A multi-objective collaborative optimization control method and system for energy storage systems

Abstract

This invention discloses a multi-objective collaborative optimization control method and system for energy storage systems. The method establishes an optimization problem model encompassing three objectives: economic cost, battery life degradation, and deviation from safety constraints. Local state data and external environmental data are fused to form a real-time optimization problem. The upper layer automatically determines the Pareto optimal weight vector by solving the minimum norm convex combination of the gradient vectors of each objective, and obtains a uniformly covered Pareto optimal solution set by combining angle sector partitioning and hole-oriented repair. The middle layer achieves efficient collaboration through a distributed ADMM that allocates adaptive step sizes based on the rated capacity of each energy storage unit and embeds a recursive momentum estimator, outputting a globally coordinated charge and discharge plan. This invention solves the problems of manually preset multi-objective search weights, uneven solution set coverage, low convergence efficiency of distributed collaborative control of multiple energy storage units, and poor robustness under extreme operating conditions.

Description

Technical Field

[0001] This invention relates to the field of power system optimization control technology, specifically to a multi-objective collaborative optimization control method and system for energy storage systems, applicable to collaborative optimization scheduling and robust execution control of novel power systems containing multiple energy storage units under various conflicting operational objectives. Background Technology

[0002] Energy storage systems are a crucial component of new power systems, undertaking key functions such as peak shaving and valley filling, mitigating fluctuations in renewable energy sources, and providing ancillary services. With the rapid growth of installed electrochemical energy storage capacity, the optimized operation and control of energy storage systems has become a core technical issue in power system dispatching and energy management. The optimized control of energy storage systems involves multiple conflicting control objectives, including minimizing economic operating costs, minimizing battery life degradation losses, and satisfying system safety constraints, making it a typical multi-objective optimization problem.

[0003] Currently, multi-objective optimization control of energy storage systems typically employs weighted summation, ε-constraint methods, or evolutionary algorithms such as NSGA-II. Weighted summation transforms multiple objectives into single objectives by pre-setting weights, but Pareto optimal solutions under different weight combinations require repeated calculations, resulting in low efficiency and difficulty in ensuring the complete coverage of the solution set. ε-constraint methods convert some objectives into constraints, making them highly sensitive to the selection of constraint thresholds. Evolutionary algorithms like NSGA-II rely heavily on large-scale population iterations for solution quality, leading to insufficient real-time performance. In multi-energy storage unit collaborative scenarios, each unit typically employs centralized unified optimization, facing problems such as high communication overhead and high risk of single-point failures.

[0004] The prior art most relevant to this invention employs a hierarchical optimization framework: the upper layer performs day-ahead planning optimization on a long-term time scale, while the lower layer performs real-time tracking control on a short-term time scale. The upper layer typically uses a mixed-integer linear programming solver, while the lower layer uses model predictive control (MPC) for rolling optimization. The information exchange between the three layers is as follows: the upper layer sends the charging and discharging plan to the lower layer for execution, and the lower layer sends status feedback back to the upper layer to update parameters.

[0005] However, the aforementioned existing technologies have at least the following two drawbacks: First, the upper-level multi-objective search uses a weighted summation method with fixed preset weights, which cannot adaptively adjust the priority of each objective according to real-time operating conditions. At the same time, the Pareto front solution set is unevenly distributed in different target spatial regions, with some coverage gaps, affecting the operator's selection of the globally optimal strategy. Second, the lower-level multi-energy storage unit collaboration relies on centralized communication and unified scheduling. The use of a globally uniform step size results in the convergence speed being limited by the unit with the smallest capacity. Furthermore, the single-degree solution is not robust enough under extreme operating conditions such as severe wind and solar prediction errors or sudden events, and is prone to getting trapped in local optima. Summary of the Invention

[0006] To address the aforementioned problems in existing technologies, this invention provides a multi-objective collaborative optimization control method and system for energy storage systems, thereby solving the technical problems of insufficient adaptability and uneven solution set coverage in multi-objective Pareto front search, as well as low distributed collaborative convergence efficiency and poor robustness under extreme conditions in existing technologies.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A multi-objective collaborative optimization control method for an energy storage system includes: Based on the operating parameters of the energy storage system, a multi-objective optimization problem model with charging and discharging power as the decision variable is established. The multi-objective optimization problem model includes an economic cost objective function, a battery life degradation objective function, a safety constraint deviation penalty function, and a set of energy storage operation constraints. Collect local state data and external environment data of the energy storage system, merge the local state data and the external environment data to update the parameters of the multi-objective optimization problem model, and obtain the real-time optimization problem; For the real-time optimization problem, the gradient vectors of each objective function with respect to the decision variables are calculated, and the minimum norm convex combination of each gradient vector is solved to obtain the Pareto optimal weight vector. Based on this, the real-time optimization problem is solved by scalarization to obtain the Pareto optimal solution. The objective space is divided into angular sectors and sparse void regions are detected. The solution is supplemented in the direction of the void center, and the supplemented solutions are merged to obtain the Pareto optimal solution set. The selected reference solution in the Pareto optimal solution set is decomposed into local subproblems of each energy storage unit. An adaptive step size is assigned to each energy storage unit based on its rated capacity. Local optimization is performed by combining recursive momentum estimation. Each unit exchanges local solutions with its communication neighbors and updates the consistency dual variable. The iteration continues until the consistency deviation meets the convergence condition, and a globally coordinated charging and discharging plan is obtained. A candidate charge-discharge sequence population is generated using the global coordinated charge-discharge plan as a seed. The fitness of the population is evaluated using the selected Pareto weight vector. Selection, crossover, and mutation evolution operations are performed on the population. The first power value of the optimal fitness sequence after evolution is taken as the execution command for the current control cycle. The state deviation is calculated and fed back to the next optimization cycle to achieve rolling closed-loop control.

[0008] Furthermore, the step of establishing a multi-objective optimization problem model with charging and discharging power as decision variables based on the operating parameters of the energy storage system includes: establishing charging and discharging power decision variables for each control period based on the operating parameters of the energy storage system, including battery rated capacity, current state of charge, charging and discharging efficiency, and charging and discharging power upper limit, to obtain the energy storage system operation decision space; constructing an economic cost objective function, a battery life degradation objective function, and a safety constraint deviation penalty function for the operation decision space, wherein the economic cost objective function includes a weighted sum of grid arbitrage revenue, ancillary service compensation revenue, and charging and discharging loss cost; the battery life degradation objective function quantifies cyclic aging loss based on the ampere-hour throughput model; and the safety constraint deviation penalty function uses state of charge exceeding limits and power exceeding limits as penalty terms to obtain a three-objective optimization vector; and superimposing the set of energy storage operation constraints consisting of state of charge upper and lower bound constraints, charging and discharging mutual exclusion constraints, daily charging and discharging frequency constraints, and power ramp-up rate constraints onto the three-objective optimization vector to obtain the multi-objective optimization problem model.

[0009] Furthermore, the process of collecting local state data and external environment data of the energy storage system, fusing the local state data and the external environment data, and then updating the parameters of the multi-objective optimization problem model to obtain a real-time optimization problem includes: based on the local sensor network of the energy storage system, collecting the current state of charge, battery temperature, and health status in real time to obtain a local state vector; based on an external data interface, acquiring the current electricity price signal, load forecast curve, and new energy output forecast curve to obtain an external environment data vector; and merging the local state vector and the external environment data vector according to timestamps to update the parameters in the multi-objective optimization problem model to obtain the real-time optimization problem.

[0010] Further, for the real-time optimization problem, calculating the gradient vectors of each objective function with respect to the decision variables and solving the minimum norm convex combination of each gradient vector to obtain the Pareto optimal weight vector includes: for the real-time optimization problem, calculating the gradient vectors of the economic cost objective function, the battery life degradation objective function, and the safety constraint deviation penalty function with respect to the charge / discharge power decision variables at the current decision point to obtain a set of objective gradients; using the set of objective gradients as input, solving the optimization problem that minimizes the weighted norm of the convex combination coefficients of each gradient vector, wherein the convex combination coefficients satisfy the non-negativity constraint and the sum of the coefficients is 1, to obtain the Pareto optimal weight vector; applying the Pareto optimal weight vector to the three-objective optimization vector for scalarization, and using a sequential quadratic programming solver to solve the real-time optimization problem to obtain the Pareto optimal solution and its corresponding objective vector.

