Power system power oscillation mode identification method based on Bayesian-DMD under complete data driving

Abstract

The invention discloses an electric power system power oscillation mode identification method based on a Bayesian-DMD (Digital Micromirror Device) under complete data driving, and belongs to the technical field of electric power system stabilization and control. Comprising the following steps of: inputting linearized random response data, preprocessing the data and improving a DMD (Digital Micromirror Device) by utilizing a Bayesian theory and Gibbs sampling, performing eigenvalue decomposition and dynamic mode fitting, and calculating the frequency and damping ratio of an oscillation mode. The method is characterized in that random response data of generator angular velocity, generator angular frequency and active power in a normal operation state of a system are used as input, and a Bayesian-DMD method is used for performing power oscillation mode parameter identification on the system. The method has the advantages of being scientific, reasonable, high in applicability, high in calculation speed, high in accuracy and good in robustness.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system stability and control, and in particular relates to a power system power oscillation mode identification method based on Bayesian-DMD under full data drive. Background Art

[0002] With the proposal of the "dual carbon" goal and the development needs of new power systems, the power grid is gradually transforming towards a clean, low-carbon and safe direction. The large-scale interconnection of new power systems has led to a trend of large-capacity, long-distance and cross-regional power transmission, and the problem of small-disturbance stability of power systems has become increasingly prominent. At the same time, due to the large-scale access of new energy sources and the complexity of the power system excitation system, the characteristics of power oscillations have become more complex. For example, the large-scale grid connection of wind turbines and the increase in the number of new energy sites have led to a sharp increase in the order of system models. The high degree of power electronics of equipment has aggravated the difficulty of modeling, making the accurate modeling of the system face huge challenges. In addition, the traditional power oscillation mode identification method is highly dependent on the system model, and it is necessary to extract the oscillation mode through eigenvalue analysis after modeling. However, due to the high model dimension and complex dynamic characteristics, it is difficult for the system modeling to capture the changes in operating status and parameters in a timely manner, resulting in a significant "dimensionality disaster" problem and difficulty in adapting to the dynamic operating environment of the power system.

[0003] With the rapid development of wide area measurement systems (WAMS), data-driven power oscillation mode parameter identification methods have been widely used. Existing WAMS data-driven methods are mostly based on transient fault recording data and rely on specific fault occurrence time, location and form. Therefore, they cannot fully cover all oscillation modes in the system and can usually only be used for offline analysis after an accident. At the same time, due to the low probability of significant disturbances in modern power grids and the limited amount of fault recording data, it is difficult to meet the high requirements for accurate identification of oscillation modes and controller design. This type of method is mainly suitable for the analysis and control of transient fault stability. It has limitations in the online identification and pre-accident control of the dominant oscillation mode of power oscillations, and it is difficult to adapt to the needs of rapid dynamic regulation. Therefore, there is an urgent need for a fully data-driven method based on real-time data that can efficiently identify the power oscillation mode in the system without relying on the model, providing a stronger guarantee for the safety and stability of the power grid. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and to propose a power oscillation mode parameter identification method based on Bayesian-DMD which is scientific and reasonable, has strong applicability, fast calculation speed, high calculation accuracy and good robustness.

[0005] Power oscillation mode parameter identification method based on Bayesian Dynamic Mode Decomposition (Bayesian DMD).

[0006] The technical solution adopted to solve the technical problem is a method for identifying power oscillation modes of power systems based on Bayesian-DMD under full data drive, characterized in that the method comprises the following steps:

[0007] Step 1: Power system dynamic data input

[0008] When the random disturbance of the power system is not considered, the power system is described as a continuous differential algebraic equation system, which contains a finite set of subsystems and only focuses on autonomous continuous differential algebraic equations, as shown in formula (1):

[0009]

[0010] 0=g(x,y) (2)

[0011] Where: f is a differential equation group, g is an algebraic equation group; x is a state variable, including generator speed, power angle, and load dynamic state; y is a node voltage amplitude and phase algebraic variable; when considering the random changes in load and the power oscillation changes in the power system caused by the active output of new energy, a probability model related to modal decomposition is established through the Koopman operator:

