Identification and separation method for chaos flicker source

Abstract

The invention belongs to the technical field of electric power, and relates to a chaos flicker source identification and separation method, which comprises the following steps of: acquiring an observation value of a nonlinear electric power system; judging that the nonlinear power system is a chaotic system through a Lyapunov exponent; measuring the invariant measure of the chaotic system to obtain the distribution condition of the chaotic signals in the state space; on-site test data and waveforms are taken as references, and a chaos flicker source is judged through short flicker values when chaos signals with different amplitudes are modulated by signal-to-mix ratio test ideal signals; reconstructing a phase space trajectory of a time delay embedded dimension by using a nonlinear time sequence constructed by observation values, and reconstructing dynamic characteristics of a chaotic system by using the phase space trajectory to identify chaotic flicker source signals and noise; a chaotic flicker source and noise are separated through a multi-channel ICA separation algorithm; and support is provided for accurate positioning of a chaotic source and a noise source.

Description

Technical Field

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

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

[0003] Chaos is ubiquitous in nonlinear systems, but it has not been paid attention to in current power quality research. Flicker caused by chaotic signal modulation is called chaotic flicker source. Research on power system loads has revealed the fractal characteristics of power loads. The chaotic attractor has been reconstructed through phase space, proving the fractal characteristics of loads. The nonlinear changes in loads are reflected in power quality as grid waveform distortion. In addition to harmonics and interharmonics, grid waveform distortion may also include chaos and noise. Due to its unique fractal and pseudo-random characteristics, the phase space reconstruction method can realize the identification of chaos and noise, but it cannot complete the separation of chaos and noise. 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 by 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. The attracting set 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 called indivisible. An indivisible attracting set is called an attractor.

[0010] Conservative systems do not have attractors because their evolution remains unchanged in phase space. The volume of the phase space of a dissipative system will gradually shrink, so an indivisible attractor set can be obtained, which is the attractor. When the dimension of the attractor of a dissipative system is an integer dimension, it is a trivial attractor. When the dimension of the attractor of a dissipative system is a non-integer dimension, it is a strange attractor. Chaos is a complex dynamic behavior of a divisive 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 the initial values ​​are actually very close, and they will gradually separate as the orbit evolves;

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

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

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

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

[0031] In short, chaotic mapping has three elements: unpredictability, indecomposability, and a regular component, that is, non-periodic, sensitive to initial conditions, and bounded.

[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, 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. With reference to the field test data and waveform, the short flicker value when the ideal signal modulates the chaotic signal 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-mixture 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: construct an n-point nonlinear time series {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. According to 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 an 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 is uniformly distributed in the range of 0 to 2π, and chaos(t) is statistically independent from the sinusoidal signal;

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

[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-mixture 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:

[0057] For n-dimensional nonlinear power system:

[0058] The observation value s=h(x) is a scalar observation sample about x, and 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 the manifold M, F be a smooth vector field, 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 reconstruction 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] On the basis of the double scroll chaotic circuit that can be generated by Cai's chaotic circuit, a single chaotic attractor is constructed according to the internal 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 public 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] In the formula, 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 in the power system at the same time, 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 This 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 It is the initial value sensitive dependency graph;

[0094] Figure 4 is the bifurcation diagram;

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

[0096] Figure 6 The phase space reconstruction diagram is τ = 2;

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

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

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

[0100] Fig.10 Separation of different types of noise for chaotic superposition;

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

[0102] Fig.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, 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] In the formula, f is the chaotic map, δ is the probability density function, and N is the number of iterations;

[0110] S4. With reference to the field test data and waveform, the short flicker value when the ideal signal modulates the chaotic signal 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-mixture 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: construct an n-point nonlinear time series {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 the time delay embedding is that the embedding dimension d>2D F , where: D F is the box dimension of the strange attractor;

[0117] S6. According to 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 internal mechanism of chaotic attractor, chaotic attractor is constructed, and 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 ρ(x) describes the distribution of points generated by the chaotic mapping iteration in the state space. The invariant measure is defined as

[0127]

[0128] In the formula, 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 twice continuously differentiable.

[0132] (3) When |f′(x)| is infinite and is greater than 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 the ensemble average based on the invariant measure:

[0135]

[0136] The time evolution equation corresponding to the one-dimensional chaotic map is expressed by an invariant measure. Given an initial value x0, the probability density function is δ(x-x0). After one iteration, it evolves into f(x0), and the probability density function is δ(xf(x0)). The first-order nonlinear deterministic difference equation is regarded 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 k iterations 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 can obtain the invariant measure of the chaotic mapping and use it 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:

[0145] According to the characteristics of independent source signals in n-dimensional nonlinear power system, considering chaos(t) as an 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 is uniformly distributed in the range of 0 to 2π, and chaos(t) is statistically independent from the sinusoidal signal;

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

[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 reconstruct the phase space;

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

[0158]

[0159] Among them, 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 the manifold M, F be a smooth vector field, 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 reconstruction 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 figure 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 the figure, 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 grid common connection point (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 shown in Fig. 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 chaotic 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. i The noise is the observed signal, and 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 separation results are as follows: Fig.10 shown.

[0180] The signal simulation results show that when chaos is superimposed with different noises, chaos and system noise cannot be separated. The result of separation is a chaotic source signal superimposed with noise. For the separation result, 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 to achieve the separation of chaos and noise.

[0181] Conclusion: From the above simulation, it can be seen that the multi-channel ICA blind source separation method can separate chaos and noise in a noisy environment, and its separation result is the source signal of each independent line. However, due to the two uncertainties of the blind source separation algorithm, the detection result can only obtain the source signal waveform, but not the amplitude of the waveform, and the initial phase of the waveform also has a certain deviation. How to accurately correct the deviation of the amplitude and initial phase to eliminate the uncertainty of blind source separation still needs further research, but the separation of the waveform of the chaotic source signal also has certain significance and value for identification and positioning.

[0182] Power grid simulation analysis:

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

[0184] From the simulation results, it can be seen 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. Fig.12 shown.

[0185] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but the scope of the rights of the present invention is not limited thereto. Any modification, equivalent substitution and improvement made by a person skilled in the art without departing from the scope and essence of the present invention should be within the scope of the rights 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, 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: In the formula, f is the chaotic map, δ is the probability density function, and N is the number of iterations; S4. With reference to the field test data and waveform, the short flicker value when the ideal signal modulates the chaotic signal 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-mixture 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: construct an n-point nonlinear time series {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 the time delay embedding is that the embedding dimension d>2D F , where: D F is the box dimension of the strange attractor; S6. According to 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 is 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 an 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 is uniformly distributed in the range of 0 to 2π, and chaos(t) is statistically independent from the sinusoidal signal; Consider the sampling time interval as T s , we can deduce the proof: 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 is characterized in that: The ideal signal is the fundamental wave of the power system.

4. The method for identifying and separating chaotic flicker sources according to claim 1 is characterized in that: The process of establishing the phase space trajectory is: For n-dimensional nonlinear power system: The observation value s=h(x) is a scalar observation sample about x, and 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 the manifold M, F be a smooth vector field, 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 {x1,x2,...,x n The phase space trajectory of the reconstruction embedding dimension d of} is:

5. The method for identifying and separating chaotic flicker sources according to claim 1 is 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: On the basis of the double scroll chaotic circuit that can be generated by Cai's chaotic circuit, a single chaotic attractor is constructed according to the internal 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, g = 3.1632, the system can generate a single vortex 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 public connection point of the power grid 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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