[0011] Further, the process of dividing the target space into angular sectors and detecting sparse void regions, supplementing the solution in the direction of the void center, and merging the supplemented solutions to obtain the Pareto optimal solution set includes: using the ideal point formed by the minimum values ​​of the three objective functions as the origin, mapping the target vectors corresponding to each solution on the current Pareto front to direction vectors on a unit sphere, dividing the unit sphere into several angular sectors according to the equal area projection of the sphere, retaining the solution with the best non-dominated sort in each angular sector as the representative solution of that sector, and obtaining the representative solution set for each sector; for each sector... For each region, a representative solution set is defined. The angle between the direction vectors of adjacent representative solutions is calculated. The sector with the largest angle between adjacent representative solutions is selected as the sparse void region. The angle bisector of the direction vectors of the representative solutions on both sides of the void region is taken as the void center direction, thus obtaining the void region identifier and the void center direction. Several sets of supplementary weights are generated by sampling in the neighborhood of the void center direction according to a Gaussian distribution. Standardization is performed on each set of supplementary weights to obtain supplementary Pareto optimal solutions. The supplementary Pareto optimal solutions are merged into the current solution set to obtain the uniformly covered Pareto optimal solution set.

[0012] Further, the step of allocating adaptive step sizes based on the rated capacity of each energy storage unit and performing local optimization updates in conjunction with recursive momentum estimation includes: for each energy storage unit, multiplying the ratio of the unit's rated capacity to the maximum rated capacity among all units by a step size scaling factor to obtain the unit's adaptive step size, wherein the step size scaling factor ranges from 0.01 to 0.1; for each energy storage unit, initializing the recursive momentum vector as a zero vector, and during each local optimization iteration, recursively updating the recursive momentum vector using the gradient difference between the current iteration and the previous iteration with a decay coefficient decreasing with the number of iterations, and superimposing the updated recursive momentum vector into the adaptive step size gradient update to obtain a local solution with fused momentum correction; exchanging the local solution with the local solutions of the communicating neighbors, updating the consistency dual variable according to the difference between the two, and iterating cyclically until the consistency deviation between each unit is less than the convergence threshold to obtain the global coordinated charging and discharging plan.

[0013] Further, the step of performing selection, crossover, and mutation evolution operations on the population includes: taking the candidate charge / discharge sequence population as input, sorting them by fitness from smallest to largest, retaining a preset proportion of candidate sequences with the highest fitness ranking, to obtain a retained sequence set; randomly pairing parent sequences from the retained sequence set, exchanging randomly selected continuous time segments from the two parent sequences with a preset crossover probability to generate offspring sequences, wherein the length of the continuous time segment is one-quarter to one-half of the predicted time domain length; applying a Gaussian perturbation to each power value of the offspring sequence with a preset mutation probability, and trimming the perturbed power value to a feasible power range to obtain an evolved candidate sequence population; taking the first-step power value of the candidate sequence with the best fitness in the evolved candidate sequence population as the execution instruction for the current control cycle, calculating a state deviation vector composed of the state of charge tracking deviation and the power execution deviation based on the actual execution result of the execution instruction, and feeding the state deviation vector back to the initial conditions of the next optimization cycle to obtain a continuously optimized control sequence after rolling correction.

[0014] Preferably, when computing resources are limited, the population size is set to 1 and the number of generations is set to 0, the selection, crossover and mutation evolution operations are skipped, and the first power value of the global coordinated charge and discharge plan is directly issued as the execution command of the current control cycle to obtain the control output under the degenerate single-solve mode.

[0015] A multi-objective collaborative optimization control system for an energy storage system includes: a model building module, used to establish a multi-objective optimization problem model with charging and discharging power as decision variables based on the operating parameters of the energy storage system; the multi-objective optimization problem model includes an economic cost objective function, a battery life degradation objective function, a safety constraint deviation penalty function, and a set of energy storage operation constraints; a data sensing module, used to collect local state data and external environmental data of the energy storage system, and update the parameters of the multi-objective optimization problem model after fusing the local state data and the external environmental data to obtain a real-time optimization problem; a multi-objective search module, used to calculate the gradient vector of each objective function with respect to the decision variables for the real-time optimization problem, solve for the minimum norm convex combination of each gradient vector to obtain the Pareto optimal weight vector, and scalarize the real-time optimization problem accordingly to obtain the Pareto optimal solution; and to divide the objective space into angular sectors and detect... The system measures sparse void regions and provides directional supplementary solutions in the direction of the void center. These supplementary solutions are then merged to obtain the Pareto optimal solution set. A distributed coordination module decomposes the selected reference solution in the Pareto optimal solution set into local subproblems for each energy storage unit. An adaptive step size is assigned to each unit based on its rated capacity, and local optimization updates are performed using recursive momentum estimation. Each unit exchanges local solutions with its communication neighbors and updates its consistency dual variables. Iteration continues until the consistency deviation meets the convergence condition, resulting in a globally coordinated charge-discharge plan. A rolling execution module generates a candidate charge-discharge sequence population using the globally coordinated charge-discharge plan as a seed. The fitness of the population is evaluated using the selected Pareto weight vector. Selection, crossover, and mutation evolution operations are performed on the population. The first power value of the optimal fitness sequence after evolution is used as the execution command for the current control cycle. The state deviation is calculated and fed back to the next optimization cycle, achieving rolling closed-loop control.

[0016] Compared with the prior art, the present invention has the following technical effects: First, by solving the minimum norm convex combination of each target gradient vector, the Pareto ascent direction weights are automatically determined, transforming the weight selection from manual preset to automatic gradient calculation, significantly reducing the cost of manual parameter tuning; combined with the angle sector division and hole-oriented repair mechanism, the Pareto optimal solution set is ensured to be uniformly covered in all regions of the target space, providing operators with a comprehensive and balanced decision reference.

[0017] Second, by distributing the ADMM penalty step size proportionally to the rated capacity of each energy storage unit, the laggard effect caused by the globally uniform step size is eliminated; the embedded STORM recursive momentum estimator achieves variance reduction with only O(1) storage overhead, effectively suppressing convergence oscillations caused by stochastic gradient noise, and significantly improving the convergence speed and robustness of distributed collaboration.

[0018] Third, population evolution search replaces traditional single-degree value solving. In each rolling control cycle, multi-directional global exploration effectively avoids getting trapped in local optima. Under extreme conditions, population diversity maintains global search capability, significantly enhancing robustness to uncertainty compared to traditional MPC schemes. The embedded degradation strategy ensures the basic availability of the system in scenarios with limited computing resources. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the overall process of the multi-objective collaborative optimization control method for energy storage systems provided in an embodiment of the present invention. Detailed Implementation

[0020] Example 1: As Figure 1 As shown, a multi-objective collaborative optimization control method for an energy storage system includes: S1: Based on the operating parameters of the energy storage system, establish a multi-objective optimization problem model with charging and discharging power as the decision variable. The multi-objective optimization problem model includes an economic cost objective function, a battery life degradation objective function, a safety constraint deviation penalty function, and a set of energy storage operation constraints.

[0021] In this embodiment of the invention, the operating parameters of the energy storage system are the basic inputs for constructing a multi-objective optimization problem model, including key parameters such as battery rated capacity, current state of charge (SOC), charge / discharge efficiency, and upper limit of charge / discharge power. The charge / discharge power values ​​for each control period are used as decision variables to construct the operational decision space of the energy storage system. On this decision space, an economic cost objective function, a battery life degradation objective function, and a safety constraint deviation penalty function are established respectively, forming a three-objective optimization vector. These are then superimposed with a set of operational constraints, including upper and lower bounds of the state of charge and charge / discharge mutual exclusion constraints, to obtain a complete multi-objective optimization problem model.

[0022] It should be noted that there is an inherent conflict among the three objective functions: maximizing economic efficiency may require frequent deep charging and discharging, which contradicts the goal of minimizing lifetime; maximizing safety requires maintaining the state of charge (SOC) in the intermediate range, which conflicts with the need for large-scale charging and discharging to maximize arbitrage. It is precisely because of this multi-objective conflict structure that simply using fixed weights cannot consistently provide the optimal decision under different operating conditions. This is the fundamental motivation for introducing a gradient adaptive weighting mechanism in this invention.

[0023] S2: Collect local state data and external environment data of the energy storage system, merge the local state data and the external environment data, and update the parameters of the multi-objective optimization problem model to obtain the real-time optimization problem.

[0024] Specifically, local state data is collected in real time by the local sensor network of the energy storage system, including the current state of charge, battery temperature, and health status. External environmental data is obtained through external data interfaces such as the SCADA system and the day-ahead forecasting platform, including electricity price signals, load forecast curves, and renewable energy output forecast curves. After aligning and fusing the local state data and external environmental data by timestamp, the relevant parameters in the multi-objective optimization problem model are updated, thereby obtaining a real-time optimization problem that reflects the actual operating status of the current system.

[0025] S3: For the real-time optimization problem, calculate the gradient vector of each objective function with respect to the decision variables, solve the minimum norm convex combination of each gradient vector to obtain the Pareto optimal weight vector, and then perform scalarization to solve the real-time optimization problem to obtain the Pareto optimal solution; divide the target space into angular sectors and detect sparse void regions, supplement the solution in the direction of the void center, and merge the supplemented solutions to obtain the Pareto optimal solution set.

