Quantitative analysis method for frequency response of new power system secondary frequency modulation stage and storage medium

Abstract

The application discloses a novel power system secondary frequency modulation stage frequency response quantitative analysis method and a storage medium, and the method comprises the following steps: acquiring frequency-active transfer functions of synchronous machines, network-constructing type converters and network-following type converters respectively, and constructing full-order transfer functions; constructing equivalent transfer functions by respectively reducing and approximating the frequency-active transfer functions of each device; applying power disturbance to the full-order transfer functions, performing time domain simulation, acquiring the lowest point time of the frequency deviation curve, determining the demarcation time according to the frequency lowest point time, and taking the demarcation time as a boundary to divide the frequency dynamic process after the disturbance into a transient period and a recovery period; outputting the unified structure parameters of the transient period and the unified structure parameters of the recovery period by iteratively adjusting inertia parameters, damping parameters and frequency modulation coefficient parameters in the equivalent transfer functions; and calculating the frequency lowest point based on the unified structure parameters of the transient period, and calculating the frequency recovery time corresponding to a preset recovery degree based on the unified structure parameters of the recovery period.

Description

Technical Field

[0001] This invention relates to the field of power system analysis technology, and in particular to a novel method and storage medium for quantitative analysis of frequency response during the secondary frequency regulation stage of a power system. Background Technology

[0002] With the deepening implementation of the "dual carbon" target, new energy sources such as wind power and photovoltaics are being integrated into the power system on a large scale. The heterogeneous power grid, where synchronous generators, grid-connected converters, and grid-linked converters coexist, is gradually becoming the norm for new power systems. New energy equipment generally has the inherent characteristics of low inertia and weak frequency regulation capability, making the frequency stability problem of the power system increasingly prominent.

[0003] In system-level frequency response modeling, traditional system frequency response models can be simplified by order reduction to obtain analytical expressions for the frequency response. Existing research has further proposed unified structural models, approximating the frequency-active power transfer function of heterogeneous devices as a unified second-order structure. However, these works mainly focus on the frequency drop process after disturbances, lacking analytical characterization of the frequency recovery process dominated by Automatic Generation Control (AGC). This results in key indicators such as frequency recovery time still relying on post-event readings from full-order simulations. Regarding heterogeneous system modeling, the frequency regulation characteristics of synchronous machines, grid-connected converters, and integrated grid-connected converters differ significantly. Existing research mainly focuses on the control design of single-type devices. For heterogeneous systems where all three types of devices coexist, there is a lack of systematic research schemes that integrate the frequency-active power dynamics of all types of devices into the system-level frequency response analysis framework. Furthermore, a single frequency modulation response is completed within a few seconds, while AGC integral control takes tens of seconds or even minutes to become dominant. The time scales of the two differ by one to two orders of magnitude. It is difficult to simultaneously take into account the fitting accuracy of the transient period and the recovery period using a reduced-order model with a single set of equivalent parameters, resulting in the inability to simultaneously achieve accuracy in the minimum frequency point and the recovery time.

[0004] In summary, existing technologies do not incorporate AGC dynamics into the analytical framework, cannot directly quantify frequency recovery time, and lack the means to unify the frequency-active dynamics of the three types of heterogeneous devices with AGC into the system-level analysis framework. They also struggle to balance the fitting accuracy of both the transient and recovery stages. Summary of the Invention

[0005] This invention provides a novel method for quantitative analysis of frequency response during the secondary frequency regulation stage of a power system, comprising: obtaining the frequency-active power transfer functions of a synchronous machine, a grid-type converter, and a grid-connected converter, respectively, and constructing a full-order transfer function; The frequency-active power transfer function of each device is approximated by a reduced order, and an equivalent transfer function is constructed. A power perturbation is applied to the full-order transfer function, and a time-domain simulation is performed to obtain the time of the lowest point of the frequency deviation curve. Based on the time of the lowest frequency point, the boundary time is determined, and the frequency dynamic process after the perturbation is divided into a transient period and a recovery period by using the boundary time as the boundary. By iterating over the inertia parameter, damping parameter, and frequency modulation coefficient parameter in the equivalent transfer function, the active response error of the full-order transfer function and the equivalent transfer function during the transient and recovery periods is minimized, respectively. The iteration terminates when the preset convergence condition is met, and the unified structural parameters during the transient and recovery periods are output. The lowest frequency point is obtained by calculating the unified structural parameters during the transient period, and the frequency recovery time corresponding to the preset recovery level is obtained by calculating the unified structural parameters during the recovery period.

[0006] Optionally, the preset convergence condition is: the maximum relative change of the unified structural parameters obtained in two adjacent iterations is less than a preset convergence threshold, or the number of iterations reaches a preset upper limit.

[0007] Optionally, terminating the iteration when a preset convergence condition is met includes: The iteration terminates when the number of iterations reaches a preset upper limit. The upper limit of the number of iterations during the transient period is greater than the upper limit of the number of iterations during the recovery period.

[0008] Optionally, the step of calculating the frequency recovery time corresponding to the preset recovery level based on the unified structural parameters of the recovery period includes: Based on the unified structural parameters of the recovery period, a characteristic equation for the recovery period is constructed. By utilizing the overdamped characteristics exhibited by the system during the recovery period, the slow response root that plays a dominant role in the characteristic equation is determined. The equivalent recovery time constant is determined based on the slow response root, and the frequency recovery time is calculated based on the equivalent recovery time constant and the preset recovery degree.

[0009] Optionally, obtaining the boundary time based on the time of the lowest frequency point includes: Calculate the difference between the time of the lowest frequency point and the time when the power disturbance is applied; The product of the difference and a preset multiple is taken as the dividing moment.

[0010] Optionally, the iterative optimization adjustment of the inertia parameter, damping parameter, and frequency modulation coefficient parameter in the equivalent transfer function includes: Initialize the inertia parameters, damping parameters, and frequency modulation coefficient parameters of each device; The system-level equivalent parameters are obtained by summing the current unified structural parameters of each device, and the approximate frequency response of the system is calculated based on the system-level equivalent parameters. With the goal of minimizing the error between the approximate frequency response of the system and the frequency response output by the full-order transfer function, the uniform structural parameters of each device are adjusted until the preset convergence condition is met.

[0011] Optionally, minimizing the active response error of the full-order transfer function and the equivalent transfer function includes: The optimization objective is to minimize the integral over the time interval of the square of the difference between the active response output by the equivalent transfer function and the active response output by the full-order transfer function.

[0012] Optionally, the preset convergence threshold is one in a thousand.

[0013] Optionally, the inertia parameter, damping parameter, and frequency modulation coefficient parameter are greater than zero during the iterative optimization process.

[0014] The present invention also proposes a storage medium storing a novel frequency response quantification analysis program for the secondary frequency regulation stage of a power system. When the program is executed by a processor, the novel frequency response quantification analysis program for the secondary frequency regulation stage of a power system implements the novel frequency response quantification analysis method for the secondary frequency regulation stage of a power system. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram illustrating the steps of an embodiment of the novel power system frequency response quantification analysis method for the secondary frequency regulation stage according to the present invention; Figure 2 This is a schematic diagram illustrating the model differentiation of an embodiment of the novel power system frequency response quantification analysis method for the secondary frequency regulation stage according to the present invention. Figure 3 This is a frequency trajectory comparison diagram of an embodiment of the novel power system secondary frequency regulation stage frequency response quantitative analysis method of the present invention; Figure 4 This is a comparison diagram of the frequency trajectory between a single-group identification method and the segmented identification method of the present invention, which is an embodiment of the novel power system secondary frequency regulation stage frequency response quantitative analysis method of the present invention. Figure 5 This is a comparison of the identification errors of two methods under different penetration rates in an embodiment of the novel power system secondary frequency regulation stage frequency response quantitative analysis method of the present invention. Figure 6This is a schematic diagram illustrating the steps of an embodiment of the novel power system frequency response quantification analysis method for the secondary frequency regulation stage according to the present invention.

