A battery real-time cyclic degradation cost forward-looking quantification method and system

Abstract

The application relates to a battery real-time cycle degradation cost forward-looking quantification method and system, and belongs to the technical field of charging batteries. The method solves the problems of degradation cost statistics based on completed cycle results and lack of real-time forward-looking prediction capability. The method comprises the following steps: modeling a mathematical model of the entire charging battery as N equivalent subunits and defining discharge and charge energy distribution in the subunits; obtaining unit energy degradation cost of a current equivalent subunit n according to the degradation degree of adjacent equivalent subunits, battery replacement cost and the rated capacity of the equivalent subunits; constructing a degradation cost calculation model of single charge-discharge behavior according to the unit energy degradation cost, the energy reduced in the current equivalent subunit in the discharge energy distribution state and the energy increased in the current equivalent subunit in the charge energy distribution state; and obtaining the total degradation cost of the charge-discharge behavior of the equivalent subunit in the entire cycle period based on the degradation cost calculation model. The real-time cycle degradation cost is explicitly represented based on energy distribution.

Description

Technical Field

[0001] This invention relates to the field of rechargeable battery technology, and in particular to a method and system for predictively quantifying the real-time cycle degradation cost of batteries. Background Technology

[0002] With the accelerated global energy transition, the installed capacity and power generation share of new energy sources such as wind power and photovoltaics in the power grid have increased significantly. However, their inherent intermittency and volatility also pose a severe challenge to the power balance of the power system. Against this backdrop, energy storage systems, as a key flexible adjustment resource, are increasingly highlighting their strategic value. In 2024, the global newly installed capacity of new energy storage reached 78.33 GW / 184.2 GWh, representing a year-on-year increase of 82.1%. By the end of 2024, China's cumulative installed capacity of new energy storage exceeded 73.76 GW / 168 GWh (168 million kWh), an increase of over 130% compared to 2023. Among them, electrochemical energy storage, with its high technological maturity and cost advantages, has shown broad development prospects, but its large-scale application is still constrained by economic challenges, with degradation costs due to battery degradation constituting a major obstacle.

[0003] While battery energy storage systems can generate economic benefits through energy arbitrage (buying low and selling high) and providing ancillary services such as frequency regulation and backup, the deep charge-discharge cycles during operation significantly accelerate battery degradation, resulting in high degradation costs. If the operating strategy only pursues short-term gains and ignores the impact of degradation, it may erode the overall project profit, weaken investor enthusiasm, and thus affect the construction of new power systems and the low-carbon transition process.

[0004] Therefore, accurately quantifying the degradation cost of batteries during real-time operation and incorporating it into charge / discharge decisions and economic assessments is crucial for optimizing energy storage operation strategies and improving the economic benefits throughout the project's lifecycle. This not only directly relates to the return on investment of individual energy storage projects but is also a key link in promoting the large-scale commercial application of electrochemical energy storage and supporting my country's construction of a new power system dominated by new energy sources. Summary of the Invention

[0005] Based on the above analysis, the embodiments of the present invention aim to provide a method and system for real-time prospective quantification of battery cycle degradation costs, in order to solve the problem that existing methods perform degradation cost statistics based on completed cycle results and lack real-time prospective prediction capabilities.

[0006] On one hand, embodiments of the present invention provide a method for prospective quantification of real-time cycle degradation costs of batteries, comprising: modeling the entire rechargeable battery mathematically into N equivalent sub-units and defining the discharge energy distribution and charging energy distribution in each equivalent sub-unit; obtaining the unit energy degradation cost of the current equivalent sub-unit n based on the degradation degree of adjacent equivalent sub-units, battery replacement cost, and rated capacity of the equivalent sub-units; constructing a degradation cost calculation model for a single charge-discharge behavior based on the unit energy degradation cost, the energy reduction of the current equivalent sub-unit n in the discharge energy distribution state, and the energy increase of the current equivalent sub-unit n in the charging energy distribution state; and obtaining the total degradation cost of the N equivalent sub-units during the entire cycle based on the degradation cost calculation model.

[0007] The beneficial effects of the above technical solution are as follows: Battery cycling often spans multiple time periods, resulting in significant temporal coupling in the degradation process, and real-time degradation costs depend on historical operating trajectories. The method presented in this paper directly quantifies the degree of degradation through energy distribution states, eliminating the need to store historical SoC trajectories. In other words, the historical information required for degradation cost calculation is compressed and mapped onto the energy distribution states, achieving state-based modeling and path independence. When calculating degradation costs in real time, analytical results can be provided across the entire power range.

[0008] Based on the further improvement of the above method, the definition of the discharge energy distribution and charging energy distribution in each equivalent sub-unit further includes: defining the energy contained in the equivalent sub-unit n in the discharge energy distribution de at the current time t. And the energy contained in the equivalent subunit n in the charging energy distribution in at the current time t. .

[0009] Further improvements to the above method, obtaining the unit energy degradation cost of the current equivalent subunit n based on the degradation degree of adjacent equivalent subunits, battery replacement cost, and rated capacity of the equivalent subunit, further include: calculating the degradation degree of the previous equivalent subunit n-1 based on a first ratio of the previous equivalent subunit n-1 to the N equivalent subunits, the number of cycles of the rechargeable battery, and the degradation rate; calculating the degradation degree of the current equivalent subunit n based on a second ratio of the current equivalent subunit n to the N equivalent subunits, the number of cycles of the rechargeable battery, and the degradation rate; and calculating the unit energy degradation cost of the current equivalent subunit n based on the difference between the degradation degree of the current equivalent subunit n and the degradation degree of the previous equivalent subunit n-1, the battery replacement cost, and the rated capacity of the equivalent subunit.

