A method for evaluating inertia of power system under colored noise

Abstract

The application provides a power system inertia evaluation method under colored noise and belongs to the technical field of power system inertia evaluation. The technical scheme is as follows: S1, the basic principle of power system inertia estimation is derived first, and the difference equation of frequency deviation about power deviation is formed; S2, the state equation and the measurement equation of the improved adaptive filtering algorithm are constructed; S3, the improved adaptive filtering algorithm with an added exponential decay variable forgetting factor is used to solve the identification equation parameters; S4, the system node inertia is solved through the equation relationship between the identification parameters and the node equivalent inertia. The application has the beneficial effects that the improved adaptive filtering algorithm is introduced, the technical problem of low inertia evaluation precision under colored noise is solved, and the universality and accuracy of the inertia identification result are improved.

Description

Technical Field

[0001] This invention relates to the field of power system inertia assessment technology, and more particularly to a method for assessing power system inertia under colored noise. Background Technology

[0002] my country's power system is showing a trend of increasing integration of new energy sources and power electronic equipment such as DC transmission networks. The traditional AC network, built from conventional power sources like synchronous machines, is gradually evolving into a new type of power network with a high proportion of power electronic integration. As of December 2023, my country's installed solar power capacity was approximately 610 million kW, a year-on-year increase of 55.2%; wind power capacity was approximately 440 million kW, a year-on-year increase of 20.7%; new energy storage is developing rapidly, with over 30 million kW already in operation; the scale of inter-regional DC transmission reached 30 circuits, and the inter-regional and inter-provincial transmission capacity exceeded 300 million kW. While the integration of new energy sources and DC transmission has alleviated energy shortages and climate issues to some extent, its weak support for the power system poses a threat to the frequency security of the power system. Therefore, accurately assessing the current inertia of the power system and providing a reference for inertia control is of great significance for the safe and stable operation of my country's power grid in the future.

[0003] In engineering, the Kalman filter algorithm is widely used for identifying the equivalent inertia of power systems due to its high estimation accuracy and strong noise suppression. However, conventional Kalman filters are mostly applied in white noise environments. When the statistical characteristics of the measured noise change or the noise becomes colored, the identification results can be biased. Furthermore, as the scale of the measured data increases, data saturation weakens the corrective effect of new measured data on the identification results, affecting the identification accuracy. Therefore, conventional Kalman filters are difficult to use to accurately assess the inertia of power systems under different noise environments.

[0004] How to solve the above-mentioned technical problems is the challenge facing this invention. Summary of the Invention

[0005] The technical problem solved by this invention is to address the low accuracy of conventional power system inertia assessment methods under colored noise environments. This invention assesses power system inertia, quantifies the stability of the power system, and expands the application scenarios of inertia assessment methods. The invention relates to the derivation of power system inertia, the derivation of difference equations, the establishment of state equations and measurement equations, the prediction and updating of estimated parameters, the estimation of noise statistical characteristics, and the solution of nodal inertia. This invention improves the accuracy of inertia identification results by introducing a forgetting factor into an improved adaptive filtering algorithm, thus solving the technical problem of biased nodal equivalent inertia estimation results under varying noise statistical characteristics or colored noise.

[0006] To achieve the above-mentioned objectives, the present invention employs the following technical solution: a method for evaluating the inertia of a power system under colored noise, comprising the following steps:

[0007] Step 1: Derive the basic principle of power system inertia estimation. The changes in power and frequency of each node are collected by the synchronous phasor measurement unit (PMU) as input and output. The difference equation representing the dynamic relationship between input and output is established by combining the forward Euler method, and the equivalent relationship between the parameter to be estimated and the node inertia is determined.

[0008] Step 2: Construct the state equation and measurement equation of the Kalman filter algorithm based on the difference equation, and use the improved adaptive filtering algorithm to identify the unknown parameters in the state equation and measurement equation;

[0009] Step 3: Based on the equivalence relationship between the parameters to be estimated and the equivalent inertia of the system, solve for the nodal inertia of the system.

[0010] Furthermore, in step 1, the basic principle of estimating the inertia of a power system is derived, and the specific method includes the following steps:

[0011] 1) Inertia of the power system

[0012]

[0013] In the formula: E k ω represents the kinetic energy stored in the rotor of a single synchronous generator; H is the inertial time constant of a single synchronous generator; n S is the rated angular velocity of the generator rotor; J is the moment of inertia; S N H is the rated capacity of the generator. sys E is the system's inertial time constant. rsg E ssg E load These are the rotational kinetic energy stored in the synchronous generator, the energy provided by the virtual inertia control of the new energy unit, and the energy provided by the load inertia response, respectively; S sys This refers to the overall capacity of the system.