[0012]

[0013] The input data of DMD is:

[0014] X0=[g(x0)…g(x m-1 )]∈C n×m (5)

[0015] X1=[g(x1)…g(x m )]∈C n×m (6)

[0016] In the formula, g represents the set of n observable data points, and m+1 represents the number of snapshots in the data set;

[0017] Step 2: Gibbs posterior sampling

[0018] At the beginning of the matrix factorization, the first step involves Gibbs posterior sampling of the input data X0 and X1; now assume that the random variable X follows the distribution X~p(X|Φ) with parameters Φ=(θ1,θ2); the prior distribution of Φ is p=(θ1,θ2); in addition, {x1,...,x n} is the set of samples drawn from this distribution; the posterior distribution can be calculated using Bayes' theorem:

[0019]

[0020] Initialization involves randomly obtaining the first sample, Φ = (θ1 1 ,θ2 1 );Use θ2 1 From p(θ1|θ2=θ2 i ,x1,...,x n ) to extract θ1 i+1 , using θ1 i+1 From p(θ2|θ1=θ1 i+1 ,x1,...,x n ) to extract θ2 i+1 ; During the sampling process, each sample Φ i are affected by the previous sample Φ i-1 The influence of; therefore, the sample sequence {Φ1,...Φ n} forms a Markov chain; on this basis, we can use the properties related to Markov chains, similar to the Metropolis-Hasting algorithm, to prove that the stationary distribution of this Markov chain is the target joint probability distribution p = (θ1, θ2);

[0021] The initial data set of the generator angular velocity, angular frequency and active power input to the system is resampled by Gibbs sampling, and the newly resampled data set A is calculated;

[0022]

[0023] In formula (6), ' represents the Moore-Penrose pseudo-inverse; due to the high-dimensional nature of the matrix data, it is challenging to directly calculate the eigenvalues ​​and eigenvectors; therefore, dynamic mode decomposition (DMD) is required;

[0024] Step 3: Dynamic Mode Decomposition (DMD) Process

[0025] First, for the matrix X (m-1) Perform singular value decomposition (SVD):

[0026]

[0027] Compute a new matrix

[0028]

[0029] Then, calculate the matrix Eigenvalue decomposition, that is, using formula (11) to calculate the eigenvector and eigenvalue λ;

[0030]

[0031] The dynamic mode is calculated using formula (10);

[0032]

[0033] Step 4: Parameter calculation

[0034] The frequency and damping ratio of the power system oscillation mode are calculated based on the eigenvalues ​​obtained in step 3. The eigenvalues ​​are converted from the measured data into system oscillation modal expressions, and the frequency and damping ratio of the i-th order mode are calculated:

[0035] η i =logλ i / Δt (13)

[0036] f i =Imag{η i} / 2π (14)

[0037] σ i =Re{η i} (15)

[0038] At this point, a power oscillation mode identification method for power systems based on Bayesian-DMD under full data drive has been calculated.

[0039] The present invention discloses a method for identifying power oscillation modes of an electric power system based on Bayesian-DMD under full data drive, which includes the following steps: power system dynamic data input, Gibbs posterior sampling, dynamic mode decomposition (DMD) process, and calculation of the frequency and damping ratio of the oscillation mode. The method is characterized in that the random response data of the generator angular velocity, generator angular frequency and active power under normal system operation is used as input, and the Bayesian-DMD method is used to identify the power oscillation mode parameters of the system. The method has the advantages of being scientific and reasonable, having strong applicability, fast calculation speed, high calculation accuracy and good robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A flow chart of a method for identifying power oscillation mode parameters of a randomized NNDDMD of the present invention;

[0041] Figure 2 This is a standard example wiring diagram of a 197-node system in an embodiment of the present invention;

[0042] Figure 3It is a time domain diagram of the active power output of three typical generators in the 197-node system of the embodiment of the present invention;

[0043] Figure 4 It is a time domain curve diagram of the damping ratio of the 197-node system in an embodiment of the present invention; DETAILED DESCRIPTION

[0044] The following is a detailed description of a method for identifying power oscillation modes of an electric power system based on Bayesian-DMD under full data drive according to the present invention using drawings and embodiments.

