A method for detecting subsynchronous oscillation of a power system based on multi-cone method

Abstract

The application relates to a power system subsynchronous oscillation detection method based on a multi-cone method, which comprises the following steps: S1, establishing a linear regression model based on discrete Fourier transform of a PMU measurement signal; S2, expressing an oscillation detection problem as statistical hypothesis testing based on the linear regression model; and S3, detecting power system subsynchronous oscillation based on the multi-cone method and oscillation detection probability, and obtaining a detection result. Compared with the prior art, the application establishes a linear regression model with higher precision based on discrete Fourier transform of a PMU measurement signal, combines statistical hypothesis and threshold value comparison verification, and utilizes stored cone degrees to detect periodic power system subsynchronous oscillation.

Description

Technical Field

[0001] This invention relates to the detection of subsynchronous oscillations in power systems, and more particularly to a method for detecting subsynchronous oscillations in power systems based on the multi-cone method. Background Technology

[0002] The power system also contains a large number of high-voltage direct current transmission equipment, series compensation equipment, and dynamic reactive power compensation equipment. These devices can improve the power grid's transmission capacity and system stability, laying the foundation for the large-scale grid connection of new energy sources. However, they also increase the number of weak links in the power system, leading to the increasingly prominent subsynchronous oscillation problem. The subsynchronous oscillation problem in the power system has a wide range of impacts and has already endangered the safe and stable operation of the power system. Moreover, its inducing factors are uncertain, so its timely detection has become increasingly important.

[0003] Subsynchronous oscillations in power grids mainly manifest as large-amplitude, continuously increasing or constant-amplitude subsynchronous and supersynchronous current, voltage, and power harmonics. Furthermore, the oscillation frequency changes with grid configuration, affecting the safe operation of the power grid and equipment, and even causing serious stability accidents or equipment damage, posing a significant threat. Subsynchronous oscillations not only cause harmonic pollution and affect power quality, but may also damage renewable energy equipment and cause large-scale grid disconnection, severely impacting the grid connection and consumption of renewable energy. They may even lead to shaft fatigue in thermal power units, causing generator shaft fracture and subsequently inducing cascading accidents in the regional power grid, posing a huge threat to the safety of generating units and power equipment in the power grid and the stable operation of the entire power system. Existing synchronous oscillation detection methods are based on periodogram techniques, relying on the actual environmental noise spectrum of the system, requiring extensive system knowledge, and cannot quickly and accurately detect subsynchronous oscillations. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology by providing a power system subsynchronous oscillation detection method based on the multi-cone method. A more accurate linear regression model is established based on the discrete Fourier transform of the PMU measurement signal, and the statistical assumptions and threshold comparison are used for verification. The stored cone values ​​are then used to detect the periodic power system subsynchronous oscillation.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A method for detecting subsynchronous oscillations in power systems based on the multi-cone method includes the following steps:

[0007] S1. Establish a linear regression model based on the discrete Fourier transform of the PMU measurement signal;

[0008] S2. Based on the linear regression model, the oscillation detection problem is expressed as a statistical hypothesis test;

[0009] The specific steps of S2 are as follows: based on the linear regression model, it is assumed whether there is oscillation at a certain frequency band, and through the analysis and testing of the hypothesis, the test statistic and the threshold are compared. The test statistic is obtained by synchronous phasor measurement. After comparison, the threshold is continuously modified until a suitable threshold is obtained, and then compared with the detector performance to obtain the oscillation detection probability.

[0010] S3. Based on the multi-cone method and oscillation detection probability, subsynchronous oscillations in the power system are detected, and the detection results are obtained.

[0011] The specific steps for S3 are as follows:

[0012] The type of cone is selected, and for a detection segment, the number of cones is determined by specifying the half-resolution bandwidth. Based on the type and number of cones, the stored cone values ​​are used to detect subsynchronous oscillations in the power system.

[0013] Furthermore, the threshold is established by the distribution of the test statistic and the general expression for the false alarm probability.

[0014] Furthermore, the expression for the threshold with respect to the false alarm probability is:

[0015]

[0016] Where γ is the threshold and K is the number of cones. For the maximum false alarm probability, N F This refers to the frequency bandwidth within the measured maximum and minimum frequency range.

[0017] Furthermore, the expression for the false alarm probability is:

[0018]

[0019] Among them, P FA Let γ be the false alarm probability, γ be the threshold, and K be the number of cones.

[0020] Furthermore, the test statistics are obtained based on complex value regression theory and harmonic analysis results.

