Energy storage cluster online frequency modulation method considering degradation cost and SOC balance

Abstract

The invention discloses an energy storage cluster online frequency modulation method considering degradation cost and state of charge (SOC) balance, which comprises the following steps of: grouping energy storage power stations by adopting an index considering a structure and using an affinity propagation algorithm to obtain an energy storage cluster; and comprehensively considering the frequency modulation cost and the consistency of the state of charge to obtain a target function of an online frequency modulation model, and obtaining a difference between Lyapunov drift functions at adjacent moments according to a dynamic constraint condition of a virtual queue backlog variable, so as to establish an online frequency modulation model of an energy storage cluster. Analyzing to obtain the optimal charging and discharging power of the energy storage cluster at each moment; based on a capacity sensing water injection algorithm, an energy storage cluster frequency modulation distribution model is established, and the charging and discharging power of each energy storage power station in the charging and discharging state is obtained. The method can respond to the power grid frequency modulation signal in real time on the premise of not depending on the future frequency modulation signal, and balance between energy storage SOC balance and degradation cost reduction is achieved.

Description

Technical Field

[0001] The present invention relates to the field of electrical engineering, and particularly to an online frequency modulation method for an energy storage cluster considering degradation cost and SOC balance. Background Art

[0002] With the continuous increase in the proportion of renewable energy sources such as wind power and photovoltaic power in the power grid, the low-inertia characteristics of these energy sources pose greater challenges to the power system in real-time maintaining the balance between power generation and load, thereby leading to increased frequency fluctuations. At this time, there is an urgent need to introduce more flexible regulation resources with flexibility and rapid response capabilities. The energy storage power station cluster has become an important means for power grid frequency modulation by virtue of its superior rapid response characteristics.

[0003] However, from the perspective of the energy storage power station cluster, the frequency modulation signal sequence of the power grid has a high degree of uncertainty and is difficult to accurately predict. Existing research mainly uses methods such as robust optimization and dynamic programming, aiming to cope with this uncertainty by formulating an energy storage frequency modulation optimization model. Although these methods provide feasible solutions, the state coupling characteristics of the energy storage make the evaluation of the economy and flexibility of frequency modulation decisions extremely complex, and these methods often have limitations such as being too conservative or failing to accurately capture the uncertainty of the frequency modulation signal. In this context, once the energy storage cluster receives a frequency modulation signal, it must determine the power optimization strategy of each energy storage power station in real time without relying on future information. In addition, accurately following the frequency modulation signal may cause the energy storage to frequently switch between the charging and discharging states, which will accelerate the degradation of the energy storage battery and shorten its service life. Therefore, in the process of power distribution within the energy storage cluster, it is necessary to fully consider the balance between flexibility and economy to avoid waste of resources and extend the service life of the equipment. Summary of the Invention

[0004] Aiming at the deficiencies of the existing technology, the present invention proposes an online frequency modulation method for an energy storage cluster considering degradation cost and SOC balance. This method can effectively solve the coupling problem of the energy constraint of the energy storage power station without relying on prediction information, realize the global optimization of the energy storage cluster frequency modulation and the reasonable distribution of the power of each energy storage power station, thereby improving the frequency modulation efficiency and reliability of the power grid.

[0005] The specific technical solutions are as follows:

[0006] An online frequency modulation method for an energy storage cluster considering degradation cost and SOC balance, comprising the following steps:

[0007] S1: Using a structure-based index and the affinity propagation algorithm, group multiple energy storage power stations to obtain multiple groups of energy storage clusters;

[0008] S2: Based on Lyapunov optimization, establish an online frequency modulation model for the energy storage cluster, and analyze to obtain the optimal charging power and discharging power of the energy storage cluster at each moment; comprehensively consider the frequency modulation cost and the consistency of the state of charge to obtain the objective function of the online frequency modulation model; according to the dynamic constraint conditions of the virtual queue backlog variable, use the virtual queue backlog variable at the current moment to represent the difference between the Lyapunov drift function at the current moment and the next moment as the constraint condition of the online frequency modulation model;

[0009] S3: Calculate the corresponding degradation cost when a certain energy storage power station executes a complete cycle to a specific depth of discharge, and calculate the corresponding incremental degradation cost in the charging and discharging states based on this; and based on the capacity-aware water filling algorithm, establish a frequency modulation allocation model for the energy storage cluster, and analyze to obtain the charging power or discharging power of each energy storage power station in the charging or discharging state.

