Evaluation index construction method for optimal estimation performance of inertia and damping of power system
By constructing a multi-source inertia estimation framework for new energy high-penetration power grids based on CRLB, the problems of insufficient inertia estimation accuracy and lack of theoretical limits in evaluation in new energy power systems are solved. The theoretical accuracy of inertia estimation methods is quantified and real-time performance is evaluated, thereby improving the frequency stability control and operation and maintenance efficiency of power systems.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SICHUAN UNIV
- Filing Date
- 2025-12-09
- Publication Date
- 2026-05-19
AI Technical Summary
Existing inertia estimation methods suffer from insufficient accuracy and a lack of theoretical limits in performance evaluation in high-penetration power systems of new energy sources. They are also difficult to adapt to complex topologies and nonlinear dynamic characteristics, and lack quantitative performance evaluation indicators.
A multi-source inertia estimation framework for high-penetration renewable energy power grids is constructed based on CRLB. By establishing a noisy dynamic model, the Fisher information matrix is derived, and CRLB is calculated to evaluate the theoretical lower limit of inertia estimation and provide the optimal estimation performance index.
This study quantifies and evaluates the theoretical accuracy of inertia estimation methods, improves the reliability and assessability of power system frequency stability control, provides real-time performance benchmarks and early warning mechanisms, and enhances system operation and maintenance efficiency.
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Figure CN122068481A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of power system frequency stability control technology, and in particular to a method for constructing evaluation indexes for the optimal estimation performance of power system inertia and damping. Background Technology
[0002] With the advancement of the "dual carbon" target, my country is accelerating the construction of a new power system dominated by new energy sources such as wind power and photovoltaics. In this system, a large number of traditional synchronous generators are being replaced by new energy sources using power electronic interfaces, driving the power system towards "low inertia, power electronics, and multi-source coupling." This transformation has brought about two profound changes: first, the proportion of synchronous generators has significantly decreased, weakening their inherent rotational inertia response capability; second, wind and photovoltaic power, connected to the grid through converters, exhibit "inertia-free" or "controllable virtual inertia" characteristics, introducing a "load inertia" effect into load-side equipment. This multi-timescale inertia coupling characteristic makes the system frequency dynamics more complex, challenging traditional inertia estimation theories based on synchronous machines.
[0003] Inertia is the "first line of defense" for power systems against power disturbances. Insufficient inertia can easily lead to serious power outages, especially in scenarios with a high proportion of renewable energy sources, where frequency changes can exceed control capabilities and trigger cascading failures. Therefore, accurate estimation of inertia is crucial for frequency stability control.
[0004] Existing inertia estimation methods are divided into model-driven and data-driven approaches. Model-driven methods establish dynamic models through parameter identification, but their accuracy is highly dependent on the system model and struggles to adapt to complex topologies and nonlinear dynamic characteristics. Data-driven methods extract inertia features from measurement data using deep learning, performing better in high-noise scenarios, but they suffer from "black box" characteristics, making it difficult to incorporate physical knowledge and are affected by data quality. Some studies combine deep learning with federated learning frameworks to alleviate the data silo problem, but cross-regional consistency is poor. Data-physical fusion methods enhance model interpretability and physical consistency, and improve estimation accuracy by embedding physical equation constraints into deep learning.
[0005] Although existing research has achieved high-precision inertia estimation, its performance evaluation relies heavily on empirical indicators and lacks quantitative analysis of theoretical limits. The Cramer-Rao lower bound (CRLB) provides a rigorous framework for quantifying the accuracy of parameter estimation and has been applied in fields such as photoelectric positioning and wireless communication.
[0006] This application proposes a multi-source inertia estimation framework for high-penetration renewable energy power grids based on CRLB. It establishes a system dynamic model and introduces noise, constructs a likelihood function and Fisher information matrix, and calculates CRLB to evaluate the theoretical lower limit of accuracy for inertia estimation. Summary of the Invention
[0007] The purpose of this application is to provide a method for constructing evaluation indicators for the optimal estimation performance of inertia and damping in power systems, which can be used to quantitatively evaluate the theoretical optimal accuracy of inertia / damping estimation methods in practical engineering. This method constructs a novel multi-source dynamic model of a power system with noise, derives the Fisher information matrix, and calculates the CRLB, thereby providing a theoretical performance benchmark for the inertia and damping monitoring algorithm of the power dispatch center. This achieves objective calibration and early warning of the accuracy of existing monitoring algorithms, improving the reliability and assessability of power system frequency stability control.
