A method for double-layer multi-objective collaborative optimization of scheduling of a fusion energy storage system and operation optimization of a power distribution network

Abstract

A two-layer, multi-objective collaborative optimization method integrating energy storage system scheduling and distribution network operation optimization is proposed. This method involves generating a load fluctuation coefficient by calculating the deviation between the current load and the average load, and dynamically generating energy storage revenue weights and peak shaving / valley filling weights using a dynamic weighting function. The upper-layer optimization model generates a charging and discharging plan with energy storage revenue and peak shaving / valley filling as dual objectives; the lower-layer optimization model aims to minimize network losses, voltage deviations, and wind and solar curtailment. Minimizing energy curtailment is incorporated into the reactive power optimization objective system, forming a multi-objective optimization framework integrating source-grid-load-storage. A combined strategy of improved whale optimization and multi-objective particle swarm optimization algorithms is employed, used for upper-layer energy storage scheduling and lower-layer reactive power optimization respectively, combined with alternating iteration and information feedback mechanisms for collaborative solution. This method enables adaptive scheduling of the energy storage system under different load conditions for multiple objectives, improving the economy, power quality, and renewable energy utilization level of the active distribution network.

Description

Technical Field

[0001] This invention relates to the field of reactive power optimization technology in power systems, specifically to a two-layer, multi-objective collaborative optimization method that integrates energy storage system scheduling and distribution network operation optimization. Background Technology

[0002] With the large-scale integration of distributed photovoltaic and wind power and other new energy sources, the operating characteristics of active distribution networks are increasingly exhibiting complex features such as strong volatility and high coupling. Traditional reactive power optimization methods are gradually revealing their insufficient adaptability in coordinating multiple objectives such as economy, power quality, and new energy consumption. Existing optimization strategies are mostly based on static weights or fixed objective preferences, lacking the ability to respond in real time to dynamic load changes, and making it difficult to guide energy storage systems to achieve dynamic balance and adjustment among multiple objectives based on their operating status.

[0003] Meanwhile, most current scheduling frameworks still adopt a single-layer structure, making it difficult to balance the economic scheduling objectives at the upper level with the operational constraints of the power grid at the lower level. This is especially true in scenarios where renewable energy accounts for a high proportion, where the lack of an effective multi-objective coordination mechanism makes it difficult to alleviate the problem of wind and solar curtailment. Although some methods attempt to introduce multi-objective optimization algorithms, the lack of necessary information feedback and dynamic coupling mechanisms between the upper and lower optimization processes makes it difficult for the overall scheduling to achieve global consistency and optimal convergence.

[0004] At the solution level, traditional heuristic optimization algorithms often face challenges such as slow convergence speed and uneven solution set distribution when dealing with complex problems involving high dimensions and multiple coupled objectives, making it difficult to meet the real-time and robust requirements of active distribution networks for optimization strategies. Therefore, there is an urgent need to construct an optimization method with dynamic weight adjustment capabilities, supporting two-layer multi-objective collaborative optimization, and integrating alternating iteration and information feedback mechanisms, in order to achieve efficient scheduling and energy collaborative control of active distribution networks with wind, solar, and energy storage in integrated wind and solar power scenarios, using a two-layer multi-objective reactive power optimization method. Summary of the Invention

[0005] To address the shortcomings of existing active distribution network optimization methods, such as insufficient target regulation capability, severe decoupling between upper and lower layers, high renewable energy curtailment rate, and low optimization efficiency, this invention proposes a two-layer multi-objective collaborative optimization method that integrates energy storage system scheduling and distribution network operation optimization. This method enhances the system's adaptive regulation capability and multi-objective collaborative optimization performance under different operating conditions. It enables adaptive scheduling of the energy storage system for multiple objectives under different load conditions, significantly improving the economy, power quality, and renewable energy utilization level of the active distribution network.

[0006] The technical solution adopted in this invention is as follows:

[0007] A two-layer, multi-objective collaborative optimization method integrating energy storage system scheduling and distribution network operation optimization includes the following steps: Step 1: A dynamic weighting adjustment mechanism based on load fluctuations is proposed. This mechanism generates a load fluctuation coefficient by calculating the deviation between the current load and the average load, and dynamically generates energy storage revenue weights and peak shaving / valley filling weights using a dynamic weighting function. These weights are updated on a rolling basis with the scheduling cycle, guiding the dynamic adjustment of optimization objectives and achieving an adaptive balance between economic efficiency and regulation capability in the energy storage system. Step 2: Construct a wind-solar-storage dual-layer collaborative optimization model driven by dynamic weights. The upper-layer optimization model generates charging and discharging plans with energy storage revenue and peak shaving as dual objectives. The lower-layer optimization model aims to minimize network losses, voltage deviation, and wind and solar curtailment. The minimization of energy curtailment is incorporated into the reactive power optimization objective system, forming a multi-objective optimization framework integrating source-grid-load-storage. Step 3: Adopt a combination strategy of improved whale optimization and multi-objective particle swarm optimization algorithm, which are used for upper-level energy storage scheduling and lower-level reactive power optimization respectively. Combine alternating iteration and information feedback mechanism to solve the problem in a collaborative manner, construct a bidirectional coupling structure between the upper and lower layers, improve the model's global convergence ability and adaptability under multi-objective collaborative tasks.

[0008] In step 1, the increasing trend of load volatility in active distribution networks was comprehensively analyzed, pointing out that traditional fixed-weight allocation mechanisms or static scheduling strategies are no longer adequate to meet the multi-objective optimization needs of energy storage systems under variable operating environments. To enhance the responsiveness of energy storage systems to load changes, this invention proposes a dynamic weight adjustment mechanism based on load volatility characteristics. This mechanism senses the real-time fluctuation of system load and dynamically generates weight factors in the optimization objectives, enabling adaptive strategy switching and trade-off scheduling of the energy storage system between maximizing economic benefits and maximizing peak shaving and valley filling efficiency.

[0009] In step 1, energy storage revenue refers to the economic benefits obtained by the energy storage system through participating in electricity market arbitrage, such as charging during off-peak hours and discharging during peak hours. It is usually calculated based on the time-of-use pricing mechanism, as shown in equation (1): (1); In equation (1), for t Electricity price at any given time; for t Total charge and discharge power of energy storage at all times; For the benefits of energy storage systems; The time step is typically set to 1 hour; T This represents the total time per day, usually taken as 24 hours. Peak shaving and valley filling refer to the use of energy storage systems to discharge during peak load periods and charge during off-peak load periods, thereby smoothing load curve fluctuations, reducing transformer load rates, and improving grid operation stability. The peak shaving and valley filling rate reflects the energy storage system's ability to adjust the load curve and is an important indicator for measuring its adjustment effect. In this invention, the analysis of load fluctuations is based on the net load curve, which is the original load minus the output of renewable energy, and can more accurately reflect the actual power demand that the grid needs to bear. The expression for the net load is shown in equation (2): (2); In equation (2), for t The system's original load at that moment; for t Renewable energy output at all times; for t Net load at any given moment.

[0010] The expression for the peak shaving and valley filling rate is shown in equation (3): (3); In equation (3), To optimize the peak-to-valley difference in net load; To optimize the peak-to-valley difference in net load; CR This refers to the peak shaving and valley filling rate.

[0011] In step 1, in order to establish a dynamic coordination relationship between maximizing the economic benefits of the energy storage system and optimizing the peak shaving and valley filling efficiency, a dynamic weight factor construction method based on load fluctuation characteristics is proposed to connect the two types of scheduling objectives.

[0012] To enable the optimization model to have real-time perception and response capabilities to the system's operating status, a characteristic index that can reflect the degree of load fluctuation is designed. Considering that the load in the active distribution network has obvious periodicity and uncertainty, the method of this invention defines a load fluctuation coefficient as shown in equation (4) based on the load data within the rolling scheduling cycle, which is used to quantify the degree of deviation of the current load level from the steady-state load; (4); In equation (4), For the current rolling cycle t Total system load at any given time; This is the arithmetic mean of the load during this period; For the system in t The magnitude of load fluctuation at any given time.

[0013] Based on the load fluctuation coefficients obtained above, a normalized dynamic weight function as shown in equation (5) is further constructed to generate the dynamic weight factors for each optimization objective: (5); In equation (5), for t The weight corresponding to the energy storage revenue target at any given time; , This is the adjustment coefficient; For the system in t The magnitude of load fluctuation at any given time. This function has good adjustability and continuity, and can dynamically adjust the preference ratio between optimization objectives according to the degree of load fluctuation.

[0014] Based on the dynamic weighting factors constructed above, they are further embedded into the energy storage scheduling optimization model containing the objective functions of equations (1) and (3). This is used to weight and integrate the economic benefit objective function shown in equation (1) and the peak shaving and valley filling objective function shown in equation (3), thereby achieving comprehensive optimization of the energy storage operation economy and load regulation capability. Since the two have different dimensions, they need to be normalized to form a multi-objective comprehensive optimization function, as shown in equation (6): (6); In equation (6), For multi-objective comprehensive optimization functions; for t The weight corresponding to the energy storage revenue target at any given time; The weights corresponding to the peak shaving and valley filling rate target; The normalized revenue of the energy storage system; This is the normalized peak-shaving and valley-filling rate.

[0015] The dynamic weights are adaptively adjusted according to the degree of load fluctuation, enabling the optimization objective to automatically switch its focus according to the system state during operation: when the load fluctuation is large, the weight of peak shaving and valley filling is adaptively adjusted according to the degree of load fluctuation, while when the load fluctuation is small, the weight of energy storage revenue is adaptively adjusted according to the degree of load fluctuation. Furthermore, the multi-objective comprehensive optimization function shown in Equation (6) serves as the core objective function of the upper-level scheduling model, guiding the energy storage system to flexibly adjust its charging and discharging behavior under different scenarios such as peak load and photovoltaic output fluctuation, thereby realizing the dynamic optimization and coordinated control of the scheduling strategy.

[0016] In step 2, in order to achieve coordinated optimization of the wind-solar-storage active distribution network under multi-objective operation, based on the dynamic weighting factor constructed in step 1, a two-layer collaborative optimization model consisting of an energy storage scheduling layer and a reactive power optimization layer is further designed to enhance the system's economy, stability and new energy absorption capacity.