[0010] Further, in the above S1, the modularity based on electrical distance is structurally selected, and its expression is as follows:

[0011]

[0012] In the formula, is the sum of all edge weights of the network, and e ij is the weight of the edge connecting node i and node j. When node i and node j are directly connected, e ij = 1, and when they are not connected, e ij = 0; represents the sum of all edge weights connected to node i, and k j = ∑ i e ij represents the sum of all edge weights connected to node j; δ(i, j) represents the cluster relationship between nodes. When node i and node j are in the same cluster, δ(i, j) = 1, otherwise δ(i, j) = 0.

[0013] Further, in the above S2, according to the dynamic constraint conditions of the virtual queue backlog variable, use the virtual queue backlog variable at the current moment to represent the difference between the Lyapunov drift function at the current moment and the next moment as the constraint condition of the online frequency modulation model, which is specifically implemented through the following operations:

[0014] Define a virtual queue backlog variable U t that can track the change of energy storage capacity, and its expression is as follows:

[0015] U t = E t - D

[0016] In the formula, E t represents the energy state of the energy storage cluster at time t; D represents the drift amount, which is a finite constant;

[0017] The dynamic constraint conditions of the virtual queue backlog variables at adjacent moments are as follows:

[0018] U t+1 = U t + Δt(ηP t c - P t d / η)

[0019]

[0020] In the formula, η represents the charge-discharge efficiency of the energy storage cluster, represents the charging power of the energy storage cluster at time t, represents the discharging power of the energy storage cluster at time t; Δt is the time difference between time t and time t + 1; T represents the total charge-discharge duration, U0 represents the virtual queue backlog variable at the initial zero moment, and U T represents the virtual queue backlog variable at time T, and E[U T represents the expected value of the virtual queue backlog variable at time T;

[0021] The expression of the difference between the Lyapunov drift functions at the current moment and the next moment is as follows:

[0022]

[0023] In the formula, L t is the Lyapunov drift function at time t, and L t+1 is the Lyapunov drift function at time t + 1;

[0024] According to the dynamic constraint conditions of the virtual queue backlog variables, the difference of the Lyapunov drift functions is transformed and scaled to obtain the transformed expression as follows:

[0025]

[0026] In the formula, is a constant, P max represents the rated power of the energy storage cluster. The constant K has no influence on the optimization process and is ignored to obtain

[0027] Furthermore, in S2, the objective function of the online frequency modulation model is obtained by comprehensively considering the frequency modulation cost and the consistency of the state of charge, and its expression is as follows:

[0028]

[0029] In the formula, π t is the response deviation penalty price; is the charging instruction, is a discharge command; represents the charging power of the energy storage cluster at time t, represents the discharge power of the energy storage cluster at time t; β is the target weight parameter, which is used to balance the response accuracy of the energy storage cluster to the frequency modulation signal and the consistency of the state of charge inside the energy storage cluster;

[0030] Based on Lyapunov optimization, the following online frequency modulation model of the energy storage cluster is established:

[0031]

[0032] In the formula, V represents the queue weight coefficient, which is used to adjust the queue size and cooperate with the virtual queue backlog variable U t to ensure that the state of charge of the energy storage power station always meets the capacity constraint. Correspondingly, the queue weight coefficient V and the virtual queue backlog variable U t meet the following conditions:

[0033]

[0034] U t = E t -(E min + ΔtP max / η + π max ηV)

[0035] In the formula, V max represents the maximum value of the queue weight coefficient, 0 ≤ V ≤ V max ; E max represents the maximum energy storage capacity of the energy storage cluster, E min represents the minimum energy storage capacity of the energy storage cluster, π max represents the maximum value of the response deviation penalty price;

[0036] Analyze the online frequency modulation model of the energy storage cluster to obtain the optimal charging power and discharge power at the current moment, and obtain a new virtual queue backlog variable for calculating the optimal charging and discharging power at the next moment until the limited charging and discharging time is reached.

