An inertia evaluation method for power system based on electromechanical response characteristics

Abstract

The present application relates to the technical field of inertia evaluation of power system based on electromechanical response characteristics, and particularly relates to a method for evaluating inertia of power system based on electromechanical response characteristics. The method comprises the following steps: extracting tie-line power and bus frequency data under steady-state operation of the power system by using a sliding data window method, and converting the data into equivalent electromechanical power and speed signals of the region; extracting electromechanical response characteristics, and extracting the electromechanical response characteristics by using a stochastic subspace algorithm; evaluating regional inertia, and evaluating the effective inertia of the system region according to the coupling relationship between the electromechanical response characteristics and the system inertia derived from the foregoing theory. The present application is mainly applied to power system stability analysis and control, has good recognition accuracy and practicability, and can effectively guide safe and stable operation of the power system according to the actual operation characteristics of the power system to obtain the equivalent inertia of the regional power grid.

Description

Technical Field

[0001] This invention relates to the field of power system stability analysis and control technology, specifically a power system inertia assessment method based on electromechanical response characteristics. Background Technology

[0002] In recent years, with the continuous development of new power systems, a large number of new energy power generation technologies will gradually replace traditional power generation technologies. The deployment of numerous new energy technologies will be accompanied by a significant influx of power electronics technologies, which will have new impacts on power systems, particularly regarding low inertia and low damping. Low inertia and low damping reduce the system's anti-interference capability and significantly affect the stable operation of the power system; therefore, assessing the system's inertia is necessary. In power systems with new energy integration, inertia assessment has become a crucial part of power system operation, enabling the determination of safe system operation and the rational optimization and allocation of inertia support resources. Therefore, accurately assessing system inertia is both important and challenging. The rapid development of wide-area measurement technology allows for relatively convenient acquisition of parameters in the power system, including generator power parameters and speed parameters, further providing a basis for system evaluation through system model identification. However, this method has certain limitations. Time-domain measurement data may be contaminated, potentially including noise, system electromechanical oscillations, and other nonlinear variables. This contamination reduces data accuracy and further contributes to calculation errors. Therefore, evaluating system inertia based on electromechanical modes in the frequency domain yields better results. The electromechanical characteristics of random signals are extracted using the random subspace method to evaluate inertia. However, this method requires calculating the equivalent reactance of the power system, adding an extra computational burden.

[0003] In summary, there is a need in the existing technology for an evaluation method for power system quantities to improve identification accuracy and practicality.

[0004] Application content

[0005] The technical problem to be solved by this invention is to propose a data-driven method for evaluating the effective inertia of a region, which uses a threshold method to avoid numerical singularities and has good identification accuracy and practicality.

[0006] Based on the above, this invention proposes an inertia assessment method based on the electromechanical response characteristics of a power system. This application does not use a system identification model, but instead uses a mathematical model for inertia assessment that establishes the coupling relationship between electromechanical response characteristics and system inertia. Based on this, the electromechanical characteristics of the system are extracted using a stochastic subspace algorithm. After converting the measurement data into regional equivalent data, the stochastic subspace algorithm can be used to extract the electromechanical response characteristics using a data-driven approach. The effective inertia of the region can then be calculated using the inertia assessment model. The specific steps of this invention are as follows: A power system inertia assessment method based on electromechanical response characteristics includes the following steps:

[0007] Step 1: Use the sliding data window method to extract tie line power and bus frequency data under steady-state operation of the power system, and convert them into equivalent machine electromagnetic power and speed signals for the region;

[0008] Step 2: Extract electromechanical response features. The electromechanical response features are extracted using the random subspace algorithm.

[0009] Step 3: Regional inertia assessment. Based on the coupling relationship between the electromechanical response characteristics and system inertia derived from the aforementioned theory, the effective regional inertia of the system is assessed.

