Trajectory sensitivity based parameter identification method for black-box model of grid-forming energy storage

Abstract

The trajectory sensitivity-based grid-connection type energy storage black box model parameter identification method comprises the following steps: S1: based on the geometric characteristics of the virtual internal potential amplitude analytical model, identifying the virtual impedance and amplitude limiting value of the grid-connection type energy storage black box model, and dividing the amplitude limiting state of the output characteristic; S2: under the virtual internal potential amplitude limiting and power constraint conditions, according to the influence of the short-circuit ratio and the voltage drop degree on the parameter boundary, the control variable method is used to determine the parameter identification range; S3: the global trajectory sensitivity of the parameter-simulation data is analyzed in the parameter identification range, and according to the sensitivity sorting result, the particle swarm algorithm is used to step-by-step identify the control parameters of the grid-connection type energy storage black box model. The trajectory sensitivity-based grid-connection type energy storage black box model parameter identification method realizes the high-precision and high-efficiency identification of the black box model parameters under the low-voltage ride-through working condition through the virtual impedance analytical identification and the global trajectory sensitivity step-by-step optimization.

Description

Technical Field

[0001] This invention relates to the field of simulation and analysis technology for grid-type energy storage power systems, specifically to a method for parameter identification of a black-box model of grid-type energy storage based on trajectory sensitivity. Background Technology

[0002] Grid-based energy storage systems can actively construct grid voltage and frequency, and have good inertia and damping support capabilities, which is of great significance for improving the safe and stable operation of high-proportion new energy power systems. However, due to the highly complex dynamic characteristics of grid-based energy storage systems in actual operation, their internal state and accurate models are often difficult to directly observe and analyze, exhibiting typical "black box" characteristics. This directly leads to certain uncertainties in their output and response behavior, as recorded in reference [1]. Therefore, after grid-based energy storage systems are connected to the grid, the unpredictability of their charging and discharging behavior may have an adverse impact on key operating indicators such as grid frequency and voltage, bringing new challenges to the safe and stable operation of the grid.

[0003] To ensure the safe and stable operation of grid-type energy storage power systems, it is necessary to conduct rapid and accurate simulation analysis of the system. Among these, the model accuracy of the energy storage unit is particularly critical. Since energy storage systems usually involve multiple physical processes such as electrochemistry, power electronics, and thermal management, and the core control strategies of various manufacturers are often not disclosed for technical confidentiality reasons, it is difficult to obtain detailed internal mechanism models, as recorded in reference [2]. Therefore, establishing a high-precision "black box" or "gray box" equivalent model that can accurately reflect its external input-output characteristics has become an important foundation for system-level simulation analysis, and obtaining the key parameters of this equivalent model is the core prerequisite.

[0004] Currently, simplified equivalent models of grid-based energy storage are widely used in electromechanical transient simulations. These models typically simplify or aggregate the rapid control dynamics of internal converters and the detailed electrochemical processes of batteries, but must ensure the accuracy and reliability of their electrical response characteristics under critical operating conditions such as fault ride-through. Due to the large number of manufacturers of grid-based energy storage devices and significant differences in their technical approaches and control system designs, their internal control parameters and detailed models are often difficult to obtain directly from technical documentation. Therefore, parameter identification based on measured operating data has become an effective way to obtain the equivalent model parameters of grid-based energy storage systems.

[0005] However, traditional parameter identification methods have obvious limitations when facing the strong nonlinearity and multi-timescale dynamic characteristics of grid-type energy storage systems. For example, reference [3] proposes a parameter identification method for energy storage systems based on weighted least squares. This method can achieve high accuracy under steady-state small disturbance conditions, but when dealing with large disturbance scenarios such as low voltage ride-through, it fails to fully consider strong nonlinear links such as current limiting and virtual internal potential limiting, resulting in impaired physical consistency of the identified parameters and a significant increase in the deviation between the model transient response and the measured data. Reference [4] uses heuristic optimization algorithms such as genetic algorithms to perform global optimization of energy storage model parameters. Although it adapts to the nonlinear characteristics of the model to a certain extent, when the dimension of the parameters to be identified is high and the dynamic response time scale spans from millisecond-level control to second-level electromechanical processes, the algorithm converges slowly and takes a long time to calculate, and the identification efficiency is difficult to meet the needs of multi-condition online applications in actual engineering.

[0006] To address the above problems, some researchers have introduced trajectory sensitivity analysis into power system parameter identification. By quantifying the influence of each parameter on the output trajectory, key parameters are screened to reduce the complexity of the identification problem. Reference [5] identified the control parameters of the photovoltaic inverter step by step based on the trajectory sensitivity ranking of a fixed initial point, and achieved good results. However, this type of method has obvious defects when used in grid-type energy storage systems: the dynamic response of grid-type energy storage systems is closely related to the parameter values, and the trajectory sensitivity ranking results under different initial values ​​of parameters are significantly different. Especially when the parameters such as virtual impedance and virtual inertia change significantly, relying solely on the sensitivity analysis of a single fixed point cannot reliably determine the global influence of the parameters, which can easily introduce incorrect identification priorities, causing the subsequent step-by-step identification process to fall into local optima, and ultimately affecting the overall identification accuracy and reliability.