[0037] Furthermore, in S3, when a certain energy storage power station executes a complete cycle to a specific discharge depth, the expression of its corresponding degradation cost is as follows:

[0038]

[0039] In the formula, C E (SoC) represents the degradation cost of the energy storage power station, C cap is the total cost of the energy storage power station; N cycleThe cycle life of the energy storage power station, i.e., the number of cycles; DoD represents the depth of discharge, and α0, α1, and α2 are curve fitting coefficients determined according to the type of energy storage power station and the experimental data provided by the manufacturer.

[0040] Furthermore, in S3, the expression for the incremental degradation cost corresponding to the charge-discharge state is as follows:

[0041]

[0042] In the formula, C B,t is the incremental degradation cost of the energy storage cluster at time t, and C E (s t ) represents the degradation cost of the energy storage power station at time t, and C E (s t-1 ) represents the degradation cost of the energy storage power station at time t - 1.

[0043] Furthermore, in S3, the frequency regulation allocation model of the energy storage cluster established based on the capacity-aware water injection algorithm is divided into two sub-models according to the charge-discharge state: the frequency regulation allocation sub-model during energy storage charging and the frequency regulation allocation sub-model during energy storage discharging;

[0044] When the energy storage power station is in the charging state, no cost is generated, and only the balance of the state of charge of the energy storage power station is concerned. The expression of the frequency regulation allocation sub-model during energy storage charging is as follows:

[0045]

[0046] In the formula, N represents the number of energy storage power stations in the energy storage cluster, E i,max represents the maximum energy storage capacity of energy storage power station i, E i,t-1 represents the energy state of energy storage power station i at time t - 1, and η i represents the charge-discharge efficiency of energy storage power station i; is the charging power of energy storage power station i at time t, is the maximum value of, p i,max represents the rated power of energy storage power station i; represents the optimal charging power of the energy storage cluster at time t, which is obtained by analyzing the online frequency regulation model;

[0047] The expression of the frequency regulation allocation sub-model during energy storage discharging is as follows:

[0048]

[0049] In the formula, C Bi,t is the incremental degradation cost of energy storage power station i at time t, represents the discharging power of energy storage power station i at time t, is The maximum value; represents the discharge power of the energy storage cluster at time t, which is obtained by parsing the online frequency modulation model; λ is a weight factor used to balance the incremental degradation cost and the state of charge balance of the energy storage power station. When λ = 0, it means that the energy storage cluster only focuses on the incremental degradation cost caused by the charge and discharge of the energy storage power station and does not pay attention to the state of charge balance of the energy storage power station. The larger the value of λ, the higher the attention to the state of charge balance of the energy storage power station.

[0050] The beneficial effects of the present invention are as follows:

[0051] (1) The present invention uses the affinity propagation algorithm to group multiple energy storage power stations. This method not only comprehensively considers the geographical distribution characteristics of the energy storage power stations, but also ensures the electrical coupling degree and structural strength between the energy storage nodes in the cluster.

[0052] (2) Under the condition of not requiring explicit energy constraints, the present invention establishes an online frequency modulation model for the energy storage cluster based on the Lyapunov optimization model. This model can respond to the power grid frequency modulation signal in real time without relying on future frequency modulation signals.

[0053] (3) The frequency modulation allocation model of the energy storage cluster proposed by the present invention achieves an effective trade-off between the energy storage SOC balance and the reduction of degradation cost, ensuring that the energy storage cluster can take into account both economy and flexibility during the frequency modulation process. Description of the Drawings

[0054] Figure 1 is the flowchart of the online frequency modulation method for the energy storage cluster considering degradation cost and SOC balance in the embodiment of the present invention.

