A method for identifying and separating chaotic flicker sources

Abstract

The present invention belongs to the field of electric power technology and relates to a method for identifying and separating chaotic flicker sources. The method comprises the following steps: collecting observation values ​​of a nonlinear power system; judging that the nonlinear power system is a chaotic system by using a Lyapunov exponent; measuring an invariant measure of the chaotic system to obtain a distribution of a chaotic signal in a state space; using field test data and waveforms as references, determining a chaotic flicker source by using a signal-to-mixture ratio to measure short flicker values ​​when an ideal signal modulates chaotic signals of different amplitudes; reconstructing a phase space trajectory of a time delay embedding dimension using a nonlinear time series constructed using the observation values, and using the phase space trajectory to reconstruct the dynamic characteristics of the chaotic system to identify chaotic flicker source signals and noise; and separating the chaotic flicker source from the noise by using a multi-channel ICA separation algorithm; thereby providing support for accurately locating the chaotic source and the noise source.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric power, and in particular relates to a method for identifying and separating chaotic flicker sources. Background Art

[0002] It is generally believed that chaos is a phenomenon that occurs in a deterministic system, has irregular pseudo-randomness in the time domain, and exhibits broadband continuous spectrum noise-like characteristics in the frequency domain.

[0003] Chaos is ubiquitous in nonlinear systems, but current power quality research has neglected its presence. Flicker caused by chaotic signal modulation is known as a chaotic flicker source. Research on power system loads has revealed the fractal nature of loads. This fractal nature has been demonstrated by reconstructing chaotic attractors in phase space. Nonlinear load variations manifest themselves in power quality as grid waveform distortion. This distortion, in addition to harmonics and interharmonics, can also include chaos and noise. Due to the unique fractal and pseudo-random nature of chaos, phase space reconstruction methods can identify chaos and noise, but they cannot completely separate them. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for identifying and separating chaotic flicker sources.

[0005] In order to achieve the purpose of the present invention, the present invention will be implemented by adopting the following technical solutions.

[0006] Before describing the technical solution, let's first introduce the basic concepts of chaos:

[0007] The complex behavior of power systems is often described using limit sets. Common simple limit sets for planar dynamic systems include limit cycles, singularities, and fixed points. If a limit set is contracting, it is called an attracting set, which is defined as:

[0008] If satisfied The set A is called the attracting set corresponding to the contraction domain U. Obviously, the essence of the definition is that the limit set of all points in a neighborhood of A is contained in A.

[0009] If any proper subset of an attracting set is not attractive, then the attracting set is said to be inseparable. An inseparable attracting set is called an attractor.

[0010] Conservative systems, because their evolution remains unchanged in phase space, lack attractors. Dissipative systems, on the other hand, experience a gradual contraction in phase space, resulting in an indivisible attractor set, known as an attractor. When the dimension of a dissipative system's attractor is integer, it's called a trivial attractor. When the dimension of a dissipative system's attractor is non-integer, it's called a strange attractor. Chaos is the complex dynamical behavior of a divided strange attractor.

[0011] Chaotic systems exhibit sensitivity to initial values, and the measure of this property is the Lyapunov number.

[0012] This value λ is defined as;

[0013]

[0014] or

[0015]

[0016] in

[0017]

[0018] If the Lyapunov number is greater than 0, chaos occurs in the system. The basic definition of chaos is introduced below.

[0019] f:J→J is called topologically transitive if for any pair of open sets U,V∈J, there exists k>0 such that

[0020] f:J→J has a sensitive dependence on the initial value, such that there exists δ>0, for any x∈J and any neighborhood U of x, there exists y∈U and n≥0, such that |f n (x)-f n (y)|>δ.

[0021] Let V be a set. f:V→V is called chaotic on V if

[0022] 1. Sensitive dependence of f on initial conditions;

[0023] 2. f is topologically transitive;

[0024] 3. Periodic points are dense in V.

