Electric power system inertia estimation method considering electrical distance and inertia center

Abstract

The invention belongs to the technical field of safety and stability of a power system, and particularly relates to a power system inertia estimation method considering an electrical distance and an inertia center, which comprises the following steps: firstly, introducing a correlation matrix to represent the electrical distance between generator buses, defining an inertia center parameter, and collecting frequency data by using the inertia center; and defining and calculating an inertia time constant of the power system through a swing equation in combination with power disturbance generated by the power system, and mastering the inertia level of the power system in real time. Due to the fact that inertia distribution in a power system is not uniform, frequency response differences after disturbance are more obvious, and inertia estimation errors when different frequency collection points are selected have randomness, the invention provides a power system inertia estimation method considering an electrical distance and an inertia center. The sampling of the single bus frequency can most accurately represent the frequency change of the inertial response of the system, so that the error of inertial evaluation is reduced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power system safety and stability, and particularly relates to a power system inertia estimation method considering electrical distance and inertia center. BACKGROUND

[0002] The large-scale integration of renewable energy through converter interfaces poses new challenges to the frequency dynamics and stability of power systems. With the gradual replacement of synchronous generators by renewable energy in power systems, the inertia of the entire power system decreases. When a relatively significant imbalance occurs between power generation and load in a power system, a large frequency rate of change and a serious frequency deviation may occur, which may lead to potential and uncontrolled cascading failures and eventually cause the power system to collapse.

[0003] Since inertia plays an important role in offsetting and controlling the initial change of grid frequency, grid operators have faced challenges related to inertia to avoid interrupting power services in operating scenarios with a large amount of renewable energy. Therefore, actively quantifying and monitoring available inertia so as to timely deploy scheduling strategies that can keep its value above a critical level has become a key issue for maintaining the stability of grid operation.

[0004] With the widespread use of wide-area measurement systems and phasor measurement units, the acquisition of measurement data has become more efficient. Inertia estimation based on measured data has been widely concerned by researchers in the field of power grid safety, which can be divided into small perturbation method and large perturbation method. The small perturbation method establishes a small signal model according to the measured data of random load or renewable energy output fluctuation, and analyzes the relationship between power system oscillation mode and inertia level. This method is susceptible to the operating state of the power system and noise. Therefore, it has poor adaptability in new energy power systems with frequent changes in operating mode. The large perturbation method estimates the inertia of the power system according to the swing equation by measuring the source-load power deviation and frequency response after a transient event. However, this method requires accurate power disturbance and frequency rate of change at the time of fault occurrence, and the quality of measurement data will have a great impact on the accuracy of inertia monitoring results. Due to the uneven distribution of inertia in the power system, the difference in frequency response after disturbance is more obvious, and the inertia estimation error when selecting different frequency collection points has randomness. SUMMARY

[0005] In order to solve the problem that the inertia estimation error has randomness when selecting different frequency collection points after disturbance in a power system, the application provides a power system inertia estimation method considering electrical distance and inertia center. First, a correlation matrix R is introduced to represent the electrical distance between generator busbars, and an inertia center parameter , frequency data is collected at the inertia center, combined with the power disturbance occurring in the power system, the inertia time constant of the power system is calculated by the swing equation definition, and the inertia level of the power system is grasped in real time.

[0006] The technical solution adopted by the present invention to solve the above problem is: a method for estimating the inertia of a power system considering electrical distance and inertia center, comprising the following steps:

[0007] S1: Introducing the correlation matrix , the correlation matrix Used to represent the electrical distance between generator buses, the correlation matrix Depends on the admittance matrix of the power system;

[0008] S2: Considering the electrical distance and the generator inertia constant, define the inertia center parameters , then the system bus The center of inertia parameters are ;

[0009] S3: Calculate each system bus The value is large, and the system bus corresponding to the maximum value is defined as the inertia center. The inertia center is used as the most appropriate frequency collection point for evaluating the inertia of the entire system, and the frequency data of the inertia center is collected;

[0010] S4: In order to improve the accuracy of inertia time constant estimation, the collected frequency data is preprocessed;

[0011] S5: After pre-processing the collected frequency data, the inertia time constant of the power system is calculated by the swing equation in combination with the power disturbance occurring in the power system.

[0012] The above-mentioned method for estimating the inertia of a power system considering the electrical distance and the center of inertia, the correlation matrix in step S1 is R =− [ Y nn + Y n + Y ln Y nm Y mn Y mm + Y lm ] − 1 , where and are the self-admittance of the generator bus and the self-admittance of other buses except the generator bus, is the mutual admittance between the generator bus and other buses, is the mutual admittance between other buses and the generator bus, It is a diagonal array composed of transient reactance of generators. and are the load equivalent admittance at the generator bus and the load equivalent admittance at other buses, respectively.

