Power system forced oscillation source progressive positioning method considering network-forming double-fed fan

Abstract

The invention discloses a progressive positioning method for a forced oscillation source of a power system considering a grid-forming type double-fed fan, and the method comprises the steps: carrying out the spectrum Granger causal analysis of the time series of the output active power of each synchronous machine which is strongly related to oscillation and the grid-forming type double-fed fan, and judging the causal relationship between power generation units; preliminarily positioning a power generation unit where the forced oscillation disturbance source is located; furthermore, an unknown input observer based on performance constraint is adopted to perform positioning verification, and the unknown input observer with the performance constraint is designed based on linear models of power generation units such as a synchronous machine with a potential forced oscillation source and a grid-forming double-fed fan. And establishing a structured residual set capable of effectively representing the forced oscillation disturbance source in the power generation unit by using the observer, and comparing each residual frequency spectrum in the residual set to realize accurate positioning of the forced oscillation disturbance source. Therefore, rapidity, convenience and accuracy required by positioning can be met.

Description

Technical Field

[0001] This invention belongs to the field of forced oscillation source localization technology, specifically relating to a progressive localization method for forced oscillation sources in power systems considering grid-type doubly fed wind turbines. Background Technology

[0002] With the rapid increase in installed capacity and grid-connected capacity of new energy power generation, grid-forming converters (GFCs) are gradually being widely used. A GFC is a power electronic converter capable of autonomously establishing and maintaining grid voltage and frequency. It simulates the characteristics of a synchronous generator through control algorithms, actively providing voltage and frequency support to the grid. However, while simulating the characteristics of a synchronous generator, a GFC can also introduce the forced oscillation (FO) problem inherent in generators. For example, MPPT (Maximum Power Point Tracking) control is one of the causes of forced oscillation in GFCs. Forced oscillation is a common dynamic anomaly in power systems, usually caused by external periodic disturbances, such as those contained in generator prime movers and governors, excitation systems, and load fluctuations. When forced oscillation approaches the natural frequency of the power grid system, it not only affects the power quality of local nodes but may also propagate through the grid to a wider area, causing system resonance, leading to increased frequency fluctuations, inverter overcurrent tripping, protection malfunctions, and in severe cases, even system cascading failure. It can be said that forced oscillations seriously affect the operational stability and safety of the power grid system. Therefore, quickly and accurately locating the oscillation source is the key to suppressing severe forced oscillations in the power grid system and maintaining safe and stable operation.

[0003] Currently, there is no available method for locating the oscillation source when considering forced oscillations in grid-type doubly-fed wind turbines. However, there has been some research on forced oscillation location methods based on traditional generators, such as online location of forced oscillation disturbance sources using energy flow theory; mode shape estimation to identify generators with the largest mode shape amplitude or phase leading as forced oscillation disturbance sources; and data-driven forced oscillation disturbance source location methods including synchronous threshold wavelet transform, machine learning, and deep learning.

[0004] Chinese patent application CN119535120A discloses a method for locating and predicting low-frequency forced oscillation disturbance sources in power systems. This method includes: acquiring the daytime active power plan of conventional generating units and the predicted daytime power of wind farms, updating the data at preset time intervals; based on the daytime active power plan of conventional generating units and the predicted daytime power of wind farms, using a dynamic time window to perform dynamic low-frequency forced oscillation detection on the daytime active power plan of conventional generating units and the predicted daytime power of wind farms within the future preset time interval, acquiring the active power data of conventional generating units and wind farms within the possible oscillation time window to construct a numerical matrix; inputting the numerical matrix into a trained CNN (Convolutional Neural Network)-SVM (Support Vector Machine) localization model to predict the potential conventional generating units and wind farms that may trigger low-frequency forced oscillations within the future preset time interval and the corresponding window occurrence time. However, this method requires extensive collection of active power data from conventional generating units and wind farms within different low-frequency forced oscillation time windows to form a numerical matrix and data labels to create a sample set in order to achieve relatively accurate oscillation source location, resulting in a large data requirement.