[0014] Equation (1) defines the kinetic energy stored in the rotor of a single synchronous generator and its inertial time constant; Equation (2) comprehensively considers the contributions of synchronous machine inertia, new energy unit inertia and load-side inertia to the power system inertia.

[0015] 2) Inertia Response and Evaluation Principles

[0016]

[0017] 2H sys sΔf(s)=-ΔP e(s)-DΔf(s) (4)

[0018]

[0019]

[0020] In the formula: P is the rate of change of frequency. m P represents mechanical power. e Δp is electromagnetic power; D is damping coefficient; Δf is frequency change; ΔP e For power deviation data; T s The sampling period; Let be the measurement matrix for the k-th iteration; θ is the parameter to be estimated.

[0021] Equation (3) describes the swing equation of the inertial response process of a power system under the action of unbalanced power after being disturbed; Equation (4) represents a variation of Equation (3) under small disturbance conditions, i.e., when the mechanical power remains constant; Equation (5) is the system difference equation obtained by the forward Euler method based on Equation (4); Equation (6) is the matrix form of the difference equation obtained based on Equation (5). Equation (7) is defined based on Equation (6), with the upper equation defining the measurement matrix and the lower matrix defining the parameter to be estimated; Equation (8) is the equivalence relationship between nodal inertia and the parameter to be estimated, and the system inertia can be obtained through Equation (8).

[0022] Furthermore, in step 2, the state equation and measurement equation of the Kalman filter algorithm are constructed based on the difference equation. The specific method includes the following steps:

[0023] 1) Constructing the state equation and measurement equation

[0024]

[0025] θ k+1 =A k+1 θ k +w k+1 (10)

[0026]

[0027] In the formula: the frequency deviation Δf(k+1) obtained in the (k+1)th iteration is simplified to Δf k+1 The same applies to other vectors or matrices that require iteration; v k+1 The system measurement noise at time k+1; A k+1 The state update matrix at time k+1; w k+1 Let be the system noise at time k+1.

[0028] Equation (10) is the measurement equation of the Kalman filter; Equation (11) is the measurement equation and state equation of the Kalman filter. Since the parameters to be estimated hardly change under small perturbations, the state update matrix is ​​set to A. k+1 For the identity matrix I.

[0029] 2) Improved adaptive filtering algorithm

[0030]

[0031]

[0032] In the formula: Let C be the innovation; C is the covariance matrix of the innovation; R is the new information. k denoted as , where is the measurement noise covariance matrix; K is the filter gain; P is the estimation error covariance matrix; α is the weighting coefficient; and b is the forgetting factor. This is an estimate of the innovation covariance; N is the innovation window size; Let θ be the estimated value of the parameter to be estimated; I is the identity matrix.

[0033] Equation (12) defines the new information Equation (13) defines the new information covariance C k Equation (14) defines the filter gain K. k+1 The form of the information reveals new information. covariance C k The term is the denominator of the filter gain; Equation (15) defines the weighting coefficient α. i Equation (16) represents the weighting coefficient α. i The equivalence relationship between the forgetting factor b; Equation (17) represents the relationship between the information covariance C and the forgetting factor b when the prior statistical properties of the noise are unknown. k The estimate; Equation (18) represents replacing the denominator term in Equation (14) with an estimate of the new information covariance. Equation (19) is a correction to the estimated parameters and the covariance matrix of the estimation error. The estimated parameters at time k can be obtained through this equation.

[0034] 3) Algorithm Summary

[0035]

[0036] Equation (21) is the recursive formula of the improved adaptive filtering algorithm obtained by induction.

[0037] Furthermore, in step 3, the equivalence relationship between the parameter to be estimated and the equivalent inertia of the system is as follows, and the specific method includes the following steps:

[0038]

[0039] In the formula: H sys For nodal inertia; T s The sampling period is given. After obtaining the parameter θ1 to be estimated in equation (7), the estimated value of the inertial time constant can be obtained according to equation (22).

[0040] Equation (22) describes the equivalent relationship between the parameter to be estimated and the nodal inertia.

[0041] The present invention proposes a power system inertia assessment method with variable forgetting factor recursive least squares. The assessment target is Equation (19). The inertia of the power system is derived by Equations (1) to (2). The inertia response and assessment principle are Equations (3) to (8). The state equation and measurement equation for parameter identification are constructed by Equations (9) to (11). The improved adaptive filtering algorithm is Equations (12) to (21). The solution of nodal inertia is Equation (22).

