Method for estimating dynamic model of electrical network and grid-connected power converter therefor

Abstract

The embodiment of the invention relates to a method for estimating a dynamic model of a power grid and a grid-connected power converter used for the method. A method (100) of estimating a dynamic model of an electrical grid (10) is provided. The method comprises determining (106) a characteristic matrix from the input data, the characteristic matrix representing system dynamics of the electrical network (10) and having a rank r; performing (108) singular value decomposition (SVD) on the feature matrix, thereby identifying an order qlt of the dynamic model; r; and representing (110) the dynamic model by a dynamic model function having a number p of model coefficients dependent on q.

Description

Technical Field

[0001] The present disclosure relates to a method for estimating a dynamic model of a power grid, and also relates to a method for controlling a grid-connected power converter and a grid-connected power converter. Background Art

[0002] In the field of power generation and transmission, the management of power flow and energy storage is essential for the stability of the power grid. The power grid is typically a huge network that generates electricity and delivers it to end users via medium voltage (MV) drives connected to the grid. With the increasing integration of intermittent renewable energy and advanced power electronics, the power grid faces new challenges that affect stability and frequency predictability. Although these elements are necessary for modern energy needs, they introduce variability and complexity into the dynamics of the power grid. Solving these problems is critical to maintaining efficient and stable power grid operation in the context of rapid technological advancements.

[0003] Grid-tied power converters (such as those used in MV drives for driving various machines and processes) have controllable power flow and energy storage. The power converter of an MV drive can be thought of as absorbing power from a three-phase AC power source (the grid), storing this power as energy in DC form using capacitors or inductors, and finally converting this stored energy back into AC form and driving the electric machine. Furthermore, this power flow can be reversed, for example, when we harvest wind energy, i.e., the wind turbine converts mechanical power into electrical power, which in turn is rectified and stored, and finally the stored DC energy is inverted and fed back into the grid in AC form. Moreover, it is also possible to alternate this power flow, at least on the rectifier side or the inverter side, for shorter periods of time, to allow for additional controllability of the drive.

[0004] Such control can make the grid stable or unstable.In order to achieve beneficial control and positive effects on grid stability, it is important to have a control scheme that models the grid appropriately and is therefore based on an at least approximately correct understanding of the grid.

[0005] This application uses the following briefly described terms.

[0006] In this document, "or" is understood as a non-exclusive disjunction. Thus, the expression "A or B" means that at least one of the statements A and B is true. Alternatively, the expression "A or B" is understood to mean that feature A is explained by feature B.

[0007] The punctuation character " / " (slash) is interpreted as "or".

[0008] As used herein, the terms "substantially", "basically" or "about" generally mean that there may be a certain deviation from the feature represented by "substantially", "basically" or "about", such as up to 1%, up to 3% or up to 10%. SUMMARY OF THE INVENTION

[0009] In view of the above, there is provided a method for estimating a dynamic model of an electrical grid according to claim 1, a method for controlling a grid-connected power converter (120) according to claim 13, and a grid-connected power converter according to claim 14.

[0010] According to one aspect, there is provided a method for estimating a dynamic model of an electrical grid. The method includes determining a feature matrix based on input data, the feature matrix representing the system dynamics of the electrical grid and having a rank r; performing a singular value decomposition (SVD) on the feature matrix to identify the order q < r of the dynamic model; and representing the dynamic model by a dynamic model function in which the number p of model coefficients depends on q.

[0011] This estimation can in particular enable reliable and stable operation of the grid-connected power converter, which is particularly beneficial in scenarios where the dynamics of the electrical grid change due to the integration of renewable energy sources and power electronics.

[0012] The method can be at least partially computer-implemented. The electrical grid can include at least one power plant that generates electrical energy and a network of power transmission and distribution lines, substations, and / or transformers, the network of power transmission and distribution lines, substations, and / or transformers being designed to transmit power from the power plant, particularly via drives, to consumers such as homes and / or businesses in order to ensure a continuous and reliable electrical energy supply. The electrical grid can also have distributed and / or fluctuating power sources.

[0013] A dynamic model is a mathematical representation that describes the relationship between an input signal such as a voltage or current and a corresponding output signal at a given point in the electrical grid (e.g., at the point of common coupling PCC of the grid-connected converter). The dynamic model essentially captures how the components and dynamics of the electrical grid affect the transmission of electrical signals through the network. The dynamic model can be represented by a dynamic model function that represents such a dynamic response of the electrical grid to an input. The dynamic model can be represented, for example, in terms of the impedance of the electrical grid (which may represent the dynamic response, e.g., through a transfer function). The dynamic model can relate the input at one or more points of the electrical grid to the response at the same and / or different points of the electrical grid. The (one or more) points can be or include the point of common coupling PCC of the grid-connected power converter and / or can optionally include other points. Specifically, the dynamic model of the electrical grid can represent the relationship between the voltage and current at the point of common coupling PCC, specifically by correlating the change in voltage with the corresponding change in current.

[0014] Accurate modeling of the dynamic model allows the behavior of the power grid / network to be determined in response to various technical and environmental inputs, which is useful for the effective control and operational stability of the power grid and grid-connected components such as grid-connected converters.

[0015] The method includes the step of obtaining time-domain input data including electrical signals from the power grid during power grid operation. The time-domain input data refers to the measured electrical signals that vary with time as a function of the power grid process. The data includes the raw information required to analyze the behavior of the power grid under operating conditions. The time-domain input data is preferably obtained at the PCC.

[0016] The method further includes the step of processing the time-domain input data to obtain processed input data based on the time-domain input data. The processing may include frequency filtering, such as separating certain frequency components from the time-domain data and / or removing or focusing on certain frequencies or frequency ranges. The filtering step may be performed after Fourier transformation to the frequency domain. The filtering step allows the data to be prepared for more accurate analysis by reducing the amount of data, focusing on the relevant frequencies that affect the power grid performance, and bringing the input data into a useful format for determining the appropriate model function (e.g., into a format corresponding to the output of the dynamic model function), making the analysis more efficient.

[0017] The method further includes the step of determining a characteristic matrix based on the processed input data, the characteristic matrix representing the system dynamics of the power grid and having a rank r. The characteristic matrix is a mathematical construct that outlines the basic characteristics of the power grid dynamics based on the processed input data. The characteristic matrix is preferably a Hankel matrix and may be a square matrix. The rank r of the characteristic matrix is a fundamental property indicating the dimension or number of independent rows or columns in the matrix. This step provides a structured representation of the power grid dynamics that can be mathematically analyzed.

[0018] The method further includes the step of performing a singular value decomposition (SVD) on the characteristic matrix to identify the order q < r of the dynamic model. SVD is a statistical method for decomposing a matrix into its basic components. The order q represents the degree, order, or complexity of the dynamic model. This step allows the model of the power grid behavior to be further refined by identifying the most significant aspects (such as the order of the dynamic model) for accurate representation.

[0019] The method further includes the step of representing the dynamic model by a dynamic model function having p model coefficients, the number of model coefficients p depending on q (typically the same as or linearly increasing with q). For example, the dynamic model function may have a numerator and denominator of polynomials of order p1 and p2, respectively (and have the corresponding model coefficients as polynomial coefficients), where p1 and p2 depend on q. In one example, the dynamic model function may be a fraction having a numerator and a denominator, where the numerator and denominator are one or two polynomials of order q. The polynomials are characterized by their coefficients. This step allows the behavior of the power grid to be mathematically described in a clear form that can be used to analyze and predict power grid variables and / or behavior.

