Electrochemical energy storage refined modeling method and system based on energy state

Abstract

The invention provides an electrochemical energy storage refined modeling method and system based on an energy state, and relates to the technical field of power system optimization scheduling, and the method obtains battery parameters through experimental data driving, and converts the nonlinear charging and discharging characteristics of a battery into linear constraints suitable for an optimization algorithm. The refined model provided by the invention can accurately reflect the actual throughput characteristics of the energy storage system in the power grid, guarantees the safety, feasibility and economy of a dispatching instruction, and greatly improves the capability of the energy storage to participate in the regulation and control of the power system.

Description

Technical Field

[0001] This invention belongs to the field of power system optimization and dispatching technology, and in particular, it is a refined modeling method and system for electrochemical energy storage based on energy state. Background Technology

[0002] Currently, electrochemical energy storage modeling in power system dispatching and optimization typically employs simplified and linear mathematical models. This traditional approach treats battery energy storage systems as ideal energy containers with fixed input and output efficiencies. Its core assumptions include constant round-trip efficiency and static charging / discharging power limitations. In large-scale optimization calculations such as grid economic dispatching and unit combination, this simplified model can transform complex physical systems into mixed-integer linear programming (MILP) problems. MILP has efficient commercial solvers and guarantees of a global optimal solution, thus becoming the mainstream choice in grid dispatching. However, this approach neglects key physical characteristics of batteries in actual operation, such as: charging / discharging efficiency is actually a nonlinear function of power rate; battery internal resistance dynamically changes with state of charge and aging; and the maximum charging power rapidly decreases as the battery approaches full charge. This linear model based on constant parameters deviates significantly from the actual response capability of batteries when facing high-frequency, high-power regulation demands, affecting the accuracy of dispatching commands and the utilization efficiency of energy storage resources.

[0003] In recent years, with the increasing penetration of renewable energy, electrochemical energy storage has taken on more ancillary services in the power grid, such as rapid frequency regulation and peak shaving, requiring it to operate over a wider power and energy range. To improve the physical fidelity of models, some studies have begun to introduce energy storage characterization methods based on equivalent circuit models (ECMs). Although ECMs can more accurately simulate the ohmic losses, polarization effects, and dynamic voltage response of batteries, their inherent nonlinear characteristics and nonconvex structures pose significant challenges to large-scale optimization solutions. Directly embedding these high-fidelity models into grid dispatching algorithms transforms the optimization problem from easily solvable linear programming into a complex nonlinear programming or nonconvex optimization problem. This not only drastically increases the solution time, making it difficult to meet the timeliness requirements of real-time grid dispatching, but also fails to guarantee finding the global optimum, potentially leading to local optima in dispatching decisions. Therefore, a core contradiction remains in existing research: how to construct an energy storage model that accurately reflects the nonlinear physical characteristics of batteries while maintaining a linear structure to ensure efficient solvability.

[0004] In summary, traditional linear models cannot meet the high precision and security requirements of modern power grids for energy storage dispatch, while high-precision physical models are difficult to apply to practical real-time dispatch systems due to computational complexity. This technological gap necessitates the proposal of this invention. Summary of the Invention

[0005] Therefore, the purpose of this invention is to propose a refined modeling method and system for electrochemical energy storage based on the state of energy (SOE), aiming to bridge the gap between traditional dispatch models and the electrochemical characteristics of batteries. By introducing SOE as the core state variable and fully considering the unidirectional energy efficiency and nonlinear charge-discharge constraints of the battery, this invention can accurately describe the actual throughput capacity of the energy storage system under different energy states, thereby improving the computational accuracy of energy storage participation in grid optimization, ensuring the safety and economy of dispatch strategies, and providing reliable model support for the large-scale participation of energy storage in the electricity market in the future.

[0006] The design concept of this invention follows a logical closed loop of "experimental characterization—parameter identification—model construction—linearization processing," driving the acquisition of model parameters through rigorous experimental data. First, an open-circuit voltage (OCV) experiment and a full-cycle constant power-constant voltage (CP-CV) experiment are designed and executed. The latter specifically selects a power control mode to match the actual grid dispatch scenario, thereby obtaining voltage and current response data of the battery at different rates. Second, based on the experimental data, the unidirectional charging and discharging efficiency of the battery is decoupled and calculated, constructing a charging / discharging power-power... Characteristic curves transform the nonlinear power-efficiency relationship into an equivalent linear input / output power relationship, effectively solving the problem of the difficulty in solving nonlinear terms in scheduling optimization. The core innovation lies in constructing... Constraint Curve: Using constant power charging experimental data, the maximum energy injection capacity of the battery as a function of the current state of energy (SOE) within a unit time step is calculated, thus accurately characterizing the battery's charging capacity decay characteristics near full charge (CV stage). Finally, a piecewise linear approximation method is used to address the nonlinearity... Curve fitting reduces computational complexity while maintaining model accuracy, enabling it to be directly embedded into standard grid dispatching algorithms such as Mixed Integer Linear Programming (MILP) to achieve high-fidelity simulation of the physical characteristics of energy storage systems.

[0007] A refined modeling method for electrochemical energy storage based on energy state, the specific steps of which are as follows: 1) Conduct an open-circuit voltage test to obtain the open-circuit voltage-state-of-charge characteristic curve of the battery; 2) Conduct a full-cycle constant power-constant voltage experiment to obtain charge / discharge timing data at different power rates; 3) Based on the open-circuit voltage-state-of-charge characteristic curve described in step 1) and the charge / discharge timing data described in step 2), calculate the unidirectional energy efficiency for charging and discharging respectively; 4) Based on the unidirectional energy efficiency obtained in step 3), calculate the correspondence between the actual power and the grid-side power to obtain the charging / discharging power-power characteristics; 5) Based on the charge / discharge timing data described in step 2), calculate the energy capacity and power capacity of the battery under a complete charge-discharge cycle; 6) Using the energy capacity obtained in step 5) as a normalization benchmark, the charge / discharge timing data in step 2) is converted into an energy state of energy (SOE) vector, thereby obtaining the energy state-energy state change increment constraint. 7) Construct a power-efficiency relationship using the unidirectional energy efficiency at different power levels in step 3), and linearize the nonlinear power-efficiency relationship by combining it with the charging / discharging power-power characteristics obtained in step 4); 8) Perform piecewise linear approximation on the energy state-energy change increment constraint obtained in step 6) to construct the charging power decay constraint under high charge state, which is approximately transformed into optimization model constraint.