[0008] To achieve the above objectives, this application provides the following solution: Firstly, this application provides a method for constructing evaluation indicators for the optimal estimation performance of power system inertia and damping, including: S1. Dynamic Model Construction of High-Penetration Power Systems with New Energy S2. Construct the optimal estimated performance index; The optimal estimation performance metrics constructed in S2 include: S201. Based on the forward Euler method, the dynamic model of the high-penetration power system of new energy is discretized to obtain the discretized observation model; S202. Based on the discretized observation model, measurement noise is added to establish a noisy discretized observation model; S203. Obtain the information matrix by combining maximum likelihood estimation; S204. Obtain the optimal estimated performance indicators of inertia and damping in a new energy high-penetration power system based on the information matrix; Furthermore, the construction of the dynamic model of the high-penetration power system of new energy sources in S1 includes: S101. Construct a dynamic model of the synchronous machine's inertia response; S102. Construct a dynamic model for the virtual inertia response of new energy sources; S103. Construct a dynamic load model; S104. Based on the linear superposition of the synchronous machine inertia response dynamic model, the new energy virtual inertia response dynamic model and the load dynamic model, a dynamic model of the new energy high-penetration power system is generated. Furthermore, the construction of the synchronous machine inertia response dynamic model in S101 specifically includes: The frequency dynamic response of the synchronous generator is described by the linear swing equation, and the dynamic model of the inertia response of the synchronous machine is obtained. (14) In the formula, The inertia of a synchronous motor; This is the difference between the current frequency and the rated frequency of the power grid. The damping coefficient; This represents the power disturbance at the current moment.
[0009] Furthermore, the construction of the new energy virtual inertia response dynamic model in S102 specifically includes: By improving the control algorithm to simulate the dynamic characteristics of synchronous generators, two dynamic control models are generated: a grid-type control model and a grid-following control model. The grid-type control dynamic model regulates the system frequency by simulating the electromechanical transient characteristics of a synchronous generator. When a frequency deviation occurs in the system, the GFM inverter provides inertial support by releasing virtual rotor kinetic energy. The dynamic response of the GFM inverter is as follows: (15) In the formula, The virtual inertia of new energy represents the inverter's inertial response capability to frequency changes. The virtual damping coefficient is used to simulate the governor damping effect of the synchronous machine. This is the dynamic adjustment amount of the inverter's active power; The grid-based control dynamic model tracks the grid voltage phase through a phase-locked loop (PLL) and achieves fast power response through current source characteristics. Dynamic equations are constructed based on the dynamic coupling of the PLL's phase tracking delay and the power loop. (16) In the formula, The gain is controlled by the phase-locked loop.
[0010] Furthermore, the load dynamic model in S103 specifically includes: A dynamic model of motor-type loads is constructed based on rotor rotational inertia. (17) A dynamic model of power electronic load is constructed based on the simulation of virtual inertia response using an active control strategy. (18) A dynamic model of constant impedance load is constructed based on the damping effect generated by the power-frequency coupling characteristics. (19) In the formula, This is the equivalent inertia of the electric motor; The equivalent inertia of the power electronic load; This is the damping coefficient of the electric motor, which originates from mechanical losses such as bearing friction and wind resistance. The equivalent damping for virtual inertia control; This is the equivalent damping for a constant impedance load. From (4) and (5), we can see that a load model containing inertia is constructed as follows: (20) In the formula, , , Therefore, the equivalent damping on the load side is: Equivalent inertia on the load side: .
[0011] Furthermore, S104 generates a dynamic model of a high-penetration renewable energy power system, specifically including: (twenty one) In the formula, This represents the total equivalent inertia of the system. The total equivalent damping of the system is given by where Includes phase-locked loop control gain in mesh control This represents the total power disturbance on the power supply side. Total power disturbance on the load side.
[0012] Furthermore, the discretized observation model is obtained in S201, specifically including: The dynamic model of a power system with high penetration of new energy sources is discretized using the forward Euler method. (twenty two) In the formula: , Sampling time.
