an optimized configuration method for retired battery energy storage systems (ESS) in the management of heavy overload in distribution networks. The method first quantifies the lifespan loss of current-carrying equipment based on a current-carrying equipment lifespan loss model, constructing a total fluctuation index of current-carrying equipment lifespan loss as a technical indicator to measure the severity of heavy overload in the distribution network. Then, considering battery capacity decay and compensation, the annual net cost of the ESS is quantified as an economic indicator to establish a dual-objective optimization model that minimizes the above two indicators. Simultaneously, to avoid the complexity of Pareto solution set decision-making, the dual objectives are transformed into a single objective by improving the fuzzy membership function. An adaptive inertial weighted particle swarm optimization algorithm combined with hybrid coding and a dynamic penalty function is used to solve for the optimal configuration and scheduling strategy of the ESS. This method provides a more accurate and economical solution for the optimized configuration of energy storage in the scenario of heavy overload management in distribution networks.

[0005] The technical solution adopted in this invention is as follows: An optimized configuration method for retired battery energy storage systems in power distribution network overload mitigation includes the following steps: Step 1: Establish a life loss model for current-carrying equipment, and use the total fluctuation of life loss of current-carrying equipment as an index to measure the severity of heavy overload in the distribution network; Step 2: Construct an economic evaluation model for an energy storage system (ESS) that takes into account battery capacity degradation and compensation, and quantify the annual net cost of the energy storage system (ESS). Step 3: Establish a dual-objective optimization model based on the sum of the fluctuations in the lifetime loss of current-carrying equipment and the annual net cost of the energy storage system (ESS). Step 4: The dual objective is transformed into a single objective optimization problem using an improved fuzzy membership function, and the optimal configuration and output strategy of the energy storage system ESS are solved based on the adaptive inertial weighted particle swarm algorithm.

[0006] In step 1, the current-carrying equipment includes a distribution transformer and an overhead line, wherein, 1) The life loss model for distribution transformers includes: ① Solving for the temperature of the distribution transformer: For oil-immersed transformers, the transformer winding hot spot temperature is equal to the sum of the top oil temperature and the hot spot temperature rise, where the top oil temperature is expressed as: (1); In formula (1): i o(n) and i o(n-1) The first n , n -Top oil temperature at 1 time point; i a(n) For the first n Ambient temperature at each time point; Δ i or Δ represents the steady-state temperature rise of the top oil under rated loss. t For time step; k 11 These are constants in the thermal model; t o The average oil time constant; R It is the ratio of load loss to no-load loss under rated current; x o Oil index; K (n) For the first n The load factor at the i-th time point is defined as the i-th time point. n Load current at each time point I (n) With rated current I rated The ratio of .

[0007] The rise in hotspot temperature is represented as: (2); In equation (2): Δ i h(n) For the first n The gradient of hot spot temperature with respect to top oil temperature at a given time point, i.e., the hot spot temperature rise, consists of two parts, including Δ i h1(n) Δ i h2(n) ;Δ i hr This refers to the temperature rise of the hot spot under rated current. k 22 , k 21 These are constants in the thermal model; t w The winding time constant; y For winding index; For the first n The winding exponent of the load factor at each time point.

[0008] By combining equations (1) and (2), the hotspot temperature can be obtained as follows: (3); In formula (3): i h(n) For the first n Hotspot temperatures at specific points in time.

[0009] ② Calculation of cumulative life loss of distribution transformers: For non-thermally modified paper transformers, calculate their cumulative life loss: (4); In equation (4): F eq,h This refers to the cumulative lifespan loss of the transformer. n To study time scales T The ordinal number of the time point within the time period. , ; 98 (unit: ℃) is the reference value for the hot spot temperature of the transformer.

[0010] 2) The overhead line life loss model includes: ① Solving for the temperature of overhead lines: Ignoring temperature differences at overhead line terminals / joints and considering the overhead line as a conductor with uniform temperature rise, a differential equation for the temperature of the overhead line can be established based on the principle of thermal balance: (5); In formula (5): i l For line temperature; ia Ambient temperature; Δ i lr This refers to the steady-state temperature rise of the line under rated current. t l The line time constant; K This is the load factor; m This is the heat dissipation correction factor.

[0011] Corresponding to discrete time and data information, equation (5) can be expressed using a difference equation: (6); In formula (6): i l(n) and i l(n-1) The first n , n -1 point in time for the line temperature.

[0012] ② Calculation of cumulative lifespan loss of overhead lines: A quantitative model of overhead line life loss is constructed using the Arrhenius equation: (7); In equation (7): The line lifespan loss is represented by e, where e is the natural constant. B is a material constant reflecting the thermal aging characteristics of the line materials, expressed in K; 60 (unit: °C) is the baseline value for line temperature. This equation can describe the cumulative effect of temperature and time on the lifespan loss of overhead lines.

[0013] In summary, defining any The life loss is For distribution transformers and overhead lines, Feq,h or Feq,l can be used. Taking the day as the research time scale, the total index of the fluctuation of the life loss of current-carrying equipment is: (8); In equation (8): N h+l The total number of devices within the study area; This is a reference value for the daily life loss of the equipment, i.e., 24 hours.

[0014] Equation (8) represents the degree of fluctuation in the daily life loss of current-carrying equipment compared to the expected life (24h).

[0015] In step 2, a quantitative model of the annual net cost of the energy storage system ESS is established. The ESS configured in the network under study consists of several distributed energy storage systems (DESS). (9); In equation (9):S ESS , P ESS These are the total rated capacity and rated power of the ESS, respectively. S DESS,l , P DESS,l The first l Rated capacity and rated power of each DESS; N DESS Configure the number of DESS.

[0016] 1) Solving for the capacity degradation of retired batteries: As the ESS (Electrical Storage System) is used for charging and discharging, the capacity of retired batteries will further degrade, thus affecting the regulation effect of the ESS. Therefore, an ESS capacity configuration and economic evaluation model is established by calculating the annual battery capacity degradation and replenishing it year by year.

[0017] Battery capacity degradation is primarily determined by the depth of discharge (DOD) and the number of cycles. A rainflow counting method is used to decompose the non-periodic state of charge (SOC) curve of the energy storage battery into independent charge-discharge cycles, and the DOD for each cycle is calculated, summing the number of cycles with different DOD values. Simultaneously, the mathematical relationship between DOD and cycle life is considered. (10); In formula (10): N eff (DOD k1 The depth of battery discharge (DOD) is the percentage of the battery discharged. k1 The maximum number of cycles corresponding to the time; the specific value in the formula is the result obtained by data fitting. Reference [1]: Zhao Wei, Yuan Xilian, Zhou Yixing, et al. Capacity configuration method of cascade battery energy storage system with optimal economic efficiency within the service life [J]. Power System Protection and Control, 2021, 49(12):16-24. Further, the daily equivalent cycle number under real-time changes in battery DOD is obtained. N 'for: (11); In equation (11): N eff (1) is the maximum number of cycles when the battery is in a fully charged and fully discharged state; N eff (DOD k1 The depth of battery discharge (DOD) is the percentage of the battery discharged. k1 The maximum number of loops corresponding to the time; n ′ represents the number of charge-discharge cycles per day of battery operation; The ordinal number of the number of charge-discharge cycles in one day of battery operation.