[0007] Furthermore, existing methods often rely on empirical methods or simple trial-and-error approaches to determine the parameter identification range, lacking systematic quantitative analysis of the impact of actual grid-connected conditions such as short-circuit ratio and voltage drop. This results in either an overly broad parameter search space, reducing identification efficiency, or an overly narrow space, omitting the optimal parameter set that reflects the key dynamic behavior of the system, failing to effectively balance identification accuracy and computational efficiency. Therefore, there is an urgent need to propose a parameter identification method that can fully consider the nonlinear characteristics of grid-connected energy storage systems under multiple operating conditions, and is accurate, reliable, and efficient.

[0008] References: Reference [1]: Wang Wei, Li Na. Modeling and grid connection characteristics analysis of grid-connected energy storage converter [J]. Automation of Electric Power Systems, 2022, 46(10): 123-130. Reference [2]: Zhang Qiang, Zhao Min. A review of black box parameter identification of energy storage system with consideration of confidentiality control [J]. Proceedings of the CSEE, 2021, 41(8): 2715-2728. Reference [3]: Liu Yang, Chen Liang. Parameter identification of electromechanical transient model of battery energy storage system based on least squares method [J]. Electric Power Construction, 2020, 41(12): 98-104. Reference [4]: ​​Zhou Ming, Wu Fang. Identification of control parameters of energy storage converter based on improved genetic algorithm [J]. Power System Protection and Control, 2019, 47(15): 45-52. Reference [5]: Yang Lei, He Jing. Step-by-step parameter identification of photovoltaic inverter based on trajectory sensitivity sorting [J]. Power System Technology, 2021, 45(6): 2187-2194. Summary of the Invention This invention addresses the shortcomings of traditional identification methods in terms of adaptability, low accuracy, and low computational efficiency under the strong nonlinearity and multi-timescale characteristics of grid-type energy storage systems. It provides a parameter identification method for black-box models of grid-type energy storage systems based on trajectory sensitivity. Through step-by-step optimization using virtual impedance analytical identification and global trajectory sensitivity ranking, it achieves high-precision and high-efficiency identification of black-box model parameters under low-voltage ride-through conditions.

[0009] The technical solution adopted in this invention is as follows: A parameter identification method for a black-box model of grid-type energy storage based on trajectory sensitivity includes the following steps: S1: Based on the geometric characteristics of the analytical model of virtual internal potential amplitude, identify the virtual impedance and limiting value of the grid-type energy storage black box model, and classify the limiting state of the output characteristics. S2: Under virtual internal potential limiting and power constraint conditions, the parameter identification range is determined by the control variable method based on the influence of short-circuit ratio and voltage drop on parameter boundaries; S3: Perform global trajectory sensitivity analysis on parameter-simulation data within the parameter identification range, and use particle swarm optimization algorithm to identify the control parameters of the grid-type energy storage black box model step by step according to the sensitivity ranking results.

[0010] S1 includes: S1.1: Establish a virtual internal potential amplitude expression. Determine the current limiting state and current limiting value based on whether the change in the output current amplitude in the collected output data is zero. If the current does not reach the limit, execute S1.2. The expression for the magnitude of the virtual internal potential is as follows: ; In the formula, The virtual internal potential amplitude, The output voltage amplitude, The output current amplitude, To output active power, To output reactive power, For virtual resistance, For virtual reactance; S1.2: Using any two sets of data from the output dataset, establish a hypothesis about the virtual resistance while keeping the virtual internal potential constant. and virtual reactance The equation of the circle is used to identify the virtual impedance by finding the intersection of the circular trajectory in the first quadrant. and ; S1.3: Based on the identified virtual impedance and combined with the output data under the limiting state, the virtual internal potential limiting value is calculated by substituting the output data into the virtual internal potential amplitude expression, thus completing the division of the limiting state.

[0011] In S1.2, a virtual resistance is established. and virtual reactance The equation of the circle is as follows: ; in, , , and These represent the changes in active power, reactive power, output voltage amplitude, and output current amplitude for any two sets of output data, respectively. The circular equation is derived from the equation regarding the change in virtual internal potential. Export at time, when When the circular trajectory intersects in the first quadrant, the true value of the virtual impedance is obtained. ; definition Distance from the center of the circle to the true value With the actual radius of the circle The difference is: ; ; ; pass The value of determines the virtual internal potential limiting state: Indicates no amplitude limit. This indicates a bandwidth limit.