[0013] In the above-mentioned method for estimating the inertia of a power system considering the electrical distance and the center of inertia, the system bus in step S2 Center of inertia parameters , where is the maximum value of the generator number in the power system, is the maximum serial number of the generator bus in the power system, is the serial number of the generator in the power system, is the serial number of the system bus in the power system, is the serial number of the generator bus in the power system, 、 Generator The inertia constant and rated capacity, is the correlation matrix The elements in Indicates the system bus in the power system With generator bus The degree of electrical coupling between them.

[0014] In the above-mentioned method for estimating the inertia of a power system considering the electrical distance and the center of inertia, the preprocessing process in step S4 is as follows: first, outliers in the frequency data are identified and eliminated, and wavelet denoising is performed. At the same time, a detrending operation is performed on the frequency data. The offsets of the frequency data after the detrending operation are respectively calculated, and then the offsets are respectively divided by their reference values ​​to convert them into per-unit values.

[0015] In the above-mentioned method for estimating the inertia of a power system considering the electrical distance and the center of inertia, the inertia time constant calculated in step S5 is , where is the inertia time constant, is the unbalanced power of the power system, is the frequency of the center of inertia, is the frequency change rate.

[0016] In the above-mentioned method for estimating the inertia of a power system considering the electrical distance and the center of inertia, in step S5 , the frequency change rate is obtained by taking the average value of the frequency change rate within the sampling time window.

[0017] The present invention proposes a method for estimating the inertia of a power system that fully considers the electrical distance and the center of inertia, and defines the inertia center parameter , the maximum The system bus corresponding to the value is taken as the inertia center, and the frequency data of the inertia center is collected. Then, the frequency data is preprocessed. Combined with the power disturbance occurring in the power system, the inertia time constant of the calculation system is defined by the swing equation to achieve accurate evaluation of the power system inertia. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for describing the embodiments or the prior art.

[0019] Figure 1 For IEEE 10 machine 39 node system diagram.

[0020] Figure 2 For the inertia time constant calculation flow chart. DETAILED DESCRIPTION

[0021] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described below in combination with the drawings and examples.

[0022] A power system inertia estimation method considering electrical distance and inertia center, the correlation matrix , the correlation matrix is used to represent the electrical distance between the generator bus, the frequency of the system bus can be represented by the frequency of the generator bus, and the frequency of the generator bus is related to the correlation matrix , the correlation matrix depends on the admittance matrix of the power system. Considering the electrical distance and the inertia constant of the generator, the inertia center parameter is defined, and the value of of each system bus is calculated, then the system bus corresponding to the maximum value is defined as the inertia center of the entire power system, and the inertia center is the most appropriate frequency acquisition point for evaluating the inertia of the entire system. In order to improve the accuracy of the inertia time constant estimation, the collected frequency data needs to be preprocessed. After preprocessing the collected frequency data, the inertia time constant of the power system is calculated by the swing equation combined with the power disturbance of the power system.

[0023] The embodiments of the present application are as follows:

[0024] S1: introduce the correlation matrix to represent the electrical distance between the generator bus;

[0025] In the power system, the electrical distance is usually used to represent the electrical coupling degree between any two buses. The electrical distance is an important factor affecting the frequency distribution characteristics, and the smaller the value is, the stronger the coupling between the two buses is.

[0026] The correlation matrix depends on the admittance matrix of the system,

[0027] R =− [ Y nn + Y n + Y ln Y nm Y mn Y mm + Y lm ] − 1

[0028] In the formula, and are the self-admittance of the generator bus and the self-admittance of other buses except the generator bus, respectively, is the mutual admittance between the generator bus and other buses, is the mutual admittance between the generator bus and other buses, is a diagonal matrix composed of generator transient reactance, and are the equivalent load admittance at the generator bus and the equivalent load admittance at the other buses, respectively.

[0029] the correlation matrix the element in the correlation matrix reflects the degree of electrical coupling between the system bus and the generator bus , i.e., the electrical distance. The smaller the value of , the stronger the coupling between the system bus and the generator bus , and the greater the electrical distance between the two buses.

[0030] S2: Considering the electrical distance and the generator inertia constant, define the inertia center parameter

[0031] When selecting the frequency collection point, if only the degree of coupling between the buses is considered, a large amount of power system information representing the inertia distribution of the system will be lost, and it is difficult to reduce the influence of the difference in frequency response on the estimation accuracy.

[0032] Therefore, a new calculation method is proposed by considering the electrical distance and the generator inertia constant. This includes frequency collection through the inertia center, which is the most appropriate frequency collection point for evaluating the inertia of the entire system. The inertia center parameter is introduced, and the inertia center parameter of the system bus is as shown in the formula:

[0033]

[0034] In the formula, is the maximum value of the generator number in the power system, is the maximum value of the generator bus number in the power system, is the generator number in the power system, is the system bus number in the power system, is the generator bus number in the power system, , are the inertia constant and rated capacity of the generator , respectively, is the element in the correlation matrix , and represents the electrical distance between the system bus and the generator bus The degree of electrical coupling between them.