[0018] Furthermore, the relationship between battery capacity retention and cycle number is as follows: (12); In equation (12): β Capacity retention rate; N b denoted as the number of charge-discharge cycles; the specific values ​​in the formula are the results obtained from data fitting. Reference [1]: Zhao Wei, Yuan Xilian, Zhou Yixing, et al. Capacity configuration method of cascaded battery energy storage system considering the optimal economic efficiency within the service life [J]. Power System Protection and Control, 2021, 49(12):16-24. The capacity retention rate when the energy storage battery is first configured for use is [percentage missing]. β 1. Capacity retention rate at the time of termination of use β 2. The corresponding values ​​can be calculated from equation (12). N b Then, the service life of the retired battery can be calculated according to formula (13). T b : (13); In equation (13): N b2 , N b1 They are respectively the corresponding β 2. β 1. Number of charge / discharge cycles; X This refers to the number of days the battery operates per year. N x ′ is the battery in the first x The equivalent number of cycles per day.

[0019] Battery l (i.e., the first) l The equivalent number of cycles per year for each DESS is Δ N l Combining equation (12), the corresponding annual battery degradation capacity Δ can be obtained by inverse solution. S DESS,l for: (14); In equation (14): X l For batteries l The number of operating days per year; N l,x 'For batteries l In the x The equivalent number of cycles per day; Δ βl For batteries l Annual decay of capacity retention rate.

[0020] Further calculate the annual attenuation capacity Δ of the ESS S ESS for: (15); 2) Net cost analysis of decommissioned battery energy storage systems: Based on annual net cost E As an economic evaluation indicator for ESS: (16); In equation (16): C The annual investment cost of ESS I The annual economic returns after configuring ESS are specifically composed of the following: ①Annual investment cost: The investment cost of a retired battery ESS includes initial investment cost, operation and maintenance cost, and compensation cost for purchasing used power batteries from external sources and for testing and reassembly when the battery capacity is insufficient. All costs are discounted to their equivalent annual value, resulting in the annual investment cost of the ESS as follows: (17); In equation (17): C 1 represents the discounted value of the initial investment cost; c s , c p These are the unit capacity cost and unit power cost of retired batteries, respectively. r The discount rate; T PCS The service life of the energy storage converter; C 2 represents the annual operating and maintenance cost; k s The unit capacity cost of operating and maintaining retired batteries is given by the formula. k s =0.05165× β -6 (Unit: Yuan / kWh) Adjusted annually; k p The unit power cost for operating and maintaining energy storage converters; C 3 represents the annual cost of compensating for the battery capacity, where the compensated battery capacity equals the degraded battery capacity.

[0021] ② Annual economic benefits: The benefits of configuring retired battery ESS mainly come from delaying the upgrading and renovation of the distribution network (mainly lines and transformers). I 1. Benefits of reducing network lossesI 2. Benefits of energy conservation and emission reduction I 3. Electricity price difference revenue I 4. The various benefits are expressed as follows: (18); In formula (18): c up Cost per unit capacity expansion of the distribution network; cos ϕ The power factor of current-carrying equipment in the distribution network; r For grid loss electricity price; { N bus} represents a set of network nodes; I ij ( t ), I ij ( t )′ represent the lines before and after energy storage access. ij exist t The effective value of the current at any given time; R ij For the line ij The resistance value; T h For annual operating time of energy storage; e The revenue per unit capacity of batteries that brings energy-saving and emission-reduction benefits from the use of retired batteries; For the first l The DESS in the first x Tianzhong t The power at any given moment is positive for discharging and negative for charging; Δ t ′ represents the power data sampling time interval; r t for t The electricity price at any given time is considered the same for any two consecutive days at the same time.

[0022] In step 3, when the lifespan loss of the current-carrying device deviates significantly from the expected lifespan, the load current can be adjusted by the energy storage output, thereby affecting the temperature change of the current-carrying device and indirectly causing… F eq,ϛ Approaching ; Therefore, the total fluctuation of the life loss of the current-carrying equipment constructed in step 1 is used as the technical index in the energy storage system ESS optimization configuration model. At the same time, the economic index in the model is obtained from equation (16), and minimizing the two indices is used as the objective function for the energy storage system ESS optimization configuration: (19); In equation (19): This represents minimizing the total fluctuation of the lifetime loss of current-carrying devices, Δ. F eq ; This represents minimizing the annual net cost of an energy storage system. E .

[0023] An improved fuzzy membership function is established to transform the bi-objective optimization model into a single-objective optimization model, as shown in equations (20) to (22), so as to achieve a dynamic trade-off between the two.

[0024] For minΔ F eq Theoretically, as long as F eq,ϛ Not equal to This will activate the penalty, therefore the domain is ,in: This is a completely unacceptable upper limit value. Therefore, Δ F eq The membership function is represented by a power function: (20); In equation (20): For Δ F eq Membership function; exponent α Greater than 1, to ensure that satisfaction varies with Δ F eq Increases and accelerates decay.

[0025] For min E , E Represented using linear membership functions: (twenty one); In equation (21): for E Membership function; The annual net cost of the energy storage system; E max This represents the acceptable upper limit of annual net cost, which can be taken as the equivalent annual value of the cost of upgrading and transforming the distribution network.

[0026] Combining equations (20) and (21), a comprehensive objective function is constructed based on the pessimistic criterion: (twenty two); In equation (22): This represents maximizing the comprehensive objective function. ; This indicates taking the minimum value within the parentheses.

[0027] Constraints of the comprehensive objective function: The configuration of energy storage takes into account both the reasonable operation of the distribution network and the charging and discharging of the ESS itself, as detailed below.

[0028] ① Network trend constraints: (twenty three); In equation (23): P i , Q i They are nodes i The active and reactive power injected at the point; U i , U j They are nodes i , j The voltage amplitude; G ij , B ij and i ij They are nodes i , j The phase angle difference between the conductance, susceptance, and voltage; ② Network node voltage constraints: (twenty four); In equation (24): U max , U min These are the upper and lower limits of the network node voltage, respectively.