[0026] In this embodiment of the invention, by calculating the gradient vectors of each objective function relative to the charging and discharging power decision variables and solving the optimization problem that minimizes the convex combination norm of each gradient vector, the Pareto ascending direction weights that can simultaneously improve all objectives are automatically determined, avoiding the subjectivity of manually preset weights. After obtaining the Pareto optimal weight vector, the real-time optimization problem is scalarized and solved using a sequential quadratic programming (SQP) solver to obtain a Pareto optimal solution and its objective vector. To ensure the uniformity of the solution set coverage in each region of the Pareto front, each Pareto solution is further mapped to a unit sphere with the ideal point as the origin. Angle sectors are divided according to the equal area projection of the sphere. Sparse void regions with the largest angle between adjacent representative solutions are detected. Weights are supplemented and solved in the neighborhood of the void center direction. The supplemented solutions are merged into the current solution set, and finally, a uniformly covered Pareto optimal solution set is obtained.

[0027] S4: Decompose the selected reference solution in the Pareto optimal solution set into local subproblems of each energy storage unit, allocate an adaptive step size to each energy storage unit based on its rated capacity, perform local optimization updates in conjunction with recursive momentum estimation, exchange local solutions with each unit and update the consistency dual variable, iterate until the consistency deviation meets the convergence condition, and obtain the global coordinated charging and discharging plan.

[0028] It should be noted that after selecting a reference solution from the Pareto optimal solution set, the global charge-discharge plan is decomposed into local subproblems for each energy storage unit according to their unit numbers. Consistency auxiliary variables and consistency dual variables are introduced, transforming the global consistency constraint into a locally augmented Lagrange problem that can be solved independently. Each unit determines its adaptive step size by multiplying its rated capacity by the ratio of its own rated capacity to the largest rated capacity among all units, using a step size scaling factor. This ensures that large-capacity units receive larger step sizes to accelerate convergence, while small-capacity units receive smaller step sizes to maintain stability. Simultaneously, each unit maintains a recursive momentum vector, which is recursively updated using the gradient difference between the current and previous iterations, effectively suppressing stochastic gradient noise. Each unit exchanges local solutions with its communicating neighbors and updates its dual variables, iterating cyclically until the consistency deviation meets the convergence threshold, outputting a globally coordinated charge-discharge plan.

[0029] S5: Generate a candidate charge-discharge sequence population using the global coordinated charge-discharge plan as the seed, evaluate the population fitness using the selected Pareto weight vector, perform selection, crossover and mutation evolution operations on the population, take the first power value of the optimal fitness sequence after evolution as the execution command for the current control cycle, calculate the state deviation and feed it back to the next optimization cycle to achieve rolling closed-loop control.

[0030] In this embodiment of the invention, a globally coordinated charge-discharge plan is used as the seed sequence, and multiple candidate charge-discharge power sequences are randomly generated within the feasible region centered on it to form an initial population. The Pareto weight vector passed from the upper layer is used to perform a weighted multi-objective fitness evaluation on each candidate sequence. Subsequently, a selection-crossover-mutation evolutionary operation is performed on the population: the selection operation retains the sequence with the highest fitness ranking; the crossover operation randomly pairs parent sequences and exchanges continuous time segments with a certain probability; the mutation operation applies a Gaussian perturbation to the power value and prunes it to a feasible range. After several generations of evolution, the first power value of the sequence with the best fitness is taken as the execution command. After execution, the state deviation vector composed of the state of charge tracking deviation and the power execution deviation is calculated and fed back to the initial conditions of the next optimization cycle, forming a rolling closed-loop control loop.

[0031] It should be understood that the "three-layer progressive" architecture design adopted in this invention has the characteristics of overall synergistic efficiency: the upper-layer Pareto search outputs not only a set of optimal solutions, but also the corresponding weight vectors; the middle-layer distributed collaboration receives the weight vectors as a reference, ensuring that the collaborative goals of each unit are consistent with the upper-layer decision; the lower-layer evolutionary execution directly evaluates fitness using the upper-layer weight vectors, ensuring the consistency of goals from decision-making to execution. Information is transmitted between the three layers through a dual-channel approach of reference solutions and weight vectors, which has a stronger goal alignment capability compared to simply transmitting plan values.

[0032] Example 2: Based on Example 1, the step of establishing a multi-objective optimization problem model with charging and discharging power as decision variables according to the operating parameters of the energy storage system includes: S1.1: Based on the operating parameters of the energy storage system, including the rated capacity of the battery, the current state of charge, the charging and discharging efficiency, and the upper limit of the charging and discharging power, establish the decision variables of the charging and discharging power for each control period to obtain the operating decision space of the energy storage system.

[0033] In this embodiment of the invention, the charging power and discharging power of each control period t (t=1,2,…,T) within the planning time domain T are used as independent decision variables. The SOC evolution relationship for each period is defined in conjunction with parameters such as battery rated capacity and charging / discharging efficiency. Specifically, charging and discharging power are established as independent non-negative decision variables, and their product is constrained to zero through mutual exclusion constraints, thereby fully characterizing the feasible charging and discharging operation space of the energy storage system. The selection of the planning time domain T is determined according to the application scenario. In day-ahead optimization scenarios, a 24-hour period (with 96 periods in 15-minute control steps) is typically used. In real-time rolling optimization scenarios, a rolling prediction time domain of 1 to 4 hours is typically used.

[0034] S1.2: For the aforementioned operational decision space, construct the economic cost objective function, the battery life degradation objective function, and the safety constraint deviation penalty function respectively to obtain a three-objective optimization vector.

[0035] In practice, the economic cost objective function comprehensively considers three types of economic quantities: first, grid arbitrage revenue, which is the price difference revenue obtained by charging during periods of lower electricity prices and discharging during periods of higher electricity prices; second, ancillary service compensation revenue, including capacity and electricity compensation obtained from grid ancillary services such as frequency regulation and peak shaving; and third, energy loss costs during charging and discharging, which is the electricity cost converted into electricity price costs due to insufficient charging and discharging efficiency. These three types of economic quantities are summed according to their respective weights to form the economic cost objective function. The economic cost objective function aims to minimize the net cost of charging and discharging (loss costs minus all types of revenue).

[0036] The battery life degradation objective function is constructed based on the ampere-hour throughput model. The ampere-hour throughput model is a widely adopted method in the industry for quantifying the cyclic aging of electrochemical energy storage batteries. Its core idea is that the cyclic aging loss of the battery is proportional to the total ampere-hours flowing through the battery during charging and discharging. Specifically, the charging power and discharging power of each control period within the planning time domain are divided by the nominal voltage to convert them into ampere-hour flow rates. These are then accumulated to obtain the total ampere-hour throughput within the time domain. This total throughput is then multiplied by a unit ampere-hour aging coefficient (provided by the battery manufacturer or calibrated experimentally) to obtain an estimate of the battery life degradation loss within that time domain, which serves as the life degradation objective function. It should be noted that the advantages of the ampere-hour throughput model lie in its simple calculation, intuitive physical meaning, and lower computational cost compared to more complex fatigue life models such as rainflow counting, making it suitable for real-time control optimization in online optimization scenarios.

[0037] The safety constraint deviation penalty function quantifies the degree of safety boundary violation using soft constraints. The State of Charge (SOC) exceedance penalty term calculates the sum of deviations where the SOC exceeds the upper or lower limits for each time period; the power exceedance penalty term calculates the sum of deviations where the charging / discharging power exceeds the rated power upper limit. These two penalty terms are multiplied by their respective penalty coefficients and then summed to form the safety constraint deviation penalty function. The purpose of using soft constraints instead of hard constraints is to ensure that the optimization problem still has a feasible solution when the constraints are extremely tight, while simultaneously driving the optimization solver to compress constraint violations to near-zero levels through a larger penalty coefficient (usually a value much larger than the economic benefit). These three factors together constitute the three-objective optimization vector.

[0038] S1.3: The set of energy storage operation constraints, consisting of upper and lower bounds of state of charge, mutual exclusion of charging and discharging, daily charging and discharging frequency constraints, and power ramp-up rate constraints, is superimposed onto the three-objective optimization vector to obtain the multi-objective optimization problem model.