[0017] The upper-level optimization model takes the dual objectives of maximizing the economic benefits of the energy storage system and maximizing the peak shaving and valley filling efficiency as the dual objectives. It uses dynamic weighting factors to weight and fuse the two objective functions shown in equation (1) and equation (3) to form the comprehensive objective function shown in equation (6).

[0018] The optimization result is the charging and discharging power plan of the energy storage system within 24 hours. When the system load fluctuates, the energy storage revenue weight shown in Equation (5) will also be dynamically adjusted. The revenue weight will then affect the energy storage revenue shown in Equation (1). The energy storage revenue is mainly determined by the time-of-use electricity price level and the charging and discharging behavior of the energy storage system. Based on a comprehensive consideration of the time-of-use electricity price mechanism, energy storage capacity constraints and other operating conditions, the obtained optimization strategy can dynamically adjust the energy storage charging and discharging plan according to the fluctuation characteristics of the system load, thereby achieving a strategy output that matches the load change characteristics.

[0019] Through a dynamic weight adjustment mechanism, the upper-level optimization model actively adjusts scheduling preferences based on the operating status, balancing economy and adjustment capability.

[0020] In step 2, after completing the upper-level energy storage charging and discharging power optimization plan, a lower-level optimization model is further constructed to achieve a dual improvement in grid operation performance and renewable energy absorption capacity. The lower-level optimization model takes the energy storage system power boundary output from the upper-level optimization model as its active power input condition, and collaboratively optimizes the reactive power distribution in the distribution network to ensure system power quality, security, and renewable energy utilization. To comprehensively improve the operation performance of the active distribution network, the lower-level optimization model proposes three collaborative optimization objective functions, as follows: 1) Minimize network loss: Based on the principle of power flow calculation, considering the active power loss of each branch, the objective function is shown in equation (7): (7); In equation (7), To minimize network loss; T This represents the total time per day, usually taken as 24 hours. For branch set; and They are respectively t Time Branch i - j The active and reactive power; This refers to the voltage at the end of the branch. For branch circuit conductance; The time step is typically set to 1 hour; the objective is to reduce branch losses by optimizing reactive power distribution.

[0021] 2) Minimum voltage deviation: The goal is to minimize the sum of squares of the deviations between the voltage at each node and the rated voltage, so as to avoid voltage exceeding the limit, as shown in equation (8).

[0022] (8); In equation (8), This is the sum of squares of the deviations between the voltage at each node and the rated voltage; A set of nodes; Let be the voltage at node i at time t; This is the node's rated voltage.

[0023] 3) Minimum wind and solar power curtailment: Considering the energy curtailment caused by the randomness of wind and solar power output, the objective function is shown in equation (9).

[0024] (9); In equation (9), Waste energy that contributes to the scenery; , Wind power output and photovoltaic power output at time t, respectively; Let t represent the load demand at time t. This objective aims to improve the wind and solar load capacity of the distribution network by optimizing reactive power distribution and energy storage scheduling.

[0025] The lower-level optimization model aims to minimize network loss, node voltage deviation, and wind and solar curtailment, as shown in Equation (10). (10); In equation (10), It is a comprehensive function that minimizes network loss, node voltage deviation, and wind and solar curtailment. , , These are network loss, node voltage deviation, and wind and solar power curtailment, respectively.

[0026] The above-mentioned two-layer collaborative optimization modeling enables the system to dynamically adapt to changes in load and renewable energy output while meeting operational constraints, thereby achieving coordinated linkage between energy storage strategies and reactive power regulation strategies and improving the overall economy and stability of the active distribution network.

[0027] In step 3, a combined strategy of integrating the improved whale optimization algorithm and the improved multi-objective particle swarm optimization algorithm is proposed, and an alternating iteration and information feedback mechanism is introduced to construct a bidirectional coupled solution structure between upper and lower layers, thereby improving the global convergence ability and the solution accuracy and robustness under multi-objective scheduling tasks.

[0028] In step 3 The upper-level optimization model employs an improved whale optimization algorithm (IWOA) to address challenges in energy storage scheduling models, such as strong nonlinearity, large search space, and dynamically changing target preferences. To enhance the algorithm's global search capability and local adjustment accuracy, the following improvement strategies are introduced to strengthen the standard whale optimization algorithm: The dynamic weighting mechanism is embedded into the individual fitness evaluation process to link the search direction with the running status, thereby improving the adaptation to multi-objective trade-offs. An adaptive factor adjustment is added to the whale position update strategy to achieve a dynamic weight adjustment mechanism that enhances global exploration capabilities in the early stage and improves local convergence accuracy in the later stage. The hybrid initialization strategy uses a mixture of uniform and Gaussian distributions to initialize the population, thereby increasing population diversity and avoiding early entrapment in local optima.

[0029] Through the above operations, the improved whale optimization algorithm can effectively improve search accuracy and optimization efficiency, and is suitable for rapid optimization and boundary output of upper-level energy storage scheduling targets in dynamic scenarios, providing a high-quality active power scheduling scheme for lower-level optimization models.

[0030] 1) Dynamic weight embedding fitness function: To achieve target guidance direction adjustment driven by operating status, the dynamic weight corresponding to load fluctuation is embedded in the fitness evaluation to realize real-time perception and adjustment of target preference, as shown in Equation (11).

[0031] (11); In equation (11): The fitness function; The weights of the objective function related to the economic benefits of the energy storage system; Represents the weights of the objective function related to load fluctuations (peak shaving and valley filling); The load fluctuation factor quantifies the degree of fluctuation in the system load at the current moment; the larger the value, the more severe the fluctuation.

[0032] 2) The Sigmoid function regulates the balance between exploration and development: The Sigmoid function adjusts the convergence rhythm of the search factors, enabling the algorithm to enhance population diversity and global exploration capabilities in the early stage, and strengthen local development in the later stage to accelerate convergence, as shown in Equation (12).

[0033] (12); In equation (12): is a control parameter that varies with the number of iterations k; μ is the kurtosis control factor of the Sigmoid function, which determines the adjustment rate; k is the current iteration number.

[0034] 3) Hybrid encoding initialization mechanism: Historical policy perturbation and local search heuristics are introduced into the initial population to improve the breadth and quality of the population distribution and reduce the risk of getting trapped in local optima, as shown in Equation (13): (13); In equation (13): for i The initial solution for an individual; Candidate solutions generated by the machine; This is a historically excellent solution or a reference solution; The sum factor (between 0 and 1) controls the proportional weight between historical experience and new solutions.

[0035] After the solution is completed, the energy storage power boundary sequence that satisfies the constraints is output as the input to the lower-level optimization model, as shown in Equation (14): (14); In equation (14): , These represent the total minimum and maximum charge / discharge power of all energy storage systems, respectively. for t The charging and discharging power of all energy storage systems at all times.

[0036] In step 3, the lower-level optimization model employs an improved multi-objective particle swarm optimization algorithm (IMOPSO) to address the complexity of the solution space and distribution requirements arising from the involvement of multiple heterogeneous objectives in the lower-level reactive power optimization model, including network loss, voltage deviation, and abandoned energy. To improve the diversity, balance, and distribution breadth of the solution set, this invention improves the standard multi-objective particle swarm optimization algorithm (MOPSO) in the following ways: The hybrid coding mechanism uses a hybrid coding method for continuous variables such as reactive power and discrete variables such as voltage regulation equipment status in the optimization model, thereby improving the modeling accuracy and solution flexibility of the algorithm for power grid control characteristics. Crowding distance control introduces a merit-based strategy based on crowding distance during particle update and solution set selection to ensure the balanced distribution of Pareto front solutions and avoid concentrated or sparse solution sets. An external elite solution archive maintenance mechanism is established to build a dynamically updated external elite archive, which saves and optimizes the current best solution in real time, and guides the population to steadily converge toward the global optimal solution region in subsequent iterations.

[0037] 1) Hybrid coding mechanism: Continuous and discrete variables, such as voltage setpoint and reactive power compensation equipment switching status, are processed by a combination of real number encoding and integer encoding, as shown in equation (15).

[0038] (15); In equation (15): The active power of the energy storage system; Provide power to the SVG reactive power compensation equipment; The node number for energy storage access (discrete variable); for i The individual's solution.

[0039] 2) Crowding distance guides the uniformity of non-dominated solution sets: The breadth and uniformity of the Pareto front distribution are maintained by calculating the crowding distance of the solution set, as shown in Equation (16): (16); In equation (16): For the first i The comprehensive distance index for individual solutions; The total number of objective functions; , The first m The values ​​of the solutions before and after in the objective function; , These represent the maximum and minimum values ​​of the target, respectively.

[0040] 3) External elite archives drive global convergence: An external elite library composed of non-dominated solutions is introduced for reference during particle updates to improve global convergence speed and multi-objective balance, as shown in Equation (17): (17); In equation (17): This represents the current update amount of the particle; Inertia weighting, balancing development and exploration; , Learning factors; , Take a random number between [0, 1]. Individual historical best position; Global historical best position; for i The individual's initial attempt to resolve the issue; This indicates the update direction and step size of the solution in the search space.

[0041] In step 3, to achieve a synergistic optimal balance between the economic efficiency of the energy storage system and the safety of grid operation, a two-layer optimization structure is constructed, where the upper and lower layers solve independently but coordinate with each other. This structure, through a nested coupled solution mechanism, promotes the dynamic interaction and evolution of the upper and lower layer objectives across multiple time periods. It employs an iterative control process with the upper layer optimization as the outer loop and the lower layer optimization as the inner loop. The specific process is as follows: Step 1: Set the initial energy storage power boundary and initialize the dynamic weighting factor. The upper-level optimization model is solved based on the multi-objective comprehensive optimization function to obtain the energy storage charging and discharging power plan for the current scheduling period; Step 2: Use the energy storage power output of the upper-level optimization model as the inner-level constraint to solve the lower-level optimization model, obtain decision variables such as reactive power compensation output, and calculate the target values ​​of network loss, node voltage deviation, and wind and solar curtailment in the lower-level optimization model.

[0042] Step 3: Feed back the network loss and energy waste indices obtained from the lower-level optimization model to the upper-level optimization model to adjust the upper-level energy storage revenue. R Simultaneously, the dynamic weighting factor is updated based on real-time load and wind-solar fluctuations. .