[0010] Based on a further improvement of the above method, the unit energy degradation cost c of the current equivalent sub-unit n is obtained according to the degradation degree of adjacent equivalent sub-units, battery replacement cost, and rated capacity of the equivalent sub-units. n Further includes: ; Among them, C rep The battery replacement cost is represented by Q(n / N), the degradation degree of the current equivalent subunit n is represented by Q(n-1 / N), and the degradation degree of the previous equivalent subunit n-1 is represented by E. max The value represents the rated capacity of the battery, and N represents the number of equivalent sub-cells in the rechargeable battery.

[0011] Based on further improvements to the above method, a degradation cost calculation model V for a single charge-discharge behavior is constructed according to the unit energy degradation cost, the energy reduction of the current equivalent sub-unit n in the discharge energy distribution state, and the energy increase of the current equivalent sub-unit n in the charging energy distribution state. t Further includes: ; in, They represent the discharge energy distribution, respectively. The energy reduction of the equivalent subunit in the state Indicates the distribution of charging energy The energy increase of the equivalent subunit in the state c n This represents the unit energy degradation cost of the current equivalent subunit n.

[0012] A further improvement to the above method, based on the degradation cost calculation model, further includes obtaining the total degradation cost V of the N equivalent sub-units' charge-discharge behavior throughout the entire cycle, including: ; in, They represent the discharge energy distribution, respectively. The energy reduction of the equivalent subunit in the state Indicates the distribution of charging energy The energy increase of the equivalent subunit in the state, C rep Let Q(n / N) represent the battery replacement cost, Q(n-1 / N) represent the degradation degree of the current equivalent subunit n, and Q(n-1 / N) represent the degradation degree of the previous equivalent subunit n-1. E max Indicates the battery's rated capacity. N This indicates the number of equivalent sub-cells in a rechargeable battery. T This indicates the entire cycle of the rechargeable battery.

[0013] Based on further improvements to the above method, the real-time cycle degradation cost look-ahead quantification method for batteries further includes calculating the energy distribution state transition caused by charging and discharging operations in each time period based on the discharge energy distribution and charging energy in each equivalent sub-unit. This involves calculating the energy contained in the equivalent sub-unit n based on the discharge energy distribution de at the current time t. And the energy increase of the equivalent subunit n in the discharge energy distribution de at the current time t. or reduced energy Calculate the energy distribution state transition caused by the discharge operation at the next moment. : ; Based on the charging energy distribution at current time t, the energy contained in the equivalent subunit n in in... And the energy increase in the equivalent sub-unit in the charging energy distribution. or reduced energy Calculate the energy distribution state transition caused by the charging operation at the next time step. : .

[0014] Based on further improvements to the above method, the real-time cycle degradation cost prospective quantification method for batteries further includes: deriving the degradation cost increment of the next charging / discharging operation at time t+1 based on the degradation cost calculation model of the single charge / discharge behavior and the energy distribution at the current time t. ,in, ; When the change in state of charge (SoC) ΔSoC is greater than zero, the unit energy degradation cost c based on the equivalent subunit n is... n The energy change of the equivalent subunit n in the state of charge energy. Calculate the degradation cost increment for the charging operation at the next time step t+1, and When the change in state of charge (SoC) ΔSoC is less than zero, the unit energy degradation cost c based on the equivalent subunit n is... n The energy change of the equivalent subunit n in the discharge energy state. Calculate the degradation cost increment of the discharge operation at the next time step t+1.

[0015] Based on the further improvement of the above method, the energy change of the equivalent subunit n in the charging energy state at the next time t+1 is calculated using the following formula. : ; in, E represents the discharge energy distribution. maxThis indicates the battery's rated capacity, and △SoC represents the change in the state of charge (SoC). The energy distribution de represents the total energy reduction of the equivalent discharge subunits 1 to n-1 in the next time step t+1. The energy change of the equivalent subunit n in the discharge energy state at the next time t+1 is calculated using the following formula. : ; in, This represents the sum of the energy increases from the equivalent subunits 1 to n-1 in the energy distribution at the next time step t+1.

[0016] On the other hand, embodiments of the present invention provide a real-time battery cycle degradation cost prospective quantification system, comprising: an energy definition module, used to model the mathematical model of the entire rechargeable battery into N equivalent sub-units and define the discharge energy distribution and charging energy distribution in each equivalent sub-unit; a unit energy degradation cost module, used to obtain the unit energy degradation cost of the current equivalent sub-unit n based on the degradation degree of adjacent equivalent sub-units, battery replacement cost, and rated capacity of the equivalent sub-units; a degradation cost calculation model, used to construct a degradation cost calculation model for a single charge-discharge behavior based on the unit energy degradation cost, the energy reduction of the current equivalent sub-unit n in the discharge energy distribution state, and the energy increase of the current equivalent sub-unit n in the charging energy distribution state; and a summation module, used to obtain the total degradation cost of the charge-discharge behavior of the N equivalent sub-units in the entire cycle based on the degradation cost calculation model.

[0017] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. Cyclic identification results obtained by the rainflow counting method are generally considered a standard reference. However, this method can only perform cyclic statistics based on a defined SoC trajectory after the energy storage operation has ended, which is a post-event simulation analysis and cannot be directly applied in the optimization stage. Since SoC is the decision variable in the optimization model, rainflow counting lacks an analytical form and is difficult to embed into the solution framework. The degradation cost model established in this paper has an analytical expression, and its calculation results are highly consistent with the degradation cost verified by the rainflow counting method posteriorly, verifying the accuracy of the model.

