Power distribution network energy storage optimization configuration method considering dynamic uncertainty and multi-target cooperation

Abstract

The invention relates to the field of power systems and automation thereof. The invention relates to a power distribution network energy storage optimization configuration method considering dynamic uncertainty and multi-target cooperation. The method is characterized by comprising the following steps: 1) constructing a two-stage robust optimization model: constructing the two-stage robust optimization model with a min-max-min structure; in the first stage, the energy storage construction position and capacity are determined with the lowest annual investment cost of energy storage as the target; in the second stage, the system scheduling cost is minimized in the worst new energy output scene; 2) convex relaxation processing of network constraint; 3) implementation of an iterative solution algorithm: based on a KKT principle and a column constraint generation algorithm, decomposing an original problem into a mixed integer linear main problem and a sub-problem; the main problem optimizes an energy storage configuration scheme, and the sub-problems solve a scheduling strategy in the worst wind and light output scene and feed back to the main problem through cut plane constraint; and carrying out iterative calculation until the solutions of the main problem and the sub-problem converge, and obtaining an optimal energy storage configuration scheme. According to the method, more accurate and efficient energy storage planning can be realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power systems and their automation, and is particularly applied to the optimal configuration and planning scenario of distributed energy storage in a distribution network containing distributed new energy, providing technical support for distribution network investors to plan and invest in energy storage, to cope with new energy output uncertainty and ensure the economic and safe operation of the distribution network. BACKGROUND

[0002] The penetration rate of distributed photovoltaic, wind power and other new energy in the distribution network continues to rise. New energy represented by distributed power sources has the advantages of zero pollution and wide distribution, but its output is affected by weather, season and other factors, and there is significant uncertainty, which leads to the dual challenges of stability and economy in the operation of the distribution network. Distributed energy storage, with its short construction period and flexible location, has become a key means to cope with new energy output fluctuations, but its access location and capacity planning directly affect the efficiency of the power grid - unreasonable configuration may lead to increased energy storage investment costs without achieving the expected new energy consumption efficiency, or safety risks due to network constraints such as voltage exceeding limits and branch overload.

[0003] Existing research on the handling of new energy uncertainty is mainly divided into two categories: stochastic optimization and robust optimization. Stochastic optimization requires a large amount of historical data to construct a probability distribution function, but in actual engineering, it is difficult to collect new energy output data, and the probability distribution is difficult to accurately depict extreme fluctuation scenarios; robust optimization replaces the probability distribution with an uncertainty set, but existing models mostly use fixed parameters (such as Γ value), which cannot dynamically adapt to real-time prediction errors, which may lead to overly conservative planning schemes or risk exposure.

[0004] Existing models mostly use a single target of power generation cost or operating income for optimization, without considering multi-dimensional indicators such as voltage stability and carbon emissions, making it difficult to meet the requirements of new power systems for reliability and low carbonization; two-stage robust optimization models usually use column constraint generation algorithms (C&CG) for solution, but this algorithm has the problems of many iteration times and slow convergence speed in large-scale distribution networks, and cannot take advantage of parallel computing to improve efficiency.

[0005] In power flow calculation of the distribution network, the traditional DC power flow model ignores the changes in node voltage and reactive power, resulting in larger errors when used in high impedance distribution networks; the AC power flow model has higher accuracy, but the branch power flow analysis lacks intuitiveness. Although the second-order cone relaxation (SOCR) technique can convert the power flow constraints into a convex optimization problem, existing research has not fully optimized the relaxation accuracy in combination with the topology characteristics of the distribution network, resulting in a gap between the model calculation efficiency and engineering needs.

[0006] The current energy storage configuration related invention focuses on capacity optimization or single robust optimization framework in fixed scenarios, and has the following unresolved technical problems: lack of dynamic adaptation mechanism for new energy output uncertainty, unable to cope with real-time prediction error fluctuations; multi-objective such as voltage stability and carbon emission is not combined with robust optimization, it is difficult to realize the collaborative optimization of economy and reliability; the solving algorithm does not consider the distributed characteristics of distribution network, and the calculation efficiency is low in large-scale system. SUMMARY

[0007] The purpose of the present application is to provide a distribution network energy storage optimization configuration method considering dynamic uncertainty and multi-objective collaboration, which can realize more accurate and efficient energy storage planning.

[0008] In order to achieve the above purpose, the technical scheme adopted by the present application is: a distribution network energy storage optimization configuration method considering dynamic uncertainty and multi-objective collaboration, characterized by comprising the following steps: 1. Two-stage robust optimization model construction: build a two-stage robust optimization model with min-max-min structure; the first stage takes the minimum annual investment cost of energy storage as the target to determine the energy storage construction location and capacity; the second stage minimizes the system dispatching cost (including power purchase and sale cost, demand response cost, and small gas turbine operation cost) under the worst scenario of new energy output; the model considers the charging and discharging constraints of distributed energy storage, demand response load shifting constraints, main and distribution network power interaction constraints, and distributed photovoltaic and wind power output fluctuation constraints; 2. Convex relaxation processing of network constraints: based on the branch flow model, the non-convex items in the flow constraint are converted into second-order cone constraints by using the second-order cone relaxation (SO CR) technology; through variable substitution and constraint reconstruction, the node voltage balance, branch power transmission and other constraints are converted into standard second-order cone form, forming a second-order cone relaxation (SO CP) problem, to ensure accurate description of the voltage level and branch capacity limit of the distribution network; 3. Iterative solving algorithm implementation: based on the KKT (Karush-Kuhn-Tucker) principle and column constraint generation algorithm (C&CG), the original problem is decomposed into a mixed integer linear main problem and a subproblem; the main problem optimizes the energy storage configuration scheme, the subproblem solves the dispatching strategy under the worst wind and light output scenario, and the cutting plane constraint is fed back to the main problem; through iterative calculation, the main and subproblem solutions are converged to obtain the optimal energy storage configuration scheme.

[0009] The invention point of the present application is: 1. Adaptive construction method of dynamic uncertainty set The present application breaks through the traditional robust optimization method of "fixed uncertain parameters (such as wind and light output) and single optimization target (such as system dispatching cost)", and combines the dynamic uncertainty set with the multi-objective optimization framework. To overcome the limitation of the "uncertainty set based on the worst-case scenario", a dynamic uncertainty set construction mechanism based on Bayesian update is proposed.The boundary of the basic uncertainty set is constructed based on historical data;The uncertainty parameter is dynamically adjusted by using the Bayesian algorithm every hour through the latest prediction error ( , and the adaptive matching of the uncertainty set to the real-time fluctuation is realized.

[0010] 2. Construction of multi-objective-robust hybrid optimization model The present application breaks through the limitation of single "degree electricity cost optimization" target, and fuses "voltage stability" and "carbon emission cost" to form a three-dimensional optimization target, so as to realize the collaborative optimization of robustness and multi-dimensional performance. The main target is to minimize the degree electricity cost; The auxiliary target 1 is voltage stability optimization, and a node voltage deviation penalty term is introduced , so as to constrain the voltage to be 0.95~1.05pu); The auxiliary target 2 is to minimize the carbon emission cost, and the carbon emission of the gas turbine unit is converted into the economic cost ; The adaptive weight strategy is used to dynamically balance the priority of the target.

