Inertia estimation method, system and equipment based on dynamic regression device expansion and mixing and medium

Abstract

The invention discloses an inertia estimation method, system and device based on dynamic regression device expansion and mixing and a medium, and belongs to the technical field of power system control, and the method comprises the steps: obtaining the power data and frequency data of a generator in a power system; determining a first system parameter and a second system parameter according to the power data and the frequency data; constructing a dynamic model of the first system parameter based on the second system parameter and the aggregation swing equation; according to the dynamic model, determining a regression model variable and constructing a differential regression equation, and obtaining an inertia estimation result according to the differential regression equation; the differential regression equation represents a dynamic relationship between the first system parameter and the second system parameter. The method solves the problems that the method cannot adapt to the rapid change of the system, the calculation complexity is high, and the real-time performance is poor.

Description

Technical Field

[0001] The present invention relates to the technical field of power system control, and in particular to an inertia estimation method, system, device and medium based on dynamic regressor expansion and mixing. Background Art

[0002] As the proportion of renewable energy (such as wind and solar) increases, the contribution of inertia in traditional power systems decreases, posing challenges to power system stability. In this context, accurate estimation of power system inertia becomes increasingly important, especially in the face of frequent disturbances and system load changes.

[0003] Currently, power system inertia estimation relies primarily on traditional offline analysis methods. These methods typically require extensive historical data and cannot provide timely inertia estimates during dynamic and real-time operations, making them difficult to meet the demands of modern power systems. Traditional methods are often unable to adapt to rapid system changes, have high computational complexity, and suffer from poor real-time performance. Therefore, a new real-time inertia estimation method is urgently needed. Summary of the Invention

[0004] In view of the above-mentioned problems, the present invention is proposed.

[0005] Therefore, the technical problem solved by the present invention is: how to overcome the problems of being unable to adapt to rapid changes in the system, high computational complexity, and poor real-time performance?

[0006] To solve the above technical problems, the present invention provides the following technical solution: an inertia estimation method based on dynamic regressor expansion and hybridization, which includes the following steps:

[0007] Obtain power data and frequency data of generators in the power system;

[0008] determining a first system parameter and a second system parameter according to the power data and the frequency data; the first system parameter being a main frequency of the system, and the second system parameter being used to characterize an operating state of the power system;

[0009] constructing a dynamic model of the first system parameters based on the second system parameters and the aggregated swing equation, wherein the dynamic model is used to describe the variation characteristics of the system main frequency;

[0010] According to the dynamic model, regression model variables are determined and a differential regression equation is constructed, and an inertia estimation result is obtained according to the differential regression equation; the differential regression equation characterizes the dynamic relationship between the first system parameter and the second system parameter.

[0011] As a preferred solution of the inertia estimation method based on dynamic regressor expansion and hybridization of the present invention, wherein: the obtaining of power data and frequency data of the generator in the power system includes:

[0012] Obtain the total electrical power and total mechanical power of the main frequency-controlled generator in the power system;

[0013] Frequency data of a plurality of generators are collected, and the total electrical power, the total mechanical power and the frequency data are used as system input signals.

[0014] As a preferred solution of the inertia estimation method based on dynamic regressor expansion and mixing of the present invention, wherein: determining the first system parameter and the second system parameter according to the power data and the frequency data includes:

[0015] Calculate the system main frequency based on the angular frequency and inertia constant of the power generation unit;

[0016] A system power parameter and a system operating parameter are calculated, the system main frequency is determined as the first system parameter, and the system power parameter and the system operating parameter are determined as the second system parameter.

[0017] As a preferred solution of the inertia estimation method based on dynamic regressor expansion and hybridization of the present invention, wherein: the dynamic model of the first system parameter is constructed based on the second system parameter and the aggregated swing equation, including:

[0018] Expressing the system main frequency as the center angular velocity of inertia;

[0019] Establishing a dynamic equation for the angular velocity of the center of inertia;

[0020] A dynamic model of the main frequency of the system is constructed.

[0021] The beneficial effects of this preferred technical solution are: by expressing the system's main frequency as the center of inertia angular velocity, a unified system frequency representation is established, effectively resolving the issue of inconsistent frequencies in multi-machine systems. The center of inertia angular velocity, as a weighted average, accurately reflects the overall system frequency state, reducing the impact of local frequency fluctuations on estimation accuracy. Furthermore, the dynamic equations established based on the aggregated swing equation simplify the complex multi-machine system into a single-machine equivalent model, significantly reducing computational complexity and enabling online real-time estimation.

[0022] As a preferred solution of the inertia estimation method based on dynamic regressor expansion and hybridization of the present invention, wherein: determining the regression model variables and constructing the differential regression equation according to the dynamic model includes:

[0023] Determining the system frequency, the total power of the master frequency controlled generator, and the total electric power of the power system as the regression model variables;

[0024] Construct a regression equation expression including the system rated frequency related constants and the parameters to be estimated;

[0025] Design differential operators;

[0026] The differential operator is multiplied by the regression equation to obtain a regression construction equation.