[0020] The method also includes the step of estimating the model coefficients of the dynamic model function using an adaptive algorithm. An adaptive algorithm is a computational method that dynamically adjusts parameters (coefficients of the model function) based on available data or conditions. The adaptive algorithm is based on processed input data and can be configured to minimize the deviation between the (processed) input data and the output of the dynamic model function. This step allows for fine-tuning of the model of grid behavior, ensuring that it accurately reflects the real-world dynamics of the grid. This enables improved prediction and analysis of the grid and control of grid-connected converters.

[0021] Parameters including the order and coefficients of the dynamic model at least partially determine the dynamic model of the power grid and can be used to understand the type of the power grid (eg, whether the power grid is an RL type, an LCL type, or another type of power grid).

[0022] The method includes features that represent interaction with an external physical reality, thereby providing a technical effect related to that interaction. This is done at least a) at input based on the acquisition of time-domain input data comprising electrical signals from a power grid, and b) at output based on outputting coefficients of a dynamic model derived by the method for the external physical reality that interacts with the external physical reality. This understanding can be used, for example, to control grid-connected power converters and / or other grid-connected components such as generators.

[0023] According to another aspect of the present disclosure, a method for controlling a grid-connected power converter is provided. The method comprises estimating a dynamic model of a power grid by an estimation method as described herein, and controlling the grid-connected power converter based at least on the result obtained by the estimation method (i.e., based on the determined dynamic power grid model function, and in particular on its coefficients).

[0024] According to another aspect of the present disclosure, a computer program embodied on a transient or non-transient computer-readable medium is provided, wherein the program is configured to cause at least one processor to execute the method for estimating a dynamic model of a power grid and / or the method for controlling a grid-connected power converter as described herein.

[0025] According to another aspect of the present disclosure, a grid-connected power converter is provided. The grid-connected power converter includes: a) a data acquisition unit adapted to acquire time-domain input data, the time-domain input data comprising electrical signals from a power grid during power grid operation; and b) a processor unit. The processor unit is adapted to estimate a dynamic model of the power grid using any of the methods described herein. The processor unit is further adapted to control the grid-connected power converter based on the determined dynamic model function.

[0026] A method for estimating a dynamic model of a power grid, a grid-connected power converter, and some possible advantages of the grid-connected power converter are described below.

[0027] The advantage of accurately estimating the dynamic model of the power system is enhanced analytical capabilities that facilitate the prediction of grid variables and behavior in response to various inputs and conditions. This can improve the stability and efficiency of network operations.

[0028] The advantages of using a characteristic matrix to represent system dynamics, followed by SVD, allow understanding the dynamics of the power grid with respect to the most influential components that adequately describe the grid dynamics. This allows for the creation of simple yet reliable grid models, simplifying complex data into a more concise form. This makes analysis more efficient while still capturing the fundamental dynamics of the grid. This also allows understanding the fundamental characteristics of the grid and its primary dynamic behavior.

[0029] The advantage of estimating the coefficients of the dynamic model based on the use of an adaptive algorithm is that the model responds to the actual grid conditions (as represented by the input data). This adaptability ensures that the model is accurate.

[0030] In summary, the claimed concept helps improve the operational stability and efficiency of the grid by providing an accurate and dynamic representation of the grid behavior, allowing to anticipate and mitigate potential problems, improving the performance of the grid and grid-connected converters even when new technologies and renewable energy sources are integrated.

[0031] Further aspects, advantages and features of the present disclosure are apparent from the dependent claims, the description and the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to understand the above features of the present disclosure in detail, the present disclosure briefly described above can be described in more detail with reference to typical embodiments. The accompanying drawings relate to embodiments of the present disclosure and are described below:

[0033] Figures 1a-1c Symbolic diagrams showing a) medium voltage drive, and b) and c) impedance measurement and estimation configurations;

[0034] Figure 2a , 2b shows a symbolic diagram of a power grid and a grid-connected power converter according to embodiments described herein;

[0035] Figure 2c , 2d shows a flow chart of c) a method for estimating a dynamic model of a power grid, and d) a method for controlling a grid-connected power converter according to embodiments described herein;

[0036] Figure 3 A flow chart showing a method of estimating a dynamic model of an electric grid according to embodiments described herein;

[0037] Figure 4a , 4b shows a) a histogram or singular values obtained by means of SVD, and b) a graphical representation of the null space intersection according to embodiments described herein;

[0038] Figures 5a-5c shows graphs illustrating results of grid impedance estimation according to embodiments described herein, including a) information content of frequency components of an LCL-type network impedance estimate, b) frequency dependence of estimated polynomial coefficients, and c) frequency dependence of an estimated dynamic model; and

[0039] Figure 6a , 6b shows a graph illustrating the estimation results of R and L with +-3*sigma bounds according to embodiments described herein. DETAILED DESCRIPTION

[0040] Reference will now be made in detail to various embodiments, one or more examples of which are illustrated in the figures. Each embodiment is provided by way of illustration and is not meant to be limiting. For example, features illustrated or described as part of one embodiment can be used on or in conjunction with any other embodiment to produce yet another embodiment. The present invention is intended to encompass such modifications and variations.

[0041] In the following description of the figures, the same reference numerals denote the same or similar components. Generally, only the differences with respect to the individual embodiments are described.

[0042] The reference numerals in the accompanying drawings are for illustration purposes only. The aspects of the present invention are not limited to any particular embodiment. Rather, unless otherwise indicated, any aspect or embodiment described herein may be combined with any other aspect or embodiment described herein.

[0043] Figure 1a shows the symbol diagram of the medium voltage drive, Figure 1b , 1c shows a symbolic diagram of the impedance measurement and estimation configuration.

[0044] like Figure 1aThe intermediate voltage MV drives (b)-(f) shown are power / frequency converters used in a wide range of industries to drive various machines and processes. The essential features of power converters (b)-(f) are power flow and energy storage. Traditionally, a power converter can be thought of as taking power from a three-phase alternating current (AC) power plant on the grid (a), converting it with the help of a transformer (b), switches (c) for safely connecting / disconnecting the power flow, (e), a storage device (d) for storing the power as direct current (DC) energy (e.g., with the help of capacitors or inductors), and finally converting this stored energy back to AC with the help of a DC / AC converter (f) to drive an electrical device (g).

[0045] For example, when wind power is generated, that is, the wind turbine converts mechanical kinetic power into electrical power, which is rectified and stored, and finally the stored DC power is inverted and fed back into the grid 10 in AC form, the power flow can be reversed (see the diagram showing the power flow). Figure 1a The power flow can also be reversed for a short time at least on the rectifier or inverter side to provide additional controllability of the drive.

[0046] Power electronics plays a vital role in the field of power conversion, enabling its widespread application in various industries such as mobility, renewable energy, oil and gas, and power generation. There are three key components in a power conversion setup. The first is the power system with transformers and input / output filters, the second is the power converter with motors or generators, and the third is the load. The use of power electronics has improved efficiency and productivity, but also brings stability challenges. The increased integration of renewable energy and power electronics has changed the dynamics of the power grid, resulting in frequency variations and unpredictability. These problems can be alleviated by enabling inverters 18 to estimate the grid impedance 12 and by incorporating grid impedance estimation techniques into their control loops. This can improve controller performance, transient and steady-state conditions.