[0011] 3. Improvement of distributed column constraint generation C&CG algorithm In view of the low solving efficiency of the traditional C&CG algorithm in the large-scale distribution network, the present application proposes an efficient solving framework of "distributed parallel + gradient guidance". The distributed decomposition is that the system is divided into multiple sub-regions according to the distribution network topology, and the edge nodes solve the "worst case scenario" of the sub-problem in parallel, so as to reduce the single node calculation load; The gradient guidance iteration is that the gradient relationship between the energy storage capacity and the degree electricity cost is derived by using the KKT condition, the main problem is preferentially searched for the optimal solution according to the gradient direction, and the iteration number is reduced by 40%; The communication optimization is that the "lazy update" strategy is adopted, and the constraint is fed back only when the scenario cost of the sub-region exceeds the current upper limit, so as to reduce the cross-region communication amount.

[0012] 4. High-precision power flow constraint processing based on branch power flow model The present application breaks through the precision limitation of the traditional direct current power flow model, combines the second-order cone relaxation (SOCR) technology, and realizes the accurate description of the power flow constraint under the high impedance characteristic of the distribution network. Based on the branch power flow model, the non-convex power flow constraint is converted into a standard second-order cone form by variable replacement (x ), as follows: The relaxation precision is optimized by combining the topological characteristics of the distribution network, so as to ensure that the voltage and branch power constraint error is less than or equal to 2%.

[0013] 5. Quantitative integration of energy storage life cycle cost The present application breaks through the limitation that the existing model only considers the investment cost of energy storage, associates the depth of charge and discharge (DOD) with the cycle life, and realizes the optimization of the whole life cycle cost. The life loss model is established: Quantitative life cost: The degree of inclusion of the cost objective function, the constraint of the depth of charging and discharging is less than or equal to 80%.

[0014] The present application has the beneficial effects of: 1. Improve system economy: balance the investment cost and operation cost of energy storage through robust optimization model, and verify in IEEE33 node system that compared with the scene without configuring energy storage, the degree of electric cost is reduced by about 3.1%, and under the price fluctuation of spot market, the daily balance cost is reduced by about 74%, and the optimal degree of electric cost in the whole cycle is realized.

[0015] 2. Enhance the ability to respond to uncertainty: describe the fluctuation of wind and light output by using dynamic uncertainty set, and adapt to different prediction error scenes by adjusting uncertainty parameter Γ. When the wind and light prediction error reaches 40%, the robust optimization scheme can still keep the degree of electric cost stable, and the cost fluctuation range of the deterministic optimization scheme is more than 20%.

[0016] 3. Optimize network security constraints: based on the branch power flow model of second-order cone relaxation, the voltage deviation is controlled within ±5%, the risk of branch power overload is reduced by more than 90%, compared with the traditional DC power flow model, the calculation accuracy is improved by 35%, and it is ensured that the energy storage configuration meets the real-time operation safety requirements of distribution network.

[0017] 4. The present application dynamically adjusts the uncertainty set parameter through the Bayesian updating mechanism, introduces the voltage deviation penalty and the carbon emission cost to construct a multi-objective model, and based on the distributed C&CG algorithm, the solving efficiency is improved, and the traditional framework of "two-stage robust optimization + fixed uncertainty set" is avoided, and the dynamic adaptive mechanism is introduced. Unlike simply improving the method of second-order cone relaxation, the model input is optimized combined with data-driven technology, so as to break through the bottleneck of the prior art, and realize more accurate and efficient energy storage planning. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is the flow chart of the present application.

[0019] Figure 2 is the IEEE33 node system diagram of the present application.

[0020] Figure 3 is the dynamic uncertainty set construction flow chart of the present application.

[0021] Figure 4 is the cost box plot of examples 1, 2 and 3 of the present application.

[0022] Figure 5 is the wind and light processing prediction range and uncertainty sensitivity analysis diagram of the present application. DETAILED DESCRIPTION

[0023] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0024] The complete steps of the method of the present application are described As Figure 1 shown, a power distribution network energy storage optimal configuration method considering dynamic uncertainty and multi-objective coordination, the specific implementation process chart is shown in Figure 1 , the method comprises the following steps: 1. Step S101: data acquisition and preprocessing.

[0025] In this step, the specific content of data acquisition and preprocessing mainly includes four aspects, which are the specific object and range of data acquisition, the specific method of data preprocessing, the specific application of data in the invention, and the key formula and technical details of data processing.

[0026] In the specific object and range of data acquisition, the wind and light output historical data include data types: active power data of distributed photovoltaic (PV) and distributed wind power (WT), time resolution is minute level, and the collection period is not less than 1 year, which is used to analyze the long-term fluctuation characteristics of new energy output. The collection nodes: taking IEEE33 node system as an example, the distributed wind power is connected to nodes 12, 17 and 21, and the distributed photovoltaic is connected to nodes 16 and 28, and the historical output data of the corresponding nodes is collected. The short-term prediction data includes the prediction period: future 24 hours, time interval is 15 minutes, the short-term prediction value of wind and light output is obtained, which is used to construct the initial input of dynamic uncertainty set. Data source: the output prediction result generated based on numerical weather prediction (NWP) or machine learning prediction model. Real-time monitoring data includes real-time error data: the deviation data of actual wind and light output and short-term prediction value, which is used to dynamically adjust the uncertainty set parameters and reflect the real-time fluctuation of prediction error. Other key parameters: real-time operation data of power distribution network node voltage, branch power, load curve, main network purchase and sale price, etc., which are used for model constraint and objective function calculation.

[0027] In the specific method of data preprocessing, the prediction error analysis and modeling use the LSTM model to perform short-term prediction of wind and light output, and calculate the prediction error (deviation rate of actual output and predicted value) for dynamic updating of the uncertainty set parameter Γ. Error statistics: Through historical prediction error data, the fluctuation range of wind and light output is determined as the initial boundary of the uncertainty set. Data standardization and normalization standardize the input data of different dimensions, eliminate the dimension effect, and improve the stability of model solving. For example, the power data is normalized to the interval [0, 1], and the voltage is expressed in per unit (pu). Outlier processing and missing value filling mainly eliminates outliers in wind and light output data, and fills missing data by using sliding average method or linear interpolation method to ensure data integrity. Scene generation and dimension reduction generate uncertainty scenarios of wind and light output based on historical data and prediction error, reduce dimension by clustering algorithm, retain typical scenarios for model solving, and reduce computational complexity.

[0028] In the specific application of data in the invention, for dynamic uncertainty set construction, historical data is used to determine the basic fluctuation range of wind and light output, and real-time prediction error is used to dynamically adjust the uncertainty set parameter Γ, realizing adaptive description of new energy uncertainty. Load data is used for power balance constraint: wherein, P buy (t) represents the electrical power purchased from the upper main grid at time t, P sell (t) represents the electrical power sold to the outside at time t, P DR (t) represents the adjusted load power at time t, P L (t) represents the total load power at time t.

[0029] Purchase and sale price data are used to calculate the main grid transaction cost: wherein, C M (t) represents the purchase and sale electricity cost at time t, λ1(t) represents the purchase electricity price of the main grid at time t, λ2(t) represents the sale electricity price of the main grid at time t, P M buy (t) represents the electrical power purchased from the main grid at time t, P M sell (t) represents the electrical power sold to the main grid at time t, t represents the time scale.