[0010] Preferably, step 1: The sliding data window method is used to extract tie-line power and bus frequency data under steady-state operation of the power system, and converts them into equivalent machine electromagnetic power and speed signals for the region. This specifically includes the following steps:

[0011] Analysis of the coupling relationship between electromechanical response characteristics and system inertia: In a power system, a subsystem can be equivalent to a generator. The dynamic model of the generator includes the generator inertial constant M, the generator damping coefficient D, and P. e Electromagnetic power, P m The swing equation for parameters such as mechanical power and generator rotor speed ω during the disturbance is as follows:

[0012]

[0013] For speed controllers, which cannot respond instantaneously, a certain delay is required during operation (P). m It can be considered a constant; the linearized expression of the rocking equation is obtained as follows:

[0014]

[0015] Where, k s δ is the synchronization coefficient, and δ is the power angle.

[0016] Based on equations (1) and (2), and by linearizing the rocking equation, we can obtain:

[0017]

[0018] Modal analysis theory shows that solving the characteristic equation yields a pair of conjugate complex roots. The real part of these eigenvalues ​​contains information about the damping ratio in the electromechanical oscillation mode, while the imaginary part contains information about the oscillation frequency.

[0019]

[0020] Preferably, based on equation (4), by eliminating D using the relationship between the damping ratio and the eigenvalue, the relationship between frequency and inertial constant can be obtained, i.e., the analytical expression of inertia based on the electromechanical response characteristics:

[0021]

[0022] The electromechanical dynamic response process can be obtained through wide-area measurement techniques, including ΔP. e Electromagnetic power and Δω e Rotational speed signal; however, during the inertia assessment of the system, the inertia constant may be negative. To avoid this unreasonable situation, a threshold method is used to ensure that the estimated inertia remains at its current value when the denominator is zero:

[0023]

[0024] Where Δt is the sampling time, and ε0 is an empirical positive threshold to avoid numerical problems, usually set according to the standard deviation of RoCoF.

[0025] Preferably, step 2: Extracting electromechanical response features. The electromechanical response features are extracted using a random subspace algorithm, specifically including the following steps: To extract the electromechanical response features of the power system, a random subspace method is used. The discretely sampled system state-space equation, considering noise, is as follows:

[0026] x k+1 =Ax k +w i

[0027] y k =Cx k +e i (7)

[0028] Where x represents the system state quantity; x represents the measured output quantity; w i Indicates process noise; e i Denotes the observation noise, and satisfies E(w) i )=E(e i ) = 0; A represents the state matrix, and C represents the output matrix.

[0029] Preferably, the extended Hankel matrix blocks representing future data are projected onto the extended Hankel matrix representing past data:

[0030] O i =Y f / Y p (8

[0031] Based on equation (8) for (O) i Perform singular value decomposition:

[0032]

[0033] in, T is the translation matrix. This is the Kalman filter state sequence matrix of the positive time series. Substitute the Kalman filter state sequence matrix and the output into the system's state equations:

[0034]

[0035] Among them (O) + ) represents the pseudo-inverse, and the state matrix A of the continuous system is calculated using equation (10). c And perform eigenvalue decomposition on it;

[0036]

[0037] Where: Λ=diag(λ) i ), where λ i Let be the eigenvalue of the i-th mode.

[0038] Preferably, step 3: Regional inertia assessment; based on the coupling relationship between the electromechanical response characteristics and system inertia derived from the aforementioned theory, and by assessing the effective regional inertia of the system, specifically including the following steps:

[0039] After a power system experiences a disturbance, the system can be partitioned based on the coherence of each generator. Each partition can then be represented by a single generator, and the equivalent electromagnetic power of the generator in each region can be calculated as the electromagnetic power P of the m interconnecting lines within the interval. eq The sum of:

[0040]

[0041] The rotational speed of the isobaric machine in each region can be represented by the regional center frequency:

[0042]

[0043] Where: Δf i χ is the frequency of the regional power grid bus. iThe weighting coefficient is defined in the paper as the reciprocal of the variance of the bus frequency.