[0042] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0043] 1. This invention proposes a method for evaluating the inertia of a power system under colored noise. Due to the complex statistical characteristics of colored noise, it is difficult to directly measure these characteristics using measuring elements before testing. By using an estimated value of the measured noise statistical characteristics to replace the true value, the most accurate estimate of the target parameter can be obtained. State equations and measurement equations for the filtering method are established to estimate the statistical characteristics of colored noise in the measured data. The estimated value is then corrected using the filtering gain, thus completing the estimation of the power system inertia under the influence of colored noise.

[0044] 2. The method of this invention utilizes real-time estimation of noise statistical characteristics to track these characteristics, enabling accurate assessment of power system inertia as noise statistical characteristics change. Finally, a simulation example is completed using this invention to verify its effectiveness and accuracy, achieving precise assessment of power system inertia under colored noise, improving the accuracy of inertia assessment, and expanding the application scenarios of the method.

[0045] 2. This invention introduces a forgetting factor into the algorithm. As the scale of measurement data increases, colored noise gradually accumulates during the recursive estimation process, affecting the correction effect of new data on the estimated value, leading to data saturation and thus reducing the evaluation accuracy. Introducing a forgetting factor can suppress the data saturation problem, enhance the correction effect of new information on the estimated value, and improve the accuracy of inertia evaluation. By introducing the forgetting factor into the estimation process of the statistical characteristics of measurement noise, the correction effect of new data in the estimation process is enhanced in a weighted manner, effectively suppressing data saturation and improving the accuracy of inertia evaluation. Attached Figure Description

[0046] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0047] Figure 1 This is an overall flowchart of the method of the present invention.

[0048] Figure 2 This is a diagram of the IEEE 30-node model in this invention.

[0049] Figure 3 This is a schematic diagram illustrating the evaluation results of the generator set under colored noise in this invention.

[0050] Figure 4 This is a schematic diagram illustrating the error in evaluating the node inertia of the generator set under different noise environments in this invention.

[0051] Figure 5 This is a schematic diagram illustrating the error in evaluating the node inertia of a generator set when the statistical characteristics of the measured noise change in this invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0053] Example 1

[0054] like Figure 1 As shown, this embodiment provides a method for evaluating the inertia of a power system under colored noise, including the following steps:

[0055] Step 1: Derive the basic principle of power system inertia estimation. The changes in power and frequency of each node are collected by the synchronous phasor measurement unit as input and output. The difference equation representing the dynamic relationship between input and output is established by combining the forward Euler method, and the equivalent relationship between the parameter to be estimated and the node inertia is determined.

[0056] Step 2: Construct the state equation and measurement equation of the Kalman filter algorithm based on the difference equation, and use the improved adaptive filtering algorithm to identify the unknown parameters in the state equation and measurement equation;

[0057] Step 3: Based on the equivalence relationship between the parameters to be estimated and the equivalent inertia of the system, solve for the nodal inertia of the system.

[0058] Specifically, in step 1, the basic principle of estimating the inertia of a power system is derived, and the specific method includes the following steps:

[0059] 1) Inertia of the power system

[0060]

[0061] In the formula: E k ω represents the kinetic energy stored in the rotor of a single synchronous generator; H is the inertial time constant of a single synchronous generator; n S is the rated angular velocity of the generator rotor; J is the moment of inertia; S N H is the rated capacity of the generator. sys E is the system's inertial time constant. rsg E ssg E load These are the rotational kinetic energy stored in the synchronous generator, the energy provided by the virtual inertia control of the new energy unit, and the energy provided by the load inertia response, respectively; S sys This refers to the overall capacity of the system.

[0062] Equation (1) defines the kinetic energy stored in the rotor of a single synchronous generator and its inertial time constant; Equation (2) comprehensively considers the contributions of synchronous machine inertia, new energy unit inertia and load-side inertia to the power system inertia.

[0063] 2) Inertia Response and Evaluation Principles

[0064]

[0065] 2H sys sΔf(s)=-ΔP e (s)-DΔf(s) (4)

[0066]

[0067] In the formula: P is the rate of change of frequency. m P represents mechanical power. e Δp is electromagnetic power; D is damping coefficient; Δf is frequency change; ΔP e For power deviation data; T s The sampling period; Let be the measurement matrix for the k-th iteration; θ is the parameter to be estimated.