[0017] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0019] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0020] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0021] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature. Additionally, the technical solutions of the various embodiments can be combined with each other, but only on the basis of being achievable by those skilled in the art. When the combination of technical solutions is contradictory or impossible to implement, such a combination of technical solutions should be considered non-existent and not within the scope of protection claimed by this invention.

[0022] This invention proposes a novel method for quantitative analysis of frequency response during the secondary frequency regulation stage of a power system, comprising: Obtain the frequency-active power transfer functions of synchronous machines, grid-type converters, and grid-connected converters respectively, and construct the full-order transfer function; The frequency-active power transfer function of each device is approximated by a reduced order, and an equivalent transfer function is constructed. A power perturbation is applied to the full-order transfer function, and a time-domain simulation is performed to obtain the time of the lowest point of the frequency deviation curve. Based on the time of the lowest frequency point, the boundary time is determined, and the frequency dynamic process after the perturbation is divided into a transient period and a recovery period by using the boundary time as the boundary. By iterating over the inertia parameter, damping parameter, and frequency modulation coefficient parameter in the equivalent transfer function, the active response error of the full-order transfer function and the equivalent transfer function during the transient and recovery periods is minimized, respectively. The iteration terminates when the preset convergence condition is met, and the unified structural parameters during the transient and recovery periods are output. The lowest frequency point is obtained by calculating the unified structural parameters during the transient period, and the frequency recovery time corresponding to the preset recovery level is obtained by calculating the unified structural parameters during the recovery period.

[0023] In the first embodiment, as Figure 1 As shown, this invention proposes a novel method for quantitative analysis of frequency response during the secondary frequency regulation stage of a power system, comprising: The frequency-active power transfer functions containing AGC commands for synchronous machines, grid-type converters, and grid-connected converters in the power system are obtained respectively, and the full-order transfer function of the power system is constructed. A second-order unified structural model including inertia parameters, damping parameters, and frequency regulation coefficient parameters is adopted to perform reduced-order approximation on the frequency-active power transfer function with AGC for each of the aforementioned devices, and to construct the equivalent transfer function of the power system. A power perturbation is applied to the full-order transfer function, and a time-domain simulation is performed to obtain the time of the lowest point of the frequency deviation curve. Based on the time of the lowest frequency point, the boundary time is determined and the frequency dynamic process after the disturbance is divided into a transient period and a recovery period using the boundary time as the boundary. Using the active response output by the full-order transfer function as the target value, the inertia parameter, damping parameter, and frequency modulation coefficient parameter in the equivalent transfer function are iteratively adjusted to minimize the active response error of the full-order transfer function and the equivalent transfer function during the transient and recovery periods, respectively. The iteration is terminated when the preset convergence condition is met, and the unified structural parameters during the transient and recovery periods are output. The lowest frequency point is calculated based on the unified structural parameters of the transient period, and the frequency recovery time corresponding to the preset recovery degree is calculated based on the unified structural parameters of the recovery period.

[0024] It should be noted that this invention first obtains relevant information on synchronous machines, grid-type converters, and grid-connected converters in a novel power system and establishes a common-mode frequency response model for a multi-machine heterogeneous system with AGC. Then, it uses a second-order unified structure of inertia-damping-frequency regulation coefficient to perform a reduced-order approximation of the frequency-active power transfer function of each device with AGC. Furthermore, it divides the frequency dynamic process after disturbance into a transient period dominated by primary frequency regulation and a recovery period dominated by AGC, and independently identifies the unified structural parameters of each device in each of the two stages. Finally, based on the reduced-order parameters identified during the recovery period, it directly calculates the frequency recovery time using a closed-form formula.

[0025] In new power systems, the frequency response of each node can be considered as the superposition of common-mode and differential-mode components. The common-mode component reflects the common frequency variation trend of the overall system, while the differential-mode component reflects the frequency differences between nodes. Since this invention mainly focuses on the frequency characteristics at the global system level, the common-mode frequency is taken as the research object. Under the premise that the common-mode frequency exists, the frequency deviation of each node in the system can be considered approximately equal. At this time, the frequency response characteristics of all equipment can be directly superimposed to obtain the overall frequency response characteristics of the system. To facilitate analytical modeling, this embodiment makes the following simplifications: the variation of the voltage amplitude at the terminals of each generator unit is ignored, and only the relationship between active power and frequency is considered; the system is regarded as a linear time-invariant element, and nonlinear and time-varying factors such as governor dead zone, low-frequency load shedding action, nonlinear terms of power flow equations, and switching processes of equipment control modes are not considered; it is assumed that the mathematical models, operating parameters, and topology information of each generator unit are all known quantities. The above simplifications are conventional practices in the field of analytical frequency response modeling. Their purpose is to make the mathematical description of complex systems analytically manageable, without affecting the effectiveness of the method of this invention in engineering applications.

[0026] Based on the aforementioned common-mode frequency assumption, setting the weight of each node to 1, the overall frequency-active power transfer function of the system can be derived by summing the frequency-active power transfer functions of all devices including AGC. The transfer function is the ratio of the Laplace transform of the system output to the Laplace transform of the input under zero initial conditions. In this invention, the input is the frequency deviation, and the output is the active power increment. The overall system transfer function obtained by summing over all devices is: In the formula, The transfer function of the system including AGC is represented; N is the total number of synchronous machines, grid-type converters and grid-connected converters in the system; Let denot be the frequency-active power transfer function of the i-th device. For the power disturbance amplitude Δ P L System frequency deviation for: The AGC (Automatic Generation Control) plays a crucial role in secondary frequency regulation. When the system frequency deviates from the rated value, the AGC calculates the total regulation based on the frequency deviation and distributes it to each participating generator through a preset allocation strategy. The dynamic characteristics of the AGC are described by a proportional-integral control law. In the formula, and These represent the proportional gain and integral gain of AGC, respectively. The proportional component responds immediately to the current frequency deviation, while the integral component responds to the cumulative effect of the frequency deviation, used to eliminate steady-state error. The presence of the integral component allows AGC to continue operating over a longer timescale until the frequency deviation is completely zero. It should be noted that the above AGC model is a linearized approximation, applicable to small disturbance scenarios where the regulation dead zone is not reached, power or rate limiting is not triggered, and communication delay is negligible. When dead zones or limiting exist, the actual recovery speed of AGC will be slower than the predicted value of this model. Therefore, the frequency recovery index calculated by the method of this invention corresponds to the results under the above ideal linearization conditions and can be used as a benchmark value for engineering evaluation and a lower bound for the recovery time; for actual operating conditions with dead zones or limiting, a conservative correction can be made based on the calculation results of this method. Figure 2 As shown, a common-mode frequency response model for a multi-machine heterogeneous system with AGC is established, incorporating the frequency-active power transfer functions of synchronous machines, grid-type converters, and grid-connected converters with AGC into the common-mode frequency response framework. Furthermore, a second-order unified structure of inertia-damping-frequency modulation coefficients is used to approximate the frequency-active power transfer functions of each device with AGC, resulting in a unified structural equivalent model at both the device and system levels.