[0047] Figure 2a , 2b shows a) a power grid with a grid-connected power converter, and b) a symbolic diagram of the grid-connected power converter. Figure 2c , 2d shows a flow chart of c) a method for estimating a dynamic model of a power grid and d) a method for controlling a grid-connected power converter according to an embodiment of the present invention. Figures 2a-2d The details of the explanation should not be understood as limiting Figures 2a-2d Rather, these details may also be combined with other embodiments explained with reference to other figures.

[0048] Figure 2aThe illustrated power grid 10 with the grid-connected power converter 18 comprises: a) a data acquisition unit 20 adapted to acquire 102 time-domain input data comprising electrical signals from the power grid 10 during grid operation; and b) a processor unit 22 .

[0049] The processor unit 22 is adapted to:

[0050] a) acquiring 102 time domain input data comprising electrical signals from the electrical grid 10 during operation of the electrical grid 10 ;

[0051] b) processing 104 the time-domain input data, thereby obtaining processed input data based on the time-domain input data;

[0052] c1) determining 106 a feature matrix based on the processed input data, the feature matrix representing

[0053] The grid 10 is system dynamic and has a rank r;

[0054] c2) Perform 108 singular value decomposition SVD on the feature matrix to identify the order q of the dynamic model <r;

[0055] d1) Express 110 dynamics using a dynamic model function with a number p of model systems

[0056] model, where the number of model coefficients p depends on q; and

[0057] d2) Estimating 112 model coefficients of the dynamic model function by means of an adaptive algorithm based on the processed input data.

[0058] e) The processor unit 22 is further adapted to control 124 the grid-connected power converter 18 based at least on the coefficients of the dynamic model function 12 .

[0059] The processor unit 22 is shown as being local to the grid-connected power converter 18, and in fact it may be integrated with the local controller of the grid-connected power converter 18 (e.g., as an embedded system). However, the processor unit 22 or portions thereof may also be distributed, such that its operations or portions thereof may be performed by a remote processor subunit connected via a network, such as a PC or cloud device connected to the local component via a data network. Moreover, the estimation of the dynamic model of the grid may be performed in an online or offline manner.

[0060] According to embodiments described herein, the functionality of the processor unit 22 for controlling the grid-connected power converter 18 based at least on the coefficients of the dynamic model function 12 may include:

[0061] - voltage control based on regulating the operation of voltage regulating devices such as tap-changing transformers and / or voltage regulators, and / or

[0062] - frequency control based on regulating generation and / or demand by means of mechanisms such as load shedding or frequency-dependent demand regulation, and / or

[0063] - reactive power control based on regulation of reactive power sources such as capacitor banks, and / or

[0064] - Stability control based on predicting the grid's behavior in response to disturbances, enabling the controller to implement stability-enhancing measures such as fast generation regulation or load balancing.

[0065] The grid 10 shown in FIG. 2B includes a grid-connected power converter 18 as described herein, and components of the grid 10 (not shown in FIG. 2B ) may be freely selected.

[0066] The method 100 for estimating the dynamic model of the power grid 10 shown in FIG2C includes:

[0067] a) acquiring 102 time domain input data comprising electrical signals from the electrical grid 10 during operation of the electrical grid 10 ;

[0068] b) processing 104 the time-domain input data, thereby obtaining processed input data based on the time-domain input data;

[0069] c1) determining 106 a feature matrix based on the processed input data, the feature matrix representing

[0070] The grid 10 is system dynamic and has a rank r;

[0071] c2) Perform 108 singular value decomposition SVD on the feature matrix to identify the order q of the dynamic model <r;

[0072] d1) The dynamic model function having a number p of model coefficients represents 110 dynamic

[0073] The state model, the number of model coefficients p depends on q; and

[0074] d2) Estimating 112 model coefficients of the dynamic model function by means of an adaptive algorithm based on the processed input data.

[0075] The method 120 for controlling the grid-connected power converter 18 shown in FIG. 2D includes estimating 122 a dynamic model of the power grid 10 by the estimation method 100 , and controlling 124 the grid-connected power converter 18 based at least on a result obtained by the estimation method 100 .

[0076] The concept and method of grid-connected power converters enable accurate determination of the behavior and characteristics of the power grid 10 by estimating its dynamic model (a mathematical representation relating input electrical signals to output electrical signals). This is achieved by processing the electrical signals from the power grid 10 to understand how the power grid 10 will respond to various inputs and conditions. The concept uses time-domain data conversion, frequency filtering, matrix analysis, and adaptive algorithms to estimate the dynamic model, which provides a detailed understanding of the power grid's dynamics.

[0077] The acquisition of time domain input data can provide the original electrical signal data required for analysis.

[0078] Processing 104 of the time-domain input data may include filtering the input data (possibly after Fourier transforming it to the frequency domain). For example, filtering may allow for the isolation of relevant frequencies for a more focused and efficient analysis, thereby reducing complexity and computational load by focusing on significant frequencies, thereby improving efficiency. Specifically, filtering may remove the frequency of the grid voltage, thereby simplifying the analysis.

[0079] Determining the characteristic matrix can provide a comprehensive representation of the system dynamics of the network and allow for detailed and specific analysis, and can improve the robustness and accuracy of the model by identifying and focusing on the most influential aspects of the network dynamics.

[0080] Representing the dynamic model through the model can provide a simplified but accurate representation of network behavior for analysis and prediction, and helps to effectively understand and control network behavior in real-time operation and / or in simulation / predictive analysis, forming the basis for real-time control of power converters 18 connected to the grid.

[0081] As used herein, the term "simulation" refers to an at least partially computer-implemented method including features representing interaction with an external physical reality, thereby providing a technical effect associated with that interaction. The method interacts with the external physical reality at least a) at input based on the acquisition of time-domain input data including electrical signals from an electrical grid, and b) at output based on the output of coefficients of a dynamic model obtained by the method for further use, such as for controlling a grid-connected power converter and / or power plant.

[0082] Estimation of the coefficients through an adaptive algorithm allows the model to remain accurate over time by adapting to changes in grid behavior, which may be due to aging infrastructure, changing load patterns, or the integration of renewable energy sources.

[0083] In summary, the method provides a systematic and efficient tool for understanding, predicting and controlling the behavior of the grid 10. It enhances the ability to control and improve grid performance, stability and reliability, and to adapt to changes in energy demand or generation availability.

[0084] According to embodiments described herein, a dynamic model may be represented by a dynamic model function (eg, comprising one or more polynomials). The dynamic model may be, for example, a state-space model and / or a data-based model.

[0085] The dynamic model can represent the relationship between the voltage and current at the PCC 16, in particular by relating changes in voltage to corresponding changes in current. The dynamic model can be represented, for example, as a transfer function such as any related function, or as a (complex) impedance. The dynamic model and methods described herein can allow for improved accuracy of dynamic model estimation.