[0008] As a further aspect of the present invention, the open-circuit voltage test specifically involves: performing a complete constant current-constant voltage cycle on each battery cell, with the charge-discharge rate being 0.05C and the cutoff current condition being 0.01C; and averaging the measured closed-circuit voltage to obtain the open-circuit voltage-state-of-charge characteristic curve.

[0009] As a further aspect of the present invention, the steps of the full-cycle constant power-constant voltage experiment are as follows: ten complete full-cycle constant power-constant voltage test cycles are performed on each battery cell, with the power rate ranging from 0.1P to 1P, in steps of 0.1P. Each cycle starts from a fully discharged battery with an energy state of 0%, and the current and voltage during the charging and discharging process are recorded.

[0010] As a further aspect of the present invention, the unidirectional energy efficiency is calculated as follows: a) The calculation of charging energy efficiency is based on comparing the total energy actually injected into the battery with the ideal total energy stored in the battery calculated using the open-circuit voltage-state-of-charge characteristic curve within the observed charging energy state range. b) The calculation of discharge energy efficiency is based on comparing the total energy actually extracted from the battery within the observed discharge energy state range with the ideal total energy released by the battery calculated using the open-circuit voltage-state-of-charge characteristic curve. c) Wherein, the total energy actually injected and extracted is calculated by using the trapezoidal integral method on the voltage and current data recorded in the full-cycle constant power-constant voltage experiment; d) The ideal total energy is determined by the open-circuit voltage-state-of-charge characteristic curve and the coulomb counting method, and is used as an ideal benchmark for measuring the total energy stored or released in the battery.

[0011] As a further aspect of the present invention, the efficiency calculation is applied to the constant power portion of the full-cycle constant power-constant voltage experimental measurement log, so that the calculated unidirectional efficiency is associated with a specific power rate; the discrete power-efficiency pairs are obtained by linear interpolation to cover a continuous power range.

[0012] As a further aspect of the present invention, the step of obtaining the charging / discharging power-power characteristics is as follows: introducing an equivalent internal power variable to represent the actual power charged into the battery when power is obtained from the grid, and the actual discharge power required by the battery when power is delivered to the grid; the introduction of the equivalent internal power variable is used to replace the product term of the nonlinear power variable and efficiency variable in the discrete model.

[0013] As a further aspect of the present invention, the charging / discharging power-power characteristic samples the correspondence between the equivalent internal power and the external power at equal intervals to obtain discrete power-power pairs for use in the linear optimization model.

[0014] As a further aspect of the present invention, the energy capacity is calculated as follows: based on the power vector recorded in half a cycle of the full-cycle constant power-constant voltage experiment, unidirectional charge / discharge efficiency is corrected point by point, and then integrated over time to obtain the energy stored in the battery during charging and the energy extracted from the battery during discharging; the energy capacity is finally determined by averaging over K complete full-cycle constant power-constant voltage cycles.

[0015] As a further aspect of the present invention, the step of obtaining the energy state-energy change increment constraint is as follows: a) Calculate the energy state vector: Perform unidirectional charging efficiency correction point by point on the power vector of the 1P charging half-cycle of the complete full-cycle constant power-constant voltage experiment, perform cumulative integration, and normalize with energy capacity to obtain the energy state range from zero to 100%. b) Calculate the energy change increment vector: For each sample point, calculate the energy state change increment within a predefined scheduling time step based on the obtained energy state vector; c) Piecewise linear approximation: The nonlinear energy state-energy change increment curve is approximated by the least squares method using multiple straight lines to obtain a monotonically decreasing slope, thereby obtaining a charging constraint that can be directly used for the optimization model.

[0016] Furthermore, the present invention also provides a refined modeling system for electrochemical energy storage based on energy state, comprising: The data acquisition module performs open-circuit voltage experiments to obtain the battery's open-circuit voltage-state-of-charge characteristic curve; it also performs full-cycle constant power-constant voltage experiments to obtain charge / discharge timing data at different power rates. The efficiency calculation module calculates the unidirectional energy efficiency for charging and discharging based on the open-circuit voltage-state-of-charge characteristic curve and the charging / discharging timing data, respectively. The feature construction module calculates the correspondence between actual power and grid-side power based on the obtained unidirectional energy efficiency, and obtains the charging / discharging power-power characteristics. The capacity determination module calculates the energy capacity and power capacity of the battery under a complete charge-discharge cycle based on the charge / discharge timing data. The constraint generation module uses the obtained energy capacity as a normalization benchmark to convert the charge / discharge time-series data into an energy state of energy (SOE) vector, thereby obtaining an energy state-energy state change increment constraint. It constructs a power-efficiency relationship using unidirectional energy efficiency at different power levels and, combined with the obtained charge / discharge power-power characteristics, linearizes the nonlinear power-efficiency relationship. It then performs a piecewise linear approximation on the obtained energy state-energy change increment constraint to construct a charging power attenuation constraint under high charge conditions, which is then approximately transformed into an optimization model constraint.

[0017] Due to the adoption of the above technical solution, the present invention has at least one of the following beneficial effects: This invention creatively constructs a refined characterization system based on energy state by introducing the FULL model. It calculates the unidirectional energy efficiency of charging and discharging by decoupling the processes, and establishes... The present invention successfully transforms the complex electrochemical nonlinear losses within a battery into an equivalent linear input / output power relationship. This method not only overcomes the shortcomings of traditional models that cannot accurately reflect the dynamic impact of current ratio on efficiency, but also ensures a high degree of consistency between the power command output by the model and the actual physical response of the battery by converting the state of charge (SOC) into an SOE index that better meets the energy settlement requirements of the power grid. This significantly improves the reliability of power system optimization calculations such as peak shaving and frequency regulation.

