Energy storage system performance model modeling method and system based on uncertain parameters

Abstract

The invention discloses an energy storage system performance model modeling method and system based on uncertain parameters, and the method comprises the steps: firstly analyzing the working principle and performance characteristics of an energy storage system, determining the performance parameters in the operation of the energy storage system, constructing an energy storage system performance model, and then recognizing and quantifying the uncertain parameters in the energy storage system performance model, the method comprises the following steps: constructing an uncertainty probability model of uncertain parameters, calculating by adopting Monte Carlo simulation to obtain an output response result of the uncertain parameters in an energy storage system performance model, and finally performing global sensitivity analysis on the uncertain parameters in the energy storage system performance model to obtain key uncertain parameters for modeling the energy storage system performance model. And the model is optimized and improved accordingly. Through an energy storage system performance model modeling technology of Monte Carlo recognition uncertain parameters, the operation characteristics of the energy storage system under different working conditions can be reflected more comprehensively, extreme conditions possibly occurring under long-time operation of the system can be reflected more accurately, and the accuracy and reliability of the energy storage system performance model are improved.

Description

Technical Field

[0001] The present invention belongs to the field of energy storage system performance modeling, and specifically relates to a method and system for energy storage system performance modeling based on uncertain parameters. Background Art

[0002] Energy storage systems are crucial in the power system of distribution networks. They effectively balance power supply and demand by releasing stored energy during high-demand periods and storing excess energy during low-demand periods, ensuring stable operation of the power grid, improving the flexibility and resilience of the power grid, and enabling the grid to respond quickly to load fluctuations and emergencies and maintain stable power output. In order to give full play to the role of energy storage systems, it is particularly important to accurately model their performance models, which not only helps to accurately predict the operating cycle and characteristics of energy storage systems under specific working conditions, but also provides strong support for the optimal configuration, operation control, and technological innovation of energy storage systems, thereby promoting the intelligent and efficient development of distribution network power systems.

[0003] At present, there are many uncertain factors in the actual operating environment of energy storage systems, such as changes in load demand, fluctuations in renewable energy generation, and performance degradation caused by equipment aging. If these uncertain factors are not fully considered and accurately modeled, the predicted results of the performance model will deviate from the actual operating conditions. Therefore, it is particularly important to incorporate uncertain parameters into the modeling process and describe these uncertainties through reasonable assumptions and probability distributions for energy storage system performance modeling.

[0004] Traditional energy storage system performance modeling methods include electromagnetic transient or electromechanical transient modeling, general modeling based on external characteristics, and modeling based on electrical quantities on the energy storage grid side. Although these traditional modeling methods have their own application scenarios, they all have obvious limitations. For example, due to the limitation of the model sampling step, the simulation speed of electromagnetic transient or electromechanical transient modeling is relatively slow, and the model's ability to simulate for a long time is poor, which is not suitable for the evaluation of long-term operating performance. The general modeling method based on external characteristics focuses more on the simulation of external characteristics, and is insufficient to describe the complex dynamic processes inside the energy storage system. The modeling method based on electrical quantities on the energy storage grid side is more dependent on the measurement data on the grid side. The accuracy and real-time nature of the data have a greater impact on the accuracy of the model. Summary of the invention

[0005] The purpose of the present invention is to provide a method and system for modeling an energy storage system performance model based on uncertain parameters in view of the above-mentioned problems existing in the prior art.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] In a first aspect, the present invention proposes a method for modeling a performance model of an energy storage system based on uncertain parameters, comprising:

[0008] S1. By analyzing the working principle and performance characteristics of the energy storage system, clarify the performance parameters of the energy storage system during operation, and build an energy storage system performance model;

[0009] S2, identify and quantify the uncertain parameters in the energy storage system performance model, and construct an uncertainty probability model of the uncertain parameters;

[0010] S3. Based on the uncertain parameters of the uncertainty probability model, the output response results of the uncertain parameters in the energy storage system performance model are obtained by Monte Carlo simulation calculation;

[0011] S4. Based on the data of the output response results of the uncertain parameters in the energy storage system performance model, a global sensitivity analysis is performed on the uncertain parameters in the energy storage system performance model, and the contribution of each uncertain parameter of the energy storage system to the output variables of the energy storage system performance model is quantified. The key uncertain parameters for modeling the energy storage system performance model are obtained, and the model is optimized and improved accordingly.

[0012] The energy storage system performance model of S1 includes:

[0013] Battery state of charge model:

[0014]

[0015] In the above formula, SOC is the state of charge, SOC0 is the initial state of charge of the battery, C nom is the nominal capacity of the battery, η is the charge and discharge efficiency, and I(τ) is the current that changes with time;

[0016] Energy storage battery model:

[0017]

[0018] In the above formula, E is the electromotive force of the battery pack, is the number of batteries in series and parallel, E0 is the initial electromotive force of the battery pack, K is the polarization voltage constant, SOC is the state of charge, Q n is the rated capacity of the battery, i (t) is the charge and discharge current of the battery, A is the voltage coefficient across the battery, B is the battery capacity coefficient, and C is the battery capacity;

[0019] Energy storage system efficiency model:

[0020] η=f(I,T,SOC);

[0021] In the above formula, η is the charge and discharge efficiency, I is the charge and discharge current, T is the battery temperature, and SOC is the state of charge.

[0022] The S2 includes:

[0023] S21. Identify the sources and nature of uncertainty in uncertain parameters, use statistical methods to quantify the range of data uncertainty, and select appropriate probability distributions for uncertain parameters based on historical data, experimental tests, or theoretical derivations;

[0024] S22. The uncertain parameters after quantification of uncertainty are expressed as random variables, and the probability distribution of the uncertain parameters is incorporated into the construction process of the uncertainty probability model, so as to construct the uncertainty probability model of the uncertain parameters, such as the battery capacity:

[0025] C=C nom ×(1+∈);

[0026] In the above formula, C is the battery capacity, C nom is the nominal capacity of the battery, ∈ is a random variable following a specific probability distribution.