[0055] Figure 2 is the flowchart of the method for establishing an online frequency modulation model for the energy storage cluster based on Lyapunov optimization in the embodiment of the present invention.

[0056] Figure 3 is the flowchart of the method for establishing a frequency modulation allocation model for the energy storage cluster based on the capacity-aware water filling algorithm in the embodiment of the present invention. Detailed Embodiments

[0057] The present invention will be described in detail below according to the drawings and preferred embodiments. The purpose and effects of the present invention will become more apparent. The present invention will be further described in detail below in conjunction with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0058] Before further elaborating on the embodiments of the present invention, the nouns and terms involved in the embodiments of the present invention are described. The nouns and terms involved in the embodiments of the present invention are applicable to the following explanations.

[0059] (1) Lyapunov Optimization is an optimization method based on Lyapunov stability theory in control theory, which is widely used in fields such as dynamic systems, communication networks, resource allocation, and energy management. Its core idea is to construct a Lyapunov function to measure the "stability" or "energy" of the system. The Lyapunov function defines a scalar function V(x) with the state vector of the system as the independent variable, and satisfies V(x) ≥ 0, and V(x) = 0 if and only if x = 0; its rate of change (i.e., drift) ΔV(x) represents the expected change of the Lyapunov function within a time slot, which is used to measure the stability of the system state. By taking functions related to system performance objectives (such as energy consumption, delay, queue backlog, etc.) as penalties, and minimizing the weighted sum of drift and penalties through control strategies, this function is made non-increasing over time, thereby optimizing performance indicators while ensuring system stability; when V → 0, the optimization focuses on minimizing drift and the system tends to be stable, when V → ∞, the optimization focuses on minimizing penalties and the system performance reaches the optimal, but stability may be sacrificed.

[0060] (2) Capacity-Aware Water-Filling Algorithm is a resource allocation algorithm based on Shannon capacity formula, mainly used in wireless communication systems (such as MIMO, OFDM) to optimize channel capacity or spectral efficiency; the goal based on Shannon capacity formula is to maximize the total system capacity under the total power constraint. Its core idea is to dynamically allocate power or resources according to channel state information (CSI) to maximize the total system capacity; the better the channel condition, the more power is allocated, and the worse the channel condition, the less power is allocated or even zero.

[0061] As Figure 1 shown, an online frequency modulation method for an energy storage cluster considering degradation cost and SOC balance includes the following steps:

[0062] S1: Using a metric considering structure and the Affinity Propagation algorithm, group multiple energy storage power stations. Grouping using the Affinity Propagation algorithm not only fully considers the operating characteristics and geographical distribution characteristics of energy storage, but also ensures the electrical coupling degree and structural strength of energy storage nodes within the cluster.

[0063] As one of the embodiments, the metric of structure is represented by modularity based on electrical distance, and the expression of modularity ρ is as follows:

[0064]

[0065] In the formula, is the sum of all edge weights of the network, e ij is the weight of the edge connecting node i and node j, and e when node i and node j are directly connectedij = 1 when not connected, e ij = 0; represents the sum of the weights of all edges connected to node i, k j = ∑ i e ij represents the sum of the weights of all edges connected to node j; δ(i, j) represents the cluster relationship between nodes. When nodes i and j are in the same cluster, δ(i, j) = 1, otherwise δ(i, j) = 0.

[0066] Use the modularity-based affinity propagation algorithm to partition the energy storage cluster. The affinity propagation algorithm performs message passing between each energy storage power station node, so as to adaptively determine the center point and cluster of the energy storage cluster. The basic idea of this algorithm is to regard all data points as potential clustering centers, construct a similarity matrix based on modularity (each pair of energy storage power stations corresponds to a modularity. If the modularity is within the set range, the two energy storage power stations are classified into one category), form a network through the connection between data points, and then calculate the clustering center of each sample through message passing (attraction and belonging degree) of the edges to achieve the partitioning of the energy storage cluster.