[0018] This invention constructs The constraint curve effectively addresses the safety hazard of the mismatch between the apparent power and actual charging capacity of energy storage under high charge conditions. At the end of the battery charging process (i.e., the constant voltage CV stage), the battery's charging capacity decreases rapidly and non-linearly with increasing SOE. Using experimental data at 1P rate, the maximum energy limit that can be injected into batteries with different SOE levels within a unit time step was precisely quantified. This constraint mechanism, based on physical measurements, can detect and avoid infeasible operating regions of "high SOE-high power" in advance, fundamentally eliminating the conflict between dispatch commands and battery BMS protection strategies. This ensures the safe operation of the energy storage system while guaranteeing 100% executability of grid dispatch commands.

[0019] This invention achieves a perfect balance between a high-fidelity physical model and low computational complexity, making it highly valuable for engineering applications. Although the FULL model introduces complex electrochemical nonlinearities, this invention, through ingenious algorithm design, utilizes a piecewise linear approximation method to address these nonlinearities. curves and The characteristics have been processed. This processing method transforms the originally complex non-convex nonlinear optimization problem into a standard mixed-integer linear programming (MILP) problem, allowing the model to be directly embedded into existing mature power grid dispatching algorithms and commercial solvers without significantly increasing the computational burden. This feature solves the long-standing industry dilemma of the trade-off between "model accuracy" and "solution speed," providing economical and effective underlying algorithmic support for the large-scale participation of electrochemical energy storage in spot market transactions and ancillary service market bidding, and greatly promoting the efficient utilization of energy storage resources in new power systems. Attached Figure Description

[0020] Figure 1 This is a flowchart of the parameter acquisition and constraint linearization process for the FULL model in this invention. Detailed Implementation

[0021] The embodiments of the present invention are described in detail below: These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention.

[0022] This invention proposes a refined modeling method for electrochemical energy storage based on energy state, referred to as the FULL model, aiming to overcome the inaccuracies and operational safety risks caused by the simplified handling of battery nonlinear characteristics in existing power grid dispatch models. The core of this invention lies in obtaining and linearizing the key physical constraints of the battery through experimental data. For the maximum power condition, this invention constructs a constraint curve between the energy state and the energy change increment. This curve accurately quantifies the maximum acceptable energy of the battery per unit time step under high charge, effectively simulating the power decay phenomenon at the end of charging. The constraints are approximated using multiple straight lines, ensuring high-precision simulation of battery physical characteristics while achieving seamless integration with existing mixed-integer linear programming algorithms for power systems. The refined model ultimately provided by this invention ensures that the energy storage dispatch commands issued by the power grid are safe, feasible, and economical.

[0023] In this embodiment of the invention, a refined modeling method for electrochemical energy storage based on energy state is described, with the following specific steps: 1) Conduct an open-circuit voltage test to obtain the open-circuit voltage-state-of-charge characteristic curve of the battery; 2) Conduct a full-cycle constant power-constant voltage experiment to obtain charge / discharge timing data at different power rates; 3) Based on the open-circuit voltage-state-of-charge characteristic curve described in step 1) and the charge / discharge timing data described in step 2), calculate the unidirectional energy efficiency for charging and discharging respectively; 4) Based on the unidirectional energy efficiency obtained in step 3), calculate the correspondence between the actual power and the grid-side power to obtain the charging / discharging power-power characteristics; 5) Based on the charge / discharge timing data described in step 2), calculate the energy capacity and power capacity of the battery under a complete charge-discharge cycle; 6) Using the energy capacity obtained in step 5) as a normalization benchmark, the charge / discharge timing data in step 2) is converted into an energy state of energy (SOE) vector, thereby obtaining the energy state-energy state change increment constraint. 7) Construct a power-efficiency relationship using the unidirectional energy efficiency at different power levels in step 3), and linearize the nonlinear power-efficiency relationship by combining it with the charging / discharging power-power characteristics obtained in step 4); 8) Perform piecewise linear approximation on the energy state-energy change increment constraint obtained in step 6) to construct the charging power decay constraint under high charge state, which is approximately transformed into optimization model constraint.

[0024] Preferably, the open-circuit voltage test steps are as follows: perform a complete constant current-constant voltage cycle on each battery cell, with the charge-discharge rate being 0.05C and the cutoff current condition being 0.01C; and take the average value of the measured closed-circuit voltage to obtain the open-circuit voltage-state-of-charge characteristic curve.

[0025] The specific steps of the full-cycle constant power-constant voltage experiment are as follows: ten complete full-cycle constant power-constant voltage experiment cycles are performed on each battery cell, with the power rate ranging from 0.1P to 1P, in 0.1P increments. Each cycle starts from a fully discharged battery with an energy state of 0%, and the current and voltage during the charging and discharging process are recorded.

[0026] The unidirectional energy efficiency is calculated as follows: a) The calculation of charging energy efficiency is based on comparing the total energy actually injected into the battery with the ideal total energy stored in the battery calculated using the open-circuit voltage-state-of-charge characteristic curve within the observed charging energy state range. b) The calculation of discharge energy efficiency is based on comparing the total energy actually extracted from the battery within the observed discharge energy state range with the ideal total energy released by the battery calculated using the open-circuit voltage-state-of-charge characteristic curve. c) Wherein, the total energy actually injected and extracted is calculated by using the trapezoidal integral method on the voltage and current data recorded in the full-cycle constant power-constant voltage experiment; d) The ideal total energy is determined by the open-circuit voltage-state-of-charge characteristic curve and the coulomb counting method, and is used as an ideal benchmark for measuring the total energy stored or released in the battery.