[0005] Chinese patent application CN118795270A discloses a forced oscillation source localization method based on the Teager energy operator theory. The method includes: acquiring and constructing a time-series output active power dataset for each generator unit based on the output active power data obtained from wide-area power grid measurements; obtaining sample data of active power change during forced oscillation by subtracting the active power output during forced oscillation from the active power output during system steady state; performing a nonlinear transformation on the sample data signal using an improved Teager energy operator to obtain the instantaneous Teager energy contained in the output active power signal of each unit at each sampling time point; accurately locating the generator unit where the forced oscillation source is located by utilizing whether the contribution weight of the Teager energy accumulated by each generator unit during forced oscillation to the total Teager energy is sufficiently large; achieving rapid and accurate localization of the forced oscillation source using only the active power information from wide-area measurements of the system's generator units, and possessing high noise interference resistance. However, each step in this method requires analysis and processing of the time-series output active power data of all generator sets before and after the forced oscillation, resulting in a large and complex amount of data calculation. Summary of the Invention

[0006] In view of the above, the present invention provides a progressive positioning method for forced oscillation sources in power systems considering grid-type doubly fed wind turbines, which can meet the requirements of speed, convenience and accuracy for positioning.

[0007] A method for progressively locating a forced oscillation source in a power system considering a grid-connected doubly-fed induction generator (DFIG) wind turbine includes the following steps:

[0008] (1) Collect the time series data of the output active power of each power generation unit in the power system, including synchronous generators and grid-type doubly fed wind turbines, and use principal component analysis to screen out the power generation units that are strongly correlated with forced oscillations. For the screened power generation units, combine each power generation unit with other power generation units to form multiple binary power generation unit groups, and calculate the autoregressive model between the time series data of the output active power of the two power generation units in the binary power generation unit group.

[0009] (2) Perform spectral Granger causality analysis on the autoregressive model of each binary power generation unit group to determine the causal relationship between the two power generation units in the binary power generation unit group, thereby initially locating several power generation units that may have forced oscillation disturbance sources as power generation units to be verified.

[0010] (3) Linearize the power generation units to be verified to obtain linearized models of these power generation units;

[0011] (4) Based on the linearized model, design a separate system for each power generation unit to be verified that satisfies H. ∞ Unknown input observers with norm performance constraints;

[0012] (5) For the power generation unit to be verified, the d-axis and q-axis subtransient potentials of these power generation units are input into their respective unknown input observers, and the residual spectrum of these power generation units is output. The power generation unit with the largest residual spectrum at the forced oscillation frequency is taken as the finally located forced oscillation disturbance source power generation unit.

[0013] Furthermore, the specific implementation of step (2) is as follows:

[0014] 2.1 For any binary power generation unit group, extract the noise term from the autoregressive model of the binary power generation unit group and establish the covariance matrix of the noise term;

[0015] 2.2 The autoregressive model is simplified using the lag operator, and a Fourier transform is performed on the simplified autoregressive model to obtain the transfer function matrix between the output active power time series data and the noise term;

[0016] 2.3 Normalize the covariance matrix and transfer function matrix;

[0017] 2.4 Calculate X based on the normalized covariance matrix and transfer function matrix. t and Y t The causal influence value between them, X t and Y t These are the time-series output active power data of the two power generation units in the binary power generation unit group, respectively.

[0018] 2.5 Determine the cause in the binary power generation unit group based on the causal influence value. For any power generation unit, if the power generation unit is the cause in all binary power generation unit groups to which it belongs, then it is preliminarily identified as a power generation unit that may have a forced oscillation disturbance source.

[0019] Furthermore, the expression for the covariance matrix in step 2.1 is as follows:

[0020]

[0021] Where: Σ is the covariance matrix, Σ2, Γ2, and Υ2 are elements in the covariance matrix Σ, and Σ2 = var(ε) 2t ), Γ2=var(η 2t ), Υ2=cov(ε 2t ,η 2t ), ε 2t and η 2t These are the noise terms for the two power generation units in the autoregressive model, where var() represents the variance and cov() represents the covariance.

[0022] Furthermore, the expression for the transfer function matrix in step 2.2 is as follows:

[0023]

[0024] Where: X(ω) and Y(ω) are X t and Y t The spectrum, where ω is the angular frequency, and H(ω) is the transfer function matrix. xx (ω), H xy (ω), H yx (ω), H yy (ω) are elements in the transfer function matrix H(ω), E x (ω) and E y (ω) represents ε 2t and η 2t The spectrum.