[0013] Furthermore, in step S202, a noisy discretized observation model is established by adding measurement noise to the discretized observation model, specifically including: set up The actual frequency deviation at the k-th sampling time is the measured value. It can be modeled as: (twenty three) In the formula, the additional noise term It follows a Gaussian distribution with zero mean, and the total variance is... It is composed of the superposition of the independent contributions of noise from multiple types of equipment: ; in, This is synchronous machine noise; For virtual inertia device noise; This is load noise.
[0014] Furthermore, the process of obtaining the information matrix in step S203 by combining maximum likelihood estimation specifically includes: S2031. Define the parameter vector to be estimated and establish a PMU discrete observation model containing multi-source Gaussian noise; S2032. Construct the joint likelihood function of the observation sequence, decompose it into a product of probabilities at each time step using the noise independence, and then take the logarithm to transform it into a summation form. S2033. Based on the definition of Fisher's information matrix, substitute the gradient and use the independent and identically distributed characteristics of noise to eliminate the cross terms, and finally obtain the form containing only the sum of the sensitivity matrix. S2034, Calculation based on equation (9) Partial derivatives of the five parameters; They were obtained respectively , , , as well as ; Construct the Fisher information matrix based on the partial derivatives of the five parameters: (twenty four).
[0015] Furthermore, in step S204, obtaining the optimal estimated performance indicators of inertia and damping in a high-penetration new energy power system based on the information matrix specifically includes: Calculate the lower bound of CRLB for the parameter vector to be estimated: (25) The optimal estimated performance indices of inertia and damping for the new power system dynamic model were obtained. in, (26) For information matrix, The mean square error of the unbiased estimation algorithm; The CRLB lower bound is used as a quantization benchmark to evaluate the performance of various estimation algorithms. The system is based on frequency and power disturbance sequences measured by PMU, and estimates the inertia and damping parameters of each component through existing algorithms, and calculates the theoretical lower bound of CRLB under the current operating condition in real time by combining dynamic model and noise characteristics. The algorithm's performance is judged by comparing the mean squared error estimated by the algorithm with CRLB: If the difference between MSE and CRLB is less than the first preset value, the algorithm is judged to be stable. If the difference between MSE and CRLB is greater than or equal to the first preset value and lasts for more than the second preset value, an alert will be triggered.
[0016] Based on the evaluation index construction method for the optimal estimation performance of power system inertia and damping provided in this application, this application has the following technical effects: Given the existing engineering context of deploying various online estimation programs based on PMU data in power dispatch centers, this method can calculate the theoretically optimal estimation accuracy in real time according to the current system operating conditions, providing a quantifiable performance evaluation benchmark for actual monitoring systems.
[0017] By comparing the estimation error of existing inertia damping monitoring algorithms with the theoretical lower limit of CRLB, the monitoring performance can be objectively judged, replacing the traditional fuzzy judgment that relies on engineering experience.
[0018] When the monitoring error continues to exceed the theoretical lower limit, the system can issue an early warning in a timely manner, indicating that the algorithm needs to be calibrated or optimized, thereby improving the reliability and operation and maintenance efficiency of the power system frequency stability control.
[0019] A quantitative evaluation of the performance of the inertia monitoring algorithm, supported by theoretical foundations, has been achieved, providing important technical support for the safe and stable operation of power grids with high penetration of new energy sources. Attached Figure Description
[0020] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0021] Figure 1 This is a flowchart of a method for constructing evaluation indexes for the optimal estimation performance of inertia and damping of a power system according to an embodiment of this application; Figure 2 Flowchart for constructing the optimal estimation performance index method. Detailed Implementation
[0022] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0023] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0024] like Figure 1 As shown, this application provides a method for constructing evaluation indicators for the optimal estimation performance of inertia and damping in a power system. The method includes: S1. Dynamic Model Construction of High-Penetration Power Systems with New Energy S2. Constructing the optimal estimated performance index: The method for constructing the optimal estimated performance index of power system inertia and damping based on CRLB is as follows: First, the observable new power system dynamic model is discretized using the forward Euler method and measurement noise is added. Then, the information matrix is obtained by combining maximum likelihood estimation (MLE). Finally, the optimal estimated performance index of inertia and damping in the system is obtained by calculation.