[0027] The efficiency calculation is applied to the constant power portion of the full-cycle constant power-constant voltage experimental measurement log, so that the calculated unidirectional efficiency is correlated with a specific power rate; discrete power-efficiency pairs are obtained by linear interpolation to cover a continuous power range.

[0028] The steps for obtaining the charging / discharging power-power characteristics are as follows: an equivalent internal power variable is introduced to represent the actual power charged into the battery when power is obtained from the grid, and the actual discharge power required by the battery when power is transmitted to the grid; the introduction of the equivalent internal power variable is used to replace the product term of the nonlinear power variable and efficiency variable in the discrete model.

[0029] The charging / discharging power-power characteristics sample the correspondence between the equivalent internal power and the external power at equal intervals to obtain discrete power-power pairs for the linear optimization model.

[0030] The energy capacity is calculated as follows: based on the power vector recorded in half a cycle of the full-cycle constant power-constant voltage experiment, the unidirectional charge / discharge efficiency is corrected point by point, and then integrated over time to obtain the energy stored in the battery during charging and the energy extracted from the battery during discharging; the energy capacity is finally determined by averaging over K complete full-cycle constant power-constant voltage cycles.

[0031] The steps for obtaining the energy state-energy change increment constraint are as follows: a) Calculate the energy state vector: Perform unidirectional charging efficiency correction point by point on the power vector of the 1P charging half-cycle of the complete full-cycle constant power-constant voltage experiment, perform cumulative integration, and normalize with energy capacity to obtain the energy state range from zero to 100%. b) Calculate the energy change increment vector: For each sample point, calculate the energy state change increment within a predefined scheduling time step based on the obtained energy state vector; c) Piecewise linear approximation: The nonlinear energy state-energy change increment curve is approximated by the least squares method using multiple straight lines to obtain a monotonically decreasing slope, thereby obtaining a charging constraint that can be directly used for the optimization model.

[0032] In this invention, the algorithm for obtaining the battery parameters required for the FULL model is as follows. First, two sets of experiments are conducted for each battery cell, as described in steps 1 and 2 respectively. The experimental results are processed to calculate the unidirectional efficiency of the battery. The charging and discharging efficiencies are calculated separately, as shown in step 3. These efficiencies are further used to obtain the charging / discharging power-to-power ratio. Characteristics are defined to describe the losses that occur during battery charging / discharging, see step 4. Finally, the battery's energy and power capacity are determined in step 5, and charging constraints that take into account the battery's nonlinear charging characteristics are obtained in step 6.

[0033] Step 1: Open Circuit Voltage Test Each battery cell underwent a complete constant current-constant voltage (CC-CV) cycle, with a charging and discharging C-rate of 0.05C and a charging and discharging cutoff current of 0.01C. The measured closed-circuit voltage (CCV) was averaged to obtain the open-circuit voltage-state-of-charge (OCV-SOC) characteristic curve, which was used to determine the unidirectional efficiency of the battery.

[0034] Step 2: Full-cycle constant power-constant voltage (CP-CV) experiment Ten complete constant power-constant voltage (CP-CV) cycles were performed on each cell, with the P-rate ranging from 0.1P to 1P in 0.1P increments. Each cycle began with a fully discharged cell at 0% SOE. The charging and discharging process terminated when the current dropped below the low cutoff threshold. Because power and energy are related to grid dispatch, the cells were cycled in CP-CV mode rather than CC-CV mode, ensuring better practicality in real-world applications. The recorded current and voltage were used to calculate the unidirectional energy efficiency in step 3.

[0035] Step 3: Unidirectional energy efficiency Charging and discharging energy efficiency is calculated using the following expression: in, This refers to the total energy injected into the battery within the observed state of charge (SOE) range, while It is the total energy extracted from the battery within the observed state of discharge energy (SOE) range. and The following can be calculated using the trapezoidal integration method from the recorded voltage U and current I: Where ∆t is the sampling time, and nc and nd are the total number of samples in a specific charge / discharge log, respectively. represents the ideal value of the total energy stored in the battery. It cannot be directly determined from the recorded voltage and current. However, a description can be obtained using the open-circuit voltage-state-of-charge (OCV-SOC) characteristic curve. The following expression.

[0036] in, It was calculated using the Coulomb count method and used to determine Calculating unidirectional energy efficiency in this way ignores coulombic losses; however, this error is acceptable for lithium-ion batteries because they have very high coulombic efficiency.

[0037] Since battery efficiency depends primarily on charging / discharging current (power), the above formula only applies to the constant power measured in step 2. This is the part. Thus, the calculated unidirectional efficiency is associated with a specific P-rate. Therefore, the purpose of step 3 is to determine that for each battery cell, there are 10 different charging efficiencies. Values ​​and 10 different discharge efficiencies These values ​​correspond to a P-rate uniformly distributed in the range of 0.1P to 1P. The power-efficiency pairs between discrete values ​​are obtained by linear interpolation.

[0038] Step 4: Charging / Discharging characteristic The input for step 4 is the unidirectional energy efficiency of the battery determined in step 3. In the discrete battery model, the SOE for each time step is calculated based on the charge and discharge energy efficiencies, as shown below.

[0039] The above equation is nonlinear because of the time-varying charging power variable. With charging efficiency variable Multiply, and The value depends directly on The same logic applies to discharge power variables. To avoid these nonlinearities, the following substitutions are introduced.

[0040] variable Indicates when drawing power from the grid The actual power supplied to the battery at that time, Indicates the power supplied to the power grid The actual discharge power required by the battery at that time.

[0041] The obtained output is sampled at equal intervals. and These represent the charging and discharging rates (P) used in the experiment, respectively.

[0042] Step 5: Energy and Power Capacity Battery energy capacity Defined as the total amount of energy that a battery can store. It cannot be measured directly, but is calculated based on the experimental data obtained in step 2. For each complete charge / discharge constant power-constant voltage (CP-CV) half-cycle, the recorded power vector is point-by-point corrected for unidirectional charge / discharge efficiency according to the characteristic curve in step 2, and then integrated over time to obtain the energy stored in the battery during charging. and the energy extracted from the battery during discharge. .

