A weak harmonic detection method based on Yang system

Abstract

The present application relates to the technical field of power signal processing and detection, and in particular to a weak harmonic detection method based on Yang system, aiming at the defect that the classical time-frequency domain analysis method cannot accurately detect the weak harmonic signal of power system in a severe noise environment, a Yang system is introduced, and the bifurcation diagram, phase trajectory, attractor distribution, fixed point coordinate and system state variable time trajectory diagram are used to analyze the change characteristics of system state. The appearance and disappearance of attractor distribution and fixed point are used as the conversion criterion of different chaotic states of the system, and a weak harmonic detection algorithm of power system is designed based on the criterion, the present application can realize the amplitude detection of each harmonic component without error in a noise environment of-100dB, and a general rule of dissipative type system for weak harmonic detection is given.

Description

Technical Field

[0001] This invention relates to the field of power signal processing and detection technology, specifically to a method for detecting weak harmonics based on the Yang system. Background Technology

[0002] With the increasing proportion of various new energy sources connected to the grid and the growing number of nonlinear electrical devices, harmonic pollution in the power system is becoming increasingly serious. Harmonics lead to a decline in power quality and a reduction in power supply stability and economy. Only by effectively controlling harmonic pollution can power quality be guaranteed, and accurate detection of harmonics is a prerequisite for carrying out effective control work.

[0003] Currently, the most widely used methods for harmonic detection in power grids are time-frequency domain analysis methods such as Discrete Fourier Transform (DFT), Mode Decomposition, and Wavelet Transform. DFT-based methods can achieve low-error detection in noise-free environments and under 70dB noise conditions. Mode Decomposition-based interharmonic detection methods can achieve low-error detection of interharmonics under 50dB noise conditions. Empirical Wavelet Transform-based harmonic detection methods for power systems can achieve harmonic detection with a relative error not exceeding 3.8% under 20dB and 30dB noise conditions. However, these time-frequency domain analysis-based harmonic detection methods process, adjust, or reconstruct the signal itself, inevitably affecting the signal and thus making it difficult to meet the required error standards. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a weak harmonic detection method based on the Yang system, which addresses the shortcomings of the classical time-frequency domain analysis method in accurately detecting weak harmonic signals in power systems under harsh noise environments.

[0005] This invention is implemented as follows:

[0006] A method for detecting weak harmonics based on the Yang system, characterized by the following steps:

[0007] Step 1: Set system parameters a, b, c and initial system values ​​(x0, y0, z0);

[0008] Step 2: Based on the system parameters and initial system values, find and set the amplitude of the system control signal to the critical threshold.

[0009] Step 3: Set the input signal weighting factor A and input the signal to the system;

[0010] Step 4: Draw the system's xz phase diagram, attractor distribution, and time history of state variables;

[0011] Step 5: Determine if the system has a fixed point or a change in attractor distribution. If no fixed point has appeared and the attractor distribution has not changed, return to step 3; if a fixed point has appeared or the attractor distribution has changed, proceed to step 6.

[0012] Step 6: Decrease the amplitude of the control signal by step size, recalculate the state of the control system, and draw the xz phase diagram of the system, as well as the attractor distribution and state variable time history diagram;

[0013] Step 7: Determine whether the system fixed point has disappeared or the attractor distribution has returned to its initial state. If the system fixed point has not disappeared and the attractor distribution has not returned to its initial state, return to step 6; if the system fixed point has disappeared or the attractor distribution has returned to its initial state, proceed to step 8.

[0014] Step 8: The ratio of the difference in the amplitude reduction of the system control signal to the weighting factor is the amplitude of the harmonic signal to be detected;

[0015] Step 9: The amplitude calculation for the detected frequency signal has been completed, and the calculation process ends.

[0016] Furthermore, in step 1, the mathematical model of the dynamic characteristics of the Yang system is as follows:

[0017]

[0018] Where x, y, z are the system's state variables, and a, b, c are dimensionless system parameters.

[0019] Furthermore, in step 2, the Yang system is controlled using a non-resonant parameter control method, based on the Yang system model:

[0020]

[0021] Where (1+f) y cosω y t) is the control signal, ω y To control the angular frequency of the periodic component of the control signal, the critical threshold of the flat chaotic state of the system control signal is found by using the bifurcation diagram of the system state variable as a function of the control signal amplitude f.

[0022] Furthermore, in step 3, the weak harmonic detection model of the Yang system is as follows:

[0023]

[0024] Where A is the weighting factor of the input signal, s(t) is the target weak periodic signal, n(t) is the random noise mixed in the signal to be detected, and the system state variable x is the system output. The signal amplitude is estimated based on the time-domain waveform of the mixed signal, and a suitable weighting factor A is designed to make Afy Not exceeding 0.15.