[0012] S2 includes: S2.1: The power flow equation and virtual internal potential equation of a single-machine-infinite system under a three-phase short-circuit fault are solved by numerical point-by-point method to determine the active and reactive power operating boundaries of the grid-type energy storage black box model under the limiting condition. S2.2: Under different short-circuit ratios and voltage drop levels, the upper and lower limits of each control parameter are obtained based on power constraints, and the boundary conditions that minimize the upper limit and maximize the lower limit are extracted as typical operating conditions. S2.3: Based on typical operating conditions, adjust different parameter combinations to obtain the value envelope range of each control parameter, and take the maximum envelope range as the parameter identification range.

[0013] In S2.2, the distribution patterns of the upper and lower limits of each control parameter include the following types: The first category is where the upper limit of the control parameter increases with the increase of the short-circuit ratio and the degree of voltage drop, and the lower limit of the control parameter decreases with the increase of both. The operating conditions corresponding to the minimum upper limit and the maximum lower limit are selected as typical operating conditions. The second category is where the upper or lower limit of the control parameter changes only with the short-circuit ratio or only with the voltage drop. The operating condition with the short-circuit ratio or voltage drop that makes the upper or lower limit reach its minimum or maximum value is selected as the typical operating condition. The third category is where the upper and lower limits of the control parameters do not show a significant change with the short-circuit ratio and voltage drop. Any set of operating conditions can be selected as the typical operating conditions. The fourth category is where the upper or lower limit of the control parameters is jointly determined by the power constraint and the trajectory sensitivity. The operating condition determined by the power constraint and conforming to the above three categories of rules is selected as the typical operating condition.

[0014] In S3, the global trajectory sensitivity analysis uses the following trajectory sensitivity calculation formula: ; In the formula, For the first The first control parameter is within its identification range. Each possible value and These are the lower and upper limits of the control parameter, respectively. To select control parameters The output waveform at that time is selected based on the terminal voltage. and output current As output observation; The change in parameter value is taken as 5% of the corresponding control parameter value; This represents the change in the corresponding output waveform.

[0015] The calculated time-series trajectory sensitivity waveform is introduced The norm is used for quantization to obtain the sensitivity norm values ​​corresponding to each control parameter, where... The norm is the sum of the absolute values ​​of the time-series trajectory sensitivity waveform at each time point.

[0016] Using each control parameter in all The average of each value Norm determines sensitivity ranking, the average The norm is the norm of each control parameter at... The average value of the sensitivity range under each value; the priority of the influence of each control parameter on the terminal voltage and output current in different time intervals is obtained according to the sensitivity ranking; and the high sensitivity parameters and low sensitivity parameters are identified in stages according to the time sequence before the fault, during the fault and after the fault.

[0017] In S3, when using the particle swarm optimization algorithm for parameter optimization, the following objective function is constructed: ; In the formula, and These are the test values ​​and simulation values, respectively. This represents the test value at time i. This represents the simulated value at time i. Indicates the simulation time; This indicates the time within the error calculation interval; and These are the start and end numbers of the test data within the error calculation interval, respectively. The average error over the steady-state interval. The average error over the transient interval. This represents the maximum error in the steady-state interval. , and These represent the time periods before the fault. During the fault period and the period after the failure of value; This is the weighted average of the average error over the steady-state interval.

[0018] It also includes: substituting the identified control parameters into the electromechanical transient simulation model to obtain the simulation response curves of terminal voltage, reactive current, active power and reactive power, and comparing them with the reference test curves obtained from the hardware-in-the-loop simulation to verify the accuracy of the identification results.

[0019] This invention provides a parameter identification method for a black-box model of grid-type energy storage based on trajectory sensitivity, with the following technical advantages: 1) Addressing the technical limitations of grid-type energy storage systems, such as the inability to directly measure the virtual internal potential and the inability of traditional methods to effectively solve for virtual impedance and classify limiting states, this invention utilizes the geometric characteristics of the analytical model of virtual internal potential amplitude. When the current is below the limit, the identification problem is transformed into an analytical solution problem of the circular equation. By determining the intersection point of the circular trajectory in the first quadrant and its radius difference Δr, high-precision identification of virtual resistance Rv and virtual reactance Xv is achieved. Simultaneously, the virtual internal potential limiting state is accurately classified based on the value of Δr. This analytical method requires no iterative optimization, has high identification efficiency, and clear physical meaning.

[0020] 2) Addressing the technical shortcomings of existing methods that perform trajectory sensitivity analysis only at a single parameter initial value, result in fluctuating rankings as parameter values ​​change, and are prone to introducing incorrect priority identification, this invention performs global trajectory sensitivity analysis across all parameter values ​​within the parameter identification range. It also introduces the average L1 norm to quantify the time-series trajectory sensitivity waveform, using the average sensitivity norm of each parameter across all values ​​to determine the final sensitivity ranking. This method overcomes the randomness and bias of traditional single-point sensitivity analysis, significantly improving the stability and reliability of the sensitivity ranking results.