[0021] Furthermore, the half-resolution bandwidth is equal to the value of the frequency resolution constraint of the current application.

[0022] Furthermore, the multi-cone method is a sinusoidal multi-cone method.

[0023] Furthermore, the assumption regarding the existence of oscillations at a certain frequency band specifically refers to:

[0024] H0:C r =0

[0025] H1:C r ≠0

[0026] Where H0 represents the assumption that there is no oscillation in a certain frequency band, H1 represents the assumption that there is oscillation in a certain frequency band, and C... r for.

[0027] Furthermore, in the process of detecting subsynchronous oscillations in the power system using the stored taper, the subsynchronous oscillations at a certain frequency are repeatedly detected.

[0028] Furthermore, during repeated detection, the repetition frequency is refined by discarding the detection frequency within the resolution bandwidth of the long detection window that is in the small detection window.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] Unlike existing periodogram-based technologies, this invention does not rely on the actual environmental noise spectrum of the system and can operate continuously in an online environment. Apart from synchronous phasor measurements, it does not require any system knowledge. It obtains a suitable threshold by comparing the test statistics obtained from the measurements with the threshold, and can quickly and accurately detect subsynchronous oscillations. Attached Figure Description

[0031] Figure 1 This is a flowchart of the present invention;

[0032] Figure 2 This is a flowchart of the process for detecting subsynchronous oscillations in power systems based on the multi-cone method and oscillation detection probability according to the present invention. Detailed Implementation

[0033] 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.

[0034] A PMU (phasor measurement unit) is a synchronous phasor measurement device that can be used to analyze phasors, which can provide information on amplitude and phase angle.

[0035] This invention provides a method for detecting subsynchronous oscillations in power systems based on the multi-cone method. The flowchart of the method is as follows: Figure 1 As shown. The method includes the following steps:

[0036] S1. Establish a linear regression model based on the discrete Fourier transform of the PMU measurement signal.

[0037] S2. Based on the linear regression model, the oscillation detection problem is expressed as a statistical hypothesis test to obtain the oscillation detection probability.

[0038] The specific steps of S2 are as follows: based on the linear regression model, it is assumed whether there is oscillation at a certain frequency band, and through the analysis and testing of the hypothesis, the test statistic and the threshold are compared. The test statistic is obtained by synchronous phasor measurement. After comparison, the threshold is continuously modified until a suitable threshold is obtained, and then compared with the detector performance to obtain the oscillation detection probability.

[0039] S3. Detect subsynchronous oscillations in the power system based on the multi-cone method and oscillation detection probability, and obtain the detection results. The specific steps of S3 are as follows:

[0040] The type of cone is selected, and for a detection segment, the number of cones is determined by specifying the half-resolution bandwidth. Based on the type and number of cones, the stored cone values ​​are used to detect subsynchronous oscillations in the power system.

[0041] In S1, based on the PMU measurement data, the discrete-time PMU measurement can be defined as:

[0042] y(n) = η(n) + s(n)

[0043] Where η(n) is the steady-state response of the power system to random load changes, i.e., the ambient noise at PMU. Typically, η(n) is modeled as a zero-mean random process. The term s(n) in the signal model can account for the existence of any subsynchronous oscillations. Since subsynchronous oscillations typically exhibit sinusoidal signals, they can be modeled as:

[0044]

[0045] Where A r f r and Let N be the amplitude, frequency (Hz), and phase of the r-th subsynchronous oscillation, respectively. SO To measure the total number of subsynchronous oscillations occurring in y(n). T s =f s / 1 is the sampling interval (seconds), where f s This is the sampling rate, measured in samples per second. (Indicator function) It is the duration of capturing the r-th sine signal within the detection window {y(n):n∈[0,n-1]} of length n, defined as:

[0046]

[0047] Where, n s (r) and n e (r) represents the starting and ending sample indices of the r-th subsynchronous oscillation in the detection window y.

[0048] Define the Discrete Fourier Transform (DFT) of the cone measurement data as:

[0049]

[0050] Where, when 0m≤N(0), For discrete frequencies, calculate the DFT at this value, where N(0)≥N is the zero-addition length. When k=0,1,…, the conical (window) w k (n), K-1, where K is the number of cones, i.e. the number of cones, K≥2.

[0051] In S1, during the Discrete Fourier Transform (DFT) of the PMU measurement signal, windowing is applied to the DFT to prevent leakage and reduce errors in the frequency and duration of the measurement data. A regression model is obtained by combining certain theories with harmonic analysis and signal-to-noise ratio analysis.

