Harmonic source modeling method and device considering background harmonic fluctuation and medium

Abstract

The invention relates to the technical field of electric power operation and maintenance, in particular to a harmonic source modeling method and device considering background harmonic fluctuation and a medium, and the method comprises the steps: collecting voltage and current data of load outer ports of various harmonic sources; establishing a load equivalence time domain circuit model, and solving load equivalence impedance parameters by using linear least squares under a non-negative condition; and constructing a harmonic source load model, and dynamically adjusting an impedance parameter in real time according to the background harmonic fluctuation by using a recursive least square method to obtain a harmonic source model adapted to the background harmonic fluctuation. Compared with the prior art, the constructed harmonic source load model can accurately represent harmonic characteristics changing along with background harmonic fluctuation, and the adaptability and accuracy of the model in a dynamic environment are improved.

Description

Technical Field

[0001] This invention relates to the field of power operation and maintenance technology, and in particular to a general harmonic source modeling method, device and medium that takes into account background harmonic fluctuations. Background Technology

[0002] In recent years, the scale and complexity of harmonic sources connected to the power system have continued to rise. On the one hand, large-capacity nonlinear loads, represented by electric arc furnaces and electric locomotives, are constantly flooding the power grid. Electric arc furnaces melt metal with an electric arc, and the randomness and nonlinearity of the arc cause severe distortion of the current waveform, injecting a large number of low-order harmonics into the power grid, causing significant interference to the voltage and current quality of the power grid. Electric locomotives rely on power electronic conversion devices to achieve traction power supply, and the harmonic currents generated in the rectification and inversion stages enter the power grid through the contact network, affecting the power supply quality and equipment safety along the line. On the other hand, various household appliances based on power electronics technology are widely used in residential life. These small-capacity, decentralized harmonic sources are spread throughout the low-voltage distribution network, such as common variable frequency air conditioners and electronic devices powered by switching power supplies. When they are working, they generate high-order harmonics through the rapid switching of power electronic switching devices. Although the harmonic content of a single device is limited, the superposition effect of harmonics generated by a large number of devices operating simultaneously should not be underestimated.

[0003] Different types of harmonic sources vary greatly in their generation mechanisms, harmonic spectrum characteristics, and adaptability to operating conditions. If traditional approaches are followed in distribution network harmonic research, involving in-depth analysis of the harmonic characteristics of each type of source before constructing an accurate model, the research process becomes cumbersome and inefficient due to the vast number and diverse characteristics of harmonic sources. Furthermore, the resulting models are often only applicable to specific scenarios and have extremely poor applicability to the complex and ever-changing actual power grid conditions, failing to meet the real-time, accuracy, and versatility requirements of power system planning, operation, and control for harmonic analysis. Therefore, constructing a universal model that can encompass the characteristics of multiple harmonic sources and adapt to different operating scenarios has become the main research direction in the field of harmonic source modeling.

[0004] Chinese patent application CN202311513971.1 discloses a general harmonic source modeling method based on load equivalent impedance. However, current technical solutions have the following shortcomings: Existing harmonic source models typically ignore the influence of background harmonic fluctuations on parameters, and the models are only applicable to a small range of voltage fluctuations. Once this range is exceeded, the model error increases rapidly. While data-driven general harmonic source models improve adaptability to background harmonic fluctuations, it is difficult to achieve a balance between accuracy, universality, and the physical interpretability of model parameters. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art, such as ignoring the influence of background harmonic fluctuations on parameters and the difficulty in achieving a balance between accuracy, universality and physical interpretability of model parameters, and to provide a universal harmonic source modeling method that considers background harmonic fluctuations.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] As a first aspect of the present invention, a harmonic source modeling method considering background harmonic fluctuations is provided, comprising the following steps:

[0008] Collect voltage and current sampling data at the external ports of various harmonic source loads, including current under different supply voltages;

[0009] A load equivalent time-domain circuit model is established, and the load equivalent impedance parameters are obtained by using voltage and current sampling data.