[0025] According to the definition of chaos, it is not difficult to understand that the unique characteristics of chaotic motion are mainly:

[0026] 1. Sensitive dependence on initial conditions. This characteristic describes that initial values ​​that are very close will gradually diverge as the orbit evolves;

[0027] 2. Boundedness. Chaos always moves within a certain domain of attraction;

[0028] 3. There are strange attractors. Since the dimension of chaotic attractors is fractal dimension, they are called strange attractors.

[0029] 4. Pseudo-randomness. This is manifested as the appearance of randomness in a certain movement;

[0030] 5. Ergodicity. Chaotic motion is ergodic within its domain of attraction, that is, the chaotic orbit passes through every state point in the chaotic region.

[0031] In short, chaotic mapping has three elements: unpredictability, indecomposability, and a regular component, namely, non-periodicity, sensitive initial conditions, and boundedness.

[0032] A method for identifying and separating chaotic flicker sources comprises the following steps:

[0033] S1. Collecting sampled values ​​or observed values ​​of an n-dimensional nonlinear power system by measurement;

[0034] S2. Use the Lyapunov index to determine whether the n-dimensional nonlinear power system has chaotic motion: if the Lyapunov index is greater than 0, then the n-dimensional nonlinear power system has chaotic motion, that is, the n-dimensional nonlinear power system is a chaotic system;

[0035] S3. By measuring the invariant measure of the chaotic system, the points generated by the chaotic mapping iteration are obtained, that is, the distribution of the chaotic signal in the state space; wherein: the invariant measure is:

[0036]

[0037] In the formula, f is the chaotic map, δ is the probability density function, and N is the number of iterations;

[0038] S4. Using the field test data and waveform as a reference, the short flicker value when the ideal signal modulates chaotic signals of different amplitudes is tested by the signal-to-mixing ratio to determine whether the chaotic system has a chaotic flicker source; wherein: the signal-to-mixing ratio is:

[0039] SN=10*log 10 (R x {NT s} / σ 2 ),

[0040] Where SN is the signal-to-mixing ratio, R x is the correlation value of the signal, σ 2 is the chaotic variance, N is the number of sampling points, T S is the sampling time interval;

[0041] S5, constructing a nonlinear time series of n points {x1, x2, ..., x n} to reconstruct the phase space trajectory of the time delay embedding dimension d, and use the phase space trajectory to reconstruct the dynamic characteristics of the chaotic system to identify the chaotic flicker source signal and noise; wherein, the phase space trajectory is:

[0042]

[0043] Where d is the embedding dimension and τ is the delay time;

[0044] The condition for time delay embedding is that the embedding dimension d>2D F , where: D F is the box dimension of the strange attractor;

[0045] S6. Based on the network topology characteristics of the n-dimensional nonlinear power system, a multi-channel ICA separation algorithm is used to separate the chaotic flicker source identified in step S5 from the noise.

[0046] As a preferred solution of the present invention, the derivation process of the signal-to-mixture ratio is:

[0047] According to the characteristics of independent source signals in n-dimensional nonlinear power system, considering chaos(t) as additive chaotic signal, a harmonic chaotic signal model is established:

[0048]

[0049] Among them, chaos(t) is the chaotic signal, A k ,ω k and are independent random variables, It obeys a uniform distribution within the range of 0 to 2π, and chaos(t) is statistically independent of the sine signal;

[0050] Consider the sampling time interval as T s , we can deduce and prove that:

[0051] R x {0}-R x {NT s}=σ 2 ,

[0052] The signal-to-mixing ratio is:

[0053] SN=10*log 10 (R x {NT s} / σ 2 ).

[0054] Where SN is the signal-to-mixing ratio, R x is the correlation value of the signal, σ 2 is the chaotic variance, N is the number of sampling points, T S is the sampling time interval.

[0055] As a preferred solution of the present invention, the ideal signal is the fundamental wave of the power system.