[0030] Real-time monitoring of node voltage, branch power and other data is used to verify the feasibility of the model solving result, to ensure that the energy storage configuration scheme meets the distribution network safety constraint C, C represents a constraint set, not a single index, covering the key safety boundaries of distribution network operation.

[0031] In the key formulas and technical details of data processing, the prediction error is calculated as follows: in, For the actual force output at time t, To predict the output, This represents the prediction error at time t. Used to dynamically adjust the Γ value, where Γ represents an uncertain budget.

[0032] Dynamic updates: In the formula, Γ t+1 Γ represents the uncertain budget for the next moment. t This represents the current moment's uncertain budget. For adjustment coefficient ( (Take a value of 0.5), and achieve real-time optimization of the uncertain set through the Bayesian update mechanism.

[0033] Power balance constraints: In the formula, P buy (t) represents the electrical power purchased from the upstream main grid at time t, P sell (t) represents the electrical power sold to the main grid at time t, P DR (t) represents the load power adjusted at time t, P L (t) represents the total load power at time t, P dis (t) represents the discharge power of the energy storage system at time t, P ch P(t) represents the charging power of the energy storage system at time t. pv (t) represents the actual output power of the photovoltaic power source at time t, P wt (t) represents the actual output power of the wind turbine at time t, P G (t) represents the output power of a conventional power source at time t.

[0034] This system integrates data on load, energy storage, and new energy sources to ensure a balance between power supply and demand in the power distribution network.

[0035] 2. Step S102: Construction of dynamic uncertain set.

[0036] This step comprises four modules. First, a basic uncertainty set is constructed, where the uncertainty of wind and solar power output is described using a "box uncertainty set" to represent the fluctuation range of distributed photovoltaic (PV) and wind power (WT) output. Based on historical data statistics, the upper and lower boundary values ​​of wind and solar power output are determined. Specifically: Uncertain set of wind power output: Uncertain set of photovoltaic output: in, This represents the actual output power of the wind turbine at time t. This represents the predicted output power of the wind turbine at time t. This represents the actual output power of the photovoltaic power source at time t. This represents the predicted output power of the photovoltaic power source at time t. The positive fluctuation coefficient of wind turbine output at time t is represented. This represents the maximum positive fluctuation in the wind turbine output at time t. The negative fluctuation coefficient of wind turbine output at time t is represented. This represents the positive fluctuation coefficient of the photovoltaic power output at time t. This represents the maximum positive fluctuation in photovoltaic power output at time t. This represents the negative fluctuation coefficient of photovoltaic power output at time t. To predict the output, For fluctuation amplitude, These are Boolean variables used to indicate whether to take upper or lower boundary values.

[0037] Uncertain parameter constraints introduce uncertain adjustment parameters to limit the total deviation of wind and solar power output fluctuations. The expression is: In the formula, The positive fluctuation coefficient of wind turbine output at time t is represented. The negative fluctuation coefficient of wind turbine output at time t is represented. This represents the positive fluctuation coefficient of the photovoltaic power output at time t. Γ represents the negative fluctuation coefficient of photovoltaic power output at time t. wt The uncertainty budget representing wind power fluctuations, Γ pv The budget represents the uncertainty of photovoltaic fluctuations. The larger the value, the wider the range of the uncertainty set, and the stronger the model's conservatism.

[0038] Secondly, there is the dynamic update mechanism and implementation steps. The Bayesian update based on prediction error mainly includes real-time error monitoring: obtaining the deviation between the actual and predicted values ​​of wind and solar power output. In the formula, For the actual force output at time t, To predict the output, This represents the prediction error at time t. Calculate the prediction error rate in real time.

[0039] Dynamic parameter adjustment: A Bayesian update algorithm is used, adjusting the parameters every hour based on the latest error. Adjusting uncertain parameters The formula is: Among them, Γ t+1 Γ represents the uncertain budget for the next moment. t This represents the current moment's uncertain budget. This represents the prediction error at time t. The adjustment factor (taken as 0.5) is calibrated using historical error data.

[0040] For linearization of Boolean variables and continuous variables, in order to solve the product terms of Boolean variables and continuous variables in uncertain sets (such as...), To address the nonlinearity caused by [the problem], auxiliary variables are introduced and the Big M method is used for linearization. Specific constraints are as follows: In the formula, , Indicates to and These auxiliary decision variables are used to "flexibly" control the value of the fluctuation coefficient in robust optimization. By associating them with binary continuous variables through linear constraints, fine-grained control over uncertainty can be achieved. ν4 represents the "conditional enablement term" for the negative fluctuation coefficient of wind power, used to control whether the uncertainty of wind power output is included in the model. The "Condition Activation Item" represents the positive fluctuation coefficient of wind power, which is used to control whether the uncertainty of wind power output is included in the model. ν4 represents a binary variable used to "switch" the fluctuation coefficient to whether it is enabled. M is a sufficiently large positive number to ensure the effectiveness of the constraint.

[0041] The third module involves designing the coupling method between the uncertainty set and the model solution. On one hand, it applies to two-stage robust optimization. The first stage involves using the initial uncertainty set (e.g., ...) Plan the location and capacity of energy storage, and determine and . Denotes the rated energy capacity of the i-th energy storage device. Let represent the rated power capacity of the i-th energy storage device. The second stage involves iteratively solving sub-problems, dynamically updating the wind and solar power output boundary under the worst-case scenario, and feeding the new constraints back to the main problem until convergence. On the other hand, it integrates with the C&CG (Column Constraint Generation Algorithm). In the column constraint generation algorithm, each iteration solves for the wind and solar power output scenario that maximizes system cost based on the current energy storage configuration, and updates the uncertainty set constraints through the following steps: When solving sub-problems, based on the current... Determine the power output boundaries of wind and solar power; during the main problem iteration, adjust based on the latest prediction error. Regenerate scene constraints.

[0042] The fourth module contains key formula expressions and the mathematical definition of uncertain sets: In the formula, Γ t This represents the current moment's uncertain budget. B wt (t) represents the negative fluctuation coefficient of the wind turbine output at time t. Γ represents the positive fluctuation coefficient of wind turbine output at time t. wt The uncertainty budget representing wind power fluctuations, Γ pv Let represent the uncertainty budget of photovoltaic and wind power fluctuations, and ∀t represent the uncertainty budget for all times t. B pv (t) represents the negative fluctuation coefficient of the photovoltaic power output at time t. The positive fluctuation coefficient of photovoltaic power output at time t is represented.

[0043] This formula defines the range of the uncertainty set of wind and solar power output, ensuring the robustness of the model under the worst-case scenario.

[0044] In addition, the dynamic adjustment of the engineering implementation is mainly achieved by setting a convergence threshold. (This is a constant, typically ranging from 0.01 to 0.05), when At that time, U B L represents the upper bound of the objective function. B This indicates the lower bound of the objective function, stops the iteration, and outputs the optimal energy storage scheme considering the dynamic uncertainty set.

[0045] 3. Step S103: Construction of multi-objective robust model.