[0021] 3) Traditional least squares methods and other approaches are ineffective at fitting the strongly nonlinear response characteristics of grid-type energy storage systems under low-voltage ride-through conditions, which involve multiple nonlinear elements such as current limiting and virtual internal potential limiting. This invention, based on time-series sensitivity ranking results, categorizes the parameters to be identified into high-sensitivity and low-sensitivity parameters according to their impact stages before, during, and after a fault. A step-by-step identification strategy is employed for targeted parameter optimization. Simultaneously, a multi-objective optimization function is constructed, incorporating steady-state error, transient error, and their weighted average. This significantly improves the accuracy of model parameter identification under large disturbance conditions and enhances adaptability to multiple operating conditions.

[0022] 4) Addressing the technical shortcomings of existing methods that rely heavily on empirical or trial-and-error approaches to determine parameter identification ranges, potentially resulting in overly broad or narrow search spaces, this invention comprehensively considers the influence of short-circuit ratio and voltage drop on parameter boundaries. It categorizes the upper and lower limit distributions of parameters into four types and formulates typical operating condition selection rules for each. The maximum envelope interval of each parameter is extracted using the controlled variable method as the identification range. This method effectively compresses the search space while ensuring no optimal parameter sets are overlooked, thus improving the optimization efficiency of subsequent particle swarm optimization algorithms.

[0023] 5) This invention comprehensively utilizes multiple techniques, including virtual impedance analysis identification, scientific definition of parameter ranges, global trajectory sensitivity ranking, and step-by-step particle swarm optimization, to identify key control parameters of a black-box model based solely on measurable input and output electrical quantities, without requiring knowledge of the detailed control structure and parameters within the grid-type energy storage system. The simulation response curves of the terminal voltage, reactive current, active power, and reactive power after substituting the identification results into the electromechanical transient model show a high degree of fit with the measured curves, demonstrating good adaptability under various operating conditions such as fault ride-through. This solves the problem of low identification accuracy and computational efficiency that plagues traditional methods. Attached Figure Description

[0024] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a diagram showing the virtual impedance identification results in an embodiment of the present invention.

[0025] Figure 2 In this invention PQ Run the boundary graph.

[0026] Figure 3 The different in this invention SCR and U n Lower parameter boundary plot.

[0027] Figure 4 This is a diagram showing the distribution pattern of parameter boundaries in this invention.

[0028] Figure 5 This is a diagram showing the typical operating conditions of the parameters in this invention.

[0029] Figure 6(a) is a graph showing the trajectory sensitivity results of the control parameters and voltage in this invention; Figure 6(b) is a graph showing the trajectory sensitivity results of the control parameters and current in this invention.

[0030] Figure 7(a) shows the control parameters in this invention. L 1. Damp graph; Figure 7(b) shows the control parameters in this invention. L 1. Curve graph ( T u ).

[0031] Figure 8(a) is a graph showing the ranking of sensitivity in the parameter-voltage range in this invention; Figure 8(b) is a graph showing the ranking of sensitivity of the parameter-current range in this invention.

[0032] Figure 9(a) is a comparison of simulation results and test results in the embodiment of the present invention (waveform comparison under discharge conditions). Figure 9(b) is a comparison of simulation results and test results in the embodiment of the present invention (waveform comparison under charging conditions). Detailed Implementation

[0033] A parameter identification method for black-box models of grid-type energy storage based on trajectory sensitivity is proposed. This method addresses the strong nonlinearity and multi-time-scale characteristics of grid-type energy storage systems under large disturbance conditions such as low-voltage ride-through. It achieves high-precision and high-efficiency identification of control parameters for the black-box model by analytically identifying virtual impedance and limiting values, scientifically defining the parameter identification range based on short-circuit ratio and voltage drop, and utilizing global trajectory sensitivity analysis and step-by-step particle swarm optimization. Specifically, it includes the following steps: Step S1: Based on the geometric characteristics of the analytical model of virtual internal potential amplitude, identify the virtual impedance and limiting value of the grid-type energy storage black box model, and classify the limiting state of the output characteristics.

[0034] Step S1.1: Analyze the control mode of the existing electromechanical transient simulation model in the Power System Analysis and Synthesis Program (PSASP), and derive the expression for the virtual internal potential amplitude based on the system output characteristics. The model output characteristics are as follows: (1); In the formula: The virtual internal potential amplitude, The output voltage amplitude, The output current amplitude, , and These are the corresponding phase angles; Let be the virtual impedance. Therefore, the square expression for the magnitude of the virtual internal potential can be obtained as: (2); In the formula: This is the virtual impedance angle. Since both active and reactive power can be directly measured, by substituting... and Equation (2) can be simplified to: (3); In the formula: and These are the output active power and reactive power, respectively. and These are virtual resistance and virtual reactance, respectively, both set as constants greater than zero in the PSASP general model, with no dynamic adjustment capability.