[0067] S2: Establish an online frequency modulation model for the energy storage cluster based on Lyapunov optimization, analyze the online frequency modulation model, and obtain the optimal charging power and discharging power of the energy storage cluster at each moment. As Figure 2 shown, S2 is specifically implemented through the following sub-steps:

[0068] S201: Define a virtual queue backlog variable U that can track the change of energy storage capacity t , and the expression is as follows:

[0069] U t = E t - D (2)

[0070] In the formula, E t represents the energy state of the energy storage cluster at time t; D represents the drift, which is a finite constant.

[0071] The virtual queue backlog variables at adjacent times dynamically satisfy the following conditions:

[0072] U t+1 = U t + Δt(ηP t c - P t d / η) (3)

[0073] In the formula, η represents the charge-discharge efficiency of the energy storage cluster, represents the charging power of the energy storage cluster at time t, represents the discharge power of the energy storage cluster at time t; Δt is the time difference between time t and time t+1.

[0074] Within a sufficiently long time T, it is deduced that the virtual queue backlog variable satisfies the following conditions:

[0075]

[0076] In the formula, U0 represents the virtual queue backlog variable at the initial zero time, and U T represents the virtual queue backlog variable at time T, and E[U T represents the expected value of the virtual queue backlog variable at time T.

[0077] S202: Define the Lyapunov drift functions at two adjacent times, and take their difference to show the change amount of the drift function over time. The expression is as follows:

[0078]

[0079] In the formula, L t is the Lyapunov drift function at time t, and L t+1 is the Lyapunov drift function at time t+1.

[0080] Since U t+1 is unknown at time t, it is necessary to use the available information at the current time (i.e., time t) to transform the difference between the drift functions at two adjacent times. That is, substitute Equation (3) into Equation (5) and scale it to obtain the transformed expression as follows:

[0081]

[0082] In the formula, is a constant, and P max represents the rated power of the energy storage cluster. Since the constant K has no influence on the optimization process, it can be ignored, and we get

[0083] S203: Considering the frequency regulation cost and the consistency of the state of charge (hereinafter referred to as SOC) comprehensively, the objective function expression of the online frequency regulation model of the energy storage cluster is as follows:

[0084]

[0085] In the formula, π t is the response deviation penalty price; is the charging instruction, is the discharging instruction; β is the target weight parameter, which is used to balance the response accuracy of the energy storage cluster to the frequency regulation signal and the SOC consistency within the energy storage cluster.

[0086] S204: Based on Lyapunov optimization, establish the following online frequency modulation model for the energy storage cluster:

[0087]

[0088] Wherein, V represents the queue weight coefficient, which is used to adjust the queue size to ensure that the state of charge of the energy storage power station always satisfies the capacity constraint.

[0089] To ensure that the energy storage capacity of the energy storage cluster remains within the constraint range throughout the scheduling period, reasonable values of V and the virtual queue backlog variable U need to be set t to ensure that all physical constraints of the energy storage cluster are satisfied. The expression is as follows:

[0090]

[0091] Wherein, V max represents the maximum value of the queue weight coefficient, 0 ≤ V ≤ V max ; E max represents the maximum energy storage capacity of the energy storage cluster, E min represents the minimum energy storage capacity of the energy storage cluster, π max represents the maximum value of the response deviation penalty price.

[0092] By minimizing the online frequency modulation model of the energy storage cluster, the stability of the system can be effectively guaranteed; since the above online optimization problem only involves and two variables, and charging and discharging do not occur simultaneously, that is, one of the variables must be fixed to zero, so its analytical solution is easy to deduce.

[0093] S205: Analyze the online frequency modulation model of the energy storage cluster to obtain the optimal and at the current moment, and obtain the new E t and U t , and return to S201 until T is reached.