[0052] A linear regression model can be established based on the discrete Fourier transform described above.

[0053] In S2, unlike traditional periodogram-based techniques, this invention does not rely on the system's actual environmental noise spectrum and can operate continuously in an online environment, requiring no system knowledge other than synchronous phasor measurements. The test statistics obtained solely from the measurements are compared with a threshold, which is established by a general expression for the distribution of the test statistics and the false alarm probability. The statistical hypotheses and verifications proposed in S2 are based on the linear regression model of S1. The following hypotheses can be tested to detect false alarms in f. r Does the subsynchronous oscillation at point y exist in the analysis window y?

[0054] H0:C r =0

[0055] H1:C r ≠0

[0056] The null hypothesis H0 is that the measurement y in f r The location does not contain subsynchronous oscillations. Assume H1 is the measurement of y at f. r The location contains subsynchronous oscillations.

[0057] Under the condition that the requirements are met, based on the complex-valued regression theory and harmonic analysis results, the test statistic can be expressed as:

[0058]

[0059] in

[0060]

[0061] The symbol “*” represents the complex conjugate of the basic quantity.

[0062] The detection threshold is set to achieve the desired false alarm probability P. FALet's represent it. If the test statistic T(y,f) is... r′ If the threshold γ is exceeded, that is, if f exceeds the threshold γ in the detection segment y... r There is no subsynchronous oscillation at this point. Under the null hypothesis H0 and the definition of the cumulative distribution function (CDF) of the central F-distribution, P FA It can be represented as:

[0063]

[0064] P(A|B) represents the probability of A given that B is true. It's worth noting that when γ = 0, P... FA 1. This confirms the non-negativity support of the F distribution, therefore (y,f r′ Both γ and γ must be greater than or equal to zero. The threshold γ can be set using p. FA express:

[0065]

[0066] Where ln(-) is the natural logarithm. At frequency f... r When detecting subsynchronous oscillations, this expression can be used to determine the threshold γ for specific settings of K and P. FA Analysis of this expression reveals P FA Alternatively, γ may be independent of the measured y, thus the detector performance can operate at a constant false alarm rate.

[0067] When there is a frequency f in the detection segment y r During a subsynchronous oscillation, the detector has a probability of detecting the oscillation:

[0068]

[0069] Where T i Let i = 1, 2, ..., K-2 be a recursive function, defined as:

[0070] T -1 =0, T0=1

[0071]

[0072] The above expression is derived from the CDF of the non-central F-distribution, simplified by the fact that 2K⁻² is even. Although the expression looks quite complex, the final result is intuitive. As mentioned earlier, for K and P… FA Specific settings, P D SNR0 increases with the increase of the power or duration of the synchronous oscillation of the detection segment.

[0073] The process for detecting subsynchronous oscillations in power systems based on the multi-cone method and oscillation detection probability in S3 is as follows: Figure 2As shown. In S3, the multi-cone method used is the sinusoidal orthogonal cone method. Using only harmonic-related sinusoidal windows, compared to the DPSS sequence, the sinusoidal cone achieves smaller local bias (the bias introduced by the smoothing of the main lobe of the window) through sidelobe suppression. The k-th element of the sinusoidal cone is:

[0074]

[0075] The windows are roughly concentrated in the interval.

[0076] When NBTs ≥ 1.5, for subsynchronous oscillation detection in power systems, the cone type is selected. For a detection segment of length N, the number of cones is determined by specifying the half-resolution bandwidth B. The value of the half-resolution bandwidth B is equal to the value of the frequency resolution constraint of the current application, and the value of the half-resolution bandwidth B is close to [2NBTs], where [.] represents the floor function. After specifying the half-resolution bandwidth B, the number of cones K is determined. Based on the cone type and the number of cones K, the stored cones are used for subsynchronous oscillation detection in the power system.

[0077] In an ideal situation, each frequency f r Each should correspond to a subsynchronous oscillation at only one frequency. However, due to leakage and zero-adjustment issues, it's possible that within a certain frequency range... r More than one subsynchronous oscillation was detected nearby. For a finite-length detection window, if a non-integer number of cycles of the subsynchronous oscillation are captured in the measurement y, the frequency content of the subsynchronous oscillation will leak into the DFT estimate f. r′ This will result in a frequency f. r This corresponds to multiple subsynchronous oscillations. This problem can be solved by discarding the corresponding f... r′ The vicinity of the subsynchronous oscillation of all [f r′ -B,f r This is resolved by subsynchronous oscillations of '+B'Hz. Corresponding to all detectable [f]Hz... r′ -B,f r Subsynchronous oscillations around ′+B]Hz The value will be f r′ The maximum value.