[0043] Step 4: Repeat Steps 1 through 3 until the objective function of the upper-level optimization model converges, and output the final optimization result. This coupling method ensures collaborative optimization of the two-level objectives, avoids the disconnect between upper-level decision-making and lower-level execution, and improves the overall optimization effect of the model.

[0044] This invention provides a two-layer, multi-objective collaborative optimization method that integrates energy storage system scheduling and distribution network operation optimization. The technical effects are as follows: 1) This invention constructs a two-layer optimization objective function structure that coordinates the multi-objective demands of "energy storage revenue – peak shaving and valley filling" and "grid loss – voltage – energy curtailment". The upper-layer optimization model introduces a dynamic weighting factor based on load fluctuations; the lower-layer optimization model focuses on system operation stability and energy loss control. In terms of algorithm design, the upper-layer optimization model uses an improved whale optimization algorithm guided by dynamic weights to optimize energy storage power strategy, while the lower-layer optimization model introduces an improved multi-objective particle swarm optimization algorithm with congestion control and a hybrid coding mechanism. By designing a nested and coupled solution mechanism, information interaction and decoupling convergence between the upper and lower layers are effectively realized, ensuring global optimization performance and coordinated control capabilities, achieving a flexible balance between economic benefits and new energy utilization efficiency, and realizing the synergistic optimization of multiple operating indicators.

[0045] 2) This invention achieves significantly better results than existing technologies in improving the economic efficiency of energy storage systems, enhancing peak shaving and valley filling capabilities, improving voltage stability, reducing grid losses, and minimizing wind and solar power curtailment. Through synergistic optimization among multiple objectives, the method of this invention significantly improves the overall operational quality of the distribution network, demonstrating outstanding system optimization capabilities.

[0046] 3) This invention maintains stable and excellent performance in active distribution networks of different scales and topologies, fully demonstrating the high versatility and strong adaptability of the method. When operating conditions change, this method can effectively improve the overall system scheduling capability, providing an efficient, stable, and scalable technical approach for the optimized control of active distribution networks with deep integration of wind, solar, and energy storage. It has extremely strong engineering practical value and application prospects. Attached Figure Description

[0047] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 Diagram showing power output and load demand for wind and solar power.

[0048] Figure 2 This is a two-layer optimization strategy diagram.

[0049] Figure 3 This is a diagram of the IEEE 33-node system.

[0050] Figure 4 Net load curves before and after optimization for the IEEE 33-node system.

[0051] Figure 5 This is a diagram showing the energy storage benefits of the IEEE 33-node system.

[0052] Figure 6 A graph showing the energy storage revenue, dynamic weights, and load fluctuations for the IEEE 33-node system.

[0053] Figure 7 This is a network loss diagram for the IEEE 33-node system.

[0054] Figure 8 This is a diagram showing the energy wastage situation of the IEEE 33-node system.

[0055] Figure 9 This is a graph showing the sum of squares of voltage deviations exceeding the limit in the IEEE 33-node system.

[0056] Figure 10 Voltage diagrams of each node in the IEEE 33-node system at different times.

[0057] Figure 11 This is a diagram of the IEEE 69-node system.

[0058] Figure 12This is a diagram showing the energy storage benefits of the IEEE 69-node system.

[0059] Figure 13 Net load curves before and after optimization for the IEEE 69-node system.

[0060] Figure 14 This is the sum of squares of voltage deviations exceeding the limit in the IEEE 69-node system.

[0061] Figure 15 This is a diagram showing the energy wastage situation of the IEEE 69-node system.

[0062] Figure 16 This is a network loss diagram for the IEEE 69-node system. Detailed Implementation

[0063] To address the problems of severe load fluctuations, high energy curtailment, and large voltage deviations in active distribution networks caused by distributed generation grid connection, this invention proposes a two-layer, multi-objective collaborative optimization method integrating energy storage system scheduling and distribution network operation optimization. A two-layer optimization model is constructed. The upper-layer optimization model aims to achieve the optimal combination of energy storage system revenue and grid-side net load peak shaving and valley filling effects, introducing a dynamic weight adjustment mechanism based on load fluctuations and employing an improved whale optimization algorithm to optimize the intraday charging and discharging strategy of the energy storage system. The lower-layer optimization model aims to minimize network losses, node voltage deviations, and wind and solar curtailment in the active distribution network, employing an improved multi-objective particle swarm optimization algorithm to collaboratively adjust the reactive power compensation device, distributed generation output, and energy storage power distribution. To achieve efficient coupling and global convergence of the two-layer optimization model, an alternating iterative solution strategy and information feedback mechanism are designed.

[0064] Matlab simulations were conducted on improved IEEE 33-node and IEEE 69-node systems to verify the proposed method. Results show that the method can improve energy storage revenue and peak shaving / valley filling rates, effectively reduce network losses, significantly reduce energy curtailment, and also significantly improve voltage deviation, essentially eliminating voltage exceedance issues. Under various load fluctuation scenarios, the method demonstrates good adaptability and significant comprehensive benefits, fully proving its advantages under complex operating conditions. The proposed two-layer multi-objective collaborative optimization scheduling can effectively address the multiple challenges brought by distributed power generation grid integration, significantly improving the operational efficiency of active distribution networks and the capacity for renewable energy absorption. This method has good operational efficiency and engineering feasibility, providing strong support for the optimized scheduling of active distribution networks under complex operating environments.

[0065] (I) Dynamic weight adjustment mechanism based on load fluctuations: In active distribution networks, load volatility is increasing, and traditional fixed-weight or static dispatch strategies are insufficient to meet the multi-objective dispatch requirements of energy storage systems under different operating conditions. To enhance the responsiveness of energy storage systems to load changes, this invention proposes a dynamic weight adjustment mechanism based on load volatility characteristics. This mechanism senses the real-time fluctuation of the system load and dynamically generates weight factors in the optimization objectives, enabling the energy storage system to adaptively switch and balance between maximizing economic benefits and maximizing peak shaving and valley filling efficiency.

[0066] Energy storage revenue refers to the revenue generated by an energy storage system through time-shift arbitrage in the electricity market in response to electricity price signals. This involves charging during off-peak hours and discharging during peak hours to profit from the price difference. This economic benefit is typically measured and calculated based on the time-of-use pricing mechanism, as shown in equation (1).

[0067] (1); In formula (1): for t Electricity price at any time for t Total charge and discharge power of energy storage at all times. R For the benefits of energy storage systems; The time step is usually set to 1 hour.

[0068] This revenue metric reflects the operational flexibility and dispatch value of energy storage systems in participating in the electricity market. Wind and solar power output and load demand are shown below. Figure 1 As shown, this further demonstrates the dynamic characteristics of typical wind and solar power output and load demand. Energy storage systems utilize these time-series differences to carry out economical scheduling.

[0069] On the other hand, peak shaving and valley filling are important operational functions of energy storage systems to actively regulate the load curve. Specifically, this involves releasing energy during peak load periods and absorbing energy during off-peak periods to recharge, thereby smoothing the fluctuations in the load curve, reducing the instantaneous load rate of transformers and distribution lines, and thus improving the stability and safety margin of the power grid. This regulation effect can be quantitatively evaluated using the key technical indicator of peak shaving and valley filling rate. In this method, load fluctuation analysis is based on the net load curve. Net load is defined as the remaining power demand after deducting renewable energy sources such as wind power and photovoltaic power output in this invention from the total load, which can more accurately reflect the actual active power demand carried by the grid side. The net load is calculated as shown in equation (2).

[0070] (2); In formula (2): for t The system's original load at that moment; for tRenewable energy output at all times; for t Net load at any given moment.

[0071] The peak shaving and valley filling rate is calculated as shown in equation (3). It is used to measure the energy storage system's ability to regulate and smooth load fluctuations.

[0072] (3); In formula (3): To optimize the peak-to-valley difference in net load; To optimize the peak-to-valley difference in net load; CR This refers to the peak shaving and valley filling rate.

[0073] To coordinate the priority conflicts between the two types of objectives under different operating states, it is urgent to construct a scheduling strategy that can adaptively adjust according to the system's operating characteristics. Especially in typical scenarios such as unstable wind and solar power output and rapid load changes, energy storage systems often struggle to simultaneously achieve economic benefits and load regulation effects. Therefore, this invention proposes a dynamic weight factor generation method based on load fluctuation characteristics to achieve dynamic coordination and trade-off between economic efficiency and operational stability objectives in multi-objective optimization scheduling. This method can adaptively adjust the objective function weights in the optimization model according to the current operating state of the system, thereby improving the flexibility and responsiveness of the scheduling strategy. To enable the optimization model to have real-time perception of the system's operating state, this invention proposes a feature index that can quantify the degree of load fluctuation. Considering that loads in active distribution networks typically have significant periodicity and uncertainty characteristics, this method defines a load fluctuation coefficient based on load data within the rolling scheduling cycle to characterize the degree of deviation of the current load level from the steady-state load, as shown in equation (4).

[0074] (4); In equation (4): The current rolling cycle's intrinsic time. t The total system load; This is the arithmetic mean of the load during this period; For the system at time t The magnitude of load fluctuations.

[0075] Based on the obtained load fluctuation coefficient, a dynamic weighting function was further constructed, as shown in equation (5).

[0076] (5); In equation (5): For a moment t The weights corresponding to the energy storage revenue targets under the given conditions; , This is the adjustment coefficient; For the system in t The function measures the magnitude of load fluctuations at any given time. It exhibits good adjustability and continuity, dynamically adjusting the preference ratio between optimization objectives based on the degree of load fluctuation. This energy storage revenue weighting function can dynamically generate weighting factors for economic revenue objectives and peak shaving / valley filling objectives based on the intensity of fluctuations, thereby guiding the energy storage system to adaptively switch its scheduling focus in different operating scenarios.

[0077] Based on this, the present invention further embeds the dynamic weighting factor constructed above into the scheduling optimization model of the energy storage system, which is used to weight and integrate the economic benefit objective function and the peak shaving and valley filling objective function. Since the two have different dimensions, they need to be normalized, thereby constructing a multi-objective comprehensive optimization function, as shown in equation (6).

[0078] (6); In formula (6): For a moment t The weights corresponding to the energy storage revenue targets under the given conditions; The weights corresponding to the peak shaving and valley filling rate target; The normalized revenue of the energy storage system; This is the normalized peak-shaving and valley-filling rate.