[0056] As a preferred solution of the present invention, the process of establishing the phase space trajectory is as follows:

[0057] For n-dimensional nonlinear power systems:

[0058] The observation value s = h(x) is a scalar observation sample about x. The dynamic characteristics of the n-dimensional nonlinear power system are recovered from the scalar observation sample, that is, the phase space reconstruction is performed;

[0059] For the observations {s1,s2,...,s n The d-dimensional delay of} is reconstructed as:

[0060]

[0061] Where: d is the embedding dimension, τ is the time interval, called the delay time;

[0062] Takens embedding theorem: Let M be a D-dimensional compact manifold, φ be the flow on manifold M, F be a smooth vector field, and h be a smooth mapping on M. Then when the reconstruction dimension is greater than or equal to 2D+1, the delayed reconstruction is an embedding of M, where h(x) is a scalar observation function of the system;

[0063] Takens embedding theorem theoretically proves the existence of appropriate delayed embedding, but chaotic attractors are complex geometric structures embedded in the phase space with a dimension lower than the dimension of the power system;

[0064] When the embedding dimension d>2D F When D F is the box dimension of the strange attractor;

[0065] Under the premise of ensuring the embedding theory, a nonlinear time series of n points {x1,x2,...,x n The phase space trajectory of the reconstructed embedding dimension d of} is:

[0066]

[0067] Where d is the embedding dimension and τ is the delay time.

[0068] As a preferred solution of the present invention, the nonlinear term of the chaotic system is expressed as:

[0069]

[0070] Wherein, p>0, q∈(0, p] is called the variable parameter of the triangular wave function, and n is a positive integer.

[0071] As a preferred solution of the present invention, the derivation process of the nonlinear term expression is:

[0072] Based on the double-scroll chaotic circuit that can be generated by Cai's chaotic circuit, a single chaotic attractor is constructed according to the inherent mechanism of the chaotic attractor. The single chaotic attractor model is as follows:

[0073]

[0074] The only nonlinear term is n(y) = exp(-y)-1;

[0075] The multiple chaotic attractor model proposed based on the single chaotic attractor model is as follows:

[0076]

[0077] The nonlinear term of the multi-chaotic attractor model is modified by using piecewise linear triangular wave function, and its mathematical expression is:

[0078]

[0079] Wherein, p>0, q∈(0, p] is called the variable parameter of the triangular wave function, and n is a positive integer.

[0080] As a preferred embodiment of the present invention, the establishment process of the multi-channel ICA separation algorithm is as follows:

[0081] Let the source signal be s1,s 2, ...,s m , are independently distributed in each power grid branch, s1,s 2, ...,s m There may be chaos and noise in the grid. The observed signal measured at the common connection point of the power grid is x1,x 2, ...,x n , the number of sampling points is N; because:

[0082]

[0083] Then: The signal detection system model is:

[0084] X=AS,

[0085] Where, X=(x1,x 2, ...,x n ), S=S(s1,s 2, ...,s m ), A∈R n×m is the hybrid system matrix;

[0086] If the influence of noise X=AS is considered, the signal separation system model is:

[0087] X=AS+v,

[0088] Where v is the system noise or measurement noise.

[0089] Beneficial effects

[0090] The present invention assumes that chaos and noise exist simultaneously in the power system, identifies chaos and noise through phase space reconstruction, and separates the chaos source and noise source through the ICA method, providing certain support and reference for the accurate positioning of the chaos source and noise source. This invention provides important reference value for the in-depth study of harmonic sources and flicker sources in power systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 is the phase plane and output waveform of Chua's circuit;

[0092] Figure 2 It is the time domain waveform and instantaneous flicker value at different signal-to-mixing ratios;

[0093] Figure 3 is the initial value sensitive dependency graph;

[0094] Figure 4 is the bifurcation diagram;

[0095] Figure 5 Reconstruct the inter-graph for the τ = 1 phase space;

[0096] Figure 6 Reconstructed diagram for the phase space of τ = 2;

[0097] Figure 7 is the phase space reconstruction diagram of the superimposed noise;

[0098] Figure 8 Reconstruct interval maps for the noisy phase space;

[0099] Figure 9 For the separation of chaos and noise;

[0100] Figure 10 Separation of different types of noise in chaotic superposition;

[0101] Figure 11 This is a diagram of the IEEE power grid node test system;

[0102] Figure 12 This is the result diagram of chaotic noise separation. DETAILED DESCRIPTION

[0103] The present invention will be further described with reference to the accompanying drawings and embodiments.