[0025] Further, in step 2.4, X is calculated using the following expression. t and Y t The causal influence values ​​between each other:

[0026]

[0027] Where: f Y → X (ω) is Y t For X t The causal effect value, f X → Y (ω) is X t For Yt The causal effect value, S xx (ω) and S yy (ω) represents X t and Y t The self-score, and The matrix elements H are respectively xx (ω) and H yy (ω) is the result after normalization. This is the result after normalizing the matrix element Γ2. They are respectively The conjugate representation of , and The matrix elements H are respectively xy (ω) and H yx The conjugate representation of (ω).

[0028] Furthermore, in step 2.5, the cause in the binary power generation unit group is determined based on the causal influence value, specifically according to the following standard: if f Y→X (ω) is greater than f X→Y (ω) represents Y t The corresponding power generation unit is the factor in the binary power generation unit group; if f Y→X (ω) is less than f X→Y (ω) represents X t The corresponding power generation unit is the cause in the binary power generation unit group.

[0029] Furthermore, the expression for the unknown input observer in step (4) is as follows:

[0030]

[0031] Where z(t) is the state variable of the observer at time t. Let z(t) be the first derivative of z(t), and x(t) be the state variable at time t in the linearized model of the power generation unit. Let x(t) be the estimated value, r(t) be the residual spectrum of the power generation unit at time t, and y(t) be the output variable at time t in the linearized model of the power generation unit, i.e., the dq-axis subtransient potential of the power generation unit. F, T, K, and H are all satisfying H ∞ The parameter matrix of the performance constraints, C is the output matrix in the linearized model of the generator unit (characterizing the relationship between the subtransient electropotential of the dq axis and the generator state variables), and t represents time.

[0032] Furthermore, the parameter matrices F, T, K, and H are solved in the following way:

[0033] First, calculate the parameter matrices H and T according to the following expressions:

[0034] H = E1(CE1) +

[0035] T = I - E1(CE1) + C

[0036] Where: I is the identity matrix, E1 is the distribution matrix of w1(t), () + The corresponding left inverse matrix is ​​expressed, where w1(t) represents the unknown input at time t in the linearized model of the power generation unit, which consists of other perturbation factors and can be completely decoupled by the traditional unknown input observer;

[0037] Then, the following matrix inequalities are solved to obtain the parameter matrices U and P;

[0038]

[0039] Where: Φ is the transpose conjugate matrix of PTE2, the parameter matrix A1 = A - HCA, r is a set small positive number (e.g., 0.02), and the superscript... T Let A represent the transpose, A be the system matrix in the linearized model of the power generation unit, and E2 be the distribution matrix of w2(t). w2(t) represents the unknown input at time t in the linearized model of the power generation unit, which consists of other perturbation factors and cannot be completely decoupled by the traditional unknown input observer.

[0040] Finally, the parameter matrices F and K are calculated from the parameter matrices U and P using the following expressions:

[0041] F = A1 - K1C

[0042] K = K1 + K2

[0043] U=PK1

[0044] K2=FH

[0045] Where K1 and K2 are parameter matrices.

[0046] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the above-described progressive localization method for forced oscillation sources in power systems considering grid-connected doubly-fed wind turbines.

[0047] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described progressive localization method for forced oscillation sources in a power system considering a grid-type doubly-fed wind turbine.

[0048] This invention performs spectral Granger causality analysis on the time series of the output active power of each grid-type doubly-fed induction generator (DFIG) strongly correlated with oscillations to determine the causal relationships between the various power generation units and preliminarily locate the power generation unit where the forced oscillation disturbance source is located. Furthermore, this invention employs a performance-constrained unknown input observer for location verification. Based on the linearized model of each power generation unit, including the grid-type DFIG with potential forced oscillation sources, a performance-constrained unknown input observer is designed. This observer is used to establish a structured residual set that can effectively characterize the forced oscillation disturbance source within the power generation unit. By comparing the spectra of each residual in the residual set, the accurate location of the forced oscillation disturbance source is achieved. Compared with existing technologies, this invention has the following advantages:

[0049] 1. This invention screens power generation units that are strongly correlated with forced oscillations based on principal component analysis, and preliminarily identifies them as oscillation source power generation units through spectral Granger causality analysis. The main positioning steps only require analyzing the time series data of the output active power of power generation units in the power grid system that are strongly correlated with the oscillations, which greatly reduces the workload and complexity of the analysis.

