A method and apparatus for real-time estimation of grid harmonic impedance

Abstract

This invention discloses a method and apparatus for real-time estimation of power grid harmonic impedance. The method includes: Step S1, real-time acquisition of voltage and current data at the point of common coupling, performing Fourier transform on the acquired data to obtain the harmonic voltage and harmonic current of a certain order as observation data; Step S2, obtaining an estimated value of the harmonic voltage through a pre-established prediction model for estimating prior state variables and an observation model for updating posterior state variables; Step S3, calculating the harmonic impedance based on the estimated value of the harmonic voltage. This invention can quickly and easily estimate the harmonic impedance of the power grid in real time, solving the problem that existing methods can only estimate harmonic impedance offline, and providing a real-time and accurate reference for harmonic mitigation work.

Description

Technical Field

[0001] This invention belongs to the field of power system technology, specifically relating to a method and apparatus for real-time estimation of power grid harmonic impedance. Background Technology

[0002] In current power systems, the high proportion of clean energy and power electronic devices connected to the grid results in a highly nonlinear system structure, leading to the generation of numerous harmonics during power conversion. These harmonic sources include the pulse width modulation (PWM) process of inverters and nonlinear loads. Control strategies and dead-time effects during PWM are major causes of these harmonics, which exhibit wide frequency domain characteristics. Furthermore, the extensive use of cables as transmission lines in transmission systems, coupled with the interaction between cable distributed capacitance and the impedance of the generation system and the grid impedance, induces harmonic amplification under system resonance conditions. This can potentially lead to excessive harmonic content throughout the system. Therefore, harmonic mitigation at the point of common coupling (PCC) has become a hot research topic.

[0003] Since the harmonic impedance on the power generation system side can be accurately calculated based on specific parameters, the primary task of harmonic mitigation is to accurately estimate the harmonic impedance on both the power grid system and the load side. However, the harmonic impedance on both the power grid system and the load side is a parameter that varies over time; therefore, accurately estimating the harmonic impedance on the power grid side is a prerequisite for harmonic mitigation. Currently, harmonic impedance analysis methods are mainly divided into invasive and non-invasive methods.

[0004] Invasive methods involve injecting harmonics into the system and then extracting data at the point of common; or switching lines and then measuring the data after the switch to estimate harmonic impedance. The disadvantage of invasive methods is that they may increase the total harmonic content of the system, affecting power quality, and more seriously, altering the system's steady-state operating point. Non-invasive methods do not introduce additional harmonics or change the original steady-state operating point of the system; they are methods for estimating harmonic impedance by extracting known data. Common methods include: fluctuation method, regression method, independent random vector method, and independent component method.

[0005] These methods assume that the grid impedance remains constant, or remains constant over a short period of time. They extract harmonic voltage and current data at the PCC point, perform Fourier transforms on the extracted data, save the harmonic voltage and current at a specific frequency, and then perform offline harmonic impedance estimation using different estimation algorithms. However, the estimated harmonic impedance is a past impedance and cannot reflect the current true harmonic impedance state. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method and apparatus for real-time estimation of power grid harmonic impedance, so as to realize real-time estimation of harmonic impedance and provide real-time and accurate reference for harmonic mitigation work.

[0007] To address the aforementioned technical problems, this invention provides a method for real-time estimation of power grid harmonic impedance, comprising:

[0008] Step S1: Real-time acquisition of voltage and current data at the point of common coupling; Fourier transform of the acquired data to obtain the harmonic voltage and harmonic current of a certain order as observation data.

[0009] Step S2: Obtain the estimated value of harmonic voltage by using a pre-established prediction model for estimating prior state variables and an observation model for updating posterior state variables.

[0010] Step S3: Calculate the harmonic impedance based on the estimated harmonic voltage value.

[0011] Furthermore, the pre-established prediction model is as follows:

[0012] U lk|k-1 =U lk-1 .

[0013] Among them, U l =I l Z l For harmonic voltage, U lk|k-1 and U lk-1 These are the prior estimate and posterior estimate of the harmonic voltage at time k, respectively.