[0045] Reference Figure 1 The present invention provides a power oscillation mode identification method for an electric power system based on Bayesian-DMD under full data drive, wherein "Bayesian-DMD" is the abbreviation of the English name of "Bayesian Dynamic Mode Decomposition", and its Chinese name is: "Bayesian Dynamic Mode Decomposition".

[0046] The method comprises the following steps:

[0047] Step 1: Power system dynamic data input

[0048] When the random disturbance of the power system is not considered, the power system is described as a continuous differential algebraic equation system, which contains a finite set of subsystems and only focuses on autonomous continuous differential algebraic equations, as shown in formula (1):

[0049]

[0050] 0=g(x,y) (2)

[0051] Where: f is a differential equation group, g is an algebraic equation group; x is a state variable, including generator speed, power angle, and load dynamic state; y is a node voltage amplitude and phase algebraic variable; when considering the random changes in load and the power oscillation changes in the power system caused by the active output of new energy, a probability model related to modal decomposition is established through the Koopman operator:

[0052]

[0053] The input data of DMD is:

[0054] X0=[g(x0)…g(x m-1 )]∈C n×m (5)

[0055] X1=[g(x1)…g(x m )]∈C n×m (6)

[0056] In the formula, g represents the set of n observable data points, and m+1 represents the number of snapshots in the data set;

[0057] Step 2: Gibbs posterior sampling

[0058] At the beginning of the matrix factorization, the first step involves Gibbs posterior sampling of the input data X0 and X1; now assume that the random variable X follows the distribution X~p(X|Φ) with parameters Φ=(θ1,θ2); the prior distribution of Φ is p=(θ1,θ2); in addition, {x1,...,x n} is the set of samples drawn from this distribution; the posterior distribution can be calculated using Bayes' theorem:

[0059]

[0060] Initialization involves randomly obtaining the first sample, Φ = (θ1 1 ,θ2 1 );Use θ2 1 From p(θ1|θ2=θ2 i ,x1,...,x n ) to extract θ1 i+1 , using θ1 i+1 From p(θ2|θ1=θ1 i+1 ,x1,...,x n ) to extract θ2 i+1 ; During the sampling process, each sample Φ i are affected by the previous sample Φ i-1 The influence of; therefore, the sample sequence {Φ1,...Φ n} forms a Markov chain; on this basis, we can use the properties related to Markov chains, similar to the Metropolis-Hasting algorithm, to prove that the stationary distribution of this Markov chain is the target joint probability distribution p = (θ 1, θ2);

[0061] The initial data set of the generator angular velocity, angular frequency and active power input to the system is resampled by Gibbs sampling, and the newly resampled data set A is calculated;

[0062]

[0063] In formula (6), ' represents the Moore-Penrose pseudo-inverse; due to the high-dimensional nature of the matrix data, it is challenging to directly calculate the eigenvalues ​​and eigenvectors; therefore, dynamic mode decomposition (DMD) is required;

[0064] Step 3: Dynamic Mode Decomposition (DMD) Process

[0065] First, for the matrix X (m-1) Perform singular value decomposition (SVD):

[0066]

[0067] Compute a new matrix

[0068]

[0069] Then, calculate the matrix Eigenvalue decomposition, that is, using formula (11) to calculate the eigenvector and eigenvalue λ;

[0070]

[0071] The dynamic mode is calculated using formula (10);

[0072]

[0073] Step 4: Parameter calculation

[0074] The frequency and damping ratio of the power system oscillation mode are calculated based on the eigenvalues ​​obtained in step 3. The eigenvalues ​​are converted from the measured data into system oscillation modal expressions, and the frequency and damping ratio of the i-th order mode are calculated:

[0075] η i =logλ i / Δt (13)

[0076] f i =Imag{η i} / 2π (14)

[0077] σ i =Re{η i} (15)

[0078] At this point, a power oscillation mode identification method for power systems based on Bayesian-DMD under full data drive has been calculated.