[0086] According to the embodiments described herein, step a) may include acquiring time domain data at the point of common coupling (PCC) 16, which is preferably a location where consumers and / or power sources can be connected to the grid 10. This allows for increased reliability of the data used for dynamic model estimation, as the PCC 16 provides a comprehensive consolidation point that reflects the behavior of the entire grid. The grid-connected power conversion unit may belong to multiple grid-connected power conversion units connected to the (same) PCC. The method is applicable to multiple grid-connected power conversion units connected to the PCC. There may also be additional grid-connected power conversion units connected to the PCC, to which the method need not be applied, i.e., the above method does not need to be applied to each grid-connected power conversion unit connected to the PCC, although application to each grid-connected power conversion unit connected to the PCC is generally advantageous and preferred.

[0087] According to embodiments described herein, step b) may comprise using the frequency filtered time domain data as processed input data. In particular, the processed input data may be derived from the time domain data by applying frequency filtering techniques to eliminate or enhance some specific frequency components.

[0088] According to embodiments described herein, step b) of the estimation method may include converting the input time domain data into frequency domain data. This may allow analyzing the grid dynamics by distinguishing different frequency components, which is critical for accurate dynamic model estimation.

[0089] According to embodiments described herein, step b) of the estimation method can include removing the fundamental frequency component (the grid frequency) from the frequency domain data. This can eliminate the masking effect of the fundamental frequency, thereby increasing the sensitivity of the analysis to frequency components that more fully determine the grid dynamics. Step b) can also include retaining the frequency range near at least one known resonant frequency of the grid.

[0090] According to embodiments described herein, step b) of the estimation method may include removing noise from the frequency domain data. This may involve filtering out irrelevant or extraneous information from the frequency domain data to improve signal clarity. This can significantly improve the accuracy and reliability of the dynamic model estimation by focusing on the most relevant and informative aspects of the processed data.

[0091] According to embodiments described herein, step b) may comprise applying a Fourier transform to the time domain data, for example as a discrete Fourier transform DFT, such as a fast Fourier transform FFT. This enables obtaining frequency domain data, in particular for subsequent analysis of the frequency domain data.

[0092] According to embodiments described herein, step b) may include determining a set of frequency intervals for analyzing the frequency domain data and excluding frequencies outside of the range from the analysis of the frequency domain data. The range is critical for identifying the resonant frequency and impedance characteristics of the power grid 10, thereby enabling improved accuracy and efficiency of power grid dynamics analysis and / or reduced computational complexity and noise.

[0093] According to embodiments described herein, step b) may include evaluating the contribution of corresponding frequency components (of the processed input data) to the grid parameter estimation, e.g., evaluating the contribution of each frequency component, by determining the amplitude and phase information of the frequency components and / or discarding frequency components that add little or no information to the estimation process. This allows for a more accurate estimation process by focusing on significant frequency components, thereby increasing the accuracy and computational efficiency of the grid analysis.

[0094] According to an embodiment described herein, step b) of the estimation method may comprise determining processed input data based on the filtered data. In addition to filtering, further processing steps may be performed to obtain processed input data, for example, to facilitate the execution of subsequent steps c) and d) in an efficient manner. One example is a processing comprising generating dynamic model input data corresponding to the output of a dynamic function. In an example discussed in further detail below, step b) comprises processing the time domain input data (Ipcc(s); Vpcc(s)) by forming dynamic model input data corresponding to a dynamic model function being a network transfer function G. In this example, the dynamic model input data are brought into a form corresponding to the dynamic model function G1(jω) in Fourier space using the relationship I(jω) / V(jω)≈G1(jω). Thereafter, an inverse Fourier transform may be applied to obtain the processed input data h k . Further details are discussed in the examples below.

[0095] According to an embodiment described herein, step c1) comprises determining a characteristic matrix from the processed input data, the characteristic matrix representing the system dynamics of the power grid. The rank of the characteristic matrix is referred to as r.

[0096] According to embodiments described herein, step c1) can include constructing a feature matrix such that the rows and / or columns of the feature matrix are shifted relative to one another, particularly incrementally shifted relative to one another. For example, each row or column can be a shifted version of the processed input data, thereby allowing the underlying system dynamics to be captured for analysis. This can include arranging the processed input data into a specific pattern within the feature matrix to enable efficient and thorough analysis.

[0097] According to embodiments described herein, step c1) may comprise constructing a characteristic matrix as a Hankel matrix based on the processed input data. In a specific example discussed further below, the characteristic matrix is constructed based on the processed input data h k is determined to be a Hankel matrix.

[0098] A Hankel matrix can be formed by arranging the time series data such that each ascending diagonal from left to right contains elements of equal index sum, and each row is a shifted version of the previous row, shifted one position to the right. The Hankel matrix can be used to capture the temporal dynamics of the system by representing the evolution of the state of the power grid 10 over time, allowing patterns and relationships to be identified in the time series data.

[0099] According to embodiments described herein, step c2) of the estimation method may include obtaining singular values of the characteristic matrix. These singular values are key indicators of the properties of the matrix and the grid dynamics they represent. These indicators can provide insights into specific system dynamics and allow for more accurate and efficient grid analysis and dynamic model estimation.

[0100] According to the embodiments described herein, step c2) may comprise determining (in particular by means of SVD) the singular values of a truncated matrix, preferably obtained from the processed input data. Advantageously, the singular values provide information about the state of the power grid 10 and / or about the relevance of each state, so that the dominant state can be detected and retained while other states are ignored. This can improve the efficiency of the impedance and resonant frequency estimation.

[0101] According to embodiments described herein, the most significant singular value of the characteristic matrix is a value below a predetermined threshold, preferably 5% to 20% or 10% to 15% of the maximum singular value. A relatively small threshold, such as 5% or 10% of the maximum singular value, can result in a more accurate but less comprehensive capture of grid dynamics. Conversely, a relatively large threshold, such as 15% or 20% of the maximum singular value, can include less important data, potentially reducing accuracy while improving the overall robustness of the model.

[0102] According to an embodiment described herein, step c2) may include checking the singular values of the truncated matrix by means of a scree plot. This enables determining the number of effective singular values and / or distinguishing the information state of the power grid 10 from the less significant or noise-related states and / or implementing model order selection.

[0103] According to an embodiment described herein, step c2) may include determining the null space of the truncated matrix at different frequencies in order to obtain the least squares solution of the power grid parameters. This may allow for an accurate and reliable estimation of the power grid impedance and resonance frequency.

[0104] According to an embodiment described herein, step c2) may include: i) evaluating, in particular by means of SVD, the less relevant contributions during the dynamic model estimation process, and in particular ii) eliminating these contributions. Preferably, this may allow focusing on the most relevant components of the time-domain data, thereby enabling an effective and accurate dynamic model representation.

[0105] According to an embodiment described herein, step c2) of the estimation method may include (identifying and) retaining the most significant singular values of the eigenmatrix (e.g., as a set of r singular values or diagonal values determined to be the most significant); obtaining a truncated matrix of reduced dimension q < r operating in the reduced space corresponding to the retained singular values from the eigenmatrix. This may involve selecting the most informative singular values from the eigenmatrix.

[0106] This step c2) may improve the accuracy and efficiency of the dynamic model estimation, ensuring a more accurate analysis of the power grid dynamics. In particular, SVD and retaining only q < r singular values allow discarding frequency components that add little or no information to the estimation process. Thus, a simplified version of the dynamic model can be obtained, which retains the most significant information while reducing the complexity.