[0014] Furthermore, an observation model is established based on the voltage and current data at the point of common coupling, and the following relationship exists at the point of common coupling:

[0015] U PCC +I PCC Z l =I l Z l

[0016] Transforming the above equation to the relationship at time k, we get:

[0017]

[0018] Using the minimum variance as the fitness function, we have

[0019]

[0020] Where m = t e f s , t e The time interval for harmonic impedance estimation, fs Where m is the sampling frequency and m is the sampling length;

[0021] Under the premise of minimizing variance, the observation model is obtained as follows:

[0022]

[0023] in, , respectively, are the observed values ​​of voltage and current at PCC at time k.

[0024] Furthermore, in step S2, the harmonic voltage is used as the state variable in the Kalman filter algorithm iteration, denoted by x, through a pre-established prediction model and observation model, to obtain the prediction equation for the state variable:

[0025] x k|k-1 =x k-1 +Q k

[0026] Among them, Q k The model error is represented by its covariance, denoted as Q, which reflects the accuracy of the prediction model.

[0027] Furthermore, the prior state variable prediction variance and Kalman gain are expressed as follows:

[0028] P k|k-1 =P k-1 +Q

[0029] M = P k|k-1 (P k|k-1 +R) -1

[0030] Where R represents the covariance of the observation data error.

[0031] Furthermore, using the results of the iteration, the final posterior state variable estimates and posterior variances are obtained as follows:

[0032]

[0033] P k =(1-M)P k|k-1 .

[0034] Furthermore, in step S2, the obtained harmonic voltage estimate is substituted into the fitness function so that the harmonic voltage value with the smallest variance is the optimal harmonic voltage estimate.

[0035] Furthermore, the optimal harmonic voltage estimate is substituted into... In the calculation, the harmonic impedance Z is obtained. l The value of .

[0036] Furthermore, by adjusting the sampling frequency f of the sampled data s The time interval t for harmonic impedance estimation is adjusted using the sampling length m. e Furthermore, once the sampling frequency of voltage and current at the point of common coupling is fixed, the time interval for harmonic impedance estimation can be adjusted by changing the number of sampling points, while satisfying the following conditions:

[0037] The present invention also provides an apparatus for real-time estimation of power grid harmonic impedance, comprising:

[0038] The acquisition module is used to acquire voltage and current data at the point of common coupling in real time, perform Fourier transform on the acquired data, and obtain the harmonic voltage and harmonic current of a certain order as observation data.

[0039] The first calculation module is used to obtain the harmonic voltage estimate by using a pre-established prediction model for estimating prior state variables and an observation model for updating posterior state variables.

[0040] The second calculation module is used to calculate the harmonic impedance based on the estimated harmonic voltage value.

[0041] Implementing this invention has the following advantages: it does not require assuming that the harmonic impedance of the power grid remains constant in a short period of time. Instead, the time interval for harmonic impedance estimation can be adjusted by selecting the data sampling frequency and the total sampling time period. When the sampling frequency is high enough and the total sampling time period is short enough, a real-time changing harmonic impedance can be estimated. It can quickly and easily estimate the harmonic impedance of the power grid in real time, solving the problem that existing methods can only estimate harmonic impedance offline, and providing a real-time and accurate reference for harmonic mitigation work. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is a flowchart illustrating a method for real-time estimation of power grid harmonic impedance according to an embodiment of the present invention.

[0044] Figure 2 This is a schematic diagram of the Norton equivalent circuit of the power generation and grid connection system in an embodiment of the present invention.

[0045] Figure 3 This is a schematic diagram of the IEEE 9-node model in an embodiment of the present invention.

[0046] Figure 4aThis is a schematic diagram illustrating the change in the amplitude of the estimated third harmonic impedance over 100 seconds in an embodiment of the present invention. Figure 4b This is a schematic diagram showing the phase change of the estimated third harmonic impedance over 100 seconds in an embodiment of the present invention. Detailed Implementation

[0047] The following description of the embodiments is taken with reference to the accompanying drawings, which illustrate specific embodiments in which the invention can be implemented.