[0029] ③ Network line capacity constraints: Considering the short-term heavy overload tolerance margin of the current-carrying equipment, this constraint is expressed in the form of a soft constraint: (25); In equation (25): P{·} is the probability that event {·} is true; For the line ij The square of the effective value threshold of the current; d 1 represents the confidence level that the line operating current will not exceed the limit.

[0030] ④ Distribution transformer capacity constraints: Similar to the network line capacity constraint, we have: (26); In equation (26): P DT and Q DT These are the active and reactive power of the feeder section at the transformer outlet, respectively. This refers to the rated capacity of the corresponding distribution transformer; d 2 represents the confidence level that the actual operating capacity of the distribution transformer does not exceed the limit.

[0031] ⑤ Energy storage energy balance constraints: (27); In equation (27): or To improve the charging and discharging efficiency of energy storage; a 1. a 2 indicates the energy storage charging and discharging state; For the first l The DESS in the first x Tianzhong t Power at time, when When ≥0, energy storage discharges. a 1=1, a 2=0; when When <0, energy storage charging occurs. a 1=0, a 2 = 1; This is the time interval for power data sampling.

[0032] ⑥ Energy storage power constraints: (28); In equation (28): For the first l The rated power of each DESS.

[0033] ⑦ Energy storage battery SOC constraint: (29); In equation (29): SOC l ( t )for t Moment Battery l State of charge; SOC max SOC min These are the upper and lower limits of the battery's state of charge (SOC); specifying the SOC values ​​at the beginning (and end) of a daily operating cycle. l ( t 0), to prevent overcharging and over-discharging, and to ensure normal operation in the next cycle; for Moment Battery l The state of charge.

[0034] In step 4 The decision variables for the single-objective optimization model are energy storage configuration parameters, including capacity. S DESS,l , S ESS ,power P DESS,l , P ESS The charging and discharging strategy includes charging and discharging power. SOC curvel ( t The variables are discrete and continuous, respectively. A hybrid encoding strategy is adopted: discrete variables are mapped to actual integer values ​​through rounding, while continuous variables are encoded as real numbers. Since the energy storage battery used is a retired battery, the constraints on its State of Charge (SOC) are more stringent. Therefore, a penalty function is introduced during the optimization process to transform the degree of constraint violation into a fitness penalty term, forcing the adaptive inertial weighted particle swarm optimization algorithm to search towards a feasible solution. This ensures that the iterative values ​​strictly approximate the feasible region while accelerating the convergence speed of the algorithm.

[0035] Definition of the first l The SOC constraint violation degree of each DESS is f l : (30); The total violation of the SOC constraint of the ESS is f : (31); The overall objective function is then modified as follows: (32); In equation (32): This represents maximizing the modified comprehensive objective function. ; This represents the overall objective function before modification; l ( k )= l 0· k , l ( k ) is a correction coefficient that varies with the number of iterations. k Incrementing to strengthen the satisfaction of later constraints.

[0036] Furthermore, in the PSO algorithm, inertia weights w The value of has a significant impact on its convergence performance. Dynamically adjusting the weights can balance global search and local exploitation capabilities, avoiding premature convergence. An adaptive weight adjustment strategy using a nonlinear weight decay approach is employed, with the weight value formula as follows: (33); In equation (33): Here is the formula for determining the weight values; w max =0.9 to enhance global search in the initial stage; w min =0.4 to improve local accuracy in later stages; K m This represents the maximum number of iterations.

[0037] Step 5: Verify the effectiveness and economy of the proposed energy storage configuration method through a 10kV distribution network example; Based on a typical IEEE 33-node distribution network system, distributed photovoltaic (DPV) power plants and electric vehicle (EV) charging stations are integrated. By adjusting the DPV output level and setting EV load power variations, a bidirectional heavy overload scenario for the distribution network is constructed. The method of this invention is then applied to address this heavy overload problem to verify the effectiveness of the method. Furthermore, the economics of configuring retired battery energy storage solutions versus configuring new battery energy storage solutions are compared to further verify the advantages of utilizing retired battery energy storage.

[0038] This invention discloses an optimized configuration method for retired battery energy storage systems in the management of heavy overload in power distribution networks, with the following technical effects: 1) For the problem of bidirectional heavy overload in the distribution network, the method proposed in this invention can be used for distribution and energy storage management, which can effectively manage the problem of heavy overload in the distribution network while reducing the net cost of management.

[0039] 2) Step 1 of this invention takes two types of current-carrying equipment, distribution transformers and overhead (transmission) lines, as objects, and establishes life loss models for each. It constructs a total index of life loss fluctuation of current-carrying equipment to measure the severity of heavy overload in the distribution network and uses it as a technical indicator to provide a basis for the establishment of the ESS dual-objective optimization configuration model in step 3.

[0040] 3) In step 2 of this invention, considering that the capacity of retired batteries will further decrease as the ESS is used for charging and discharging, an economic evaluation model for the ESS is established by calculating the annual battery capacity degradation and replenishing it year by year. This quantifies the annual net cost of the ESS and provides a basis for establishing the dual-objective optimization configuration model of the ESS in step 3.

[0041] 4) Steps 3 and 4 of this invention establish the optimal ESS dual-objective optimization configuration model based on the technical indicators in step 1 and the economic indicators in step 2, and provide specific measures for dual-objective equilibrium and algorithm improvement, providing a basis for solving the model.

[0042] 5) Step 5 of the present invention uses a typical distribution network system as an example to simulate and solve the energy storage configuration results, and verifies the feasibility and economic advantages of retired battery energy storage in the scenario of heavy overload management of distribution network. Attached Figure Description

[0043] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of an embodiment of the present invention.

[0044] Figure 2 This is a simulation system diagram of an embodiment of the present invention.

[0045] Figure 3(a) shows the daily power generation strategy and SOC curve of the energy storage system deployed at node 17; Figure 3(b) shows the daily power generation strategy and SOC curve of the energy storage system deployed at node 23; Figure 3(c) shows the daily power generation strategy and SOC curve of the energy storage system deployed at node 1.