[0046] In the specific structure of the multi-objective function, the multi-objective function of this invention takes "optimal cost per kilowatt-hour" as the core and integrates two auxiliary objectives, "voltage stability" and "carbon emission cost," to form a three-dimensional optimization objective system, the specific expression of which is as follows: Main objective: Minimize the cost per kilowatt-hour The cost per kilowatt-hour encompasses the investment cost of energy storage and the system operating cost (electricity purchase and sale, gas turbine units, and demand response), and is expressed as follows: in, Annualized investment cost for energy storage; The cost of electricity purchased and sold online. For the operating costs of gas turbine units, Cost of responding to demand.

[0047] Auxiliary objective 1: Voltage stability optimization By introducing a voltage deviation penalty term, the node voltage is constrained to be within a safe range. The expression is: Where N represents the total number of nodes in the distribution network, and T represents the time period for optimal scheduling. Let be the voltage at node i at time t. The rated voltage is used, and the penalty factor is set based on the risk of voltage exceeding the limit.

[0048] Secondary objective 2: Minimize carbon emission costs For the carbon emissions of small gas turbine units, their conversion into economic costs is incorporated into the objective function, expressed as: in, This is the carbon emission cost coefficient. To provide power to the gas turbine unit, For time intervals.

[0049] Next, in the design of the two-stage model structure for robust optimization, multi-objective functions are combined with robust optimization to form a "two-stage multi-objective robust model", the structure of which is as follows: The first stage, which is also the main problem, involves energy storage planning and decision-making, with the optimization variable being the location of energy storage (a Boolean variable). ) and capacity , The goal is to minimize the "basic cost" of the multi-objective function while satisfying network constraints, providing an initial planning scheme for the second stage. The second stage is a sub-problem of operation optimization under the worst-case scenario. Considering the uncertainty of renewable energy output, and given that the planning scheme in the first stage is fixed, the "worst-case scenario" is solved, and the multi-objective cost under this scenario is minimized by optimizing the scheduling strategy.

[0050] The core logic is: (Total cost across multiple objectives) Meanwhile, based on existing technologies and solutions, this invention adds constraints related to multiple objectives, forming a complete constraint system: The original core constraints include energy storage operation constraints: charging and discharging power, energy balance, and SOC (State of Charge) range; power flow constraints: second-order cone relaxation constraints based on branch power flow models to ensure node voltage and branch power safety; and power balance constraints: power purchase and sale balance between the main grid and distribution grid, and wind and solar curtailment constraints. The newly added constraints related to multiple objectives include voltage safety margin constraints. V i Represents the voltage at the i-th node, and the engineering feasibility of strengthening the voltage stability target; total carbon emission constraints: Among them, P G (t) represents the output power of the conventional power source at time t. As the upper limit for carbon emissions, Limiting total carbon emissions from gas turbine units ( (Carbon emission ceiling); multi-objective weight constraints: through adaptive weight coefficients , , )(satisfy Balance the three objectives. Indicates the weight of cost per kilowatt-hour. Indicates voltage weighting. This represents the carbon emission cost weight (not a constant; the priority among multiple objectives can be flexibly controlled by adjusting the weight).

[0051] Finally, in the model convexity and solution adaptation module, the transformation from multi-objective to single-objective optimization is achieved using the "ε-constraint method": with the cost per kilowatt-hour as the primary objective, voltage deviation and carbon emission costs are transformed into constraints, and these constraints are adjusted (…). , To obtain the Pareto optimal solution, This indicates the maximum permissible threshold for voltage deviation. This represents the maximum permissible threshold for carbon emission costs. Robust optimization's convex relaxation process utilizes the second-order cone relaxation technique from the documentation to transform non-convex terms in power flow constraints into second-order cone constraints. Combined with KKT conditions, the duality of the subproblems is transformed into a mixed-integer linear form, adapted to the column constraint generation algorithm (C&CG) for solution: Main problem: Optimize energy storage planning, incorporating the "worst-case scenario" constraints returned by the subproblems; Subproblems: Solve for the scenario that maximizes multi-objective costs within the dynamic uncertainty set, generating a cutting plane that is fed back to the main problem, iterating until convergence. Among them, U B L represents the upper bound of the objective function.B ε represents the lower bound of the objective function, and ε represents the convergence threshold (a constant, typically ranging from 0.01 to 0.05).

[0052] 4. Step S104: Solve using the distributed C&CG algorithm.

[0053] The distributed column constraint generation algorithm (C&CG) is the core method of this invention for solving multi-objective robust models. Its core principle is to decompose the large-scale robust optimization problem into distributed sub-problems and a global master problem, achieving efficient solutions through parallel iteration and constraint feedback. Details are as follows: The algorithm's distributed decomposition logic is as follows: Based on the topological characteristics of the distribution network, the network is divided into several sub-regions according to electrical distance. Each sub-region is configured with edge computing nodes responsible for solving local sub-problems. The global master problem is coordinated by the control center, integrating the results from each sub-region and optimizing the energy storage planning scheme. The decomposition is based on the following: Wind and solar power output, load, and energy storage within a sub-region have strong local correlations and can be solved independently for the worst-case scenario. The global master problem only needs to focus on the interaction constraints between sub-regions, reducing the problem size.

[0054] The main problem and its subproblems are structured as follows: The main problem aims to minimize the total multi-objective cost (cost per kilowatt-hour + voltage penalty + carbon emission cost) to determine the location of energy storage. Constraints include energy storage investment cost constraints, configuration variable constraints, the "worst-case scenario" cutting plane constraint from sub-region feedback, and cross-regional branch power constraints. The mathematical form is Mixed Integer Linear Programming (MILP), which can be solved quickly using the Gurobi solver. In the distributed subproblems, each sub-region independently solves for its operating strategy under the "worst-case scenario," aiming to maximize the total multi-objective cost. Specific optimization variables include: energy storage charging and discharging power, gas turbine output, and demand response load within the sub-region. Constraints include dynamic uncertainty set constraints on local wind and solar power output, power balance constraints and energy storage operation constraints within the sub-region, and node voltage safety margin constraints. The solution method transforms the duality of the subproblems into a mixed-integer linear form based on KKT conditions to avoid non-convexity; a parallel computing framework enables simultaneous solving across multiple sub-regions.

[0055] The iterative process, taking into account the characteristics of distributed systems, begins with initialization settings, including setting a convergence threshold. =0.05, iteration number k=1, upper bound of objective function Lower Boundary The main problem is to solve for the initial energy storage planning scheme based on the initial forecast data. Next, the distributed sub-problems are solved, and the energy storage schemes for each sub-region are based on the main problem. Solve the worst-case scenario within a dynamic uncertainty set and calculate the corresponding multi-objective total cost. Cutting plane constraints are generated for each sub-region and aggregated into the global master problem. Finally, the master problem is updated and convergence is checked. The master problem incorporates the cutting plane constraints of all sub-regions, and the optimal energy storage scheme is solved again. Update the lower bound of the objective function ; Calculate the upper bound If satisfied If the solution converges, output the optimal solution; otherwise, k = k + 1.

[0056] Among them, U B L represents the upper bound of the objective function. B J represents the lower bound of the objective function. i Let represent the total cost of the multi-objective task, and k represent the iteration counter (not a constant, with an initial value of 1).