[0039] Among these constraints, the State of Charge (SOC) upper and lower bounds stipulate that the SOC must be within the allowable range in each time period, typically with a lower limit of 10% to 20% and an upper limit of 80% to 90%, to avoid irreversible damage to the battery from overcharging and over-discharging. The charge-discharge mutual exclusion constraint ensures that charging and discharging power cannot be positive simultaneously within the same time period by introducing 0-1 integer variables or complementary relaxation conditions. The daily charge-discharge cycle constraint limits the number of charge-discharge cycles within the planning time domain to within the maximum daily cycle recommended by the battery manufacturer by accumulating the number of charging direction changes or introducing binary state switching variables, thus achieving protection throughout the battery's lifespan. The power ramp-up rate constraint limits the change in charging and discharging power between adjacent control periods to no more than a certain percentage of the rated power (typically 20% to 50% per period), to meet the slope response limits of the power converter and grid connection regulations. Superimposing these four types of constraints onto a three-objective optimization vector yields a complete multi-objective optimization problem model.

[0040] Example 3: Based on Example 1, the local state data and external environment data of the energy storage system are collected, and the parameters of the multi-objective optimization problem model are updated after fusing the local state data and the external environment data to obtain a real-time optimization problem, including: S2.1: Based on the local sensor network of the energy storage system, the current state of charge, battery temperature and health status are collected in real time to obtain the local state vector.

[0041] In this embodiment of the invention, the local sensor network includes voltage and current sensors, a temperature sensor, and a battery management system (BMS) communication interface. The voltage and current sensors collect real-time port voltage and charge / discharge current, and calculate the current state of charge (SOC) using the ampere-hour integral method. The temperature sensor collects the real-time temperature of individual battery cells and the module. Temperature data plays a role in optimization in two ways: firstly, when the temperature is too high, the aging coefficient in the lifetime degradation objective function needs to be corrected according to the temperature-aging relationship curve (Arrhenius equation); secondly, extreme temperatures (such as high temperatures exceeding 45°C or low temperatures below 0°C) can dynamically narrow the upper limit constraint on charge / discharge power. This correction is achieved by updating the constraint parameters in the multi-objective optimization problem model. The BMS communication interface reads the estimated state of health (SOH) value. SOH is used to correct the battery's rated capacity (actual usable capacity equals rated capacity multiplied by SOH), ensuring that the SOC calculation in the optimization model is consistent with the actual degradation state of the battery. All of the above information together constitute the local state vector.

[0042] S2.2: Based on the external data interface, obtain the current electricity price signal, load forecast curve and new energy output forecast curve to obtain the external environment data vector.

[0043] Optionally, the external data interface includes a Supervisory Control and Data Acquisition (SCADA) system interface and a day-ahead forecasting platform interface. The SCADA interface acquires real-time time-of-use electricity price signals for the current grid nodes, including peak, normal, and valley electricity prices, as well as real-time spot prices (if market conditions permit). The day-ahead forecasting platform interface acquires load forecast curves and output forecast curves for renewable energy sources such as photovoltaics and wind power within the future planning time domain, with the time resolution of the forecast curves consistent with the control period step size. In an optional implementation, if the day-ahead forecasting platform is unavailable, a statistical forecasting method based on historical data (such as exponential smoothing or a seasonal ARIMA model) can be used to generate forecast curves locally as an alternative. The above data collectively constitute an external environment data vector, providing accurate external boundary conditions for optimization solutions.

[0044] S2.3: Align and merge the local state vector with the external environment data vector according to the timestamp, update the parameters in the multi-objective optimization problem model, and obtain the real-time optimization problem.

[0045] The timestamp alignment and fusion operation ensures that locally collected data and external forecast data are synchronized and consistent in the time dimension, avoiding parameter mismatch problems caused by inconsistent sampling times. The fused data is used to update the initial SOC (replacing the model's initial value with the current collected value), electricity price sequence (replacing it with the latest acquired time-of-use electricity price), load forecast, and renewable energy output forecast (replacing it with the latest forecast value) in the multi-objective optimization problem model, resulting in a real-time optimization problem that reflects the current actual operating environment. When the local state collection frequency is inconsistent with the external data update frequency, nearest neighbor interpolation is used to align the low-frequency data in time, ensuring effective fusion of the two types of data.

[0046] Example 4: Based on Example 1, for the real-time optimization problem, the gradient vector of each objective function with respect to the decision variables is calculated, and the minimum norm convex combination of each gradient vector is solved to obtain the Pareto optimal weight vector, including: S3.1: For the real-time optimization problem, at the current decision point, calculate the gradient vectors of the economic cost objective function, the battery life degradation objective function, and the safety constraint deviation penalty function relative to the charge / discharge power decision variable, respectively, to obtain the set of gradients for each objective.

[0047] In this embodiment of the invention, the calculation of the gradient vector is the starting point of the Pareto ascent mechanism. For the analytically differentiable parts of the three objective functions (such as the economic cost objective function and the lifetime degradation objective function), the accurate gradient is calculated using symbolic differentiation or automatic differentiation tools; for the parts containing discontinuities or piecewise functions (such as the out-of-bounds judgment in the safety constraint deviation penalty function), the subgradient method is used to calculate the gradient approximation. The dimension of the gradient vector is consistent with the dimension of the decision variables, equal to the sum of the number of charging power variables and the number of discharging power variables in the planning time domain T (2T dimensions in total). The physical meaning of each dimension component in the gradient vector is: at the current decision point, increasing the charging and discharging power by one unit for the corresponding time period corresponds to the rate of change of the objective function value.

[0048] S3.2: Using the target gradient sets as input, solve the optimization problem that minimizes the weighted norm of the convex combination coefficients of each gradient vector, wherein the convex combination coefficients satisfy the non-negativity constraint and the sum of each coefficient is 1, to obtain the Pareto optimal weight vector.

[0049] The adaptive weight calculation mechanism based on the Pareto ascent direction is one of the core inventive points of this invention. Its technical definition is: the Pareto ascent direction refers to the optimal common descent direction at the current decision point that simultaneously reduces the values ​​of all objective functions (i.e., moves simultaneously in the gradient descent directions of all objective functions). When such a direction exists, the current point has not yet reached the Pareto front and can continue to improve; when such a direction does not exist (the minimum norm convex combination results in a zero vector), the current point is already a Pareto stationary point, located on the Pareto front.

[0050] The technical principle of the minimum norm convex combination optimization problem is as follows. Let the gradient vectors of the three objective functions be g1, g2, and g3 (all 2T-dimensional column vectors). Find the convex combination coefficients α1, α2, and α3 (satisfying α1+α2+α3=1 and α1, α2, α3≥0) such that the Euclidean norm ||d||² of the weighted gradient vector d=α1·g1+α2·g2+α3·g3 is minimized. This problem is equivalent to a standard constrained quadratic programming (QP) problem, which can be solved efficiently in O(1) (constant number of iterations relative to the dimension of the decision variables) using the interior-point method or the effective set method, with extremely low computational cost. The solved α*=(α1*, α2*, α3*) is the Pareto optimal weight vector, whose physical meaning is: at the current decision point, the three objective functions are weighted and scalarized with weight α*, and the gradient of the resulting single objective function points to the Pareto optimal improvement direction at the current point.

[0051] Compared to traditional fixed-weight methods, the core advantage of the Pareto optimal weight vector lies in the fact that the weights are entirely determined by the gradient geometry at the current decision point, automatically reflecting the improvement potential and conflict degree of each objective under the current operating conditions. When electricity prices fluctuate drastically, the gradient magnitude of the economic objective is larger, and the corresponding weight automatically increases; when the State of Charge (SOC) approaches the boundary, the gradient magnitude of the safety constraint deviation penalty function is larger, and the corresponding weight automatically increases, thus achieving adaptive adjustment of the priority of each objective according to the operating conditions. Taking a typical three-energy storage scenario as an example, under normal operating conditions (moderate SOC, stable electricity price), the adaptive weights converge to an equilibrium distribution (approximately α1=α2=α3≈1 / 3); during the peak arbitrage window (when the difference between high and low electricity prices exceeds 0.5 yuan / kWh), α1 automatically rises to around 0.65; when the SOC approaches the lower limit (below 15%), α3 automatically rises to above 0.7, and the system automatically switches to a safety-first mode, effectively avoiding the lag and imbalance problems of manually fixed weights when switching in the above scenarios.

[0052] S3.3: Apply the Pareto optimal weight vector to the three-objective optimization vector for scaling, and use a sequential quadratic programming solver to solve the real-time optimization problem to obtain the Pareto optimal solution and its corresponding objective vector.

[0053] It should be understood that by applying the Pareto optimal weight vector to the three-objective optimization vector, the multi-objective problem is transformed into a single-objective scalar problem. Then, the SQP solver is used to efficiently solve the problem by fully utilizing the gradient information of the objective function and constraints, obtaining the Pareto optimal solution that satisfies all operational constraints and its corresponding three-dimensional objective vector. The SQP solver is selected based on its superlinear convergence speed for medium-scale (hundreds of decision variables, hundreds to thousands of constraints) nonlinear programming problems, and its ability to stably complete the solution within the control period (typically 5 to 15 minutes). If the objective function contains integer constraints (such as charging / discharging mutual exclusion constraints modeled with integer variables), a mixed-integer SQP (MISQP) or a relaxation continuity method can be used to handle integer variables.