[0027] The S3 includes:

[0028] S31, initialize the Monte Carlo simulation, using the uncertain parameters x1, x2, x3, ..., x in the energy storage system performance model with known uncertainty probability distribution. n They represent uncertain input variables, and their probability distribution is expressed as p(x1, x2, x3, ..., x n ); Assume that the output variable of the energy storage system performance model is Y, and the functional relationship between the input and output variables is Y=f(x1, x2, x3, ..., x n ), set the number of simulations of Monte Carlo simulation to N;

[0029] S32, using a descriptive sampling method to obtain uncertain input variables required for Monte Carlo simulation, and using a random number generator to extract uniformly distributed random numbers for each uncertain input variable;

[0030] S33, converting the extracted random numbers into sampling values ​​of each uncertain input variable, gradually increasing the number of samplings, and observing the stability of the sampling results to determine the appropriate number of samplings to form the input variable sample {x1, x2, x3, ..., x m}, construct the following output response model, and obtain the output response results of uncertain parameters in the energy storage system performance model:

[0031]

[0032] In the above formula, F is the output response result, x is used to construct the N-dimensional input variable of the output response model, and x i 、x jare the input variables of the i-th simulation and the j-th simulation respectively, a0 and b i 、c i 、c ij ,d i 、e i are the polynomial coefficients that need to be solved, and N is the number of Monte Carlo simulations.

[0033] The S4 includes:

[0034] S41. The first-order sensitivity index of each uncertainty parameter is calculated using the following formula:

[0035]

[0036] In the above formula, S i is a fixed parameter X i The first-order sensitivity index of is a fixed parameter X i When , the expected conditional variance of output Y, Var(Y) is the total variance of output Y;

[0037] The overall sensitivity index of each uncertainty parameter is calculated using the following formula:

[0038]

[0039] In the above formula, ST i is a fixed parameter X i The overall sensitivity index, is a fixed parameter X i When , the expected conditional variance of the output Y;

[0040] S42. Compare the calculated first-order sensitivity index and total sensitivity index of each uncertainty parameter with the set threshold or with each other to determine the contribution of each uncertainty parameter to the output variable of the energy storage system performance model. The uncertainty parameter with a large contribution is the key uncertain parameter that affects the performance of the energy storage system.

[0041] In a second aspect, the present invention proposes a modeling system for an energy storage system performance model based on uncertain parameters, including an energy storage system performance model building module, an uncertainty probability model building module, a Monte Carlo simulation calculation module, and a global sensitivity analysis module;

[0042] The energy storage system performance model building module is used to analyze the working principle and performance characteristics of the energy storage system, clarify the performance parameters of the energy storage system during operation, and build an energy storage system performance model;

[0043] The uncertainty probability model building module is used to identify and quantify uncertain parameters in the energy storage system performance model and build an uncertainty probability model of the uncertain parameters;

[0044] The Monte Carlo simulation calculation module is used to obtain the output response results of the uncertain parameters in the energy storage system performance model by using Monte Carlo simulation calculation based on the uncertain parameters of the uncertainty probability model;

[0045] The global sensitivity analysis module is used to perform a global sensitivity analysis on the uncertain parameters in the energy storage system performance model based on the data of the uncertain parameter output response results in the energy storage system performance model, quantify the contribution of each uncertain parameter of the energy storage system to the output variables of the energy storage system performance model, obtain the key uncertain parameters for modeling the energy storage system performance model, and optimize and improve the model accordingly.

[0046] The energy storage system performance model building module includes a battery power state model building unit, an energy storage battery model building unit, and an energy storage system efficiency model building unit;

[0047] The battery power state model construction unit is used to construct the following battery power state model:

[0048]

[0049] In the above formula, SOC is the state of charge, SOC0 is the initial state of charge of the battery, C nom is the nominal capacity of the battery, η is the charge and discharge efficiency, and I(τ) is the current that changes with time;

[0050] The energy storage battery model construction unit is used to construct the following energy storage battery model:

[0051]

[0052] In the above formula, E is the electromotive force of the battery pack, is the number of batteries in series and parallel, E0 is the initial electromotive force of the battery pack, K is the polarization voltage constant, SOC is the state of charge, Q n is the rated capacity of the battery, i (t) is the charge and discharge current of the battery, A is the voltage coefficient across the battery, B is the battery capacity coefficient, and C is the battery capacity;

[0053] The energy storage system efficiency model building unit is used to build the following energy storage system efficiency model:

[0054] η=f(I,T,SOC);

[0055] In the above formula, η is the charge and discharge efficiency, I is the charge and discharge current, T is the battery temperature, and SOC is the state of charge.

[0056] The uncertainty probability model construction module includes an uncertainty parameter quantification unit and an uncertainty probability model construction unit;

[0057] The uncertain parameter quantification unit is used to identify the source and nature of uncertainty of the uncertain parameter, use statistical methods to quantify the range of data uncertainty, and select a suitable probability distribution for the uncertain parameter based on historical data, experimental tests or theoretical derivation;

[0058] The uncertainty probability model construction unit is used to express the uncertain parameters after quantifying the uncertainty as random variables, and incorporate the probability distribution of the uncertain parameters into the construction process of the uncertainty probability model, so as to construct the uncertainty probability model of the uncertain parameters, such as the battery capacity:

[0059] C=C nom ×(1+∈);

[0060] In the above formula, C is the battery capacity, C nom is the nominal capacity of the battery, ∈ is a random variable following a specific probability distribution.