[0079] The weight parameters in this function can be adaptively adjusted in real time according to the degree of load fluctuation, enabling the optimization model to dynamically switch the focus of its objectives based on the system state during operation, thus achieving intelligent adjustment of the operating strategy. This weighted comprehensive objective function, as a core component of the upper-level scheduling model, provides a unified modeling framework for coordinated optimization among multiple objectives. In practical applications, this mechanism can guide energy storage systems to flexibly adjust their charging and discharging strategies according to operating scenarios such as peak load periods, drastic electricity price fluctuations, and renewable energy output fluctuations, achieving dual guarantees of economic efficiency and operational stability, and improving the overall operational efficiency and control flexibility of the distribution network.

[0080] (II) Constructing a dynamic weight-driven wind-solar-storage dual-layer collaborative optimization model: To address the operational and control complexities arising from the large-scale integration of renewable energy into active distribution networks, this invention proposes a multi-objective, two-layer collaborative optimization scheduling model integrating wind power, photovoltaic, and energy storage systems. This model employs a typical two-layer optimization control architecture, addressing both economic optimization and system operational stability assurance to collaboratively achieve efficient operation of the multi-energy complementary system.

[0081] In the model structure design, the upper-layer optimization model serves as the scheduling optimization layer of the energy storage system. Its core objective is to achieve the comprehensive optimization of energy storage economic benefits and peak shaving and valley filling capabilities under the guidance of a dynamic weighting mechanism. The lower-layer model serves as the reactive power optimization control layer, focusing on the safety of system operation and power quality. Its main objectives include minimizing network losses, voltage deviation, and wind and solar power curtailment. Since the three have different dimensions, a weighted summation method is used to transform the multi-objective into a single objective.

[0082] 1) Minimize network loss: Based on the principle of power flow calculation, considering the active power loss of each branch, the objective function is shown in equation (7): (7); In equation (7): For branch set; and They are respectively t Time Branch ij The active and reactive power; This refers to the voltage at the end of the branch. For branch circuit conductance; The time step is typically set to 1 hour; T This represents the total daily time, typically taken as 24 hours. The goal is to reduce branch losses by optimizing reactive power distribution.

[0083] 2) Minimum voltage deviation: The goal is to minimize the sum of squares of the deviations between the voltage at each node and the rated voltage, so as to avoid voltage exceeding the limit, as shown in equation (8).

[0084] (8); In equation (8): A set of nodes; for t Time Node i Voltage; The node's rated voltage; T It represents the total time per day, usually taken as 24 hours.

[0085] 3) Minimum wind and solar power curtailment: Considering the energy curtailment caused by the randomness of wind and solar power output, the objective function is shown in equation (9).

[0086] (9); In equation (9): , for t Wind power output and solar power output at all times; for t The load demand at any given moment; TThis refers to the total daily time, typically taken as 24 hours. The goal is to improve the wind and solar energy integration capacity of the distribution network by optimizing reactive power distribution and energy storage scheduling.

[0087] The lower layer aims to minimize network loss, node voltage deviation, and wind and solar curtailment, as shown in equation (10): (10); In formula (10): , , These are network loss, node voltage deviation, and wind and solar power curtailment, respectively.

[0088] The two-layer optimization model constructs closed-loop control logic through the information interaction of key variables, forming a dynamic operating mechanism of "perception-optimization-feedback-adjustment". The overall model structure is as follows: Figure 2 As shown: The upper-level optimization model is responsible for generating the intraday charging and discharging strategy of the energy storage system and is the core of the feedforward control of the entire scheduling system. Its inputs include typical daily load forecast curves, wind and solar power output forecast curves, and time-of-use electricity price data. Under dynamic weight adjustment, the optimization objective function comprehensively considers the arbitrage benefits of energy storage and the ability to adjust the load curve. The main decision variable of the upper level is the total charging and discharging power allocation scheme of the energy storage system at each time, as shown in Equation (18).

[0089] (18); In equation (18): The charging and discharging power of the energy storage system at 1 o'clock; The charging and discharging power of the energy storage system at 2 o'clock. for t The charging and discharging power of the energy storage system at all times.

[0090] The total charge and discharge power command of the energy storage system output by the upper-level optimization model needs to be further decomposed based on the operating status, capacity constraints, and local network conditions of each energy storage unit in the lower-level model to achieve coordinated power allocation at the unit level. This power allocation process must not only consider power matching but also ensure that the allocation result is within the feasible operating domain of each energy storage device. Therefore, the decomposition and distribution of the total energy storage power must meet a series of operational constraints, mainly including: 1) Power boundary constraints, as shown in equation (14).

[0091] (14); In equation (14): , These represent the total minimum and maximum charge / discharge power of all energy storage systems, respectively. for t The charging and discharging power of all energy storage systems at all times.

[0092] 2) SOC boundary constraints, as shown in equations (19) and (20).

[0093] (19); (20); In equations (19) and (20): for t The total energy storage SOC at any given time must ensure that the total energy storage system SOC is within the allowable range during the scheduling cycle. for t- Total SOC at time 1; For time step; This refers to the rated capacity of the energy storage system. For charge and discharge efficiency; for t The charging and discharging power of the energy storage system at any given time.

[0094] 3) Capacity constraint, the total energy storage capacity is shown in equation (21).

[0095] (twenty one); In equation (21): For the first k The capacity of the energy storage system; This represents the total energy storage system capacity.

[0096] The total charge and discharge amount within the scheduling cycle must not exceed the total capacity, as shown in equation (22): (twenty two); In equation (22): for t The charging and discharging power of the energy storage system at all times; For time step; For charge and discharge efficiency; This represents the total energy storage system capacity.

[0097] Based on the scheduling boundary conditions generated by the upper-level optimization model, the system further calls the lower-level optimization model to perform real-time optimization control of the network operation status, ensuring the overall optimal combination of physical layer scheduling feasibility and grid operation quality. The lower-level model is primarily responsible for reactive power optimization control at the active distribution network operation level, combining real-time operation data to perform fine-grained system adjustments to ensure grid voltage stability, improve power transmission efficiency, and further reduce renewable energy curtailment. This model, based on the total energy storage power boundary output from the upper-level model, combines actual load changes and renewable energy output to achieve dynamic coordinated control of distributed energy resources. To achieve the above operational objectives, the model introduces multiple control methods as decision variables, mainly including: 1) Reactive power compensation output: Output of reactive power compensation device It must satisfy the condition shown in equation (23): (twenty three); In equation (23): and These are the minimum and maximum capacities of the reactive power compensation device, respectively.

[0098] 2) DG Output: The actual active power output of wind and solar power is and and reactive power output The reactive power must satisfy the following equation (24): (twenty four); In equation (24): and They are nodes i The minimum and maximum reactive power output of the DG.

[0099] In the lower-level optimization model, the final system output includes the reactive power of the energy storage system, the output of the reactive power compensation equipment, and the active and reactive power outputs of the distributed generation. To ensure that the control strategy is effectively implemented without compromising system stability, all control variables involved must strictly meet the physical feasibility requirements of grid operation, specifically including the following requirements: 1) Current constraints: The node power balance is satisfied as shown in equation (25): (25); In equation (25): and They are nodes i exist t At any given moment, DG contributes effort and does not contribute any effort. t and They are nodes i exist t Active and reactive power of the load at any given time; For nodes ij The voltage phase angle difference; For branch circuit susceptance; For nodes i exist t The charging and discharging power of the energy storage system at all times; N This represents the total number of nodes.

[0100] 2) Voltage amplitude constraint: The voltage amplitude must meet the requirements shown in equation (26): (26); In equation (26): For nodes i exist t Voltage at any given moment; , They are nodes i The maximum and minimum voltages at the node are specified. The allowable voltage offset range for each node is 0.95 pu to 1.05 pu to ensure voltage quality and system safety.

[0101] 3) Output constraints of distributed power sources: The active and reactive power outputs of the DG need to be adjusted within the rated range. The active power output constraint is shown in equation (27): (27); In equation (27): for t Time Node i The maximum active power that the DG can generate; for t Time Node i The active power generated by the DG.

[0102] The reactive power output constraint is shown in equation (28): (28); In equation (28): and They are respectively t Time Node i The maximum and minimum reactive power that the DG can generate; for t Time Node i The DG can generate reactive power.

[0103] 4) Branch power constraints: The transmission power of each branch must not exceed its rated capacity to avoid line overload, as shown in equation (29): (29); In equation (29): for t Time Branch ij Apparent power; branch road ij The rated transmission capacity.

[0104] 5) Capacitor bank switching: The output of the capacitor bank must be within the configured capacity range, and the switching state must conform to the discrete adjustment characteristics, that is, the output constraint is as shown in equation (30): (30); In equation (30): for t time k Number of capacitor banks switched on / off; This refers to the capacitance of a single capacitor group. The number of capacitor groups switched on / off at a single node should not exceed two groups at any given time to avoid frequent switching that could affect equipment lifespan.

[0105] 6) ESS charge / discharge constraints: To ensure the safe and stable operation of energy storage, the charging and discharging power constraints are as shown in equation (31): (31); In equation (31): for t Time Node i Energy storage charging and discharging power; and for t Time Node i The maximum and minimum charge and discharge power of the energy storage.

[0106] 7) Capacity constraints: The total charge and discharge of energy storage during the scheduling cycle shall not exceed the rated capacity, as shown in equations (32) and (33): (32); (33); In equations (32) and (33): This refers to the rated capacity of the energy storage. For charge and discharge efficiency; for t Real-time energy storage and charging power; for t Energy storage and discharge power at all times; T This represents the total time per day, usually taken as 24 hours. The time step is typically set to 1 hour. The core logic is to constrain the actual input power during charging and convert it to an equivalent charging power during discharging to avoid exceeding the actual capacity limit due to differences in charging and discharging efficiency.

[0107] In summary, the lower-level optimization model constructs a complete feasible domain for regulation by introducing a constraint system covering multiple aspects such as grid security, equipment capacity, and power quality. All constraints together constitute the feasible solution space of the lower-level optimization problem, which limits the adjustment range of decision variables and ensures that the scheduling results are technically operable and engineering implementable.