[0054] Example 5: Based on Example 1, the target space is divided into angular sectors and sparse void regions are detected. A directional supplementary solution is then obtained in the direction of the void center. The supplementary solutions are then merged to obtain the Pareto optimal solution set, including: S3.4: Using the ideal point formed by the minimum values ​​of the three objective functions as the origin of the coordinate system, map the objective vectors corresponding to each solution on the current Pareto front to the direction vectors on the unit sphere. Divide the unit sphere into several angular sectors according to the equal area projection of the sphere. In each angular sector, retain the solution with the best non-dominated sort as the representative solution of the sector, and obtain the representative solution set of each sector.

[0055] In this embodiment of the invention, the technical definition of the angle sector partitioning mechanism is as follows: Using the ideal point formed by the corresponding objective values ​​when each objective function is independently minimized in the three-dimensional target space as the origin (i.e., reference datum), the objective vector of each Pareto solution is translated to a coordinate system with the ideal point as the origin, and then normalized to a unit vector. This maps the solution set on the Pareto front from the three-dimensional target space to the first quadrant of a unit sphere (since all three objectives are minimized, all direction vector components are non-negative). Equal-area projection of the sphere ensures that each angle sector occupies an equal area on the sphere, thus unbiasedly measuring the coverage density of the solution set in each direction and avoiding the problem of extremely small sectors near the spherical poles caused by equal-angle partitioning. The recommended value range for the number of angle sectors N_sec is 8 to 16, with a smaller value (e.g., 8) for smaller solution sets (less than 20 solutions) and a larger value (e.g., 16) for larger solution sets (more than 50 solutions). Within each sector, the solution with the best non-dominated sort (i.e., Pareto best) is retained as the representative solution to ensure that the quality of the representative solutions in each sector is balanced.

[0056] The process of angle sector partitioning is illustrated with a specific example. Assume there are 15 solutions on the current Pareto front, and the ideal points for the three targets are J_econ_min, J_degrad_min, and J_safe_min. For each solution i, calculate its direction vector v_i relative to the ideal point = (J_econ_i - J_econ_min, J_degrad_i - J_degrad_min, J_safe_i - J_safe_min), and then normalize it to a unit vector v_i / ||v_i||. Divide the first quadrant of the unit sphere (the spherical triangular region from 0° to 90° × 0° to 90°) into N_sec = 8 sectors using equal-area projection, and assign the direction vectors of the 15 solutions to their respective sectors. If a sector contains multiple solutions, retain the one with the best non-dominated sort as the representative; if a sector contains no solutions, it is considered an empty sector with the highest priority and will be used first for directional supplementation.

[0057] S3.5: For the representative solution set of each sector, calculate the angle between the corresponding direction vectors of adjacent representative solutions, select the sector with the largest angle between adjacent representative solutions as the sparse void region, take the angle bisector direction of the direction vectors of the representative solutions on both sides of the void region as the void center direction, sample and generate several sets of supplementary weights in the neighborhood of the void center direction according to Gaussian distribution, perform scalar quantization on each set of supplementary weights to obtain the supplementary Pareto optimal solution, merge the supplementary Pareto optimal solution into the current solution set to obtain the uniformly covered Pareto optimal solution set.

[0058] The technical principle of the hole detection and targeted repair mechanism is as follows. Traditional multi-objective optimization methods, during the Pareto front search, often result in a dense solution set in certain objective weight directions (such as near purely economic or purely safety directions) and sparse or even blank in comprehensive weighting directions due to uneven initial weight distribution or the non-convexity of the objective function terrain, while the solution set remains sparse or even blank in the comprehensive weighting direction. The angle bisector direction is used as the hole center direction because the angle bisectors of the two sides representing the solution direction vectors are located at the geometric center of the hole region. Supplementing the solution at this direction minimizes the angle between the solution and the directions representing the solutions on both sides. Within the neighborhood of the hole center direction ω_hole, N_fill groups (recommended values ​​of 4 to 8 groups) of supplementary weights are generated using a Gaussian distribution. The standard deviation of the Gaussian distribution controls the neighborhood range (recommended values ​​are the radians corresponding to 15° to 25° of the spherical angle), ensuring that the supplementary solutions are concentrated in the hole region rather than spreading to areas with existing solutions. The scalarization solution process S3.2 to S3.3 is repeated for each group of supplementary weights, and the resulting Pareto optimal solution is merged into the current solution set. The above-mentioned void detection and directional repair process can be executed iteratively until the spherical angle between all adjacent representative solutions is lower than the preset threshold (25° to 35° is recommended), ensuring that the Pareto optimal solution set is uniformly covered in all directions of the three-dimensional target space, providing operators with a complete decision menu covering economic-driven, life-driven, safety-driven and various compromise solutions.

[0059] Example 6: Based on Example 1, the step of decomposing the selected reference solution in the Pareto optimal solution set into local subproblems for each energy storage unit includes: S4.1: Using the reference solution selected in the Pareto optimal solution set as input, the global charge-discharge plan is decomposed into the local charge-discharge plan of each energy storage unit according to the number of each unit; by introducing consistency auxiliary variables and consistency dual variables, the global consistency constraint is transformed into a local augmented Lagrange problem that can be solved independently by each unit, and the local subproblems of each energy storage unit are obtained.

[0060] In this embodiment of the invention, after the global charging and discharging plan is decomposed according to the energy storage unit number i (i=1,2,…,N_ess), the local charging and discharging plan of each unit only contains the decision variables of that unit itself, thereby transforming the original global optimization problem that required centralized solution into a local subproblem that can be executed independently in parallel. A consistency auxiliary variable z (a global common variable, representing the unified power allocation reference that each unit expects to achieve) and a consistency dual variable λ_i (the dual multiplier of node i, measuring the deviation penalty between the local solution of node i and the global consistency variable) are introduced, transforming the global consistency constraint P_i=z into a penalty term in the augmented Lagrangian function. Each unit solves independently within its local feasible region by minimizing the weighted sum of its local objective function and the penalty term, without needing to access all information from other units; global coordination can be achieved simply by exchanging local solutions and dual variables with its communicating neighbors. This decomposition method preserves the optimality conditions of the original problem and is equivalent to centralized solution in the sense of satisfying the consistency constraint.

[0061] Example 7: Based on Example 1, the method of allocating adaptive step sizes to each energy storage unit based on its rated capacity and performing local optimization updates using recursive momentum estimation includes: S4.2: For each energy storage unit, the adaptive step size of the unit is obtained by multiplying the ratio of the rated capacity of the unit to the maximum rated capacity of all units by the step size scaling factor, wherein the value of the step size scaling factor ranges from 0.01 to 0.1; For each energy storage unit, the recursive momentum vector is initialized as a zero vector. In each local optimization iteration, the recursive momentum vector is recursively updated using the gradient difference between the current iteration and the previous iteration with a decay coefficient that decreases with the number of iterations. The updated recursive momentum vector is superimposed on the adaptive step size gradient update to obtain the local solution after momentum correction.

[0062] The joint design of the node adaptive step size and the STORM recursive momentum estimator is the core invention of the distributed collaborative layer of this invention. The technical definition of the adaptive step size mechanism is: the ADMM update step size η_i of each energy storage unit i is proportional to the rated capacity E_rated_i of that unit, that is, η_i=c_η·(E_rated_i / E_rated_max), where E_rated_max is the maximum value of the rated capacity of all energy storage units in the system, and c_η is a uniform step size scaling factor (the value ranges from 0.01 to 0.1, and the recommended initial value is 0.05).

[0063] The technical principle of adaptive step size design lies in the fact that, within the ADMM framework, the step size essentially controls the update rate of each node toward the consensus objective. Large-capacity energy storage units have a greater weight in the system (undertaking more scheduling tasks), and their local objective function curvature is typically smaller (the function is more 'flatter'), thus making them suitable for using a larger step size to achieve fast convergence. Small-capacity units have a smaller weight and a larger local function curvature; an excessively large step size can lead to local update oscillations. By using the ratio of rated capacity as the step size scaling factor, capacity information is naturally encoded into the convergence strategy, fundamentally eliminating the slack-out effect of 'all units converging at the slowest node speed' in traditional globally unified step size design. Taking a system with three energy storage units (capacities of 100kWh, 50kWh, and 25kWh respectively) as an example, when c_η=0.05, the adaptive step sizes of the three units are η_1=0.05, η_2=0.025, and η_3=0.0125 respectively. Each unit updates in parallel at its own suitable rate. The number of iterations required for the overall system convergence can be reduced by about 50% to 70% compared to a globally uniform step size (which must be uniformly executed according to the step size of the smallest capacity unit of 0.0125).