[0027] When allocating the total AGC adjustment to each device, it is necessary to consider the participation factor of each device. α i Satisfy normalization constraints: In the formula n AGC This represents the total number of units participating in AGC. The participation factor reflects the share of each unit in AGC regulation, and its value is determined by the AGC power command allocation strategy—it can be allocated according to the unit's adjustable capacity ratio, according to economic dispatch principles, or directly issued by the dispatching AGC plan. (Under uniform allocation...) α i =1 / n AGC .

[0028] Under the aforementioned unified framework, the frequency-active power transfer functions (including AGC) for the three types of typical equipment are established as follows. For the i-th synchronous machine, the AGC command and the droop control of the primary frequency regulation are used together as the input setpoint of the speed governor. After passing through the speed governor-turbine integrated transmission link, it is converted into the actual mechanical power output, and its frequency-active power transfer function including AGC is: In the formula, J SG This refers to the rotor inertia of the synchronous machine. D SG R is the damping coefficient of the synchronous machine; R is the droop coefficient. G T (s) represents the governor-turbine integrated transfer function; the droop control mentioned here refers to a local rapid adjustment mechanism in which the power generation equipment automatically and proportionally changes its output according to the grid frequency deviation. Its core characteristic is that the lower the frequency, the greater the output, and the higher the frequency, the smaller the output, and the characteristic curve has a downward sloping (drooping) shape. The rotor inertia reflects the physical inertia of the synchronous machine rotor to the frequency change, the damping coefficient reflects the damping effect of the synchronous machine on the frequency deviation, and the droop coefficient determines the slope of the primary frequency regulation droop characteristic.

[0029] For the j-th grid-type converter, there are no mechanical components such as the governor-turbine. Its primary frequency regulation damping and AGC commands are both directly adjusted by the power electronic controller to regulate the power output. The transfer function is: ; In the formula, J GFM Virtual inertia for grid-type converters; D GFM This refers to the virtual damping coefficient of a grid-connected converter. The core characteristic of a grid-connected converter lies in its ability to autonomously construct voltage and frequency references for the power grid, exhibiting voltage source characteristics externally—the virtual inertia determines its ability to suppress the rate of frequency change in the early stages of frequency variation, while the virtual damping determines its response amplitude to frequency deviation.

[0030] For the k-th grid-connected converter, the AGC command directly modifies its power reference value. Together with the primary frequency regulation path, it passes through the phase-locked loop closed-loop transmission stage, the control delay stage, and the power output stage to generate an active power response. Its transfer function is: In the formula, H PLL ( s ) is the closed-loop transfer function of the phase-locked loop, where J GFL , D GFL These are the virtual inertia and virtual damping coefficient of the grid-type converter, respectively. K P ,K I For the proportional and integral gains of the phase-locked loop PI controller; T F The first-order filtering time constant of the phase-locked loop frequency estimation stage; The system's nominal angular frequency; T D To control the delay time constant, T O This is the power output time constant.

[0031] The phase-locked loop (PLL) is the core synchronization component of a grid-connected converter. Its function is to extract phase and frequency information from the grid voltage. The dynamic characteristics of the PLL's closed-loop transfer function directly affect the frequency response performance of the grid-connected converter. The control delay reflects the inherent delay between command generation and actual power output (including pulse width modulation delay, sampling delay, and communication delay). The power output stage reflects the dynamic tracking process of power from the command value to the actual output value. In the modeling framework of this invention, the PLL is treated as a small-signal linearization. The inner current loop is not modeled separately because its response speed is much faster than the frequency dynamics of interest. Its influence, along with modulation and sampling stages, is approximated by the first-order inertia of the control delay and the first-order inertia of the power output.

[0032] Thus, the three types of devices with different physical characteristics and control mechanisms have been uniformly described as a transfer function of "frequency deviation - active power output". However, the order of the above full-order model may be high (when the system contains multiple synchronous machines with complex speed controller models, the total order of the transfer function can reach tens or even hundreds of orders), making direct analytical analysis mathematically very difficult. Therefore, this invention uses a second-order unified structural model that includes inertia parameters, damping parameters, and frequency modulation coefficient parameters to reduce the order of the above full-order model. This unified structural model has the following form: In the formula, J u,i To unify the structural inertia and characterize the device's ability to suppress the rate of frequency change in the early stages of disturbance; D u,i To unify structural damping, characterizing the equipment's ability to limit frequency drop depth, corresponding to the droop characteristics in primary frequency modulation; K u,i To unify the structure's frequency modulation coefficient, it can be correlated with AGC integral control. The rationale for this reduced-order approximation lies in the fact that although the physical structures of the three types of equipment differ, their external characteristics in frequency-active response can all be characterized by three core features: inertia, damping, and frequency modulation coefficient. Inertia determines the initial slope of the response, damping determines the steady-state deviation of the response, and the frequency modulation coefficient determines the final zero-return capability of the response.

[0033] The specific implementation of the reduced-order approximation is as follows: For each device, its active response Δ under a given input is expressed as a function of its full-order transfer function. P L Based on this, three parameters in the unified structure model are adjusted to optimize the active power response of the unified structure model. Approximate Δ as closely as possible P L The optimization objective of this approximation process can be expressed as: In Phase 1 t a = t 0, t b = t split Phase 2 t a = t split , t b = t end The integration interval is uniformly denoted as [ta, tb]. The physical meaning of the nonnegative constraint is that the inertia, damping, and frequency modulation coefficient are all nonnegative physical quantities.

[0034] This means minimizing the squared integral of the difference between the outputs of the two models within a specified time interval [ta, tb]. In this way, the higher-order transfer function of each device is replaced by a lower-order model with only three parameters.

[0035] After reducing the order of each device, summing the unified structural models of all devices yields the equivalent system-level model: Correspondingly, system-level equivalent parameters , and These are the weighted sums of the corresponding parameters for each device, namely: After obtaining the system-level second-order unified structural equivalent model, the next key issue is to determine the three parameters in this model so that they can accurately reflect the true frequency response characteristics of the system. As mentioned earlier, a single set of parameters cannot simultaneously account for the accuracy of both the transient and recovery stages. The fundamental reason is that the primary frequency modulation response is completed within a few seconds after the disturbance, while AGC integral control takes tens of seconds or even minutes to become dominant, with a time scale difference of one to two orders of magnitude. Therefore, this invention divides the frequency dynamic process after the disturbance into two stages: a transient period dominated by primary frequency modulation and a recovery period dominated by AGC, and independently identifies the unified structural parameters in each stage.

[0036] Specifically, firstly, the frequency deviation curve of the system under power disturbance is obtained through time-domain simulation. Then, the moment when the frequency deviation reaches its minimum value (i.e., the lowest frequency point) is recorded from this curve, denoted as [the point where the frequency deviation reaches its minimum value].t nadir This moment marks the turning point where the system frequency shifts from decreasing to increasing, and is also the natural boundary between the transient process and the recovery process. In determining... t nadir Then, set the dividing time: t split = t dist +λ( t nadir - t dist ),in t dist The disturbance application time is defined by λ, which is a preset boundary coefficient. The value of λ should ensure that the boundary time is later than the time when the frequency modulation transient process basically ends, thereby fully decoupling the transient period and the recovery period physically and dynamically. In one embodiment of the present invention, the boundary coefficient λ is taken as 3 to 5, and the specific value can be appropriately adjusted according to the system characteristics and simulation results. t split The entire frequency dynamic process after the disturbance is divided into two time periods, with the time of disturbance as the boundary: from the moment the disturbance occurs... t 0 to t split For the transient period, from t split By the end of the simulation t end This is the recovery period.