[0010] A load model for harmonic sources is constructed based on the equivalent impedance parameters of the load.

[0011] By using the recursive least squares method to dynamically adjust the impedance parameters of the harmonic source load model in real time according to the background harmonic fluctuations, a harmonic source model adapted to the background harmonic fluctuations is obtained.

[0012] As a preferred technical solution, the time-domain circuit model of the load equivalent is established as follows:

[0013] The internal structure of the load is equivalent to a time-domain equivalent circuit consisting of a time-varying resistor and a time-varying reactance connected in series; wherein, the equivalent impedance parameters of the load include the time-varying resistor and the time-varying reactance, and the time-varying reactance includes inductive reactance and capacitive reactance.

[0014] As a preferred technical solution, the equivalent impedance parameters of the load are calculated as follows:

[0015] Using linear least squares under nonnegativity conditions, with the objective of minimizing the sum of squared residuals between the observed values ​​and the predicted values ​​from the time-domain load equivalent circuit model, the equivalent load impedance parameters are obtained:

[0016]

[0017] In the formula: u(t1), u(t2) and i(t1), i(t2) are the instantaneous values ​​of voltage and current at adjacent sampling points, respectively; i ′ (t1) and i ′ (t2) are the derivatives of i(t1) and i(t2), respectively; R(t) is the time-varying resistance, and L(t) is the time-varying reactance.

[0018] As a preferred technical solution, the harmonic source load model

[0019] The voltage and current data at the load port are acquired, the equivalent impedance parameters of the load are calculated based on the acquired voltage and current data, and the calculated equivalent impedance parameters of the load are used to assign values ​​to the time-varying resistance and time-varying reactance in the equivalent time-domain circuit of the load.

[0020] The input voltage is applied to the equivalent time-domain circuit of the load after assignment to obtain the output current value of the harmonic source.

[0021] As a preferred technical solution, during the continuous operation of the harmonic source load model, whenever a new set of test data is acquired, the similarity between consecutive periodic voltage arrays is calculated using a sliding window function, and it is determined whether the similarity meets the model parameter update conditions.

[0022] When the similarity satisfies the model parameter update condition, the previous parameter estimation result is used as a benchmark, and the existing estimation result is recursively corrected using a new set of test data based on the recursive least squares method.

[0023] As a preferred technical solution, the determination of whether the similarity satisfies the model parameter update condition is as follows:

[0024] Establish a sliding window, within which there are multiple consecutive characteristic voltage arrays, and the number of characteristic voltage arrays within the sliding window is less than the number of periodic current arrays during the shortest steady-state operation time of the load equipment;

[0025] Calculate the cumulative sum of similarity coefficients between the current periodic voltage array and each feature voltage array in the sliding window, and determine whether the supply voltage has changed;

[0026] If the cumulative sum of similarity coefficients is greater than or equal to the update threshold, the model parameters are determined not to need to be updated; if the cumulative sum of similarity coefficients is less than the update threshold, the model parameters are updated.

[0027] As a preferred technical solution, the similarity coefficient between the current time period voltage array and each feature voltage array in the sliding window is calculated as follows:

[0028]

[0029] In the formula: s(·,·) represents the correlation coefficient; u a u b Two sets of time-series data for equivalent load parameters; and This represents the sequence data u a and u b Data at time t in ascending order and The grade number; for and The difference in grade between them; n is the length of the voltage data.

[0030] As a preferred technical solution, for the new set of test data, the impedance parameter Y(k) is identified using a recursive least squares algorithm to recursively correct the existing estimation results, as follows:

[0031]

[0032] In the formula: Here, is the impedance parameter; K(k) is the gain matrix; P(k) is the covariance matrix, P(0) is the identity matrix; u(k) is the k-th voltage; i(k) is the k-th current;

[0033] The function for the k-th current i(k) is constructed as follows:

[0034] f(i(k))=i(k)-U(k)Y(k-1)+U(k)K(k)[i(k)-u T (k)Y(k-1)]

[0035] The iterative relationship of i(k) is as follows:

[0036]

[0037] In the formula: the superscript n indicates the nth iteration; f ′ (·) represents the first derivative of f(·).