[0104] As an embodiment of the present invention, a method for identifying and separating chaotic flicker sources includes the following steps:

[0105] S1. Collecting sampled values ​​or observed values ​​of an n-dimensional nonlinear power system by measurement;

[0106] S2. Use the Lyapunov index to determine whether the n-dimensional nonlinear power system has chaotic motion: if the Lyapunov index is greater than 0, then the n-dimensional nonlinear power system has chaotic motion, that is, the n-dimensional nonlinear power system is a chaotic system;

[0107] S3. By measuring the invariant measure of the chaotic system, the distribution of the points generated by the chaotic mapping iteration, i.e., the chaotic signal, in the state space is obtained; wherein: the invariant measure is:

[0108]

[0109] Where f is the chaotic map, δ is the probability density function, and N is the number of iterations;

[0110] S4. Using the field test data and waveform as a reference, the short flicker value when the ideal signal modulates chaotic signals of different amplitudes is tested by the signal-to-mixing ratio to determine whether the chaotic system has a chaotic flicker source; wherein: the signal-to-mixing ratio is:

[0111] SN=10*log 10 (R x {NT s} / σ 2 ),

[0112] Where SN is the signal-to-mixing ratio, R x is the correlation value of the signal, σ 2 is the chaotic variance, N is the number of sampling points, T S is the sampling time interval;

[0113] S5, constructing a nonlinear time series of n points {x1, x2, ..., x n} to reconstruct the phase space trajectory of the time delay embedding dimension d, and use the phase space trajectory to reconstruct the dynamic characteristics of the chaotic system to identify the chaotic flicker source signal and noise; wherein, the phase space trajectory is:

[0114]

[0115] Where d is the embedding dimension and τ is the delay time;

[0116] The condition for time delay embedding is that the embedding dimension d>2D F , where: D F is the box dimension of the strange attractor;

[0117] S6. Based on the network topology characteristics of the n-dimensional nonlinear power system, a multi-channel ICA separation algorithm is used to separate the chaotic flicker source identified in step S5 from the noise.

[0118] As an embodiment of the present invention, Figure 1 As shown, the derivation process of the nonlinear term expression is:

[0119] Based on the double scroll chaotic circuit that Chua's chaotic circuit can generate, the phase plane and signal waveform of Chua's chaotic circuit are as follows: Figure 1 As shown, according to the inherent mechanism of chaotic attractor, chaotic attractor is constructed. The single chaotic attractor model is as follows:

[0120]

[0121] The only nonlinear term n(y)=exp(-y)-1. The multiple chaotic attractor model proposed based on the single chaotic attractor model is as follows:

[0122]

[0123] The nonlinear term of the multi-chaotic attractor model is modified by using piecewise linear triangular wave function, and its mathematical expression is:

[0124]

[0125] Wherein, p>0, q∈(0, p] is called the variable parameter of the triangular wave function, and n is a positive integer.

[0126] As an embodiment of the present invention, the invariant measure (Invariant Measure) ρ(x) describes the distribution of points generated by the chaotic map iteration in the state space. The invariant measure is defined as

[0127]

[0128] Where f is the chaotic map, δ is the probability density function, and N is the number of iterations;

[0129] If the invariant measure ρ(x) is independent of the initial value x0, the chaotic system is said to be ergodic in state space. Li--Yorke proved that the sequence {x k} ergodicity. For f(x) in general, under the condition:

[0130] (1) f(x) is continuous.

[0131] (2) Except for a certain point z∈J, f(x) is quadratically continuously differentiable.

[0132] (3) Under infinite |f′(x)|>1, there exists a density ρ(x) function that satisfies:

[0133]

[0134] Under the condition of satisfying ergodicity, the chaotic sequence {x k The time average of the function g(x) of} can be written as an ensemble average based on the invariant measure:

[0135]

[0136] The time evolution equation corresponding to the one-dimensional chaotic map is expressed using an invariant measure. Given an initial value x0, the probability density function is δ(x-x0). After one iteration, it evolves into f(x0), with a probability density function of δ(xf(x0)). The first-order nonlinear deterministic difference equation is considered as a special Markov process, and its one-step transition probability density function is:

[0137] ρ(x|y)=δ(xf(y))

[0138] so,

[0139] It is usually written as an arbitrary density function ρ with the number of iterations k k Evolution of (x):

[0140]

[0141] This is the Frobenius-Perron equation. It should be noted that ergodicity is meaningful only when the density function ρ(x) is independent of the number of iterations, that is, the invariant measure ρ(x) must be stationary, so:

[0142]

[0143] For f(x) in a general sense, the above formula has a unique solution, which allows us to obtain the invariant measure of the chaotic map, which is used to represent the distribution of sequence points in the state space.