[0048] Please refer to Figure 1 As shown, Embodiment 1 of the present invention provides a method for real-time estimation of power grid harmonic impedance, comprising:

[0049] Step S1: Real-time acquisition of voltage and current data at the point of common coupling; Fourier transform of the acquired data to obtain the harmonic voltage and harmonic current of a certain order as observation data.

[0050] Step S2: Obtain the estimated value of harmonic voltage by using a pre-established prediction model for estimating prior state variables and an observation model for updating posterior state variables.

[0051] Step S3: Calculate the harmonic impedance based on the estimated harmonic voltage value.

[0052] Specifically, such as Figure 2 The diagram shows a typical power generation grid-connected system model represented by the Norton equivalent principle. The system side and user side on either side of point PCC are equivalent to current source series impedances. The system side mainly includes the power generation system, such as traditional thermal power, wind power, and photovoltaic power, while the user side mainly includes the power grid and load centers.

[0053] In step S1, the voltage U at point PCC is collected. PCC and current I PCC The data is collected and Fourier transformed to obtain the harmonic voltage and harmonic current of a certain order as observation data.

[0054] It should be noted that this invention estimates harmonic impedance based on the Kalman filter algorithm, which requires the prior establishment of a prediction model for estimating prior state variables and an observation model for updating posterior state variables.

[0055] Prediction Model: Since the estimated impedance fluctuates very little in a short time, and the impedance changes continuously and smoothly over a short time, we can assume that the impedance value at the previous moment is equal to the impedance value at the next moment. Therefore, the prediction model is as follows:

[0056] U lk =U lk|k-1 (1)

[0057] Observation model: An observation model is established based on the voltage and current data at point PCC. The following relationship exists at point PCC:

[0058] U PCC +I PCC Z l =I l Z l (2)

[0059] Transforming equation (1) into the relationship at time k, we get:

[0060]

[0061] Using the minimum variance as the fitness function, we have

[0062]

[0063] Where m = t e f s , t e The time interval for harmonic impedance estimation, f s is the sampling frequency, and m is the sampling length.

[0064] According to equation (4), under the premise of minimum variance, the observation model can be obtained as follows:

[0065]

[0066] in, , respectively, are the observed values ​​of voltage and current at PCC at time k.

[0067] Step S2 uses the established prediction and observation models to determine the harmonic voltage U. l As the state variable obtained through iteration of the Kalman filter algorithm, denoted by x, the prediction equation for the state variable is:

[0068] x k|k-1 =x k-1 +Q k (5)

[0069] Among them, Q k The model error is represented by its covariance, denoted as Q, which reflects the accuracy of the prediction model.

[0070] To reflect the estimation bias of the prior state variables, this embodiment expresses the prediction variance and Kalman gain of the prior state variables as follows:

[0071] P k|k-1 =P k-1 +Q(6)

[0072] M = P k|k-1 (Pk|k-1 +R) -1 (7)

[0073] Where R represents the covariance of the observation data error.

[0074] Using the results of the iterations of equations (5), (6), and (7), the final posterior state variable estimates and posterior variances can be obtained as follows:

[0075]

[0076] P k =(1-M)P k|k-1 (9)

[0077] Through the iterative process of equations (5)-(9), m harmonic voltage estimates can be obtained. Substituting these m estimates into equation (4) makes δ 2 Minimum harmonic voltage The value is the optimal harmonic voltage estimate.

[0078] Step S3: Using the obtained harmonic voltage estimate, the harmonic impedance Z can be calculated by substituting it into equation (3). l The value of .

[0079] The following simulation demonstrates the effectiveness of the real-time estimation method for power grid harmonic impedance proposed in this invention.

[0080] This embodiment can be adapted to actual working conditions by adjusting the sampling frequency (f) of the sampled data. s The time interval (t) for harmonic impedance estimation is adjusted using the sampling length (m). e Once the sampling frequency of voltage and current at the PCC point is fixed, the time interval for harmonic impedance estimation can be adjusted by changing the number of sampling points according to the actual situation, and the following conditions must be met. Using the IEEE-9-node model as an example, such as Figure 3 As shown.