[0061] The Monte Carlo simulation calculation module includes an initialization unit, a sampling unit, and an output response model construction unit;

[0062] The initialization unit is used to initialize the Monte Carlo simulation, using the uncertain parameters x1, x2, x3, ..., x n They represent the uncertain input variables in the energy storage system performance model, and their probability distribution is expressed as p(x1, x2, x3, ..., x n ); Assume that the output variable of the energy storage system performance model is Y, and the functional relationship between the input and output variables is Y=f(x1, x2, x3, ..., x n ), set the number of simulations of Monte Carlo simulation to N;

[0063] The sampling unit is used to obtain uncertain input variables in the energy storage system performance model required for Monte Carlo simulation by using a descriptive sampling method, and use a random number generator to extract uniformly distributed random numbers for each uncertain input variable;

[0064] The output response model building unit is used to convert the extracted random numbers into the sampling values ​​of each uncertain input variable, and to determine the appropriate sampling number to form the input variable sample {x1, x2, x3, ..., x m}, construct the following output response model, and obtain the output response results of uncertain parameters in the energy storage system performance model:

[0065]

[0066] In the above formula, F is the output response result, x is used to construct the N-dimensional input variable of the output response model, and x i 、x j are the input variables of the i-th simulation and the j-th simulation respectively, a0 and b i 、c i 、c ij ,d i 、e i are the polynomial coefficients that need to be solved, and N is the number of Monte Carlo simulations.

[0067] The global sensitivity analysis module includes a sensitivity index calculation unit and a comparison and judgment unit;

[0068] The sensitivity index calculation unit is used to calculate the first-order sensitivity index and the total sensitivity index of each uncertainty parameter using the following formula:

[0069]

[0070] In the above formula, S i is a fixed parameter X i The first-order sensitivity index of is a fixed parameter X i When , the expected conditional variance of output Y, Var(Y) is the total variance of output Y;

[0071]

[0072] In the above formula, ST i is a fixed parameter X i The overall sensitivity index, is a fixed parameter X i When , the expected conditional variance of the output Y;

[0073] The comparison and judgment unit is used to compare the calculated first-order sensitivity index and total sensitivity index of each uncertainty parameter with the set threshold or with each other, to determine the contribution degree of each uncertainty parameter to the output variable of the energy storage system performance model. The uncertainty parameter with a large contribution degree is the key uncertain parameter affecting the performance of the energy storage system.

[0074] Compared with the prior art, the present invention has the following beneficial effects:

[0075] The present invention proposes a method and system for modeling a performance model of an energy storage system based on uncertain parameters. The method first analyzes the working principle and performance characteristics of the energy storage system, clarifies the performance parameters of the energy storage system in operation, and constructs a performance model of the energy storage system. Then, the uncertain parameters in the performance model of the energy storage system are identified and quantified, and an uncertainty probability model of the uncertain parameters is constructed. Based on the uncertain parameters of the constructed uncertainty probability model, Monte Carlo simulation is used to calculate the output response results of the uncertain parameters in the performance model of the energy storage system. Finally, based on the data of the output response results of the uncertain parameters in the performance model of the energy storage system, a global sensitivity analysis is performed on the uncertain parameters in the performance model of the energy storage system, and the contribution of each uncertain parameter of the energy storage system to the output variables of the performance model of the energy storage system is quantified. The key uncertain parameters for modeling the performance model of the energy storage system are obtained, and the model is optimized and improved accordingly. On the one hand, this method calculates the output response of uncertain parameters in the energy storage system performance model through Monte Carlo simulation, which can more comprehensively reflect the operating characteristics of the energy storage system under different working conditions, which is crucial to understanding and evaluating the performance of the energy storage system. The modeling technology based on Monte Carlo simulation is not directly limited to the sampling step of the model, but simulates the long-term operation process of the system through multiple random sampling. Through sufficient sample simulation, it can more accurately reflect the average performance, performance fluctuation range and possible extreme situations of the system under long-term operation, providing strong support for long-term operation performance evaluation. On the other hand, this method quantifies the contribution of each uncertain parameter to the output response through global sensitivity analysis, which helps to identify the key factors affecting system performance and improve the accuracy and reliability of the energy storage system performance model. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 The figure is an overall flow chart of the method of the present invention.

[0077] Figure 2 This is a comparison diagram of the simulation and experimental results of the state of charge SOC described in Example 1.

[0078] Figure 3 The structure diagram of the system of the present invention is shown in FIG. DETAILED DESCRIPTION

[0079] The present invention is further described in detail below in conjunction with specific implementations and drawings.

[0080] The present invention proposes a performance modeling method and system for an energy storage system based on uncertain parameters. The method analyzes the working principle and performance characteristics of the energy storage system, clarifies the performance parameters of the energy storage system in operation, constructs the performance model of the energy storage system according to the physical and chemical characteristics of the energy storage system, identifies and quantifies the uncertain parameters in the performance model of the energy storage system, and constructs an uncertainty probability model of the uncertain parameters. Then, based on the uncertain parameters of the constructed uncertainty probability model, Monte Carlo simulation is used to calculate the output response results of the uncertain parameters in the performance model of the energy storage system, analyzes the output response results of the uncertain input variables, and describes the overall distribution characteristics of the output response results in multiple Monte Carlo simulations. Finally, based on the data of the output response results of the uncertain parameters in the performance model of the energy storage system, a global sensitivity analysis is performed on the uncertain parameters in the performance model of the energy storage system, the contribution of each uncertain parameter of the energy storage system to the output variables of the performance model of the energy storage system is quantified, the key uncertain parameters for modeling the performance model of the energy storage system are obtained, and the model is optimized and improved accordingly to improve the accuracy and reliability of the performance model of the energy storage system.