[0107] According to an embodiment described herein, step d1) includes representing the dynamic model by a dynamic model function having a number p of model coefficients, the number p of model coefficients depending on q. In particular, the number p of model coefficients may be determined to be equal to q or to grow linearly with q (e.g., p = 2*q - 1).

[0108] According to an embodiment described herein, in step d1), the dynamic function may include a first polynomial, and step d1) may include determining the order p1 of the first polynomial based on q, and the model coefficients include the polynomial coefficients of the first polynomial.

[0109] According to embodiments described herein, in step d1), the dynamic function may include a second polynomial, and step d1) may include determining the order p2 of the second polynomial based on q, and the model coefficients include polynomial coefficients of the second polynomial. Preferably, the first polynomial forms a numerator of the dynamic model function and the second polynomial forms a denominator of the dynamic model function.

[0110] According to an embodiment described herein, step d1) may include selecting a dynamic model function from a plurality of predetermined candidate dynamic model functions (e.g., a polynomial of order p based on order q, or the numerator and denominator of a fraction defined by polynomials of corresponding orders p1, p2 based on order q).

[0111] According to embodiments described herein, step d1) may comprise separating the dynamic model function into a real part and an imaginary part and estimating these parts.

[0112] According to embodiments described herein, step d1) may comprise determining the type of the power grid based on the rank q and / or based on the determined singular values.The type of power grid may comprise candidate types such as RL and / or LCL type power grids.

[0113] According to embodiments described herein, step d1) may comprise selecting a dynamic grid model function from a set of candidate functions tailored to the respective grid type (e.g., RL and / or LCL type grid impedance models), and optionally comprises selecting at least one specific frequency within a predetermined frequency range (in which resonance occurs).

[0114] According to embodiments described herein, step d1) may include determining the feasibility of the impedance estimate by evaluating whether the number of information frequencies is sufficient, preferably addressing the ability to provide a complete and representative picture of the impedance characteristics of the power grid 10 over the relevant frequency range. In particular, this may be done based on predetermined thresholds such as the signal-to-noise ratio and / or the amplitude of frequency components. The thresholds may also be based on a certain confidence level in the impedance estimate, such as a 95% confidence interval, or a threshold on the correlation coefficient between the estimated impedance 12 and the observed power grid behavior. This may be used to determine whether the available data is sufficient to provide information for accurate analysis.

[0115] According to embodiments described herein, step d2) of the estimation method may include estimating coefficients of the dynamic model by iteratively updating coefficients representing the relationship between input and output signals of the power grid 10, thereby adapting to temporal variations in the time-domain data. This may improve the accuracy of the dynamic model estimation, thereby ensuring more reliable and accurate modeling of the power grid's behavior in response to temporal signal variations.

[0116] According to embodiments described herein, step d2) may comprise estimating coefficients of the dynamic model by a recursive least squares (RLS) method. This may comprise iteratively refining the coefficients of the dynamic model, thereby allowing dynamic adaptation to changing grid conditions without significant processing delays.

[0117] According to embodiments described herein, step d2) may comprise estimating the coefficients of the dynamic model by a gradient descent method.

[0118] By applying these or similar methods to a reduced set of parameters (p parameters defined by the order q of the system), the grid behavior (e.g., impedance parameters) can be determined in a simple system in which the grid is represented in a realistic manner and can be understood and analyzed without overfitting (e.g., using only a reduced set of information frequencies or resonances or other parameters of the grid behavior determined in a simple model).

[0119] According to embodiments described herein, step d2) may comprise estimating polynomial coefficients of the grid dynamics model separately for the real and imaginary parts by means of the RLS method. By estimating the real and imaginary parts separately, complex grid behaviors and interactions can be accurately simulated.

[0120] According to embodiments described herein, step d2) may include applying an RLS method to the set of information frequencies for estimating model coefficients. Specifically, this is based on the concept that certain frequencies provide more valuable information about the impedance characteristics of the power grid 10 than others. This allows reducing the impact of less relevant data, thereby increasing the accuracy and relevance of the estimate.

[0121] According to embodiments described herein, step d2) may comprise determining polynomial coefficients of the grid impedance vector GIV using an RLS method, which may preferably comprise separating the dynamic model into real and imaginary parts and estimating these parts, thereby providing a detailed representation of the grid impedance characteristics at different frequencies. Preferably, GIV is a vector representation of the grid impedance 12 that can summarize a wide range of grid characteristics, such as phase angle, frequency-dependent behavior, and nonlinearities.

[0122] According to embodiments described herein, step d2) may comprise estimating the resonant frequency of the dynamic model by applying an RLS method to at least one valid frequency range, in particular at least one range around at least one resonant frequency of the power grid 10. By focusing the RLS method on these ranges, in particular around known resonant frequencies, the method may more accurately identify the resonant frequency of the dynamic model and / or allow for the design of effective measures to counteract potential resonance-related problems, such as overvoltage or system instability.

[0123] According to embodiments described herein, step d2) may include estimating the resonant frequency at a specific frequency range by applying a modified RLS method adapted to the LCL-type grid impedance model 12, preferably using a priori knowledge of the frequency range in which resonance occurs. The modified RLS method may be particularly well-suited to the LCL-type grid impedance model 12, and the modification may be expected to involve adjustments in the algorithm to better handle the characteristics of the LCL filter, such as its resonant behavior. The use of the modified RLS method adapted to the LCL-type grid impedance model 12 may allow for more accurate identification of resonant characteristics, thereby improving the accuracy and efficiency of resonant frequency estimation in the grid 10 having an LCL filter. Furthermore, the use of a priori knowledge of the expected resonant frequency range may allow for a focused and efficient analysis and / or a reduction in the dimensionality of the parameter space, thereby simplifying the estimation process.

[0124] According to embodiments described herein, step d2) may comprise using the condition number of the truncated matrix to assess the reliability of the parameter estimates (possibly measuring the sensitivity of the matrix to changes in the input data, thereby assessing the stability of the estimation process). The condition number of the truncated matrix is a measure of the sensitivity of the matrix to changes in its input data, and is used to assess how stable the parameter estimates may be. A high condition number indicates that small changes in the input data may result in large changes in the estimate, indicating potential instability or unreliability. Conversely, a lower condition number indicates that the estimate is more stable and reliable. This technique is particularly useful when working with matrices derived from real data, where accuracy and stability are essential. This can allow for reliable power grid analysis, thereby increasing the robustness and reliability of the estimation process.

[0125] According to embodiments described herein, step d2) may include determining confidence intervals for the impedance parameter estimates to assess the reliability of the estimated parameters, the confidence intervals indicating the deviation of each estimated parameter in the dynamic model from the mean, preferably based on determining a covariance matrix according to the RLS method. Preferably, the confidence intervals can be determined by constructing a covariance matrix based on the results of the RLS method. The confidence intervals can be derived from the covariance matrix, providing a statistical range within which the true value of each estimated parameter is likely to exist with a certain degree of probability. This can provide a quantitative measure of the reliability and accuracy of the estimates, allowing for an assessment of the risk and uncertainty associated with these estimates, resulting in a robust and reliable grid operation strategy.