[0108] Based on the aforementioned construction of various operational constraints, to further coordinate the coupling relationship between local control behavior and global operational objectives, the system introduces an upper-lower layer linkage mechanism in its two-layer optimization architecture. This mechanism not only ensures the feasibility and real-time performance of the lower-layer scheduling scheme but also feeds back operational status information to the upper layer through feedback channels, driving dynamic adjustment of weight factors and strategy updates, thereby achieving adaptive coordination and closed-loop optimization among multiple objectives. The upper-layer model provides the lower layer with the total energy storage power boundary, while the lower-layer model feeds back network loss data, node voltage deviation data, etc., to the upper layer for dynamic weight factor adjustment and revenue calculation, forming a closed-loop collaboration.

[0109] To achieve the optimal balance between energy storage economics and grid operation safety, a two-layer optimization structure is constructed, with independent but coordinated upper and lower layers. This structure coordinates the interactive evolution of the two objectives through a nested coupling approach, where the upper-layer optimization acts as the outer loop and the lower-layer optimization acts as the inner loop. The specific process is as follows: 1) Initialize dynamic weight factors Set an initial value for the total energy storage power, solve the upper-level objective function, and obtain the initial value. .

[0110] 2) As an inner constraint, solve the lower-level multi-objective reactive power optimization model to obtain decision variables such as reactive power compensation output, and calculate the lower-level target values ​​of network loss, node voltage deviation, and wind and solar curtailment.

[0111] 3) Calculate network losses and wasted energy losses at the lower layer to adjust the energy storage benefits at the upper layer. R Simultaneously, the dynamic weighting factor is updated based on real-time load and wind-solar fluctuations. .

[0112] 4) Repeat steps 1) through 3) until the upper-level objective function converges, and output the final optimization result. This coupling method ensures collaborative optimization of the two-level objectives, avoids the disconnect between upper-level decision-making and lower-level execution, and improves the overall optimization effect of the model.

[0113] (III) Improved combination of whale optimization algorithm and multi-objective particle swarm optimization algorithm with bidirectional coupling iterative mechanism: To achieve the goal of coordinated operation of energy sources, loads, and storage in active distribution networks, while ensuring operational economy, system safety, and physical feasibility, this invention constructs a two-layer multi-objective optimization model and designs a nested collaborative solution mechanism jointly driven by an improved whale optimization algorithm and an improved multi-objective particle swarm optimization algorithm. Considering the significant differences between the upper and lower layer models in terms of objective structure, variable dimensions, and solution requirements, differentiated optimization strategies are adopted for matching solutions. Furthermore, a bidirectional coupled iterative mechanism is used to achieve coordinated optimization and information feedback.

[0114] The upper-level optimization model improves the whale optimization algorithm. This model integrates the economic benefits and peak-shaving / valley-filling capabilities of the energy storage system in a weighted single-objective manner, with the optimization variable being a 24-hour continuous charge-discharge power sequence. It requires continuous, low-dimensional, and global search capabilities. To accommodate these characteristics, the whale optimization algorithm, which has good global search performance and a simple parameter structure, is selected, and improvements are made in the following three aspects: 1) Dynamic weight embedding fitness function: To achieve target-guided direction adjustment driven by operational status, the dynamic weights corresponding to load fluctuations are embedded in the fitness evaluation to realize real-time perception and adjustment of target preferences, as shown in Equation (11): (11); In equation (11): The weights of the objective function related to the economic benefits of the energy storage system; Represents the weights of the objective function related to load fluctuations (peak shaving and valley filling); The load fluctuation factor quantifies the degree of fluctuation in the system load at the current moment; a larger value indicates more severe fluctuation. 2) The Sigmoid function regulates the balance between exploration and development: The Sigmoid function adjusts the convergence rhythm of the search factors, enabling the algorithm to enhance population diversity and global exploration capabilities in the early stages, and strengthen local development to accelerate convergence in the later stages, as shown in Equation (12): (12); In equation (12): To control parameters, with the number of iterations... k change; μ This is the kurtosis control factor for the Sigmoid function, which determines the adjustment rate; k This represents the current iteration number.

[0115] 3) Hybrid encoding initialization mechanism: Historical strategy perturbation and local search heuristics are introduced into the initial population to improve the breadth and quality of the population distribution and reduce the risk of getting trapped in local optima, as shown in Equation (13).

[0116] (13); In equation (13): for i The initial solution for an individual; Candidate solutions generated by the machine; This is a historically excellent solution or a reference solution; The sum factor (between 0 and 1) controls the proportional weight between historical experience and new solutions.

[0117] After the solution is completed, the energy storage power boundary sequence that satisfies the constraints is output as the input to the lower-level optimization model.

[0118] The lower-level optimization model employs an improved multi-objective particle swarm optimization algorithm. This model involves reactive power optimization control of the distribution network, requiring the simultaneous minimization of network losses, node voltage deviations, and energy curtailment. Furthermore, it involves a mix of variable types, including energy storage node location, reactive power output, and voltage control, resulting in high decision-making dimensionality and strong objective conflicts, making it suitable for solving using a multi-objective particle swarm optimization algorithm. This invention improves the standard multi-objective particle swarm optimization algorithm as follows: 1) Hybrid coding mechanism: Continuous and discrete variables, such as voltage setpoint and reactive power compensation equipment switching status, are processed by a combination of real number encoding and integer encoding, as shown in equation (15).

[0119] (15); In equation (15): The active power of the energy storage system; Provide power to the SVG reactive power compensation equipment; The node number for energy storage access (discrete variable); for i The individual's solution.

[0120] 2) Crowding distance guides the uniformity of non-dominated solution sets: The breadth and uniformity of the Pareto front distribution are maintained by calculating the crowding distance of the solution set, as shown in Equation (16).

[0121] (16); In equation (16): , For the first m The values ​​of the solutions before and after in the objective function; , For the maximum and minimum values ​​of the target.

[0122] 3) External elite archives drive global convergence: An external elite library composed of non-dominated solutions is introduced for reference during particle updates, in order to improve global convergence speed and multi-objective balance, as shown in Equation (17).

[0123] (17); In equation (17): Inertia weighting, balancing development and exploration; , Learning factors; , Take a random number between [0, 1]. Individual historical best position; Global historical best position; for i The individual's initial attempt to resolve the issue; This indicates the update direction and step size of the solution in the search space.

[0124] To address the issues of information isolation and target deviation between upper and lower optimization models, a nested iterative solution process is constructed, consisting of an outer-layer improved whale algorithm and an inner-layer improved multi-objective particle swarm optimization algorithm. This ensures that the upper-layer strategy is physically feasible in the lower layer, while feedback from the lower layer can correct the upper-layer target.

[0125] Step 1: Upper-level initialization and solution: Initialize energy storage scheduling parameters The power boundary scheme is obtained by performing the improved whale algorithm according to formulas (11) to (13). .

[0126] Step 2: Optimize the state of the lower-layer network: by As the boundary input, the lower-level optimization model is solved using an improved multi-objective particle swarm optimization algorithm, and the reactive power optimization scheme and index set are output. .

[0127] Step 3: Feedback Correction and Weight Update The upper-level economic objectives and weighting function parameters are dynamically adjusted based on the impact of energy curtailment and network losses, and the scheduling forecasts are updated based on actual load and renewable energy fluctuations.

[0128] Step 4: Iterate alternately until convergence: When the changes in the scheduling results of two consecutive iterations satisfy the convergence condition shown in equation (34), the iteration stops, and the optimal scheduling result of the two-layer collaborative optimization is output. (34); In equation (34): For the first k The multi-objective scheduling result vector of the next iteration; For the firstk The result vector of multi-objective scheduling after one iteration; Convergence threshold.

[0129] This bidirectional coupling mechanism effectively solves the problem of "difficulty in executing upper-level strategies at the lower level" caused by traditional upper-lower-level optimization decoupling. It ensures that the optimization process takes into account both the goals of higher-level strategies and the operational constraints of the lower-level power grid, thereby achieving multi-objective, multi-time-scale, and multi-device collaborative operation optimization, significantly improving the intelligent scheduling capability and overall operational efficiency of the active distribution network.

[0130] In summary, by introducing a dynamic weight adjustment mechanism based on load fluctuation characteristics, the upper-level scheduling model can optimize the adaptive charging and discharging strategy of the energy storage system according to the dynamic changes in time-of-use pricing and load, significantly improving economic response capability and control flexibility. With this multi-objective strategy, the system achieves dynamic balance among multiple operational objectives such as revenue acquisition, peak shaving and valley filling, and voltage support, demonstrating the comprehensive operational benefits of the energy storage system under the background of source-load-storage synergistic optimization.

[0131] To further verify the feasibility and universality of the proposed optimization method, this invention conducts a case study analysis based on a typical test system. An IEEE 33-node active distribution network incorporating wind, solar, and energy storage is selected as the simulation platform. Figure 3 As shown, based on the multi-objective two-layer optimization framework proposed in this invention, system scheduling optimization is performed by combining predicted load, renewable energy output, and electricity price information. The specific results are as follows: 1) Analysis of upper-level optimization results: The optimization results at the upper level show the changes in the net load curve of the active distribution network before and after the energy storage system's participation, as well as the corresponding intraday revenue distribution of the energy storage system, such as... Figure 4 and Figure 5 As shown.

[0132] The changes in the net load curve of the active distribution network before and after the participation of the energy storage system are shown in the figure. Figure 4 As shown, before the integration of energy storage, the system's net load curve exhibited a distinct "double-peak" characteristic. During periods such as 0:00–5:00, 12:00–14:00, and 23:00–24:00, the net load turned negative due to wind and solar power output exceeding load demand, indicating significant energy curtailment. By introducing an energy storage system and optimizing its scheduling, it actively absorbs redundant electricity during low-load periods and discharges it in an orderly manner during high-load periods. This significantly reduced the fluctuation range of the net load, increasing the peak shaving rate to 15.1% and decreasing the peak-to-valley difference from 2477.4 kWh to 1653.2 kWh, a 34% reduction in fluctuation, thus significantly improving the system's load distribution.

[0133] The intraday charging and discharging behavior and economic benefit distribution of energy storage systems in different electricity price ranges are shown in the figure. Figure 5 As shown in the figure, the results indicate that during periods of high electricity prices, such as 7:00, 10:00, and 16:00–21:00, the energy storage system prioritizes discharging to generate revenue; while during periods of low electricity prices, such as 1:00–4:00 and 12:00–15:00, the system schedules energy storage charging to achieve price arbitrage. The total daily revenue reached 427.4 yuan, demonstrating that this scheduling strategy is significantly economical while ensuring safe operation.