[0079] Specific implementation example: The implementation is carried out through a 197-node system example built with equivalent parameters of a certain actual example in China. The example is that after the AC channel N-1 of the power system with a high proportion of hydropower, the system has an ultra-low frequency oscillation phenomenon in the entire network. The typical method introduction, standard example wiring diagram and three typical generator export active power time domain diagrams are shown in Figure 2 and Figure 3 shown.

[0080] First, the Power System Analysis Comprehensive Program (PSASP) simulation software is used to collect the export active power and generator angular frequency data of each synchronous generator. Generator GENDZ-1, generator Gen1A-1 and generator Gen1B-1 are set as balancing units. All other generators use the balancing units as reference units to collect the angular frequency data of each generator. The fault is set as the Sanyong N-1 fault of the high-proportion hydropower transmission system bus1A-17~bus1A-13 line. The system has an ultra-low frequency oscillation problem with an oscillation frequency of 0.03Hz. The Bayesian-DMD method is used to slide the window of the collected data within a time period of 50s, sliding once every 2 seconds, for a total of 1000 times, so as to obtain the parameter statistical mean of the oscillation mode. The specific results can be seen in Table 1, and the time domain curve is shown in the following figure. Figure 4 .

[0081] Table 1197 Node Standard Example Compressed-DMD Method Weak (Negative) Damping Mode Identification Results

[0082]

[0083] The results in Table 1 indicate that the Bayesian-DMD method is used to calculate the input synchronous generator angular frequency, synchronous generator power angle and synchronous generator export active power data set, and the calculated frequency and damping ratio results are very close to the results listed by the PSASP simulation software. It can be proved that in the 197-node example with a large number of new energy sources connected, the numerical power oscillation parameter identification method based on Bayesian-DMD can accurately extract and identify the frequency and damping ratio of the 197-node example system. Figure 4 It can be seen from the time domain curve that all calculation results are evenly distributed around the mean, with accurate results and high reliability.

[0084] The key technologies in the technical solution adopted by the present invention are:

[0085] The traditional dynamic mode decomposition is updated by using Bayesian theory. By introducing the Bayesian probability model and Gibbs posterior sampling, the speed of singular value decay is improved, and better accuracy can be obtained for the data processed by Bayesian-DMD.

[0086] At the beginning of the matrix factorization, the first step involves Gibbs posterior sampling of the input data X0 and X1; now assume that the random variable X follows the distribution X~p(X|Φ) with parameters Φ=(θ1,θ2); the prior distribution of Φ is p=(θ1,θ2); in addition, {x1,...,x n} is the set of samples drawn from this distribution; the posterior distribution can be calculated using Bayes' theorem:

[0087]

[0088] Initialization involves randomly obtaining the first sample, Φ = (θ1 1 ,θ2 1 );Use θ2 1 From p(θ1|θ2=θ2 i ,x1,...,x n ) to extract θ1 i+1 , using θ1 i+1 From p(θ2|θ1=θ1 i+1 ,x1,...,x n ) to extract θ2 i+1 ; During the sampling process, each sample Φ i are affected by the previous sample Φ i-1 The influence of; therefore, the sample sequence {Φ1,...Φ n} forms a Markov chain; on this basis, we can use the properties related to Markov chains, similar to the Metropolis-Hasting algorithm, to prove that the stationary distribution of this Markov chain is the target joint probability distribution p = (θ 1, θ2);

[0089] The initial data set of the generator angular velocity, angular frequency and active power input to the system is resampled by Gibbs sampling, and the newly resampled data set A is calculated;

[0090]

[0091] In formula (6), ' represents the Moore-Penrose pseudo-inverse; due to the high-dimensional nature of the matrix data, it is challenging to directly calculate the eigenvalues ​​and eigenvectors; therefore, dynamic mode decomposition (DMD) is required;