[0046] Figure 4 A cost-benefit comparison chart of configuring new battery energy storage and retiring battery energy storage solutions. Detailed Implementation

[0047] An optimal configuration method for retired battery energy storage systems (ESS) in the management of heavy overload in distribution networks is proposed. First, a lifetime loss model for current-carrying equipment is established, using the sum of the fluctuations in the lifetime loss of current-carrying equipment as an index to measure the severity of heavy overload in the distribution network. Then, an economic evaluation model for ESS considering battery capacity degradation and compensation is constructed to quantify the annual net cost of the ESS. Subsequently, a bi-objective optimization model is established with the goal of minimizing the sum of the fluctuations in the lifetime loss of current-carrying equipment and the annual net cost of the ESS. An improved fuzzy membership function is used to transform the bi-objective model into a single-objective optimization problem, and an adaptive inertial weighted particle swarm optimization algorithm is used to solve for the optimal energy storage configuration and output strategy. Finally, a 10kV distribution network example is used to verify the effectiveness and economy of the proposed energy storage configuration method. The flowchart is shown below. Figure 1 As shown, it includes the following steps: Step 1: Establish a lifetime loss model for current-carrying equipment, and use the sum of the lifetime loss fluctuations of current-carrying equipment as an index to measure the severity of heavy overload in the distribution network. When current-carrying equipment is under heavy overload, the load current will exceed the rated value. Since current is the dominant factor in temperature rise, the temperature of the current-carrying equipment will rise rapidly, thus accelerating the aging of its insulation and causing greater lifespan loss than under rated load current. If we take a day as the research timescale, the theoretical lifespan loss under rated load current is 24 hours, but under heavy overload, the lifespan loss will exceed 24 hours. Therefore, from the perspective of overall distribution network operation optimization, this method proposes to use the sum of the lifespan loss fluctuations of all current-carrying equipment within the research area of ​​the distribution network as an indicator to measure the severity of heavy overload in the distribution network. The current-carrying equipment involved in this method refers to distribution transformers and overhead (transmission) lines; only these two will be modeled and analyzed below.

[0048] 1) Distribution transformer life loss model: ① Solving for the temperature of the distribution transformer: Taking an oil-immersed transformer as an example, the hot spot temperature of the transformer winding is equal to the sum of the top oil temperature and the hot spot temperature rise, where the top oil temperature is expressed as: (1); In formula (1): i o(n) and i o(n-1) The first n , n -Top oil temperature at 1 time point; i a(n) For the first n Ambient temperature at each time point; Δ i or Δ represents the steady-state temperature rise of the top oil under rated loss. t For time step; k 11 These are constants in the thermal model; t o The average oil time constant; R It is the ratio of load loss to no-load loss under rated current; x o Oil index; K (n) For the first n The load factor at the i-th time point is defined as the i-th time point. n Load current at each time point I (n) With rated current I rated The ratio of .

[0049] The rise in hotspot temperature is represented as: (2); In equation (2): Δ i h(n) For the first n The gradient of hot spot temperature with respect to top oil temperature at each time point, i.e., the hot spot temperature rise, consists of two parts (Δ i h1(n) Δ i h2(n) );Δ i hr This refers to the temperature rise of the hot spot under rated current. k 22 , k 21 These are constants in the thermal model; t w The winding time constant; y This represents the winding index.

[0050] By combining equations (1) and (2), the hotspot temperature can be obtained as follows: (3); In formula (3): ih(n) For the first n Hotspot temperatures at specific points in time.

[0051] ② Calculation of cumulative life loss of distribution transformers: Since most distribution transformers currently use non-thermally modified oil-impregnated insulating paper in their insulation systems, the following calculation of their cumulative lifespan loss will be based on a non-thermally modified paper transformer as an example: (4); In equation (4): F eq,h This refers to the cumulative lifespan loss of the transformer. n To study time scales ( T The ordinal number of the time point within ) , 98 (°C) is the reference value for the hot spot temperature of the transformer.

[0052] 2) Overhead line life loss model: ① Solving for the temperature of overhead lines: If we ignore the temperature differences at the terminals / joints of the overhead line and consider the overhead line as a conductor with a uniform temperature rise, then according to the principle of thermal balance, we can establish the differential equation for the temperature of the overhead line: (5); In formula (5): i l For line temperature; i a Ambient temperature; Δ i lr This refers to the steady-state temperature rise of the line under rated current. t l The line time constant; K This is the load factor; m This is the heat dissipation correction factor.

[0053] Corresponding to discrete time and data information, equation (5) can be expressed using a difference equation: (6); In formula (6): i l(n) and i l(n-1) The first n , n -1 point in time for the line temperature.

[0054] ② Calculation of cumulative lifespan loss of overhead lines: This method proposes to construct a quantitative model of the life loss of overhead lines using the Arrhenius equation: (7); In equation (7): F eq,l The line lifespan loss is represented by e, where e is the natural constant. B is a material constant reflecting the thermal aging characteristics of the line materials, with units of K; 60 (°C) is the baseline value for the line temperature. This equation can be used to describe the cumulative effect of temperature and time on the lifespan loss of overhead lines.

[0055] In summary, defining any The life loss is F eq,ϛ The corresponding distribution transformer and line can be selected F eq,h or F eq,l Using daily as the research timescale, the total index of the fluctuation in the lifespan loss of current-carrying equipment is: (8); In equation (8): N h+l The total number of devices within the study area; The reference value for the daily life loss of the equipment is 24h. Equation (8) represents the degree of fluctuation of the daily life loss of the current-carrying equipment compared to the expected life (24h).

[0056] Step 2: Construct an economic evaluation model for the Energy Storage System (ESS) that takes into account battery capacity degradation and compensation, and quantify the annual net cost of the ESS: Establish a quantitative model for the annual net cost of ESS. The ESS in the network consists of several Distributed Energy Storage Systems (DESS): (9); In equation (9): S ESS , P ESS These are the total rated capacity and rated power of the ESS, respectively. S DESS,l , P DESS,l The first l Rated capacity and rated power of each DESS; N DESS Configure the number of DESS.

[0057] 1) Solving for the capacity degradation of retired batteries: As the ESS (Emerging Power Supply) is used for charging and discharging, the capacity of retired batteries will further degrade, thus affecting the regulation effect of the ESS. Therefore, an ESS capacity configuration and economic evaluation model is established by calculating the annual battery capacity degradation and replenishing it year by year.

[0058] Battery capacity degradation is primarily determined by the depth of discharge (DOD) and the number of cycles. A rainflow counting method is used to decompose the non-periodic state of charge (SOC) curve of the energy storage battery into independent charge-discharge cycles. The DOD for each cycle is calculated, and the number of cycles with different DOD values ​​is summarized. Simultaneously, by combining the mathematical relationship between DOD and cycle life, the equivalent daily operating cycle count under real-time changes in battery DOD can be obtained. N 'for: (11); In equation (11): N eff (1) is the maximum number of cycles when the battery is in a fully charged and fully discharged state; N eff (DOD k1 The depth of battery discharge (DOD) is the percentage of the battery discharged. k1 The maximum number of loops corresponding to the time; n ′ represents the number of charge / discharge cycles the battery completes in one day.

[0059] Furthermore, the relationship between battery capacity retention and cycle number is as follows: (12); In equation (12): β Capacity retention rate; N b This represents the number of charge-discharge cycles.