[0043] For K complete CP-CV cycles, the energy capacity The calculation formula is as follows.

[0044] Battery power capacity This refers to the battery's maximum charging / discharging power. In this invention, the maximum power is always 1P. According to the definition of P-rate, that is... The value corresponds to the battery watt-hour capacity declared by the manufacturer.

[0045] Step 6: SOE- Charging constraints The curve describes the maximum energy charging capability of the battery within a predefined time step under a given state of energy (SOE), thus taking into account the nonlinear charging characteristics of the battery. The curve should be determined for the maximum charging P-rate, which is 1P in this example. The process involves the following steps.

[0046] Step 6.1: Calculate the SOE vector. For a complete constant power-constant voltage (CP-CV) 1P charging half-cycle (obtained in Step 2), the SOE vector is calculated as follows: First, based on the characteristic curve in Step 2, perform unidirectional charging efficiency correction on the recorded power vector point by point; then, perform cumulative integration over time; finally, use the energy capacity... (As determined in step 5) Normalization is performed to obtain a range of 0-100%. Since a complete charge half-cycle means charging from 0% SOE to 100% SOE, it is assumed that the battery actually stores its full energy capacity after accounting for losses. (Wh). Normalization to 100% ensures comparability between different batteries and facilitates the application of the model in various power grid control scenarios.

[0047] Step 6.2: Calculation Vector. For each sample, calculate based on the obtained SOE vector (step 6.1). vector: Where i is the sample index. The sampling frequency (Hz) is used, so ∆i samples correspond to one hour. One hour is chosen as the standard time step for the future energy trading market. For cases with high SOE values ​​where batteries can be fully charged in less than one hour, the above formula is not used for calculation.

[0048] Step 6.3: Piecewise linear approximation. Nonlinearity is approximated using multiple straight lines. The curve, this method finds the minimum approximate deviation using the least squares method at a step size of 1% SOE. Since the charging capacity of lithium-ion batteries gradually decreases at higher power levels, this... The approximation has a monotonically decreasing slope, so the model can be used directly.

[0049] During the experimental characterization phase of this invention, to ensure high accuracy and repeatability of model parameter identification, all tests should be conducted in a controlled experimental environment. The test platform should include a high-precision battery testing system and a programmable constant temperature and humidity chamber. The voltage acquisition accuracy of the battery testing system should be no less than 1mV, and the current control accuracy should reach 0.02% of full scale to accurately capture minute voltage fluctuations and current responses. The temperature of the constant temperature chamber is set to 25°C (±0.5°C) to eliminate the interference of temperature fluctuations on the battery's internal resistance and electrochemical reaction rate, ensuring that all characteristic curves only reflect the electrochemical characteristics of the battery itself under standard operating conditions. The data acquisition frequency is set to 1Hz to 10Hz. For the final stage of charging and discharging where voltage changes drastically, the sampling frequency can be adaptively increased to avoid the loss of critical inflection point data.

[0050] Before the experiment, all individual battery cells under test must undergo a standard pretreatment process, namely, standing at a standard temperature for at least 4 hours to eliminate thermal history effects and ensure that the internal electrochemical state of the battery reaches thermodynamic equilibrium. A computer terminal connects to the testing equipment via TCP / IP protocol to store time-series data such as time, voltage, current, temperature, and cumulative capacity in real time, providing a raw database for subsequent MATLAB or Python data processing programs.

[0051] Each battery cell was subjected to a complete constant current-constant voltage cycle, with a charge-discharge rate of 0.05C and a cutoff current of 0.01C for both charging and discharging. The measured closed-circuit voltages were averaged to obtain the open-circuit voltage-state-of-charge characteristic curve, which was used to determine the unidirectional efficiency of the battery.

[0052] When performing open-circuit voltage experiments, choosing an extremely low rate of 0.05C, i.e., a quasi-static C / 20 rate, has clear physical significance. At this rate, the ohmic polarization, concentration polarization, and electrochemical polarization voltage drop within the battery are minimized, allowing the measured closed-circuit voltage (CCV) to approximate the battery's thermodynamic equilibrium potential (EMF) as closely as possible. Although a perfectly ideal OCV requires an infinitely long settling time to eliminate polarization, in engineering applications, the voltage curve obtained from constant current charging and discharging at 0.05C contains a very small dynamic overpotential. By averaging the voltage curves in both charging and discharging directions, the overpotential components and hysteresis effects in opposite directions can be effectively offset, thereby extracting a highly accurate and unique OCV-SOC relationship curve. This curve is not only the benchmark for determining the battery's remaining energy but also the core basis for subsequent calculations of "ideal stored energy." Inaccurate measurement of the OCV curve will directly lead to systematic deviations in unidirectional efficiency calculations, thus affecting the prediction accuracy of the FULL model in the low-power range.

[0053] Ten complete constant power-constant voltage (CP-CV) cycles were performed on each battery cell, with the P-rate ranging from 0.1P to 1P in 0.1P increments. Each cycle began with a fully discharged battery at 0% SOE. The charging and discharging process terminated when the current dropped below the low cutoff threshold. Since power and energy are related to grid dispatch, traditional battery modeling is often based on constant current conditions. However, in actual power system operation, whether for frequency regulation, fluctuation mitigation, or spot market trading, dispatch commands are essentially power commands. The thermal effects and internal resistance changes of the battery in constant power mode differ significantly from those in constant current mode. For example, at the end of constant power discharge, as the voltage decreases, the current must increase non-linearly to maintain constant power, leading to a sharp increase in Joule heating and accelerated voltage drop. The CP-CV experimental protocol used in this invention fully reproduces this condition: when the battery terminal voltage reaches the cutoff voltage, the control strategy does not immediately stop but seamlessly switches to constant voltage mode. This process simulates the protection logic of a real battery management system, which utilizes remaining capacity or injected energy as much as possible while ensuring that the voltage does not exceed the limit. Recording multiple sets of CP-CV data at gradients from 0.1P to 1P allows for the construction of a three-dimensional "power-voltage-efficiency" response surface covering the entire operating domain of the battery, which is impossible to achieve with traditional single-rate experiments. Therefore, the battery is cycled in a constant power-constant voltage mode, rather than a constant current-constant voltage mode, ensuring better practicality of the model in real-world applications.