[0018] 2. Battery cycling often spans multiple time periods, resulting in significant temporal coupling in the degradation process, with real-time degradation costs dependent on historical operating trajectories. Our proposed method directly quantifies the degree of degradation through energy distribution states, eliminating the need to store historical SoC trajectories. In other words, the historical information required for degradation cost calculation is compressed and mapped onto the energy distribution states, achieving state-based modeling and path independence.

[0019] 3. When calculating degradation costs in real time, the model can provide analytical results across the entire power range. For example, when the rated power of energy storage is 10 MW, the proposed method can accurately assess the degradation costs corresponding to different power levels within the range of [-10MW, 10MW] (negative values ​​represent charging, and positive values ​​represent discharging). In contrast, traditional methods can only obtain local marginal costs, i.e., the degradation impact of small power changes, and cannot reflect the cost characteristics across the entire power range.

[0020] 4. This method is applicable to systems with convex cost characteristics. In addition to battery degradation, it can also be extended to areas such as fuel costs of thermal power units and vehicle fuel consumption, demonstrating strong cross-domain scalability.

[0021] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0022] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Figure 1 A flowchart of a method for prospective quantification of real-time cycle degradation costs of batteries according to an embodiment of the present invention; Figure 2 A schematic diagram for calculating existing rainflow; Figure 3 This is a schematic diagram of the dual energy distribution of a rechargeable battery according to an embodiment of the present invention; Figure 4 The real-time cost of the rechargeable battery at time S3 according to an embodiment of the present invention; Figure 5 A flowchart illustrating the overall process of a method for prospective quantification of real-time cycle degradation costs of batteries according to an embodiment of the present invention; Figure 6 A block diagram of a battery real-time cycle degradation cost prospective quantification system according to an embodiment of the present invention. Detailed Implementation

[0023] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0024] refer to Figure 1 A specific embodiment of the present invention discloses a method for prospective quantification of real-time cycle degradation costs of batteries, comprising the following steps: In step S101, the mathematical model of the entire rechargeable battery is modeled into N equivalent sub-units (only for modeling and analysis, without changing the physical structure), and the discharge energy distribution and charging energy distribution in each equivalent sub-unit are defined, where 1, 2, 3...N represent the 1st equivalent sub-unit, the 2nd equivalent sub-unit, the 3rd equivalent sub-unit, ..., the Nth equivalent sub-unit, respectively. (Refer to...) Figure 3 Set a differentiated unit energy degradation cost coefficient for each equivalent subunit. Since a larger value of N is more accurate but slower, the value of N ranges from [10, 80], for example, 10 equivalent subunits, 20 equivalent subunits, 30 equivalent subunits, 50 equivalent subunits, or 80 equivalent subunits.

[0025] The definition of the discharge energy distribution and charging energy distribution in each equivalent sub-unit further includes: defining the energy contained in the equivalent sub-unit n in the discharge energy distribution de at the current time t. And the energy contained in the equivalent subunit n in the charging energy distribution at the current time t. .

[0026] In step S102, the unit energy degradation cost of the current equivalent sub-unit n is obtained based on the degradation degree of adjacent equivalent sub-units, battery replacement cost, and rated capacity of the equivalent sub-units.

[0027] Specifically, the unit energy degradation cost c of the current equivalent sub-unit n is obtained based on the degradation level of adjacent equivalent sub-units, battery replacement cost, and rated capacity of the equivalent sub-units. n Further includes: (1) Calculate the degradation degree Q(n / N) of the previous equivalent subunit n-1 based on the first ratio n-1 / N of the previous equivalent subunit n-1 to N equivalent subunits, the number of cycles a of the rechargeable battery and the degradation rate z: Current battery degradation level Q(u): Formula 1; By replacing u in Formula 1 with n-1 / N, we obtain the following Formula 2: Q(n-1 / N)=ka(n-1 / N) z Formula 2.

[0028] (2) Calculate the degradation degree Q(n / N) of the current equivalent subunit n based on the second ratio n / N of the current equivalent subunit n to N equivalent subunits, the number of cycles a of the rechargeable battery, and the degradation rate z. By replacing u in Formula 1 with n / N, we obtain the following Formula 3: Q(n / N)=ka(n / N) z Formula 3; For a complete cycle, k equals 1; for a half cycle (charging or discharging), k equals 0.5.

[0029] (3) Calculate the unit energy degradation cost c of the current equivalent subunit n based on the difference between the degradation degree of the current equivalent subunit n and the degradation degree of the previous equivalent subunit n-1, the battery replacement cost, and the rated capacity of the equivalent subunit. n The unit energy degradation cost c of the current equivalent subunit n is calculated using the following formula 4. n : Formula 4; Among them, C rep Let Q(n / N) represent the battery replacement cost, Q(n-1 / N) represent the degradation level of the current equivalent subunit n, and Q(n-1 / N) represent the degradation level of the previous equivalent subunit n-1. E max The value represents the rated capacity of the battery, and N represents the number of equivalent sub-cells in the rechargeable battery.

[0030] In step S103, a degradation cost calculation model for a single charge-discharge behavior is constructed based on the unit energy degradation cost, the energy reduction of the current equivalent sub-unit n in the discharge energy distribution state, and the energy increase of the current equivalent sub-unit n in the charging energy distribution state.

[0031] The degradation cost calculation model for a single charge-discharge cycle is expressed by the following formula 5: V t Further includes: Formula 5; in, They represent the discharge energy distribution, respectively. The energy reduction of the equivalent subunit in the state Indicates the distribution of charging energy The energy increase of the equivalent subunit in the state c n This represents the unit energy degradation cost of the current equivalent subunit n.