[0060] The capacity retention rate when the energy storage battery is first configured for use is [percentage missing]. β 1. Capacity retention rate at the time of termination of use β 2. The corresponding values ​​can be calculated from equation (12). N b Then, the service life of the retired battery can be calculated according to formula (13). T b : (13); In equation (13): N b2 , N b1 They are respectively the corresponding β 2. β 1. Number of charge / discharge cycles; XThis refers to the number of days the battery operates per year. N x ′ is the battery in the first x The equivalent number of cycles per day.

[0061] Battery l (i.e., the first) l The equivalent number of cycles per year for each DESS is Δ N l Combining equation (12), the corresponding annual battery degradation capacity Δ can be obtained by inverse solution. S DESS,l for: (14); In equation (14): X l For batteries l The number of operating days per year; N l,x 'For batteries l In the x The equivalent number of cycles per day; Δ β l For batteries l Annual decay of capacity retention rate.

[0062] Further calculate the annual attenuation capacity Δ of the ESS S ESS for: (15); 2) Net cost analysis of decommissioned battery energy storage systems: The method of this invention is based on annual net cost E As an economic evaluation indicator for ESS: (16); In equation (16): C The annual investment cost of ESS I The specific composition of the annual economic returns after configuring ESS is as follows.

[0063] ①Annual investment cost: The investment cost of a retired battery ESS (Emerging System for End-of-Life) mainly includes the initial investment cost of purchasing used power batteries, conducting capacity testing, and reassembling them during the initial year of system construction; operation and maintenance costs; and compensation costs for purchasing used power batteries again, conducting testing, and reassembling them when the battery capacity degrades. All costs are converted to equivalent annual values, resulting in the annual investment cost of the ESS: (17); In equation (17): C 1 represents the discounted value of the initial investment cost; c s ,c p These are the unit capacity cost and unit power cost of retired batteries, respectively. r The discount rate; T PCS This refers to the service life of the energy storage converter. C 2 represents the annual operating and maintenance cost; k s The unit capacity cost of operating and maintaining retired batteries is given by the formula. k s =0.05165× β -6 (RMB / kWh) will be adjusted annually; k p The unit power cost for operating and maintaining energy storage converters. C 3 represents the annual cost of compensating for the battery capacity, where the compensated battery capacity equals the degraded battery capacity.

[0064] ② Annual economic benefits: The benefits of configuring retired battery ESS mainly come from delaying the upgrading and renovation of the distribution network (mainly lines and transformers). I 1. Benefits of reducing network losses I 2. Benefits of energy conservation and emission reduction I 3. Electricity price difference revenue I 4. The various benefits are expressed as follows: (18); In formula (18): c up Cost per unit capacity expansion of the distribution network; cos ϕ The power factor of current-carrying equipment in the distribution network. r For grid loss electricity price; { N bus} represents a set of network nodes; I ij ( t ), I ij ( t )′ represent the lines before and after energy storage access. ij exist t The effective value of the current at any given time; R ij For the line ij The resistance value; T h This refers to the annual operating time of the energy storage system. e The revenue per unit capacity of batteries that brings energy-saving and emission-reduction benefits from the use of retired batteries. For the first l The DESS in the first x Tianzhong tThe power at any given moment is positive for discharging and negative for charging; Δ t ′ represents the power data sampling time interval; r t for t The electricity price at any given time is considered the same for any two consecutive days at the same time.

[0065] Step 3: Establish a bi-objective optimization model that minimizes the total fluctuation of current-carrying equipment lifetime losses and the annual net cost of the energy storage system (ESS). An improved fuzzy membership function is used to transform the bi-objective problem into a single-objective optimization problem. The optimal energy storage configuration and output strategy are then solved using an adaptive inertial weighted particle swarm optimization algorithm. When the lifespan loss of current-carrying equipment deviates significantly from its expected lifespan, the load current can be adjusted by storing energy, thereby affecting the temperature change of the current-carrying equipment and indirectly causing… F eq,ϛ Approaching Therefore, the total fluctuation of the life loss of current-carrying equipment constructed in step one is used as the technical index in the energy storage optimization configuration model. At the same time, the economic index in the model is obtained from equation (16), and minimizing the two indices is used as the objective function of the configuration model: (19); The two objectives exhibit a negative correlation, therefore, their trade-off mechanism is quantified using mathematical methods. Specifically, an improved fuzzy membership function is established to transform the bi-objective optimization model into a single-objective optimization model, thereby realizing the dynamic trade-off between the two.

[0066] For minΔ F eq Theoretically, as long as F eq,ϛ Not equal to This will activate the penalty, therefore the domain is ,in If the upper limit is completely unacceptable (the theoretical limit, such as in the event of equipment failure), then Δ F eq The membership function can be represented by a power function: (20); In equation (20): exponent α It should be greater than 1 to ensure that satisfaction varies with Δ. F eq Increases and accelerates decay.

[0067] For min E , E Represented using linear membership functions: (twenty one); In equation (21): Emax This represents the acceptable upper limit of annual net cost, which can be taken as the equivalent annual value of the cost of upgrading and transforming the distribution network.

[0068] Combining equations (20) and (21), a comprehensive objective function is constructed based on the pessimistic criterion: (twenty two); 1) Constraints: The configuration of energy storage mainly considers the constraints of the reasonable operation of the distribution network and the charging and discharging of the ESS itself, as follows.

[0069] ① Network trend constraints: (twenty three); In equation (23): P i , Q i They are nodes i The active and reactive power injected at the point; U i , U j They are nodes i , j The voltage amplitude; G ij , B ij and i ij They are nodes i , j The phase angle difference between conductance, susceptance and voltage.

[0070] ② Network node voltage constraints: (twenty four); In equation (24): U max , U min These are the upper and lower limits of the network node voltage, respectively.

[0071] ③ Network line capacity constraints: Considering the short-term heavy overload tolerance margin of the current-carrying equipment, this constraint is expressed in the form of a soft constraint: (25); In equation (25): P{·} is the probability that event {·} is true; For the line ij The square of the effective value threshold of the current; d 1 represents the confidence level that the line operating current will not exceed the limit.

[0072] ④ Distribution transformer capacity constraints: Similar to the network line capacity constraint, we have: (26); In equation (26): P DT and Q DT These are the active and reactive power of the feeder section at the transformer outlet, respectively. This refers to the rated capacity of the corresponding distribution transformer; d 2 represents the confidence level that the actual operating capacity of the distribution transformer does not exceed the limit.

[0073] ⑤ Energy storage energy balance constraints: (27); In equation (27): or To improve the charging and discharging efficiency of energy storage; a 1. a 2 indicates the energy storage charging and discharging state, when When ≥0, energy storage discharges. a 1=1, a 2=0; when When <0, energy storage charging occurs. a 1=0, a 2 = 1.