[0057] Key technologies for distributed solution: Gradient-guided acceleration of iteration: The gradient relationship between energy storage capacity and multi-objective cost is derived using KKT conditions. The main problem prioritizes searching for optimal energy storage configurations based on the gradient direction, reducing the number of iterations. Sub-region communication optimization adopts a "lazy update" strategy: only when the worst-case scenario cost of the sub-region exceeds the current upper bound... Only when the cutting plane is fed back to the main problem does it reduce cross-regional communication. When solving the worst-case scenario with the adaptation subproblem of the multi-objective model, the joint maximization of cost per kilowatt-hour, voltage deviation, and carbon emissions is considered simultaneously to ensure that the cutting plane constraint can accurately reflect the "worst-case" of the multi-objectives.

[0058] 5. Step S105: Result verification and output.

[0059] Three sets of comparative examples are designed to quantify the advantages of the proposed method: Example 1 (no energy storage), without configuring distributed energy storage, only day-ahead economic dispatch is performed to verify the necessity of energy storage configuration; Example 2 (deterministic energy storage planning), energy storage is configured but the uncertainty of wind and solar power output is ignored, and planning is based on predicted values, comparing the advantages of robust optimization; Example 3 (the method of this invention), considering multi-objective robust energy storage planning with dynamic uncertainty sets, verifies the comprehensive performance of the model. The core comparative indicators include levelized cost of electricity (LCOE), intraday balancing cost, voltage deviation, and computation time. The influence of the core parameters affecting the model on the results is analyzed to verify the model's stability: wind and solar uncertainties. :set up =0,3,6,9,12,15,18, analyze the variation of cost per kilowatt-hour with the range of uncertainty (e.g., (As the capacity increases, the energy storage configuration capacity increases, and the cost rises); Prediction error range: set the error range to 0%~40% to verify the adaptability of the dynamic uncertainty set to different error scenarios; Energy storage investment cost: set the unit capacity cost to 1000~3500 yuan / (kW・h) to analyze the impact of cost on the energy storage configuration capacity. Engineering feasibility also needs to be verified, including network constraint satisfaction: verifying the node voltage (whether it is within [0.95,1.05] pu) and branch power under the optimal scheme to ensure the safe operation of the distribution network; Extreme scenario testing: simulating extreme weather to verify whether the energy storage charging and discharging strategy can respond quickly and maintain system stability.

[0060] After the model converges, the following core results are output, providing a direct reference for energy storage planning in distribution networks: Optimal energy storage configuration scheme: The location and capacity of each node are clearly defined; Investment cost details: Annualized investment cost and percentage of energy storage, such as a total investment of 1.04 million yuan, with capacity cost accounting for 65%.

[0061] Operating strategy parameters: Energy storage charging and discharging plan: charging and discharging power curves of energy storage at each node within 24 hours; Other equipment scheduling schemes: gas turbine output, demand response load transfer, and main grid power purchase and sales plan.

[0062] Economic and reliability indicators: Cost per kilowatt-hour: total cost per kilowatt-hour and the percentage of each component; Voltage and carbon emission optimization results: maximum voltage deviation and total carbon emissions.

[0063] Model convergence process data: Iteration curve: Lower bound of the main problem Upper bound of the AND problem The convergence trend is used to verify the stability of the algorithm; the worst-case scenario description is: the final convergent wind and solar power output combination is used to clarify the robustness boundary of the model.

[0064] Through the synergistic effect of the five steps S101-S105, clear conclusions can be drawn and multi-dimensional technical effects can be achieved, as detailed below: Key findings include: dynamic uncertainty sets can accurately adapt to fluctuations in new energy output; multi-objective robust models achieve optimal synergy between "economy, safety, and low carbon"; distributed C&CG algorithms significantly improve the solution efficiency of large-scale systems; and high-precision power flow constraints ensure the engineering reliability of planning schemes.

[0065] The achieved results include improved economic efficiency: significantly reduced cost per kilowatt-hour and total lifecycle costs; enhanced reliability: improved ability to cope with uncertainties and voltage stability; optimized low-carbon performance: reduced carbon emissions and environmental costs of gas turbine units; and improved engineering practicality: improved feasibility of the solution and scalability of the algorithm.

[0066] The five steps form a closed loop of "data-driven, model optimization, efficient solution, and verification and implementation", ultimately achieving "economic, safe, and low-carbon coordinated optimization of distributed energy storage in distribution networks under the uncertainty of new energy output", providing a feasible technical solution for energy storage planning in distribution networks with a high proportion of new energy.

[0067] In one embodiment, such as Figure 4 The diagram shows the cost box plots for examples 1, 2, and 3. During implementation, the wind and solar uncertainty parameter was set to 12, the wind and solar prediction error to 20%, the electricity purchase price was twice the day-ahead market price, and the electricity sales price was 0.5 times the day-ahead market price. The Monte Carlo method was used to randomly generate scenarios, resulting in the following... Figure 4 The simulation diagram is shown. As can be seen from the diagram, Example 1 has the highest cost, while Example 2 and Example 3 have significantly lower costs. Example 3 is more economical than Example 2, which proves that the method of the present invention is more capable of dealing with the uncertainty of wind and solar power output, has better economic efficiency, and has better performance in most cases. Figure 5 This invention analyzes the prediction range and uncertainty sensitivity of wind and solar power processing. The prediction error of wind and solar power output is set to 0-40%, and the uncertainty of wind and solar power output is set to 0-40%. As the prediction error and uncertainty of wind and solar power output increase, the average daily cost will increase to a certain extent. However, compared with the cost increase trend of traditional common methods, the economic efficiency obtained by the robust optimization is better than before. Moreover, as the accuracy of wind and solar power output prediction and wind and solar uncertainty prediction continues to improve in the future, the average daily cost will have a further downward trend.

[0068] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0069] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for optimizing the configuration of energy storage in distribution networks considering dynamic uncertainty and multi-objective collaboration, characterized in that... Includes the following steps: 1) Construction of a two-stage robust optimization model: A two-stage robust optimization model with a min-max-min structure is built. The first stage aims to minimize the annualized investment cost of energy storage and determine the location and capacity of energy storage construction. The second stage minimizes the system scheduling cost under the worst scenario of renewable energy output. The model considers the charging and discharging constraints of distributed energy storage, the load shifting constraints of demand response, the power interaction constraints of the main distribution network, and the power fluctuation constraints of distributed photovoltaic and wind power output. 2) Convex relaxation of network constraints: Based on the branch power flow model, the non-convex terms in the power flow constraints are transformed into second-order cone constraints using the second-order cone relaxation technique; through variable substitution and constraint reconstruction, constraints such as node voltage balance and branch power transmission are transformed into standard second-order cone form, forming a second-order cone programming problem, ensuring accurate characterization of the distribution network voltage level and branch capacity limits; 3) Implementation of iterative solution algorithm: Based on the KKT principle and column constraint generation algorithm, the original problem is decomposed into a mixed integer linear main problem and sub-problems; the main problem optimizes the energy storage configuration scheme, and the sub-problems solve the scheduling strategy under the worst wind and solar power output scenario, and feed back to the main problem through cutting plane constraints; through iterative calculation, until the solutions of the main problem and sub-problems converge, the optimal energy storage configuration scheme is obtained.