[0032] In step S104, the total degradation cost of the charging and discharging behavior of N equivalent sub-units during the entire cycle is obtained based on the degradation cost calculation model.

[0033] (1) Based on the degradation cost calculation model of single charge and discharge behavior, the degradation cost increment of the charge and discharge operation at the next time t+1 is derived from the energy distribution at the current time t. ,in, Formula 6; When the change in state of charge (SoC) ΔSoC is greater than zero, the unit energy degradation cost c based on the equivalent sub-cell n is... nThe energy change of the equivalent subunit n in the state of charge energy. Calculate the degradation cost increment for the charging operation at the next time step t+1, and When the change in state of charge (SoC) ΔSoC is less than zero, the unit energy degradation cost c based on the equivalent sub-cell n is... n The energy change of the equivalent subunit n in the discharge energy state. Calculate the degradation cost increment of the discharge operation at the next time step t+1.

[0034] (2) During the discharge process, the first difference between the product of the battery rated capacity and the change in the state of charge SoC and the energy reduction of the discharge equivalent sub-units 1 to n-1 in the discharge energy distribution de at the next time t+1, and then the minimum value between the energy distribution state transition caused by the discharge operation and the first difference is taken as the energy reduction of the discharge equivalent sub-units n-1 in the discharge energy distribution de at the next time t+1. The energy change of the equivalent subunit n in the charging energy state at the next time t+1 is calculated using the following formula. : Formula 7; in, Indicates the distribution of discharge energy. E max This indicates the battery's rated capacity, and ΔSoC indicates the change in state of charge (SoC). The energy distribution de represents the total energy reduction of the equivalent subunits 1 to n-1 in the discharge energy distribution at the next time t+1.

[0035] (3) During the charging process, calculate the second difference between the rated capacity of each equivalent sub-cell in the battery and the energy distribution state transition caused by the charging operation, and the third difference between the product of the rated capacity of the battery and the change in the state of charge (SoC) and the energy increase of the charging equivalent sub-cells 1 to n-1 in the charging energy distribution in the next time t+1. Then, the minimum of the second difference and the third difference is taken as the energy increase of the discharging equivalent sub-cells 1 to n-1 in the charging energy distribution in the next time t+1. The energy change of the equivalent subunit n in the discharge energy state at the next time t+1 is calculated using the following formula. : Formula 8; in, This represents the sum of the energy increases from the equivalent subunits 1 to n-1 in the energy distribution at the next time step t+1.

[0036] (4) The energy contained in the equivalent subunit n based on the discharge energy distribution de at the current time t. And the energy increase of the equivalent subunit n in the discharge energy distribution de at the current time t. or reduced energy Calculate the energy distribution state transition caused by the discharge operation at the next time step t+1. : Formula 9.

[0037] (5) The energy contained in the equivalent subunit n based on the charging energy distribution in at the current time t. And the energy increase in the equivalent sub-unit in the charging energy distribution. or reduced energy Calculate the energy distribution state transition caused by the charging operation at the next time step t+1. : Formula 10.

[0038] (6) Based on Formulas 5 to 10 above, the degradation costs of the charging and discharging behavior of N equivalent sub-units throughout the entire cycle are summed to obtain the following total degradation cost V: Formula 11; in, They represent the discharge energy distribution, respectively. The energy reduction of the equivalent subunit in the state Indicates the distribution of charging energy The energy increase of the equivalent subunit in the state, C rep Let Q(n / N) represent the battery replacement cost, Q(n-1 / N) represent the degradation level of the current equivalent subunit n, and Q(n-1 / N) represent the degradation level of the previous equivalent subunit n-1. E max Indicates the battery's rated capacity. N This indicates the number of equivalent sub-cells in a rechargeable battery. T This indicates the entire cycle time of a rechargeable battery.

[0039] The cyclical nature of System-on-Chips (SoCs) presents a challenge to proactive cost quantification during real-time battery operation. Unlike offline cycle counting based on the complete SoC (State of Charge) trajectory, as described above, real-time operation requires assessing the impact of future charge / discharge operations on degradation in the current state. Real-time degradation quantification must consider both historical SoCs and future operations, as different operations may combine with past behaviors to form different cycles, leading to different degradation outcomes. This raises two key challenges: (1) Real-time degradation costs are closely related to past SoC trajectories and vary non-linearly with power. For example, in Figure 1 midpoint If the discharge depth is less than 0.3, only a local discharge half-cycle is formed; once the depth exceeds 0.3, it will interact with the previous SoC trajectory ( Pairing. When the power exceeds a certain threshold, this action combines with the previous half-cycle to form a deeper full cycle, leading to a sharp increase in marginal degradation costs. This does not reflect an actual change in the physical degradation process of the battery, but rather a statistical acceleration of degradation costs.

[0040] (2) In order to accurately calculate degradation costs, complete SoC trajectory data must be recorded. As SoC data accumulates, the storage burden increases, and the amount of computation required for cyclic extraction also increases, resulting in slower processing speed.

[0041] Although rainflow counting is currently the most commonly used method for calculating battery cycle degradation, it is essentially a posterior statistical method. Its core shortcomings are reflected in two aspects: First, this method relies on complete SoC extreme point sequence information and can only perform offline cost assessment after the operation is completed. It cannot predict the cycle degradation cost caused by different operations in the future. Second, it lacks explicit mathematical representation capabilities and cannot mathematically analyze the cost impact of specific operations.

[0042] This real-time cost forward-looking quantification method is accurate, independent of historical SoC characteristics, has full-condition resolution, and generalization ability.