[0134] Furthermore, during periods with moderate electricity prices but low load fluctuations (such as 4:00–6:00, 9:00–10:00, 12:00, and 20:00), the energy storage system did not perform any discharge operations, resulting in zero revenue. However, this operational state is not due to resource idleness, but rather stems from the intelligent selection of the scheduling model under a multi-objective function trade-off. Its core lies in achieving a synergistic optimization between system revenue, power quality, and renewable energy utilization.

[0135] The main purpose of introducing a dynamic weighting mechanism is to achieve a real-time trade-off between maximizing revenue and optimizing load regulation capacity in energy storage systems. In this mechanism, the dynamic weighting factor acts as a regulator of the objective function, adaptively changing with the degree of load fluctuation, thereby driving the energy storage system to automatically switch the optimization target focus under different operating conditions, achieving refined control at the strategy level.

[0136] To further reveal the coupling relationship between the operating behavior of energy storage systems and dynamic weighting factors, Figure 5 and Figure 6 The study jointly demonstrated the behavioral characteristics and strategic responses of energy storage systems under different load and electricity price conditions. Revenue, revenue weight, and load fluctuations exhibited a dynamic game-like relationship of "inverse relationship" throughout the day. Figure 6 As shown, this exhibits typical state-driven control characteristics in the scheduling strategy. For example, during the period from 1:00 to 5:00, although the electricity price is low, the load fluctuation is not significant. The system prioritizes charging operations by increasing the revenue weight to provide energy reserves for peak periods. During the period from 7:00 to 10:00, the electricity price increases and the load fluctuation weakens. The weight further shifts towards the revenue target, and the energy storage system fully discharges to maximize economic benefits. However, when the load fluctuation significantly increases at 20:00, even though the electricity price is still high, the system automatically reduces the revenue weight to prioritize load balance and grid security, reflecting the rapid adaptability of the energy storage scheduling system to sudden load disturbances.

[0137] It is particularly noteworthy that after frequent discharges in the early stage, the energy storage system enters the capacity protection phase. In order to avoid deep discharge leading to SOC exceeding the limit, the dispatch system actively suppresses discharge behavior. Even if there is still arbitrage space in the electricity price or fluctuation level, the system still prioritizes the safety of the equipment and leaves room for adjustment in subsequent strategies, reflecting the overall optimization concept of "efficiency-safety-sustainability".

[0138] In summary, guided by this scheduling model, the energy storage system can adjust its behavior strategy in real time according to its operating status, achieving balanced regulation under multi-dimensional objectives. This strategy demonstrates strong engineering practicality and operational intelligence, laying a theoretical and applied foundation for its subsequent promotion in larger-scale and complex power grids.

[0139] 2) Analysis of optimization results of the lower-level optimization model: Lower-level optimization primarily focuses on the comprehensive improvement of active distribution network operation indicators. By coordinating and regulating the output behavior of energy storage systems in both spatial and temporal dimensions, it further enhances grid operating efficiency, power quality, and renewable energy absorption capacity. Based on the upper-level dispatch strategy which has determined the total power boundary of the energy storage system, the lower-level optimization model comprehensively considers operational objectives such as network loss suppression, energy curtailment control, and node voltage stability, and performs fine-tuning of the underlying physical state under various operational constraints. Changes in key indicators such as network active power loss, energy curtailment, and node voltage deviation before and after optimization are shown below. Figures 7-10 As shown.

[0140] Network active power loss before and after optimization, such as Figure 7 As shown, before the energy storage system participates in dispatching, the active power loss of the active distribution network lines generally increases with the increase of load level, exhibiting a strong positive correlation. Especially during the evening peak period at 20:00, due to the long-distance power supply from the main grid and the dense concurrent load of users, the power flow of the lines is significantly enhanced, resulting in a rapid increase in feeder current and the network loss reaching the peak level.

[0141] After introducing lower-level optimized scheduling, the system fully utilizes the spatiotemporal flexibility of energy storage, dynamically adjusting its output based on multi-dimensional state variables such as electricity price, voltage, and power flow distribution. During off-peak hours at night (e.g., 0:00–5:00), the load is low, limiting the regulatory effect of energy storage, and the loss curves before and after optimization largely overlap. However, from 10:00–15:00 at noon, photovoltaic output is abundant, the proportion of local power supply in the distribution network increases, and power flow redistribution becomes significant, causing local voltage shifts and power backflow, leading to increased network losses. During this period, the energy storage system actively absorbs excess power and participates in voltage support, alleviating power flow pressure and slightly reducing losses.

[0142] During the evening peak period (16:00–21:00), as renewable energy output decreases and system load increases, the energy storage system reduces the main grid power supply pressure and effectively lowers the branch power flow amplitude through pre-charging and precise discharging strategies. This significantly suppresses network active power loss during this period, demonstrating the effectiveness of the scheduling strategy in co-optimizing load centers and power flow paths.

[0143] The changes in energy wastage of the system at different operating stages are as follows: Figure 8As shown. Before optimization, due to the high penetration of photovoltaic and wind power resources in the active distribution network, especially during the midday when there is sufficient sunlight (11:00–14:00) and the early morning when the wind speed is high (0:00–5:00), the peak output of renewable energy is high, far exceeding the local load absorption capacity, resulting in the peak energy curtailment exceeding 1000kWh at one point.

[0144] After optimized scheduling, the energy storage system adopts a load-tracking absorption strategy based on system status and output forecasts, actively charging during peak renewable energy output periods. This effectively buffers localized energy surplus and significantly improves the utilization rate of clean energy. Compared to before optimization, energy curtailment is significantly reduced, especially during midday, demonstrating the effectiveness of the proposed multi-objective scheduling strategy in renewable energy absorption.

[0145] The system's node voltage exceedance risk and voltage distribution before and after optimization, such as... Figure 9 and Figure 10 As shown. The node voltage exceedances of the system before and after optimization are as follows: Figure 9 As shown, before optimization, the distribution network experienced voltage fluctuations during high-output periods (midday photovoltaic power generation) and high-load periods (evening peak). The voltage at some nodes exceeded the allowable operating range (0.95–1.05 pu), posing a risk of voltage exceeding limits and resulting in poor system stability.

[0146] After optimized scheduling, the energy storage system achieves flexible regulation of local voltage through precise time-of-day output control and node power injection adjustment. During the midday period, energy storage primarily absorbs loads, reducing node voltage fluctuations; in areas with concentrated evening peak loads, energy storage provides active and reactive power support, raising the lower limit of local voltage and significantly reducing the overall grid voltage deviation. The optimized node voltage three-dimensional surface diagram is shown below. Figure 10 As shown in the figure. The results show that the overall voltage curve tends to be smoother, and the voltages of all nodes fall within the safe range, indicating that the system voltage control performance has been significantly enhanced.

[0147] 3) Scene comparison: After validating the effectiveness of the two-layer optimization model under typical operating conditions, multiple typical operating scenarios were further constructed to comprehensively evaluate the adaptability and optimization performance of the proposed dynamic weight-driven two-layer collaborative optimization architecture under different power grid operating states and strategy configurations. This comparative analysis aims to quantitatively reveal the performance differences between the dynamic weight mechanism, upper-lower-layer collaborative control, and traditional fixed strategies in key operating indicators, and to verify the universality and promotion potential of the proposed method.

[0148] To conduct comparative evaluation of the system, five operational scenarios with progressive characteristics are defined as follows: Scenario 1 is the original network without optimization and without energy storage configuration; Scenario 2 is active distribution network with only reactive power optimization and no energy storage participation; Scenario 3 is active distribution network with fixed weights where energy storage optimization scheduling and reactive power optimization are performed independently; Scenario 4 is active distribution network with fixed weights where energy storage optimization scheduling and reactive power optimization are operated jointly; Scenario 5 is active distribution network with dynamic weights where energy storage optimization scheduling and reactive power optimization are operated jointly.

[0149] Scenarios 1 and 2 are used to calibrate basic benefits; Scenarios 3 and 4 are used to quantify joint and independent strategies; Scenarios 4 and 5 focus on the differences between fixed and dynamic weight strategies to verify the adaptability and superiority of the proposed strategy in multiple scenarios. The optimization results for each scenario are shown in Table 1.

[0150]

[0151] As shown in Table 1, after introducing reactive power optimization from Scenario 1 to Scenario 2, the total network loss of the system decreased by 19.3%, the energy curtailment decreased by 4.52%, and the sum of squares of voltage exceedances decreased by 21.7%, indicating that basic reactive power optimization has a good effect on improving power quality. Further, in Scenario 3, an energy storage system was introduced for independent optimization, resulting in a further decrease of 8.84% in network loss compared to Scenario 2, a peak shaving rate of 9.4%, and an increase in energy storage revenue to 278.6 yuan. Simultaneously, energy curtailment decreased by 54%, fully demonstrating the significant role of energy storage systems in load regulation and renewable energy absorption. In Scenario 4, after adopting joint optimization of energy storage and reactive power, although the network loss increased slightly by 8.57% compared to Scenario 3, the voltage exceedance problem was significantly improved, the peak shaving rate increased by 43.8%, and the energy storage revenue increased by 13.2%, indicating that the multi-objective collaborative mechanism improved the overall system performance. After introducing a hierarchical control strategy with dynamic weights in scenario 5, network losses decreased significantly by 25.0% compared to scenario 4, energy storage revenue increased by 35.4%, abandoned energy decreased by 22.9%, voltage over-limit issues were almost eliminated, and all indicators reached their optimal state.

[0152] This optimization strategy, while balancing multiple objectives such as loss reduction, efficiency improvement, voltage and energy curtailment constraints, overcomes the scheduling dilemma of traditional models that struggle to balance economy and safety. It provides a smoother, safer, and more economical operating boundary for upper-level energy storage systems, further enhances the closed-loop coupling capability of the two-layer collaborative model, and achieves multi-dimensional synergistic improvement in operating efficiency, grid stability, and renewable energy utilization. This provides strong support for distribution network operation and scheduling in practical engineering projects.