[0144] As an embodiment of the present invention, the derivation process of the signal-to-mixture ratio is as follows:

[0145] According to the characteristics of independent source signals in n-dimensional nonlinear power system, considering chaos(t) as additive chaotic signal, a harmonic chaotic signal model is established:

[0146]

[0147] Among them, chaos(t) is the chaotic signal, A k ,ω k and are independent random variables, It obeys a uniform distribution within the range of 0 to 2π, and chaos(t) is statistically independent of the sine signal;

[0148] Consider the sampling time interval as T s , we can deduce and prove that:

[0149] R x {0}-R x {NT s}=σ 2 ,

[0150] The signal-to-mixing ratio is:

[0151] SN=10*log 10 (R x {NT s} / σ 2 ).

[0152] The time domain waveform and instantaneous flicker value at different signal-to-mixing ratios are as follows: Figure 2 shown.

[0153] As an embodiment of the present invention, the process of establishing the phase space trajectory is as follows:

[0154] For an n-dimensional nonlinear power system:

[0155]

[0156] The observation value s = h(x) is a scalar observation sample about X. How to recover the dynamic characteristics of the power system from the scalar observation sample, that is, to perform phase space reconstruction;

[0157] For the observations {s1,s2,...,s n The d-dimensional delay of} is reconstructed as:

[0158]

[0159] Where d is the embedding dimension, τ is the time interval, called the delay time;

[0160] Takens embedding theorem: Let M be a D-dimensional compact manifold, φ be the flow on manifold M, F be a smooth vector field, and h be a smooth mapping on M. Then when the reconstruction dimension is greater than or equal to 2D+1, the delayed reconstruction is an embedding of M, where h(x) is a scalar observation function of the system;

[0161] Takens embedding theorem theoretically proves the existence of appropriate delayed embedding, but chaotic attractors are complex geometric structures embedded in the phase space with a dimension lower than the dimension of the power system;

[0162] When the embedding dimension d>2D F When D F is the box dimension of the strange attractor;

[0163] Under the premise of ensuring the embedding theory, a nonlinear time series of n points {x1,x2,...,x n The phase space trajectory of the reconstructed embedding dimension d of} is:

[0164]

[0165] The simplest Logistics system is used to demonstrate the initial value sensitivity and phase space reconstruction of chaos. The orbital separation is shown in the following example when the initial values ​​are 0.60001 and 0.60002. Figure 3 and Figure 4 As shown in the figure, it can be seen that the beginning is very close to the initial value, and the orbits almost overlap at the beginning, but as the orbits evolve, the orbits separate and the two orbits are completely different.

[0166] According to Takens embedding theory, the phase space reconstruction method is used to reconstruct the original chaotic system. Figures 5 to 8 As shown in , it can be seen from the reconstructed phase space that the phase space can reconstruct the original system. This characteristic can be used to identify chaos and noise.

[0167] As an embodiment of the present invention, the establishment process of the multi-channel ICA separation algorithm is as follows:

[0168] Let the source signals be s1,s2,...,s m , are independently distributed in each power grid branch, s1,s2,...,s m There may be chaos and noise in the grid. The observed signals measured at the point of common connection (PCC) are x1, x2, ..., x n , the number of sampling points is N; because:

[0169]

[0170] Then: The signal detection system model is:

[0171] X=AS,

[0172] Where, X=(x1,x2,...,x n ), S=S(s1,s2,...,s m ), A∈R n×m is the hybrid system matrix;

[0173] If the influence of noise X=AS is considered, the signal separation system model is:

[0174] X=AS+v,

[0175] Where v is the system noise or measurement noise.