[0043] Compared to existing technologies, the real-time battery cycle degradation cost look-ahead quantification method provided in this embodiment addresses the issue that battery cycling often spans multiple time periods, resulting in significant temporal coupling in the degradation process, with real-time degradation costs dependent on historical operating trajectories. This method directly quantifies the degree of degradation through energy distribution states, eliminating the need to store historical SoC trajectories. In other words, the historical information required for degradation cost calculation is compressed and mapped onto the energy distribution states, achieving state-based modeling and path independence. Furthermore, it provides analytical results across the entire power range during real-time degradation cost calculation.

[0044] In the following text, refer to Figures 2 to 5 The present invention provides a detailed description of a method for prospective quantification of real-time cycle degradation costs of batteries according to specific examples.

[0045] refer to Figure 5This method consists of four stages: The first stage analyzes the battery's cyclic degradation mechanism, pointing out the shortcomings of existing rain-flow counting methods (defined as a counting algorithm that breaks down random load histories into equivalent constant-amplitude cycles according to the "raindrops flowing down a roof" rule, used to estimate material or structural fatigue damage). Rain-flow counting relies on simulation processes, lacks a clear mathematical expression, and can only perform degradation cost statistics based on completed cycle results, lacking real-time forward-looking prediction capabilities. The second stage calculates the battery's cyclic degradation cost based on a dual energy distribution. A cyclic degradation cost calculation method based on "dual energy distribution" is proposed, which can accurately characterize the battery's cyclic degradation characteristics with a clear mathematical expression. The third stage uses the cyclic degradation cost calculation method based on dual energy distribution to perform real-time forward-looking cyclic degradation cost quantification of the battery. Based on this, a real-time forward-looking cyclic degradation cost quantification method is further proposed, realizing real-time prediction of degradation costs for subsequent operations during operation. The fourth stage analyzes the characteristics of this method. The core advantages are as follows: (1) Accuracy: Through mathematical proof, the forward degradation cost quantified by this method is consistent with the result of rainflow counting after operation, and theoretical proof has been provided. Through mathematical proof, it is verified that it is equivalent to the actual cyclic degradation cost result after post-verification; (2) No dependence on historical SoC: The calculation can be completed only with the current "dual energy distribution" without relying on historical SoC data. The real-time cyclic degradation cost is explicitly represented based on the energy distribution, and no storage burden is generated; (3) Full-condition characterization capability: It can analyze the corresponding nonlinear degradation cost at any charge and discharge depth; (4) Generalization characteristics: It is applicable to all degradation function model systems that satisfy the convexity condition.

[0046] When the active materials in a battery complete a full cycle of carrier insertion and extraction—that is, when the SoC (State of Charge, representing the ratio of the battery's current remaining energy to its rated capacity) deviates from a certain value and then returns to the same value—accumulated and quantifiable degradation occurs. Typically, degradation is quantified based on complete cycles, rather than on a single charge or discharge event. The battery degradation process is influenced by the combined effect of the number of cycles and the cycle depth. The mapping relationship between the degree of degradation Q per cycle and the cycle depth u can be characterized by a power function: ; In the formula, and These are battery life parameters. This determines the number of cycles the battery can complete over its entire lifespan. For example, when a battery can cycle 5000 times... .parameter This reflects the acceleration of degradation with increasing cycle depth. Both can be obtained by fitting actual experimental data of the battery. For a complete cycle, k equals 1; for a half-cycle (charge or discharge), k equals 0.5.

[0047] The degradation cost is obtained by multiplying the degree of degradation by the battery replacement cost: ; In the formula; C rep This refers to the cost of replacing the battery.

[0048] Battery degradation increases exponentially with cycle depth, making accurate identification of each cycle and its depth crucial for real-time cost quantification. In practice, different levels of charge and discharge often occur alternately, making it difficult to define a clear cycle. Instead, a cycle is typically formed by multiple time steps of charging and discharging.

[0049] Rainflow counting is a standard method for fatigue cycle identification and has been incorporated into international standards. In battery degradation calculations, this method effectively avoids cycle segmentation errors by simulating the "roof rainflow" mechanical process of the State of Charge (SoC) curve and extracting cycle features using the topology of the rainflow path.

[0050] However, rainflow counting does not have a clear analytical expression; instead, it is defined by an algorithm, which can be represented as follows: ; Among them, u full u dis u ch These represent the full cycle set, the discharge half cycle set, and the charging half cycle set, respectively.

[0051] The steps for cyclical statistics using the rainflow counting method are as follows: (1) Simulate the mechanical effect of gravity to the right, with rainwater flowing down the slope from the inside of the peaks / troughs (S0, S2, S3, S4, S5, S6, S7) of the SoC trajectory; (2) When encountering an extreme point, the raindrops fall to the right under the influence of gravity and continue to flow until the trajectory ends. For example, the rain stream starting at S0 drips to the right at S2 and continues to flow to S. 4； (3) The flow terminates when the rain stream encounters an extreme point that is higher than its initial peak or lower than its initial trough. For example, a rain stream that starts at the trough of S2 drips at S3, but terminates at the opposite position of S4 because the trough of S4 is lower than S2, and no longer drips to the right; (4) When rain streams from different paths converge, the subsequent rain stream immediately terminates. For example, the rain stream starting at S3 stops after converging with the rain stream along the path S0-S2-S'2 at S'2; (5) Each complete rainflow path corresponds to one battery half-cycle, and its horizontal projected length characterizes the depth of cycle discharge. For Figure 2 The SoC loop results are shown in Table 1.