[0153] 4) Comparison under different loads: After verifying the performance under normal operating conditions, to further examine the adaptability of the proposed two-layer dynamic weighted optimization scheduling method to load fluctuations in actual power grid operation, the model was placed in extreme operating scenarios for testing and comparative evaluation. Specifically, two typical extreme operating scenarios, underload and overload, were designed to simulate the scheduling response capability of the energy storage system and the effectiveness of the optimization strategy under conditions of low load energy surplus and high load system strain.

[0154] In underload scenarios, grid load demand is assumed to be 80% of the original load, simulating a low-load operating state. In this scenario, renewable energy output often exceeds grid demand, resulting in energy surplus. Energy storage systems absorb excess electricity during low-load periods, reducing energy curtailment and optimizing grid load balance. Through optimized scheduling, energy storage systems can effectively improve grid stability and economic efficiency.

[0155] In an overload scenario, the grid load demand increases to 130% of the original load, simulating a high-load operation of the grid. At this time, the energy storage system primarily supports the grid by discharging power, alleviating grid load pressure. The dispatching of the energy storage system during high-load periods can reduce network losses, support grid voltage, and improve economic efficiency.

[0156] To more intuitively demonstrate the coordinated scheduling effect of the energy storage system under two extreme load conditions, Table 2 summarizes and compares the main operating indicators under underload and overload scenarios.

[0157]

[0158] In underload scenarios, energy storage primarily absorbs surplus energy through charging. Table 2 shows that a peak shaving rate of 16.5% was achieved, and the total abandoned energy was controlled at 5430.6 kWh. Simultaneously, the sum of squares of voltage exceedances was nearly zero, ensuring grid stability. The energy storage system also generated revenue of 448.8 yuan. In overload scenarios, energy storage supports the grid through discharging. Table 2 shows that the energy storage system generated 114.8 yuan in revenue, controlled total network losses at 2589.3 kWh, reduced total abandoned energy, and the sum of squares of voltage exceedances was nearly zero. This effectively alleviated grid supply pressure while also ensuring overall system economic efficiency.

[0159] 5) Algorithm verification: After verifying the operational adaptability and system profitability of the proposed dynamic weighted two-layer collaborative optimization model under multiple scenarios, loads, and topology conditions, it is further necessary to conduct a quantitative comparative analysis of the differences in scheduling performance at the algorithm level. To this end, an algorithm combination comparison experiment was designed to evaluate the collaborative control capability, optimization objective convergence effect, and global scheduling performance of different optimization strategies under the two-layer architecture.

[0160] This experiment constructed three typical algorithm combinations for simulation comparison: the upper and lower layers both adopted the standard Whale Optimization Algorithm (WOA), focusing on preserving global search capability; both upper and lower layers adopted the Multi-Objective Particle Swarm Optimization Algorithm (MOPSO), emphasizing multi-objective balanced search and solution set distribution performance; the upper layer used the improved Whale Optimization Algorithm (IWOA) for continuous charging and discharging strategy search, and the lower layer used IMOPS to solve reactive power optimization and voltage regulation problems under multi-objective constraints, forming a differentiated collaborative solution mechanism. The optimization results are shown in Table 3.

[0161] As shown in Table 3, the IWOA and IMOPSO combination outperforms the WOA+WOA and MOPSO+MOPSO combinations in terms of peak shaving rate, energy storage revenue, network loss suppression, energy curtailment control, and voltage stability, based on the optimization results. Specifically, the dynamic weighting mechanism, combined with IWOA's efficient search capability for energy storage charging and discharging strategies at the upper layer and IMOPSO's advantages in multi-objective trade-offs at the lower layer, increases the system's peak shaving rate to 15.11%, energy storage revenue to 427.4 yuan, and significantly reduces energy curtailment and voltage exceedance indicators, demonstrating stronger operational adaptability and collaborative optimization capabilities.

[0162] 6) Simulation of the IEEE 69-node system: Based on the aforementioned comparison of strategies across multiple scenarios, to further verify the applicability and robustness of the proposed dynamic weight-driven two-layer collaborative optimization scheduling method under different distribution network topologies, this invention introduces a larger-scale and more complex IEEE 69-bus system as a test platform, such as... Figure 11 As shown. Compared to the IEEE 33-node system, this network has longer feeders, more complex power distribution characteristics, and more stringent voltage control requirements, thus enabling a more effective evaluation of the proposed optimization strategy's migration capability and control generalization performance in multi-topology, multi-node environments.

[0163] This simulation is based on the standard IEEE 69-node distribution network structure, and performance analysis is conducted by combining typical operating loads and output curves of distributed renewable energy (wind and solar power). To ensure comparability, the load curves, wind and solar power output data, and time-of-use pricing used are consistent with those of the IEEE 33-node test, and the load has been adaptively scaled according to the node's rated capacity. The initialization parameters of the control algorithm remain unchanged to allow for horizontal comparison of the adaptability of various scheduling strategies under different system structures.

[0164] The energy storage revenue diagram for the IEEE 69-bus system is shown below. Figure 12As shown, the energy storage system achieved a daily revenue of 347.93 yuan under optimized scheduling, maintaining an arbitrage capability similar to that of the 33-node system, reflecting that the strategy still maintains good economic performance under cross-system structures.

[0165] Net load curves of the IEEE 69-bus system before and after optimization, such as... Figure 13 As shown, the system achieved a peak reduction rate of 15.11%, successfully reducing the daily peak load, significantly decreasing the dependence on the main grid power supply during peak hours, and improving the stability of the load curve.

[0166] The sum of squares of voltage deviations exceeding the limit in the IEEE 69-bus system, such as Figure 14 As shown, the optimized network's daily cumulative loss decreased from the original peak of approximately 290 kWh to 180 kWh, a reduction of 38%, demonstrating that the power flow path scheduling and energy storage power coordination mechanism still possesses strong loss reduction capabilities in large-scale systems.

[0167] A diagram illustrating energy curtailment in the IEEE 69-node system is shown below. Figure 15 As shown, the amount of wind and solar power curtailed decreased from 4999.2 kWh to 2842.2 kWh, a reduction of 43%, indicating that energy storage systems have a strong redundancy absorption capacity during periods of high output, which can effectively curb the waste of new energy resources.

[0168] Network loss in the IEEE 69-node system, such as Figure 16 As shown, the sum of squares of voltage over-limits decreased from 0.055 before optimization to 0.001, almost completely eliminating the risk of over-limits and effectively ensuring that the voltage of each node in the system is within the safe operating range.

[0169] In summary, the optimization results further validate the broad adaptability and portability of the proposed two-layer cooperative scheduling strategy in the IEEE 69-node system, fully demonstrating its versatility and engineering practical value in power distribution systems of different scales and structures. These results not only solidify the effectiveness of the method in standard network models but also provide strong data support for its widespread application in real-world complex power distribution scenarios.

Claims

1. A method for two-layer multi-objective collaborative optimization integrating energy storage system scheduling and distribution network operation optimization, characterized in that... Includes the following steps: Step 1: Propose a dynamic weight adjustment mechanism based on load fluctuation. The load fluctuation coefficient is generated by calculating the deviation between the current load and the average load, and the energy storage revenue weight and peak shaving and valley filling weight are dynamically generated by the dynamic weight function. Step 2: Construct a two-layer collaborative optimization model for wind, solar and storage driven by dynamic weights. The upper-layer optimization model generates charging and discharging plans with energy storage revenue and peak shaving as dual objectives; the lower-layer optimization model aims to minimize network losses, voltage deviation and wind and solar curtailment; thus forming a multi-objective optimization framework integrating source-grid-load-storage. Step 3: A combined strategy of improved whale optimization and multi-objective particle swarm optimization algorithms is adopted, which are used for upper-level energy storage scheduling and lower-level reactive power optimization, respectively, and the solution is solved collaboratively by alternating iteration and information feedback mechanism.

2. The method for dual-layer multi-objective collaborative optimization integrating energy storage system scheduling and distribution network operation optimization as described in claim 1, characterized in that: In step 1, energy storage revenue refers to the economic benefits obtained by the energy storage system through participating in off-peak charging and peak discharging in the electricity market, calculated based on the time-of-use pricing mechanism, as shown in equation (1): （1）； In equation (1), for t Electricity price at any given time; for t Total charge and discharge power of energy storage at all times; For the benefits of energy storage systems; For time step; T Total time per day; Peak shaving and valley filling refer to the charging and discharging behavior of energy storage systems, discharging during peak load and charging during off-peak load. The peak shaving and valley filling rate reflects the energy storage system's ability to adjust the load curve. The basis for analyzing load fluctuations is the net load curve, which is the load amount after deducting the output of renewable energy from the original load. The expression for the net load is shown in equation (2): （2）； In equation (2), for t The system's original load at that moment; for t Renewable energy output at all times; for t Net load at any given time; The expression for the peak shaving and valley filling rate is shown in equation (3): （3）； In equation (3), To optimize the peak-to-valley difference in net load; To optimize the peak-to-valley difference in net load; CR This refers to the peak shaving and valley filling rate.

3. The method for dual-layer multi-objective collaborative optimization integrating energy storage system scheduling and distribution network operation optimization as described in claim 2, characterized in that: In step 1, in order to establish a dynamic coordination relationship between maximizing the economic benefits of the energy storage system and optimizing the peak shaving and valley filling efficiency, a dynamic weight factor construction method based on load fluctuation characteristics is proposed to connect the two types of scheduling objectives. Considering that the load in the active distribution network has obvious periodicity and uncertainty, based on the load data in the rolling scheduling cycle, the load fluctuation coefficient shown in Equation (4) is defined to quantify the degree of deviation of the current load level from the steady-state load. （4）； In equation (4), For the current rolling cycle t Total system load at any given time; This is the arithmetic mean of the load during this period; For the system in t The magnitude of load fluctuations at any given time; Based on the obtained load fluctuation coefficient, a normalized dynamic weight function as shown in equation (5) is further constructed to generate the dynamic weight factors for each optimization objective: （5）； In equation (5), for t The weight corresponding to the energy storage revenue target at any given time; , This is the adjustment coefficient; For the system in t The magnitude of load fluctuation at any given time.