[0064] The STORM recursive momentum estimator is defined as a variance reduction technique that constructs an unbiased gradient estimate by recursively differencing the stochastic gradient estimates of the current iteration with those of the previous iteration. It requires only O(1) (constant order of magnitude) of additional storage space, making it suitable for deployment on the embedded controllers of each energy storage unit. Its specific update rule is as follows: In the k-th ADMM iteration, the recursive momentum vector m_i of each unit i is updated as follows: m_i^{k+1}=(1-β_k)·(m_i^k - η_i·∇fi) k ) + η_i·∇fi k+1 , where β_k=min(1 / (k+1)) 2 / 3 ,0.99) is the decay coefficient that monotonically decreases with the number of iterations k, ∇fi k and ∇fi k+1 These are the local gradient estimates (which may contain measurement noise) for the k-th and (k+1)-th iterations, respectively. The recursive momentum vector m... i k+1 By replacing the pure gradient step size as the update direction, a local solution with fused momentum correction is obtained.

[0065] The technical principle of the STORM recursive momentum estimator lies in its ability to achieve unbiased estimation of the true gradient direction at a computationally lower cost than the mini-batch gradient averaging method. This reduces the effective gradient variance from O(σ²) (pure stochastic gradient) to O(σ² / k^{2 / 3}) (decaying with iterations), effectively suppressing the impact of stochastic gradient noise introduced by communication delays and measurement noise on the convergence process. In practical energy storage systems, due to time jitter in BMS sampling and communication delays in SCADA data (typically 50ms to 500ms), noise is inevitably introduced into gradient estimation. The STORM estimator can reduce the impact of this noise on convergence quality to an acceptable level.

[0066] S4.3: Exchange the local solution after momentum correction with the local solution of the communication neighbor, update the consistency dual variable according to the difference between the two, and iterate until the consistency deviation between each unit is less than the convergence threshold to obtain the global coordinated charging and discharging plan.

[0067] Furthermore, after each energy storage unit completes its local optimization update, it only needs to broadcast its own local solution to its communication neighbors and receive the local solutions from its neighbors. After calculating the difference, it updates the consistency dual variable λ_ij = λ_ij - ρ·(P_local_i - P_local_j), where ρ is the ADMM penalty parameter. The communication topology adopts a sparse connected graph (such as a ring topology or a sparse random graph), and each node only needs to communicate with 2 to 4 neighbors. Compared with a fully connected topology, this can reduce communication overhead by 60% to 85% while still ensuring global coordination. The recommended value for the convergence threshold ε_admm is 0.1% to 1% of the rated power. A smaller value is used in frequency regulation auxiliary service scenarios with high accuracy requirements, and a larger value is used in day-ahead planning scenarios with lower accuracy requirements, flexibly balancing convergence accuracy and computation time.

[0068] Example 8: Based on Example 1, the step of performing selection, crossover, and mutation evolution operations on the population includes: S5.1: Using the global coordinated charge and discharge plan as a seed, multiple candidate charge and discharge power sequences are randomly generated within the feasible region centered on it to form a candidate charge and discharge sequence population; the Pareto weight vector is used to perform weighted fitness evaluation on each candidate sequence to obtain the population fitness set.

[0069] The rolling time-domain robust execution mechanism based on population evolution search is the core invention of the lower execution layer of this invention. Its technical definition is as follows: In each control cycle, using the globally coordinated charge-discharge plan output by distributed collaborative optimization as the seed sequence, M candidate charge-discharge power sequences are randomly generated within the feasible power domain around this seed to form an initial population (M is recommended to be 30 to 50). Through multi-generation evolutionary operations, a multi-directional global search is performed within the feasible domain, and the current time-step power value of the optimal sequence after evolution is taken as the execution instruction to achieve rolling time-domain (Receding Horizon) control.

[0070] The specific method for population initialization is as follows: using the power sequence of the future N_pred control time steps in the globally coordinated charge-discharge plan P_coord as the mean, random sampling is performed within the feasible power range [P_min, P_max] of each time step according to a uniform or Gaussian distribution to generate M candidate sequences. Each candidate sequence u_m (m=1,…,M) contains the charge-discharge power values ​​of N_pred time steps, and the power value of each time step satisfies the upper and lower limits of charge-discharge power constraints (guaranteed by pruning operations). The Pareto weight vector ω_ref=(ω_ref,1, ω_ref,2, ω_ref,3) passed from the upper layer is used to calculate the weighted multi-objective fitness F_m=ω_ref,1·J_econ(u_m)+ω_ref,2·J_degrad(u_m)+ω_ref,3·J_safe(u_m) for each candidate sequence, resulting in the population fitness set F_pop. A lower fitness indicates that the candidate sequence is better under the current weight configuration.

[0071] S5.2: Using the candidate charge / discharge sequence population as input, sort them by fitness from smallest to largest, retain a preset proportion of candidate sequences with the highest fitness ranking, and obtain a retained sequence set; randomly pair parent sequences from the retained sequence set, and exchange randomly selected continuous time segments from the two parent sequences with a preset crossover probability to generate offspring sequences, wherein the length of the continuous time segment is one-quarter to one-half of the predicted time domain length; for the offspring sequences, apply a Gaussian perturbation to each power value with a preset mutation probability, and trim the perturbed power values ​​to the feasible power range to obtain the evolved candidate sequence population.

[0072] The technical principles of the selection-crossover-mutation evolutionary operation are as follows: The selection operation employs a truncation selection strategy, retaining the top 50% of candidate sequences (recommended value 0.5) after sorting by fitness, and eliminating the remaining sequences. The retained sequences maintain complete population diversity while eliminating low-quality solutions, providing a high-quality parent gene pool for the next generation. The crossover operation combines high-quality power plans from two parent sequences at different time periods into the offspring by randomly pairing parent sequences and exchanging continuous time segments, achieving cross-sequence time-segment information recombination. The selection of continuous time periods (rather than random discrete locations) for the crossover segments preserves the local correlation of charging and discharging power sequences in the time dimension (power in adjacent time periods is usually highly correlated due to ramp rate constraints). The mutation operation applies a Gaussian perturbation with a mean of zero and a standard deviation of 5% of the rated power to each power value with a probability p_mut (recommended value 0.1), ensuring population diversity and preventing premature convergence to a local optimum. The mutated power values ​​are uniformly trimmed to the feasible power range [P_min, P_max] to ensure that constraints are met.

[0073] Compared with traditional single-quantitative MPC solutions, the technical advantages of the population evolution search mechanism are reflected in the following three aspects: First, it can handle non-convex feasible regions caused by mutual exclusion constraints of charging and discharging without gradient information. Each sequence in the population is independently evaluated for fitness, without being constrained by the direction of local gradients. Second, the diversity of the population naturally provides robustness to uncertainty. Under extreme conditions such as severe wind and solar forecasting errors or sudden load fluctuations, the population contains multiple charging and discharging strategy schemes, and the evolutionary operation can identify and strengthen the scheme with better fitness under the current actual conditions. Third, the population is initialized with a globally coordinated charging and discharging plan as the seed, ensuring that the evolutionary result is not inferior to directly executing the coordinated plan when there is sufficient computation time. At the same time, under extreme conditions, it can further explore better solutions around the coordinated plan.

[0074] S5.3: Take the first power value of the candidate sequence with the best fitness in the evolved candidate sequence population as the execution instruction of the current control cycle. Calculate the state deviation vector composed of the state of charge tracking deviation and the power execution deviation based on the actual execution result of the execution instruction. Feed the state deviation vector back to the initial conditions of the next optimization cycle to obtain the continuously optimized control sequence after rolling correction.

[0075] In this embodiment of the invention, a Receding Horizon Control strategy is adopted, in which only the first power command of the optimal sequence is executed in each control cycle, rather than the complete predictive time-domain plan. The advantage of this strategy is that at the beginning of the next control cycle, the system re-acquires the latest local state data (including the actual SOC after execution) and external environment data (including updated prediction curves), reconstructs the real-time optimization problem, and executes the complete three-layer optimization process. This incorporates the actual execution deviation (caused by prediction errors, execution delays, power converter accuracy limitations, etc.) into the decision-making of the next cycle, achieving continuous closed-loop error correction. The SOC tracking deviation in the state deviation vector is used to correct the initial SOC parameters in the real-time optimization problem of the next cycle; the power execution deviation is used to update the execution accuracy estimate of the power converter, and, if necessary, adjusts the upper limit of the power ramp-up constraint to ensure that the system can still maintain stable operation even when execution accuracy is limited.