[0027] The beneficial effects of this preferred technical solution are: by selecting system frequency and power as regression model variables, a direct mapping relationship between system dynamic characteristics and inertia parameters is established, avoiding the complex intermediate variable conversion required in traditional methods. In particular, the introduction of a differential operator to process the signal forms a filtered differential structure that effectively suppresses the impact of measurement noise on the estimation results, filtering out high-frequency interference components while preserving the signal's dynamic characteristics. This design makes the method more resistant to interference when applied in actual power systems, and can provide accurate inertia estimation even in the presence of noisy measurement data.

[0028] As a preferred solution of the inertia estimation method based on dynamic regressor expansion and mixing of the present invention, it also includes:

[0029] Construct dynamic regression parameter estimators;

[0030] introducing the dynamic regression parameter estimator into the regression equation;

[0031] estimating parameters to be estimated in the regression equation, the parameters to be estimated comprising a first estimation parameter related to a system inertia constant and a second estimation parameter related to a system frequency response;

[0032] A system inertia prediction value is calculated based on the first estimated parameter and the second estimated parameter.

[0033] As a preferred solution of the inertia estimation method based on dynamic regressor expansion and mixing of the present invention, the estimating the parameters to be estimated in the regression equation includes:

[0034] determining an intermediate form of the first estimated parameter and the second estimated parameter;

[0035] Set the iterative gain of the parameter estimator;

[0036] Iteratively updating the first estimated parameter and the second estimated parameter using a gradient descent method;

[0037] Introduce error coordinates and construct error coordinate expressions;

[0038] Set the constraints of the error coordinates;

[0039] When the error coordinates satisfy the constraint condition, the estimated values ​​of the first estimated parameter and the second estimated parameter are determined as final values.

[0040] The beneficial effects of this preferred technical solution are: by using the gradient descent method combined with the error coordinate technology for parameter estimation, adaptive optimization of the estimation process is achieved, and the system can dynamically adjust the parameter estimation direction and step size according to real-time data. The high-gain design (iterative gain is on the order of 10^10) ensures the convergence speed, while the error coordinate constraint ensures the stability of convergence, effectively solving the problem of slow convergence or instability in traditional estimation methods. In particular, when the system inertia undergoes a sudden change (such as a large generator set going offline), this method can quickly capture the inertia change and provide real-time warnings.

[0041] Another object of the present invention is to provide an inertia estimation system based on dynamic regressor expansion and hybridization.

[0042] To solve the above technical problems, the present invention provides the following technical solutions: an inertia estimation system based on dynamic regressor expansion and hybridization, comprising: a data acquisition module for acquiring power data and frequency data of a generator in a power system;

[0043] a parameter identification module, configured to determine a first system parameter and a second system parameter based on the power data and the frequency data; the first system parameter being the system main frequency, and the second system parameter being used to characterize an operating state of the power system;

[0044] A dynamic modeling module, configured to construct a dynamic model of the first system parameters based on the second system parameters and the aggregated swing equation; the dynamic model is configured to describe a variation characteristic of the system main frequency;

[0045] A regression analysis module is used to determine regression model variables and construct a differential regression equation based on the dynamic model, and obtain an inertia estimation result based on the differential regression equation; the differential regression equation characterizes the dynamic relationship between the first system parameter and the second system parameter.

[0046] The present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and is characterized in that when the processor executes the computer program, the steps of the inertia estimation method based on dynamic regressor expansion and mixing are implemented.

[0047] The present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the inertia estimation method based on dynamic regressor expansion and mixing.

[0048] The beneficial effects of the present invention are as follows: First, the present invention can realize accurate online estimation of the inertia of the power system by real-time acquisition of frequency and power data of the power system, combined with a dynamic regression model and hybrid technology, ensuring that the system can respond promptly to disturbances and improving the stability of the system; second, the present invention adopts a dynamic regression estimation framework and uses a delay operator for signal processing, which effectively reduces the interference of noise on the inertia estimation results and significantly improves the accuracy and reliability of inertia estimation; in addition, the method of the present invention has strong adaptability and can be widely used in different types of power systems including traditional power systems and smart grids, and is particularly suitable for systems with a large amount of renewable energy access, helping to ensure the stability and efficient operation of the power system under complex dynamic conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0050] Figure 1 An overall flow chart of an inertia estimation method based on dynamic regressor expansion and hybridization provided by one embodiment of the present invention;

[0051] Figure 2 A block diagram of an online inertia estimator based on a dynamic regression estimation method, which is an inertia estimation method based on dynamic regressor expansion and hybridization, provided by one embodiment of the present invention;

[0052] Figure 3 A system structure diagram of an inertia estimation system based on dynamic regressor expansion and hybridization provided by one embodiment of the present invention;

[0053] Figure 4 A comparison chart of the accuracy of frequency dynamic models of an inertia estimation method based on dynamic regressor expansion and hybridization provided by one embodiment of the present invention;

[0054] Figure 5 A graph showing changes in parameters to be estimated for an inertia estimation method based on dynamic regressor expansion and hybridization provided by one embodiment of the present invention;

[0055] Figure 6 A diagram showing the relative error of parameter estimation for an inertia estimation method based on dynamic regressor expansion and hybridization according to one embodiment of the present invention.