[0037] Subsequently, parameter identification was performed independently during the transient and recovery periods. The transient period identification used the frequency response data within that period as the fitting object, and its optimization objective was to optimize the transient response during the […]. t 0， t split Within the recovery period, the active response of the unified structure model is made to approximate the active response of the full-order model, thereby ensuring the prediction accuracy of the rate of change of frequency and the minimum frequency point. The identification of the recovery period uses the frequency response data within the recovery period as the fitting object, and its optimization objective is to […]. t split , t end The active response of the unified structure model is made to approximate the active response of the full-order model, thereby ensuring the prediction accuracy of the frequency recovery process. The identification of the two stages does not affect each other and is carried out independently. Therefore, the unified structure parameters obtained are also different—the transient parameters focus on characterizing the inertia response and the primary frequency modulation transient process, while the recovery parameters focus on characterizing the long-term frequency recovery process dominated by the AGC stage.

[0038] The identification process itself is an iterative optimization problem. Since system-level parameters are obtained by summing the parameters of each device, and the identification of each device parameter is based on the system-level frequency response, there is a mutual dependency between the system-level parameters and the device parameters. To solve this problem, this invention employs an iterative algorithm: in each iteration, the system-level parameters are first obtained by summing the unified structural parameters of each device, then the approximate system frequency response is calculated, and then the unified structural parameters of each device are updated based on this approximate frequency response. This process is repeated until convergence. The iteration terminates when a preset convergence condition is met. The convergence condition includes two cases: first, the maximum relative change of the unified structural parameters obtained in two consecutive iterations is less than a preset convergence threshold. ε tol Secondly, the number of iterations reaches the preset upper limit. N max In one embodiment of the present invention, the convergence threshold is set to 10. -3 The maximum number of iterations during the transient period is 20, and the maximum number of iterations during the recovery period is 15. In this embodiment, both the transient and recovery periods only require 4 iterations to achieve ε < 10. -3 The convergence condition indicates that the algorithm converges relatively quickly. The above values ​​can be adjusted appropriately according to the specific system size and accuracy requirements. When the convergence condition is met, the iteration terminates. For identification during the transient period, the unified structure parameters for the transient period are output; for identification during the recovery period, the unified structure parameters for the recovery period are output.

[0039] Obtaining system-level unified structural parameters during the recovery period through segmented identification Then, the closed-form formula for calculating the frequency recovery time can be derived. A closed-form formula is a calculation formula that directly obtains the result from known parameters through a finite number of algebraic operations and elementary function operations, without relying on iterative solutions or numerical simulations—this characteristic enables the present invention to quickly obtain a quantitative estimate of the frequency recovery time without running time-consuming large-scale time-domain simulations.

[0040] During the recovery period ( Within this period, the system dynamics are determined by the unified system-level structural parameters identified during the recovery phase. Decision. Faced with power disturbances. P step The characteristic equation of this second-order closed-loop system is: During the recovery period, because the transient process has sufficiently decayed, the equivalent damping effect of the system is significantly greater than the combined effect of inertia and frequency modulation coefficient, that is, let The system exhibits strongly overdamped characteristics; in this case, the above characteristic equation has two unequal negative real roots: Among them, | r 1 | | r 2∣, that isr 1 is a slow root. r 2 is a fast root.

[0041] Based on the initial conditions, the time-domain frequency response of the overdamped system during the recovery period is... It can be represented as: ,in, τ = t - t dist , t dist The timing at which the disturbance is applied.

[0042] Let the evaluation threshold for system frequency recovery be... ,(Pick Corresponding to 80% recovery (corresponding to 95% recovery) This represents the deviation at the lowest frequency point. The equation that the recovery time must satisfy can be obtained as follows: .

[0043] The above equation is a transcendental equation containing two exponential terms, and cannot be solved directly. The analytical expression of this usually requires numerical iterative methods to solve. To obtain a closed-form formula that is easy to use in engineering, note the identification results in Stage 2. Typically close to zero, the system is in a strongly overdamped state; at this time, the fast root... r The absolute value of 2 is much greater than that of the slow root. r 1. During the recovery period e r2τ Since the term has decayed to negligible levels, the above equation simplifies to a single-exponential equation, from which τ can be directly solved, thus yielding the closed-form formula for the recovery time: in: In the formula, T eff The equivalent recovery time constant reflects the time scale by which the AGC integral circuit pulls the frequency back to steady state; correspond t 80% , correspond t 95% The formula requires that stage 2 be overdamped, which is almost always true in systems containing AGC.

[0044] During the recovery period dominated by AGC, the frequency deviation decays exponentially, and the decay time constant is determined by the system's equivalent damping and equivalent frequency modulation coefficient. The larger the equivalent recovery time constant, the slower the frequency recovery; the smaller the equivalent recovery time constant, the faster the frequency recovery.

[0045] To verify the practical effect of the above method, a specific embodiment is provided below. This embodiment uses a simulation platform based on the IEEE 39-bus system built in the MATLAB / Simulink environment. The system includes 10 generating units: 6 synchronous generators, 2 grid-type converters, and 2 grid-connected converters, all with the same rated capacity. The synchronous generators use a multi-stage reheat turbine model with a droop factor R = 0.05; the grid-type converters have a virtual inertia... J GFM =8, Virtual Damping D GFM =20. The proportional gain and integral gain of the system's AGC are uniformly set to 20. , The AGC adopts a proportional allocation strategy, with the participation factor of each unit evenly distributed. The disturbance is set to apply a step active disturbance of ΔPL = 0.5 pu at t = 1 s to simulate a typical unit tripping fault scenario, with a total simulation time of 600 s.

[0046] The segmented identification algorithm proposed in this invention is used to identify parameters of the aforementioned 10-machine system. First, the time of the lowest frequency point is obtained through time-domain simulation; in this embodiment, the time of the lowest frequency point is obtained. t nadir =3.040 s, taking the boundary coefficient λ=5, the boundary time is calculated. t split =10.640 s; the first stage of identification is performed during the transient period [1,10.640] s, and converges after 4 iterations; the second stage of identification is performed during the recovery period [10.640,600] s, and converges after 4 iterations.

[0047] Figure 3 This embodiment demonstrates a comparison of frequency trajectories, in which... Figure 3 (a) is the frequency response over the entire time period, which includes three curves: full-order simulation, transient period fitting, and recovery period fitting. The 80% recovery time and 95% recovery time calculated by the closed-form formula are also marked. Figure 3 (b) is a local magnification during the transient period. From Figure 3 It can be clearly seen that the segmented splicing trajectory matches the full-order simulation well in both the transient and recovery periods, indicating that the segmented identification method proposed in this invention can maintain high fitting accuracy throughout the entire time period.

[0048] The initial frequency change rate and the minimum frequency point are calculated based on a piecewise unified structural model, and the recovery time is calculated using a closed-form formula. Compared with the full-order simulation values, the errors are as follows: initial frequency change rate error is 3.29%, minimum frequency point error is 1.45%, 80% recovery time error is 2.72%, and 95% recovery time error is 0.48%. All errors are within the acceptable accuracy range for engineering applications. This result verifies the effectiveness of the method of this invention in quantifying frequency recovery time.

[0049] To further verify the necessity of segmented identification in this invention, a single set of unified structural parameters (i.e., non-segmented identification) is introduced for comparison. Figure 4 A comparison of frequency trajectories between the single-group identification method and the segmented identification method of this invention is presented. From Figure 4 It is clear that while the single-set identification method has a certain tracking ability in the long-scale dynamics of the recovery period, it produces severe fitting distortion during the frequency drop transient period. Its lowest frequency point is only -0.1295 Hz, with an error as high as 41.40% compared to the true lowest point of -0.2209 Hz, far exceeding the acceptable range for engineering applications. This comparison powerfully illustrates that using a single set of equivalent parameters cannot simultaneously ensure the fitting accuracy of both the transient and recovery periods. The segmented identification strategy adopted in this invention effectively decouples the transient and recovery periods on the time scale, ensuring that the unified structure model has good fitting accuracy throughout the entire process.