[0068] Equation (3) describes the swing equation of the inertial response process of a power system under the action of unbalanced power after being disturbed; Equation (4) represents a variation of Equation (3) under small disturbance conditions, i.e., when the mechanical power remains constant; Equation (5) is the system difference equation obtained by the forward Euler method based on Equation (4); Equation (6) is the matrix form of the difference equation obtained based on Equation (5). Equation (7) is defined based on Equation (6), with the upper equation defining the measurement matrix and the lower matrix defining the parameter to be estimated; Equation (8) is the equivalence relationship between nodal inertia and the parameter to be estimated, and the system inertia can be obtained through Equation (8).

[0069] Specifically, in step 2, the state equation and measurement equation of the Kalman filter algorithm are constructed based on the difference equation. The specific method includes the following steps:

[0070] 1) Constructing the state equation and measurement equation

[0071]

[0072] θ k+1 =A k+1 θ k +w k+1 (10)

[0073]

[0074] In the formula: the frequency deviation Δf(k+1) obtained in the (k+1)th iteration is simplified to Δf k+1 The same applies to other vectors or matrices that require iteration; v k+1 The system measurement noise at time k+1; A k+1 The state update matrix at time k+1; w k+1 Let be the system noise at time k+1.

[0075] Equation (10) is the measurement equation of the Kalman filter; Equation (11) is the measurement equation and state equation of the Kalman filter. Since the parameters to be estimated hardly change under small perturbations, the state update matrix is ​​set to A. k+1 For the identity matrix I.

[0076] 2) Improved adaptive filtering algorithm

[0077]

[0078] In the formula: Let C be the innovation; C is the covariance matrix of the innovation; R is the new information. k denoted as , where is the measurement noise covariance matrix; K is the filter gain; P is the estimation error covariance matrix; α is the weighting coefficient; and b is the forgetting factor. This is an estimate of the innovation covariance; N is the innovation window size; Let θ be the estimated value of the parameter to be estimated; I is the identity matrix.

[0079] Equation (12) defines the new information Equation (13) defines the new information covariance C k Equation (14) defines the filter gain K. k+1 The form of the information reveals new information. covariance C k The term is the denominator of the filter gain; Equation (15) defines the weighting coefficient α. iEquation (16) represents the weighting coefficient α. i The equivalence relationship between the forgetting factor b; Equation (17) represents the relationship between the information covariance C and the forgetting factor b when the prior statistical properties of the noise are unknown. k The estimate; Equation (18) represents replacing the denominator term in Equation (14) with an estimate of the new information covariance. Equation (19) is a correction to the estimated parameters and the covariance matrix of the estimation error. The estimated parameters at time k can be obtained through this equation.

[0080] 3) Algorithm Summary

[0081]

[0082] Equation (21) is the recursive formula of the improved adaptive filtering algorithm obtained by induction.

[0083] Specifically, in step 3, the equivalence relationship between the parameter to be estimated and the equivalent inertia of the system is as follows, and the specific method includes the following steps:

[0084]

[0085] In the formula: H sys For nodal inertia; T s The sampling period is given. After obtaining the parameter θ1 to be estimated in equation (7), the estimated value of the inertial time constant can be obtained according to equation (22).

[0086] Equation (22) describes the equivalent relationship between the parameter to be estimated and the nodal inertia.

[0087] The present invention proposes a power system inertia assessment method with variable forgetting factor recursive least squares. The assessment target is Equation (19). The inertia of the power system is derived by Equations (1) to (2). The inertia response and assessment principle are Equations (3) to (8). The state equation and measurement equation for parameter identification are constructed by Equations (9) to (11). The improved adaptive filtering algorithm is Equations (12) to (21). The solution of nodal inertia is Equation (22).

[0088] To verify the reliability and accuracy of the power system inertia assessment method proposed in this invention, the following methods were employed: Figure 2 The IEEE 12-machine, 30-node system shown is used for deployment verification. This system includes 12 generators, with node 1 being the balancing node. The generators connected to this node typically have large inertia settings and do not require identification. The simulation parameters for each generator are shown in Table 1.

[0089] Table 1 Generator Parameters

[0090]

[0091]

[0092] Figure 3 The inertia evaluation results for each generator under colored noise are presented. The inertia evaluation is performed using the improved adaptive Kalman filter method (IAKF) considering colored noise proposed in this invention.