[0081] Embodiment 1:

[0082] like Figure 1 As shown, a method for modeling a performance model of an energy storage system based on uncertain parameters is performed in the following steps:

[0083] 1. Analyze the working principle and performance characteristics of the energy storage system, clarify the performance parameters of the energy storage system during operation, and build a performance model of the energy storage system;

[0084] The performance parameters of the energy storage system during operation include input parameters: charge and discharge current I, battery temperature T, battery initial state of charge SOC0, etc.; output parameters, that is, variables that the model needs to predict or respond to: state of charge SOC, terminal voltage V, battery remaining available capacity C avail , charge and discharge efficiency η, etc.;

[0085] According to the physical and chemical characteristics of the energy storage system, the following energy storage system performance model is constructed:

[0086] The battery state of charge model constructed using the ampere-hour integration method is:

[0087]

[0088] In the above formula, SOC is the state of charge, SOC0 is the initial state of charge of the battery, C nom is the nominal capacity of the battery, η is the charge and discharge efficiency, and I(τ) is the current that changes with time;

[0089] The energy storage battery model is:

[0090]

[0091] In the above formula, E is the electromotive force of the battery pack, is the number of batteries in series and parallel, E0 is the initial electromotive force of the battery pack, K is the polarization voltage constant, SOC is the state of charge, Q n is the rated capacity of the battery, i (t) is the charge and discharge current of the battery, A is the voltage coefficient across the battery, B is the battery capacity coefficient, and C is the battery capacity;

[0092] The energy storage system efficiency model is:

[0093] η=(I,T,SOC);

[0094] In the above formula, η is the charge and discharge efficiency, T is the charge and discharge current, T is the battery temperature, and SOC is the state of charge;

[0095] The following constraints are introduced into the energy storage system performance model to ensure that the model can accurately reflect the operating limitations and boundary conditions of the actual system and ensure the rationality and practicality of the simulation results:

[0096] The battery status constraints are:

[0097] SOC min ≤SOC≤SOC max ;

[0098] The charge and discharge current constraints are:

[0099] I min ≤I≤I max ;

[0100] The battery temperature constraint is:

[0101] T min ≤T≤T max ;

[0102] In the above formula, SOC min , SOC max are the minimum and maximum battery power states, respectively. min ,I max are the minimum and maximum charge and discharge currents, T min , T max are the minimum and maximum battery temperatures respectively.

[0103] 2. Identify and quantify uncertain parameters in the energy storage system performance model and construct an uncertainty probability model for the uncertain parameters;

[0104] Identifying and quantifying uncertain parameters in the energy storage system performance model includes identifying the source and nature of the uncertainty of the uncertain parameters, collecting experimental data of the uncertain parameters or data from actual operation for data processing, such as cleaning outliers, converting units, interpolating missing data, etc., to ensure the quality and availability of the data, assessing the sources of uncertainty in the data, and systematically identifying all uncertainties in internal factors, external factors, data quality, and model assumptions that may cause the results to deviate from expectations; using statistical methods to quantify the range of data uncertainty, and selecting appropriate probability distributions for these uncertain parameters based on historical data, experimental tests, or theoretical derivations;

[0105] The uncertain parameters that can be identified in the energy storage system performance model include the battery nominal capacity C nom 、Internal resistance R int , battery temperature T, and the relationship curve parameters between open circuit voltage OCV and state of charge SOC, among which the battery nominal capacity C nom Affected by battery aging; internal resistance R int It is the internal resistance generated by the energy storage system during the charging and discharging process. It increases with the increase of the number of charge and discharge cycles, which will affect the energy conversion efficiency and heat generation of the energy storage system. In the energy storage system performance model, the size of the internal resistance will directly affect the calculation of the state of charge SOC and the evaluation of the charge and discharge efficiency η; the open circuit voltage OCV is the voltage measured after the battery is disconnected from the external circuit and left to stand for a period of time. It is closely related to the battery's state of charge SOC. The relationship curve between the open circuit voltage and the state of charge is affected by factors such as temperature. Its accuracy will directly affect the calculation accuracy of the SOC and the remaining available capacity C of the battery. avail predictions;

[0106] The uncertain parameters after quantification of uncertainty are expressed as random variables, and appropriate probability distributions are selected to represent these uncertain parameters. The probability distribution of uncertain parameters is incorporated into the construction process of its uncertainty probability model for simulation analysis and verification, and the uncertainty probability model of uncertain parameters is constructed, including:

[0107] Assume that the uncertain parameters follow the probability distribution rule, such as normal distribution or lognormal distribution, use the mean and standard deviation of the uncertain parameter sample to describe the distribution of the uncertain parameters, and estimate the distribution parameters by maximum likelihood estimation (MLE) or other statistical methods;

[0108] Among them, the probability density function PDF of the normal distribution is:

[0109]

[0110] In the above formula, x is the uncertain parameter sample, μ is the mean, σ 2 is the variance;

[0111] In the energy storage system performance model, battery capacity is an important uncertainty parameter. Due to slight differences in the manufacturing process, material aging, and changes in usage conditions, the actual battery capacity may deviate from its nominal value. Taking this uncertainty into account, the random variable of battery capacity is expressed as the following uncertainty probability model:

[0112] C=C nom ×(1+∈);

[0113] In the above formula, C is the battery capacity, C nom is the nominal capacity of the battery, ∈ is a random variable that follows a specific probability distribution. Assume that ∈ follows a normal distribution with a mean of 0 indicating no deviation and a standard deviation of σ ε Indicates the discrete degree of capacity change.