[0050] To examine the adaptability of this invention under different new energy penetration rates, the number of grid-connected converters was kept constant at 2, and synchronous machines and grid-connected converters were replaced one-to-one, keeping the total number of units in the system constant at 10, and the proportion of grid-connected converters was gradually increased from 10% to 60%. Figure 5 A comparison of the identification errors of the two methods under different penetration rates is presented. From Figure 5 As can be seen, with the increase in the penetration rate of grid-type converters from 10% to 60%, the frequency minimum point error of the segmented method proposed in this invention remains within 2.0%, and the recovery time error is no more than 0.9% for 95% of the time. In contrast, the frequency minimum point error of the single-parameter method ranges from 13.1% to 48.6%, and the recovery time error ranges from 3.7% to 23.8%. Even under the relatively stable operating condition of a grid-type converter penetration rate of 60%, the frequency minimum point error of the single-parameter method still reaches 13.1%, far exceeding the acceptable range for engineering. The above results fully demonstrate that the segmented unified structure method proposed in this invention has good adaptability to grid configurations under different grid-type converter penetration rates and can support frequency security assessments at various stages of the evolution of new power systems.

[0051] The segmentation identification results of each device after iterative convergence in this embodiment are shown in Tables 1 and 2.

[0052]

[0053] Table 1. Uniform structural identification parameters for each device during the transient period (Phase 1)

[0054] Table 2. Unified structural identification parameters for all equipment during the recovery period (Phase 2) Table 1 presents the unified structural identification parameters and system-level total parameters for each device during the transient period. From Table 1, it can be observed that the system-level inertia parameter during the transient period is 66.39, a relatively large value, reflecting the system's strong ability to suppress the rate of frequency change during the transient period; the system-level damping parameter is 101.06, reflecting the ability to limit the frequency drop depth. Table 2 presents the unified structural identification parameters and system-level total parameters for each device during the recovery period. From Table 2, it can be observed that the system-level inertia parameter during the recovery period approaches zero (0.001), while the system-level damping parameter significantly increases to 198.75, indicating that the system exhibits strong overdamped characteristics. This is completely consistent with the overdamping assumption upon which the closed-form formula derivation for the recovery period relies, verifying the applicability premise of the closed-form formula. Comparing Tables 1 and 2, it can also be found that there are significant differences in the system-level parameters between the transient and recovery periods—the inertia parameter during the transient period is much larger than that during the recovery period, while the damping parameter during the recovery period is much larger than that during the transient period. This difference fully illustrates the essential difference in the dynamic characteristics of the two stages and also verifies the necessity of segmented identification: only by identifying them independently can the optimal parameters of each stage be obtained, thereby ensuring the accuracy and reliability of the model throughout the entire time range.

[0055] In summary, this invention incorporates the frequency-active power transfer functions (including AGC) of synchronous machines, grid-connected converters, and grid-connected converters into a unified structural model. It employs a segmented identification strategy to independently identify equivalent parameters for the primary frequency regulation transient period and the AGC recovery period, thereby achieving quantitative analysis of the frequency response characteristics during the secondary frequency regulation stage of a novel power system. Furthermore, based on the reduced-order parameters during the recovery period, this invention derives a closed-form quantitative index for the frequency recovery time using the system's strong overdamping characteristics during the recovery period. This simplifies the double-exponential response of a complex second-order system into a single-exponential form, directly obtaining the explicit expression for the recovery time through logarithmic operations. This method avoids the "curse of dimensionality" problem caused by constructing and inverting the transfer function of a full-order system, and overcomes the fitting contradiction of a single set of equivalent parameters that cannot simultaneously account for the primary frequency regulation transient and the long-scale recovery process of AGC. It can achieve analytical quantification of the frequency recovery index while significantly reducing analytical complexity, demonstrating good adaptability and engineering application value for heterogeneous systems with different renewable energy penetration rates.

[0056] In the second embodiment, the preset convergence condition is: the maximum relative change of the unified structural parameters obtained from two adjacent iterations is less than the preset convergence threshold, or the number of iterations reaches the preset upper limit.

[0057] It is important to explain that during the iterative identification process, a clear termination criterion needs to be set to ensure that the algorithm converges to an acceptable parameter estimate within a finite number of steps. As described above regarding the segmented identification algorithm, this invention uses a preset convergence condition to control the iteration process—when this condition is met, the iteration terminates and the current parameters are output. The specific setting of the convergence condition directly relates to the balance between identification accuracy and computational efficiency: overly strict conditions may lead to too many iterations and excessive computation time; overly lenient conditions may cause the iteration to terminate before the parameters have fully converged, affecting model accuracy. Therefore, this invention sets the convergence condition as the union of two optional criteria, meaning that the iteration terminates when either condition is met.

[0058] The first criterion is based on the relative magnitude of parameter changes. After each iteration, the degree of change of the system-level unified structural parameters obtained in this iteration relative to the parameters obtained in the previous iteration is calculated. Specifically, for the three components of the system-level unified structural parameters—inertia, damping, and frequency modulation coefficient—the relative change of the current iteration value relative to the previous iteration value is calculated (i.e., the absolute value of the difference divided by the absolute value of the previous iteration value), and the maximum value among the three is taken as the comprehensive change index of the current iteration step. This index reflects whether the parameter sequence has tended to stabilize—when the parameter change between two adjacent iterations is sufficiently small, it indicates that the room for improvement of the parameters in subsequent iterations is very limited, and the parameters have converged to near the optimal value. At this point, continuing the iteration is not very meaningful and can be terminated. The threshold corresponding to this criterion is a preset convergence threshold, the value of which determines the order of magnitude of the identification accuracy: the smaller the threshold, the lower the tolerance for parameter changes, and the higher the identification accuracy, but the more iterations may be required; the larger the threshold, the lower the identification accuracy, but the faster the calculation speed. In one embodiment of the present invention, the threshold is set to one-thousandth, a value that can ensure a relatively fast convergence speed within the engineering-acceptable accuracy range.

[0059] The second criterion is based on the number of iterations. If the aforementioned criterion for parameter change cannot be met due to numerical issues (e.g., slow convergence caused by improper initial values, or complex parameter space due to large system size), an upper limit on the number of iterations is set to prevent the algorithm from entering an infinite loop. When the actual number of iterations reaches this upper limit, the iteration is forcibly terminated and the current parameters are output, regardless of whether the parameter change has fallen below the threshold. This criterion ensures that the algorithm can complete within a finite number of steps under any circumstances, exhibiting good engineering robustness. In this invention, the transient period and the recovery period each have independent upper limits on the number of iterations—20 for the transient period and 15 for the recovery period. The reason for the different upper limits in the two stages is that the transient period requires simultaneously fitting multiple transient features such as the rate of change of frequency and the minimum frequency point, resulting in relatively high complexity of the parameter space, thus requiring more iterations to achieve sufficient convergence; while the dynamics of the recovery period are relatively smooth, the complexity of the parameter space is lower, and the required number of iterations is correspondingly reduced. The above upper limits can be adjusted appropriately according to the system size and accuracy requirements, and are not limited to these specific values.