[0035] Low-voltage ride-through fault tests were conducted on the above model, setting up three-phase short-circuit faults with different voltage drop levels. Multiple sets of data were obtained. , , and The output dataset constitutes : (4); Select any two sets of output data and Calculate the change and substitute it into equation (3) to obtain the equation for the change of virtual internal potential: (5); The variables of change are defined as follows: (6); When the output current changes or virtual internal potential change At that time, the output characteristics correspond to current limiting and virtual internal potential limiting, respectively. Because... It can be directly measured, using The current limiting status can be directly determined, and the current limiting value can be determined. .and It cannot be directly measured. If the data is directly substituted into equation (5), unknowns will be introduced. This results in an underdetermined equation, making it impossible to directly solve for the virtual internal potential limit value. Therefore, it is necessary to first identify the virtual impedance before proceeding to the next step. This completes the division of the amplitude-limited state.

[0036] Step S1.2: When the current has not yet reached the limit, identify the virtual impedance. (Ignore...) and In the case of simultaneous bandwidth limitation, when When the limit is not reached, equation (5) can be rewritten as: (7); This formula is in - Represent the equation of a circle on the complex plane, with the coordinates of its center being... Theoretically, by substituting all the output data into equation (7) and plotting the circular trajectory, the intersection point in the first quadrant... This is the true value of the virtual impedance. However, due to... Unpredictable, when Since the radius of the circle cannot be determined, direct drawing is not feasible.

[0037] Therefore, based on The following equation for the circle is established based on the given conditions: (8); when When the circle in equation (8) directly gives the true value, ;when At that time, none of the points on the circle are true values. Define the distance from the center of the circle to the true value. distance Let the radius be the radius of the circle corresponding to equation (7), that is: (9); The radius of the circle corresponding to the definition (8) is : (10); The difference between the two radii is denoted as From geometric relationships, we know that This holds true. Therefore, we can utilize the obtained intersection points. And calculate This allows us to determine the virtual internal potential limiting state of the data: when At that time, it is in an unlimited state; when At that time, it was in a limited amplitude state.

[0038] Step S1.3: After identifying the true value of the virtual impedance, combine it with the identified limiting state data, and then... , , , and , Substituting into equation (3), the virtual internal potential limit value can be solved. This allows for a comprehensive classification of the output characteristic limiting state.

[0039] Step S2: Under the conditions of virtual internal potential limiting and power constraint, taking into account the influence of short-circuit ratio and voltage drop on parameter boundaries, the parameter identification range is determined step by step using the control variable method.

[0040] To ensure that parameter changes have a significant impact on output characteristics, trajectory sensitivity is introduced to screen parameters to be identified and define their ranges. Considering the degree of influence of control parameters on output characteristics and the identification requirements, parameters related to state of charge, phase shifting, and DC blocking are excluded. Furthermore, primary frequency regulation and primary voltage regulation parameters are not considered in the single-unit output characteristic analysis. Finally, 15 parameters to be identified are determined, including the current limiting value. Virtual resistance Virtual Reactance Virtual internal potential limit value and proportional-integral control parameters , , , Inertial time constant Damping coefficient $Damp$, sag coefficient Delay time constant Gain time constant and minimum voltage reference value .in , , and It has already been identified in step S1, that is , , Therefore, it is only necessary to define the range and identify the parameters of the remaining 11 control parameters step by step.

[0041] Step S2.1: Solve the power flow equations and virtual internal potential equations of the single-machine-infinite loop system under a three-phase short-circuit fault using the numerical point-by-point method, and determine the following... Figure 2 The image shown is under the limiting condition. - The operational boundary on the complex plane.

[0042] Step S2.2: Under output power constraints, compare and analyze different short-circuit ratios (SCR) and voltage sags. The running boundary under ) such as Figure 3 As shown, the upper and lower limits of each control parameter are extracted. The control variable method is used to obtain the upper and lower limits of each parameter at different SCRs and... The distribution patterns of the upper and lower limits are summarized as follows: Figure 4 The four typical cases shown are: The first category, such as Figure 4 As shown in subgraph a, with Taking the upper limit as an example, its value varies with SCR and The increase is due to the increase in [something]. To improve recognition efficiency and meet the needs of multiple operating conditions, the upper limit is set to the minimum value corresponding to the SCR and [something]. The operating condition is defined as the condition where the lower limit is the maximum value. A similar pattern is also reflected in... , And the lower bound of $Damp$, and The upper limit, and and The upper and lower limits.