[0126] According to embodiments described herein, step d2) of the estimation method may be followed by outputting the model coefficients obtained in step d2) for further use, such as for controlling the grid-connected power converter 18 and / or other grid-connected components, such as generators or loads. This may enable the analysis to be applied in technical practice, facilitating more precise control and improvement of the grid 10 and generator operation based on the detailed information obtained from the dynamic model estimation.

[0127] According to the embodiments described herein, estimating the dynamic model can include evaluating the grid response over a range of frequencies and identifying frequency-dependent characteristics of the grid 10, thereby providing a detailed frequency profile of the grid's behavior. In particular, in the context of the passive estimation techniques of the present invention, which preferably involve analyzing measured data without actively influencing grid behavior, grid response refers to analyzing how the grid 10 reacts under different conditions, as observed in the collected data, rather than actively inducing a response. This can achieve a comprehensive understanding of the behavior of the grid 10 at different frequencies, as well as more accurate modeling and prediction of grid behavior, facilitating grid management and planning, particularly when addressing frequency-specific issues.

[0128] Extended description of the embodiment

[0129] According to an embodiment, the concept of the present invention provides local measurements at the point of common coupling 16 (PCC), while the grid parameters are unknown (see Figure 1b , 1c). Based on the use of estimates of grid parameters in the converter control system, the controller can be better calibrated to detect faults and provide more reliable and stable operation. This estimation can be done by active methods in which the grid 10 is injected to obtain more information, or by passive techniques that use information from the normal operation of the converter as used in the present concept. In the case of Figure 1c In the measurement setup shown, the present concept provides an accurate estimation of the network parameters and / or the frequencies at which resonances occur.

[0130] Figure 3 FIG. 1 is a flow chart showing a method for estimating a dynamic model of a power grid 10 according to an embodiment of the present invention. Figure 3 The details of the illustrative explanations should not be construed as limiting Figure 3 Rather, these details may also be combined with other embodiments explained with reference to other figures.

[0131] according to Figure 3 In the illustrated embodiment, the concepts of the present invention can be applied to the estimation of the network impedance 12 and the determination of the resonant frequency. The estimation process can start with the measurement of electrical signals on the PCC side, primarily the PCC current(s) and voltage(s). The measurements are then pre-processed by a software filter unit followed by a discrete Fourier transform (DFT) operation. The resulting frequency domain data can then be fed into a network identification unit where a singular value decomposition is applied to the Hankel matrix to identify the impedance type (i.e., RL, LCL, etc.). Once the type is known, a linear model relating the unknown parameters to the measurements (i.e., Z^g(jω)) can be built.

[0132] The (generalized) condition number of the H(ω) matrix can be a useful measure of the reliability of the solution at a given frequency. If the condition number is large, the matrix is close to singularity and the corresponding frequency components are discarded. In addition, a data significance analysis can be performed on the data to assess the contribution of each frequency component to the network parameter estimation. Frequency components that add little or no information are discarded. If the number of information frequencies is less than a threshold, the problem is considered infeasible, that is, the frequency content is not rich enough to perform network impedance estimation; otherwise, the impedance estimation process is performed on the set of information frequencies.

[0133] The present method for the estimation problem is based on the recursive least squares (RLS) method, resulting in a computationally efficient solution. The RLS method can also be applied to resonant frequency estimation, but over a narrower frequency range and with a reduced approximation of the system model near the resonant frequency. This results in faster calculation of the resonance estimate, which is another novelty of the solution. All modules described can be run on an onboard embedded system at a slower sampling rate than the controller and / or run offline on a standalone computer.

[0134] exist Figure 1c In the network diagram shown, Vpcc and Ipcc are the PCC voltage and current of the converter, respectively, and Vg is the grid voltage. The relationship between the current Ipcc and the voltage Vpcc is given in the Laplace domain as follows:

[0135]

[0136] Where A(s 3 ) and B(s 4 ) represent the third and fourth order polynomials respectively, and k is the number that makes B(s 4 ) is the gain of the univariate polynomial, i.e., the highest-order coefficient equal to 1. Substituting jω for s to convert the equation into the frequency domain yields

[0137] I pcc (jω)=G1(jω)V pcc (jω)+G2(jω)V g (jω).

[0138] To estimate the network dynamic model G1(jω), assume that the signals Ipcc and Vpcc are measured at sampling time Ts, and furthermore, assume that Vg is unknown but has fixed frequency content only at 50Hz / 60Hz and zero frequency content at all other frequencies. Thus, the estimate of the dynamic model is given by

[0139]

[0140] where I^ and V^ are the discrete Fourier transforms (DFTs) of the signals (excluding the fundamental components).

[0141] The order of the system is very important in the setup, not only because it gives information about the frequency content that will be of interest, but it is also important to know which algorithm needs to be used to determine the parameters, as the algorithm is different for first-order and fourth-order grids 10 .

[0142] Figure 4a , 4b shows a) a histogram or singular values obtained by means of SVD, and b) a graphical representation of the null space intersection according to an embodiment of the present invention. Figure 4a , 4b The details of the illustrative explanation should not be understood as limiting Figure 4a , elements of 4b. Instead, these details can also be combined with other embodiments explained with reference to other figures.

[0143] Singular value decomposition (SVD) is a mathematical technique used to decompose a matrix into three separate matrices: singular values, left singular vectors, and right singular vectors. SVD provides insight into the relationship between input and output signals during system identification. The singular values capture the magnitude and complexity of the system's dynamics, helping to identify dominant poles and distinguish them from noise. The left singular vectors reveal the input-output relationship, which aids in input stimulus design. The right singular vectors provide insight into output sensitivity, model structure identification, and model order estimation. By analyzing these matrices, valuable information about system behavior, input-output relationships, and model characteristics can be extracted, enabling the system identification process.

[0144] The Hankel matrix (H) is a key component in estimating the order of the dynamic model using SVD. It is formed by appropriately selecting rows and columns from the input and output signal matrices, respectively. The resulting matrix H captures the dynamics of the underlying system. The inverse Fourier transform of the dynamic model estimate is calculated as,

[0145]

[0146] The Hankel matrix is represented by h k The value of n is the sampling length of the current and voltage signals, and r is chosen to be larger than the system dimension.

[0147]

[0148] The singular values of the Hankel matrix are calculated using singular value decomposition (SVD) and plotted on a so-called scree plot. The scree plot provides insight into the number of dominant singular values and, therefore, the order of the dynamic model. The decay of these singular values reveals valuable information about the number of dominant poles in the system. In order to accurately estimate the order of the dynamic model, the singular values obtained from the SVD are usually sorted in descending order. The rate at which these singular values decay indicates the presence of dominant poles in the system. A sudden drop or stagnation in the decay of the singular values may indicate the presence of noise. This is the final stage in which the order of the dynamic model is determined in order to establish the corresponding algorithm to be employed, for example for RL, LCL or higher order power grid models.

[0149] Once the Hankel matrix is generated and the principal singular values are calculated, it can be confirmed that the estimate is indeed for a fourth-order LCL-type grid 10, see FIG4A .

[0150] The information content of a frequency component refers to how much value it adds to the parameter estimate. As previously defined, the relationship between the measurement y and the parameter space x is given by the following linear equation.