[0025] like Figure 2 As shown, the optimal estimation performance index in S2 includes: S201. Discretize the dynamic model of the high-penetration power system of new energy based on the forward Euler method to obtain a discretized observation model; S202. Add measurement noise to the discretized observation model to establish a noisy discretized observation model; S203. Obtain the information matrix by combining maximum likelihood estimation; S204. Obtain the optimal estimation performance index of inertia and damping in the high-penetration power system of new energy based on the information matrix. Optionally, the construction of the dynamic model of the high-penetration power system of new energy in S1 includes: S101. Construct a dynamic model of the synchronous machine's inertia response; S102. Construct a dynamic model for the virtual inertia response of new energy sources; S103. Construct a dynamic load model; S104. Based on the linear superposition of the synchronous machine inertia response dynamic model, the new energy virtual inertia response dynamic model and the load dynamic model, a dynamic model of the new energy high-penetration power system is generated. Optionally, the construction of the synchronous machine inertia response dynamic model in S101 specifically includes: The frequency dynamic response of the synchronous generator is described by the linear swing equation, and the dynamic model of the inertia response of the synchronous machine is obtained. (27) In the formula, The inertia of a synchronous motor; This is the difference between the current frequency and the rated frequency of the power grid. The damping coefficient; This represents the power disturbance at the current moment.
[0026] Optionally, the construction of the new energy virtual inertia response dynamic model in step S102 specifically includes: The large-scale grid connection of new energy power generation devices (such as photovoltaic and energy storage systems) and variable-speed wind turbines (including direct-drive and doubly-fed) has significantly reduced the proportion of traditional synchronous generators in the system, leading to a step-like decay trend in the equivalent rotational inertia of the power grid. To address the frequency stability risks posed by low-inertia systems, active inertia support technology based on power electronic converters has emerged. This technology simulates the dynamic characteristics of synchronous generators by improving control algorithms, and is mainly implemented in the following two ways: A. Grid-Forming (GFM) Dynamic Model Network-based control actively participates in system frequency regulation by simulating the electromechanical transient characteristics of a synchronous generator. Its core lies in establishing voltage source characteristics and reproducing the power-frequency coupling relationship of a synchronous generator using a virtual synchronous generation (VSG) algorithm. When a frequency deviation occurs in the system, the GFM inverter provides inertial support by releasing virtual rotor kinetic energy; its dynamic response can be characterized as follows: (28) In the formula, The virtual inertia of new energy represents the inverter's inertial response capability to frequency changes. The virtual damping coefficient is used to simulate the governor damping effect of the synchronous machine. This represents the dynamic adjustment of the inverter's active power. It's worth noting that the damping term in GFM control is achieved by actively adjusting the power-frequency droop characteristic. Excessively high damping coefficients may lead to hysteresis in dynamic response, requiring a trade-off between inertia support and stability margin.
[0027] B. Grid-Following (GFL) Dynamic Model Grid-based control relies on a phase-locked loop (PLL) to track the grid voltage phase, achieving rapid power response through current source characteristics. Its dynamic equations must consider the PLL's phase tracking delay and the dynamic coupling of the power loop. (29) In the formula, This represents the phase-locked loop (PLL) control gain, reflecting the frequency tracking response speed. Unlike GFM, the damping effect of GFL originates from the dynamic delay of the PLL rather than active control; its virtual inertia... The effectiveness is limited by the PLL bandwidth.
[0028] Optional, the load dynamic model in S103 specifically includes: To fully construct the dynamic response model of the system, it is necessary to deeply analyze the differentiated contributions of the dynamic behavior of the load side. When the system power imbalance causes the system frequency to change, the energy in the rotating mass of the load side of the system will change to prevent the system frequency from changing. This process is called load inertial response.
[0029] Among them, when the power grid is subjected to active power disturbances, the initial slip response of electric motor loads (mainly asynchronous motors) causes the power grid to exhibit a small inertia, and the inertia support power it provides is almost negligible. Subsequently, the rotor rotational inertia begins to play a role, and its response characteristics are similar to those of a synchronous machine. Then, it supplies inertia support power to the power grid. Power electronic loads (such as data centers and variable frequency drive systems) rely on active control strategies to simulate virtual inertia response, while constant impedance loads (such as lighting and electric heating equipment) generate a damping effect through power-frequency coupling characteristics. The load dynamics are described by the following linear equation.