[0044] Beneficial effects

[0045] This data-driven method for assessing effective regional inertia derives an inertia assessment model based on electromechanical response characteristics. By analyzing the coupling relationship between electromechanical response features and system inertia in the frequency domain, it further derives the inertia assessment model based on electromechanical response features. The threshold method effectively avoids cases where the inertial constant is negative. This invention exhibits good identification accuracy and engineering practicality. Based on the frequency domain perspective, this invention provides a new stenographic method for assessing system inertia using electromechanical response feature extraction. This invention does not require system model identification and can extract electromechanical features through a random subspace algorithm. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in this invention or the prior art, the accompanying drawings involved in the embodiments or the prior art are briefly described below. Obviously, these drawings illustrate several embodiments of the present invention, and those skilled in the art can derive other possible drawings based on these drawings without creative effort. The purpose of the drawings is limited to illustrating specific embodiments and does not limit the scope of the present invention.

[0047] Figure 1 It is the rotational speed signal of a single-machine infinite bus system;

[0048] Figure 2 It is the power signal of a single-machine infinite bus system;

[0049] Figure 3 This is a diagram of the IEEE 4-machine, 2-area system architecture. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0051] A power system inertia assessment method based on electromechanical response characteristics includes the following steps: Step 1: Extract tie-line power and bus frequency data under steady-state operation of the power system using the sliding data window method, and convert them into equivalent machine electromagnetic power and speed signals for the region;

[0052] Step 2: Extract electromechanical response features. The electromechanical response features are extracted using the random subspace algorithm.

[0053] Step 3: Regional inertia assessment. Based on the coupling relationship between the electromechanical response characteristics and system inertia derived from the aforementioned theory, the effective regional inertia of the system is assessed.

[0054] Preferably, step 1: The sliding data window method is used to extract tie-line power and bus frequency data under steady-state operation of the power system, and converts them into equivalent machine electromagnetic power and speed signals for the region. This specifically includes the following steps:

[0055] Analysis of the coupling relationship between electromechanical response characteristics and system inertia: In a power system, a subsystem can be equivalent to a generator. The dynamic model of the generator includes the generator inertial constant M, the generator damping coefficient D, and P. e Electromagnetic power, P m The swing equation for parameters such as mechanical power and generator rotor speed ω during the disturbance is as follows:

[0056]

[0057] For speed controllers, which cannot respond instantaneously, a certain delay is required during operation (P). m It can be considered a constant; the linearized expression of the rocking equation is obtained as follows:

[0058]

[0059] Where, k s δ is the synchronization coefficient, and δ is the power angle.

[0060] Based on equations (1) and (2), and by linearizing the rocking equation, we can obtain:

[0061]

[0062] Modal analysis theory shows that solving the characteristic equation yields a pair of conjugate complex roots. The real part of these eigenvalues ​​contains information about the damping ratio in the electromechanical oscillation mode, while the imaginary part contains information about the oscillation frequency.

[0063]

[0064] Preferably, based on equation (4), by eliminating D using the relationship between the damping ratio and the eigenvalue, the relationship between frequency and inertial constant can be obtained, i.e., the analytical expression of inertia based on the electromechanical response characteristics:

[0065]

[0066] The electromechanical dynamic response process can be obtained through wide-area measurement techniques, including ΔP. e Electromagnetic power and Δω eRotational speed signal; however, during the inertia assessment of the system, the inertia constant may be negative. To avoid this unreasonable situation, a threshold method is used to ensure that the estimated inertia remains at its current value when the denominator is zero:

[0067]

[0068] Where Δt is the sampling time, and ε0 is an empirical positive threshold to avoid numerical problems, usually set according to the standard deviation of RoCoF.

[0069] Preferably, step 2: Extracting electromechanical response features. The electromechanical response features are extracted using a random subspace algorithm, specifically including the following steps: To extract the electromechanical response features of the power system, a random subspace method is used. The discretely sampled system state-space equation, considering noise, is as follows:

[0070] x k+1 =Ax k +w i

[0071] y k =Cx k +e i (7)

[0072] Where x represents the system state quantity; x represents the measured output quantity; w i Indicates process noise; e i Denotes the observation noise, and satisfies E(w) i )=E(e i ) = 0; A represents the state matrix, and C represents the output matrix.