[0052] Table 1. Loop Results ; Substitute the obtained loop result into The cycle degradation cost V of the battery can then be calculated: ; In the formula, u full This indicates the cycle depth of a full charge / discharge cycle; "full" represents a full charge / discharge cycle. A full charge / discharge cycle is formed by pairing a charge half-cycle and a discharge half-cycle. dis Indicates the cycle depth of a half-cycle of discharge; u ch Indicates the cycle depth of a charging half-cycle; u full u dis u ch These represent the full cycle set, the discharge half cycle set, and the charging half cycle set, respectively.

[0053] The cyclical nature of System-on-Chips (SoCs) presents a challenge to proactive cost quantification during real-time battery operation. Unlike offline cycle counting based on the complete SoC (State of Charge) trajectory, as described above, real-time operation requires assessing the impact of future charge / discharge operations on degradation in the current state. Real-time degradation quantification must consider both historical SoCs and future operations, as different operations may combine with past behaviors to form different cycles, leading to different degradation outcomes. This raises two key challenges: (1) Real-time degradation costs are closely related to past SoC trajectories and vary non-linearly with power. For example, in Figure 2 midpoint If the discharge depth is less than 0.3, only a local discharge half-cycle is formed; once the depth exceeds 0.3, it will interact with the previous SoC trajectory ( Pairing. When the power exceeds a certain threshold, this action combines with the previous half-cycle to form a deeper full cycle, leading to a sharp increase in marginal degradation costs. This does not reflect an actual change in the physical degradation process of the battery, but rather a statistical acceleration of degradation costs.

[0054] (2) In order to accurately calculate degradation costs, complete SoC trajectory data must be recorded. As SoC data accumulates, the storage burden increases, and the amount of computation required for cyclic extraction also increases, resulting in slower processing speed.

[0055] Although rainflow counting is currently the most commonly used method for calculating battery cycle degradation, it is essentially a posterior statistical method. Its core shortcomings are reflected in two aspects: First, this method relies on complete SoC extreme point sequence information and can only perform offline cost assessment after the operation is completed. It cannot predict the cycle degradation cost caused by different operations in the future. Second, it lacks explicit mathematical representation capabilities and cannot mathematically analyze the cost impact of specific operations.

[0056] First, the battery is mathematically modeled into N equivalent sub-units (for modeling and analysis only, without changing the physical structure). A differentiated unit energy degradation cost coefficient is assigned to each sub-unit. The unit energy degradation cost c of the nth sub-unit is... n (Unit: Yuan / MW) The expression is as follows: ; In the formula, E max This refers to the battery's rated capacity.

[0057] Two energy distributions, de and in, are defined in the sub-cell; where energy distribution de is used to calculate the effect of discharge on the discharge half-cycle. Indicates in t In the energy distribution at time t, sub-unit n The energy contained in; the energy distribution in is used to calculate the energy state of charging for a charging half-cycle; Indicates in t In the energy distribution at time in, sub-unit n The energy contained within. Let the initial time be... t When the value is 0, the energy of the battery is E 0. The energy distribution of the equivalent subunit in both energy distribution states is as follows: ; ; In the formula, 1 {A} The value is 1 when condition A is met, and 0 otherwise. For example, when E0 = 0.6E max At that time, the two energy distribution states are as follows Figure 3 As shown in S0, the degradation cost c of the sub-unit n Increasing from left to right.

[0058] Define state transition variables: and They represent The energy that increases or decreases in an equivalent subunit in a state. and They represent The energy increase or decrease of the equivalent sub-unit in the state. The energy distribution state transition caused by the charge / discharge operation in each time period is as follows: ; ; The battery is designed to always fill or release energy from the equivalent sub-cell from left to right. For example, in... Figure 3 In S After performing a discharge operation in state 0, it is depleted first. Energy of subunit 1-2 in state and The energy of sub-units 5-6 in the state is updated to the battery state. S 1.

[0059] The incremental degradation cost of discharge operation is due to The degradation cost of each sub-unit in the state is accumulated, and the charging process is determined by... The degradation cost is obtained by summing the degradation costs of each sub-unit. The degradation cost calculation model for a single charge-discharge behavior is as follows: ; In the formula, Vt represents the degradation cost of the battery within time period t. This model explicitly establishes a mathematical mapping relationship between charge / discharge operations and the increment of degradation cost across the entire time domain through the dynamic evolution of dual energy distribution states.

[0060] Based on the degradation cost calculation model, the degradation cost increment of the charge / discharge operation in time period t+1 can be derived from the energy distribution at the current time t: ; ; ; Mode and The energy changes of each sub-unit were determined during different ΔSoC charge and discharge operations.

[0061] by Figure 3 Taking the energy distribution of S3 as an example, the unit degradation cost of charging and discharging at different depths in the next time period can be directly derived as follows: Figure 4 As shown, the sum of the cost contributions of each sub-unit is the total degradation cost corresponding to ΔSoC.

[0062] This real-time cost forward-looking quantification method is accurate, independent of historical SoC characteristics, has full-condition resolution, and generalization ability.

[0063] (1) Proof of accuracy by Figure 2 Taking the SOC trajectory as an example, the rated capacity Emax = 10, the equivalent number of sub-units N = 10, and the degradation cost of each sub-unit c are assumed to be... n ={1,2,3,4,5,6,7,8,9,10}. Table 2 shows the time-period cost calculation results of the method presented in this paper, and Table 3 presents the cumulative cost calculation results of the rainflow counting method. Comparative analysis shows that the marginal cost assessment results of the two methods are consistent across different time periods.

[0064] Table 2. Time-based degradation costs quantified by this method.