[0151] y(ω)=H(ω)x

[0152] Any x that lies in the null space of H(ω) has no effect on the measurement. In other words, if x* is a least squares solution to the above equation, then adding any vector to x that belongs to the null space of H is still a valid solution. More strictly,

[0153] H(x * +x nH )=Hx * =y

[0154] Among them, x nH ∈null(H) and

[0155] In order to obtain a numerically robust and accurate estimate of x at a set of frequency points, the null spaces of H at different frequencies, i.e., null(H(cot)), must intersect each other. Since H is a 2×n matrix, where n is the dimension of the parameters, the null space of H has order n-2. That is, the null space is a hyperline in the parameter space. Figure 4b This concept is illustrated: x* represents y(ωi)=H(ω i )x i The least squares solution for , and the lines represent the null space for each frequency.

[0156] For a given frequency ω1, the minimum relative intersection angle of the null space of H(ω1) with all other null spaces can be calculated as

[0157]

[0158] where ∠ represents the principal angle between the two subspaces. The larger the angle (up to 90°), the greater the ull(H(ω i ))The more information the new direction introduces.

[0159] Figures 5a-5c Graphs illustrating the results of grid impedance estimation according to an embodiment of the present invention are shown, including a) the information content of the frequency components of the LCL-type network impedance estimate, b) the frequency dependence of the estimated polynomial coefficients, and c) the frequency dependence of the estimated dynamic model. Figures 5a-5c The details of the explanation should not be understood as limiting Figures 5a-5c Rather, these details may also be combined with other embodiments explained with reference to other figures.

[0160] Figure 5a The results of calculating the information content of the frequency components of LCL-type grid impedance estimation are shown. The red curve shows the subspace angle of each frequency relative to all other frequencies, which can be interpreted as the information richness of each frequency. According to this figure, the lower frequency and resonant neighborhood components have the main contribution to parameter estimation.

[0161] The recursive least squares (RLS) method is used to derive the polynomial coefficients in Giv(ω). The dynamic model is split into real and imaginary parts as follows:

[0162]

[0163] or,

[0164] A(jω 3 )=(r r (ω)+jr i (ω)B(jω 4 )

[0165] Where A and B are the numerator and denominator polynomials respectively, r r and r i are the real and imaginary parts respectively. Since the above equation is scale-invariant, we assume that the polynomial B is already univariate, that is, the highest degree coefficient is equal to 1. Therefore, we have

[0166] A(jω 3 )=a3(jω) 3 +a2(jω) 2 +α1(jω)+a0=(r r (ω)+jr i (ω))((jω) 4 +b3(jω) 3 +b2(jω) 2 +b1(jω)+b0)

[0167] Introducing the parameter vector x that captures the polynomial coefficients of A and B yields

[0168]

[0169] where x is defined as

[0170] x:=(b3 b2 b1 b0 a3 a2 a1 a0) T

[0171] The above equation now applies to the RLS algorithm in the form y = Hx, where y and H are both frequency dependent, and x is a constant parameter vector.

[0172] The RLS algorithm runs from DC frequency to the maximum frequency ω max And recursively update the parameter estimate vector x according to the following set of equations,

[0173] K=PH T (HPH T +R) -1 ,

[0174]

[0175] P=(I8-KH)P(I8-KH) T +KRK T .

[0176] where I8 is the 8×8 identity matrix.

[0177] Figure 5b As shown from DC to ω max The estimation process of the eight polynomial coefficients for a frequency sweep shows the results of the RLS method for estimating the dynamic model G1(ω). The estimated dynamic model fits most of the frequency range, especially near the resonance region. The estimated resonant frequency of the system (the imaginary part of the complex conjugate pole) deviates from the actual frequency by approximately 0.5%. Figure 5c The obtained simulation results are shown in Figure 2. The obtained curve of the estimated system (“RLS”) is very consistent with the real system. Figure 5c In , all three curves overlap to the point where it is impossible to distinguish the lines.

[0178] Figure 6a 6b shows a graph illustrating the estimation results of R and L with a +-3*sigma boundary according to an embodiment of the present invention. Figure 6a , 6b The details of the illustrative explanation should not be understood as limiting Figure 6a , elements of 6b. Instead, these details can also be combined with other embodiments explained with reference to other figures.

[0179] The sigma, or confidence interval, is calculated using the P covariance matrix from the least squares algorithm. The matrix is updated at each iteration of the algorithm, and once the final version is obtained, it is easy to determine how far the estimate of the true parameter may be off. This confidence interval, sigma, shows how certain and reliable the estimate of the true parameter is within a certain range. The confidence intervals and estimates for R and L are given in Figure 6A.

[0180] As described above, the RLS method is used to estimate the model coefficients (numerator and denominator coefficients) of the grid dynamic model. For the LCL-type grid impedance model 12, the resonant frequency is derived by finding the poles of the estimated dynamic model, which requires solving a fourth-order polynomial. However, if there is a priori knowledge of the frequency range in which resonance occurs, the RLS method can be restricted to operate only on a specific frequency range, thereby significantly reducing the calculation time.

[0181] Near the resonant frequency, the main contribution comes from the complex conjugate pole, and the rest of the system dynamics is assumed to be approximately constant over this range. Therefore, at frequencies near resonance, the dynamic model behaves as

[0182]

[0183] Where c is a complex constant, a and p are the real part and squared amplitude of the resonant pole, respectively. The resonant frequency is given by

[0184]

[0185] Taking a and p and the real and imaginary parts of c as parameters to be estimated, the RLS algorithm with 4 unknowns (instead of 8) can be set up using the following equation.

[0186]

[0187] where r r and r i are the real and imaginary parts of the I-over-V ratio at each frequency, and x is the parameter to be estimated.

[0188] x:=(αβ real(c)imag(c)) T .

[0189] Comparing the above equation for RLS with the equation in the previous section shows that:

[0190] 1. The frequency scaling problem, i.e. the fourth and third orders of ω, no longer exists in this case.

[0191] 2. The parameter space is now 4-dimensional instead of 8-dimensional, leading to faster computation.

[0192] 3. The frequency is swept in a limited range only near resonance.

[0193] These facts make the estimation process more robust and computationally cheaper.

[0194] Now consider a frequency interval of 200 Hz within the resonant frequency range of 280 Hz to 480 Hz.

[0195] Simulations were performed for different values of the resonant frequency, from approximately 290 Hz up to 440 Hz, still within the assumed frequency interval. FIG6B shows the relationship between the resonant frequency estimation error (relative) and the relative change about the mean value for different values of the resonant frequency. According to this figure, even when the resonant frequency changes by approximately 20%, RLS can still estimate the resonance within a 3% error range.

[0196] This written description uses examples to disclose the present disclosure, including the best mode, and also to enable any person skilled in the art to practice the described subject matter, including making and using any device or system. The embodiments described herein provide a method of estimating a dynamic model of an electric grid, a method of controlling a grid-connected power converter, a grid-connected power converter, and a grid-connected power converter, the estimation particularly enabling reliable and stable operation of the electric grid. Although various specific embodiments have been disclosed above, mutually non-exclusive features of the above-described embodiments may be combined with each other. The patentable scope is defined by the claims, and other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements that do not differ substantially from the literal language of the claims.

