Thevenin equivalent parameter estimation method adaptive to irregular load fluctuation

Abstract

The invention discloses a Thevenin equivalent parameter estimation method suitable for irregular load fluctuation. According to the method, an external system Thevenin equivalent parameter recursion model is established, the fluctuation amplitude of equivalent parameters is analyzed, and the fluctuation form of the equivalent parameters is modeled as follows: in a calculation time window, equivalent impedance is approximate to a constant value; the equivalent potential fluctuates slightly around a central value and follows two-dimensional normal distribution. And constructing a likelihood function by using an indirect observation value of equivalent potential represented by equivalent point measurement voltage, measurement current and unknown equivalent impedance. And taking a negative logarithm of the likelihood function as a target function, and solving by using an optimization algorithm to obtain equivalent impedance and equivalent potential distribution parameters. According to the method, the problem that an existing Thevenin equivalent parameter estimation method based on the statistical law is limited by the fluctuation amplitude and form of the load side parameters is solved, the application range of the equivalent parameter estimation method is widened, and the accuracy of equivalent parameter estimation is improved.

Description

Technical Field

[0001] The present invention belongs to the field of electric power technology and relates to a Thevenin equivalent parameter estimation method, specifically an equivalent parameter estimation method that uses equivalent impedance and equivalent potential distribution parameters as unknown parameters for maximum likelihood estimation. Background Art

[0002] The Thevenin equivalent circuit effectively simplifies power system calculations and is currently widely used in voltage stability analysis, protection setting calculations, and loop current calculations. The rapid and accurate calculation of its equivalent parameters is crucial. In real-world power grids, detailed information about external systems is unknown, necessitating the calculation of Thevenin equivalent parameters using local measurements.

[0003] The most classic method for calculating Thevenin equivalent parameters using local information is the least squares method. This method assumes that the equivalent potential and equivalent impedance remain constant within a calculation time window. Least squares regression is performed on multiple samples collected for the purpose of obtaining the Thevenin equivalent parameters. This method suffers from parameter drift, and subsequent improvements have been made based on this method. These improvements can be divided into three categories, depending on the constraints imposed. The first category establishes constraints under which the Thevenin equivalent parameters remain constant. Specifically, these methods use certain data screening methods to select valid measurements that meet the conditions. This type of method is difficult to apply in scenarios where the Thevenin equivalent parameters fluctuate moment by moment. The second category assumes that the Thevenin equivalent parameters vary moment by moment and tracks the calculation of the equivalent parameters by establishing numerical constraints between two moments. However, this type of method suffers from the difficulty of selecting the initial value for iteration. The third category assumes that the Thevenin equivalent parameters fluctuate slightly around a central value within a calculation time window. Multiple data sets are collected and the solution is derived based on the statistical laws they satisfy. However, the accuracy of these methods is limited by the amplitude and form of the load-side parameter fluctuations, limiting their scope of application. Summary of the Invention

[0004] The purpose of the present invention is to propose a Thevenin equivalent parameter estimation method that is adaptable to irregular load fluctuations, so as to solve the problem that the existing equivalent parameter estimation method based on statistical laws is limited by the amplitude and form of load side parameter fluctuations, and to improve the accuracy of equivalent parameter estimation.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A Thevenin equivalent parameter estimation method adapted to irregular load fluctuations includes the following steps:

[0007] S1. Determine the time window length and moving step size for estimating the Thevenin equivalent parameter;

[0008] S2. Establish a recursive model of the Thevenin equivalent parameters of the external system and analyze the fluctuation range of the Thevenin equivalent parameters;

[0009] S3. Model the fluctuation form of the Thevenin equivalent parameter and construct the probability density function of the equivalent potential;

[0010] S4. collecting real-time samples of voltage and current at equivalent points, and representing the equivalent potential samples as a set of indirect observation samples calculated from the measured voltage, the measured current, and the unknown equivalent impedance;

[0011] S5. construct a likelihood function based on the equivalent potential according to the probability density function of the equivalent potential obtained in S3 and the indirect observation sample of the equivalent potential obtained in S4;

[0012] S6. Take the negative logarithm of the likelihood function obtained in S5 as the objective function, and use the optimization algorithm to solve and obtain the probability distribution parameters of equivalent impedance and equivalent potential.

[0013] The present invention provides a beneficial effect by theoretically deriving and rationally modeling the fluctuation amplitude and form of the Thevenin equivalent parameter. Compared to other Thevenin equivalent parameter estimation methods based on statistical laws, the present invention is unaffected by the fluctuation amplitude and form of load-side parameters and achieves higher estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 The calculation flow chart is shown in Figure 2.