[0094] S3: Based on the capacity-aware water filling algorithm, establish a frequency modulation allocation model for the energy storage cluster. This model includes two sub-models in the charging state and the discharging state, and analyze to obtain the optimal charging power and discharging power of each energy storage power station. Specifically, it includes the following sub-steps:

[0095] S301: Calculate the corresponding degradation cost when an energy storage power station executes a complete cycle to a specific depth of discharge (hereinafter referred to as DoD). The expression is as follows:

[0096]

[0097] In the formula, C E (SoC) represents the degradation cost of the energy storage power station, and C cap is the total cost of the energy storage power station; N cycle is the cycle life of the energy storage power station, that is, the number of cycles.

[0098] N cycle The relationship between and DoD can be obtained from the energy storage power station manufacturer and can be approximated using an exponential function or a quadratic function. The expression is as follows:

[0099]

[0100] In the formula, α0, α1, and α2 are curve fitting coefficients, which can be determined according to the energy storage power station type and experimental data provided by the manufacturer.

[0101] The average value of the degradation cost of the energy storage power station under different DoDs is the lifetime operating cost of the energy storage power station.

[0102] S302: Calculate the incremental degradation cost of a certain energy storage power station. The expression is as follows:

[0103]

[0104] In the formula, C B,t is the incremental degradation cost of the energy storage cluster at time t. During the period from time t - 1 to time t, the SOC of the energy storage power station changes from s t-1 to s t , C E (s t ) represents the degradation cost of the energy storage power station at time t, and C E (s t-1 ) represents the degradation cost of the energy storage power station at time t - 1. If s t < s t-1 , it means that the energy storage power station is in the discharging state; if s t > s t-1 , it means that the energy storage power station is in the charging state. Since no cost is generated when the energy storage power station is charging, the corresponding degradation cost is 0 at this time.

[0105] S303: Based on the capacity-aware water injection algorithm, obtain the frequency modulation allocation sub-model during energy storage charging. At this time, only the SOC balance of the energy storage power station is concerned. The expression of this sub-model is as follows:

[0106]

[0107] In the formula, N represents the number of energy storage power stations in the energy storage cluster, and E i,max represents the maximum energy storage capacity of energy storage power station i, and E i,t-1represents the energy state of energy storage power station i at time t-1, η i represents the charge-discharge efficiency of energy storage power station i; is the charging power of energy storage power station i at time t, is the maximum value of, p i,max represents the rated power of energy storage power station i; is obtained by analyzing the online frequency modulation model of the energy storage cluster.

[0108] Analyze the frequency modulation distribution sub-model during energy storage charging to obtain the discharge power of each energy storage power station in the charging state.

[0109] At the same time, based on the capacity-aware water injection algorithm, obtain the frequency modulation distribution sub-model during energy storage discharge. The expression of this sub-model is as follows:

[0110]

[0111] In the formula, C Bi,t is the incremental degradation cost of energy storage power station i at time t, represents the discharge power of energy storage power station i at time t, is the maximum value of; is obtained by analyzing the online frequency modulation model of the energy storage cluster. λ is a weight factor used to balance the incremental degradation cost of the energy storage power station and the SOC consistency; when λ = 0, it means that the energy storage cluster only focuses on the incremental degradation cost caused by the charge and discharge of the energy storage power station and does not pay attention to the SOC balance of the energy storage power station; when λ takes a larger value, it means that the energy storage cluster pays more attention to the SOC balance of the energy storage power station.

[0112] Analyze the frequency modulation distribution sub-model during energy storage discharge to obtain the charging power of each energy storage power station in the discharge state.

[0113] In summary, the method of the present invention realizes the internal power distribution of the energy storage cluster participating in frequency modulation, and the method of the present invention does not need to rely on information of future moments, and can realize the optimal distribution of the power of the energy storage power station only according to the state of charge of the energy storage and the current frequency modulation signal, so as to realize the online frequency modulation of the energy storage cluster.

[0114] Those of ordinary skill in the art can understand that the above description is only a preferred example of the invention and is not used to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, for those skilled in the art, they can still modify the technical solutions recorded in the foregoing examples, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, etc. made within the spirit and principle of the invention shall be included within the protection scope of the invention.