[0114] 3. Based on the uncertain parameters of the uncertainty probability model, the output response results of the uncertain parameters in the energy storage system performance model are obtained by Monte Carlo simulation;

[0115] Initialize the Monte Carlo simulation with the uncertain parameters x1, x2, x3, ..., x in the energy storage system performance model with known uncertainty probability distribution. n They represent uncertain input variables, and their probability distribution is expressed as p(x1, x2, x3, ..., x n ), let the output variable of the energy storage system performance model be Y, and the functional relationship between the input and output variables be Y=f(x1, x2, x3, ..., x n ), set the number of simulations of Monte Carlo simulation to N;

[0116] The descriptive sampling method is used to obtain the uncertain input variables required for Monte Carlo simulation, and a random number generator is used to extract uniformly distributed random numbers for each uncertain input variable, and the extracted random numbers are converted into sampling values ​​of each uncertain input variable. By gradually increasing the number of samplings and observing the stability of the sampling results, the appropriate number of samplings is determined to form the input variable sample {x1, x2, x3, ..., x m}, construct the following output response model to obtain the output response results of the uncertain parameters in the energy storage system performance model. The output response results reflect the behavior of the energy storage system under different input parameter combinations. These performances are the basic data required for sensitivity analysis:

[0117]

[0118] In the above formula, F is the output response result, x is used to construct the N-dimensional input variable of the output response model, and x i 、x jare the input variables of the i-th simulation and the j-th simulation respectively, a0 and b i 、c i 、c ij ,d i 、e i are the polynomial coefficients that need to be solved, and N is the number of Monte Carlo simulations;

[0119] Analyze the output response results of uncertain input variables and obtain statistical probability information of the output response results, including mean, variance, and standard deviation. These statistics can describe the overall distribution characteristics of the output response results F in multiple Monte Carlo simulations and are important indicators for evaluating the output stability and uncertainty of the energy storage system performance model.

[0120] Among them, the mean represents the average level of the output response result F, which is calculated using the following formula:

[0121]

[0122] The variance indicates the degree of deviation between the output response result F and its mean, and is calculated using the following formula:

[0123]

[0124] The standard deviation is the square root of the variance, which is used to measure the degree of dispersion of the output response result F and is calculated using the following formula:

[0125]

[0126] In the above formula, F i is the output response result obtained from the ith simulation.

[0127] 4. Based on the data of the output response results of the uncertain parameters in the energy storage system performance model, a global sensitivity analysis is conducted on the uncertain parameters in the energy storage system performance model, and the contribution of each uncertain parameter of the energy storage system to the output variables of the energy storage system performance model is quantified. The key uncertain parameters for modeling the energy storage system performance model are obtained, and the model is optimized and improved accordingly;

[0128] According to the uncertain parameters of the energy storage system and given operating conditions, such as discharge current, time step, etc., calculate the performance index of the energy storage system and its statistical probability information, including mean, variance, standard deviation, etc., wherein the performance index of the energy storage system is a quantitative representation of the output response of the energy storage system performance model;

[0129] The first-order sensitivity index of each uncertainty parameter is:

[0130]

[0131] In the above formula, Si is a fixed parameter X i The first-order sensitivity index of is a fixed parameter X i When , the expected conditional variance of output Y, Var(Y) is the total variance of output Y; the first-order sensitivity index measures the impact of a single uncertainty parameter on the output. The larger the first-order sensitivity index, the greater the impact of the parameter on the output;

[0132] The overall sensitivity index of each uncertainty parameter is:

[0133]

[0134] In the above formula, ST i is a fixed parameter X i The overall sensitivity index, is a fixed parameter X i The expected conditional variance of the output Y when ; the overall sensitivity index takes into account the parameters X i The total impact of the main effect of and its interaction effects with other parameters on the output;

[0135] The calculated first-order sensitivity index and total sensitivity index of each uncertainty parameter are compared with the set threshold or with each other to determine the contribution of each uncertainty parameter to the output response. The uncertainty parameters with large contribution are the key uncertain parameters of the energy storage system performance. For uncertainty parameters with large contribution, more detailed modeling and verification should be carried out to ensure the accurate description of their uncertainty, and the changes of these parameters should be monitored and controlled during the actual operation of the energy storage system to avoid system performance problems caused by fluctuations in these parameters. For uncertainty parameters with small contribution, although these parameters contribute less to the output response, their uncertainty should still be considered in the modeling process to optimize and improve the model to ensure the integrity and accuracy of the model.

[0136] 5. Select appropriate evaluation indicators, including root mean square error, mean absolute error, and coefficient of determination, to verify the energy storage system performance model based on Monte Carlo parameter identification and quantify the accuracy of model prediction;

[0137] The root mean square error RMSE is calculated using the following formula:

[0138]

[0139] The mean absolute error MAE is calculated using the following formula:

[0140]

[0141] The coefficient of determination R 2It is calculated using the following formula:

[0142]

[0143] In the above formula, n is the number of samples, y is i is the actual value of the i-th sample parameter, is the model prediction value of the i-th sample parameter, y - is the average of the actual values;

[0144] RMSE measures the difference between the model prediction value and the actual value. The smaller the RMSE value, the closer the model prediction value is to the actual value, that is, the higher the accuracy of the model prediction;

[0145] MAE calculates the average absolute value of the difference between the model prediction value and the actual value. The smaller the MAE value, the smaller the average error of the model prediction and the higher the prediction accuracy.

[0146] R 2 Describes the degree of fit between the model prediction value and the actual value, R 2 The range is from 0 to 1, where 1 indicates a perfect fit and 0 indicates that the model does not explain any variation in the actual values, that is, there is no correlation between the model predictions and the actual values. 2 The closer the value is to 1, the higher the prediction accuracy of the model.