[0050] 2. This invention introduces an H-based approach into the traditional unknown input observer. ∞ The constraint term of the norm performance index can further minimize the perturbation of high-dimensional unknown inputs, based on the decoupling of some low-dimensional unknown input perturbations by the traditional unknown input observer, so that the calculated residuals can accurately reflect the existence of internal forced oscillation sources under various external perturbations.

[0051] 3. By designing and applying a performance-constrained unknown input observer, this invention can accurately locate the oscillation source unit among multiple grid-connected power generation units when forced oscillations occur in the power grid system. This can help dispatchers take timely measures to reduce the adverse impact on power grid stability. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the progressive positioning method for the forced oscillation source in the power system of a grid-type doubly fed wind turbine, which is considered in this invention. Detailed Implementation

[0053] To describe the present invention in more detail, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] like Figure 1 As shown, the present invention considers the progressive localization method for forced oscillation sources in power systems using grid-connected doubly-fed induction generators, comprising the following steps:

[0055] (1) Collect the time series of the output active power of each power generation unit with potential forced oscillation source, and use principal component analysis to screen the power generation units that are strongly correlated with forced oscillation.

[0056] Assume the collected time series data matrix is ​​as follows It represents m time-series observations from n power generation units. Matrix U can be decomposed into a weight matrix T and a load matrix P:

[0057] U=TP T +E

[0058] Where E is the residual matrix, and each column of T is interpreted as a principal component.

[0059] Each principal component can express a linear reconstruction of the original variables, that is:

[0060] t i =x1p 1i +x2p 2i +…+x j p ji +…+x n p ni

[0061] The factor |p of the j-th power generation unit ji | is used to represent the contribution of the generating unit to the i-th oscillatory principal component. The index of the j-th generating unit, i.e., the Oscillation Participation Index (OPI), is calculated to measure the impact of each generating unit on the oscillatory principal component:

[0062]

[0063] Where: λ i It is a forced oscillation O pc The eigenvalues ​​of the corresponding PCs in each PC.

[0064] By following the steps above, the k power generation units that have the most significant impact on the principal component of the oscillation can be identified, thus determining the power generation units C1 to C2 that are strongly correlated with the oscillation. k .

[0065] (2) For these strongly correlated power generation units C1 to C k For each power generation unit and other power generation units forming multiple binary power generation unit groups, obtain the autoregressive model of the binary active power time series group for each binary group.

[0066] For a given binary active power time series X t =[X 1t ,X 2t ,…,X pt ] T If p = 2, an m-order autoregressive model can be used to describe this:

[0067] X t +A(1)X t-1+…+A(m)X t-m =E t

[0068] Where: A(i) is a p×p coefficient matrix, E t =[E 1t E 2t ,…,E pt ] T It is a zero-mean uncorrelated noise vector with a covariance matrix of Σ.

[0069] The order of the model can be selected using the Akaike Information Criterion (AIC) to find the optimal order that minimizes the AIC:

[0070]

[0071] Where: N total It is the total sequence length of all implementations.

[0072] Alternatively, the minimum order can be found by evaluating the Bayesian Information Criterion (BIC).

[0073]

[0074] Multiply the above autoregressive model by Where k = 1, 2, ..., m. Taking its expected value, we obtain the Yule-Walker equation:

[0075] R(-k)+A(1)R(-k+1)+…+A(m)R(-k+m)=0

[0076] in: It is X t The lagged n covariance matrix.

[0077] Solving the above equations will determine the model coefficients A(i) and yield the specific autoregressive model.

[0078] (3) For strongly correlated power generation units C1~C k Spectral Granger causality analysis was performed on the autoregressive model of the output active power time series data of all binary power generation units. By analyzing the obtained spectral Granger causality curves, the causal relationship of each strongly correlated oscillation power generation unit was obtained, and the forced oscillation disturbance source power generation unit was preliminarily located.