[0054] One of the key innovations of this invention is decoupling the round-trip efficiency into unidirectional charging efficiency and unidirectional discharging efficiency during the calculation of unidirectional energy efficiency. From a physical mechanism perspective, battery energy loss mainly stems from Joule heating caused by internal resistance and overpotential of electrode reactions. These losses result in more energy being absorbed from the grid during charging than the actual stored capacity of the battery, while the energy released to the grid during discharging is less than the reduced chemical energy within the battery. The assumption of ignoring coulombic losses is based on the fact that modern commercial lithium-ion batteries have extremely low side reaction rates and charge exchange efficiencies typically exceeding 99.9% during their normal lifespan. Therefore, energy efficiency loss is almost entirely dominated by voltage difference, rather than charge loss. The ideal value of total stored energy calculated using the OCV curve actually represents the energy throughput under ideal reversible processes without internal resistance and polarization effects. By comparing the actual measured energy with this ideal value, we are essentially quantifying the additional voltage loss caused by power load. This efficiency definition based on a physical benchmark ensures that the calculated efficiency value has a rigorous thermodynamic connotation, rather than merely being a statistical fitting parameter.

[0055] In the discrete battery model, the SOE for each time step is calculated based on the charging and discharging energy efficiency, as shown below.

[0056] The above equation is nonlinear because of the time-varying charging power variable. With charging efficiency variable Multiply, and The value depends directly on The same logic applies to discharge power variables. To avoid these nonlinearities, the following substitutions are introduced: variable Indicates when drawing power from the grid The actual power supplied to the battery at that time, Indicates the power supplied to the power grid The actual discharge power required by the battery at that time.

[0057] The obtained output is sampled at equal intervals. and These represent the charging and discharging rates (P) used in the experiment, respectively.

[0058] Introduction The fundamental purpose of this transformation is to solve the "bilinear nonconvexity" problem in power grid dispatch optimization. In the original equations, the actual power P is multiplied by the efficiency dependent on that power, forming a difficult-to-handle nonlinear term. By constructing a mapping relationship between the equivalent internal power P̂ and the external measured power P, this complex nonlinear characteristic is encapsulated in a piecewise linear function. In practice, this mapping relationship is discretized into a series of linear constraints. This approach transforms the problem, which originally required nonlinear programming or dynamic programming, into a standard mixed-integer linear programming problem. This not only guarantees the discovery of a globally optimal solution but also utilizes modern commercial solvers with a computation speed 2-3 orders of magnitude faster than handling nonlinear models, fully meeting the timeliness requirements of the electricity spot market for 5-minute or 15-minute dispatch.

[0059] According to the measurement The characteristic curve is used to perform point-by-point unidirectional charging / discharging efficiency correction on the recorded power vector, and then integrated over time to obtain the energy stored in the battery during charging. and the energy extracted from the battery during discharge. .

[0060] for K A complete CP-CV cycle, energy capacity The calculation formula is as follows.

[0061] Battery power capacity This refers to the battery's maximum charging / discharging power. In this invention, the maximum power is always 1P. According to the definition of P-rate, that is... The value corresponds to the battery watt-hour capacity declared by the manufacturer.

[0062] The curve describes the maximum energy charging capability of the battery within a predefined time step under a given battery energy state, thus taking into account the nonlinear charging characteristics of the battery. The curve should be determined for the maximum charging P-rate, which is 1P in this example. The process involves the following steps.

[0063] Calculating the SOE vector: For a complete constant power-constant voltage 1P charging half-cycle (obtained in step 2), the SOE vector is calculated as follows. First, based on the characteristic curve in step 2, the recorded power vector is corrected point-by-point for unidirectional charging efficiency; then, cumulative integration is performed over time; finally, the energy capacity is used... Normalization is performed to obtain a range of 0-100%. Since a complete charge half-cycle means charging from 0% SOE to 100% SOE, it is assumed that the battery actually stores its full energy capacity after accounting for losses. Normalization to 100% ensures comparability between different batteries and facilitates the application of the model in various power grid control scenarios.

[0064] calculate Vector: For each sample, calculate based on the obtained SOE vector. vector.

[0065] in, i It is a sample index. It is the sampling frequency, therefore ∆ i Each sample corresponds to one hour. One hour is chosen as the standard time step for the future energy trading market. For cases with high SOE values ​​where batteries can be fully charged in less than one hour, the above formula is not used for calculation.

[0066] Piecewise linear approximation: approximating nonlinearity using multiple straight lines. The curve, this method finds the minimum approximate deviation using the least squares method at a step size of 1% SOE. Since the charging capacity of lithium-ion batteries gradually decreases at higher power levels, this... The approximation has a monotonically decreasing slope, so the model can be used directly.

[0067] In the actual implementation of power grid dispatching algorithms, The constraint curve is applied using a "rolling time domain" approach. For each optimization time step t, the algorithm first reads the battery's current state of energy (SOE). Then, based on the generated piecewise linear function, it calculates the maximum energy injection the battery can accept over the next 11 hours. This constraint is transformed into a dynamic power upper limit constraint. When the battery is in the low SOE region, the constraint is relatively relaxed, allowing for fast charging at the rated power of 1P; however, once the battery enters the high SOE region... The rapid decrease in values ​​forces the optimization model to proactively reduce charging power commands. This mechanism mathematically constructs a "soft landing" trajectory, making the scheduling commands naturally conform to the physical characteristics of the battery during the constant voltage phase, thus avoiding the risk of passive BMS disconnection due to excessive commands, which is common in traditional models.