[0074] ⑥ Energy storage power constraints: (28); ⑦ Energy storage battery SOC constraint: (29); In equation (29): SOC l ( t )for t Moment Battery l State of charge; SOC max SOC min These are the upper and lower limits of the battery's state of charge (SOC); specifying the SOC values ​​at the beginning (and end) of a daily operating cycle. l ( t 0) to prevent overcharging and over-discharging, and to ensure normal operation in the next cycle.

[0075] 2) Adaptive solution algorithm and its improvement: Adaptive Inertia Weighted Particle Swarm Optimization (AIW-PSO) is an improved PSO algorithm that dynamically adjusts the inertia weights, improving convergence speed and accuracy, and is suitable for complex optimization problems. AIW-PSO performs well in handling continuous variables, but requires appropriate adjustment for discrete variables.

[0076] The decision variables in the aforementioned single-objective optimization model are energy storage configuration parameters (capacity).S DESS,l , S ESS ;power P DESS,l , P ESS ), charging and discharging strategy (charging and discharging power) SOC curve l ( t These are discrete and continuous variables, respectively. A hybrid encoding strategy is adopted: the discrete variables are mapped to actual integer values ​​through rounding encoding; while the continuous variables are encoded as real numbers.

[0077] Since the energy storage battery used in this invention is a retired battery, the constraints on the battery's State of Charge (SOC) are more stringent. Therefore, during the optimization process, a penalty function is introduced to transform the degree of constraint violation into a fitness penalty term, forcing the algorithm to search towards a feasible solution. This ensures that the iterative values ​​strictly approximate the feasible region while accelerating the convergence speed of the algorithm. Define the... l The SOC constraint violation degree of each DESS is f l : (30); The total violation of the SOC constraint of the ESS is f : (31); In equation (31): the square term amplifies the penalty for severe over-limit constraints, preventing minor over-limit constraints from dominating the optimization direction.

[0078] The overall objective function is then modified as follows: (32); In equation (32): l ( k )= l 0· k With the number of iterations k Incrementing to strengthen the satisfaction of later constraints.

[0079] Furthermore, in the PSO algorithm, inertia weights w The value of has a significant impact on its convergence performance. Dynamically adjusting the weights can balance global search and local exploitation capabilities, avoiding premature convergence. An adaptive weight adjustment strategy using a nonlinear weight decay approach is employed, with the weight value formula as follows: (33); In equation (33): w max =0.9 to enhance global search in the initial stage; w min=0.4 to improve local accuracy in later stages; K m This represents the maximum number of iterations.

[0080] Step 4: The effectiveness and economy of the above-mentioned optimized configuration method for retired battery energy storage systems in the management of heavy overload in distribution networks are verified through simulation. For example... Figure 2 The typical distribution network system shown is used as a case study, connecting DPV and EV loads to construct a bidirectional heavy overload scenario for the distribution network. The method of this invention is used to optimize and manage this heavy overload problem. The distribution and storage information obtained from the solution is shown in Table 1, and the daily power generation strategy of the energy storage is shown in Figures 3(a) to 3(c). After distribution and storage, the total fluctuation of the lifespan loss of current-carrying equipment Δ F eq The lifetime loss fluctuation of the current-carrying device in the simulation system was greatly improved from 458.36h to 81.69h, which verified the effectiveness of the method of the present invention.

[0081]

[0082] Furthermore, to further compare and verify the advantages of utilizing retired batteries for energy storage, the following section presents an optimized energy storage configuration using new batteries to form an ESS (Energy Storage System). The results are as follows: Figure 4 The chart shows a comparison of the annual investment cost, annual economic benefit, and annual net cost of new and retired battery energy storage solutions. In terms of annual net cost, the annual net cost of new battery energy storage is 3.0051 million yuan, while the annual net cost of retired battery energy storage is only 1.5306 million yuan, the latter being only 50.93% of the former. This result highlights the core advantage of retired batteries in "reducing costs without sacrificing efficiency." The economic threshold for retired battery energy storage is lower than that of new batteries. In scenarios involving heavy overload management of distribution networks, retired battery energy storage can reduce the system's annual net cost to nearly half that of new battery energy storage solutions, providing an economically feasible technical paradigm for the widespread application of energy storage in distribution networks.

Claims

1. An optimized configuration method for retired battery energy storage systems in the management of heavy overload in power distribution networks, characterized in that... Includes the following steps: Step 1: Establish a life loss model for current-carrying equipment, and use the sum of the life loss fluctuations of current-carrying equipment as an index to measure the severity of heavy overload in the distribution network; Step 2: Construct an economic evaluation model for the Energy Storage System (ESS) that takes into account battery capacity degradation and compensation, and quantify the annual net cost of the ESS. Step 3: Establish a dual-objective optimization model based on the sum of the fluctuations in the lifetime loss of current-carrying equipment and the annual net cost of the energy storage system (ESS). Step 4: The dual objective is transformed into a single objective optimization problem using an improved fuzzy membership function, and the optimal configuration and output strategy of the energy storage system ESS are solved based on the adaptive inertial weighted particle swarm algorithm.

2. The optimized configuration method of a decommissioned battery energy storage system in the overload mitigation of a power distribution network according to claim 1, characterized in that: In step 1, the current-carrying equipment includes distribution transformers and overhead lines, wherein the life loss model of the distribution transformer includes: ①Calculation of temperature of distribution transformer: For oil-immersed transformers, the transformer winding hot spot temperature is equal to the sum of the top oil temperature and the hot spot temperature rise, where the top oil temperature is expressed as: （1）； In formula (1): θ o(n) and θ o(n-1) The first n , n -Top oil temperature at 1 time point; θ a(n) For the first n Ambient temperature at each time point; Δ θ or Δ represents the steady-state temperature rise of the top oil under rated loss. t For time step; k 11 These are constants in the thermal model; τ o The average oil time constant; R It is the ratio of load loss to no-load loss under rated current; x o Oil index; K (n) For the first n The load factor at the i-th time point is defined as the i-th time point. n Load current at each time point I (n) With rated current I rated The ratio; The rise in hotspot temperature is represented as: （2）； In equation (2): Δ θ h(n) For the first n The gradient of hot spot temperature with respect to top oil temperature at a given time point, i.e., the hot spot temperature rise, consists of two parts, including Δ θ h1(n) Δ θ h2(n) ;Δ θ hr This refers to the temperature rise of the hot spot under rated current. k 22 , k 21 These are constants in the thermal model; τ w The winding time constant; y For winding index; For the first n The winding exponent of the load factor at each time point; By combining equations (1) and (2), the hotspot temperature can be obtained as follows: （3）； In formula (3): θ h(n) For the first n Hotspot temperatures at specific points in time; ② Calculation of cumulative life loss of distribution transformers: For non-thermally modified paper transformers, calculate their cumulative life loss: （4）； In equation (4): F eq,h This refers to the cumulative lifespan loss of the transformer. n To study time scales T The ordinal number of the time point within the time period. , ; 98 (unit: ℃) is the reference value for the hot spot temperature of the transformer.