[0043] The second category, such as Figure 4 As shown in the b-subgraph, with Taking the lower limit as an example, its value decreases only as SCR increases, and... Irrelevant. At this point, the upper and lower limits are selected from the SCR operating conditions corresponding to their minimum and maximum values, respectively. (Any). Similar patterns are also reflected in... , and The lower limit, and and The upper limit.

[0044] The third category, such as Figure 4 As shown in the c-subgraph, with Taking the upper limit as an example, its value varies with SCR and The changes are not governed by a clear pattern, and in this case, the upper and lower limits of the parameters can be determined by any set of operating conditions. A similar pattern can be seen in the upper limit of Damp. when The time is determined by power constraints, when The timing is determined by trajectory sensitivity; exceeding the limit has no impact on output characteristics. In such cases, the operating condition determined by power constraints should be prioritized, followed by selecting typical operating conditions according to the three rules mentioned above. Similar principles apply... The lower limit and The upper and lower limits.

[0045] Based on the above rules, the boundary conditions that minimize the upper limit and maximize the lower limit are extracted as typical conditions for each parameter, and the results are as follows. Figure 5 As shown.

[0046] Step S2.3: To take into account the coupling effect between parameters, based on the typical working conditions corresponding to each parameter, different parameter combinations are adjusted to obtain the value envelope range of each parameter, and the maximum envelope is taken as the final parameter identification range. The results are shown in Table 1, which lists the identification range of 11 control parameters.

[0047]

[0048] Step S3: Perform global trajectory sensitivity analysis on the parameter-simulation data within the identification range, and use the particle swarm optimization algorithm to identify the control parameters of the grid-type energy storage black box model step by step using the sensitivity ranking results.

[0049] Step S3.1: Due to the effects of electrical parameters, system topology, and different limiting components, the trajectory sensitivity obtained based on a single fixed parameter value varies significantly. Therefore, it is necessary to perform a full-domain trajectory sensitivity analysis within the parameter value range, that is, for the first... The first control parameter Each value The trajectory sensitivity is: (11); In the formula: and The first The lower and upper limits of the values ​​for each control parameter; Take this parameter The output waveform at that time; The parameter change is taken as 5% of the corresponding parameter value; This represents the change in the corresponding output waveform.

[0050] Equation (9) requires two conditions to be met for trajectory sensitivity calculation: first, a small perturbation (5%) must be used to achieve linearization; second, the results must be distorted to avoid zero crossings in parameter values ​​and corresponding output waveforms. Given that in the power flow equations... and Depend on The square term dominates, resulting in large transient amplitudes and a higher likelihood of zero-point occurrences; therefore, the terminal voltage is selected. and output current As an output observation. In the electromechanical model Under constant conditions, and Once confirmed, and That is, uniquely determined. A global trajectory sensitivity analysis was performed on the parameter range in Table 1, and some results are shown in Figures 6(a) and 6(b). Example parameter Damp corresponds to... , correspond .

[0051] Step S3.2: Since the above results are time-series waveforms, to facilitate quantization and comparison, we introduce... The norm is used to quantize the time-series trajectory sensitivity waveforms corresponding to each parameter, obtaining the sensitivity norm values ​​corresponding to each control parameter, as shown in Figures 7(a) and 7(b). The norm is the sum of the absolute values ​​of the sensitivity waveform of the time series trajectory at each time point.

[0052] Step S3.3: To avoid The norm causes fluctuations in the sorting results due to changes in parameter values. This is addressed by using various control parameters across all [various parameters]. The average of each value The norm determines the final sensitivity ranking. The average The norm is the parameter in The average value of the sensitivity range for each value. Each control parameter in... and The average below The norm calculation results are shown in Table 2.

[0053]

[0054] Combined with the average in Table 2 The influence range of parameters obtained from norm and global trajectory sensitivity is used to determine the effect of each control parameter on... and The identification priorities within each time interval are ranked as shown in Figures 8(a) and 8(b). In Figures 8(a) and 8(b), the numbers from smallest to largest represent the degree of influence from strongest to weakest. It can be seen that... , and Damp during the fault recovery transient and The impact is significant, and Although the transient impact is small, it plays a crucial role in the steady state after the fault. Therefore, the parameters to be identified can be divided into high-sensitivity parameters and low-sensitivity parameters according to the stage of impact, and identification can be carried out step by step.

[0055] Step S3.4: Based on the above sensitivity ranking conclusions, the Particle Swarm Optimization (PSO) algorithm, which has a fast convergence speed and high computational efficiency, is selected for parameter optimization. The optimization objective is to minimize the error, and the following objective function is constructed: (12); In the formula: and These are the test values ​​and simulation values, respectively. and These are the start and end numbers of the test data within the error calculation interval, respectively. and These represent the average error and maximum error in the steady-state interval, respectively, corresponding to Figure 8(a) and Figure 8(b). , and Time period; The average error of the transient interval, corresponding to and Time period; , and These represent the periods before, during, and after the fault, respectively. value; The average error over the steady-state interval is weighted, with weights of 0.1, 0.6, and 0.3 for before, during, and after the fault, respectively. The maximum allowable deviation is shown in Table 3.