[0038] As a second aspect of the present invention, an electronic device is provided, including a memory, a processor, and a program stored in the memory, wherein the processor, when executing the program, implements the harmonic source modeling method considering background harmonic fluctuations as described above.

[0039] As a third aspect of the present invention, a storage medium is provided on which a program is stored, which, when executed, implements the harmonic source modeling method considering background harmonic fluctuations as described above. Compared with the prior art, the present invention has the following advantages:

[0040] 1) This invention proposes a harmonic source modeling method based on the equivalent impedance parameters of the load. By establishing an equivalent time-domain circuit model of the load, the relationship between the equivalent impedance parameters of the load and the electrical quantities at the ports is derived, and the equivalent impedance parameters of the load are obtained. Then, a harmonic source load model is constructed based on the equivalent impedance parameters of the load, which can obtain the current estimate of the harmonic source based on the input voltage data. This method is easy to obtain data and has strong engineering applicability. At the same time, this model can not only model single harmonic sources of different load types, but also be used for modeling multiple types of harmonic sources. The model has high accuracy and strong versatility, and the model parameters have physical interpretability, which is beneficial to harmonic analysis.

[0041] 2) Based on the equivalent impedance parameters of the load and combined with the recursive least squares method, this invention establishes a dynamic self-adjusting model that can adapt to the background voltage change environment. This allows the model parameters to be adaptively adjusted in accordance with the background harmonic fluctuations, accurately characterizing the harmonic characteristics of the harmonic source load as the background harmonic fluctuations change, and improving the adaptability and accuracy of the model in dynamic environments. Attached Figure Description

[0042] Figure 1 This is a flowchart of a general harmonic source modeling method that takes into account background harmonic fluctuations according to the present invention;

[0043] Figure 2 This is the equivalent load time-domain circuit diagram of the present invention. Detailed Implementation

[0044] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0045] Example 1

[0046] This invention proposes a general harmonic source modeling method that considers background harmonic fluctuations, the principle flowchart of which is as follows: Figure 1 The specific steps are as shown:

[0047] S1. Data Acquisition and Processing: Acquire voltage and current sampling data from the external ports of various harmonic source loads, including current under different supply voltage conditions, and synchronize the measured voltage and current waveform data.

[0048] S2. Solve for model parameters: Construct a unified time-domain equivalent circuit model of the load, derive the mathematical relationships of the port electrical quantities, and solve for the equivalent impedance parameters of the load.

[0049] S3. Construction of a general model for harmonic source loads: a general model for harmonic source loads based on the equivalent impedance parameters of the loads.

[0050] S4. Dynamic Self-Adjusting Model Construction: The recursive least squares method is used to adaptively adjust the impedance parameters of the harmonic source load model according to background harmonic fluctuations. This establishes a harmonic source model that can adapt to background harmonic fluctuations.

[0051] Furthermore, the equivalent circuit model of the load in the time domain in step S2 is constructed as follows:

[0052] This invention, based on measured data, equates the internal structure of the load to an equivalent time-domain circuit consisting of a time-varying resistance and a time-varying reactance connected in series, such as... Figure 2As shown in the figure, the equivalent impedance parameter of the load comprises two parts: time-varying resistance and time-varying reactance (including inductive and capacitive reactance), which can be expressed as Z(t) = R(t) + jL(t), where R(t) is the time-varying resistance, L(t) is the time-varying reactance, and j is the imaginary unit. When the equivalent impedance parameter of the load exhibits a non-linear change, it indicates that the load is a harmonic source load and will generate harmonics. Conversely, it is a non-harmonic source load.