2. The method for optimizing the configuration of energy storage in a distribution network considering dynamic uncertainty and multi-objective collaboration as described in claim 1, characterized in that, In step 1), the system scheduling cost to be minimized includes the cost of purchasing and selling electricity, the demand response cost, and the operating cost of small gas turbine units.

3. The method for optimizing the configuration of energy storage in a distribution network considering dynamic uncertainty and multi-objective collaboration as described in claim 1, characterized in that, Specifically, the steps include the following: Step S101: Data acquisition and preprocessing; In terms of the specific objects and scope of data collection, historical wind and solar power output data includes data types: active power data of distributed photovoltaic (PV) and distributed wind power (WT), with a time resolution of minutes and a collection period of no less than one year, used to analyze the long-term fluctuation characteristics of new energy power output; collection nodes: taking the IEEE 33-node system as an example, distributed wind power is connected at nodes 12, 17, and 21, and distributed photovoltaic power is connected at nodes 16 and 28, and historical power output data of the corresponding nodes are collected; short-term forecast data includes a forecast period of the next 24 hours, with a time interval of 15 minutes, to obtain short-term forecast values ​​of wind and solar power output, used as the initial input for constructing a dynamic uncertainty set; data sources: power output forecast results generated based on numerical weather prediction or machine learning prediction models; Real-time monitoring data includes real-time error data: deviation data between actual wind and solar power output and short-term forecast values, used to dynamically adjust uncertainty set parameters and reflect real-time fluctuations in forecast errors; other key parameters: real-time operating data such as distribution network node voltage, branch power, load curve, and main grid purchase and sale electricity price, used for model constraints and objective function calculation; In the specific methods of data preprocessing, prediction error analysis and modeling use an LSTM model to make short-term predictions of wind and solar power output and calculate the prediction error to dynamically update the uncertainty set parameter Γ; error statistics: through historical prediction error data, the fluctuation range of wind and solar power output is determined as the initial boundary of the uncertainty set; data standardization and normalization: input data of different dimensions are standardized to eliminate the influence of dimensions and improve the stability of model solution; for example, power data is normalized to the [0,1] interval, and voltage is represented by per-unit value pu; outlier handling and missing value filling: outliers in wind and solar power output data are mainly removed, and missing data are filled by moving average or linear interpolation to ensure data integrity; scene generation and dimensionality reduction: based on historical data and prediction errors, uncertain scenes of wind and solar power output are generated, and dimensionality is reduced by clustering algorithm to retain typical scenes for model solution and reduce computational complexity; In the specific applications of data in the invention, for the construction of dynamic uncertainty sets, historical data is used to determine the basic fluctuation range of wind and solar power output, and real-time prediction errors are used to dynamically adjust the uncertainty set parameter Γ, achieving an adaptive description of the uncertainty of new energy sources; model constraints and objective function calculations use load data for power balance constraints. In the formula, P buy (t) represents the electrical power purchased by the distribution network from the upstream main grid at time t, P sell P(t) represents the electrical power sold by the distribution network to the outside at time t. DR (t) represents the load power adjusted at time t, P L (t) represents the total load power at time t; Electricity purchase and sale price data are used to calculate main grid transaction costs: In the formula, C M λ(t) represents the cost of purchasing and selling electricity with the main grid at time t, λ1(t) represents the purchase price of electricity from the main grid at time t, λ2(t) represents the sale price of electricity from the main grid at time t, and P M buy (t) represents the electrical power purchased from the main grid at time t, P M sell (t) represents the electrical power sold to the main grid at time t, where t represents the time scale; The algorithm iteration and convergence judgment use real-time monitored node voltage, branch power and other data to verify the feasibility of the model solution results and ensure that the energy storage configuration scheme meets the distribution network safety constraint C. C represents a set of constraints, not a single indicator, and covers the key safety boundaries of distribution network operation. In the key formulas and technical details of data processing, the prediction error is calculated as follows: in, For the actual force output at time t, To predict the output, This represents the prediction error at time t. Used to dynamically adjust the Γ value, where Γ represents an uncertain budget; Dynamic updates: In the formula, Γ t+1 Γ represents the uncertain budget for the next moment. t This represents the current moment's uncertain budget. To adjust the coefficient, We set the value to 0.5 and use a Bayesian update mechanism to achieve real-time optimization of the uncertain set. Power balance constraints: In the formula, P buy (t) represents the electrical power purchased from the upstream main grid at time t, P sell (t) represents the electrical power sold to the main grid at time t, P DR (t) represents the load power adjusted at time t, P L (t) represents the total load power at time t, P dis (t) represents the discharge power of the energy storage system at time t, P ch P(t) represents the charging power of the energy storage system at time t. pv (t) represents the actual output power of the photovoltaic power source at time t, P wt (t) represents the actual output power of the wind turbine at time t, P G (t) represents the output power of the conventional power source at time t; This method integrates data on load, energy storage, and new energy sources to ensure a balance between power supply and demand in the distribution network. Step S102: Construction of dynamic uncertain set; This step comprises four modules. First, a basic uncertainty set is constructed, where the uncertainty of wind and solar power output is described using a "box uncertainty set" to represent the fluctuation range of distributed photovoltaic (PV) and wind power (WT) output. Based on historical data statistics, the upper and lower boundary values ​​of wind and solar power output are determined. Specifically: Uncertain set of wind power output: Uncertain set of photovoltaic output: in, This represents the actual output power of the wind turbine at time t. This represents the predicted output power of the wind turbine at time t. This represents the actual output power of the photovoltaic power source at time t. This represents the predicted output power of the photovoltaic power source at time t. The positive fluctuation coefficient of wind turbine output at time t is represented. This represents the maximum positive fluctuation in the wind turbine output at time t. The negative fluctuation coefficient of wind turbine output at time t is represented. This represents the positive fluctuation coefficient of the photovoltaic power output at time t. This represents the maximum positive fluctuation in photovoltaic power output at time t. This represents the negative fluctuation coefficient of photovoltaic power output at time t. To predict the output, For fluctuation amplitude, These are Boolean variables used to indicate whether to take upper or lower boundary values; Uncertain parameter constraints introduce uncertain adjustment parameters to limit the total deviation of wind and solar power output fluctuations. The expression is: In the formula, The positive fluctuation coefficient of wind turbine output at time t is represented. The negative fluctuation coefficient of wind turbine output at time t is represented. This represents the positive fluctuation coefficient of the photovoltaic power output at time t. Γ represents the negative fluctuation coefficient of photovoltaic power output at time t. wt The uncertainty budget representing wind power fluctuations, Γ pv The budget represents the uncertainty of photovoltaic fluctuations. The larger the value, the wider the range of the uncertainty set, and the stronger the model's conservatism. Secondly, there is the dynamic update mechanism and implementation steps. The Bayesian update based on prediction error mainly includes real-time error monitoring: obtaining the deviation between the actual and predicted values ​​of wind and solar power output. In the formula, For the actual force output at time t, To predict the output, This represents the prediction error at time t. Real-time calculation of prediction error rate; Dynamic parameter adjustment: A Bayesian update algorithm is used, adjusting the parameters every hour based on the latest error. Adjusting uncertain parameters The formula is: Among them, Γ t+1 Γ represents the uncertain budget for the next moment. t This represents the current moment's uncertain budget. This represents the prediction error at time t. To adjust the coefficient, Set the value to 0.5 and calibrate using historical error data; For linearization of Boolean variables and continuous variables, in order to solve the product terms of Boolean variables and continuous variables in uncertain sets (such as...), To address the nonlinearity caused by [the problem], auxiliary variables are introduced and the Big M method is used for linearization. Specific constraints are as follows: In the formula, , Indicates to and The auxiliary decision variables are used to "flexibly" control the value of the fluctuation coefficient in robust optimization. By associating them with binary continuous variables through linear constraints, fine-grained control over uncertainty can be achieved. ν4 represents the "conditional enable term" for the negative fluctuation coefficient of wind power, used to control whether the uncertainty of wind power output is included in the model. The "conditional enablement item" represents the positive fluctuation coefficient of wind power, which is used to control whether the uncertainty of wind power output is included in the model. ν4 represents a binary variable used to "switch" whether the fluctuation coefficient is enabled. M is a sufficiently large positive number to ensure the effectiveness of the constraint. The third module involves designing the coupling method between the uncertainty set and the model solution. On one hand, it applies to two-stage robust optimization. The first stage involves planning the energy storage location and capacity based on the initial uncertainty set, such as... ,Sure and ; Denotes the rated energy capacity of the i-th energy storage device. Let represent the rated power capacity of the i-th energy storage device. The second stage involves iteratively solving sub-problems, dynamically updating the wind and solar power output boundary under the worst-case scenario, and feeding the new constraints back to the main problem until convergence. On the other hand, integration with the C&CG algorithm is incorporated into the column constraint generation algorithm. Each iteration, based on the current energy storage configuration, solves for the wind and solar power output scenario that maximizes system cost, and updates the uncertainty set constraints through the following steps: When solving sub-problems, based on the current... Determine the power output boundaries of wind and solar power; during the main problem iteration, adjust based on the latest prediction error. Regenerate scene constraints; The fourth module contains key formula expressions and the mathematical definition of uncertain sets: In the formula, Γ t This represents the current moment's uncertain budget. B wt (t) represents the negative fluctuation coefficient of the wind turbine output at time t. Γ represents the positive fluctuation coefficient of wind turbine output at time t. wt The uncertainty budget representing wind power fluctuations, Γ pv Let represent the uncertainty budget for fluctuations in photovoltaic and wind power, and ∀t represent the uncertainty budget for all times t; B pv (t) represents the negative fluctuation coefficient of photovoltaic power output at time t. The positive fluctuation coefficient of photovoltaic power output at time t; This formula defines the range of the uncertainty set of wind and solar power output, ensuring the robustness of the model under the worst-case scenario; In addition, the dynamic adjustment of the engineering implementation is mainly achieved by setting a convergence threshold. , The value ranges from 0.01 to 0.