[0176] As an embodiment of the present invention, chaos and noise separation simulation:

[0177] Assume that the source signal of the power grid system is s1, which is the fundamental signal, s2 and s3 are chaotic signals, and the source signal s4 is noise. i =chaos i The observed signal is a mixture of various signals. The simulation still uses random mixing matrix mixing, and then uses the ICA method to separate the source signal. The simulation results are as follows Figure 9 shown.

[0178] The above simulations show that the multi-channel ICA blind source separation method can effectively separate chaos and noise, and the separated estimation signal 1 and the separated estimation signal 3 are actual chaos estimation signals.

[0179] Assume that the source signals of the power grid system are s1, s2, s3 and s4, which are chaotic source signals, and different noises are superimposed to different degrees, that is, s i =chaos i +w i ,i=1,2,3,4. w i The noise is the observed signal, and the mixed signal is a mixture of various signals. The simulation still uses random mixing matrix mixing, and then uses the ICA method to separate the source signal. The separation results are as follows: Figure 10 shown.

[0180] Signal simulation results show that when chaos is superimposed with different noises, chaos and system noise cannot be separated. The separation result is a chaotic source signal superimposed with noise. To achieve the separation of chaos and noise, it is necessary to continue to use the multi-channel ICA blind source separation method in the next-level power grid line of the source to separate chaos and noise step by step.

[0181] Conclusion: The above simulations demonstrate that the multi-channel ICA blind source separation method is capable of separating chaos from noise in a noisy environment, resulting in the separation of the source signals for each independent line. However, due to two uncertainties inherent in the blind source separation algorithm, the detection result only yields the source signal waveform, not the waveform amplitude. The initial phase of the waveform also exhibits a certain deviation. Accurately correcting the amplitude and initial phase deviations to eliminate the uncertainty in blind source separation requires further research. However, separating the chaotic source signal waveform is also valuable for identification and location.

[0182] Power grid simulation analysis:

[0183] The simulation model is built in MATLAB Simulink as shown in the figure. The power generation system is set with a fundamental voltage source, a chaotic source is set at the 8th node, a chaotic source superimposed noise is set at the 16th node, and a noise source is set at the 10th node. The simulation results are as follows Figure 11 shown.

[0184] From the simulation results, we can see that the multi-channel ICA separation model can separate the chaotic source and noise source waveforms, but the chaotic source superimposed with noise cannot be completely separated. Figure 12 shown.

[0185] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and essence of the present invention should be within the scope of the present invention.

Claims

1. A method for identifying and separating chaotic flicker sources, characterized in that: The steps include: S1. Collecting sampled values ​​or observed values ​​of an n-dimensional nonlinear power system by measurement; S2. Use the Lyapunov index to determine whether the n-dimensional nonlinear power system has chaotic motion: if the Lyapunov index is greater than 0, then the n-dimensional nonlinear power system has chaotic motion, that is, a chaotic system; S3. By measuring the invariant measure of the chaotic system, the distribution of the points generated by the chaotic mapping iteration, i.e., the chaotic signal, in the state space is obtained; wherein: the invariant measure is: Where f is the chaotic map, δ is the probability density function, and N is the number of iterations; S4. Using the field test data and waveform as a reference, the short flicker value when the ideal signal modulates chaotic signals of different amplitudes is tested by the signal-to-mixing ratio to determine whether the chaotic system has a chaotic flicker source; wherein: the signal-to-mixing ratio is: SN=10*log 10 (R x {NT s } / s 2 ), Where SN is the signal-to-mixing ratio, R x is the correlation value of the signal, σ 2 is the chaotic variance, N is the number of sampling points, T S is the sampling time interval; S5, constructing a nonlinear time series of n points {x1, x2, ..., x n } to reconstruct the phase space trajectory of the time delay embedding dimension d, and use the phase space trajectory to reconstruct the dynamic characteristics of the chaotic system to identify the chaotic flicker source signal and noise; wherein, the phase space trajectory is: Where d is the embedding dimension and τ is the delay time; The condition for time delay embedding is that the embedding dimension d>2D F , where: D F is the box dimension of the strange attractor; S6. Based on the network topology characteristics of the n-dimensional nonlinear power system, a multi-channel ICA separation algorithm is used to separate the chaotic flicker source identified in step S5 from the noise.