[0025] Further, in step 4, by inputting the signal to be measured into the critical state Yang system, the Runge-Kutta method is used to solve equation (3), and the xz phase trajectory, attractor distribution diagram and time history diagram of the state variables of the system are plotted based on the calculation results.

[0026] Furthermore, in step 5, if the system phase trajectory and attractor distribution do not change or the system does not have a fixed point, the weighting factor A is modified and recalculated and drawn until the position of the system's indeterminate point or the attractor distribution changes.

[0027] Furthermore, in step 7, when the system's indeterminate points disappear or the phase trajectory and attractor distribution return to their initial state, the difference Δf in the decrease of the control signal amplitude is recorded. y .

[0028] Further, in step 8, Δf is calculated. y / A obtains the amplitude of the weak harmonic signal at the target frequency.

[0029] Compared with the prior art, the beneficial effects of this invention are as follows:

[0030] This invention introduces the Yang system and uses bifurcation diagrams, phase trajectories, attractor distributions, fixed-point coordinates, and system state variable time trajectory diagrams to analyze the characteristics of system state changes and the features of the Yang system. Using attractor distributions and the appearance and disappearance of fixed points as transition criteria for different chaotic states of the system, a weak harmonic detection algorithm for power systems is designed based on these criteria. Simulations are performed on weak harmonic signals consisting of a mixture of multiple integer harmonics and interharmonics under different noise environments ranging from -10dB to -120dB. The results show that the proposed method can achieve error-free amplitude detection of each harmonic component in noise environments below -100dB. By comparing simulation results, a general rule for weak harmonic detection in dissipative systems is qualitatively given. Attached Figure Description

[0031] Figure 1 A flowchart of the method provided in an embodiment of the present invention;

[0032] Figure 2 -100dB phase trajectory and attractor distribution;

[0033] Figure 3 A time history plot of the -100dB state variable x;

[0034] Figure 4 -120dB phase trajectory and attractor distribution;

[0035] Figure 5Time history plot of the -120dB state variable x. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0037] See Figure 1 This invention discloses a method for detecting weak harmonics in a power system based on the Yang system. The method includes the following steps:

[0038] Step 1: Set system parameters a, b, c and initial system values ​​(x0, y0, z0);

[0039] The mathematical model describing the dynamic characteristics of the Yang system is as follows:

[0040]

[0041] Where x, y, z are the system's state variables, and a, b, c are dimensionless system parameters.

[0042] Step 2: Based on the system parameters and initial values, find and set the amplitude of the system control signal to the critical value;

[0043] The Yang system is controlled using a non-resonant parameter control method. The system model is as follows:

[0044]

[0045] Where (1+f) y cosω y t) is the control signal, ω y To determine the angular frequency of the periodic component of the control signal, a bisection iterative method is used to find the critical threshold of the flat chaotic state of the system control signal based on the bifurcation diagram of the system state variables as a function of the control signal amplitude f.

[0046] Step 3: Set the input signal weighting factor A and input the signal to the system;

[0047] The weak harmonic detection model of the Yang system is as follows:

[0048]

[0049] Where A is the weighting factor of the input signal, s(t) is the target weak periodic signal, n(t) is the random noise mixed in the signal to be detected, and the system state variable x is the system output. Based on the time-domain waveform of the mixed signal, the signal amplitude is estimated, and a suitable weighting factor A is designed to make Af y Not exceeding 0.15.

[0050] Step 4: Draw the system's xz phase diagram, attractor distribution, and time history of state variables;

[0051] Step 5: Determine if the system has a fixed point or a change in attractor distribution. If no fixed point has appeared and the attractor distribution has not changed, return to step 3; if a fixed point has appeared or the attractor distribution has changed, proceed to step 6.

[0052] Step 6: Decrease the amplitude of the control signal by step size, recalculate the state of the control system, and draw the xz phase diagram of the system, as well as the attractor distribution and state variable time history diagram;

[0053] Step 7: Determine whether the system fixed point has disappeared or the attractor distribution has returned to its initial state. If the system fixed point has not disappeared and the attractor distribution has not returned to its initial state, return to step 6; if the system fixed point has disappeared or the attractor distribution has returned to its initial state, proceed to step 8.

[0054] Step 8: The ratio of the difference in amplitude reduction of the system control signal to the weighting factor is the amplitude of the harmonic signal to be detected;

[0055] Step 9: The amplitude calculation for the detected frequency signal has been completed, and the calculation process ends.

[0056] Example 1

[0057] The Yang system parameters are set to (a,b,c)=(35,3,35), and the initial values ​​are set to (x0,y0,z0)=(1.15,3.5,3.3). Weak harmonic signals from the power system are used.