[0053] Furthermore, in step S2, the equivalent impedance parameters of the load are solved using the least squares method, as detailed below:

[0054] The identification of the equivalent impedance parameters of the load needs to be based on the equivalent circuit model of the load in the time domain. Based on Thevenin's law, the equivalent time domain port voltage and current relationship of the load can be obtained, as shown in equation (1). For a general steady-state harmonic source load, the voltage u(t) and current i(t) data at its port are collected. When the sampling frequency is much greater than the frequency of load parameter changes, the equivalent impedance parameters of the load can be assumed to be equal at two adjacent sampling points according to the idea of ​​the infinitesimal method, and the equivalent impedance parameters R(t) and X(t) of the load can be calculated using the least squares method. Given the voltage and current signal sequences, equation (2) can be established based on equation (1) through two adjacent sample data points. Furthermore, the solution of the equivalent impedance parameters of the load can be obtained as equation (3).

[0055]

[0056]

[0057] In the formula: u(t1), u(t2) and i(t1), i(t2) are the instantaneous values ​​of voltage and current at adjacent sampling points, respectively; i ′ (t1) and i ′ (t2) are the derivatives of i(t1) and i(t2), respectively.

[0058]

[0059] Equation (2) can be equivalent to:

[0060] B=AX+δ (4)

[0061] In the formula: δ is the measurement noise vector.

[0062] Considering that the values ​​of resistance and inductance are non-negative, the linear least squares under non-negative conditions are used to solve X in equation (4). According to the least squares criterion, the sum of squared residuals between the observed values ​​and the model prediction values ​​is minimized, and the objective function is established as shown in equation (5).

[0063]

[0064] In the formula: This indicates that the sum of squared errors is minimized.

[0065] Furthermore, in step S3, a general model for harmonic source loads is constructed, as follows:

[0066] The harmonic source load model mainly consists of three core modules: a data acquisition module, an impedance module, and a current output module. During model operation, the data acquisition module is responsible for accurately acquiring voltage and current sampling data at the load port. Based on the acquired voltage and current data, the equivalent impedance parameters of the load can be accurately calculated according to the method described above. After obtaining the equivalent impedance parameters of the load, the time-varying resistance and time-varying reactance in the equivalent time-domain circuit of the load can be accurately assigned values. Finally, when the input voltage is applied to the impedance module, the current value estimated by the model can be output through the current output module. The calculation of this estimated current follows the formula given in equation (6).

[0067]

[0068] Furthermore, in step S4, a dynamic adaptive model is constructed based on the recursive least squares method, as detailed below:

[0069] In actual load operation scenarios, the operating point is not in a static steady state but changes dynamically with voltage fluctuations. This characteristic dictates that model parameters cannot remain constant, necessitating a dynamic correction strategy to ensure accurate model representation of load characteristics. To achieve recursive estimation of model parameters, during the continuous operation of the harmonic source load, whenever a new set of test data is acquired, the previous parameter estimation result is used as a benchmark, and the existing estimation results are recursively corrected using this new set of test data. Through this iterative update mechanism, more accurate parameter estimates are gradually derived. Therefore, the harmonic source load model considering background harmonic fluctuations is essentially a model with dynamic adaptive capabilities.

[0070] Assuming the voltage of the kth time is u(k) and the current is i(k), the coefficient matrix after adding the new data is shown in equation (7).

[0071]

[0072] In the formula: U k =[U k-1 ,u(k)] T ;I k =[I k-1 ,i(k)] T .

[0073] The impedance parameters are identified and updated using a recursive least squares algorithm, and the calculation formula is shown in equation (8):

[0074]

[0075] In the formula: K(k) is the gain matrix; P(k) is the covariance matrix; P(0) is the identity matrix;

[0076] Since i(k) is unknown in the actual modeling process, it is necessary to construct a function about i(k). For this purpose, the following function is constructed:

[0077] f(i(k))=i(k)-U(k)Y(k-1)+U(k)K(k)[i(k)-u T (k)Y(k-1)] (9)

[0078] The iterative formula is obtained using Newton's method:

[0079]

[0080] In the formula: the superscript n indicates the nth iteration; f′(·) represents the first derivative.