[0079] Granger causality analysis requires sequentially performing analysis on two specific time series, assuming strongly correlated oscillating power generation units C1 to C2. k The time series of the active power output of the two power generation units are X. t and Y t Its autoregressive (AR) model is as follows:

[0080] var(ε 1t )=Σ1

[0081] var(η 1t )=Γ1

[0082] Since the two are interdependent, the above AR model can be rewritten as:

[0083]

[0084] Wherein: noise term ε 2t and η 2t Regardless of time, its covariance matrix for the same period is:

[0085]

[0086] Where: Σ2=var(ε 2t ), Γ2=var(η 2t ), Υ2=cov(ε 2t ,η 2t If X t and Y t If it is independent, then {b} 2j} and {c 2j} is uniformly zero, Υ2=0, Σ1=Σ2 and Γ1=Γ2.

[0087] LX is represented using the hysteresis operator L. t =X t-1 Then the rewritten AR model can be simplified to:

[0088]

[0089] Performing a Fourier transform on it yields:

[0090]

[0091] Its transfer function format can be expressed as:

[0092]

[0093] Where H(ω)=A -1 The formula for calculating the element (ω) is:

[0094]

[0095] By applying an appropriate ensemble average to the transfer function, we obtain the spectrum matrix:

[0096] S(ω)=H(ω)ΣH * (ω)

[0097] in: * This represents complex conjugation and matrix transpose.

[0098] The spectrum matrix contains cross-spectrum and self-spectrum. To eliminate cross terms, a normalization transformation is introduced, which involves left-multiplying both sides of the AR model after the Fourier transform by the following matrix:

[0099]

[0100] get:

[0101]

[0102] in: Its corresponding transfer function It is a transformation matrix The reverse:

[0103]

[0104] because Therefore:

[0105]

[0106] By normalization, X can be decoupled. t and Y t And generate a pair of unrelated E x and Right now Driven normalized Y t Reconstruction noise term The variance is

[0107] Two time series X t and Y t The spectrum representation of the total interdependence between them is defined as:

[0108]

[0109] Where: |S(ω)|=S xx (ω)S yy (ω)-S xy (ω)S yx (ω),

[0110] From this, we can obtain X. t The self-composed score:

[0111]

[0112] In the self-spectrum, term ① represents X. tThe intrinsic power, term ② represents Y t For X t The causal power of X. t For Y t Y t For X t The causal effect is defined as follows:

[0113]

[0114] in:

[0115] The causal influence values ​​at different frequency points ω were calculated, and the corresponding spectral Granger causality curves were obtained. In all strongly correlated oscillation generator units C1 to C2... k In this study, causal relationship analysis is performed on multiple binary power generation unit groups composed of each power generation unit and other power generation units to obtain causal relationship curves for multiple binary groups of each power generation unit. If a power generation unit is a cause of all other power generation units in multiple binary groups, then that power generation unit is taken as the power generation unit where the forced oscillation disturbance source is located. Using the following logic, the causal power generation unit is distinguished from other power generation units, thereby locating the possible power generation unit of the forced oscillation disturbance source:

[0116] where j=1,…,i-1,i+1,…,n

[0117] Through spectral Granger causality analysis, the possible disturbance source power generation units can be reduced to the most probable D1 to D2. g .

[0118] (4) For power generation units D1 to D2 with strong correlation and possible forced oscillation sources g Linearization modeling is performed to obtain a linearized model of the power generation unit.

[0119] Taking a grid-type doubly-fed induction generator (DFIG) as an example, its generator, prime mover, shaft system, and other models are the same as those of a typical DFIG. The grid-type virtual synchronous outer loop control model of its rotor-side converter is as follows:

[0120]

[0121] The voltage loop and current loop are represented as follows:

[0122]

[0123] The entire grid-type doubly-fed induction generator unit can be represented by the following simplified linear representation:

[0124]

[0125] Where: x(t) is the system's state variable vector, and y(t) is the output variable vector. (Power generation unit system matrix) E p It consists of parameters from the power generation unit and control equipment. w1(t) represents the unknown input composed of other disturbance factors that can be completely decoupled by a traditional unknown input observer, and w2(t) represents the unknown input composed of other disturbance factors that cannot be completely decoupled by a traditional unknown input observer. p f This refers to the forced oscillation source within the power generation unit.