Claims

1. An online frequency modulation method for an energy storage cluster considering degradation cost and SOC balance, characterized in that, Including the following steps: S1: Using metrics considering structure and the affinity propagation algorithm, group multiple energy storage power stations to obtain multiple groups of energy storage clusters; S2: Based on Lyapunov optimization, establish an online frequency modulation model for the energy storage cluster, and analyze to obtain the optimal charging power and discharging power of the energy storage cluster at each moment; comprehensively consider the frequency modulation cost and the consistency of the state of charge to obtain the objective function of the online frequency modulation model; according to the dynamic constraint conditions of the virtual queue backlog variable, use the virtual queue backlog variable at the current moment to represent the difference between the Lyapunov drift functions at the current moment and the next moment, as the constraint condition of the online frequency modulation model; S3: Calculate the corresponding degradation cost when an energy storage power station executes a complete cycle to a specific depth of discharge, and based on this, calculate the corresponding incremental degradation cost in the charge and discharge states; and based on the capacity-aware water filling algorithm, establish a frequency modulation allocation model for the energy storage cluster, and analyze to obtain the charging power or discharging power of each energy storage power station in the charge or discharge state.

2. The online frequency modulation method for an energy storage cluster considering degradation cost and SOC balance according to claim 1, wherein In the above S1, the structure-based metric selects the modularity based on electrical distance, and its expression is as follows: Wherein, is the sum of the weights of all edges in the network, and e ij is the weight of the edge connecting node i and node j. When node i and node j are directly connected, e ij = 1, and when they are not connected, e ij = 0; represents the sum of the weights of all edges connected to node i, and k j = ∑ i e ij represents the sum of the weights of all edges connected to node j; δ(i,j) represents the cluster relationship between nodes. When nodes i and j are in the same cluster, δ(i,j)=1; otherwise, δ(i,j)=0.

3. The online frequency modulation method for an energy storage cluster considering degradation cost and SOC balance according to claim 1, characterized in that In the above S2, according to the dynamic constraint conditions of the virtual queue backlog variable, use the virtual queue backlog variable at the current moment to represent the difference between the Lyapunov drift functions at the current moment and the next moment, as the constraint condition of the online frequency modulation model, which is specifically implemented through the following operations: Define a virtual queue backlog variable U that can track changes in energy storage capacity t , and the expression is as follows: U t = E t - D where, E t represents the energy state of the energy storage cluster at time t; D represents the drift, which is a finite constant; The dynamic constraint conditions of the virtual queue backlog variables at adjacent moments are as follows: U t+1 = U t + Δt(ηP t c - P t d / η) where η represents the charge-discharge efficiency of the energy storage cluster, represents the charging power of the energy storage cluster at time t, represents the discharging power of the energy storage cluster at time t; Δt is the time difference between time t and time t+1; Let \(T\) denote the total charge-discharge duration, \(U_0\) denote the virtual queue backlog variable at the initial zero moment, and \(U\) T denote the virtual queue backlog variable at moment \(T\), and \(E[U\) T denote the expected value of the virtual queue backlog variable at moment \(T\); The expression of the difference between the Lyapunov drift functions at the current moment and the next moment is as follows: where, L t is the Lyapunov drift function at time t, and L t+1 is the Lyapunov drift function at time t + 1; According to the dynamic constraint conditions of the virtual queue backlog variable, transform and scale the difference between the Lyapunov drift functions to obtain the transformed expression as follows: wherein, is a constant, and P max represents the rated power of the energy storage cluster. The constant K has no influence on the optimization process and can be ignored to obtain 4. The online frequency modulation method for an energy storage cluster considering degradation cost and SOC balance according to claim 1, characterized in that In the above S2, comprehensively consider the frequency modulation cost and the consistency of the state of charge to obtain the objective function of the online frequency modulation model, and its expression is as follows: where π t is the response deviation penalty price; is the charging instruction, is the discharging instruction; represents the charging power of the energy storage cluster at time t, represents the discharging power of the energy storage cluster at time t; β is the objective weight parameter, which is used to balance the response accuracy of the energy storage cluster to the frequency modulation signal and the consistency of the state of charge within the energy storage cluster; Based on Lyapunov optimization, establish the following online frequency modulation model for the energy storage cluster: wherein, V represents the queue weight coefficient, which is used to adjust the queue size and cooperate with the virtual queue backlog variable U t to ensure that the state of charge of the energy storage power station always satisfies the capacity constraint. Correspondingly, the queue weight coefficient V and the virtual queue backlog variable U t satisfy the following conditions: U t = E t -(E min + ΔtP max / η + π max ηV) Where, V max represents the maximum value of the queue weight coefficient, 0 ≤ V ≤ V max ; E max represents the maximum energy storage capacity of the energy storage cluster, E min represents the minimum energy storage capacity of the energy storage cluster, π max represents the maximum value of the response deviation penalty price; Analyze the online frequency modulation model of the energy storage cluster to obtain the optimal charging power and discharging power at the current moment, and obtain a new virtual queue backlog variable for calculating the optimal charge and discharge power at the next moment until the limited charge and discharge time is reached.