[0092] For the matrix X (m-1) Perform singular value decomposition (SVD):

[0093]

[0094] Compute a new matrix

[0095]

[0096] Then, calculate the matrix Eigenvalue decomposition, that is, using formula (11) to calculate the eigenvector and eigenvalue λ;

[0097]

[0098] The dynamic mode is calculated using formula (10);

[0099]

[0100] The calculation conditions, legends, tables, etc. in the embodiments of the present invention are only used to further illustrate the present invention, but are not exhaustive and do not constitute a limitation on the scope of protection of the claims. Based on the inspiration obtained from the embodiments of the present invention, those skilled in the art can think of other substantially equivalent alternatives without creative work, and all of them are within the scope of protection of the present invention.

Claims

1. A method for identifying power oscillation patterns of power systems based on Bayesian-DMD under full data drive, characterized in that: The method comprises the following steps: Step 1: Power system dynamic data input When the random disturbance of the power system is not considered, the power system is described as a continuous differential algebraic equation system, which contains a finite set of subsystems and only focuses on autonomous continuous differential algebraic equations, as shown in formula (1): 0=g(x,y) (2) Where: f is a differential equation group, g is an algebraic equation group; x is a state variable, including generator speed, power angle, and load dynamic state; y is a node voltage amplitude and phase algebraic variable; when considering the random changes in load and the power oscillation changes in the power system caused by the active output of new energy, a probability model related to modal decomposition is established through the Koopman operator: The input data of DMD is: X0=[g(x0)…g(x m-1 )]∈C n×m (5) X1=[g(x1)…g(x m )]∈C n×m (6) In the formula, g represents the set of n observable data points, and m+1 represents the number of snapshots in the data set; Step 2: Gibbs posterior sampling At the beginning of the matrix factorization, the first step involves Gibbs posterior sampling of the input data X0 and X1; now assume that the random variable X follows the distribution X~p(X|Φ) with parameters Φ=(θ1,θ2); the prior distribution of Φ is p=(θ1,θ2); in addition, {x1,...,x n } is the set of samples drawn from this distribution; the posterior distribution can be calculated using Bayes' theorem: Initialization involves randomly obtaining the first sample, Φ = (θ1 1 ,θ2 1 );Use θ2 1 From p(θ1|θ2=θ2 i ,x1,...,x n ) to extract θ1 i+1 , using θ1 i+1 From p(θ2|θ1=θ1 i+1 ,x1,...,x n ) to extract θ2 i+1 It can be seen that in the sampling process, each sample Φ i are affected by the previous sample Φ i-1 Therefore, the sample sequence {Φ1,...Φ n } forms a Markov chain. On this basis, we can use the properties related to Markov chains, similar to the Metropolis-Hasting algorithm, to prove that the stationary distribution of this Markov chain is the target joint probability distribution p = (θ 1, θ2); The initial data set of the generator angular velocity, angular frequency and active power input to the system is resampled by Gibbs sampling, and the newly resampled data set A is calculated; In formula (6), ' represents the Moore-Penrose pseudo-inverse. Due to the high-dimensional nature of matrix data, it is challenging to directly calculate eigenvalues ​​and eigenvectors. Therefore, dynamic mode decomposition (DMD) is required. Step 3: Dynamic Mode Decomposition (DMD) Process First, for the matrix X (m-1) Perform singular value decomposition (SVD): Compute a new matrix Then, calculate the matrix Eigenvalue decomposition, that is, using formula (11) to calculate the eigenvector and eigenvalue λ; The dynamic mode is calculated using formula (10). Step 4: Parameter calculation The frequency and damping ratio of the power system oscillation mode are calculated based on the eigenvalues ​​obtained in step 3. The eigenvalues ​​are converted from the measured data into system oscillation modal expressions, and the frequency and damping ratio of the i-th order mode are calculated: or i =logλ i / Δt (13) f i =Image i } / 2π (14) s i =Re{η i } (15).

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