[0030] Electric motor loads (inertia-driven) (30) Electronic load (virtual inertia control) (31) Constant impedance load (no inertia, only damping) (32) In the formula, This is the equivalent inertia of the electric motor; The equivalent inertia of the power electronic load; This is the damping coefficient of the electric motor, which originates from mechanical losses such as bearing friction and wind resistance. The equivalent damping for virtual inertia control; This is the equivalent damping for a constant impedance load.
[0031] From (4) and (5), we can see that the load model containing inertia is as follows: (33) In the formula, , , Therefore, the equivalent damping on the load side is: Equivalent inertia on the load side:
[0032] Optionally, in S104, a dynamic model of a high-penetration renewable energy power system is generated, specifically including: Based on the above, the dynamic model of the synchronous generator, the dynamic model of the new energy virtual inertia control, and the dynamic model of the load side are linearly superimposed to obtain the overall dynamic model of the system as follows: (34) In the formula, This represents the total equivalent inertia of the system. The total equivalent damping of the system is given by where Includes phase-locked loop control gain in mesh control This represents the total power disturbance on the power supply side. Total power disturbance on the load side.
[0033] By linearly superimposing synchronous generators, new energy virtual inertia control, and load-side dynamic models, the theoretical model established in this invention not only fully describes the dynamic characteristics of the system, but more importantly, provides a unified mathematical framework for parameter estimation in subsequent engineering applications. This model is directly linked to the frequency and active power data of key nodes in the power system actually measured by the synchronous phasor measurement unit (PMU), ensuring the data consistency between theoretical derivation and engineering practice. The collected node data is transmitted to the master station system via a communication network, becoming the data foundation for subsequent optimal performance index construction methods.
[0034] Optionally, the discretized observation model is obtained in S201, specifically including: Currently, power system inertia estimation methods mainly rely on power unit (PMU) data collection, which is presented in discrete time series format. However, the system dynamic model used in this invention is a continuous-time model. To make the discrete sampled data more suitable for recursive calculations, and also to reduce differential calculations and computational complexity in subsequent derivations, this paper uses the forward Euler method to discretize the model: (35) In the formula: , Sampling time.
[0035] The forward Euler method is used to discretize the continuous model. This theoretical transformation enables the model to directly process discrete time series data collected by the PMU, solving the key problem of mismatch between the theoretical model and the actual engineering data format. This lays the foundation for subsequent recursive calculation and online application in practical systems.
[0036] Optionally, in step S202, a noisy discretized observation model is established by adding measurement noise to the discretized observation model, specifically including: In practical scenarios of power system inertia estimation, frequency deviation signals are inevitably contaminated by multi-source noise. To achieve unbiased estimation of the total system inertia and damping coefficient, a noisy, discretized observation model needs to be established. Let... The actual frequency deviation at the k-th sampling time is the measured value. It can be modeled as: (36) In the formula, the additional noise term It follows a Gaussian distribution with zero mean, and its total variance is... It is composed of the superposition of the independent contributions of noise from multiple types of equipment: ,in Synchronous generator noise is caused by mechanical vibration, excitation control error, and PMU quantization noise in traditional synchronous generators. For virtual inertia device noise, the high-frequency ripple and control delay introduced by the GFM or GFL device at the inverter interface in power point tracking, phase-locked loop dynamics; The addition of various types of noise accurately reflects the actual situation of PMU measurement data being affected by multi-source interference in the engineering site, including load noise, random power fluctuations from motors, constant power loads, and other sources of interference on the frequency signal. This realistic modeling of noise characteristics ensures that the subsequently derived CRLB can provide a practical and usable performance evaluation benchmark for actual monitoring systems.
[0037] Optionally, obtaining the information matrix in step S203 by combining maximum likelihood estimation specifically includes: S2031. Define the parameter vector to be estimated and establish a PMU discrete observation model containing multi-source Gaussian noise; S2032. Construct the joint likelihood function of the observation sequence, decompose it into a product of probabilities at each time step using the noise independence, and then take the logarithm to transform it into a summation form. S2033. Based on the definition of Fisher's information matrix, substitute the gradient and use the independent and identically distributed characteristics of noise to eliminate the cross terms, and finally obtain the form containing only the sum of the sensitivity matrix. S2034, Calculation based on equation (9) Partial derivatives of the five parameters; They were obtained respectively , , , as well as ; The Fisher information matrix is constructed based on the partial derivatives of the five parameters.