[0081] In order to dynamically track changes in model parameters, this invention constructs a sliding window function and uses this function to calculate the similarity between consecutive periodic voltage arrays.

[0082] The change in the supply voltage of the harmonic source load can directly reflect the change in model parameters. In order to evaluate the degree of change between voltages, a voltage similarity coefficient is defined. The similarity between voltage data is quantified by calculating the correlation coefficient, thereby determining whether the load model parameters need to be updated. The calculation process is shown in equations (11)-(12):

[0083]

[0084] In the formula: u a u b Timing data for two sets of supply voltages; and This represents the sequence data u a and u b Data at time t in ascending order and The grade number; for and The difference in grade between them; n is the length of the voltage data. Correlation coefficient s(u a ,u b The value of u is between [-1, 1], and the larger the value, the greater the u. a with u b The higher the similarity.

[0085] A sliding window is established based on the similarity coefficient. Each sliding window contains multiple characteristic voltage sequences, and all characteristic voltage arrays within the window are in the same state. The continuous characteristic voltage arrays within the sliding window are used as reference data to judge the changes in load model parameters.

[0086]

[0087] In the formula: {u1,…,u m Let} represent the set of characteristic voltage arrays in the current sliding window, and m be the dynamic index value of the number of characteristic voltage arrays. m can be used to characterize the current sliding window size, and the sliding window size is less than the number of periodic current arrays in the shortest steady-state operating time of the load equipment, so that the characteristic voltage arrays obtained in the sliding window are in the same state. F(u) is the cumulative sum of similarity coefficients between the current periodic voltage array u and each characteristic voltage array in the sliding window, and its effective value range is greater than 0.

[0088] The value of F(u) is calculated to determine whether the supply voltage has changed, i.e., whether the model parameters need to be updated, as shown in Equation (13). Based on actual measurement experience, 0.9 is defined as the threshold for determining whether the model parameters need to be updated. When F(u) ≥ 0.9, it is determined that the model parameters do not need to be updated; otherwise, it indicates that the model parameters need to be updated.

[0089]

[0090] Example 2

[0091] As a second aspect of the present invention, this application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the harmonic source modeling method considering background harmonic fluctuations as described above. In addition to the processors, memory, and interfaces described above, any data processing device in the embodiments may also include other hardware depending on the actual function of the data processing device, which will not be elaborated further.

[0092] Example 3

[0093] As a third aspect of the present invention, this application also provides a computer-readable storage medium storing computer instructions thereon, which, when executed by a processor, implement the harmonic source modeling method considering background harmonic fluctuations as described above. The computer-readable storage medium can be an internal storage unit of any data-processing device as described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units of any data-processing device and external storage devices. The computer-readable storage medium is used to store the computer program and other programs and data required by the data-processing device, and can also be used to temporarily store data that has been output or will be output.

[0094] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for modeling harmonic sources considering background harmonic fluctuations, characterized in that the steps include... include: Collect voltage and current data at the external ports of various harmonic source loads; Establish a load equivalent time-domain circuit model and solve for the load equivalent impedance parameters using linear least squares under non-negativity conditions; A harmonic source load model is constructed, and the impedance parameters are dynamically adjusted in real time according to the background harmonic fluctuations using the recursive least squares method to obtain a harmonic source model that adapts to the background harmonic fluctuations.

2. The harmonic source modeling method considering background harmonic fluctuations according to claim 1, characterized in that, The load equivalent time-domain circuit model adopts a time-domain equivalent circuit that treats the internal structure of the load as a time-varying resistance and a time-varying reactance connected in series; wherein, the load equivalent impedance parameters include time-varying resistance and time-varying reactance, and the time-varying reactance includes inductive reactance and capacitive reactance.