[0081] First, build the structure in PSCAD software, such as Figure 3 The IEEE-9 node model shown uses bus 9 as the PCC point. A branch is added at bus 9 as a verification branch to validate the method of this invention. The branch added at the PCC point serves as the user side, and the remaining portion serves as the system side. The verification branch is a variable impedance Z. c =10+n*j*1e-3 connected in series with a power supply G4, where n represents a positive integer from 1 to 10. The specific change process of the variable impedance is as follows: n is 1 from 1 to 10 seconds, n is 2 from 11 to 20 seconds, ..., n is 10 from 91 to 100 seconds.

[0082] The total simulation time is 100 seconds, with the variable impedance Z increasing every 10 seconds. c The imaginary part is doubled, meaning n increases by 1 every 10 seconds, used to simulate the changing harmonic impedance on the user side over time. Voltage and current transformers are installed at the PCC point to extract voltage and current data in real time, with a sampling frequency f. s Set to 100Hz.

[0083] Based on the aforementioned rules for data extraction, a Fourier transform is performed on the extracted data every 0.1 seconds, meaning that an observation of harmonic voltage and harmonic current can be obtained every 0.1 seconds. Each second constitutes a calculation cycle, i.e., t... e = 1 second, and 10 Fourier transforms are performed every 1 second. Therefore, 10 points can be obtained as observations for the Kalman filter algorithm iteration, i.e., m = 10.

[0084] The third harmonic impedance is estimated based on the Kalman filter algorithm: the third harmonic impedance is used as the experimental verification target.

[0085] First, set Q = 10R, R = 0.01. Initial values ​​P0 = 0.01, x0 = 1. By iterating through equations (5)-(9), 10 values ​​of the third harmonic impedance in the first period can be estimated. Then, substitute the 10 estimated values ​​into equation (4) and select the estimated value with the smallest variance as the optimal harmonic voltage U in one period. l Estimate the value, then use U l Substituting into equation (3) yields the optimal estimate of the harmonic impedance.

[0086] Since each cycle is only 1 second, and the time of each cycle can be shortened by adjusting the sampling frequency, this process can be considered a real-time estimation process. Figure 4a , Figure 4b The figures shown are schematic diagrams of the amplitude and phase of the harmonic impedance estimated in real time within 100 seconds. The solid lines and dashed lines represent the actual value and the estimated value, respectively. It can be clearly seen that the solid line of the estimated value coincides perfectly with the dashed line of the actual value, which verifies the practicality and effectiveness of the method of the present invention.

[0087] Corresponding to the method for real-time estimation of power grid harmonic impedance described in Embodiment 1 of the present invention, Embodiment 2 of the present invention also provides an apparatus for real-time estimation of power grid harmonic impedance, comprising:

[0088] The acquisition module is used to acquire voltage and current data at the point of common coupling in real time, perform Fourier transform on the acquired data, and obtain the harmonic voltage and harmonic current of a certain order as observation data.

[0089] The first calculation module is used to obtain the harmonic voltage estimate by using a pre-established prediction model for estimating prior state variables and an observation model for updating posterior state variables.

[0090] The second calculation module is used to calculate the harmonic impedance based on the estimated harmonic voltage value.

[0091] For the working principle and process of this embodiment, please refer to the description of Embodiment 1 of the present invention, which will not be repeated here.

[0092] As can be seen from the above description, compared with the prior art, the beneficial effects of the present invention are as follows: it does not require assuming that the harmonic impedance of the power grid remains unchanged in a short period of time, but can adjust the time interval for harmonic impedance estimation by selecting the data sampling frequency and the total sampling time period. When the sampling frequency is high enough and the total sampling time period is short enough, a real-time changing harmonic impedance can be estimated. It can quickly and easily estimate the harmonic impedance of the power grid in real time, solving the problem that the existing methods can only estimate the harmonic impedance offline, and providing a real-time and accurate reference for harmonic mitigation work.

[0093] The above description is merely a preferred embodiment of the present invention and should not be construed as limiting the scope of the invention. Therefore, any equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.