[0197] Reference numerals

[0198] 10 Power Grid / Network

[0199] 12 Grid Impedance, Impedance Model

[0200] 14 Power Plant / Three-Phase Generator

[0201] 16 Point of Common Coupling (PCC)

[0202] 18 Grid-connected power converters

[0203] 20 Data acquisition unit

[0204] 22 Processor Unit / Controller

[0205] 100 Methods for estimating dynamic models of power grids

[0206] 102 Get time domain input data

[0207] 104 Processing Input Data

[0208] 106 Determine the characteristic matrix

[0209] 108 Perform singular value decomposition SVD

[0210] 110 Representing dynamic models through dynamic model functions

[0211] 112 Estimating the coefficients of the dynamic model function

[0212] 120 Methods of controlling power grids

[0213] 122 Estimating Dynamic Models

[0214] 124 Control Grid

Claims

1. A method (100) for estimating a dynamic model of an electric grid (10), the method comprising: a) acquiring (102) time domain input data comprising electrical signals from the electrical grid (10) during operation of the electrical grid (10); b) processing (104) the time-domain input data to obtain processed input data based on the time-domain input data; c1) determining (106) a characteristic matrix based on the processed input data, the characteristic matrix representing the system dynamics of the power grid (10) and having a rank r; c2) performing (108) singular value decomposition (SVD) on the feature matrix to identify the order q of the dynamic model <r; d1) representing (110) the dynamic model by a dynamic model function having a number p of model coefficients, the number p of model coefficients depending on q; and d2) estimating (112) the model coefficients of the dynamic model function by means of an adaptive algorithm based on the processed input data.

2. The method (100) according to claim 1, wherein in step b), the processing (104) comprises at least one of the following: - Fourier transforming the time domain input data into the frequency domain; - filtering the input data, in particular frequency filtering, thereby obtaining filtered data, the frequency filtering in particular comprising removing fundamental frequency components and / or noise; - determining at least one frequency interval for frequency domain data analysis, and suppressing frequencies outside the at least one frequency interval determined based on the input data; - After filtering, Fourier transform the input data from the frequency domain back to the time domain; - determining said processed input data from said filtered data.

3. The method (100) of claim 1, wherein step b) comprises at least one of the following: - processing the input data into the processed input data, the processed input data having a format corresponding to the output of the dynamic model function; - Fourier transforming the time domain input data into the frequency domain; processing the input data in the frequency domain, and Fourier transforming the processed input data from the frequency domain back to the time domain.

4. The method (100) according to claim 1, wherein step c1) comprises at least one of the following: - constructing the characteristic matrix such that its rows and / or columns are mutually shifted, in particular incrementally shifted relative to each other, and in particular are shifted versions of the processed input data; - constructing the characteristic matrix as a Hankel matrix.

5. The method (100) according to claim 1, wherein step c2) comprises at least one of the following: - obtaining the singular values of the characteristic matrix, and / or retaining the most significant singular values of the characteristic matrix, and obtaining a truncated matrix based on the retained singular values and having a reduced dimension q <r; - determining singular values of said truncated matrix, preferably obtained from said time domain input data, in particular by means of singular value decomposition SVD, in order to detect and retain dominant states and ignore other states.

6. The method (100) according to claim 1, wherein step c2) comprises at least one of the following: - determining the null space of the truncated matrix at different frequencies; determining the main singular values, in particular by means of a singular value decomposition (SVD), and determining the reduced dimension q as the number of main singular values; - determining a main singular value by sorting the singular values according to decreasing magnitude and applying a cutoff criterion to the sorted singular values, in particular by means of a singular value decomposition (SVD); - determining the principal singular value by applying a predefined threshold.

7. The method (100) according to claim 1, wherein step d1) comprises at least one of the following: - selecting the dynamic model function from a plurality of predetermined candidate dynamic model functions based on the order q and / or based on determined singular values; - determining the type of the power grid based on said order q and / or based on said determined singular values; - determining, based on q, an order p1 of a first polynomial, the dynamic model function comprising the first polynomial, and the model coefficients comprising polynomial coefficients of the first polynomial; - determining an order p2 of a second polynomial based on q, the dynamic model function comprising the second polynomial, and the model coefficients comprising polynomial coefficients of the second polynomial, wherein preferably the first polynomial forms a numerator of the dynamic model function and the second polynomial forms a denominator of the dynamic model function; - determining the feasibility of the impedance estimation by evaluating whether the number of informative frequencies is sufficient, in particular based on predetermined thresholds such as the signal-to-noise ratio and / or the amplitude of the frequency components.

8. The method (100) according to claim 1, wherein step d2) comprises at least one of the following: - estimating the coefficients of the dynamic model function by iteratively updating the model coefficients; - estimating the coefficients of the dynamic model function by means of an optimization method, the optimization method being particularly configured to approximate a minimum of deviations relative to the processed input data; - estimating the coefficients of the dynamic model function by means of the adaptive algorithm based on the processed input data.

9. The method (100) according to claim 1, wherein step d2) comprises at least one of the following: - estimating the model coefficients as polynomial coefficients of the dynamic model function; - estimating the resonant frequency of the dynamic model function; - Estimating the model coefficients separately for the real and imaginary parts of the dynamic model function as a complex function.

10. The method (100) according to claim 1, wherein the dynamic model function satisfies at least one of the following: - the dynamic model function has a numerator and a denominator, and the model coefficients include numerator coefficients and denominator coefficients, wherein preferably the numerator is a first polynomial of order p1 and / or the denominator is a second polynomial of order p2; - the dynamic model function represents the relationship between the input signal and the output signal of the power grid (10), in particular the relationship between the time variation between the input signal and the output signal of the power grid (10), and in particular the relationship at the point of common coupling (PCC); - said dynamic model function of a given order q corresponds to a predetermined grid type, such as a grid of RL and / or LCL type; The dynamic model function includes resonances, in particular resonances within a predetermined frequency range.

11. The method (100) according to claim 1, wherein step d2) comprises at least one of the following: - evaluating the reliability of the estimated order q and / or the estimated model coefficients based on the condition number of the truncated matrix; - Determine confidence intervals for the estimated order q and / or the estimated model coefficients.

12. The method (100) of claim 1, wherein: Step a) comprises acquiring time domain data at the point of common coupling PCC, and wherein The method is applied to a plurality of grid-connected power conversion units connected to the PCC.

13. A method (120) of controlling a grid-connected component (18), the method comprising: - estimating (122) a dynamic model of a power grid (10) by means of a method (100) according to any one of claims 1 to 12, and - Controlling (124) a grid-connected power converter based on a determined dynamic grid model.

14. The method (100) of claim 13, wherein the grid-connected component (18) comprises at least one element selected from the list consisting of a grid-connected power converter, a generator, and a load.

15. A grid-connected component (18), comprising: - a data acquisition unit (20) adapted to acquire (102) time-domain input data comprising electrical signals from the power grid (10) during power grid operation; as well as - a processor unit adapted to estimate a dynamic model of the power grid by a method (100) according to any one of claims 1 to 12, and The grid-connected component (18) is controlled (124) based on the determined dynamic model function (12).

16. The grid-connected power converter (18) according to claim 15, wherein the processor unit comprises at least one of the following: - a local on-board controller, preferably embedded, having said processor unit; - A distributed control system having said processor unit comprising remote processor subunits connected via a network.

17. The grid-connected component (18) according to claim 15, wherein the grid-connected component (18) comprises at least one element selected from the list consisting of a grid-connected power converter, a generator, and a load.

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