[0015] Figure 2 It is the recursive model of the Thevenin equivalent parameters of the external system.

[0016] Figure 3 Study model for Thevenin equivalent parameters.

[0017] Figure 4 For application case.

[0018] Figure 5 The figure shows the calculation results of the present invention in the application example. DETAILED DESCRIPTION

[0019] The present invention will be further described below with reference to the accompanying drawings.

[0020] This application discloses a Thevenin equivalent parameter estimation method adapted to irregular load fluctuations, referring to Figure 1 , including the following steps:

[0021] S101: Determine the time window length and moving step size for estimating the Thevenin equivalent parameter;

[0022] S102: Establish a recursive model of the Thevenin equivalent parameters of the external system and analyze the fluctuation range of the Thevenin equivalent parameters;

[0023] S103: Model the fluctuation form of the Thevenin equivalent parameter and construct the probability density function of the equivalent potential;

[0024] S104: collecting real-time samples of voltage and current at equivalent points, and representing the samples of equivalent potential as a set of indirect observation samples calculated from the measured voltage, the measured voltage, and the unknown equivalent impedance;

[0025] S105: constructing a likelihood function based on the equivalent potential according to the equivalent potential probability density function obtained in step S103 and the equivalent potential indirect observation sample obtained in step S104;

[0026] S106: Taking the negative logarithm of the likelihood function obtained in step S105 as the objective function, and using an optimization algorithm to solve and obtain the probability distribution parameters of the equivalent impedance and the equivalent potential.

[0027] Furthermore, statistically based methods for estimating the Thevenin equivalent parameters require collecting a sufficient number of samples within a time window. Practical systems also require an update rate for real-time estimation of the Thevenin equivalent parameters. To meet these requirements, in step S101, the time window length and moving step size are determined based on the sampling frequency of the measurement equipment.

[0028] Furthermore, in step S102, according to the actual grid structure, the situations involved in recursively calculating the Thevenin equivalent parameters of any external system can be summarized as follows: Figure 2 The three categories shown are: power supply branches in parallel, load branches in parallel, and lines (transformers) in series.

[0029] As a preferred embodiment of the present application, in step S102, the process of analyzing the fluctuation amplitude of the Thevenin equivalent parameter is as follows:

[0030] S102-1: For each calculation scenario, construct expressions for calculating the Thevenin equivalent potential and equivalent impedance;

[0031] S102-2: According to error propagation theory, when the independent variable changes, the change in the function can be expressed by its total differential. Therefore, the equivalent potential / equivalent impedance obtained in S102-1 is totally differentiated with respect to the variables in the system.

[0032] S102-3: Divide the total differential expression of the equivalent potential / equivalent impedance obtained in S102-2 by its own expression in S102-1 to obtain the influence of each variable in the system on the equivalent potential / equivalent impedance. Each term corresponds to the relative change of a variable, and the coefficient of each term is the transfer coefficient of the variable, reflecting its influence on the equivalent potential / equivalent impedance.

[0033] S102-4: By comprehensively analyzing the transfer coefficients of the variables obtained in S102-3 and the fluctuation ranges of the variables in the actual system, the fluctuation ranges of the Thevenin equivalent parameters can be obtained.

[0034] Furthermore, as a preferred embodiment of the present invention, in step S102, the analysis of the fluctuation amplitude of the Thevenin equivalent parameter concludes that: the fluctuation amplitude of the equivalent impedance is very small and can be ignored; the fluctuation amplitude of the equivalent potential is much larger than the fluctuation amplitude of the equivalent impedance, and is equivalent to the average fluctuation level of the external system power supply voltage.

[0035] Furthermore, as a preferred embodiment of the present invention, in step S103, the fluctuation form of the Thevenin equivalent parameter is modeled according to its fluctuation amplitude: within a calculation time window, the equivalent impedance approximately does not fluctuate and is simplified to a constant; the equivalent potential fluctuates slightly around a central value and obeys a certain prior probability distribution.

[0036] Furthermore, as a preferred embodiment of the present invention, in step S103, the potential in the actual system is a complex number, so the equivalent potential can be expressed as a binary variable consisting of its real part and imaginary part The prior probability distribution it obeys is the most common normal distribution in nature, that is, the equivalent electric potential obeys a two-dimensional normal distribution.

[0037] Furthermore, as a preferred embodiment of the present invention, in step S103, the probability density function of the equivalent potential is:

[0038]

[0039] where μ and Σ are the expectation vector and covariance matrix of the two-dimensional normal distribution, respectively.