[0065] Table 3. Cumulative degradation costs obtained from rainflow counting ; Reasoning: When the number of sub-units N approaches infinity, the proposed method and the actual degradation cost defined by equation (3) are strictly mathematically equivalent.

[0066] Proof: For the SOC trajectory within the time interval [0, T], the battery degradation cost can be expressed as the sum of the degradation costs of all sub-cells within that interval. Let the sub-cell cost c... n expression Substituting the values, we obtain the expression for the total cost V: ; when N As the size approaches infinity, each sub-unit becomes sufficiently small, existing in only two states: full energy or no energy. Based on the first-in-first-out (FIFO) rule of a queue, the sub-unit... n Every time The release of energy will correspond to a depth greater than n / N The discharge half-cycle. This half-cycle may be unpaired or may eventually pair with other charging half-cycles to form a full cycle. Therefore, the sub-cell n exist The total energy released is equivalent to its rated energy and depth greater than [amount missing]. n / N The product of the sum of the number of half-cycles and the number of full cycles. Similarly, sub-units. n exist Energy is absorbed in the middle, corresponding to a depth greater than n / NThe total energy absorbed during a charging half-cycle also follows the same relationship: ; ; Will and Substitution The total degradation cost is as follows: ; When N is infinite, the expression can be further written in continuous form. and with formula The actual cyclic degradation cost is consistent with the defined cost, thus proving that the method in this paper is mathematically equivalent to the real degradation cost; .

[0067] (2) Not dependent on historical SoC The proposed method can achieve explicit analytical calculation of degradation cost in real time using only the current energy distribution, eliminating the dependence on historical SoC data and eliminating the need to perform historical extreme point matching calculations. At the same time, it effectively avoids the technical problem of the expansion of the data storage scale of continuously recorded historical SoC data.

[0068] (3) Full-condition analytical performance Traditional methods, based on rainflow counting, propose "online rainflow counting" for real-time cyclic degradation cost quantification. However, these methods only assume sufficiently small SoC changes due to future operations and estimate the marginal degradation cost per unit energy. Therefore, they can only provide the marginal cost of charging and discharging in the current state and cannot predict cost changes under large ΔSoC. For example, in state S3, the online rainflow method can only provide a single marginal charging cost c4 and marginal discharging cost c1. This method overcomes this limitation, enabling accurate calculation of the degradation cost corresponding to ΔSoC in any direction and magnitude.

[0069] (4) Generalization properties The proposed method is not only applicable to the power function degradation model defined by equation (1), but can also be extended to any degradation cost calculation system that satisfies the convexity condition.

[0070] refer to Figure 6 A specific embodiment of the present invention discloses a method for prospective quantification of real-time cycle degradation cost of batteries, including a system for prospective quantification of real-time cycle degradation cost of batteries, comprising: an energy definition module 601, a unit energy degradation cost module 602, a degradation cost calculation model 603, and a summation module 604.

[0071] The energy definition module 601 is used to model the mathematical model of the entire rechargeable battery into N equivalent sub-units and define the discharge energy distribution and charging energy distribution in each equivalent sub-unit.

[0072] The unit energy degradation cost module 602 is used to obtain the unit energy degradation cost of the current equivalent sub-unit n based on the degradation degree of adjacent equivalent sub-units, battery replacement cost, and the rated capacity of the equivalent sub-units.

[0073] The degradation cost calculation model 603 is used to construct a degradation cost calculation model for a single charge and discharge behavior based on the unit energy degradation cost, the energy reduction of the current equivalent sub-unit n in the discharge energy distribution state, and the energy increase of the current equivalent sub-unit n in the charging energy distribution state.

[0074] The summation module 604 is used to obtain the total degradation cost of the charging and discharging behavior of N equivalent sub-units throughout the entire cycle based on the degradation cost calculation model.

[0075] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0076] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for prospectively quantifying the real-time cycle degradation cost of batteries, characterized in that, include: The mathematical model of the entire rechargeable battery is modeled as N equivalent sub-units and the discharge energy distribution and charging energy distribution in each equivalent sub-unit are defined. The N equivalent sub-units include the first equivalent sub-unit to the Nth equivalent sub-unit. The unit energy degradation cost of the current equivalent sub-unit n is obtained based on the degradation degree of adjacent equivalent sub-units, battery replacement cost, and rated capacity of the equivalent sub-units. A degradation cost calculation model for a single charge / discharge cycle is constructed based on the unit energy degradation cost, the energy reduction of the current equivalent subunit n in the discharge energy distribution state, and the energy increase of the current equivalent subunit n in the charging energy distribution state; and The total degradation cost of the N equivalent sub-units during the entire cycle is obtained based on the degradation cost calculation model.

2. The method for prospective quantification of real-time battery cycle degradation costs according to claim 1, characterized in that, The definition of the discharge energy distribution and charge energy distribution in each equivalent sub-unit further includes: Define the energy contained in the equivalent subunit n in the discharge energy distribution de at the current time t, and the energy contained in the equivalent subunit n in the charging energy distribution in at the current time t.

3. The method for prospective quantification of real-time cycle degradation costs of batteries according to claim 2, characterized in that, The unit energy degradation cost of the current equivalent sub-unit n, obtained based on the degradation level of adjacent equivalent sub-units, battery replacement cost, and rated capacity of the equivalent sub-units, further includes: The degradation degree of the previous equivalent subunit n-1 is calculated based on the first ratio of the previous equivalent subunit n-1 to the N equivalent subunits, the number of cycles of the rechargeable battery, and the degradation rate. The degree of degradation of the current equivalent subunit n is calculated based on the second ratio of the current equivalent subunit n to the N equivalent subunits, the number of cycles of the rechargeable battery, and the degradation rate. The unit energy degradation cost of the current equivalent subunit n is calculated based on the difference between the degradation degree of the current equivalent subunit n and the degradation degree of the previous equivalent subunit n-1, the battery replacement cost, and the rated capacity of the equivalent subunit.