[0060] The two criteria mentioned above are related by an "OR" logic. That is, the iteration terminates as long as the maximum relative change of the unified structural parameters obtained from two adjacent iterations is less than the preset convergence threshold, or the actual number of iterations reaches the preset upper limit, and the unified structural parameters of the current stage are output. The former ensures the accuracy of parameter identification, while the latter ensures the computational efficiency and engineering feasibility of the algorithm. The two complement each other and together form a complete convergence control mechanism.

[0061] In the third embodiment, as Figure 6 As shown, the calculation of the frequency recovery time corresponding to the preset recovery level based on the unified structural parameters of the recovery period includes: Based on the unified structural parameters of the recovery period, a characteristic equation for the recovery period is constructed. By utilizing the overdamped characteristics exhibited by the system during the recovery period, the slow response root that plays a dominant role in the characteristic equation is determined. The equivalent recovery time constant is determined based on the slow response root, and the frequency recovery time is calculated based on the equivalent recovery time constant and the preset recovery degree.

[0062] It should be noted that, as in the aforementioned analysis regarding the derivation of the closed-form index of frequency recovery time, the system dynamics during the recovery period are derived from the unified system-level structural parameters identified in the second stage. This is determined by the parameters. In actual frequency recovery time calculation, the characteristic equation for the recovery period needs to be constructed based on these three parameters. This characteristic equation is the key mathematical expression characterizing the dynamic behavior of the system during the recovery period. The construction method is as follows: directly substitute the unified structural parameters of the recovery period system into the closed-loop characteristic equation of the second-order system, thus obtaining a quadratic algebraic equation with the complex variable s as the unknown. All coefficients of this equation come from the identification results—the coefficients of the quadratic terms are the inertia parameters. The coefficient of the first term is the damping parameter. The constant term is the frequency modulation coefficient parameter. The specific values ​​for these parameters can be obtained after the recovery period identification is completed; no additional calculations are required.

[0063] After constructing the characteristic equation, it needs to be solved to obtain the modal information of the system response. During the recovery period, due to... It typically approaches zero (physically meaning that during the recovery process dominated by AGC, the inertia effect has largely dissipated), while The discriminant of the characteristic equation increases significantly, therefore... The system exhibits a strongly overdamped state. In this state, the characteristic equation has two unequal negative real roots, corresponding to the two exponentially decaying modes of the system response: one decays more slowly (its absolute value is smaller, called the slow response root), and the other decays more quickly (its absolute value is larger, called the fast response root). The specific values ​​of the two roots can be obtained from the root-finding formula... , , It is obtained directly. Of the two roots mentioned above, the slow response root plays a dominant role because, on the long timescale of the recovery period, the exponential term corresponding to the fast response root... e r2τ The frequency deviation has been reduced to a negligible level, and the system's frequency deviation is mainly due to the exponential term corresponding to the slow response root. e r1τ The "dominant" here refers to the fact that the slow response root determines the overall rate of decay of the frequency deviation during the recovery period—the frequency deviation approaches zero exponentially, and its decay time constant is determined by the absolute value of the slow response root.

[0064] Once the slow response root is determined, the equivalent recovery time constant can be determined accordingly. The equivalent recovery time constant is defined as the reciprocal of the absolute value of the slow response root. Its physical meaning lies in its ability to uniformly characterize the overall speed at which the AGC integral control pulls the frequency back to its rated value, comprehensively reflecting the combined effect of the system's equivalent damping and equivalent frequency modulation coefficient during the recovery period. A larger equivalent recovery time constant results in slower frequency deviation decay and a longer time required for the system to recover to the target value; conversely, a smaller equivalent recovery time constant results in faster frequency deviation decay and a shorter time required for the system to recover to the target value.

[0065] After obtaining the equivalent recovery time constant, the specific frequency recovery time can be calculated by combining it with the preset recovery level. The preset recovery level refers to the frequency deviation recovery target set by the user in advance—for example, when the frequency deviation has recovered to 80% of the initial maximum deviation, it is considered that the system has achieved 80% recovery. After determining the target recovery level, the recovery time is calculated by multiplying the equivalent recovery time constant by a coefficient corresponding to the preset recovery level. This coefficient is obtained through logarithmic operation and reflects the "time multiple" required to reach the specified recovery level. For example, when the preset recovery level is 80%, the corresponding logarithmic coefficient is ln(5); when the preset recovery level is 95%, the corresponding logarithmic coefficient is ln(20). By multiplying the equivalent recovery time constant by the corresponding logarithmic coefficient, the frequency recovery time calculated from the moment the disturbance occurred can be obtained directly. The above calculation process only involves two basic mathematical operations: multiplication and logarithm, without the need for iterative solution or numerical integration. Therefore, it has the advantages of minimal computational load and uniquely determined results. Among them, the equivalent recovery time constant needs to be calculated in advance, while the logarithmic coefficient depends on the specific value of the preset recovery level.

[0066] In the fourth embodiment, the iterative optimization adjustment of the inertia parameter, damping parameter, and frequency modulation coefficient parameter in the equivalent transfer function includes: Initialize the inertia parameters, damping parameters, and frequency modulation coefficient parameters of each device; The system-level equivalent parameters are obtained by summing the current unified structural parameters of each device, and the approximate frequency response of the system is calculated based on the system-level equivalent parameters. With the goal of minimizing the error between the approximate frequency response of the system and the frequency response output by the full-order transfer function, the uniform structural parameters of each device are adjusted until the preset convergence condition is met.

[0067] It should be explained that, as mentioned earlier, the essence of segmented identification is to independently solve a parameter optimization problem during the transient and recovery periods—to make the active response of the unified structure model approximate the active response of the full-order model. This optimization problem is solved using an iterative algorithm, and its specific execution flow is as follows.

[0068] The first step in the iteration is to determine the initial values ​​of the unified structural parameters for each device. Since optimization problems are usually non-convex, the choice of initial values ​​affects the convergence speed and the final local optimum. In this invention, the initial values ​​can be determined in two ways: First, by directly assigning a set of preset engineering experience values, such as assigning typical values ​​to inertia parameters, damping parameters, and frequency regulation coefficient parameters. This method is suitable for application scenarios lacking detailed physical parameters of the devices. Second, by obtaining the initial values ​​through a weighted sum after a rough mapping of the physical parameters of each device. For example, for a synchronous machine, the initial values ​​of the unified structural parameters can be estimated based on its rotor inertia, damping coefficient, and governor gain; for a grid-type converter, they can be directly calculated based on its virtual inertia and virtual damping control parameters; and for a grid-connected converter, they can be indirectly estimated based on the phase-locked loop bandwidth and power loop response speed. Regardless of the method used, the initial values ​​only need to provide a rough estimate with an accurate order of magnitude, and subsequent iterations will automatically correct them.

[0069] After assigning initial values, the iterative loop begins. In each iteration, the current unified structural parameters of each device are summed to obtain the system-level equivalent parameters. The physical meaning of this summation is that, under the premise of a common-mode frequency, the frequency-active response of each device is a parallel superposition. Therefore, the system-level equivalent inertia, equivalent damping, and equivalent frequency modulation coefficient are respectively the algebraic sum of the corresponding parameters of each device. Based on these system-level equivalent parameters, a system-level equivalent second-order model can be established, and then the approximate frequency response of the system after applying a power disturbance under this model can be calculated. This approximate frequency response is a low-order description of the system's true frequency response. Although it cannot completely match the full-order model in detail, its overall trend and main dynamic characteristics have been captured by the three equivalent parameters.