[0073] Preferably, the extended Hankel matrix blocks representing future data are projected onto the extended Hankel matrix representing past data:

[0074] O i =Y f / Y p (8

[0075] Based on equation (8) for (O) i Perform singular value decomposition:

[0076]

[0077] in, T is the translation matrix. This is the Kalman filter state sequence matrix of the positive time series. Substitute the Kalman filter state sequence matrix and the output into the system's state equations:

[0078]

[0079] Among them (O) + ) represents the pseudo-inverse, and the state matrix A of the continuous system is calculated using equation (10). c And perform eigenvalue decomposition on it;

[0080]

[0081] Where: Λ=diag(λ) i ), where λ i Let be the eigenvalue of the i-th mode.

[0082] Preferably, step 3: Regional inertia assessment; based on the coupling relationship between the electromechanical response characteristics and system inertia derived from the aforementioned theory, and by assessing the effective regional inertia of the system, specifically including the following steps:

[0083] After a power system experiences a disturbance, the system can be partitioned based on the coherence of each generator. Each partition can then be represented by a single generator, and the equivalent electromagnetic power of the generator in each region can be calculated as the electromagnetic power P of the m interconnecting lines within the interval. eq The sum of:

[0084]

[0085] The rotational speed of the isobaric machine in each region can be represented by the regional center frequency:

[0086]

[0087] Where: Δf i χ is the frequency of the regional power grid bus. i The weighting coefficients are defined in the paper as the reciprocal of the variance of the bus frequency.

[0088] The technical solution of this invention will be further explained in detail below through implementation examples and data analysis. This section verifies and analyzes the results using examples of a single-machine infinite bus system and an IEEE 4-machine 2-zone system. The examples are simulated using Digsilent software. Scenario A: By setting a three-phase short-circuit fault at 0.02s and clearing the fault after 0.05s, the transient signal is extracted by the PMU for the single-machine infinite bus system, which includes... Figure 1 Speed ​​signal and Figure 2 The power signal. The electromechanical response characteristics of the single-machine infinite bus system were extracted using the random subspace algorithm in this invention. The identification result was -2.272. The identification result and measurement data were substituted into the inertia evaluation model, and the calculation results are shown in Table 1.

[0089] Table 1. Inertia assessment results at different times

[0090]

[0091] Table 1 shows the inertia assessment results at different times. As can be seen from Table 1, the method in this paper is close to the true value, with a maximum error of 9.93% and an absolute error of 0.5s, verifying the effectiveness of the method.

[0092] Scenario B: such as Figure 3 As shown, a three-phase short circuit with a current of 0.02 seconds was set at bus 4 and cut off at 0.05 seconds. The inertia evaluation method of the present invention was used, and the results are shown in Table 2.

[0093] Table 2. Regional inertia assessment results based on different assessment methods

[0094]

[0095] According to Table 2, the proposed method has relatively good computational results. This is because the proposed method uses a Hankel matrix with twice the amount of data compared to the DMD algorithm. By utilizing orthogonal projection, it can filter out noise components in the measurement signal and has more accurate identification capabilities.

[0096] Those skilled in the art should understand that the above embodiments are merely illustrative of the content of this disclosure and do not limit its scope. The system capacity, voltage, line parameters, etc., shown may vary depending on the specific circumstances of the power electronic grid-connected generator set and its grid connection. Based on this disclosure, those skilled in the art can make other changes or adjustments, and these changes still fall within the scope of this disclosure.

Claims

1. A method for evaluating the inertia of a power system based on electromechanical response characteristics, characterized in that, Includes the following steps: Step 1: Use the sliding data window method to extract tie line power and bus frequency data under steady-state operation of the power system, and convert them into equivalent machine electromagnetic power and speed signals for the region; Step 2: Extract electromechanical response features. The electromechanical response features are extracted using the random subspace algorithm. Step 3: Regional inertia assessment. Based on the coupling relationship between the electromechanical response characteristics and system inertia derived from the aforementioned theory, the effective regional inertia of the system is assessed.