4. The method for prospective quantification of real-time battery cycle degradation costs according to claim 3, characterized in that, The unit energy degradation cost c of the current equivalent sub-unit n is obtained based on the degradation level of adjacent equivalent sub-units, battery replacement cost, and rated capacity of the equivalent sub-units. n Further includes: ； Among them, C rep The battery replacement cost is represented by Q(n / N), the degradation degree of the current equivalent subunit n is represented by Q(n-1 / N), and the degradation degree of the previous equivalent subunit n-1 is represented by E. max The value represents the rated capacity of the battery, and N represents the number of equivalent sub-cells in the rechargeable battery.

5. The method for prospective quantification of real-time cycle degradation costs of batteries according to claim 3, characterized in that, Based on the unit energy degradation cost, the energy reduction of the current equivalent subunit n in the discharge energy distribution state, and the energy increase of the current equivalent subunit n in the charging energy distribution state, a degradation cost calculation model V for a single charge-discharge behavior is constructed. t Further includes: ； in, They represent the discharge energy distribution, respectively. The energy reduction of the equivalent subunit in the state Indicates the distribution of charging energy The energy increase of the equivalent subunit in the state c n This represents the unit energy degradation cost of the current equivalent subunit n.

6. The method for prospective quantification of real-time cycle degradation costs of batteries according to claim 5, characterized in that, The total degradation cost V obtained based on the degradation cost calculation model for the charge-discharge behavior of the N equivalent sub-units throughout the entire cycle further includes: ； in They represent the discharge energy distribution, respectively. The energy reduction of the equivalent subunit in the state Indicates the distribution of charging energy The energy increase of the equivalent subunit in the state, C rep Let Q(n / N) represent the battery replacement cost, Q(n-1 / N) represent the degradation degree of the current equivalent subunit n, and Q(n-1 / N) represent the degradation degree of the previous equivalent subunit n-1. E max Indicates the battery's rated capacity. N This indicates the number of equivalent sub-cells in a rechargeable battery. T This indicates the entire cycle of the rechargeable battery.

7. The method for prospective quantification of real-time cycle degradation costs of batteries according to claim 6, characterized in that, Further, it includes calculating the energy distribution state transition caused by the charging and discharging operation in each time period based on the discharge energy distribution and charging energy in each equivalent sub-unit, wherein, The energy contained in the equivalent subunit n based on the discharge energy distribution de at the current time t. And the energy increase of the equivalent subunit n in the discharge energy distribution de at the current time t. or reduced energy Calculate the energy distribution state transition caused by the discharge operation at the next moment. : ； Based on the charging energy distribution at current time t, the energy contained in the equivalent subunit n in in... And the energy increase in the equivalent sub-unit in the charging energy distribution. or reduced energy Calculate the energy distribution state transition caused by the charging operation at the next time step. : 。 8. The method for prospective quantification of real-time cycle degradation costs of batteries according to claim 5, characterized in that, Further includes: Based on the degradation cost calculation model for the single charge-discharge behavior, the degradation cost increment for the next charge-discharge operation at time t+1 is derived from the energy distribution at the current time t. ,in, ； When the change in state of charge (SoC) ΔSoC is greater than zero, the unit energy degradation cost c based on the equivalent subunit n is... n The energy change of the equivalent subunit n in the state of charge energy. Calculate the degradation cost increment for the charging operation at the next time step t+1, and When the change in state of charge (SoC) ΔSoC is less than zero, the unit energy degradation cost c based on the equivalent subunit n is... n The energy change of the equivalent subunit n in the discharge energy state. Calculate the degradation cost increment of the discharge operation at the next time step t+1.

9. The method for prospective quantification of real-time cycle degradation costs of batteries according to claim 8, characterized in that, The energy change of the equivalent subunit n in the charging energy state at the next time t+1 is calculated using the following formula. : ； in, E represents the discharge energy distribution. max This indicates the battery's rated capacity, and △SoC represents the change in the state of charge (SoC). The energy distribution de represents the total energy reduction of the equivalent discharge subunits 1 to n-1 in the next time step t+1. The energy change of the equivalent subunit n in the discharge energy state at the next time t+1 is calculated using the following formula. : ； in, This represents the sum of the energy increases from the equivalent subunits 1 to n-1 in the energy distribution at the next time step t+1.

10. A system for predictively quantifying the real-time cycle degradation cost of batteries, characterized in that, include: The energy definition module is used to model the mathematical model of the entire rechargeable battery into N equivalent sub-units and define the discharge energy distribution and charging energy distribution in each equivalent sub-unit. The unit energy degradation cost module is used to obtain the unit energy degradation cost of the current equivalent sub-unit n based on the degradation degree of adjacent equivalent sub-units, battery replacement cost, and the rated capacity of the equivalent sub-units. A degradation cost calculation model is used to construct a degradation cost calculation model for a single charge-discharge behavior based on the degradation cost per unit energy, the energy reduction of the current equivalent subunit n in the discharge energy distribution state, and the energy increase of the current equivalent subunit n in the charging energy distribution state. as well as The summation module is used to obtain the total degradation cost of the charging and discharging behavior of the N equivalent sub-units throughout the entire cycle based on the degradation cost calculation model.

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