[0070] After obtaining the approximate frequency response of the system, it is compared with the true frequency response output by the full-order transfer function, and the error between the two is calculated. This error reflects the distance between the current unified structural parameter combination of each device and the optimal parameter combination. The larger the error, the less accurate the current parameter estimation; the smaller the error, the closer the current parameter estimation is to the true value. To reduce the error, the unified structural parameters of each device need to be adjusted according to the magnitude and direction of the error. The adjustment strategy is based on gradient-based algorithms in optimization theory: calculate the gradient information of the objective function (i.e., the error) with respect to the parameters of each device, and then update the parameters along the gradient descent direction, so that the error corresponding to the updated parameters is reduced compared to the original error. This adjustment process is performed independently for synchronous machines, grid-type converters, and mesh-type converters—each device has its own inertia parameters, damping parameters, and frequency regulation coefficient parameters, and they are updated independently without affecting each other. The reason why the parameters of different devices are adjusted independently is that they have different physical roles and dynamic characteristics in the system (synchronous machines rely on mechanical rotors to provide inertia, grid-type converters rely on algorithms to simulate inertia, and the response of grid-type converters is dynamically constrained by phase-locked loops). Their parameters also contribute to the overall frequency response of the system in different ways and to different degrees. Therefore, it is necessary to retain their independent degrees of freedom, rather than binding all devices together for unified adjustment.

[0071] The process described above—"summing → calculating the approximate response → comparing errors → adjusting the parameters of each device"—constitutes a complete iteration. Each iteration moves the parameters of each device one step closer to the optimal value, but a single iteration is usually insufficient to fully converge to the optimal solution. Therefore, the above process needs to be repeated until the preset convergence condition is met—the iteration terminates when the change in parameters obtained from two adjacent iterations is sufficiently small, or when the number of iterations reaches a preset upper limit. At this point, the uniform structural parameters of each device have stabilized near the optimal value, and this set of parameters is output as the identification result for this stage.

[0072] It is worth noting that in the above iterative process, the direction of parameter adjustment for each device is determined by the backpropagation of the system-level error under the current parameter combination to each device layer. The larger the system-level error, the larger the step size of parameter adjustment; the smaller the system-level error, the smaller the step size of parameter adjustment. This closed-loop iterative mechanism of "system-level error → device-level parameter adjustment → recalculation of system-level error" ensures that the finally identified device parameters have consistency and coordination at the system level, avoiding the problem of each device parameter acting independently and being mismatched. At the same time, since the parameters of each device are updated independently in each iteration, the final identification result can reflect the differences in frequency modulation characteristics between different devices, rather than forcibly unifying heterogeneous devices into a set of identical parameters.

[0073] In the aforementioned iterative optimization process, a quantifiable optimization objective needs to be established to guide the adjustment direction of each device parameter. The choice of optimization objective directly determines the quality of the identification results—different optimization objectives will lead to different parameter estimation results. In this invention, the optimization objective is set as: minimizing the square integral value of the error between the active response output by the equivalent transfer function and the active response output by the full-order transfer function over the time interval of interest.

[0074] The specific meaning of this optimization objective is as follows: For a given device, within a given time interval (transient period or recovery period), the active power increment output by the unified structure model is compared with the active power increment output by the full-order model at every moment, and the instantaneous difference between the two is calculated. This instantaneous difference is squared and then integrated over the entire time interval to obtain a non-negative scalar value. This value reflects the overall deviation between the unified structure model and the full-order model under the current parameter combination. The reason for squaring the instantaneous difference before integration is that squaring has two important properties: First, it avoids the cancellation of positive and negative errors—if only the difference is directly integrated, positive and negative errors may cancel each other out during integration, masking the true degree of deviation; second, squaring assigns a greater penalty weight to large errors, forcing the optimization algorithm to prioritize eliminating larger fitting deviations, thereby ensuring a more uniform fitting accuracy over the entire time interval. The integration operation accumulates the errors at all moments within the time interval into a comprehensive index, enabling the optimization objective to reflect the overall fitting quality of the entire dynamic process, rather than focusing solely on the accuracy at a few moments.

[0075] It should be noted that the active power response in the above optimization objective refers to the increment of active power output by the equipment under system frequency deviation excitation, not the transfer function itself. The transfer function describes the mathematical relationship between input and output, while the active power response is the specific output value of this relationship under a specific input. Under the same frequency deviation input, the active power response of the full-order transfer function and the active power response of the equivalent transfer function are calculated respectively. The difference between the two reflects the approximation error of the unified structure model to the real model. The optimization algorithm adjusts the three parameters in the unified structure model to continuously reduce this error square integral value until it reaches a minimum. When this integral value reaches a minimum, the unified structure model is the best second-order approximation of the full-order model in the least squares sense. The so-called "least squares sense" means that under this optimization objective, the parameter estimation results minimize the sum of squares (or square integral) of the error among all possible parameter combinations. At this time, the dynamic behavior of the unified structure model is statistically closest to the dynamic behavior of the full-order model, and it can be considered that the unified structure model has fully captured the main dynamic characteristics of the full-order model within the time interval of interest. From an information theory perspective, this is precisely the process of approximating high-dimensional dynamic characteristics with a low-dimensional parameter space. Although the number of parameters is greatly reduced (from the original high-order transfer function to only three parameters), by optimizing the constraints of the objective function, the three parameters can retain the key information of the original system on specific input-output behavior to the greatest extent, thereby maintaining the fitting accuracy to the greatest extent while reducing the model complexity.

[0076] During the iterative optimization and adjustment of the unified structural parameters of various devices, non-negativity constraints need to be applied to the values ​​of three parameters. The inertia parameter, damping parameter, and frequency modulation coefficient each have a clear physical meaning: the inertia parameter corresponds to the system's inertial response in the initial stage of frequency change; its essence is a physical quantity that resists frequency changes and cannot be negative. The damping parameter corresponds to the system's damping effect on frequency deviation; its essence is a physical quantity that consumes oscillation energy and also cannot be negative. The frequency modulation coefficient corresponds to the equivalent gain of AGC integral control; its essence is a proportional coefficient that converts the accumulated frequency deviation into power regulation, and similarly, it cannot be negative. In other words, the non-negativity of these three parameters is not an artificially set rule, but is determined by the inherent properties of the physical processes they represent—if any parameter takes a negative value, the system response will be physically unrealizable (for example, negative inertia means the system accelerates when the frequency increases, negative damping means the system deviates further when the deviation is greater, and a negative frequency modulation coefficient means the AGC reduces output when the frequency is low; all of these violate basic physical laws). Therefore, when updating parameters at each step of the iterative optimization, the parameters need to be restricted to the non-negative feasible region. Specifically, after each parameter update, it is checked whether the three parameters satisfy the non-negativity constraint. If a parameter becomes negative after the update, it is directly assigned the value of zero or a very small positive number to bring it back into the feasible region. The existence of the non-negativity constraint reduces the search space of the optimization algorithm from the entire real number domain to the non-negative quadrant. This reduces the search range and improves computational efficiency, while also ensuring the physical interpretability and engineering feasibility of the identification results—any set of identified parameters can be directly mapped to a real physical system and has a clear physical meaning.

[0077] The present invention also proposes a storage medium storing a novel frequency response quantification analysis program for the secondary frequency regulation stage of a power system. When the program is executed by a processor, the novel frequency response quantification analysis program for the secondary frequency regulation stage of a power system implements the novel frequency response quantification analysis method for the secondary frequency regulation stage of a power system.

[0078] It should be explained that the novel frequency response quantification analysis method for the secondary frequency regulation stage of a power system provided in the above embodiments of the present invention can be implemented by hardware or software related to computer program instructions. In practical engineering applications, this method is usually deployed as a computer program on the computing equipment of the power system dispatch center or operation analysis department, and the processor executes the corresponding program instructions to complete the complete analysis process from data acquisition to frequency recovery time output.