[0056] Figure 7Error diagram of each power generation unit of the inertia estimation method based on dynamic regressor expansion and hybridization provided by one embodiment of the present invention. DETAILED DESCRIPTION

[0057] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, the following detailed description of the specific embodiments of the present invention is given in conjunction with the accompanying drawings. It is obvious that the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in this field without creative work should fall within the scope of protection of the present invention.

[0058] Example 1, reference Figure 1 , which is the first embodiment of the present invention, provides an inertia estimation method based on dynamic regressor expansion and hybridization, including:

[0059] S100: Acquire power data and frequency data of generators in the power system;

[0060] S200: Determine a first system parameter and a second system parameter based on the power data and the frequency data; the first system parameter is the system main frequency, and the second system parameter is used to characterize the operating state of the power system;

[0061] S300: constructing a dynamic model of the first system parameter based on the second system parameter and the aggregated swing equation, where the dynamic model is used to describe a change characteristic of the system main frequency;

[0062] S400: Determine regression model variables and construct a differential regression equation based on the dynamic model, and obtain an inertia estimation result based on the differential regression equation; the differential regression equation represents the dynamic relationship between the first system parameter and the second system parameter.

[0063] It should be noted that as the proportion of renewable energy (such as wind and solar energy) in the power system continues to increase, the inertia contribution of traditional power systems is gradually decreasing, posing a challenge to the stability of the power system. During system operation, system parameters such as frequency and power vary significantly, causing dynamic changes in the system's frequency and power. The operating power system is in a complex operating environment, making it difficult to measure system inertia, and system stability assessments are often delayed. At the same time, due to the randomness and volatility of renewable energy, system frequency fluctuations are exacerbated, which in turn endangers system stability. Complex operating conditions have a significant impact on inertia measurement and can also cause system instability due to frequency fluctuations. Therefore, inertia estimation and stability prediction of power systems are also very important.

[0064] Therefore, in order to address the above-mentioned inertia estimation and stability assessment problems, a model is constructed through steps S100 to S400 to simulate the operating status of the power system under typical operating conditions, and the system parameters and their relationship based on power and frequency data are obtained to achieve an accurate description of the dynamic characteristics of the system main frequency; real-time estimation of the system inertia is achieved, and a differential regression equation is dynamically constructed to accurately predict the change in system inertia; at the same time, based on the dynamic regression parameter estimation method, an accurate assessment of the stability of the power system is achieved.

[0065] Example 2, reference Figures 1 to 7 , which is an embodiment of the present invention, provides an inertia estimation method based on dynamic regressor expansion and mixing based on the above embodiments.

[0066] In the embodiment of the present invention, in step S100 , power data and frequency data of the generator in the power system are obtained, and various parameters of the power system are acquired through a system monitoring device for data collection.

[0067] In an optional embodiment, the power data and frequency data of the generator in the power system obtained in step S100 can also be collected in real time through a wide area measurement system (WAMS), and the frequency, phase angle, voltage and other data in the power system are synchronously measured to provide a high-precision input signal for inertia estimation.

[0068] In another optional embodiment, the power data and frequency data of the generator in the power system obtained in step S100 can also be obtained by using distributed measurement devices to monitor the frequency and power of multiple nodes in the system in real time to construct a more comprehensive description of the system status.

[0069] In the embodiment of the present invention, determining the first system parameter and the second system parameter according to the power data and the frequency data in step S200 includes the following steps A1-A2:

[0070] A1: Calculate the system main frequency based on the angular frequency and inertia constant of the power generation unit;

[0071] A2: Calculate system power parameters and system operating parameters, determine the system main frequency as the first system parameter, and determine the system power parameters and system operating parameters as the second system parameters.

[0072] Specifically, in A1, the system main frequency can be expressed as the angular velocity of the center of inertia, and its calculation formula is:

[0073]

[0074] Where, ω COI Indicates the angular velocity of the system's center of inertia (rad / s), which is a representation of the system's main frequency; N represents the total number of power generation units; ωi is the rotor angular frequency of the i-th generator unit (rad / s); H i is the inertia constant of the i-th generator unit (s). It should be noted that this weighted average calculation method can more accurately reflect the frequency state of the entire system and provide a reliable basis for subsequent analysis.

[0075] In A2, the calculation of system power parameters and system operating parameters includes the total rated power S of the system B , the total inertia constant of the system H tot , system mechanical power P m,tot , system power P e,tot And the system power difference ΔP.

[0076] System total rated power S B The calculation formula is:

[0077]

[0078] Where S B Indicates the total rated power of the system (MVA); S Bi represents the rated power (MVA) of the i-th generator unit. The total rated power of the system is an important indicator for evaluating system capacity and directly affects the system's ability to resist disturbances.

[0079] The total inertia constant of the system H tot The calculation formula is:

[0080]

[0081] Where H tot It represents the total inertia constant (s) of the system and is a comprehensive representation of the system inertia level. The larger the value, the stronger the system inertia and the better the frequency stability.