[0056]

[0057] The step-by-step identification strategy is as follows: Check whether each electrical quantity exceeds the maximum allowable deviation. If it does, for the electrical quantities with larger deviations, step-by-step identification is performed according to the fault sequence shown in Figures 8(a) and 8(b). Within each stage, high-sensitivity parameters are identified first, and the remaining parameters are fixed; after the key parameters are determined, low-sensitivity parameters are identified. Once the error of the current stage meets the requirements, the process proceeds to the next stage for optimization according to the fault sequence. This process is iterated until the stage errors of all electrical quantities are less than the maximum deviation, and the parameter set with the smallest sum of output errors is determined.

[0058] Step S3.5: Substitute the identified control parameters of the grid-type energy storage black box model into the electromechanical transient simulation model to perform simulation and obtain the terminal voltage. reactive current Active power and reactive power The simulation response curves were obtained and compared with the response curves generated from the reference dataset obtained from the hardware-in-the-loop simulation to verify the accuracy of the identification results.

[0059] An example is given below to verify the correctness and effectiveness of the method proposed in this invention.

[0060] Based on a black-box electromechanical transient model of grid-connected energy storage, test datasets under low-voltage ride-through conditions were obtained. The basic simulation parameters were set as follows: infinite grid voltage amplitude of 1 pu, initial power of 0.2 pu, and line impedance of... Simulation at the PCC bus A three-phase short-circuit fault was simulated. The total simulation time was set to 20 s, the integration step size was 0.01 s, and the short-circuit fault occurred at 4 s and lasted for 10 s. The control parameter results and relative errors identified using the method of this invention are shown in Table 4.

[0061]

[0062] The identified parameters were substituted into the electromechanical transient model, and simulations were performed under discharge and charging conditions, respectively. The results were compared with the test data. The waveforms are shown in Figure 9(a) and Figure 9(b), and the deviations of each electrical quantity are shown in Table 5 and Table 6.

[0063]

[0064]

[0065] As can be seen from the comparison of the waveforms in Tables 5 and 6 and Figures 9(a) and 9(b), the simulation results and test results have a high degree of fit, and the deviations of all electrical quantities meet the allowable error limits in Table 3. In particular, the dynamic process during fault ride-through is accurately reproduced. This indicates that the identification method proposed in this invention can effectively identify the control parameters of the grid-type energy storage black box model under low voltage ride-through conditions, solving the problems of insufficient adaptability, low accuracy, and low efficiency of traditional identification methods, and verifying its correctness and effectiveness.

Claims

1. A method for parameter identification of a black-box model of grid-type energy storage based on trajectory sensitivity, characterized in that... Includes the following steps: S1: Based on the geometric characteristics of the analytical model of virtual internal potential amplitude, identify the virtual impedance and limiting value of the grid-type energy storage black box model, and classify the limiting state of the output characteristics. S2: Under virtual internal potential limiting and power constraint conditions, the parameter identification range is determined by the control variable method based on the influence of short-circuit ratio and voltage drop on parameter boundaries; S3: Perform global trajectory sensitivity analysis on parameter-simulation data within the parameter identification range, and use particle swarm optimization algorithm to identify the control parameters of the grid-type energy storage black box model step by step according to the sensitivity ranking results.

2. The parameter identification method for a grid-type energy storage black box model based on trajectory sensitivity according to claim 1, characterized in that: S1 includes: S1.1: Establish a virtual internal potential amplitude expression. Determine the current limiting state and current limiting value based on whether the change in the output current amplitude in the collected output data is zero. If the current does not reach the limit, execute S1.

2. The expression for the magnitude of the virtual internal potential is as follows: ； In the formula, The virtual internal potential amplitude, The output voltage amplitude, The output current amplitude, To output active power, To output reactive power, For virtual resistance, For virtual reactance; S1.2: Using any two sets of data from the output dataset, establish a hypothesis about the virtual resistance while keeping the virtual internal potential constant. and virtual reactance The equation of the circle is used to identify the virtual impedance by finding the intersection of the circular trajectory in the first quadrant. and ; S1.3: Based on the identified virtual impedance and combined with the output data under the limiting state, the virtual internal potential limiting value is calculated by substituting the output data into the virtual internal potential amplitude expression, thus completing the division of the limiting state.