3. The optimized configuration method of a decommissioned battery energy storage system in the overload mitigation of a power distribution network according to claim 2, characterized in that: The overhead line life loss model includes: ① Solving for the temperature of overhead lines: Ignoring temperature differences at overhead line terminals / joints and considering the overhead line as a conductor with uniform temperature rise, a differential equation for the temperature of the overhead line can be established based on the principle of thermal balance: （5）； In equation (5): θ l For line temperature; θ a For ambient temperature; Δ θ lr This refers to the steady-state temperature rise of the line under rated current. τ l The line time constant; K This is the load factor; m This is a heat dissipation correction factor; Corresponding to discrete time and data information, equation (5) can be expressed using a difference equation: （6）； In formula (6): θ l(n) and θ l(n-1) The first n , n Line temperature at -1 time point; ② Calculation of cumulative lifespan loss of overhead lines: A quantitative model of overhead line life loss is constructed using the Arrhenius equation: （7）； In equation (7): The line lifespan loss is represented by e, where e is the natural constant. B is a material constant reflecting the thermal aging characteristics of the line material, with units of K; 60 (unit: °C) is the reference value for line temperature; using this equation, the cumulative effect of temperature and time on the life loss of overhead lines can be described. In summary, defining any The life loss is The corresponding distribution transformers and overhead lines can be selected as follows: F eq,h or F eq,l Using daily as the research time scale, the total index of the fluctuation in the lifespan loss of current-carrying equipment is: （8）； In equation (8): N h+l The total number of devices within the study area; This is a reference value for the daily lifespan loss of the equipment. Equation (8) represents the degree of fluctuation in the daily life loss of current-carrying equipment compared to its expected life.

4. The optimized configuration method of a decommissioned battery energy storage system in the overload mitigation of a power distribution network according to claim 3, characterized in that: In step 2, a quantitative model of the annual net cost of the energy storage system ESS is established. The ESS configured in the network consists of several distributed energy storage systems (DESS). （9）； In equation (9): S ESS , P ESS These are the total rated capacity and rated power of the ESS, respectively. S DESS,l , P DESS,l The first l The rated capacity and rated power of each DESS; N DESS Configure the number of DESS.

5. The optimized configuration method of a decommissioned battery energy storage system in the overload mitigation of a power distribution network according to claim 4, characterized in that: The specific steps for calculating the capacity degradation of retired batteries are as follows: An ESS capacity configuration and economic evaluation model is established by calculating the annual battery degradation capacity and replenishing it year by year. Battery capacity degradation is primarily determined by the depth of discharge (DOD) and the number of cycles. A rainflow counting method is used to decompose the non-periodic State of Charge (SOC) curve of the energy storage battery into independent charge-discharge cycles. The DOD for each cycle is calculated, and the number of cycles with different DOD values ​​is summarized. Simultaneously, the mathematical relationship between DOD and cycle life is considered. （10）； In formula (10): N eff (DOD k1 The depth of battery discharge (DOD) is the percentage of the battery discharged. k1 The maximum number of loops corresponding to the time; Further, the daily equivalent cycle number under real-time changes in battery DOD is obtained. N 'for: （11）； In equation (11): N eff (1) is the maximum number of cycles when the battery is in a fully charged and fully discharged state; N eff (DOD k1 The depth of battery discharge (DOD) is the percentage of the battery discharged. k1 The maximum number of loops corresponding to the time; n ′ represents the number of charge-discharge cycles per day of battery operation; The ordinal number of the number of charge-discharge cycles in one day of battery operation; Furthermore, the relationship between battery capacity retention and cycle number is as follows: （12）； In equation (12): β Capacity retention rate; N b This refers to the number of charge-discharge cycles. The capacity retention rate when the energy storage battery is first configured for use is [percentage missing]. β 1. Capacity retention rate at the time of termination of use β 2. The corresponding values ​​can be calculated from equation (12). N b Then, the service life of the retired battery can be calculated according to formula (13). T b : （13）； In equation (13): N b2 , N b1 They are respectively the corresponding β 2. β 1. Number of charge / discharge cycles; X This refers to the number of days the battery operates per year. N x ′ is the battery in the first x The equivalent number of cycles per day; Battery l The equivalent number of cycles per year is Δ N l Combining equation (12), the corresponding annual battery degradation capacity Δ can be obtained by inverse solution. S DESS,l for: （14）； In equation (14): X l For batteries l The number of operating days per year; N l,x 'For batteries l In the x The equivalent number of cycles per day; Δ β l For batteries l Annual decay of capacity retention rate; Further calculate the annual attenuation capacity Δ of the ESS S ESS for: （15）。 6. The optimized configuration method of a decommissioned battery energy storage system in the management of heavy overload in a power distribution network according to claim 5, characterized in that: Net cost analysis of retired battery energy storage systems: Based on annual net cost E As an economic evaluation indicator for ESS: （16）； In equation (16): C The annual investment cost of ESS I The annual economic returns after configuring ESS are specifically composed of the following: ①Annual investment cost: The investment cost of a retired battery ESS includes initial investment cost, operation and maintenance cost, and compensation cost for purchasing used power batteries from external sources and for testing and reassembly when the battery capacity is insufficient. All costs are discounted to their equivalent annual value, resulting in the annual investment cost of the ESS as follows: （17）； In equation (17): C 1 represents the discounted value of the initial investment cost; c s , c p These are the unit capacity cost and unit power cost of retired batteries, respectively. r The discount rate; T PCS The service life of the energy storage converter; C 2 represents the annual operating and maintenance cost; k s The unit capacity cost of operating and maintaining retired batteries is given by the formula. k s =0.05165× β -6 (Unit: Yuan / kWh) Adjusted annually; k p The unit power cost for operating and maintaining energy storage converters; C 3 represents the annual cost of compensating for the battery capacity, where the compensated battery capacity equals the degraded battery capacity. ② Annual economic benefits: The benefit of configuring retired battery ESS comes from the benefit of delaying the upgrading and transformation of the distribution network. I 1. Benefits of reducing network losses I 2. Benefits of energy conservation and emission reduction I 3. Electricity price difference revenue I 4. The various benefits are expressed as follows: （18）； In formula (18): c up Cost per unit capacity expansion of the power distribution network; cos ϕ The power factor of current-carrying equipment in the distribution network; ρ For grid loss electricity price; { N bus } represents a set of network nodes; I ij ( t ), I ij ( t )′ represent the lines before and after energy storage access. ij exist t The effective value of the current at any given time; R ij For the line ij The resistance value; T h For annual operating time of energy storage; e The revenue per unit capacity of batteries that brings energy-saving and emission-reduction benefits from the use of retired batteries; For the first l The DESS in the first x Tianzhong t The power at any given moment is positive for discharging and negative for charging; Δ t ′ represents the power data sampling time interval; ρ t for t The electricity price at any given time is considered the same for any two consecutive days at the same time.