[0058] x(t)=sin(ωt)+0.15sin(2.2ωt)+0.25sin(3ωt)

[0059] +0.2sin(5ωt)+0.1sin(7ωt)

[0060] The target signal is ω = 100π rad / s, and the input signal weighting factor A is set to 10. -6 The system parameters of the Chen system are set as a = 35, b = 3, c = 35, and the angular frequency of the control signal is taken as the angular frequency of each harmonic component. Taking ω = 100π rad / s as an example, the initial values ​​of the system are set as (1.15, 3.5, 3.3).

[0061] The noise intensity D of Gaussian white noise is determined by the signal-to-noise ratio (SNR) as follows:

[0062]

[0063] Gaussian white noise was introduced at signal-to-noise ratios of -100dB and -120dB to form a mixed signal. This mixed signal was then input to the Yang system in its critical state. The phase diagram and attractor distribution under each signal-to-noise ratio condition are shown below. Figure 2 and Figure 4 And the time history graph of the state variable x, as shown below Figure 3 and Figure 5 As shown.

[0064] Depend on Figure 3 It can be seen that the system changed state under the three signal-to-noise ratio environments. The amplitude of the control signal was reduced by step size until the system returned to the initial state. The difference in the reduction of the control signal amplitude was recorded. The ratio of this difference to the input signal weighting factor is the amplitude of the target weak harmonic signal. The detection results under the three signal-to-noise ratios are shown in Table 1.

[0065] Table 1. Detection results of weak harmonic signals in the Yang system under different signal-to-noise ratios.

[0066]

[0067] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for detecting weak harmonics based on the Yang system, characterized in that, The method includes the following steps: Step 1: Set system parameters a, b, c and initial system values The mathematical model of the dynamic characteristics of the Yang system is as follows: （1）， Where x, y, z are the system state variables, and a, b, c are dimensionless system parameters; Step 2: Based on the system parameters and initial system values, find and set the system control signal amplitude to the critical threshold; control the Yang system using a non-resonant parameter control method, based on the Yang system model: （2）， in For control signals, To control the angular frequency of the periodic component of the control signal, the critical threshold of the flat chaotic state of the system control signal is found by using the bifurcation diagram of the system state variables as a function of the control signal amplitude f. Step 3: Set the input signal weighting factor A, and input the signal into the system. The weak harmonic detection model of the Yang system is as follows: （3）， Where A is the weighting factor of the input signal. For the target weak periodic signal, To introduce random noise into the signal under test, the system state variable x is used as the system output. The signal amplitude is estimated based on the time-domain waveform of the mixed signal, and a weighting factor A is designed to... Not exceeding 0.15; Step 4: Draw the system's xz phase diagram, attractor distribution, and time history of state variables; Step 5: Determine if the system has a fixed point or a change in attractor distribution. If no fixed point has appeared and the attractor distribution has not changed, return to step 3; if a fixed point has appeared or the attractor distribution has changed, proceed to step 6. Step 6: Decrease the amplitude of the control signal by step size, recalculate the state of the control system, and draw the xz phase diagram of the system, as well as the attractor distribution and state variable time history diagram; Step 7: Determine whether the system fixed point has disappeared or the attractor distribution has returned to its initial state. If the system fixed point has not disappeared and the attractor distribution has not returned to its initial state, return to step 6; if the system fixed point has disappeared or the attractor distribution has returned to its initial state, proceed to step 8. Step 8: The ratio of the difference in the amplitude reduction of the system control signal to the weighting factor is the amplitude of the harmonic signal to be detected; Step 9: The amplitude calculation for the detected frequency signal has been completed, and the calculation process ends.

2. The weak harmonic detection method based on the Yang system according to claim 1, characterized in that, In step 4, the signal to be measured is input into the critical state of the Yang system, and the Runge-Kutta method is used to solve the equation. Based on the calculation results, the xz phase trajectory, attractor distribution diagram, and time history diagram of the state variables of the system are plotted.

3. The weak harmonic detection method based on the Yang system according to claim 1, characterized in that, In step 5, if the system phase trajectory and attractor distribution do not change or the system does not have a fixed point, the weighting factor A is modified and the calculation and drawing are repeated until the position of the system indeterminate point or the attractor distribution changes.

4. The weak harmonic detection method based on the Yang system according to claim 1, characterized in that, In step 7, when the system's indeterminate points disappear or the phase trajectory and attractor distribution return to their initial state, record the difference in the decrease in the control signal amplitude at this time. .

5. The weak harmonic detection method based on the Yang system according to claim 4, characterized in that, In step 8, calculate The amplitude of the weak harmonic signal at the target frequency is obtained.

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