[0147] In order to verify the reliability of the energy storage system performance model based on Monte Carlo parameter identification, the simulated energy storage system performance model is kept consistent with the actual experimental platform working conditions. By comparing the difference between the state of charge SOC of the simulation model and the actual operating data, the accuracy and reliability of the model are verified.

[0148] Comparison of simulation results and experimental results of state of charge SOC Figure 2 As shown: After calculation, the root mean square error between the simulated SOC result and the measured SOC result is 4. Figure 3 The changing trend of SOC in the simulation model and the experimental platform under the same working conditions is basically consistent, indicating that the actual simulation effect is good, and the energy storage system performance model based on the uncertain parameter identification of Monte Carlo simulation has high accuracy.

[0149] Embodiment 2:

[0150] like Figure 3 As shown, a modeling system for energy storage system performance model based on uncertain parameters includes an energy storage system performance model building module, an uncertainty probability model building module, a Monte Carlo simulation calculation module, and a global sensitivity analysis module;

[0151] The energy storage system performance model building module is used to analyze the working principle and performance characteristics of the energy storage system, clarify the performance parameters of the energy storage system during operation, and build an energy storage system performance model;

[0152] The uncertainty probability model building module is used to identify and quantify uncertain parameters in the energy storage system performance model and build an uncertainty probability model of the uncertain parameters;

[0153] The Monte Carlo simulation calculation module is used to obtain the output response results of the uncertain parameters in the energy storage system performance model by using Monte Carlo simulation calculation based on the uncertain parameters of the uncertainty probability model;

[0154] The global sensitivity analysis module is used to perform a global sensitivity analysis on the uncertain parameters in the energy storage system performance model based on the data of the uncertain parameter output response results in the energy storage system performance model, quantify the contribution of each uncertain parameter of the energy storage system to the output variables of the energy storage system performance model, obtain the key uncertain parameters for modeling the energy storage system performance model, and optimize and improve the model accordingly.

[0155] The energy storage system performance model building module includes a battery power state model building unit, an energy storage battery model building unit, and an energy storage system efficiency model building unit;

[0156] The battery power state model building unit is used to build the following battery power state model:

[0157]

[0158] In the above formula, SOC is the state of charge, SOC0 is the initial state of charge of the battery, C nom is the nominal capacity of the battery, η is the charge and discharge efficiency, and I(τ) is the current that changes with time;

[0159] The energy storage battery model construction unit is used to construct the following energy storage battery model:

[0160]

[0161] In the above formula, E is the electromotive force of the battery pack, is the number of batteries in series and parallel, E0 is the initial electromotive force of the battery pack, K is the polarization voltage constant, SOC is the state of charge, Q n is the rated capacity of the battery, i (t) is the charge and discharge current of the battery, A is the voltage coefficient across the battery, B is the battery capacity coefficient, and C is the battery capacity;

[0162] The energy storage system efficiency model building unit is used to build the following energy storage system efficiency model:

[0163] η=f(I,T,SOC);

[0164] In the above formula, η is the charge and discharge efficiency, I is the charge and discharge current, T is the battery temperature, and SOC is the state of charge.

[0165] The uncertainty probability model construction module includes an uncertainty parameter quantification unit and an uncertainty probability model construction unit;

[0166] The uncertain parameter quantification unit is used to identify the source and nature of uncertainty of the uncertain parameter, use statistical methods to quantify the range of data uncertainty, and select a suitable probability distribution for the uncertain parameter based on historical data, experimental tests or theoretical derivation;

[0167] The uncertainty probability model construction unit is used to express the uncertain parameters after quantifying the uncertainty as random variables, and incorporate the probability distribution of the uncertain parameters into the construction process of the uncertainty probability model, so as to construct the uncertainty probability model of the uncertain parameters, such as the battery capacity:

[0168] C=C nom ×(1+∈);

[0169] In the above formula, C is the battery capacity, C nom is the nominal capacity of the battery, ∈ is a random variable following a specific probability distribution.

[0170] The Monte Carlo simulation calculation module includes an initialization unit, a sampling unit, and an output response model construction unit;

[0171] The initialization unit is used to initialize the Monte Carlo simulation, using the uncertain parameters x1, x2, x3, ..., x1 with known uncertainty probability distribution. n They represent the uncertain input variables in the energy storage system performance model, and their probability distribution is expressed as p(x1, x2, x3, ..., x n ); Assume that the output variable of the energy storage system performance model is Y, and the functional relationship between the input and output variables is Y=f(x1, x2, x3, ..., x n ), set the number of simulations of Monte Carlo simulation to N;

[0172] The sampling unit is used to obtain uncertain input variables in the energy storage system performance model required for Monte Carlo simulation by using a descriptive sampling method, and use a random number generator to extract uniformly distributed random numbers for each uncertain input variable;

[0173] The output response model building unit is used to convert the extracted random numbers into the sampling values ​​of each uncertain input variable, and to determine the appropriate sampling number to form the input variable sample {x1, x2, x3, ..., x m}, construct the following output response model, and obtain the output response results of uncertain parameters in the energy storage system performance model:

[0174]

[0175] In the above formula, F is the output response result, x is used to construct the N-dimensional input variable of the output response model, and x i 、x j are the input variables of the i-th simulation and the j-th simulation respectively, a0 and b i 、c i 、c ij ,d i 、e i are the polynomial coefficients that need to be solved, and N is the number of Monte Carlo simulations.