[0040] Further, as a preferred embodiment of the present invention, in step S104, referring to Figure 3 , the indirect observation sample of the equivalent potential E is expressed as:

[0041] E=U+IZ

[0042] Where U is the measured voltage vector, I is the measured current matrix, and Z is the equivalent impedance vector.

[0043] Furthermore, as a preferred embodiment of the present invention, in step S105, a likelihood function is constructed based on the probability density function obtained in step S103, and the equivalent potential in the formula is replaced by the equivalent potential indirect observation sample obtained in step S104 to obtain a likelihood function based on the equivalent potential:

[0044]

[0045] Where θ = (μ, Σ, Z) is the unknown parameters such as the equivalent potential distribution parameters and the equivalent impedance, N is the number of samples, Represents a transpose operation.

[0046] Furthermore, for the convenience of calculation, the negative logarithm of the objective function is taken, and the objective function in step S106 can be expressed as:

[0047]

[0048] By solving this problem, we can obtain unknown parameters such as equivalent potential distribution parameters and equivalent impedance.

[0049] Furthermore, as a preferred embodiment of the present invention, in step S106, the problem is an unconstrained optimization problem, and the optimization algorithm used is the quasi-Newton method.

[0050] Embodiment: In order to make the purpose, technical solution and advantages of the embodiment of the present invention clearer, the following is a Figure 4 , a complete and clear description of the technical solutions in the embodiments of the present invention is given.

[0051] In order to verify the effectiveness of the present invention in the estimation of Thevenin equivalent parameters, a Figure 4 The power grid model shown.

[0052] The left side of busbar B4 is the upper 35kV system, and the right side is the 10kV system. The structure in the dotted box is subjected to the Thevenin equivalent. Represents the upper system of the 35kV power grid, and the system impedance is (1.2+5j)Ω; The internal impedance is (0.8+5j)Ω, representing the parallel power supply. Transformer T1 has a capacity of 5000kVA, a transformation ratio of 6.3kV / 38.5kV, and a high-voltage side impedance of (2.67+20.75j)Ω. The double-circuit line between B2 and B3 is 30km long, with an impedance of (0.27+0.379j)Ω per kilometer, used to simulate the switching of lines within the network. L1 is load No. 1, used to simulate the fluctuation of the internal load of the equivalent grid. T2 is a step-down transformer with a capacity of 1600kVA, a transformation ratio of 35kV / 10.5kV, and a low-voltage side impedance of (2.58+13.44j)Ω. The internal impedance is (0.5+3j)Ω, which is used to simulate another power supply of the 10kV system; L2 is the equivalent point 10kV system load.

[0053] exist and Voltage fluctuations of ±1.5% were superimposed on the load. The base power of load L1 was (2+1.5j)MVA, and a sinusoidal power variation with a 20% amplitude was superimposed on the base power to simulate load fluctuations. The power of equivalent point load L2 was based on actual load data measured on the 10kV side of a substation, with one data point per second for a total of 24 hours.

[0054] In order to verify the effectiveness of the present invention in identifying the switching of the external system operation mode, according to the actual power supply situation of the distribution network, Figure 4 The dashed box shows four operating modes: Mode 1: All equipment except power source G2 is operational; Mode 2: Power source G1 is disconnected in addition to Mode 1; Mode 3: One circuit between B2 and B3 is disconnected in addition to Mode 2; Mode 4: Transformer T2 is disconnected for maintenance, and power source G2 is activated to supply the 10kV system. The operating mode is switched every six hours.

[0055] The specific application steps of the present invention are as follows:

[0056] According to the sampling frequency of the measuring device, the time window length is determined to be 4 minutes, that is, each time window contains 240 sampling points, and the moving step length is equal to the time window length;

[0057] The measured voltage and measured current of bus B4 are collected and expressed as a set of equivalent potential indirect observation values calculated from the measured voltage, measured current and unknown equivalent impedance;

[0058] According to the above indirect observation values of equivalent potential, a likelihood function that the equivalent potential obeys the two-dimensional normal distribution is constructed;

[0059] The negative logarithm of the likelihood function is taken as the objective function, and the quasi-Newton method is used to solve this unconstrained optimization problem to obtain the distribution parameters of equivalent impedance and equivalent potential.

[0060] The present invention tracks and calculates the equivalent resistance and equivalent reactance like Figure 5 In each operating mode, the average error of the tracking and calculation of the equivalent impedance of the present invention is shown in the following table:

[0061] Operation mode Equivalent impedance / Ω Calculate the average error / % Method 1 1.34+5.41j 4.94 Method 2 1.34+5.42j 1.63 Method 3 1.70+5.90j 2.29 Method 4 0.500+3.00j 1.15

[0062] As can be seen from the above embodiments, the present invention has a small equivalent impedance calculation error in each operating mode, verifying the accuracy of the present invention in tracking and calculating equivalent impedance and the effectiveness of identifying changes in external system topology when facing irregularly fluctuating actual load data.