7. The optimized configuration method of a decommissioned battery energy storage system in the overload mitigation of a power distribution network according to claim 5, characterized in that: In step 3, when the lifespan loss of the current-carrying device deviates significantly from the expected lifespan, the load current is adjusted by the energy storage output, thereby affecting the temperature change of the current-carrying device and indirectly causing… F eq,ϛ Approaching ; Therefore, the total fluctuation of the life loss of the current-carrying equipment constructed in step 1 is used as the technical index in the energy storage system ESS optimization configuration model. At the same time, the economic index in the model is obtained from equation (16), and minimizing the two indices is used as the objective function for the energy storage system ESS optimization configuration: （19）； In equation (19): This represents minimizing the total fluctuation of the lifetime loss of current-carrying devices, Δ. F eq ; This represents minimizing the annual net cost of an energy storage system. E .

8. The optimized configuration method of a decommissioned battery energy storage system in the overload mitigation of a power distribution network according to claim 7, characterized in that: An improved fuzzy membership function is established to transform the bi-objective optimization model into a single-objective optimization model, as shown in equations (20) to (22), so as to achieve a dynamic trade-off between the two. For minΔ F eq Theoretically, as long as F eq,ϛ Not equal to This will activate the penalty, therefore the domain is ,in: If the upper limit is completely unacceptable, then Δ F eq The membership function is represented by a power function: （20）； In equation (20): For Δ F eq Membership function; exponent α Greater than 1, to ensure that satisfaction varies with Δ F eq Increases and accelerates decay; For min E , E Represented using linear membership functions: （21）； In equation (21): for E Membership function; The annual net cost of the energy storage system; E max This represents the acceptable upper limit of annual net cost, which can be taken as the equivalent annual value of the cost of upgrading and transforming the power distribution network. Combining equations (20) and (21), a comprehensive objective function is constructed based on the pessimistic criterion: （22）； In equation (22): This represents maximizing the comprehensive objective function. ; This indicates taking the minimum value within the parentheses.

9. The optimized configuration method of a decommissioned battery energy storage system in the management of heavy overload in a power distribution network according to claim 8, characterized in that: Constraints of the comprehensive objective function: The configuration of energy storage takes into account both the reasonable operation of the distribution network and the charging and discharging of the ESS itself, as detailed below; ① Network trend constraints: （23）； In equation (23): P i , Q i They are nodes i The active and reactive power injected at the point; U i , U j They are nodes i , j The voltage amplitude; G ij , B ij and θ ij They are nodes i , j The phase angle difference between the conductance, susceptance, and voltage; ② Network node voltage constraints: （24）； In equation (24): U max , U min These are the upper and lower limits of the network node voltage, respectively; ③ Network line capacity constraints: Considering the short-term heavy overload tolerance margin of the current-carrying equipment, this constraint is expressed in the form of a soft constraint: （25）； In equation (25): P{·} is the probability that event {·} is true; For the line ij The square of the effective value threshold of the current; δ 1 represents the confidence level that the line operating current will not exceed the limit; ④ Distribution transformer capacity constraints: Similar to the network line capacity constraint, we have: （26）； In equation (26): P DT and Q DT These are the active and reactive power of the feeder section at the transformer outlet, respectively. This refers to the rated capacity of the corresponding distribution transformer; δ 2 represents the confidence level that the actual operating capacity of the distribution transformer does not exceed the limit; ⑤ Energy storage energy balance constraints: （27）； In equation (27): η To improve the charging and discharging efficiency of energy storage; a 1. a 2 indicates the energy storage charging and discharging state; For the first l The DESS in the first x Tianzhong t Power at time, when When ≥0, energy storage discharges. a 1=1, a 2=0; when When <0, energy storage charging occurs. a 1=0, a 2 = 1; The power data sampling time interval; ⑥ Energy storage power constraints: （28）； In equation (28): For the first l The rated power of each DESS; ⑦ Energy storage battery SOC constraint: （29）； In equation (29): SOC l ( t )for t Moment Battery l State of charge (SOC) max SOC min These are the upper and lower limits of the battery's state of charge (SOC); specifying the SOC values ​​at the beginning (and end) of a daily operating cycle. l ( t 0), to prevent overcharging and over-discharging, and to ensure normal operation in the next cycle; for Moment Battery l The state of charge.

10. The optimized configuration method of a decommissioned battery energy storage system in the management of heavy overload in a power distribution network according to claim 9, characterized in that: In step 4, the decision variables of the single-objective optimization model are energy storage configuration parameters, including capacity. S DESS,l , S ESS ,power P DESS,l , P ESS The charging and discharging strategy includes charging and discharging power. SOC curve l ( t The two variables are discrete and continuous, respectively. To address this, a hybrid encoding strategy is adopted, which maps the discrete variables to actual integer values ​​through rounding encoding. Continuous variables are encoded as real numbers; Since the energy storage battery used is a retired battery, the constraints on the state of charge and discharge (SOC) of the battery are more stringent. Therefore, during the optimization process, a penalty function is introduced to transform the degree of violation of this constraint into a fitness penalty term, forcing the adaptive inertial weighted particle swarm algorithm to search in the direction of feasible solutions; while ensuring that the iterative values ​​strictly approximate the feasible region, the convergence speed of the algorithm is accelerated. Definition of the first l The SOC constraint violation degree of each DESS is φ l : （30）； The total violation of the SOC constraint of the ESS is φ : （31）； The overall objective function is then modified as follows: （32）； In equation (32): This represents maximizing the modified comprehensive objective function. ; This represents the overall objective function before modification; λ ( k )= λ 0· k , λ ( k ) is a correction coefficient that varies with the number of iterations. k Incrementing to strengthen the satisfaction of later constraints; Furthermore, in the PSO algorithm, inertia weights w The value of has a significant impact on its convergence performance. Dynamically adjusting the weights can balance global search and local exploitation capabilities, avoiding premature convergence. A nonlinear weight decay strategy is used for adaptive weight adjustment, and the weight value formula is as follows: （33）； In equation (33): Here is the formula for determining the weight values; w max =0.9 to enhance global search in the initial stage; w min =0.4 to improve local accuracy in later stages; K m This represents the maximum number of iterations.

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