[0038] Specifically, in the inertia parameter identification framework based on maximum likelihood estimation (MLE), the parameter vector to be estimated is defined as... ; in, This represents the total equivalent inertia of the system. The total equivalent damping of the system; This is the equivalent damping including inertial load; This is the equivalent damping for a constant impedance load. The equivalent inertia including the inertial load; It covers synchronous machine inertia, virtual inertia, equipment equivalent inertia, load dynamic inertia, and the total damping coefficient of the system.
[0039] Assuming noise is measured at each time point If the observed sequences are independent and identically distributed and follow a Gaussian distribution, then... The joint probability density function can be decomposed into the product of the conditional probabilities at each time step: (37) Taking the natural logarithm of equation (11), we obtain the log-likelihood function: (38) Fisher Information Matrix Defined as the negative expectation of the second derivative of the log-likelihood function, or equivalently as the expectation of the outer product of the gradients: (39) For the log-likelihood function in equation (11) Regarding parameters Taking the partial derivative, we get: (40) Substituting equation (13) into equation (14), and expanding, we obtain a double summation form: (41) According to the measurement model residual For independent Gaussian noise, its covariance satisfies: (42) The information matrix is finally simplified to: (43) The construction of the Fisher information matrix depends on state variables. For parameters The partial derivatives. For the problem of estimating multi-source inertia parameters in a power system, it is assumed that the partial derivatives of all parameters are zero at the initial time (k=0), i.e.: By taking the partial derivatives of equation (9), we can obtain the partial derivatives. The following are the partial derivatives of equation (9). Recurrence relation for partial derivatives of the five parameters: right Partial derivatives: (44) right Partial derivatives: (45) right Partial derivatives: right In the differentiation, besides considering For coefficients In addition to coupling, the load power deviation was also considered. Power deviation component of load model containing inertia The differential equation (7) is discretized using the backward Euler method. This method has the characteristic of unconditional stability and is suitable for dynamic simulation of power systems. Further... Taking the partial derivative, we can obtain: (46) This method can solve the problem of linear correlation of multi-source inertia parameters in power systems. By introducing differentiated dynamic responses of load power deviation components, the identifiability of the parameters is guaranteed.
[0040] right The partial derivatives are similar to those described above. The partial derivative can be obtained by processing the partial derivative: (47) right Partial derivatives: (48) Based on equation (17) and the known partial derivatives of the five parameters, the fifth-order information matrix can be obtained as follows: (49) Optionally, the optimal estimated performance index of inertia and damping in the high-penetration power system of new energy in step S204 specifically includes: The variance of the CRLB lower bound unbiased estimator provides a theoretical lower bound for the estimation of each parameter, defined as the diagonal elements of the inverse of the information matrix. For the vector of parameters to be estimated... The lower bound of CRLB for each parameter can be calculated using the following formula: (50) The calculated results are the optimal estimation performance indices of the inertia and damping of the new power system dynamic model in equations (1)-(8) above. These indices indicate that the mean square error (MSE) of any unbiased estimation algorithm for the joint estimation of system inertia and damping must satisfy: (51) The CRLB lower bound is used as a quantization benchmark to evaluate the performance of various estimation algorithms. The system is based on frequency and power disturbance sequences measured by PMU, and estimates the inertia and damping parameters of each component through existing algorithms, and calculates the theoretical lower bound of CRLB under the current operating condition in real time by combining dynamic model and noise characteristics. The algorithm's performance is judged by comparing the mean squared error estimated by the algorithm with CRLB: If the difference between MSE and CRLB is less than the first preset value, the algorithm is judged to be stable. If the difference between MSE and CRLB is greater than or equal to the first preset value and lasts for more than the second preset value, an alert will be triggered.
[0041] The above content completes the construction of a new method for optimal estimation of inertia and damping performance indicators in power systems. In engineering practice, the system acquires the frequency and power disturbance sequences measured by the PMU in real time. On the one hand, it is input into the existing inertia and damping estimation algorithm for parameter estimation to obtain the estimated values of inertia and damping of various synchronous machines, new energy sources and loads. On the other hand, using the same data sequence, based on the dynamic model and noise statistical characteristics constructed in this invention, the CRLB theoretical lower bound of the estimated inertia and damping parameters under the current operating conditions is calculated in real time.