5. The online frequency modulation method for an energy storage cluster considering degradation cost and SOC balance according to claim 1, wherein In the above S3, when an energy storage power station executes a complete cycle to a specific depth of discharge, the expression of its corresponding degradation cost is as follows: Where, C E (SoC) represents the degradation cost of the energy storage power station, and C cap is the total cost of the energy storage power station; N cycle is the cycle life of the energy storage power station, that is, the number of cycles; DoD represents the depth of discharge, and α0, α1, and α2 are curve fitting coefficients, which are determined according to the type of energy storage power station and the experimental data provided by the manufacturer.

6. The online frequency modulation method for an energy storage cluster considering degradation cost and SOC balance according to claim 5, characterized in that, In the above S3, the expression of the corresponding incremental degradation cost in the charge and discharge states is as follows: Where, C B,t is the incremental degradation cost of the energy storage cluster at time t, and C E (s t ) represents the degradation cost of the energy storage power station at time t, and C E (s t-1 ) represents the degradation cost of the energy storage power station at time t - 1.

7. The online frequency modulation method for an energy storage cluster considering degradation cost and SOC balance according to claim 6, characterized in that, In the above S3, the frequency modulation allocation model for the energy storage cluster established based on the capacity-aware water filling algorithm is divided into two sub-models according to the charge and discharge states: the frequency modulation allocation sub-model during energy storage charging and the frequency modulation allocation sub-model during energy storage discharging; When the energy storage power station is in the charging state, no cost is generated, and only the balance of the state of charge of the energy storage power station is concerned. The expression of the frequency modulation allocation sub-model during energy storage charging is as follows: Wherein, N represents the number of energy storage power stations in the energy storage cluster, E i,max represents the maximum energy storage capacity of energy storage power station i, E i,t-1 represents the energy state of energy storage power station i at the (t - 1)th moment, η i represents the charge-discharge efficiency of energy storage power station i; is the charging power of energy storage power station i at the tth moment, is the maximum value of, p i,max represents the rated power of energy storage power station i; represents the optimal charging power of the energy storage cluster at the tth moment, which is obtained by analyzing the online frequency modulation model; The expression of the frequency modulation distribution sub-model during energy storage discharge is as follows: Where C Bi,t is the incremental degradation cost of energy storage power station i at time t, represents the discharge power of energy storage power station i at time t, is the maximum value of; represents the discharge power of the energy storage cluster at time t, which is obtained by analyzing the online frequency modulation model; λ is a weight factor used to balance the incremental degradation cost of the energy storage power station and the charge state balance. When λ = 0, it means that the energy storage cluster only focuses on the incremental degradation cost caused by the charge and discharge of the energy storage power station and does not pay attention to the charge state balance of the energy storage power station. The larger the value of λ, the higher the attention to the charge state balance of the energy storage power station.

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