[0082] System mechanical power P m,tot The calculation formula is:

[0083]

[0084] Where, P m,tot Indicates the total mechanical power of the system (MW); P m,PFC Indicates the total mechanical power of the PFC generator (MW); P m,unc represents the total mechanical power of the non-PFC generator (MW); P mi represents the mechanical power of the i-th generator unit (MW); N PFC Indicates the total number of PFC generators; N unc Represents the total number of non-PFC generators. System mechanical power reflects the energy input from the prime mover and is an important component of system power balance.

[0085] System power P e,tot The calculation formula is:

[0086] P e,tot =P e,PFC +P e,unc =P load +P loss -P ren ;

[0087] Where, P e,tot Indicates the total power of the system (MW); P e,PFC Indicates the total power of the PFC generator (MW); P e,unc Indicates the total power of non-PFC generator (MW); P load Indicates the total power consumption of the load (MW); P loss is the total power loss of the system (MW); P ren is the total power generation of renewable energy (MW). System electrical power reflects the electrical energy output by the system, and the difference between it and mechanical power directly affects the system frequency change.

[0088] The calculation formula for the system power difference ΔP is:

[0089] ΔP=-P e,unc +P load +P loss -P ren ;

[0090] Where ΔP represents the system power difference (MW), a direct indicator of the system power balance. When ΔP > 0, the system frequency increases; when ΔP < 0, the system frequency decreases; and when ΔP = 0, the system frequency remains stable.

[0091] For example, assume a power system with five generator sets, with the following parameters:

[0092] Generator 1: H1 = 5s, S B1 =500MVA,ω1=314rad / s,P m1 =400MW;

[0093] Generator 2: H2=4s,S B2 =400MVA,ω2=313.5rad / s,P m2 =320MW;

[0094] Generator 3: H3=6s,S B3 =600MVA,ω3=314.2rad / s,P m3 =550MW;

[0095] Generator 4: H4=3s,S B4 =300MVA,ω4=313.8rad / s,P m4 =280MW;

[0096] Generator 5: H5 = 4.5s, S B5 =450MVA,ω5=314.1rad / s,P m5 =400MW;

[0097] Among them, generators 1, 2, and 3 are PFC generators, and generators 4 and 5 are non-PFC generators.

[0098] Calculate the angular velocity of the system's center of inertia:

[0099]

[0100] Calculate the total system rated power:

[0101] S B =500+400+600+300+450=2250MVA;

[0102] Calculate the total inertia constant of the system:

[0103]

[0104] Calculate the system mechanical power:

[0105] P m,PFC =400+320+550=1270MW;

[0106] P m,unc =280+400=680MW;

[0107] P m,tot =1270+680=1950MW;

[0108] Assuming the system load is 1900MW, the system loss is 30MW, and the renewable energy generation is 0MW, the system power is:

[0109] P e,tot =1900+30-0=1930MW.

[0110] In an optional implementation, the determination of the first system parameter and the second system parameter in step S200 may further represent the changing state of the system frequency more intuitively by expressing the system frequency as a frequency deviation, that is, the difference between the actual system frequency and the rated frequency.

[0111] In another optional implementation, the determination of the first system parameter and the second system parameter in step S200 may further include introducing a system damping coefficient to quantify the system's natural suppression capability for frequency changes and enhance the descriptive capability of the system parameters.

[0112] In the embodiment of the present invention, in step S300, a dynamic model of the first system parameter is constructed based on the second system parameter and the aggregate swing equation, including the following steps B1-B3:

[0113] B1: Express the system main frequency as the angular velocity of the center of inertia;

[0114] B2: Establish the dynamic equation of the angular velocity of the center of inertia;

[0115] B3: Construct a dynamic model of the system's main frequency.

[0116] Specifically, in B2, the angular velocity of the center of inertia ω COI The kinetic equation can be expressed by the polymerization rocking equation as follows:

[0117]

[0118] Where, ω COI is the angular velocity of the center of inertia of the system (rad / s), which represents the main frequency of the power system; is the rate of change of the angular velocity of the center of inertia of the system (rad / s 2 ), which indicates the speed of frequency change; ω0 is the rated angular velocity of the system (rad / s), usually 314rad / s (corresponding to 50Hz); H tot is the total inertia constant of the system (s), which represents the ratio of the rotational kinetic energy stored in the system to the rated power of the system; S B is the total rated power of the system (MVA); ΔP is the system power difference (MW), which indicates the imbalance between mechanical power and electrical power; P m,tot is the total mechanical power of the system (MW); P PFC,tot is the total mechanical power injection due to PFC (MW); P e,tot is the total electrical power of the system (MW).

[0119] In B3, the angular velocity of the center of inertia of the system is ω COI Approximate average frequency ω of the PFC unit av ,Right now:

[0120]

[0121] Where, ω av The average frequency (rad / s) of the PFC unit is used to approximate the angular velocity of the center of inertia of the system; ω irepresents the rotor angular frequency of the i-th PFC generator (rad / s); N PFC Indicates the total number of PFC generators.

[0122] Angular velocity of the center of inertia of the system ω COI The approximate value of the kinetic equation is expressed as:

[0123]

[0124] Among them, P m,PFC is the total mechanical power of the PFC generator (MW); P e,PFC is the total electrical power of the PFC generator (MW); is the rate of change of the average frequency of the PFC unit (rad / s 2 ).