[0035] S3: Calculate each system bus The value is determined, the system bus corresponding to the maximum value is defined as the inertia center, and then frequency data is collected;

[0036] Combine the rated capacity and inertia constant of the generator to calculate the The value of each system bus is then compared The value of the system bus of The value is the largest, it is defined as the inertia center of the entire power system. The inertia center is the most appropriate frequency collection point for evaluating the inertia of the entire system, and frequency data is collected at the inertia center.

[0037] S4: In order to improve the accuracy of inertia time constant estimation, the collected frequency data is preprocessed;

[0038] After collecting frequency data, in order to improve the accuracy of inertia time constant estimation, it is first necessary to identify and remove outliers in the frequency data. To prevent individual outliers from affecting the inertia estimation of the entire period, the median absolute deviation (MAD) algorithm can be used to remove outliers in the frequency data. Finally, the mean of the remaining frequency data is taken as the final result within the estimation period. MAD is defined as the median of the absolute deviations of the data points to the median:

[0039]

[0040] Where, are the values ​​in the frequency data, is the median of frequency data.

[0041] After removing outliers, wavelet denoising is performed and the frequency data is detrended. The frequency data after detrending are then offset and divided by their reference values ​​to convert them into per-unit values.

[0042] S5: After pre-processing the collected frequency data, the inertia time constant of the power system is calculated by the swing equation in combination with the power disturbance occurring in the power system;

[0043] The swing equation is: ,in, is the disturbance power of the power system, is the mechanical power of the power system, , is the unbalanced power of the power system; is the equivalent inertia time constant; is the damping factor of the power system; is the frequency response deviation after disturbance; denotes time;

[0044] Since the controller in the power system has not yet acted, in the above equation = 0, the frequency response deviation after power disturbance can be obtained from the frequency response model:

[0045]

[0046] where, is the initial frequency response deviation;

[0047] The equivalent inertia time constant, unbalanced power and frequency rate of change satisfy the rotor motion equation, and further the frequency rate of change expression in the inertia response stage after power disturbance can be obtained:

[0048]

[0049] where, is the rated frequency, is the kinetic energy stored in the power system under the rated state, is the total rated capacity of the power system;

[0050] Therefore, according to the power system after power disturbance, the size of the power disturbance, the equivalent inertia time constant and the frequency satisfy the swing equation among them, and the inertia time constant of the power system is calculated by the swing equation definition. The calculation of the inertia time constant is shown in the equation:

[0051]

[0052] where is the inertia time constant, is the unbalanced power of the power system, is the frequency of the inertia center.

[0053] In the calculation of the above equation, the selection of the time window affects the accuracy of the inertia estimation. The sampling period should be selected as the period in which the power system primary frequency controller does not work. At the same time, in order to eliminate the random error brought by a single data collection point, the frequency rate of change in the above equation takes the average value of the frequency rate of change in the sampling time window.

[0054] To verify the above-mentioned power system inertia estimation method, in the attached Figure 1The effectiveness is tested in the IEEE 10-machine 39-bus system. The power system includes 10 generators (numbered from 1-10), 19 loads, 12 transformers and 39 system buses (including other buses numbered from 1-29 and generator buses numbered from 30-39). The modeling and simulation of the power system and the frequency data acquisition process are carried out in DIGSILENT / Powerfactory, and the frequency data preprocessing is performed in MATLAB 2018b.

[0055] Before the experiment starts, a known inertia constant is set as the actual value in each generator of the power system, and during the simulation process, the inertia constant is based on the power system reference capacity of 1000 MVA, as shown in Table 1.

[0056] Table 1

[0057] In order to verify the effectiveness of the inertia center, the dynamic response of the power system under large disturbance is simulated. The following simulation scenario is built:

[0058] The power system accesses new energy generator sets, and the G07 generator is replaced by 79 single-capacity 5.6 MVA, output 5 MW double-fed wind turbine generators. Among them, the double-fed wind turbine adopts maximum power point tracking control.

[0059] In order to verify the effectiveness of the frequency sampling point selected according to the inertia center, first, according to the network structure and system parameters of the improved IEEE 10-machine 39-bus system in the simulation scenario, the inertia center parameters of the 39 system buses are calculated . Secondly, the values of the 39 system buses are arranged in descending order, and the 2 system buses with the largest values and the 2 system buses with the smallest values are selected, and the selected system buses are shown in Table 2.