[0176] The global sensitivity analysis module includes a sensitivity index calculation unit and a comparison and judgment unit;

[0177] The sensitivity index calculation unit is used to calculate the first-order sensitivity index and the total sensitivity index of each uncertainty parameter using the following formula:

[0178]

[0179] In the above formula, S i is a fixed parameter X i The first-order sensitivity index of is a fixed parameter X i When , the expected conditional variance of output Y, Var(Y) is the total variance of output Y;

[0180]

[0181] In the above formula, ST i is a fixed parameter X i The overall sensitivity index, is a fixed parameter X i When , the expected conditional variance of the output Y;

[0182] The comparison and judgment unit is used to compare the calculated first-order sensitivity index and total sensitivity index of each uncertainty parameter with the set threshold or with each other, to determine the contribution degree of each uncertainty parameter to the output variable of the energy storage system performance model. The uncertainty parameter with a large contribution degree is the key uncertain parameter affecting the performance of the energy storage system.

Claims

1. A method for modeling a performance model of an energy storage system based on uncertain parameters, characterized in that: The method comprises: S1. By analyzing the working principle and performance characteristics of the energy storage system, clarify the performance parameters of the energy storage system during operation, and build an energy storage system performance model; S2, identify and quantify the uncertain parameters in the energy storage system performance model, and construct an uncertainty probability model of the uncertain parameters; S3. Based on the uncertain parameters of the uncertainty probability model, the output response results of the uncertain parameters in the energy storage system performance model are obtained by Monte Carlo simulation calculation; S4. Based on the data of the output response results of the uncertain parameters in the energy storage system performance model, a global sensitivity analysis is performed on the uncertain parameters in the energy storage system performance model, and the contribution of each uncertain parameter of the energy storage system to the output variables of the energy storage system performance model is quantified. The key uncertain parameters for modeling the energy storage system performance model are obtained, and the model is optimized and improved accordingly.

2. The method for modeling a performance model of an energy storage system based on uncertain parameters according to claim 1, characterized in that: The energy storage system performance model of S1 includes: Battery state of charge model: In the above formula, SOC is the state of charge, SOC0 is the initial state of charge of the battery, C nom is the nominal capacity of the battery, η is the charge and discharge efficiency, and I(τ) is the current that changes with time; Energy storage battery model: In the above formula, E is the electromotive force of the battery pack, is the number of batteries in series and parallel, E0 is the initial electromotive force of the battery pack, K is the polarization voltage constant, SOC is the state of charge, Q n is the rated capacity of the battery, i (t) is the charge and discharge current of the battery, A is the voltage coefficient across the battery, B is the battery capacity coefficient, and C is the battery capacity; Energy storage system efficiency model: η=f(I,T,SOC); In the above formula, η is the charge and discharge efficiency, I is the charge and discharge current, T is the battery temperature, and SOC is the state of charge.

3. The method for modeling a performance model of an energy storage system based on uncertain parameters according to claim 1, characterized in that: The S2 includes: S21. Identify the sources and nature of uncertainty in uncertain parameters, use statistical methods to quantify the range of data uncertainty, and select appropriate probability distributions for uncertain parameters based on historical data, experimental tests, or theoretical derivations; S22. The uncertain parameters after quantification of uncertainty are expressed as random variables, and the probability distribution of the uncertain parameters is incorporated into the construction process of the uncertainty probability model, so as to construct the uncertainty probability model of the uncertain parameters, such as the battery capacity: C=C nom ×(1+∈); In the above formula, C is the battery capacity, C nom is the nominal capacity of the battery, ∈ is a random variable following a specific probability distribution.

4. The method for modeling a performance model of an energy storage system based on uncertain parameters according to claim 1, characterized in that: The S3 includes: S31, initialize the Monte Carlo simulation, using the uncertain parameters x1, x2, x3, ..., x in the energy storage system performance model whose uncertainty probability distribution is known. n They represent uncertain input variables, and their probability distribution is expressed as p(x1, x2, x3, ..., x n ); Assume that the output variable of the energy storage system performance model is Y, and the functional relationship between the input and output variables is Y=f(x1, x2, x3, ..., x n ), set the number of simulations of Monte Carlo simulation to N; S32, using a descriptive sampling method to obtain uncertain input variables required for Monte Carlo simulation, and using a random number generator to extract uniformly distributed random numbers for each uncertain input variable; S33, converting the extracted random numbers into sampling values ​​of each uncertain input variable, gradually increasing the number of samplings, and observing the stability of the sampling results to determine the appropriate number of samplings to form the input variable sample {x1, x2, x3, ..., x m }, construct the following output response model, and obtain the output response results of uncertain parameters in the energy storage system performance model: In the above formula, F is the output response result, x is used to construct the N-dimensional input variable of the output response model, and x i 、x j are the input variables of the i-th simulation and the j-th simulation respectively, a0 and b i 、c i 、c ij d i 、e i are the polynomial coefficients that need to be solved, and N is the number of Monte Carlo simulations.

5. The method for modeling a performance model of an energy storage system based on uncertain parameters according to claim 1, characterized in that: The S4 includes: S41. The first-order sensitivity index of each uncertainty parameter is calculated using the following formula: In the above formula, S i is a fixed parameter X i The first-order sensitivity index of is a fixed parameter X i When , the expected conditional variance of output Y, Var(Y) is the total variance of output Y; The overall sensitivity index of each uncertainty parameter is calculated using the following formula: In the above formula, ST i is a fixed parameter X i The overall sensitivity index, is a fixed parameter X i When , the expected conditional variance of the output Y; S42. Compare the calculated first-order sensitivity index and total sensitivity index of each uncertainty parameter with the set threshold or with each other to determine the contribution of each uncertainty parameter to the output variable of the energy storage system performance model. The uncertainty parameter with a large contribution is the key uncertain parameter that affects the performance of the energy storage system.