2. The method for identifying and separating chaotic flicker sources according to claim 1, characterized in that: The derivation process of the signal-to-mixture ratio is: According to the characteristics of independent source signals in n-dimensional nonlinear power system, considering chaos(t) as additive chaotic signal, a harmonic chaotic signal model is established: Among them, chaos(t) is the chaotic signal, A k ,ω k and are independent random variables, It obeys a uniform distribution within the range of 0 to 2π, and chaos(t) is statistically independent of the sine signal; Consider the sampling time interval as T s , we can deduce and prove that: R x {0}-R x {NT s }=s 2 , The signal-to-mixing ratio is: SN=10*log 10 (R x {NT s } / s 2 )。 3. The method for identifying and separating chaotic flicker sources according to claim 1, characterized in that: The ideal signal is the power system fundamental wave.

4. The method for identifying and separating chaotic flicker sources according to claim 1, characterized in that: The process of establishing the phase space trajectory is as follows: For n-dimensional nonlinear power systems: The observation value s = h(x) is a scalar observation sample about x. The dynamic characteristics of the n-dimensional nonlinear power system are recovered from the scalar observation sample, that is, the phase space reconstruction is performed; For the observations {s1,s2,...,s n The d-dimensional delay of} is reconstructed as: Where: d is the embedding dimension, τ is the time interval, called the delay time; Takens embedding theorem: Let M be a D-dimensional compact manifold, φ be the flow on manifold M, F be a smooth vector field, and h be a smooth mapping on M. Then when the reconstruction dimension is greater than or equal to 2D+1, the delayed reconstruction is an embedding of M, where h(x) is a scalar observation function of the system; Takens embedding theorem theoretically proves the existence of appropriate time-delay embedding, but chaotic attractors are complex geometric structures embedded in the phase space with a dimension lower than the dimension of the power system; When the embedding dimension d>2D F When D F is the box dimension of the strange attractor; Under the premise of ensuring the time delay embedding theory, a nonlinear time series of n points {x1,x2,...,x n The phase space trajectory of the reconstructed embedding dimension d of} is:

5. The method for identifying and separating chaotic flicker sources according to claim 1, characterized in that: The nonlinear term of the chaotic system is expressed as: Where: p>0, q∈(0, p] is called the variable parameter of the triangular wave function, and n is a positive integer.

6. The method for identifying and separating chaotic flicker sources according to claim 5, characterized in that: The derivation process of the nonlinear term expression is: Based on the double-scroll chaotic circuit that can be generated by Cai's chaotic circuit, a single chaotic attractor is constructed according to the inherent mechanism of the chaotic attractor. The single chaotic attractor model is as follows: Among them, the only nonlinear term n(y) = exp(-y)-1; when the normalization parameters are set to k = 0.5, Q = 1.4158, and g = 3.1632, the system can generate a single-scroll chaotic attractor. The multiple chaotic attractor model proposed based on the single chaotic attractor model is as follows: Among them, the control parameters a>0, b>0; the nonlinear term of the multi-chaotic attractor model is modified by using the piecewise linear triangular wave function, and its mathematical expression is: Where p>0, q∈(0, p] is called the variable parameter of the triangular wave function, and n is a positive integer.

7. The method for identifying and separating chaotic flicker sources according to claim 1, characterized in that: The establishment process of the multi-channel ICA separation algorithm: Let the source signals be s1,s2,...,s m , are independently distributed in each power grid branch, s1,s2,...,s m There may be chaos and noise in the grid. The observed signals measured at the common connection point are x1, x2, ..., x n , the number of sampling points is N; because: Then: The signal detection system model is: X=AS, Where, X=(x1,x2,...,x n ), S=S(s1,s2,...,s m ), A∈R n×m is the hybrid system matrix; If the influence of noise X=AS is considered, the signal separation system model is: X=AS+v, Where v is the system noise or measurement noise.

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