[0126] Other synchronous generator units can also be represented similarly using a linearized simplified representation.

[0127] Depending on whether it can be completely decoupled from a traditional unknown input observer, E w and w E (t) can be divided into two parts accordingly: And w1(t) and w2(t), where E1 and w1(t) represent a portion of the unknown inputs that can be completely decoupled from the traditional unknown input observer. At this point, the rewritten linearized model of each power generation unit can be obtained:

[0128]

[0129] (5) Based on this linearized model, design a model that satisfies H ∞ Unknown input observer with performance constraints.

[0130] Based on the linearized model of each power generation unit, if only w1(t) is considered as an unknown input, while w2(t) and p are considered as unknown inputs... f If (t) is considered as a system state variable, then the unknown input observer of the power generation unit is:

[0131]

[0132] in: It is the observer's state variable vector. These are the estimated values ​​of the state variables, r(t) is the residual, and F, T, K, and H are the values ​​to satisfy H. ∞ A matrix designed with performance constraints.

[0133] Define the state estimation error as Based on the system linearization model and the unknown input observer model, we can obtain:

[0134]

[0135] When the following conditions are met:

[0136]

[0137] The error dynamic system can be obtained:

[0138]

[0139] Introduce a lemma that correlates system performance with its Lyapunov function:

[0140] For a given system:

[0141]

[0142] in: It is the system's state variable vector. It is the output variable vector. A is the input variable vector, and A, B, and C are system parameter matrices of appropriate dimensions.

[0143] Introduce the following H ∞ Performance metrics:

[0144]

[0145] For a given constant 0 < α < 1 and γ > 0, if there exists a Lyapunov function V(x(t)) that satisfies the following conditions:

[0146]

[0147] Therefore, the above system is exponentially stable, and y(t) satisfies H with respect to u(t). ∞ Performance constraints.

[0148] H ∞ The performance constraints are transformed into linear matrix inequalities of the unknown input observer design matrix, and the error dynamic system can be rewritten as:

[0149]

[0150] The Lyapunov function of e(t) in the above error dynamic system is defined as follows:

[0151] V(e)=e T Pe

[0152] Combining the above conditions and the expression for the error dynamic system, we can obtain:

[0153]

[0154] Where: U = PK1, A1 = A - HCA = TA.

[0155] When w2 = 0, it must satisfy That is, A1 must be satisfied. TP+PA1-C T U T -UC < 0.

[0156] Therefore, in order to improve robustness and ensure the asymptotic stability of the error dynamic system, the following must be satisfied:

[0157] I+A1 T P+PA1-C T U T -UC<0

[0158] definition:

[0159]

[0160] Combining the above formula and From the expression, we can obtain:

[0161]

[0162] in:

[0163] Under zero initial conditions, we have:

[0164]

[0165] When Π < 0, combining the above formula, we can obtain Γ < 0, that is, ||e|| Tf ≤r||w2|| Tf At this point, the error dynamic system is globally exponentially stable and satisfies H ∞ Performance constraints. Therefore, the error dynamic system must satisfy H ∞ The performance constraints are as follows:

[0166]

[0167] The left inverse of CE1 can be calculated using the relation rank(CE1) = rank(E1):

[0168] (CE1) + =((CE1) T CE1) -1 (CE1) T

[0169] Based on the following conditions:

[0170]

[0171] We can obtain H and T:

[0172]

[0173] From the following formula:

[0174]

[0175] The above equation can be solved to obtain P and U, thus yielding K1 = P. -1 The solutions for U, F, and K are determined by the conditions described above.

[0176] Therefore, H is satisfied. ∞ The F, T, K, and H matrices of the performance constraints have all been calculated.

[0177] (6) For power generation units D1 to D2 with strong correlation and possible forced oscillation sources g Using an unknown input observer with constraints, power generation units D1 to D2 are established. g Structured residual sets.