[0125] In an optional embodiment, the dynamic model of the system main frequency constructed in step S300 may also consider the load-frequency characteristics, that is, introduce the load damping coefficient D and modify the dynamic equation to:

[0126]

[0127] Where D represents the load damping coefficient (MW / Hz), Δω COI This correction takes into account the natural regulation characteristics of system load as the frequency changes, thus improving the accuracy of the model.

[0128] In another optional implementation, the dynamic model of the system main frequency constructed in step S300 may also introduce a frequency control gain to construct a dynamic model including a primary frequency modulation characteristic:

[0129]

[0130] Among them, R represents the speed regulator's adjustment coefficient, This method can more accurately describe the system frequency dynamic response when the generator set participates in the primary frequency regulation.

[0131] In the embodiment of the present invention, step S400 determines the regression model variables and constructs the differential regression equation based on the dynamic model, including the following steps C1-C4:

[0132] C1: The system frequency, the total power of the main frequency-controlled generators, and the total electric power of the power system are determined as regression model variables;

[0133] C2: Construct a regression equation that includes the system rated frequency related constants and the parameters to be estimated;

[0134] C3: Design differential operators;

[0135] C4: Multiply the differential operator by the regression equation to obtain the regression construction equation.

[0136] Specifically, in C1, the regression model variables are expressed as:

[0137] y=ω av ,x=P PFC,tot ,u=P e,PFC ;

[0138] Where y represents the system output variable, that is, the average frequency of the PFC unit (rad / s); x represents the total mechanical power injection caused by the PFC action (MW); and u represents the total electrical power of the PFC generator (MW).

[0139] This variable definition method uses the three most critical physical quantities in the system as regression variables, directly reflecting the frequency and power status of the system, laying the foundation for subsequent parameter estimation.

[0140] In C2, the regression equation expression and the parameters to be estimated are expressed as:

[0141]

[0142] in, Indicates the rate of change of system frequency (rad / s 2 ); b1 is a constant related to the rated frequency and rated capacity of the system; η1 and η2 are the parameters to be estimated in the regression model.

[0143] It should be noted that the design of this regression equation has several advantages:

[0144] The parameter to be estimated η1 and the system inertia constant H tot Directly related, the system inertia can be accurately inferred by estimating the parameters. In particular This relationship makes the estimation of system inertia direct and clear. By introducing the parameter b1 and rationally organizing the regression equation structure, the originally complex nonlinear system dynamic equation is transformed into a linear parameter estimation problem, which greatly simplifies the computational complexity. The term captures the effect of power imbalance on frequency variation, while The term takes into account the basic contribution of mechanical power, which enables the model to fully describe the dynamic characteristics of the system. The design consolidates the system's basic parameters into a single constant, reducing multiplication and division operations in real-time calculations and improving algorithm execution efficiency. The equation structure design considers the coupling relationship between system frequency and power, enabling effective estimation of system parameters in the presence of measurement noise and improving the algorithm's anti-interference capabilities.

[0145] The regression equation constructed in this way not only accurately describes the dynamic relationship between system frequency and power, but also transforms complex system dynamics into a manageable parameter estimation problem. This dynamic regression method is particularly useful for power systems containing a large amount of renewable energy, where inertia varies over time. This method can track changes in system inertia in real time, providing a crucial basis for system stability assessment and control.

[0146] In C3, the representation of differential operators is:

[0147]

[0148] Where p represents the differential operator, which performs a differential operation on the signal. This operator is a fundamental tool for building dynamic system models and is used to describe the rate of change of system variables over time.

[0149] In C4, the expression obtained by multiplying the differential operator by the regression equation is:

[0150]

[0151] The regression construction equation is expressed as:

[0152]

[0153] This regression construction equation uses the filter differential operator Instead of directly using the differential operator p, the traditional differential operation is extremely sensitive to noise. The filtered differential operator introduces the parameter α to form a high-pass filter, which can suppress high-frequency noise while extracting the signal change rate, greatly improving the robustness of parameter estimation.

[0154] In practical applications, the selection of the α parameter is crucial to filtering effectiveness. For example, when α = 0.5, the filter has strong filtering capabilities and is suitable for noisy environments; while when α = 2, the filter has a faster response speed and is suitable for scenarios where system parameters change rapidly. For typical power systems, α is usually selected between 0.5 and 2 to balance filtering effectiveness and response speed.

[0155] The regression construction equation converts the original signal into variables ξ1, ξ2 and ξ3, establishes a linear relationship between them, and transforms the parameter estimation problem into a standard form. This form facilitates the application of various parameter estimation algorithms, such as the least squares method or recursive least squares method.

[0156] For example, in a 50 Hz power system, assuming that the measured system frequency is 49.8 Hz (corresponding to ω av=313 rad / s), the total mechanical power of the PFC generator is 1200 MW, the total electrical power of the PFC generator is 1180 MW, and the total rated power of the system is 5000 MVA. After processing with the filter differential operator, high-frequency noise in the measurement signal is effectively filtered out, resulting in smoothed system variables ξ1, ξ2, and ξ3. These processed variables are used to construct a regression equation. Using the parameter estimation algorithm, we obtain η1≈0.22 and η2≈0.53, thereby calculating the system inertia H. tot ≈4.5s, which is very close to the actual inertia of the system.