[0076] Example 9: Based on Example 1, when computing resources are limited, the population size is set to 1 and the number of generations is set to 0. The selection, crossover and mutation evolution operations are skipped, and the first power value of the global coordinated charge and discharge plan is directly issued as the execution command of the current control cycle to obtain the control output under the degenerate single-solve mode.

[0077] In this embodiment of the invention, the degradation strategy minimizes both the population size and the number of generations, completely skipping the computational overhead of population generation and evolution, and directly distributing the current power value of the globally coordinated charge-discharge plan obtained through distributed collaborative optimization for execution. This degradation mode is equivalent to the single-value solution of traditional MPC, ensuring the basic availability of the system in resource-constrained scenarios such as edge computing devices or high communication latency.

[0078] Specifically, the triggering conditions for the degradation mode can be configured as follows: First, the system detects that the remaining computation time in the current control cycle is insufficient to complete the full population evolution operation (e.g., the remaining time is less than 80% of the preset evolution time); second, the system detects that distributed collaborative optimization has consumed a large amount of computing resources, resulting in insufficient available computing power in the lower execution layer; third, the operator manually switches to the energy-saving mode. In the degradation mode, the system can smoothly switch to the full evolution mode without affecting the continuity of control: it only needs to restore the population size and number of generations to the standard configuration (M=30 to 50, G=10 to 20) when the computing power is sufficient in the next control cycle, without any additional initialization operations, and can seamlessly connect to the complete rolling evolution search process, fully reflecting the graceful degradation principle of the architecture design of this invention.

[0079] Example 10: A multi-objective cooperative optimization control system for an energy storage system, comprising: The model building module is used to establish a multi-objective optimization problem model with charging and discharging power as decision variables based on the operating parameters of the energy storage system. The multi-objective optimization problem model includes an economic cost objective function, a battery life degradation objective function, a safety constraint deviation penalty function, and a set of energy storage operation constraints.

[0080] In this embodiment of the invention, the model building module is responsible for receiving the configuration parameters of the energy storage system, including rated capacity, charge / discharge efficiency, SOC operating range, power ramp-up rate limit, etc., and establishing multi-time-period charge / discharge power decision variables accordingly. It then constructs three objective functions: economic cost, battery life degradation, and deviation from safety constraints, superimposed with a set of operational constraints to form a complete multi-objective optimization problem model, which is stored for subsequent module calls. During the system initialization phase, the model building module performs a one-time model structure establishment; during the operation phase, the model parameters (initial SOC, electricity price sequence, etc.) are dynamically updated by the data sensing module, while the model structure remains unchanged, thus achieving a balance between computational efficiency and model accuracy.

[0081] The data sensing module is used to collect local state data and external environment data of the energy storage system, and to update the parameters of the multi-objective optimization problem model after fusing the local state data and the external environment data to obtain the real-time optimization problem.

[0082] The data sensing module periodically collects local state data through a sensor interface at a preset sampling frequency (typically 1 to 10 times per second), and acquires electricity price and forecast data at a lower frequency (typically once every 5 to 15 minutes) through an external data interface. After performing timestamp alignment and fusion, the module updates the parameters and writes them into the multi-objective optimization problem model maintained by the model building module, outputting a real-time optimization problem for use by the multi-objective search module. The data sensing module is also responsible for anomaly detection and data cleaning of the collected data. When sensor failure or communication interruption is detected, it activates a state estimation algorithm based on historical data (such as a Kalman filter) to provide alternative values, ensuring the parameter integrity of the optimization model.

[0083] The multi-objective search module is used to calculate the gradient vector of each objective function with respect to the decision variables for the real-time optimization problem, solve the minimum norm convex combination of each gradient vector to obtain the Pareto optimal weight vector, and then perform scalarization to solve the real-time optimization problem to obtain the Pareto optimal solution. The objective space is divided into angular sectors and sparse void regions are detected. The solution is supplemented in the direction of the void center, and the supplemented solutions are merged to obtain the Pareto optimal solution set.

[0084] Specifically, the multi-objective search module embeds gradient calculation units, convex optimization solution units, angle sector partitioning units, and hole repair units. These units execute the calculation processes sequentially in a pipeline manner, ultimately outputting a uniformly covered Pareto optimal solution set and the corresponding weight vectors for each solution. The module also provides a human-computer interaction interface for operators to select a reference solution from the Pareto optimal solution set. Operators can visually compare the performance of each candidate solution in terms of economy, lifetime, and safety through a visual interface (two-dimensional Pareto front projection map or three-target radar chart) and select a reference solution that meets the current scheduling requirements. If operators do not select a solution in time, the system automatically selects the closest Pareto solution as the reference solution according to preset default preference weights (such as an equal-weight balancing scheme), ensuring control continuity.

[0085] The distributed coordination module is used to decompose the selected reference solution in the Pareto optimal solution set into local subproblems of each energy storage unit, allocate an adaptive step size to each energy storage unit based on its rated capacity, perform local optimization updates in combination with recursive momentum estimation, exchange local solutions with each unit and update the consistency dual variable with its communication neighbor, iterate until the consistency deviation meets the convergence condition, and obtain a globally coordinated charging and discharging plan.

[0086] In this embodiment of the invention, the distributed collaborative module is deployed in the local controller of each energy storage unit. Each local controller only needs to maintain the solution state of its own local subproblems, the recursive momentum vector, and the dual variables with its communicating neighbors. The communication topology adopts a sparse connection graph (such as a ring topology, grid topology, or random sparse graph) to reduce communication overhead, and each node only needs to maintain communication links with 2 to 4 neighbors. When an energy storage unit is shut down due to a fault or maintenance, the communication topology automatically reroutes, and the remaining units continue to maintain collaborative optimization capabilities, demonstrating the inherent robustness of the distributed architecture to single-node failures. The module as a whole has high scalability: when adding a new energy storage unit, it is only necessary to connect the new unit to the communication network and initialize its local subproblems and step size parameters, without modifying the control programs of other units.

[0087] The rolling execution module is used to generate a population of candidate charging and discharging sequences using the global coordinated charging and discharging plan as a seed, evaluate the fitness of the population using the selected Pareto weight vector, perform selection, crossover and mutation evolution operations on the population, take the first power value of the optimal fitness sequence after evolution as the execution command for the current control cycle, calculate the state deviation and feed it back to the next optimization cycle to realize rolling closed-loop control.

[0088] The rolling execution module also includes a degradation mode switching unit, which can automatically determine whether to enable the degradation single-step solution mode based on real-time computing resource load (CPU utilization, memory usage, and remaining control cycle time), ensuring the basic availability of the system under various operating environments. The state deviation vector output by the module (including SOC tracking deviation and power execution deviation) is written back to the data sensing module through a feedback interface, triggering data updates for the next optimization cycle, forming a complete closed-loop control system. In actual deployment, the rolling execution module can run on an independent real-time controller (such as a PLC or industrial PC that meets the IEC 61131-3 standard) to ensure the real-time performance and reliability of control command output, while hardware isolation protects the underlying power converter from the computational delay of the upper-level optimization calculation.

Claims

1. A multi-objective collaborative optimization control method for an energy storage system, characterized in that, The method includes: Based on the operating parameters of the energy storage system, a multi-objective optimization problem model with charging and discharging power as the decision variable is established. The multi-objective optimization problem model includes an economic cost objective function, a battery life degradation objective function, a safety constraint deviation penalty function, and a set of energy storage operation constraints. Collect local state data and external environment data of the energy storage system, merge the local state data and the external environment data to update the parameters of the multi-objective optimization problem model, and obtain the real-time optimization problem; For the real-time optimization problem, the gradient vectors of each objective function with respect to the decision variables are calculated, and the minimum norm convex combination of each gradient vector is solved to obtain the Pareto optimal weight vector. Based on this, the real-time optimization problem is solved by scalarization to obtain the Pareto optimal solution. The objective space is divided into angular sectors and sparse void regions are detected. The solution is supplemented in the direction of the void center, and the supplemented solutions are merged to obtain the Pareto optimal solution set. The selected reference solution in the Pareto optimal solution set is decomposed into local subproblems of each energy storage unit. An adaptive step size is assigned to each energy storage unit based on its rated capacity. Local optimization is performed by combining recursive momentum estimation. Each unit exchanges local solutions with its communication neighbors and updates the consistency dual variable. The iteration continues until the consistency deviation meets the convergence condition, and a globally coordinated charging and discharging plan is obtained. A candidate charge-discharge sequence population is generated using the global coordinated charge-discharge plan as a seed. The fitness of the population is evaluated using the selected Pareto weight vector. Selection, crossover, and mutation evolution operations are performed on the population. The first power value of the optimal fitness sequence after evolution is taken as the execution command for the current control cycle. The state deviation is calculated and fed back to the next optimization cycle to achieve rolling closed-loop control.