[0079] Specifically, each step involved in this method—construction of the full-order transfer function, order reduction approximation of the second-order unified structure model, time-domain simulation and reading of the lowest frequency point, determination of the boundary time and division of the dynamic process, segmented iterative identification of the transient and recovery periods, and closed-loop calculation of the frequency recovery time based on the unified structure parameters of the recovery period—can be written as corresponding program modules. These program modules can be centrally deployed on a single computing device or distributed across multiple computing devices, collaboratively completing the analysis task through data communication.

[0080] The computer program can be stored on various types of storage media. The storage media can be any medium capable of storing program code, including but not limited to: read-only memory (ROM), random access memory (RAM), disk storage, solid-state drive (SSD), optical disc (such as CD-ROM, DVD), flash drive, portable hard drive, magnetic tape, or other forms of magnetic, optical, or electrical readable storage media. These storage media can exist independently or be integrated into the computing device as a component thereof.

[0081] When the computer program stored in the storage medium is read and executed by the processor, the processor performs the following operations sequentially according to the program instructions: Obtain the frequency-active power transfer function containing AGC instructions for the synchronous machine, grid-type converter, and grid-connected converter in the power system, and construct the full-order transfer function; use a second-order unified structure model to perform a reduced-order approximation of the transfer function of each device and construct an equivalent transfer function; apply a power disturbance to the full-order transfer function and perform time-domain simulation to obtain the time of the lowest frequency point; determine the boundary time based on the time of the lowest frequency point and divide the transient period and recovery period; minimize the active power response error between the full-order transfer function and the equivalent transfer function during the transient period and recovery period, respectively; iteratively adjust the inertia parameter, damping parameter, and frequency regulation coefficient parameter in the equivalent transfer function until the preset convergence condition is met, and output the corresponding unified structure parameters; calculate the frequency recovery time corresponding to the preset recovery level based on the unified structure parameters of the recovery period and output the analysis results. The specific implementation methods of each step have been described in detail in the foregoing embodiments and will not be repeated here.

[0082] It should be noted that the steps implemented by the program stored in the aforementioned storage medium during execution can be understood by referring to the corresponding steps in the foregoing method embodiments. Since the method implemented during program execution is substantially the same as the technical solutions in the foregoing method embodiments, the technical effect it achieves is also consistent with the foregoing embodiments—that is, it can directly quantify the frequency recovery time of the secondary frequency regulation stage while performing order reduction analysis on the frequency response of heterogeneous power systems, overcoming the technical contradiction that a single set of equivalent parameters cannot simultaneously consider the fitting accuracy of both transient and recovery stages. For technical details not fully described in the storage medium embodiments, a full understanding can be obtained by referring to the relevant descriptions in the foregoing method embodiments. Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The program can be stored in a computer-readable storage medium, and when executed, it performs the steps of the above method embodiments.

[0083] The above description is merely an optional embodiment of the present invention and does not limit the patent scope of the present invention. All equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A novel method for quantitative analysis of frequency response during the secondary frequency regulation stage of a power system, characterized in that, include: Obtain the frequency-active power transfer functions of synchronous machines, grid-type converters, and grid-connected converters respectively, and construct the full-order transfer function; The frequency-active power transfer function of each device is approximated by a reduced order, and an equivalent transfer function is constructed. A power perturbation is applied to the full-order transfer function, and a time-domain simulation is performed to obtain the time of the lowest point of the frequency deviation curve. Based on the time of the lowest frequency point, the boundary time is determined, and the frequency dynamic process after the perturbation is divided into a transient period and a recovery period by using the boundary time as the boundary. By iterating over the inertia parameter, damping parameter, and frequency modulation coefficient parameter in the equivalent transfer function, the active response error of the full-order transfer function and the equivalent transfer function during the transient and recovery periods is minimized, respectively. The iteration terminates when the preset convergence condition is met, and the unified structural parameters during the transient and recovery periods are output. The lowest frequency point is obtained by calculating the unified structural parameters during the transient period, and the frequency recovery time corresponding to the preset recovery level is obtained by calculating the unified structural parameters during the recovery period.

2. The novel frequency response quantitative analysis method for the secondary frequency regulation stage of a power system as described in claim 1, characterized in that, The preset convergence condition is: the maximum relative change of the unified structural parameters obtained in two adjacent iterations is less than the preset convergence threshold, or the number of iterations reaches the preset upper limit.

3. The novel frequency response quantitative analysis method for the secondary frequency regulation stage of a power system as described in claim 2, characterized in that, The step of terminating the iteration when the preset convergence condition is met includes: The iteration terminates when the number of iterations reaches a preset upper limit. The upper limit of the number of iterations during the transient period is greater than the upper limit of the number of iterations during the recovery period.

4. The novel frequency response quantitative analysis method for the secondary frequency regulation stage of a power system as described in any one of claims 1 to 3, characterized in that, The calculation of the frequency recovery time corresponding to the preset recovery level based on the unified structural parameters of the recovery period includes: Based on the unified structural parameters of the recovery period, a characteristic equation for the recovery period is constructed. By utilizing the overdamped characteristics exhibited by the system during the recovery period, the slow response root that plays a dominant role in the characteristic equation is determined. The equivalent recovery time constant is determined based on the slow response root, and the frequency recovery time is calculated based on the equivalent recovery time constant and the preset recovery degree.

5. The novel frequency response quantitative analysis method for the secondary frequency regulation stage of a power system as described in any one of claims 1 to 3, characterized in that, The step of obtaining the boundary time based on the time of the lowest frequency point includes: Calculate the difference between the time of the lowest frequency point and the time when the power disturbance is applied; The product of the difference and a preset multiple is taken as the dividing moment.

6. The novel frequency response quantification analysis method for the secondary frequency regulation stage of a power system as described in any one of claims 1 to 3, characterized in that, The iterative optimization adjustment of the inertia parameter, damping parameter, and frequency modulation coefficient parameter in the equivalent transfer function includes: Initialize the inertia parameters, damping parameters, and frequency modulation coefficient parameters of each device; The system-level equivalent parameters are obtained by summing the current unified structural parameters of each device, and the approximate frequency response of the system is calculated based on the system-level equivalent parameters. With the goal of minimizing the error between the approximate frequency response of the system and the frequency response output by the full-order transfer function, the uniform structural parameters of each device are adjusted until the preset convergence condition is met.

7. The novel frequency response quantitative analysis method for the secondary frequency regulation stage of a power system as described in claim 6, characterized in that, Minimizing the active response error of the full-order transfer function and the equivalent transfer function includes: The optimization objective is to minimize the integral over the time interval of the square of the difference between the active response output by the equivalent transfer function and the active response output by the full-order transfer function.

8. The novel frequency response quantitative analysis method for the secondary frequency regulation stage of a power system as described in claim 2, characterized in that, The preset convergence threshold is one in a thousand.

9. The novel frequency response quantitative analysis method for the secondary frequency regulation stage of a power system as described in claim 1, characterized in that, The inertia parameter, damping parameter, and frequency modulation coefficient are all greater than zero during the iterative optimization process.

10. A storage medium, characterized in that, The storage medium stores a frequency response quantification analysis program for the secondary frequency regulation stage of a novel power system. When the program is executed by the processor, the frequency response quantification analysis program for the secondary frequency regulation stage of a novel power system implements the frequency response quantification analysis method for the secondary frequency regulation stage of a novel power system as described in any one of claims 1 to 9.

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