[0157] The differential regression method of this invention is particularly suitable for handling situations where system inertia is dynamically changing. For example, when a large amount of wind power is connected to the system, the system inertia fluctuates with changes in wind power output. Traditional methods have difficulty tracking such changes in real time. However, this invention, through dynamic regression, can quickly capture the changing trends of system inertia, providing important support for stable system operation.

[0158] In an optional embodiment, the differential regression equation constructed in step S400 can also use an adaptive filter to design a differential operator. The specific implementation method is to dynamically adjust the filter parameter α by introducing a recursive least squares algorithm so that it is adaptively updated as the system noise level changes. The basic filter parameter is usually set to 0.5 and is dynamically adjusted based on the sum of squared errors between the measured value and the estimated value. This method can automatically increase the α value to enhance the filtering effect when the system noise suddenly changes (such as when a large load is switched on or a short-circuit disturbance occurs), and reduce the α value to improve the response speed when the system is operating normally, thereby maintaining a high estimation accuracy under various operating conditions.

[0159] In another optional embodiment, a second-order Butterworth filter differential operator can be introduced when constructing the differential regression equation in step S400, where the damping ratio is typically set to 0.707 to achieve optimal frequency response, and the cutoff frequency can be set to 2-3 times the system's dynamic response frequency. This second-order operator has a steeper roll-off than the first-order operator, more effectively suppressing high-frequency noise while preserving the second-order oscillation characteristics in the system. It is particularly suitable for complex power networks containing large synchronous generators and HVDC systems. It can capture low-frequency oscillation modes in the system (such as 0.1-1 Hz inter-area oscillations), providing more comprehensive frequency domain information for system stability analysis.

[0160] In an embodiment of the present invention, the following steps D1-D6 are also included:

[0161] D1: Construct dynamic regression parameter estimator;

[0162] D2: Introducing dynamic regression parameter estimators into the regression equation;

[0163] D3: Estimate the parameters to be estimated in the regression equation, where the parameters to be estimated include a first estimation parameter related to the system inertia constant and a second estimation parameter related to the system frequency response;

[0164] D4: Calculate the system inertia prediction value based on the first estimated parameter and the second estimated parameter.

[0165] Specifically, in D1, the expression of the dynamic regression parameter estimator is:

[0166] [H(·)](t)=(·)(td);

[0167] Where H(·) = (·)(td) represents the delay operator, which delays the input signal by d time units; W(s) and Z1(s) represent the transfer functions of the dynamic regression parameter estimator; γ1 and γ2 are the iterative gains of the parameter estimator, which are used to adjust the convergence speed. Larger values ​​lead to faster convergence but may cause oscillation; λ is the differential operator parameter, which controls the filtering characteristics. Smaller values ​​lead to stronger filtering effects. s is a complex variable, which represents the differential operator in Laplace transform.

[0168] In D2, after the introduction of the dynamic regression parameter estimator, the regression equation is expressed as:

[0169]

[0170] Where z(td) represents the system output after delay; represents the delayed regression vector; η represents the parameter vector to be estimated [η1η2] T .

[0171] In D3, the estimation process of the parameters η1 and η2 in the regression equation is expressed as:

[0172]

[0173] The parameter estimation process is iterative updating. By continuously adjusting the parameter value, the error is gradually reduced and eventually converges to the true value. T =Δη represents the parameter vector after processing by the differential operator; and They represent the estimated values ​​of parameters η1 and η2 respectively; Δ is the differential operator, which performs differential processing on the signal; and for and The derivative of , which represents the rate of change of the parameter estimate over time.

[0174] Introducing error coordinates The expression is:

[0175]

[0176] Where, represents the parameter estimation error vector derivative vector representing parameter estimates diag(γ1,γ2) represents a diagonal matrix with γ1 and γ2 as diagonal elements; The second-order differential of the difference between the true value and the estimated value of the parameter; Represents the second-order differential of the error vector. η1 and the system inertia constant H tot Directly related, η2 is related to the system frequency response, Typical values ​​for γ1 and γ2 are 10 10 , this high gain design can ensure fast convergence; d represents the delay time, which is usually selected to be smaller than the minimum time constant of the system to ensure the real-time performance of the estimation.

[0177] When the error coordinate value When the following constraints are met, the parameters to be estimated η1 and η2 are considered to be final values, and the system inertia estimation is achieved. The specific constraints are expressed as:

[0178]

[0179] In the formula, the first constraint It means that the error coordinate tends to zero over time, which means that the parameter estimate converges asymptotically to the true value.

[0180] The second constraint is the continuous incentive condition, where: is the regression vector [ξ2ξ3]; τ is the integration time window, which indicates the time length of the observation data; δ is a positive constant, which indicates the lower bound of the minimum eigenvalue; I2 is the second-order unit matrix.

[0181] The continuous excitation condition ensures the richness of the system input, ensuring that there is enough information to estimate all unknown parameters. When the system input is not rich enough, some parameters may not be accurately identified.