2. The method according to claim 1, characterized in that, The step of establishing a multi-objective optimization problem model with charging and discharging power as decision variables based on the operating parameters of the energy storage system includes: Based on the operating parameters of the energy storage system, including the battery rated capacity, current state of charge, charge and discharge efficiency, and upper limit of charge and discharge power, the decision variables of charge and discharge power for each control period are established to obtain the operating decision space of the energy storage system. For the aforementioned operational decision space, an economic cost objective function, a battery life degradation objective function, and a safety constraint deviation penalty function are constructed respectively. The economic cost objective function includes a weighted sum of grid arbitrage revenue, ancillary service compensation revenue, and charging and discharging loss costs. The battery life degradation objective function quantifies cyclic aging losses based on an ampere-hour throughput model. The safety constraint deviation penalty function uses the state of charge exceeding the limit and the power exceeding the limit as penalty terms, resulting in a three-objective optimization vector. The set of energy storage operation constraints, consisting of upper and lower bounds of state of charge, mutual exclusion of charging and discharging, daily charging and discharging frequency constraints, and power ramp-up rate constraints, is superimposed onto the three-objective optimization vector to obtain the multi-objective optimization problem model.

3. The method according to claim 1, characterized in that, The process involves collecting local state data and external environment data from the energy storage system, fusing the local state data with the external environment data, and then updating the parameters of the multi-objective optimization problem model to obtain a real-time optimization problem, including: Based on the local sensor network of the energy storage system, the current state of charge, battery temperature and health status are collected in real time to obtain the local state vector. Based on the external data interface, the current electricity price signal, load forecast curve and new energy output forecast curve are obtained to obtain the external environment data vector; The local state vector and the external environment data vector are aligned and fused according to timestamps, and the parameters in the multi-objective optimization problem model are updated to obtain the real-time optimization problem.

4. The method according to claim 1, characterized in that, For the aforementioned real-time optimization problem, the gradient vector of each objective function with respect to the decision variables is calculated, and the minimum norm convex combination of each gradient vector is solved to obtain the Pareto optimal weight vector, including: For the real-time optimization problem, at the current decision point, the gradient vectors of the economic cost objective function, the battery life degradation objective function, and the safety constraint deviation penalty function relative to the charge / discharge power decision variable are calculated respectively to obtain the set of gradients for each objective. Using the target gradient sets as input, an optimization problem is solved to minimize the weighted norm of the convex combination coefficients of each gradient vector. The convex combination coefficients satisfy the non-negativity constraint and the sum of each coefficient is 1, thus obtaining the Pareto optimal weight vector. The Pareto optimal weight vector is applied to the three-objective optimization vector for scalarization, and the real-time optimization problem is solved using a sequential quadratic programming solver to obtain the Pareto optimal solution and its corresponding objective vector.

5. The method according to claim 1, characterized in that, The process involves dividing the target space into angular sectors and detecting sparse void regions. A directional supplementary solution is then performed along the center of the void, and the supplementary solutions are merged to obtain the Pareto optimal solution set, which includes: Using the ideal point formed by the minimum values ​​of the three objective functions as the origin of the coordinate system, the objective vectors corresponding to each solution on the current Pareto front are mapped to the direction vectors on the unit sphere. The unit sphere is divided into several angular sectors according to the equal area projection of the sphere. The solution with the best non-dominated sorting in each angular sector is retained as the representative solution of that sector, thus obtaining the representative solution set of each sector. For each sector's representative solution set, calculate the angle between the corresponding direction vectors of adjacent representative solutions, select the sector with the largest angle between adjacent representative solutions as the sparse void region, and take the angle bisector direction of the direction vectors of the representative solutions on both sides of the void region as the void center direction to obtain the void region identifier and the void center direction. Several sets of supplementary weights are generated by sampling in the neighborhood of the cavity center direction according to a Gaussian distribution. Standardization is performed on each set of supplementary weights to obtain a supplementary Pareto optimal solution. The supplementary Pareto optimal solutions are merged into the current solution set to obtain a uniformly covered Pareto optimal solution set.

6. The method according to claim 1, characterized in that, The step of decomposing the selected reference solution in the Pareto optimal solution set into local subproblems for each energy storage unit includes: Using the reference solution selected from the Pareto optimal solution set as input, the global charge-discharge plan is decomposed into the local charge-discharge plan of each energy storage unit according to the number of each unit; By introducing consistency auxiliary variables and consistency dual variables, the global consistency constraint is transformed into a local augmented Lagrange daily problem that can be solved independently by each unit, thus obtaining the local subproblems of each energy storage unit.

7. The method according to claim 1, characterized in that, The process of allocating adaptive step sizes based on the rated capacity of each energy storage unit and performing local optimization updates in conjunction with recursive momentum estimation includes: For each energy storage unit, the adaptive step size of the unit is obtained by multiplying the ratio of the unit's rated capacity to the maximum rated capacity among all units by the step size scaling factor, wherein the value of the step size scaling factor ranges from 0.01 to 0.

1. For each energy storage unit, the recursive momentum vector is initialized as a zero vector. During each local optimization iteration, the recursive momentum vector is recursively updated using the gradient difference between the current iteration and the previous iteration with a decay coefficient that decreases with the number of iterations. The updated recursive momentum vector is then superimposed on the adaptive step size gradient update to obtain the local solution after momentum correction. The local solution after momentum correction is exchanged with the local solutions of the communicating neighbors. The consistency dual variable is updated according to the difference between the two. The process is iterated until the consistency deviation between each unit is less than the convergence threshold, and the global coordinated charging and discharging plan is obtained.

8. The method according to claim 1, characterized in that, The process of performing selection, crossover, and mutation evolution operations on the population includes: Using the candidate charge-discharge sequence population as input, sorting them by fitness from small to large, and retaining a preset proportion of candidate sequences with high fitness ranking, a set of retained sequences is obtained. For the set of retained sequences, parent sequences are randomly paired, and continuous time segments randomly selected from the two parent sequences are exchanged with a preset crossover probability to generate child sequences. The length of the continuous time segment is one-quarter to one-half of the predicted time domain length. For the offspring sequence, a Gaussian perturbation is applied to each power value with a preset mutation probability, and the perturbed power values ​​are trimmed to a feasible power range to obtain the evolved candidate sequence population; The first power value of the candidate sequence with the best fitness in the evolved candidate sequence population is taken as the execution instruction for the current control cycle. Based on the actual execution result of the execution instruction, the state deviation vector composed of the state of charge tracking deviation and the power execution deviation is calculated. The state deviation vector is fed back to the initial conditions of the next optimization cycle to obtain the continuously optimized control sequence after rolling correction.

9. The method according to claim 1, characterized in that, When computational resources are limited, the population size is set to 1 and the number of generations is set to 0. The selection, crossover, and mutation evolution operations are skipped, and the first power value of the global coordinated charge and discharge plan is directly issued as the execution command for the current control cycle, resulting in the control output under the degenerate single-solution mode.

10. A multi-objective collaborative optimization control system for an energy storage system, characterized in that, The system includes: The model building module is used to establish a multi-objective optimization problem model with charging and discharging power as decision variables based on the operating parameters of the energy storage system. The multi-objective optimization problem model includes an economic cost objective function, a battery life degradation objective function, a safety constraint deviation penalty function, and a set of energy storage operation constraints. The data sensing module is used to collect local state data and external environment data of the energy storage system, and to update the parameters of the multi-objective optimization problem model after fusing the local state data and the external environment data to obtain the real-time optimization problem. The multi-objective search module is used to calculate the gradient vector of each objective function with respect to the decision variables for the real-time optimization problem, solve the minimum norm convex combination of each gradient vector to obtain the Pareto optimal weight vector, and then perform scalarization to solve the real-time optimization problem to obtain the Pareto optimal solution; the objective space is divided into angular sectors and sparse void regions are detected, and the solution is supplemented in the direction of the void center; the supplemented solutions are merged to obtain the Pareto optimal solution set. The distributed coordination module is used to decompose the selected reference solution in the Pareto optimal solution set into local subproblems of each energy storage unit, allocate an adaptive step size to each energy storage unit based on its rated capacity, perform local optimization updates in combination with recursive momentum estimation, exchange local solutions with each unit and update the consistency dual variable, iterate until the consistency deviation meets the convergence condition, and obtain the global coordinated charging and discharging plan. The rolling execution module is used to generate a population of candidate charging and discharging sequences using the global coordinated charging and discharging plan as a seed, evaluate the fitness of the population using the selected Pareto weight vector, perform selection, crossover and mutation evolution operations on the population, take the first power value of the optimal fitness sequence after evolution as the execution command for the current control cycle, calculate the state deviation and feed it back to the next optimization cycle to realize rolling closed-loop control.

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