[0068] As a preferred embodiment of the present invention, the present invention also provides a refined modeling system for electrochemical energy storage based on energy state, comprising: The data acquisition module performs open-circuit voltage experiments to obtain the battery's open-circuit voltage-state-of-charge characteristic curve; it also performs full-cycle constant power-constant voltage experiments to obtain charge / discharge timing data at different power rates. The efficiency calculation module calculates the unidirectional energy efficiency for charging and discharging based on the open-circuit voltage-state-of-charge characteristic curve and the charging / discharging timing data, respectively. The feature construction module calculates the correspondence between actual power and grid-side power based on the obtained unidirectional energy efficiency, and obtains the charging / discharging power-power characteristics. The capacity determination module calculates the energy capacity and power capacity of the battery under a complete charge-discharge cycle based on the charge / discharge timing data. The constraint generation module uses the obtained energy capacity as a normalization benchmark to convert the charge / discharge time-series data into an energy state of energy (SOE) vector, thereby obtaining an energy state-energy state change increment constraint. It constructs a power-efficiency relationship using unidirectional energy efficiency at different power levels and, combined with the obtained charge / discharge power-power characteristics, linearizes the nonlinear power-efficiency relationship. It then performs a piecewise linear approximation on the obtained energy state-energy change increment constraint to construct a charging power attenuation constraint under high charge conditions, which is then approximately transformed into an optimization model constraint.

[0069] Optionally, a data acquisition module is used to perform a complete constant current-constant voltage cycle on each battery cell, with a charge / discharge rate of 0.05C and a cutoff current condition of 0.01C. The measured closed-circuit voltage is averaged to obtain the open-circuit voltage-state-of-charge characteristic curve.

[0070] Optionally, the steps of the full-cycle constant power-constant voltage experiment are as follows: ten complete full-cycle constant power-constant voltage experiment cycles are performed on each battery cell, with the power rate ranging from 0.1P to 1P, in 0.1P increments. Each cycle starts from a fully discharged battery with an energy state of 0%, and the current and voltage during the charging and discharging process are recorded.

[0071] Optionally, the unidirectional energy efficiency is calculated as follows: a) The calculation of charging energy efficiency is based on comparing the total energy actually injected into the battery with the ideal total energy stored in the battery calculated using the open-circuit voltage-state-of-charge characteristic curve within the observed charging energy state range. b) The calculation of discharge energy efficiency is based on comparing the total energy actually extracted from the battery within the observed discharge energy state range with the ideal total energy released by the battery calculated using the open-circuit voltage-state-of-charge characteristic curve. c) Wherein, the total energy actually injected and extracted is calculated by using the trapezoidal integral method on the voltage and current data recorded in the full-cycle constant power-constant voltage experiment; d) The ideal total energy is determined by the open-circuit voltage-state-of-charge characteristic curve and the coulomb counting method, and is used as an ideal benchmark for measuring the total energy stored or released in the battery.

[0072] Optionally, the efficiency calculation is applied to the constant power portion of the full-cycle constant power-constant voltage experimental measurement log, so that the calculated unidirectional efficiency is correlated with a specific power rate; discrete power-efficiency pairs are obtained by linear interpolation to cover a continuous power range.

[0073] Optionally, the data acquisition module is specifically used to: introduce an equivalent internal power variable to represent the actual power charged into the battery when power is obtained from the grid, and the actual discharge power required by the battery when power is transmitted to the grid; the introduction of the equivalent internal power variable is used to replace the product term of the nonlinear power variable and efficiency variable in the discrete model.

[0074] Optionally, the charging / discharging power-power characteristics sample the correspondence between the equivalent internal power and the external power at equal intervals to obtain discrete power-power pairs for the linear optimization model.

[0075] Optionally, the energy capacity is calculated as follows: based on the power vector recorded in half a cycle of the full-cycle constant power-constant voltage experiment, unidirectional charge / discharge efficiency is corrected point by point, and then integrated over time to obtain the energy stored in the battery during charging and the energy extracted from the battery during discharging; the energy capacity is finally determined by averaging over K complete full-cycle constant power-constant voltage cycles.

[0076] Optionally, the steps for obtaining the energy state-energy change increment constraint are as follows: a) Calculate the energy state vector: Perform unidirectional charging efficiency correction point by point on the power vector of the 1P charging half-cycle of the complete full-cycle constant power-constant voltage experiment, perform cumulative integration, and normalize with energy capacity to obtain the energy state range from zero to 100%. b) Calculate the energy change increment vector: For each sample point, calculate the energy state change increment within a predefined scheduling time step based on the obtained energy state vector; c) Piecewise linear approximation: The nonlinear energy state-energy change increment curve is approximated by the least squares method using multiple straight lines to obtain a monotonically decreasing slope, thereby obtaining a charging constraint that can be directly used for the optimization model.

[0077] As a preferred embodiment of the present invention, the present invention also provides a computer-readable storage medium for executing the electrochemical energy storage fine modeling method based on energy state described in the present invention.

[0078] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0079] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0080] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0081] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0082] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention.

[0083] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A refined modeling method for electrochemical energy storage based on energy state, characterized in that, The specific steps are as follows: 1) Conduct an open-circuit voltage test to obtain the open-circuit voltage-state-of-charge characteristic curve of the battery; 2) Conduct a full-cycle constant power-constant voltage experiment to obtain charge / discharge timing data at different power rates; 3) Based on the open-circuit voltage-state-of-charge characteristic curve described in step 1) and the charge / discharge timing data described in step 2), calculate the unidirectional energy efficiency for charging and discharging respectively; 4) Based on the unidirectional energy efficiency obtained in step 3), calculate the correspondence between the actual power and the grid-side power to obtain the charging / discharging power-power characteristics; 5) Based on the charge / discharge timing data described in step 2), calculate the energy capacity and power capacity of the battery under a complete charge-discharge cycle; 6) Using the energy capacity obtained in step 5) as a normalization benchmark, the charge / discharge timing data in step 2) is converted into an energy state of energy (SOE) vector, thereby obtaining the energy state-energy state change increment constraint. 7) Construct a power-efficiency relationship using the unidirectional energy efficiency at different power levels in step 3), and linearize the nonlinear power-efficiency relationship by combining it with the charging / discharging power-power characteristics obtained in step 4); 8) Perform piecewise linear approximation on the energy state-energy change increment constraint obtained in step 6) to construct the charging power decay constraint under high charge state, which is approximately transformed into optimization model constraint.