4. The method for dual-layer multi-objective collaborative optimization integrating energy storage system scheduling and distribution network operation optimization as described in claim 3, characterized in that: Based on the constructed dynamic weighting factor, it is further embedded into the energy storage scheduling optimization model containing the objective functions of equations (1) and (3) to perform weighted integration of the economic benefit objective function shown in equation (1) and the peak shaving and valley filling objective function shown in equation (3), thereby achieving comprehensive optimization of the energy storage operation economy and load regulation capability; since the two have different dimensions, they need to be normalized to form a multi-objective comprehensive optimization function, as shown in equation (6): （6）； In equation (6), For multi-objective comprehensive optimization functions; for t The weight corresponding to the energy storage revenue target at any given time; The weights corresponding to the peak shaving and valley filling rate target; The normalized revenue of the energy storage system; This is the normalized peak-shaving and valley-filling rate; The dynamic weights are adaptively adjusted according to the degree of load fluctuation, so that the optimization objectives can automatically switch the focus according to the system state during operation: when the load fluctuation is large, the weight of peak shaving and valley filling is adaptively adjusted according to the degree of load fluctuation, while when the load fluctuation is small, the weight of energy storage revenue is adaptively adjusted according to the degree of load fluctuation; and the multi-objective comprehensive optimization function shown in Equation (6) serves as the core objective function of the upper-level scheduling model, realizing the dynamic optimization and collaborative control of the scheduling strategy.

5. The method for dual-layer multi-objective collaborative optimization integrating energy storage system scheduling and distribution network operation optimization according to claim 4, characterized in that: In step 2, in order to achieve coordinated optimization of the wind-solar-storage active distribution network under multi-objective operation, a two-layer collaborative optimization model consisting of an energy storage scheduling layer and a reactive power optimization layer is designed based on the dynamic weighting factor constructed in step 1, so as to enhance the system's economy, stability and new energy consumption capacity. The upper-level optimization model takes the dual objectives of maximizing the economic benefits of the energy storage system and maximizing the peak shaving and valley filling efficiency as the dual objectives. The two objective functions shown in Equation (1) and Equation (3) are weighted and fused using dynamic weight factors to form the comprehensive objective function shown in Equation (6). The optimization result is the charging and discharging power plan of the energy storage system within 24 hours. When the system load fluctuates, the energy storage revenue weight shown in Equation (5) will also be dynamically adjusted. The revenue weight will then affect the energy storage revenue shown in Equation (1). The energy storage revenue is mainly determined by the time-of-use electricity price level and the charging and discharging behavior of the energy storage system. Through a dynamic weight adjustment mechanism, the upper-level optimization model actively adjusts scheduling preferences based on the operating status, balancing economy and adjustment capability.

6. The method for dual-layer multi-objective collaborative optimization of energy storage system scheduling and distribution network operation optimization according to claim 5, characterized in that: In step 2, after completing the upper-level energy storage charging and discharging power optimization plan, a lower-level optimization model is further constructed to achieve a dual improvement in grid operation performance and new energy absorption capacity. The lower-level optimization model takes the energy storage system power boundary from the upper-level optimization model as its active power input condition and collaboratively optimizes the reactive power distribution in the distribution network. The lower-level optimization model proposes three collaborative optimization objective functions, as follows: 1) Minimize network loss: Based on the principle of power flow calculation, considering the active power loss of each branch, the objective function is shown in equation (7): （7）； In equation (7), To minimize network loss; T Total time per day; For branch set; and They are respectively t Time Branch i - j The active and reactive power; This refers to the voltage at the end of the branch. For branch circuit conductance; For time step; 2) Minimum voltage deviation: The goal is to minimize the sum of squares of the deviations between the voltage at each node and the rated voltage, so as to avoid voltage exceeding the limit, as shown in equation (8). （8）； In equation (8), This is the sum of squares of the deviations between the voltage at each node and the rated voltage; A set of nodes; Let be the voltage at node i at time t; The node's rated voltage; 3) Minimum wind and solar power curtailment: Considering the energy curtailment caused by the randomness of wind and solar power output, the objective function is shown in equation (9); （9）； In equation (9), Waste energy that contributes to the scenery; , Wind power output and photovoltaic power output at time t, respectively; Let be the load demand at time t; The lower-level optimization model aims to minimize network loss, node voltage deviation, and wind and solar curtailment, as shown in Equation (10). (10); In equation (10), It is a comprehensive function that minimizes network loss, node voltage deviation, and wind and solar curtailment. , , These are network loss, node voltage deviation, and wind and solar power curtailment, respectively.

7. The method for dual-layer multi-objective collaborative optimization integrating energy storage system scheduling and distribution network operation optimization according to claim 6, characterized in that: In step 3, the upper-level optimization model adopts the Improved Whale Optimization Algorithm (IWOA), and the following improvement strategies are introduced to enhance the standard whale optimization algorithm, specifically including: 1) Dynamic weight embedding fitness function: To achieve target guidance direction adjustment driven by operating status, the dynamic weight corresponding to load fluctuation is embedded in the fitness evaluation to realize real-time perception and adjustment of target preference, as shown in Equation (11); （11）； In equation (11): The fitness function; The weights of the objective function related to the economic benefits of the energy storage system; This represents the weights of the objective function related to load fluctuations; The load fluctuation factor quantifies the degree of fluctuation in the system load at the current moment; the larger the value, the more severe the fluctuation. 2) The Sigmoid function regulates the balance between exploration and development: The Sigmoid function adjusts the convergence rhythm of the search factor, as shown in equation (12); （12）； In equation (12): The parameter is a control parameter that varies with the number of iterations k; μ is the kurtosis control factor of the sigmoid function, which determines the adjustment rate; k is the current iteration number. 3) Hybrid encoding initialization mechanism: The initial population is introduced with historical policy perturbation and local search heuristics, as shown in Equation (13): （13）； In equation (13): for i The initial solution for an individual; Candidate solutions generated by the machine; This is a historically excellent solution or a reference solution; The summation factor (between 0 and 1) controls the proportional weight between historical experience and new solutions; After the solution is completed, the energy storage power boundary sequence that satisfies the constraints is output as the input to the lower-level optimization model, as shown in Equation (14): （14）； In equation (14): , These represent the total minimum and maximum charge / discharge power of all energy storage systems, respectively. for t The charging and discharging power of all energy storage systems at all times.

8. The method for dual-layer multi-objective collaborative optimization of energy storage system scheduling and distribution network operation optimization according to claim 7, characterized in that: In step 3, the lower-level optimization model employs an improved multi-objective particle swarm optimization algorithm (IMOPSO), including: 1) Hybrid coding mechanism: Continuous and discrete variables, such as voltage setpoint and reactive power compensation equipment switching status, are processed by a combination of real number encoding and integer encoding, as shown in equation (15). （15）； In equation (15): The active power of the energy storage system; Provide power to the SVG reactive power compensation equipment; This is the node number for energy storage access; for i Individual solutions; 2) Crowding distance guides the uniformity of non-dominated solution sets: The breadth and uniformity of the Pareto front distribution are maintained by calculating the crowding distance of the solution set, as shown in Equation (16): （16）； In equation (16): For the first i The comprehensive distance index for individual solutions; The total number of objective functions; , The first m The values ​​of the solutions before and after in the objective function; , These are the maximum and minimum values ​​of the target, respectively. 3) External elite archives drive global convergence: An external elite library composed of non-dominated solutions is introduced for reference during particle updates to improve global convergence speed and multi-objective balance, as shown in Equation (17): （17）； In equation (17): This represents the current update amount of the particle; Inertia weighting, balancing development and exploration; , Learning factors; , Generate a random number between [0, 1]. Individual historical best position; Global historical best position; for i The individual's initial attempt to resolve the issue; This indicates the update direction and step size of the solution in the search space.

9. The method for dual-layer multi-objective collaborative optimization integrating energy storage system scheduling and distribution network operation optimization according to claim 8, characterized in that: To achieve a synergistic optimal balance between the economic efficiency of energy storage systems and the safety of grid operation, a two-layer optimization structure is constructed, where the upper and lower layers solve independently but are interconnected and coordinated. This structure utilizes a nested, coupled solution mechanism to drive the dynamic interaction and evolution of the upper and lower layer objectives across multiple time periods. It employs an iterative control process with the upper layer optimization as the outer loop and the lower layer optimization as the inner loop. The specific process is as follows: Step 1: Set the initial energy storage power boundary and initialize the dynamic weighting factor. The upper-level optimization model is solved based on the multi-objective comprehensive optimization function to obtain the energy storage charging and discharging power plan for the current scheduling period; Step 2: Use the energy storage power output of the upper-level optimization model as the inner-level constraint to solve the lower-level optimization model, obtain decision variables such as reactive power compensation output, and calculate the target values ​​of network loss, node voltage deviation, and wind and solar curtailment of the lower-level optimization model. Step 3: Feed back the network loss and energy waste indices obtained from the lower-level optimization model to the upper-level optimization model to adjust the upper-level energy storage revenue. R Simultaneously, the dynamic weighting factor is updated based on real-time load and wind-solar fluctuations. ; Step 4: Repeat Step 1 to Step 3 until the objective function of the upper-level optimization model converges, and output the final optimization result.

10. The method for dual-layer multi-objective collaborative optimization of energy storage system scheduling and distribution network operation optimization according to claim 9, characterized in that: To address the issues of information isolation and target deviation between upper and lower optimization models, a nested iterative solution process is constructed, consisting of an outer-layer improved whale algorithm and an inner-layer improved multi-objective particle swarm optimization algorithm. This ensures that the upper-layer strategy is physically feasible at the lower layer, while feedback from the lower layer can correct the upper-layer target. A1: Upper-level initialization and solution: Initialize energy storage scheduling parameters The improved whale algorithm is used to obtain the power boundary scheme. ; A2: Optimization of lower-layer network state: by As the boundary input, the lower-level optimization model is solved using an improved multi-objective particle swarm optimization algorithm, and the reactive power optimization scheme and index set are output. ; A3: Feedback Correction and Weight Update: The upper-level economic objectives and weighting function parameters are dynamically adjusted based on the impact of energy curtailment and network losses, and the scheduling forecasts are updated based on actual load and renewable energy fluctuations. A4: Alternate iterations until convergence: When the changes in the scheduling results of two consecutive iterations satisfy the convergence condition shown in equation (34), the iteration stops, and the optimal scheduling result of the two-layer collaborative optimization is output. （34）； In equation (34): For the first k The multi-objective scheduling result vector of the next iteration; For the first k The result vector of multi-objective scheduling after one iteration; Convergence threshold.

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