[0063] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, can make equivalent replacements or changes based on the technical solution and inventive concept of the present invention, which should be within the scope of protection of the present invention.

Claims

1. A Thevenin equivalent parameter estimation method adapted to irregular load fluctuations, characterized in that: The steps include: S1. Determine the time window length and moving step size for estimating the Thevenin equivalent parameter; S2. Establish a recursive model of the Thevenin equivalent parameters of the external system and analyze the fluctuation range of the Thevenin equivalent parameters; S3. Model the fluctuation form of the Thevenin equivalent parameter and construct the probability density function of the equivalent potential; S4. collecting real-time samples of voltage and current at equivalent points, and representing the equivalent potential samples as a set of indirect observation samples calculated from the measured voltage, the measured current, and the unknown equivalent impedance; S5. construct a likelihood function based on the equivalent potential according to the probability density function of the equivalent potential obtained in S3 and the indirect observation sample of the equivalent potential obtained in S4; S6. Take the negative logarithm of the likelihood function obtained in S5 as the objective function, and use the optimization algorithm to solve and obtain the probability distribution parameters of equivalent impedance and equivalent potential.

2. The Thevenin equivalent parameter estimation method adapted to irregular load fluctuations according to claim 1, characterized in that: In S1, the time window length and the moving step length are determined by the sampling frequency of the measurement equipment.

3. The Thevenin equivalent parameter estimation method adapted to irregular load fluctuations according to claim 1, characterized in that: In S2, a recursive model of the Thevenin equivalent parameters of the external system is established, that is, three types of calculation situations involved in the calculation of the Thevenin equivalent parameters of any external system are established: The first type of calculation situation: the power supply branches are connected in parallel; The second type of calculation situation: load branches in parallel; The third calculation scenario: lines or transformers are connected in series.

4. The Thevenin equivalent parameter estimation method adapted to irregular load fluctuations according to claim 3 is characterized in that: In S2, the process of analyzing the fluctuation range of the Thevenin equivalent parameter is divided into the following steps: S2-1, construct expressions for calculating the Thevenin equivalent potential and equivalent impedance for each calculation case; S2-2, perform total differentiation on the calculated equivalent potential and equivalent impedance; S2-3, divide the total differential expression of the equivalent potential obtained in S2-2 by itself to obtain the transfer coefficient of the influence of each variable on the equivalent potential; Divide the total differential expression of the equivalent impedance obtained by S2-2 by itself to obtain the transfer coefficient of each variable on the equivalent impedance; S2-4, analyze the transfer coefficient of the influencing factors obtained in S2-3 to obtain the fluctuation range of the Thevenin equivalent parameter.

5. The Thevenin equivalent parameter estimation method adapted to irregular load fluctuations according to claim 4, characterized in that: In S3, the fluctuation form of the Thevenin equivalent parameter is modeled as follows: within a calculation time window, the equivalent impedance does not fluctuate approximately and is simplified to a constant; the equivalent potential fluctuates slightly around a central value and obeys a certain prior probability distribution.

6. The Thevenin equivalent parameter estimation method adapted to irregular load fluctuations according to claim 5, characterized in that: Represent the equivalent potential as a binary variable consisting of its real and imaginary parts The prior probability distribution it obeys is the normal distribution, that is, the equivalent potential obeys the two-dimensional normal distribution, then the probability density function of the equivalent potential is: where μ and Σ are the expectation vector and covariance matrix of the two-dimensional normal distribution, respectively.

7. The Thevenin equivalent parameter estimation method adapted to irregular load fluctuations according to claim 1, characterized in that: In S4, the indirect observation sample of the equivalent potential E is expressed as: E=U+IZ Where U is the measured voltage vector, I is the measured current matrix, and Z is the equivalent impedance vector.

8. The Thevenin equivalent parameter estimation method adapted to irregular load fluctuations according to claim 7, characterized in that: In S5, the likelihood function based on the equivalent potential is: Where θ = (μ, Σ, Z) is the unknown parameters such as the equivalent potential distribution parameters and the equivalent impedance, N is the number of samples, Represents a transpose operation.

9. The Thevenin equivalent parameter estimation method adapted to irregular load fluctuations according to claim 8, characterized in that: In S6, the objective function is expressed as:

10. The Thevenin equivalent parameter estimation method adapted to irregular load fluctuations according to claim 1, characterized in that: In S6, the optimization algorithm used is the quasi-Newton method.

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