3. The harmonic source modeling method considering background harmonic fluctuations according to claim 1, characterized in that, The equivalent impedance parameters of the load are calculated as follows: Using linear least squares under nonnegativity conditions, with the objective of minimizing the sum of squared residuals between the observed values ​​and the predicted values ​​from the time-domain load equivalent circuit model, the equivalent load impedance parameters are obtained: In the formula: u(t1), u(t2) and i(t1), i(t2) are the instantaneous values ​​of voltage and current at adjacent sampling points, respectively; i ′ (t1) and i ′ (t2) are the derivatives of i(t1) and i(t2), respectively; R(t) is the time-varying resistance, and L(t) is the time-varying reactance.

4. The harmonic source modeling method considering background harmonic fluctuations according to claim 1, characterized in that, The harmonic source load model is as follows: Acquire voltage and current data at the load port, and calculate the equivalent impedance parameters of the load based on the acquired voltage and current data; The time-varying resistance and time-varying reactance in the equivalent time-domain circuit of the electrical load are assigned values ​​using the calculated equivalent load impedance parameters; The input voltage is applied to the equivalent time-domain circuit of the load after assignment to obtain the output current value of the harmonic source.

5. A harmonic source modeling method considering background harmonic fluctuations according to claim 1, characterized in that, During the continuous operation of the harmonic source load model, whenever a new set of test data is acquired, the similarity between consecutive periodic voltage arrays is calculated using a sliding window function, and it is determined whether the similarity meets the model parameter update conditions. When the similarity satisfies the model parameter update condition, the previous parameter estimation result is used as a benchmark, and the existing estimation result is recursively corrected using a new set of test data based on the recursive least squares method.

6. A harmonic source modeling method considering background harmonic fluctuations according to claim 5, characterized in that, The determination of whether the similarity satisfies the model parameter update condition is as follows: Establish a sliding window, within which there are multiple consecutive characteristic voltage arrays, and the number of characteristic voltage arrays within the sliding window is less than the number of periodic current arrays during the shortest steady-state operation time of the load equipment; Calculate the cumulative sum of similarity coefficients between the current periodic voltage array and each feature voltage array in the sliding window, and determine whether the supply voltage has changed; If the cumulative sum of similarity coefficients is greater than or equal to the update threshold, the model parameters are determined not to need to be updated; if the cumulative sum of similarity coefficients is less than the update threshold, the model parameters are updated.

7. A harmonic source modeling method considering background harmonic fluctuations according to claim 6, characterized in that, The similarity coefficient between the current time period voltage array and the feature voltage arrays in the sliding window is calculated as follows: In the formula: s(·,·) represents the correlation coefficient; u a u b Two sets of time-series data for equivalent load parameters; and This represents the sequence data u a and u b Data at time t in ascending order and The grade number; for and The difference in grade between them; n is the length of the voltage data.

8. A harmonic source modeling method considering background harmonic fluctuations according to claim 5, characterized in that, Using the new set of test data, the impedance parameter Y(k) is identified using a recursive least squares algorithm to recursively correct the existing estimation results, as follows: In the formula: Here, is the impedance parameter; K(k) is the gain matrix; P(k) is the covariance matrix, P(0) is the identity matrix; u(k) is the k-th voltage; i(k) is the k-th current; The function for the k-th current i(k) is constructed as follows: f(i(k))=i(k)-U(k)Y(k-1)+U(k)K(k)[i(k)-u T (k)Y(k-1)] The iterative relationship of i(k) is as follows: In the formula: the superscript n indicates the nth iteration; f ′ (·) represents the first derivative of f(·).

9. An electronic device comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it implements the harmonic source modeling method that considers background harmonic fluctuations as described in any one of claims 1-8.

10. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements the harmonic source modeling method that considers background harmonic fluctuations as described in any one of claims 1-8.

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