[0042] The system further compares the mean squared error (MSE) of the algorithm's estimation results with the real-time calculated CRLB and automatically diagnoses and monitors the system's performance status. If the algorithm's MSE is close to or reaches the CRLB, it indicates that the estimation algorithm has reached statistically optimal performance under the current operating conditions, and its estimation results are highly reliable. The system will provide a "superior algorithm performance" status signal, which schedulers can use for frequency stability assessment and control decisions, avoiding unnecessary resource investment in algorithm optimization. If the algorithm's MSE is consistently and significantly higher than the CRLB, the system will trigger a "performance warning" signal. This indicates that the current algorithm may not be fully utilizing measurement information, has model mismatch, or parameter drift. Maintenance personnel can use this warning to specifically check data quality, retrain the model, or switch to a backup estimation algorithm, thereby achieving a shift from "experience-based maintenance" to "precision maintenance."
[0043] Through this process, the CRLB provided by this invention is no longer an offline theoretical value, but a core evaluation module deeply embedded in the online monitoring system. It provides end-to-end technical support for power system inertia monitoring, from data input and algorithm evaluation to state diagnosis and operation and maintenance guidance. This achieves an effective transformation from theoretical limits to engineering evaluation, enabling dispatching departments to achieve precise operation and scientific management of the inertia monitoring system, and significantly improving the reliability and operational efficiency of frequency stability control in power grids with high penetration of new energy sources.
[0044] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.
[0045] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (Read-Only Memory). Memory includes ROM, magnetic tape, floppy disk, flash memory, optical storage, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).
[0046] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.
[0047] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0048] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A method for constructing evaluation indexes for the optimal estimation performance of inertia and damping in power systems, characterized in that, The method includes: S1. Construct a dynamic model of a power system with high penetration of new energy sources; S2. Construct the optimal estimated performance index based on the dynamic model of a power system with high penetration of new energy sources; The optimal estimation performance metrics constructed in S2 include: S201. Based on the forward Euler method, the dynamic model of the high-penetration power system of new energy is discretized to obtain the discretized observation model; S202. Based on the discretized observation model, measurement noise is added to establish a noisy discretized observation model; S203. Obtain the information matrix by combining maximum likelihood estimation; S204. Obtain the optimal estimated performance indicators of inertia and damping in a new energy high-penetration power system based on the information matrix.
2. The method for constructing evaluation indexes for the optimal estimation performance of power system inertia and damping according to claim 1, characterized in that, The construction of the dynamic model of the high-penetration power system of new energy in S1 includes: S101. Construct a dynamic model of the synchronous machine's inertia response; S102. Construct a dynamic model for the virtual inertia response of new energy sources; S103. Construct a dynamic load model; S104. Based on the linear superposition of the synchronous machine inertia response dynamic model, the new energy virtual inertia response dynamic model and the load dynamic model, a dynamic model of the new energy high-penetration power system is generated.
3. The method for constructing evaluation indexes for the optimal estimation performance of power system inertia and damping according to claim 2, characterized in that, The construction of the synchronous machine inertia response dynamic model in S101 specifically includes: The frequency dynamic response of the synchronous generator is described by the linear swing equation, and the dynamic model of the inertia response of the synchronous machine is obtained. (1) In the formula, The inertia of a synchronous motor; This is the difference between the current frequency and the rated frequency of the power grid. The damping coefficient; This represents the power disturbance at the current moment.
4. The method for constructing evaluation indexes for the optimal estimation performance of power system inertia and damping according to claim 2, characterized in that, The construction of the new energy virtual inertia response dynamic model in S102 specifically includes: By improving the control algorithm to simulate the dynamic characteristics of synchronous generators, two dynamic control models are generated: a grid-type control model and a grid-following control model. The grid-type control dynamic model regulates the system frequency by simulating the electromechanical transient characteristics of a synchronous generator. When a frequency deviation occurs in the system, the GFM inverter provides inertial support by releasing virtual rotor kinetic energy. The dynamic response of the GFM inverter is as follows: (2) In the formula, The virtual inertia of new energy represents the inverter's inertial response capability to frequency changes. This is a virtual damping coefficient, simulating the governor damping effect of a synchronous machine; This is the dynamic adjustment amount of the inverter's active power; The grid-based control dynamic model tracks the grid voltage phase through a phase-locked loop (PLL) and achieves fast power response through current source characteristics. Dynamic equations are constructed based on the dynamic coupling of the PLL's phase tracking delay and the power loop. (3) In the formula, The gain is controlled by the phase-locked loop.