2. The refined modeling method for electrochemical energy storage based on energy state according to claim 1, characterized in that, The specific steps of the open-circuit voltage test are as follows: perform a complete constant current-constant voltage cycle on each battery cell, with a charge / discharge rate of 0.05C and a cutoff current condition of 0.01C; take the average value of the measured closed-circuit voltage to obtain the open-circuit voltage-state-of-charge characteristic curve.

3. The refined modeling method for electrochemical energy storage based on energy state according to claim 2, characterized in that, The specific steps of the full-cycle constant power-constant voltage experiment are as follows: ten complete full-cycle constant power-constant voltage experiment cycles are performed on each battery cell, with the power rate ranging from 0.1P to 1P, in 0.1P increments. Each cycle starts from a fully discharged battery with an energy state of 0%, and the current and voltage during the charging and discharging process are recorded.

4. The refined modeling method for electrochemical energy storage based on energy state according to claim 3, characterized in that, The unidirectional energy efficiency is calculated as follows: a) The calculation of charging energy efficiency is based on comparing the total energy actually injected into the battery with the ideal total energy stored in the battery calculated using the open-circuit voltage-state-of-charge characteristic curve within the observed charging energy state range. b) The calculation of discharge energy efficiency is based on comparing the total energy actually extracted from the battery within the observed discharge energy state range with the ideal total energy released by the battery calculated using the open-circuit voltage-state-of-charge characteristic curve. c) Wherein, the total energy actually injected and extracted is calculated by using the trapezoidal integral method on the voltage and current data recorded in the full-cycle constant power-constant voltage experiment; d) The ideal total energy is determined by the open-circuit voltage-state-of-charge characteristic curve and the coulomb counting method, and is used as an ideal benchmark for measuring the total energy stored or released in the battery.

5. The refined modeling method for electrochemical energy storage based on energy state according to claim 4, characterized in that, The efficiency calculation is applied to the constant power portion of the full-cycle constant power-constant voltage experimental measurement log, so that the calculated unidirectional efficiency is correlated with a specific power rate; discrete power-efficiency pairs are obtained by linear interpolation to cover a continuous power range.

6. The refined modeling method for electrochemical energy storage based on energy state according to claim 5, characterized in that, The steps for obtaining the charging / discharging power-power characteristics are as follows: an equivalent internal power variable is introduced to represent the actual power charged into the battery when power is obtained from the grid, and the actual discharge power required by the battery when power is transmitted to the grid; the introduction of the equivalent internal power variable is used to replace the product term of the nonlinear power variable and efficiency variable in the discrete model.

7. The refined modeling method for electrochemical energy storage based on energy state according to claim 6, characterized in that, The charging / discharging power-power characteristics sample the correspondence between the equivalent internal power and the external power at equal intervals to obtain discrete power-power pairs for the linear optimization model.

8. The refined modeling method for electrochemical energy storage based on energy state according to claim 7, characterized in that, The energy capacity is calculated as follows: based on the power vector recorded in half a cycle of the full-cycle constant power-constant voltage experiment, the unidirectional charge / discharge efficiency is corrected point by point, and then integrated over time to obtain the energy stored in the battery during charging and the energy extracted from the battery during discharging; the energy capacity is finally determined by averaging over K complete full-cycle constant power-constant voltage cycles.

9. The refined modeling method for electrochemical energy storage based on energy state according to claim 8, characterized in that, The steps for obtaining the energy state-energy change increment constraint are as follows: a) Calculate the energy state vector: Perform unidirectional charging efficiency correction point by point on the power vector of the 1P charging half-cycle of the complete full-cycle constant power-constant voltage experiment, perform cumulative integration, and normalize with energy capacity to obtain the energy state range from zero to 100%. b) Calculate the energy change increment vector: For each sample point, calculate the energy state change increment within a predefined scheduling time step based on the obtained energy state vector; c) Piecewise linear approximation: The nonlinear energy state-energy change increment curve is approximated by the least squares method using multiple straight lines to obtain a monotonically decreasing slope, thereby obtaining charging constraints that can be directly used for the optimization model.

10. A refined modeling system for electrochemical energy storage based on energy state, characterized in that, include: The data acquisition module performs open-circuit voltage experiments to obtain the battery's open-circuit voltage-state-of-charge characteristic curve; it also performs full-cycle constant power-constant voltage experiments to obtain charge / discharge timing data at different power rates. The efficiency calculation module calculates the unidirectional energy efficiency for charging and discharging based on the open-circuit voltage-state-of-charge characteristic curve and the charging / discharging timing data, respectively. The feature construction module calculates the correspondence between actual power and grid-side power based on the obtained unidirectional energy efficiency, and obtains the charging / discharging power-power characteristics. The capacity determination module calculates the energy capacity and power capacity of the battery under a complete charge-discharge cycle based on the charge / discharge timing data. The constraint generation module uses the obtained energy capacity as a normalization benchmark to convert the charge / discharge time-series data into an energy state of energy (SOE) vector, thereby obtaining an energy state-energy state change increment constraint. It constructs a power-efficiency relationship using unidirectional energy efficiency at different power levels and linearizes the nonlinear power-efficiency relationship by combining the obtained charge / discharge power-power characteristics. It then performs a piecewise linear approximation on the obtained energy state-energy change increment constraint to construct a charging power attenuation constraint under high charge conditions, which is then approximately transformed into an optimization model constraint.

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