3. The parameter identification method for a grid-type energy storage black box model based on trajectory sensitivity according to claim 2, characterized in that: In S1.2, a virtual resistance is established. and virtual reactance The equation of the circle is as follows: ； in, , , and These represent the changes in active power, reactive power, output voltage amplitude, and output current amplitude for any two sets of output data, respectively. The circular equation is derived from the equation regarding the change in virtual internal potential. Export at time, when When the circular trajectory intersects in the first quadrant, the true value of the virtual impedance is obtained. ; definition Distance from the center of the circle to the true value With the actual radius of the circle The difference is: ； ； ； pass The value of determines the virtual internal potential limiting state: Indicates no amplitude limit. This indicates a bandwidth limit.

4. The parameter identification method for a grid-type energy storage black box model based on trajectory sensitivity according to claim 3, characterized in that: S2 includes: S2.1: The power flow equation and virtual internal potential equation of a single-machine-infinite system under a three-phase short-circuit fault are solved by numerical point-by-point method to determine the active and reactive power operating boundaries of the grid-type energy storage black box model under the limiting condition. S2.2: Under different short-circuit ratios and voltage drop levels, the upper and lower limits of each control parameter are obtained based on power constraints, and the boundary conditions that minimize the upper limit and maximize the lower limit are extracted as typical operating conditions. S2.3: Based on typical operating conditions, adjust different parameter combinations to obtain the value envelope range of each control parameter, and take the maximum envelope range as the parameter identification range.

5. The parameter identification method for a grid-type energy storage black box model based on trajectory sensitivity according to claim 4, characterized in that: In S2.2, the distribution patterns of the upper and lower limits of each control parameter include the following types: The first category is where the upper limit of the control parameter increases with the increase of the short-circuit ratio and the degree of voltage drop, and the lower limit of the control parameter decreases with the increase of both. The operating conditions corresponding to the minimum upper limit and the maximum lower limit are selected as typical operating conditions. The second category is where the upper or lower limit of the control parameter changes only with the short-circuit ratio or only with the voltage drop. The operating condition with the short-circuit ratio or voltage drop that makes the upper or lower limit reach its minimum or maximum value is selected as the typical operating condition. The third category is where the upper and lower limits of the control parameters do not show a significant change with the short-circuit ratio and voltage drop. A set of operating conditions can be selected as the typical operating conditions. The fourth category is where the upper or lower limit of the control parameters is jointly determined by the power constraint and the trajectory sensitivity. The operating condition determined by the power constraint and conforming to the above three categories of rules is selected as the typical operating condition.

6. The parameter identification method for a grid-type energy storage black box model based on trajectory sensitivity according to claim 5, characterized in that: In S3, the global trajectory sensitivity analysis uses the following trajectory sensitivity calculation formula: ； In the formula, For the first The first control parameter is within its identification range. Each possible value and These are the lower and upper limits of the control parameter, respectively. To select control parameters The output waveform at that time is selected based on the terminal voltage. and output current As output observation; For parameter changes; This represents the change in the corresponding output waveform.

7. The parameter identification method for a grid-type energy storage black box model based on trajectory sensitivity according to claim 6, characterized in that: The calculated time-series trajectory sensitivity waveform is introduced The norm is used for quantization to obtain the sensitivity norm values ​​corresponding to each control parameter, where... The norm is the sum of the absolute values ​​of the time-series trajectory sensitivity waveform at each time point.

8. The parameter identification method for a grid-type energy storage black box model based on trajectory sensitivity according to claim 7, characterized in that: Using each control parameter in all The average of each value Norm determines sensitivity ranking, the average The norm is the norm of each control parameter at... The average value of the sensitivity norm for each value; Based on the sensitivity ranking, the influence priority of each control parameter on the terminal voltage and output current in different time intervals is obtained. According to the time sequence before the fault, during the fault, and after the fault, high-sensitivity parameters and low-sensitivity parameters are identified in stages.

9. The parameter identification method for a grid-type energy storage black box model based on trajectory sensitivity according to claim 8, characterized in that: In S3, when using the particle swarm optimization algorithm for parameter optimization, the following objective function is constructed: ； In the formula, This represents the test value at time i. This represents the simulated value at time i. Indicates the simulation time; This indicates the time within the error calculation interval; and These are the start and end numbers of the test data within the error calculation interval, respectively. The average error over the steady-state interval. The average error over the transient interval. This represents the maximum error in the steady-state interval. , and These represent the time periods before the fault. During the fault period and the period after the failure of value; This is the weighted average of the average error over the steady-state interval.

10. The parameter identification method for a grid-type energy storage black box model based on trajectory sensitivity according to claim 9, characterized in that: Also includes: The identified control parameters are substituted into the electromechanical transient simulation model to obtain the simulation response curves of terminal voltage, reactive current, active power and reactive power. These curves are then compared with the reference test curves obtained from the hardware-in-the-loop simulation to verify the accuracy of the identification results.

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