2. The power system inertia assessment method based on electromechanical response characteristics according to claim 1, characterized in that, Step 1: Extract tie-line power and bus frequency data under steady-state operation of the power system using the sliding data window method, and convert them into equivalent electromagnetic power and speed signals for the region. This includes the following steps: Analysis of the coupling relationship between electromechanical response characteristics and system inertia: In a power system, a subsystem can be equivalent to a generator. The dynamic model of the generator includes the generator inertial constant M, the generator damping coefficient D, and P. e Electromagnetic power, P m The swing equation for parameters such as mechanical power and generator rotor speed ω during the disturbance is as follows: For speed controllers, which cannot respond instantaneously, a certain delay is required during operation (P). m It can be considered a constant; the linearized expression of the rocking equation is obtained as follows: Where, k s δ is the synchronization coefficient, and δ is the power angle.

3. The power system inertia assessment method based on electromechanical response characteristics according to claim 2, characterized in that, It also includes the following steps: Based on equations (1) and (2), and by linearizing the rocking equation, we can obtain: Modal analysis theory shows that solving the characteristic equation yields a pair of conjugate complex roots. The real part of these eigenvalues ​​contains information about the damping ratio in the electromechanical oscillation mode, while the imaginary part contains information about the oscillation frequency.

4. The power system inertia assessment method based on electromechanical response characteristics according to claim 3, characterized in that, Also includes: Based on equation (4), by eliminating D using the relationship between the damping ratio and the eigenvalue, the relationship between frequency and inertial constant can be obtained, i.e., the analytical expression of inertia based on the electromechanical response characteristics: The electromechanical dynamic response process can be obtained through wide-area measurement techniques, including ΔP. e Electromagnetic power and Δω e Rotational speed signal; however, during the inertia assessment of the system, the inertia constant may be negative. To avoid this unreasonable situation, a threshold method is used to ensure that the estimated inertia remains at its current value when the denominator is zero: Where Δt is the sampling time, and ε0 is an empirical positive threshold to avoid numerical problems, usually set according to the standard deviation of RoCoF.

5. The power system inertia assessment method based on electromechanical response characteristics according to claim 1, characterized in that, Step 2: Extract electromechanical response features. The electromechanical response features are extracted using a stochastic subspace algorithm, specifically including the following steps: To extract the electromechanical response features of the power system, a stochastic subspace method is used. The system state-space equation, discretized and considering noise, is as follows: x k+1 =Ax k +w i and k =Cx k +e i (7) Where x represents the system state quantity; x represents the measured output quantity; w i Indicates process noise; e i Denotes the observation noise, and satisfies E(w) i )=E(e i ) = 0; A represents the state matrix, and C represents the output matrix.

6. The power system inertia assessment method based on electromechanical response characteristics according to claim 5, characterized in that, Also includes: Project the extended Hankel matrix blocks representing future data onto the extended Hankel matrix representing past data: EITHER i =Y f / AND p (8) Based on equation (8) for (O) i Perform singular value decomposition: in, T is the translation matrix. This is the Kalman filter state sequence matrix of the positive time series. Substitute the Kalman filter state sequence matrix and the output into the system's state equations: Among them (O) + ) represents the pseudo-inverse, and the state matrix A of the continuous system is calculated using equation (10). c And perform eigenvalue decomposition on it; Where: Λ=diag(λ) i ), where λ i Let be the eigenvalue of the i-th mode.

7. The power system inertia assessment method based on electromechanical response characteristics according to claim 1, characterized in that, Step 3: Regional Inertia Assessment; Based on the coupling relationship between the electromechanical response characteristics and system inertia derived from the aforementioned theory, the effective regional inertia of the system is assessed, specifically including the following steps: After a power system experiences a disturbance, the system can be partitioned based on the coherence of each generator. Each partition can then be represented by a single generator, and the equivalent electromagnetic power of the generator in each region can be calculated as the electromagnetic power P of the m interconnecting lines within the interval. eq The sum of: The rotational speed of the isobaric machine in each region can be represented by the regional center frequency: Where: Δf i χ is the frequency of the regional power grid bus. i The weighting coefficient is defined in the paper as the reciprocal of the variance of the bus frequency.

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