05. At that time, U B L represents the upper bound of the objective function. B This indicates the lower bound of the objective function, stops the iteration, and outputs the optimal energy storage scheme considering the dynamic uncertainty set; Step S103: Construction of a multi-objective robust model; In the specific structure of the multi-objective function, the multi-objective function of this invention takes "optimal cost per kilowatt-hour" as the core and integrates two auxiliary objectives, "voltage stability" and "carbon emission cost," to form a three-dimensional optimization objective system, the specific expression of which is as follows: Main objective: Minimize the cost per kilowatt-hour The cost per kilowatt-hour includes the investment cost of energy storage and the system operating cost, and is expressed as: in, Annualized investment cost for energy storage; The cost of electricity purchased and sold online. For the operating costs of gas turbine units, Cost of responding to demand; Auxiliary objective 1: Voltage stability optimization By introducing a voltage deviation penalty term, the node voltage is constrained to stay within a safe range. The expression is: Where N represents the total number of nodes in the distribution network, and T represents the time period for optimal scheduling. Let be the voltage at node i at time t. The penalty factor is set based on the risk of voltage exceeding the limit, and is the rated voltage. Secondary objective 2: Minimize carbon emission costs For the carbon emissions of small gas turbine units, their conversion into economic costs is incorporated into the objective function, expressed as: in, This is the carbon emission cost coefficient. To provide power to the gas turbine unit, For time intervals; Next, in the design of the two-stage model structure for robust optimization, multi-objective functions are combined with robust optimization to form a "two-stage multi-objective robust model", the structure of which is as follows: The first stage involves energy storage planning and decision-making, which is also the main problem. The optimization variables are the location and capacity of energy storage. , Location of energy storage: Boolean variable The goal is to minimize the "basic cost" of the multi-objective function while satisfying network constraints, providing an initial planning scheme for the second stage. The second stage is to optimize the operation under the worst-case scenario as a subproblem. Considering the uncertainty of new energy output, the "worst-case scenario" is solved under the premise that the planning scheme in the first stage is fixed, and the multi-objective cost under this scenario is minimized by optimizing the scheduling strategy. The core logic is: Multi-objective total cost Simultaneously, based on existing technologies and solutions, new constraints related to multiple objectives are added to form a complete constraint system: The original core constraints include energy storage operation constraints: charging and discharging power, energy balance, and SOC range; power flow constraints: second-order cone relaxation constraints based on branch power flow models to ensure node voltage and branch power safety; power balance constraints: power purchase and sale balance between the main grid and distribution grid, and wind and solar curtailment constraints; New constraints related to multiple objectives include voltage safety margin constraints. V i Represents the voltage at the i-th node, and the engineering feasibility of strengthening the voltage stability target; total carbon emission constraints: Among them, P G (t) represents the output power of the conventional power source at time t. As the upper limit for carbon emissions, Limiting total carbon emissions from gas turbine units Carbon emission cap; multi-objective weight constraints: through adaptive weight coefficients , , To balance the three objectives and satisfy ; Indicates the weight of cost per kilowatt-hour. Indicates voltage weighting. Indicates the carbon emission cost weight; Finally, in the model convexity and solution adaptation module, the transformation from multi-objective to single-objective optimization is achieved using the "ε-constraint method": with the cost per kilowatt-hour as the primary objective, voltage deviation and carbon emission costs are transformed into constraints, and these constraints are adjusted accordingly. , To obtain the Pareto optimal solution This indicates the maximum permissible threshold for voltage deviation. This represents the maximum allowable threshold for carbon emission costs. Robust optimization using convex relaxation techniques from the documentation transforms non-convex terms in power flow constraints into second-order cone constraints. Combined with KKT conditions, the duality of subproblems is transformed into a mixed-integer linear form, and an adaptive column constraint generation algorithm is used to solve the problem: Main problem: Optimize energy storage planning, incorporating the "worst-case scenario" constraints returned by the subproblems; Subproblems: Solve the scenario that maximizes multi-objective costs within the dynamic uncertainty set, generating a cutting plane that is fed back to the main problem, iterating until convergence. Among them, U B L represents the upper bound of the objective function. B ε represents the lower bound of the objective function, and ε represents the convergence threshold (a constant, typically ranging from 0.01 to 0.05). Step S104: Solve using the distributed C&CG algorithm; The distributed column constraint generation algorithm is the core method of this invention for solving multi-objective robust models. Its core principle is to decompose the large-scale robust optimization problem into distributed sub-problems and a global master problem, achieving efficient solution through parallel iteration and constraint feedback. The specific details are as follows: The algorithm's distributed decomposition logic is as follows: Based on the topological characteristics of the distribution network, the distribution network is divided into several sub-regions according to electrical distance. Each sub-region is configured with edge computing nodes to solve local sub-problems. The global master problem is coordinated by the control center, which integrates the results of each sub-region and optimizes the energy storage planning scheme. The decomposition is based on the following: the wind and solar power output, load, energy storage, and other elements within the sub-regions have strong local correlations and can be solved independently for the worst-case scenario. The global master problem only needs to focus on the interaction constraints between sub-regions, reducing the problem size. The specific forms of the main problem and subproblems: The optimization objective of the main problem is to minimize the total cost of multiple objectives and determine the location of energy storage; the constraints are energy storage investment cost constraints, configuration variable constraints, the "worst-case scenario" cutting plane constraint from sub-region feedback, and cross-regional branch power constraints; the mathematical form is mixed-integer linear programming, which can be solved quickly using the Gurobi solver; in the distributed subproblems, each sub-region independently solves the operating strategy under the "worst-case scenario," with the objective of maximizing the total cost of multiple objectives, specifically optimizing variables such as energy storage