[0060] Table 2

[0061] As can be seen from Table 2, the value of system bus 4 is the largest, which is 2748.53. According to the proposed inertia center concept, the system bus with the largest value among all system buses is defined as the inertia center of the power system, so system bus 4 is defined as the inertia center of the improved IEEE 10-machine 39-bus system. The frequency sampling point selection based on the inertia center is to make the sampling frequency of a single bus most accurately represent the frequency change in the system inertia response process, thereby reducing the error of inertia evaluation. Therefore, the accuracy of inertia evaluation is used to verify the effectiveness of the inertia center.

[0062] The load 12 is set to increase 100 MW active load in 1 second, which causes power disturbance to the power system. The evaluation error of the system inertia at different frequency sampling points in the scenario is shown in Table 3.

[0063] Table 3

[0064] The inertia time constant calculated by the power system is obtained and compared with the equivalent inertia time constant of the system. The equivalent inertia time constant is shown in the following formula:

[0065]

[0066] In the formula, is the maximum value of the sequence number of the generator in the power system, and in this simulation, = 10, is the sequence number of the generator in the power system, , are the inertia constant and rated capacity of the generator, is the maximum value of the sequence number of the doubly-fed wind generator, is the sequence number of the doubly-fed wind generator, is the rated capacity of the doubly-fed wind generator.

[0067] As can be seen from Table 3, as the value of the selected system busbar decreases, the evaluation error of the inertia obtained by using the frequency data of the busbar as the calculation parameter increases. The value of the of the inertia center system busbar 4 is the largest, and the inertia time constant of the power system calculated by sampling the frequency of the inertia center system busbar 4 is 4.887 s, and the evaluation error is the smallest, which is 5.21%. On the contrary, the value of the of the system busbar 38 is the smallest, and the inertia time constant of the system calculated by sampling the frequency of the system busbar 38 is 5.608 s, and the evaluation error is the largest, which is 20.73%. Therefore, the evaluation error of the inertia is more random when sampling the frequency of different system busbars, and the sampling of the frequency of a single busbar can most accurately represent the frequency change of the system inertia response when the inertia center is used as the frequency sampling point, thereby reducing the evaluation error of the inertia and verifying the effectiveness of the inertia center.​

Claims

1. A method for estimating inertia of a power system considering electrical distance and center of inertia, characterized by: The following steps are involved: S1: Introducing the correlation matrix , the correlation matrix Used to indicate the electrical distance between generator buses; S2: Considering the electrical distance and the generator inertia constant, define the inertia center parameters , then the system bus The center of inertia parameters are ; S3: Calculate each system bus The value is large, and the system bus corresponding to the maximum value is defined as the inertia center. The inertia center is used as the most appropriate frequency collection point for evaluating the inertia of the entire system, and the frequency data of the inertia center is collected; S4: In order to improve the accuracy of inertia time constant estimation, the collected frequency data is preprocessed; S5: After pre-processing the collected frequency data, the inertia time constant of the power system is calculated by the swing equation in combination with the power disturbance occurring in the power system.

2. The method for estimating the inertia of a power system considering electrical distance and center of inertia according to claim 1, characterized in that: Correlation matrix in step S1 , where and are the self-admittance of the generator bus and the self-admittance of other buses except the generator bus, is the mutual admittance between the generator bus and other buses, is the mutual admittance between other buses and the generator bus, It is a diagonal array composed of transient reactance of generators. and are the load equivalent admittance at the generator bus and the load equivalent admittance at other buses, respectively.

3. The method for estimating the inertia of a power system considering electrical distance and center of inertia according to claim 2, characterized in that: System bus in step S2 Center of inertia parameters , where is the maximum value of the generator number in the power system, is the maximum serial number of the generator bus in the power system, is the serial number of the generator in the power system, is the serial number of the system bus in the power system, is the serial number of the generator bus in the power system, 、 Generator The inertia constant and rated capacity, is the correlation matrix The elements in Indicates the system bus in the power system With generator bus The degree of electrical coupling between them.

4. The method for estimating the inertia of a power system considering electrical distance and center of inertia according to claim 3, characterized in that: The preprocessing process in step S4 is as follows: first, identify and remove outliers in the frequency data, perform wavelet denoising, and perform a detrending operation on the frequency data. The frequency data after the detrending operation are respectively calculated for their respective offsets, and then divided by their reference values ​​to convert them into per-unit values.

5. The method for estimating the inertia of a power system considering electrical distance and center of inertia according to claim 4, characterized in that: The inertia time constant calculated in step S5 , where is the inertia time constant, is the unbalanced power of the power system, is the frequency of the center of inertia, is the frequency change rate.

6. The method for estimating the inertia of a power system considering electrical distance and inertia center according to claim 5, characterized in that: In step S5 , the frequency change rate is the average value of the frequency change rate within the sampling time window.

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