6. A performance modeling system for an energy storage system based on uncertain parameters, characterized in that: The system includes an energy storage system performance model building module, an uncertainty probability model building module, a Monte Carlo simulation calculation module, and a global sensitivity analysis module; The energy storage system performance model building module is used to analyze the working principle and performance characteristics of the energy storage system, clarify the performance parameters of the energy storage system during operation, and build an energy storage system performance model; The uncertainty probability model building module is used to identify and quantify uncertain parameters in the energy storage system performance model and build an uncertainty probability model of the uncertain parameters; The Monte Carlo simulation calculation module is used to obtain the output response results of the uncertain parameters in the energy storage system performance model by using Monte Carlo simulation calculation based on the uncertain parameters of the uncertainty probability model; The global sensitivity analysis module is used to perform a global sensitivity analysis on the uncertain parameters in the energy storage system performance model based on the data of the uncertain parameter output response results in the energy storage system performance model, quantify the contribution of each uncertain parameter of the energy storage system to the output variables of the energy storage system performance model, obtain the key uncertain parameters for modeling the energy storage system performance model, and optimize and improve the model accordingly.

7. The energy storage system performance modeling system based on uncertain parameters according to claim 6, characterized in that: The energy storage system performance model building module includes a battery power state model building unit, an energy storage battery model building unit, and an energy storage system efficiency model building unit; The battery power state model building unit is used to build the following battery power state model: In the above formula, SOC is the state of charge, SOC0 is the initial state of charge of the battery, C nom is the nominal capacity of the battery, η is the charge and discharge efficiency, and I(τ) is the current that changes with time; The energy storage battery model construction unit is used to construct the following energy storage battery model: In the above formula, E is the electromotive force of the battery pack, is the number of batteries in series and parallel, E0 is the initial electromotive force of the battery pack, K is the polarization voltage constant, SOC is the state of charge, Q n is the rated capacity of the battery, i (t) is the charge and discharge current of the battery, A is the voltage coefficient across the battery, B is the battery capacity coefficient, and C is the battery capacity; The energy storage system efficiency model building unit is used to build the following energy storage system efficiency model: η=f(I,T,SOC); In the above formula, η is the charge and discharge efficiency, I is the charge and discharge current, T is the battery temperature, and SOC is the state of charge.

8. The energy storage system performance modeling system based on uncertain parameters according to claim 6, characterized in that: The uncertainty probability model construction module includes an uncertainty parameter quantification unit and an uncertainty probability model construction unit; The uncertain parameter quantification unit is used to identify the source and nature of uncertainty of the uncertain parameter, use statistical methods to quantify the range of data uncertainty, and select a suitable probability distribution for the uncertain parameter based on historical data, experimental tests or theoretical derivation; The uncertainty probability model construction unit is used to express the uncertain parameters after quantifying the uncertainty as random variables, and incorporate the probability distribution of the uncertain parameters into the construction process of the uncertainty probability model, so as to construct the uncertainty probability model of the uncertain parameters, such as the battery capacity: C=C nom ×(1+∈); In the above formula, C is the battery capacity, C nom is the nominal capacity of the battery, ∈ is a random variable following a specific probability distribution.

9. The energy storage system performance modeling system based on uncertain parameters according to claim 6, characterized in that: The Monte Carlo simulation calculation module includes an initialization unit, a sampling unit, and an output response model construction unit; The initialization unit is used to initialize the Monte Carlo simulation, using the uncertain parameters x1, x2, x3, ..., x1 whose uncertainty probability distribution is known. n They represent the uncertain input variables in the energy storage system performance model, and their probability distribution is expressed as p(x1, x2, x3, ..., x n ); Assume that the output variable of the energy storage system performance model is Y, and the functional relationship between the input and output variables is Y=f(x1, x2, x3, ..., x n ), set the number of simulations of Monte Carlo simulation to N; The sampling unit is used to obtain uncertain input variables in the energy storage system performance model required for Monte Carlo simulation by using a descriptive sampling method, and use a random number generator to extract uniformly distributed random numbers for each uncertain input variable; The output response model building unit is used to convert the extracted random numbers into the sampling values ​​of each uncertain input variable, and to determine the appropriate sampling number to form the input variable sample {x1, x2, x3, ..., x m }, construct the following output response model, and obtain the output response results of uncertain parameters in the energy storage system performance model: In the above formula, F is the output response result, x is used to construct the N-dimensional input variable of the output response model, and x i 、x j are the input variables of the i-th simulation and the j-th simulation respectively, a0 and b i 、c i 、c ij d i 、e i are the polynomial coefficients that need to be solved, and N is the number of Monte Carlo simulations.

10. The energy storage system performance modeling system based on uncertain parameters according to claim 6, characterized in that: The global sensitivity analysis module includes a sensitivity index calculation unit and a comparison and judgment unit; The sensitivity index calculation unit is used to calculate the first-order sensitivity index and the total sensitivity index of each uncertainty parameter using the following formula: In the above formula, S i is a fixed parameter X i The first-order sensitivity index of is a fixed parameter X i When , the expected conditional variance of output Y, Var(Y) is the total variance of output Y; In the above formula, ST i is a fixed parameter X i The overall sensitivity index, is a fixed parameter X i When , the expected conditional variance of the output Y; The comparison and judgment unit is used to compare the calculated first-order sensitivity index and total sensitivity index of each uncertainty parameter with the set threshold or with each other, to determine the contribution degree of each uncertainty parameter to the output variable of the energy storage system performance model. The uncertainty parameter with a large contribution degree is the key uncertain parameter affecting the performance of the energy storage system.

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