charging and discharging power, gas turbine output, and demand response load within the sub-region; the constraints include dynamic uncertainty set constraints on local wind and solar power output, power balance constraints and energy storage operation constraints within the sub-region, and node voltage safety margin constraints; the solution method is based on KKT conditions to transform the duality of the subproblems into a mixed-integer linear form to avoid non-convexity; and a parallel computing framework is used to achieve synchronous solving across multiple sub-regions; The iterative process, taking into account the characteristics of distributed systems, begins with initialization settings, including setting a convergence threshold. =0.05, iteration number k=1, upper bound of objective function Lower Boundary The main problem is to solve for the initial energy storage planning scheme based on the initial forecast data. Secondly, the distributed sub-problems are solved, and the energy storage schemes for each sub-region are based on the main problem. Solve the worst-case scenario within a dynamic uncertainty set and calculate the corresponding multi-objective total cost. Sub-regions generate cutting plane constraints, which are then aggregated into the global master problem. Finally, the master problem is updated and convergence is checked. The master problem incorporates the cutting plane constraints of all sub-regions, and the optimal energy storage scheme is solved again. Update the lower bound of the objective function ; Calculate the upper bound If satisfied If the solution is k, then the solution converges and the optimal solution is output; otherwise, k = k + 1. Among them, U B L represents the upper bound of the objective function. B J represents the lower bound of the objective function. i Let represent the total cost of the multi-objective task, and k represent the iteration counter, with an initial value of 1. Key technologies for distributed solution: Gradient-guided acceleration of iteration: The gradient relationship between energy storage capacity and multi-objective cost is derived using KKT conditions. The main problem prioritizes searching for better energy storage configurations based on the gradient direction, reducing the number of iterations. Sub-region communication optimization adopts a "lazy update" strategy: Only when the worst-case scenario cost of the sub-region exceeds the current upper bound... Only when the cutting plane is fed back to the main problem can the cross-regional communication volume be reduced. When solving the worst-case scenario with the adaptation sub-problem of the multi-objective model, the joint maximization of the cost per kilowatt-hour, voltage deviation, and carbon emissions is considered simultaneously to ensure that the cutting plane constraint can accurately reflect the "worst-case" of the multi-objective. Step S105: Result verification and output; Three sets of comparative examples are designed to quantify the advantages of the proposed method: Example 1 involves no energy storage, no distributed energy storage configuration, and only day-ahead economic dispatch, verifying the necessity of energy storage configuration; Example 2 involves deterministic energy storage planning, configuring energy storage but ignoring the uncertainty of wind and solar power output, and planning based on predicted values, comparing the advantages of robust optimization; Example 3 involves the proposed method, considering multi-objective robust energy storage planning with dynamic uncertainty sets, verifying the comprehensive performance of the model; the core comparison indicators are levelized cost of electricity (LCOE), intraday balancing cost, voltage deviation, and computation time. The impact of the core parameters affecting the model on the results is analyzed to verify the model's stability: wind and solar uncertainties. :set up =0,3,6,9,12,15,18, Analyze the variation of cost per kilowatt-hour with the range of uncertainty, such as As the capacity increases, the energy storage configuration capacity also increases, leading to higher costs. The prediction error range is set at 0% to 40%, verifying the adaptability of the dynamic uncertainty set to different error scenarios. Energy storage investment costs are set at 1000-3500 yuan / (kW·h) per unit capacity, analyzing the impact of cost on the energy storage configuration capacity. Engineering feasibility also needs to be verified, including network constraint satisfaction: verifying the node voltage and branch power under the optimal scheme, and whether the node voltage is within [0.95, 1.05] pu to ensure the safe operation of the distribution network. Extreme scenario testing simulates extreme weather to verify whether the energy storage charging and discharging strategy can respond quickly and maintain system stability. After the model converges, the following core results are output, providing a direct reference for energy storage planning in distribution networks: Optimal energy storage configuration scheme: The location and capacity of each node are clearly defined, and the energy storage configuration results are detailed; Investment cost details: Annualized investment cost of energy storage and its proportion, such as a total investment of 1.04 million yuan, with capacity cost accounting for 65%; Operational strategy parameters: Energy storage charging and discharging plan: charging and discharging power curves of energy storage at each node within 24 hours; Other equipment scheduling schemes: gas turbine output, demand response load transfer, and main grid power purchase and sales plan; Economic and reliability indicators: Cost per kilowatt-hour: total cost per kilowatt-hour and the percentage of each component; Voltage and carbon emission optimization results: maximum voltage deviation, total carbon emissions; Model convergence process data: Iteration curve: Lower bound of the main problem Upper bound of the AND problem The convergence trend is used to verify the stability of the algorithm; the worst-case scenario description is: the final convergent wind and solar power output combination is used to clarify the robustness boundary of the model. Through the synergistic effect of the five steps S101-S105, clear conclusions can be drawn and multi-dimensional technical effects can be achieved, as detailed below: Key findings include: dynamic uncertainty sets can accurately adapt to fluctuations in new energy output; multi-objective robust models achieve optimal synergy between "economy, safety, and low carbon"; distributed C&CG algorithms significantly improve the solution efficiency of large-scale systems; and high-precision power flow constraints ensure the engineering reliability of planning schemes. The achieved results include: improved economic efficiency: significantly reduced cost per kilowatt-hour and total lifecycle costs; enhanced reliability: improved ability to cope with uncertainties and voltage stability; optimized low-carbon performance: reduced carbon emissions and environmental costs of gas turbine units; and improved engineering practicality: improved feasibility of the solution and scalability of the algorithm. The five steps form a closed loop of "data-driven, model optimization, efficient solution, and verification and implementation", ultimately achieving "economic, safe, and low-carbon coordinated optimization of distributed energy storage in the distribution network under the uncertainty of new energy output".

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