[0182] In D4, the formula for calculating the predicted value of system inertia based on the parameter estimates is:

[0183]

[0184] Where H est represents the estimated system inertia value (seconds); ω0 is the system rated angular velocity (rad / s), usually 314 rad / s (corresponding to 50 Hz); is the estimated value of parameter η1.

[0185] This formula is directly derived from the parameter η1 and the system inertia H tot The relationship between Derived, the system inertia can be inferred from the parameter estimates through the reciprocal relationship.

[0186] In an optional embodiment, the parameter estimation of the differential regression equation in step S500 may also be performed by batch estimation using the least squares method, which uses historical data within a period of time to centrally estimate parameters, and is suitable for situations where system parameters change slowly.

[0187] In another optional embodiment, the parameter estimation of the differential regression equation in step S500 may also be combined with a Kalman filter algorithm to transform the parameter estimation problem into a state estimation problem, thereby providing an optimal estimate while taking into account system and measurement noise.

[0188] It should be noted that frequency fluctuations in power systems are closely related to system inertia. The greater the system inertia, the slower the frequency changes, and the better the system stability. As the proportion of renewable energy integration increases, system inertia gradually decreases, and the rate of frequency change accelerates, posing challenges to system stability. During system disturbances or sudden load changes, frequency shifts occur, and the rate of shift is inversely proportional to the system inertia. Accurately estimating system inertia is crucial for assessing system stability and formulating control strategies.

[0189] Therefore, to meet the aforementioned power system inertia estimation requirements, we constructed an inertia estimation method based on the expansion and hybridization of dynamic regressors through the above steps. This method utilizes system frequency and power data, along with dynamic models, differential regression equations, and parameter estimation techniques, to achieve accurate system inertia estimation. Compared to traditional methods, this method offers strong real-time performance, high accuracy, and excellent adaptability, meeting the needs of modern power systems for real-time inertia monitoring and stability assessment.

[0190] In addition, the present invention introduces a differential operator to process signals, effectively reducing the interference of noise on the inertia estimation results; adopts a dynamic regression parameter estimation framework to achieve real-time parameter updates, improving the accuracy and reliability of the estimation; and uses error coordinates to determine the convergence conditions, ensuring the reliability of the estimation results. These technical features make the present invention widely applicable to various power systems, and are particularly suitable for systems with a large number of renewable energy sources connected. By accurately estimating the system inertia, it can provide an important basis for system operation scheduling, stability analysis, and control strategy optimization, thereby improving the safe and stable operation level of the power system.

[0191] Example 3 is the third embodiment of the present invention, which differs from the first two embodiments in that:

[0192] If the function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the various embodiments of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0193] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0194] More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic devices), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering, or processing in another suitable manner as necessary, and then stored in a computer memory.

[0195] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0196] Embodiment 4 is the fourth embodiment of the present invention, which provides an inertia estimation system based on dynamic regressor expansion and mixing, including.

[0197] A data acquisition module is used to obtain power data and frequency data of generators in the power system;

[0198] a parameter identification module, configured to determine a first system parameter and a second system parameter based on the power data and the frequency data; the first system parameter being the system main frequency, and the second system parameter being used to characterize the operating state of the power system;

[0199] A dynamic modeling module is used to construct a dynamic model of the first system parameters based on the second system parameters and the aggregate swing equation; the dynamic model is used to describe the change characteristics of the system main frequency;

[0200] The regression analysis module is used to determine the regression model variables and construct a differential regression equation based on the dynamic model; the differential regression equation represents the dynamic relationship between the first system parameter and the second system parameter.

[0201] Example 5, with reference to Figures 1 to 7 , which is the third embodiment of the present invention. It is different from the previous two embodiments in that it is used to verify the technical effects adopted in the present invention in order to verify the real effects of this method.

[0202] Traditional inertia estimation methods typically rely on historical system data and offline calculations, making them slow to respond to frequent disturbances and difficult to adapt to rapidly changing power system environments. In contrast, the present invention uses real-time monitoring of the power system's frequency and power data, combined with a dynamic regression model and hybrid technology, to quickly and accurately estimate the power system's inertia within a short period of time after a disturbance occurs. Experimental results show that this method can effectively reduce inertia estimation errors, especially under high-frequency disturbances and complex system dynamics, ensuring the stability and reliability of the power system.

[0203] like Figure 4 The following is a comparison chart of the accuracy of the frequency dynamic model. Figure 4 It can be seen that using the dynamic regressor extension and hybrid inertia estimation method proposed in this invention, the aggregated system center frequency dynamic model provides a good approximation of the full-order model, indicating that the online inertia estimator design using the model meets the engineering error requirements.

[0204] like Figure 5 As shown in , it is the change diagram of the parameters to be estimated. Figure 5 It can be seen that although there is a certain disturbance at the beginning, the estimated value gradually converges to a stable value over time. After about 15 seconds, the parameter estimate has almost no obvious change, indicating that the inertia estimate of the system has stabilized. This shows that the dynamic regression estimator can effectively perform real-time estimation and converge to the true value in a short time after the disturbance.