5. The method for constructing evaluation indexes for the optimal estimation performance of power system inertia and damping according to claim 2, characterized in that, The load dynamic model in S103 specifically includes: A dynamic model of motor-type loads is constructed based on rotor rotational inertia. (4) A dynamic model of power electronic load is constructed based on the simulation of virtual inertia response using an active control strategy. (5) A dynamic model of constant impedance load is constructed based on the damping effect generated by the power-frequency coupling characteristics. (6) In the formula, This is the equivalent inertia of the electric motor; Equivalent inertia of power electronic loads; This is the damping coefficient of the electric motor, which originates from mechanical losses such as bearing friction and wind resistance. The equivalent damping for virtual inertia control; This is the equivalent damping for a constant impedance load. From (4) and (5), we can see that a load model containing inertia is constructed as follows: (7) In the formula, , , Therefore, the equivalent damping on the load side is: Equivalent inertia on the load side: .
6. The method for constructing evaluation indexes for the optimal estimation performance of power system inertia and damping according to claim 2, characterized in that, The generation of the dynamic model of the high-penetration power system of new energy in S104 specifically includes: (8) In the formula, This represents the total equivalent inertia of the system. For the total equivalent damping of the system, where Includes phase-locked loop control gain in mesh control This represents the total power disturbance on the power supply side. Total power disturbance on the load side.
7. The method for constructing evaluation indexes for the optimal estimation performance of power system inertia and damping according to claim 1, characterized in that, The discretized observation model obtained in S201 specifically includes: The dynamic model of a power system with high penetration of new energy sources is discretized using the forward Euler method. (9) In the formula: , Sampling time.
8. The method for constructing evaluation indexes for the optimal estimation performance of power system inertia and damping according to claim 1, characterized in that, S202, which establishes a noisy discrete observation model by adding measurement noise to the discrete observation model, specifically includes: set up The actual frequency deviation at the k-th sampling time is the measured value. It can be modeled as: (10) In the formula, the additional noise term It follows a Gaussian distribution with zero mean, and the total variance is... It is composed of the superposition of the independent contributions of noise from multiple types of equipment: ; in, This is synchronous machine noise; For virtual inertia device noise; This is load noise.
9. The method for constructing evaluation indexes for the optimal estimation performance of power system inertia and damping according to claim 1, characterized in that, The information matrix obtained in step S203 by combining maximum likelihood estimation specifically includes: S2031. Define the parameter vector to be estimated and establish a PMU discrete observation model containing multi-source Gaussian noise; S2032. Construct the joint likelihood function of the observation sequence, decompose it into a product of probabilities at each time step using the noise independence, and then take the logarithm to transform it into a summation form. S2033. Based on the definition of Fisher's information matrix, substitute the gradient and use the independent and identically distributed characteristics of noise to eliminate the cross terms, and finally obtain the form containing only the sum of the sensitivity matrix. S2034, Calculation based on equation (9) Partial derivatives of the five parameters; They were obtained respectively , , , as well as ; Construct the Fisher information matrix based on the partial derivatives of the five parameters: (11).
10. The method for constructing evaluation indexes for the optimal estimation performance of power system inertia and damping according to claim 9, characterized in that, The optimal estimated performance indicators of inertia and damping in a high-penetration power system of new energy sources, obtained in S204 based on the information matrix, specifically include: Calculate the lower bound of CRLB for the parameter vector to be estimated: (12) The optimal estimated performance indices of inertia and damping for the new power system dynamic model were obtained. in, (13) For information matrix, The mean square error of the unbiased estimation algorithm; The CRLB lower bound is used as a quantization benchmark to evaluate the performance of various estimation algorithms. The system is based on frequency and power disturbance sequences measured by PMU, and estimates the inertia and damping parameters of each component through existing algorithms, and calculates the theoretical lower bound of CRLB under the current operating condition in real time by combining dynamic model and noise characteristics. The algorithm's performance is judged by comparing the mean squared error estimated by the algorithm with CRLB: If the difference between MSE and CRLB is less than the first preset value, the algorithm is judged to be stable. If the difference between MSE and CRLB is greater than or equal to the first preset value and lasts for more than the second preset value, an alert will be triggered.