[0178] For a grid-connected doubly-fed induction generator unit or synchronous generator unit system:

[0179]

[0180] Using the unknown input observers already determined by each matrix:

[0181]

[0182] The residual value r(t) can be obtained from the power generation units D1 to D2. g The structured residual set is composed of {r1(t), r2(t), ..., r g (t)}.

[0183] (7) Power generation units D1 to D g By comparing the residual spectrum, the power generation unit that causes the forced oscillation is located.

[0184] Further calculations are performed on the residual spectra r(t) and y(t) of each residual in the residual set, as well as the transfer function matrix G from y(t) to r(t). ry (s); G can be derived from the expression of the unknown input observer. ry (s):

[0185] G ry (s)=(I-CH)-C(sI-F) -1 K

[0186] When forced oscillation occurs within the i-th power generation unit, its residual spectrum will form a residual peak at the forced oscillation frequency, which is significantly larger than that of other power generation units that have not oscillated, i.e., it satisfies:

[0187]

[0188] Where: j = 1, ..., i-1, i+1, ..., g.

[0189] By comparing the residual spectra of strongly correlated and possible forced oscillation source power generation units, the power generation unit that meets the above conditions can be found, which is the final oscillation source power generation unit that generates forced oscillations, thus completing the accurate location of the oscillation source.

[0190] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0191] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0192] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0193] The above description of the embodiments is provided to enable those skilled in the art to understand and apply the present invention. Those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention.

Claims

1. A method for progressively locating a forced oscillation source in a power system considering a grid-connected doubly-fed induction generator (DFIG), comprising the following steps: (1) Collect the time series data of the output active power of each power generation unit in the power system, including synchronous generators and grid-type doubly fed wind turbines, and use principal component analysis to screen out the power generation units that are strongly correlated with forced oscillations. For the screened power generation units, combine each power generation unit with other power generation units to form multiple binary power generation unit groups, and calculate the autoregressive model between the time series data of the output active power of the two power generation units in the binary power generation unit group. (2) Perform spectral Granger causality analysis on the autoregressive model of each binary power generation unit group to determine the causal relationship between the two power generation units in the binary power generation unit group, thereby initially locating several power generation units that may have forced oscillation disturbance sources as power generation units to be verified. (3) Linearize the power generation units to be verified to obtain linearized models of these power generation units; (4) Based on the linearized model, design a separate system for each power generation unit to be verified that satisfies H. ∞ Unknown input observers with norm performance constraints; (5) For the power generation unit to be verified, the d-axis and q-axis subtransient potentials of these power generation units are input into their respective unknown input observers, and the residual spectrum of these power generation units is output. The power generation unit with the largest residual spectrum at the forced oscillation frequency is taken as the finally located forced oscillation disturbance source power generation unit.

2. The progressive localization method for forced oscillation sources in power systems considering grid-connected doubly-fed wind turbines as described in claim 1, characterized in that: The specific implementation method of step (2) is as follows: 2.1 For any binary power generation unit group, extract the noise term from the autoregressive model of the binary power generation unit group and establish the covariance matrix of the noise term; 2.2 The autoregressive model is simplified using the lag operator, and a Fourier transform is performed on the simplified autoregressive model to obtain the transfer function matrix between the output active power time series data and the noise term; 2.3 Normalize the covariance matrix and transfer function matrix; 2.4 Calculate X based on the normalized covariance matrix and transfer function matrix. t and Y t The causal influence value between them, X t and Y t These are the time-series output active power data of the two power generation units in the binary power generation unit group, respectively. 2.5 Determine the cause in the binary power generation unit group based on the causal influence value. For any power generation unit, if the power generation unit is the cause in all binary power generation unit groups to which it belongs, then it is preliminarily identified as a power generation unit that may have a forced oscillation disturbance source.

3. The progressive localization method for forced oscillation sources in power systems considering grid-connected doubly-fed wind turbines as described in claim 2, characterized in that: The expression for the covariance matrix in step 2.1 is as follows: Where: Σ is the covariance matrix, Σ2, Γ2, and Υ2 are elements in the covariance matrix Σ, and Σ2 = var(ε) 2t ), Γ2=var(η 2t ), Υ2=cov(ε 2t ,η 2t ), ε 2t and η 2t These are the noise terms for the two power generation units in the autoregressive model, where var() represents the variance and cov() represents the covariance.