[0205] like Figure 6 As shown in Figure 2, the relative error diagram of parameter estimation is shown. Figure 6 It can be seen that although there is a certain error in the relative trajectory at the initial moment, the relative error gradually decreases over time. Ultimately, the error between the estimated value and the true value is very small (less than 7%), indicating that the proposed method can achieve accurate estimation of inertia parameters in a short time.

[0206] like Figure 7 The following is the error diagram of each power generation unit. Figure 7 It can be seen that among the 25 generator outage scenarios considered, the estimation error is 15% or lower in 21 scenarios, and even lower than 1% in some cases. Only in 4 cases, the estimation error is greater than 15%. These cases correspond to disturbances with power outages of more than 800 MW, which shows that neither the location nor the size of the disturbance is a key determinant of the estimator's performance.

[0207] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. An inertia estimation method based on dynamic regressor expansion and hybridization, characterized by: include, Obtain power data and frequency data of generators in the power system; determining a first system parameter and a second system parameter according to the power data and the frequency data; the first system parameter being a main frequency of the system, and the second system parameter being used to characterize an operating state of the power system; constructing a dynamic model of the first system parameters based on the second system parameters and the aggregated swing equation, wherein the dynamic model is used to describe the variation characteristics of the system main frequency; According to the dynamic model, regression model variables are determined and a differential regression equation is constructed, and an inertia estimation result is obtained according to the differential regression equation; the differential regression equation characterizes the dynamic relationship between the first system parameter and the second system parameter.

2. The inertia estimation method based on dynamic regressor expansion and hybridization according to claim 1, characterized in that: The obtaining of power data and frequency data of a generator in the power system includes: Obtain the total electrical power and total mechanical power of the main frequency-controlled generator in the power system; Frequency data of a plurality of generators are collected, and the total electrical power, the total mechanical power and the frequency data are used as system input signals.

3. The inertia estimation method based on dynamic regressor expansion and hybridization according to claim 2, characterized in that: Determining a first system parameter and a second system parameter according to the power data and the frequency data includes: Calculate the system main frequency based on the angular frequency and inertia constant of the power generation unit; A system power parameter and a system operating parameter are calculated, the system main frequency is determined as the first system parameter, and the system power parameter and the system operating parameter are determined as the second system parameter.

4. The inertia estimation method based on dynamic regressor expansion and hybridization according to claim 3, characterized in that: The constructing of a dynamic model of the first system parameter based on the second system parameter and the aggregate swing equation includes: Expressing the system main frequency as the center angular velocity of inertia; Establishing a dynamic equation for the angular velocity of the center of inertia; A dynamic model of the main frequency of the system is constructed.

5. The inertia estimation method based on dynamic regressor expansion and hybridization according to claim 4, characterized in that: Determining regression model variables and constructing a differential regression equation based on the dynamic model includes: Determining the system frequency, the total power of the master frequency controlled generator, and the total electric power of the power system as the regression model variables; Construct a regression equation expression including the system rated frequency related constants and the parameters to be estimated; Design differential operators; The differential operator is multiplied by the regression equation to obtain a regression construction equation.

6. The inertia estimation method based on dynamic regressor expansion and hybridization according to claim 5, characterized in that: Also includes: Construct dynamic regression parameter estimators; introducing the dynamic regression parameter estimator into the regression equation; estimating parameters to be estimated in the regression equation, the parameters to be estimated comprising a first estimation parameter related to a system inertia constant and a second estimation parameter related to a system frequency response; A system inertia prediction value is calculated based on the first estimated parameter and the second estimated parameter.

7. The inertia estimation method based on dynamic regressor expansion and hybridization according to claim 6, characterized in that: The estimating the parameters to be estimated in the regression equation includes: determining an intermediate form of the first estimated parameter and the second estimated parameter; Set the iterative gain of the parameter estimator; Iteratively updating the first estimated parameter and the second estimated parameter using a gradient descent method; Introduce error coordinates and construct error coordinate expressions; Set the constraints of the error coordinates; When the error coordinates satisfy the constraint condition, the estimated values ​​of the first estimated parameter and the second estimated parameter are determined as final values.

8. An inertia estimation system based on dynamic regressor expansion and hybridization, applying the inertia estimation method based on dynamic regressor expansion and hybridization according to any one of claims 1 to 7, characterized in that: include: A data acquisition module is used to obtain power data and frequency data of generators in the power system; a parameter identification module, configured to determine a first system parameter and a second system parameter based on the power data and the frequency data; the first system parameter being the system main frequency, and the second system parameter being used to characterize an operating state of the power system; a dynamic modeling module for constructing a dynamic model of the first system parameters based on the second system parameters and an aggregate swing equation; The dynamic model is used to describe the changing characteristics of the main frequency of the system; A regression analysis module is used to determine regression model variables and construct a differential regression equation based on the dynamic model, and obtain an inertia estimation result based on the differential regression equation; the differential regression equation characterizes the dynamic relationship between the first system parameter and the second system parameter.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the inertia estimation method based on dynamic regressor expansion and mixing according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the inertia estimation method based on dynamic regressor expansion and mixing according to any one of claims 1 to 7 are implemented.

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