[0093] Table 2 and Figure 4 The evaluation results of the generator G2 inertia set under different noise environments are presented. It can be seen that under noise-free conditions, the estimation error of the method of this invention is generally below 2%, with a minimum of 0.0092% (G3); when the noise condition is zero-mean white noise, the evaluation error of each generator is also generally below 2%, with a minimum of 0.0972% (G3); when the noise condition is colored noise, the evaluation error of each generator is generally below 2%, with a minimum of 0.1304% (G8). It can be seen that the evaluation results obtained using the method of this invention are basically similar under different noise environments, and the evaluation accuracy is not affected by changes in the noise environment, further verifying the superiority of the proposed algorithm.

[0094] Table 2. Evaluation results of generator inertia under different noise environments.

[0095]

[0096] From Table 2 and Figure 4 It can be seen that the IAKF algorithm proposed in this invention can accurately assess the inertia of each generator, with the overall error controlled within 2%. The largest error is 7.4% (G31), and the smallest error is only 0.88% (G30), demonstrating the effectiveness of the proposed identification algorithm.

[0097] Table 3. Inertia Assessment Results When the Statistical Characteristics of Measurement Noise Change

[0098]

[0099] Table 3 and Figure 5 It can be seen that when the statistical characteristics of the measurement noise change, the evaluation error of the method of this invention can be controlled within 3%, with the lowest evaluation error being 0.63% (G5). Therefore, when using the proposed algorithm for identification, changes in the statistical characteristics of the measurement noise have almost no impact on the evaluation results. This verifies the accuracy and stability of the IAKF-based evaluation method.

[0100] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for evaluating the inertia of a power system under colored noise, characterized in that, Includes the following steps: Step 1: Derive the basic principle of power system inertia estimation. Collect the power and frequency deviations of each node as input and output through the synchronous phasor measurement unit, and form a difference equation of frequency deviation with respect to power deviation. Step 2: Establish the state equation and measurement equation representing the relationship between the parameters to be estimated and the frequency deviation and power deviation data; In step 2, the state equation and measurement equation are determined as follows: Constructing the state equation and measurement equation of the adaptive filtering algorithm (7) ； (8) ； In the formula: This is the measurement matrix at time k+1; The parameters to be estimated at time k+1; This is the state update matrix at time k+1; The measurement noise at time k+1; The system noise at time k+1; Step 3: Identify the parameters to be estimated using an improved adaptive filtering algorithm; In step 3, the improved adaptive filtering algorithm includes the following steps: 31) Prediction and Correction of Adaptive Filtering Algorithms (13)； (14)； (15)； (16)； (17)； In the formula: The unknown parameters are obtained from the (k-1)th correction; For the unknown parameters in the k-th prediction; the estimated value of the unknown parameters; This is the error covariance matrix obtained after the (k-1)th correction; Let be the error covariance matrix of the (k-1)th prediction; This is the new information for the k-th revision; This is the denominator term for the filter gain; The covariance matrix of the measurement noise; Let k be the filter gain for the kth correction; 32) Estimation of the statistical characteristics of noise (21)； In the formula: This is for estimating the denominator term of the filter gain; 33) Introduction of the forgetting factor (22)； (23)； (24)； In the formula: d is the weighting coefficient; d is the coefficient related to b. The forgetting factor is N; the information window size is N. Step 4: Further solve for the system nodal inertia by using the equation relationship between the parameters to be estimated and the equivalent inertia of the power system.

2. The method for evaluating the inertia of a power system under colored noise according to claim 1, characterized in that, Step 1, which involves estimating the power system inertia and constructing the difference equations, includes the following steps: 11) Inertia of the power system (1)； (2)； In the formula: H represents the kinetic energy stored in the rotor of a single synchronous generator; H is the inertial time constant of a single synchronous generator. This is the rated angular velocity of the generator rotor; It is the moment of inertia; This refers to the rated capacity of the generator; The system's inertial time constant; , , These are the rotational kinetic energy stored in the synchronous generator, the energy provided by the virtual inertia control of the new energy unit, and the energy provided by the load inertia response, respectively. For the overall capacity of the system; 12) Inertia Response and Evaluation (3)； (4)； (5)； (6)； In the formula: The rate of change of frequency; Mechanical power; Electromagnetic power; The damping coefficient; It is the change in frequency; Power deviation; The sampling period.

3. The method for evaluating the inertia of a power system under colored noise according to claim 1, characterized in that, In step 4, the equation relating the identification parameters to the nodal equivalent inertia is as follows: (24)； (25)； In estimate Then, the estimated value of the inertial time constant is obtained according to equation (25).

Images