4. The method for progressively locating the forced oscillation source in a power system considering a grid-type doubly-fed wind turbine, as described in claim 3, is characterized in that: The expression for the transfer function matrix in step 2.2 is as follows: Where: X(ω) and Y(ω) are X t and Y t The spectrum, where ω is the angular frequency, and H(ω) is the transfer function matrix. xx (ω), H xy (ω), H yx (ω), H yy (ω) are elements in the transfer function matrix H(ω), E x (ω) and E y (ω) represents ε 2t and η 2t The spectrum.

5. The method for progressively locating the forced oscillation source in a power system considering a grid-type doubly-fed wind turbine, as described in claim 4, is characterized in that: In step 2.4, X is calculated using the following expression. t and Y t The causal influence values ​​between them; Where: f Y→X (ω) represents Y t For X t The causal effect value, f X→Y (ω) is X t For Y t The causal effect value, S xx (ω) and S yy (ω) represents X t and Y t The self-score, and The matrix elements H are respectively xx (ω) and H yy (ω) is the result after normalization. This is the result after normalizing the matrix element Γ2. They are respectively The conjugate representation of , and The matrix elements H are respectively xy (ω) and H yx The conjugate representation of (ω).

6. The progressive localization method for forced oscillation sources in power systems considering grid-connected doubly-fed wind turbines according to claim 5, characterized in that: In step 2.5, the cause in the binary power generation unit group is determined based on the causal influence value. The specific standard is: if f Y→X (ω) is greater than f X→Y (ω) represents Y t The corresponding power generation unit is the factor in the binary power generation unit group; if f Y→X (ω) is less than f X→Y (ω) represents X t The corresponding power generation unit is the cause in the binary power generation unit group.

7. The method for progressively locating the forced oscillation source in a power system considering a grid-connected doubly-fed wind turbine, as described in claim 1, is characterized in that: The expression for the unknown input observer in step (4) is as follows: Where z(t) is the state variable of the observer at time t. Let z(t) be the first derivative of z(t), and x(t) be the state variable at time t in the linearized model of the power generation unit. Let x(t) be the estimated value, r(t) be the residual spectrum of the power generation unit at time t, and y(t) be the output variable at time t in the linearized model of the power generation unit, i.e., the dq-axis subtransient potential of the power generation unit. F, T, K, and H are all satisfying H ∞ The parameter matrix of the performance constraints, C is the output matrix in the linearized model of the power generation unit, and t represents time.

8. The method for progressively locating the forced oscillation source in a power system considering a grid-type doubly-fed wind turbine, as described in claim 7, is characterized in that: The parameter matrices F, T, K, and H are solved in the following way: First, calculate the parameter matrices H and T according to the following expressions: H=E1(CE1) + T=I-E1(CE1) + C Where: I is the identity matrix, E1 is the distribution matrix of w1(t), () + The corresponding left inverse matrix is ​​expressed, where w1(t) represents the unknown input at time t in the linearized model of the power generation unit, which consists of other perturbation factors and can be completely decoupled by the traditional unknown input observer; Then, the following matrix inequalities are solved to obtain the parameter matrices U and P; Where: Φ is the transpose conjugate matrix of PTE2, the parameter matrix A1 = A - HCA, r is a small positive number, and the superscript... T Let A represent the transpose, A be the system matrix in the linearized model of the power generation unit, and E2 be the distribution matrix of w2(t). w2(t) represents the unknown input at time t in the linearized model of the power generation unit, which consists of other perturbation factors and cannot be completely decoupled by the traditional unknown input observer. Finally, the parameter matrices F and K are calculated from the parameter matrices U and P using the following expressions: F = A1 - K1C K = K1 + K2 U = PK1 K2=FH Where K1 and K2 are parameter matrices.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: The processor is used to execute the computer program to implement the progressive localization method for forced oscillation sources in power systems considering grid-type doubly fed wind turbines as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by the processor, it implements the progressive localization method for forced oscillation sources in power systems considering grid-type doubly fed wind turbines as described in any one of claims 1 to 8.

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