Claims

1. A method for real-time estimation of power grid harmonic impedance, characterized in that, include: Step S1: Real-time acquisition of voltage and current data at the point of common coupling; Fourier transform of the acquired data to obtain the harmonic voltage and harmonic current of a certain order as observation data. Step S2: Obtain the estimated value of harmonic voltage by using a pre-established prediction model for estimating prior state variables and an observation model for updating posterior state variables. Step S3: Calculate the harmonic impedance based on the estimated harmonic voltage value; The pre-established prediction model is: IN lk|k-1 =U lk-1 Among them, U l =I l Z l For harmonic voltage, U lk|k-1 and U lk-1 These are the prior estimate and posterior estimate of the harmonic voltage at time k, respectively; Based on the voltage and current data at the point of common coupling, an observation model is established, and the following relationship exists at the point of common coupling: U PCC +I PCC Z l =I l Z l Transforming the above equation to the relationship at time k, we get: Using the minimum variance as the fitness function, we have Where m = t e f s , t e The time interval for harmonic impedance estimation, f s Where m is the sampling frequency and m is the sampling length; Under the premise of minimizing variance, the observation model is obtained as follows: in, These are the observed values ​​of voltage and current at PCC at time k, respectively.

2. The method according to claim 1, characterized in that, Step S2 uses a pre-established prediction model and an observation model to treat the harmonic voltage as a state variable in the Kalman filter algorithm iteration, denoted by x, and obtains the prediction equation for the state variable as follows: x k|k-1 =x k-1 +Q k Among them, Q k The model error is represented by its covariance, denoted as Q, which reflects the accuracy of the prediction model.

3. The method according to claim 2, characterized in that, The prior state variable prediction variance and Kalman gain are expressed as follows: P k|k-1 =P k-1 +Q M=P k|k-1 (P k|k-1 +R) -1 Where R represents the covariance of the observation data error.

4. The method according to claim 3, characterized in that, Using the results of the iteration, the final posterior state variable estimates and posterior variances are obtained as follows: P k =(1-M)P k|k-1 。 5. The method according to claim 4, characterized in that, In step S2, the obtained harmonic voltage estimate is substituted into the fitness function so that the harmonic voltage value with the smallest variance is the optimal harmonic voltage estimate.

6. The method according to claim 5, characterized in that, Substitute the optimal harmonic voltage estimate into In the calculation, the harmonic impedance Z is obtained. l The value of .

7. The method according to claim 1, characterized in that, By adjusting the sampling frequency f of the sampled data s The time interval t for harmonic impedance estimation is adjusted using the sampling length m. e Furthermore, once the sampling frequency of voltage and current at the point of common coupling is fixed, the time interval for harmonic impedance estimation can be adjusted by changing the number of sampling points, while satisfying the following conditions:

8. A device for real-time estimation of power grid harmonic impedance, characterized in that, include: The acquisition module is used to acquire voltage and current data at the point of common coupling in real time, perform Fourier transform on the acquired data, and obtain the harmonic voltage and harmonic current of a certain order as observation data. The first calculation module is used to obtain the harmonic voltage estimate by using a pre-established prediction model for estimating prior state variables and an observation model for updating posterior state variables. The second calculation module is used to calculate the harmonic impedance based on the estimated harmonic voltage value; The pre-established prediction model is: IN lk|k-1 =U lk-1 Among them, U l =I l Z l For harmonic voltage, U lk|k-1 and U lk-1 These are the prior estimate and posterior estimate of the harmonic voltage at time k, respectively; Based on the voltage and current data at the point of common coupling, an observation model is established, and the following relationship exists at the point of common coupling: U PCC +I PCC Z l =I l Z l Transforming the above equation to the relationship at time k, we get: Using the minimum variance as the fitness function, we have Where m = t e f s , t e The time interval for harmonic impedance estimation, f s Where m is the sampling frequency and m is the sampling length; Under the premise of minimizing variance, the observation model is obtained as follows: in, These are the observed values ​​of voltage and current at PCC at time k, respectively.

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