[0078] When using multi-detection segment technology, there will be repeated detections corresponding to the next synchronous oscillation at a certain frequency. This method can refine the repetition frequency by discarding detection frequencies within the resolution bandwidth of a longer detection window that fall within a smaller detection window. This makes longer detection windows more suitable for detection than shorter windows. A long detection window is a detection window whose length exceeds a certain threshold.

[0079] 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 detecting subsynchronous oscillations in power systems based on the multi-cone method, characterized in that, Includes the following steps: S1. Establish a linear regression model based on the discrete Fourier transform of the PMU measurement signal; S2. Based on the linear regression model, the oscillation detection problem is expressed as a statistical hypothesis test; The specific steps of S2 are as follows: based on the linear regression model, it is assumed whether there is oscillation at a certain frequency band, and through the analysis and testing of the hypothesis, the test statistic and the threshold are compared. The test statistic is obtained by synchronous phasor measurement. After comparison, the threshold is continuously modified until a suitable threshold is obtained, and then compared with the detector performance to obtain the oscillation detection probability. S3. Detect subsynchronous oscillations in the power system based on the multi-cone method and oscillation detection probability, and obtain the detection results; the specific steps of S3 are as follows: Select the type of cone, determine the number of cones for a detection segment by specifying the half-resolution bandwidth, and use the stored cones to detect subsynchronous oscillations in the power system based on the type and number of cones. Under the condition that the requirements are met, based on the complex-valued regression theory and harmonic analysis results, the test statistic can be expressed as: in ,symbol" " indicates the complex conjugate of the fundamental quantity; The number of cones; The detection threshold is set to achieve the desired false alarm probability. To represent; if the test statistic Exceeding the threshold γ, i.e., within the detection segment y There is no subsynchronous oscillation at this point; under the null hypothesis Under the definition of the cumulative distribution function of the central F-distribution, Represented as: P(A|B) represents the probability of A given that B is true; it is worth noting that when hour, This confirms the non-negativity support of the F distribution, therefore And γ must be greater than or equal to zero; the threshold γ is used express: Where ln(-) is the natural logarithm; To maximize the false alarm probability, This refers to the frequency bandwidth within the measured maximum and minimum frequency ranges. This assumes that there is no oscillation at a certain frequency band; At frequency This expression is used when detecting subsynchronous oscillations to determine the threshold γ as a specific set of K and Analysis of the expression revealed... or Since it is independent of the measurement y, the detector performance can operate with a constant false alarm probability; When the frequency exists in the detection segment y is During a subsynchronous oscillation, the detector has a probability of detecting the oscillation: in , For recursive functions, it is defined as: in This assumes that oscillations exist at a certain frequency band; The above expression is non-central The CDF of the distribution is derived, simplified by the fact that 2K-2 is even; although the expression looks quite complex, the final result is intuitive; as mentioned before, for K and Specific settings, along with Increased with the increase, It increases with the increase of the power or duration of the subsynchronous oscillation in the detection segment; In S3, the multi-cone method used is the sinusoidal orthogonal cone method; only harmonic-related sinusoidal windows are used. Compared with the DPSS sequence, the sinusoidal cone achieves a smaller local bias by suppressing side lobes; the k-th element of the sin cone is: The windows are concentrated in the interval. Hz; It is the sampling rate per second; When NBTs ≥ 1.5, for subsynchronous oscillation detection in power systems, the type of cone is selected. For a detection segment of length N, the number of cones is determined by specifying the half-resolution bandwidth B. The value of the half-resolution bandwidth B is equal to the value of the frequency resolution constraint of the current application, and the value of the half-resolution bandwidth B is close to [2NBTs], where [.] represents the floor function. After specifying the half-resolution bandwidth B, the number of cones K is determined. Based on the type of cone and the number of cones K, the stored cones are used to detect subsynchronous oscillations in power systems, and Ts is the sampling interval.

2. The method for detecting subsynchronous oscillations in power systems based on the multi-cone method according to claim 1, characterized in that, In the process of detecting subsynchronous oscillations in power systems using stored taper, the subsynchronous oscillations at a certain frequency are repeatedly detected.

3. The method for detecting subsynchronous oscillations in power systems based on the multi-cone method according to claim 2, characterized in that, During repeated detection, the repetition frequency is refined by discarding the detection frequency within the resolution bandwidth of the long detection window that is in the small detection window.

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