Multi-harmonic superposition waveform generation method and system

Abstract

The invention discloses a multi-harmonic superposition waveform generation method and system, and relates to the technical field of waveform generation, and the method comprises the steps: carrying out the user-defined setting of harmonic parameters; based on a discrete Fourier transform algorithm, respectively generating a digital signal sequence of each harmonic; superposing the digital signal sequence according to the harmonic parameters to generate a composite signal sequence containing multiple harmonic components; performing real-time optimization on the composite signal sequence by adopting an adaptive filtering algorithm; and according to a preset waveform precision index, dynamically adjusting each harmonic parameter to correct the waveform error, and generating a multi-harmonic superposition waveform. The invention provides a multi-harmonic superposition waveform generation method and system with customizable parameters, high waveform precision, strong anti-interference capability and excellent real-time performance aiming at the defects in the aspects of precision, flexibility, anti-interference capability and the like in the prior art, and solves the problems of higher harmonic attenuation, waveform distortion, low parameter optimization efficiency and the like. And high-precision synthesis of multiple harmonic components is realized.

Description

Technical Field

[0001] This invention relates to the field of waveform generation technology, and more specifically to a method and system for generating multi-harmonic superposition waveforms. Background Technology

[0002] Currently, harmonics refer to the components greater than integer multiples of the fundamental frequency obtained by Fourier series decomposition of a periodic non-sinusoidal alternating current, commonly known as higher harmonics. The fundamental frequency refers to the component with the same frequency as the power frequency (50Hz). In existing technologies, the generation of multi-harmonic superposition waveforms mainly falls into two categories: one is a synthesis method based on analog circuits, which generates specific harmonics through hardware combinations such as reactors and tuning filters. This method is structurally complex, harmonic parameter adjustment relies on mechanical components, resulting in poor flexibility, and it can only support low-order harmonics, with severe attenuation of high-order harmonic signals. The other is a generation method based on digital signal processing, which uses inverse fast Fourier transform (IFFT) to synthesize composite waveforms. Although it supports higher-order harmonics, it is limited by spectral leakage and sampling synchronization issues, and it does not consider waveform distortion caused by hardware nonlinearity.

[0003] Therefore, how to provide a method and system for generating multi-harmonic superposition waveforms to improve the accuracy, flexibility and real-time performance of waveform generation has become an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0004] In view of this, the present invention provides a method and system for generating multi-harmonic superposition waveforms. In view of the shortcomings of the prior art in terms of accuracy, flexibility and anti-interference ability, the present invention provides a method and system for generating multi-harmonic superposition waveforms with customizable parameters, high waveform accuracy, strong anti-interference ability and good real-time performance. It solves problems such as high-order harmonic attenuation, waveform distortion and low parameter optimization efficiency, and realizes high-precision synthesis of multi-harmonic components.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a method for generating multi-harmonic superposition waveforms, comprising:

[0006] Customize harmonic parameters;

[0007] Based on the discrete Fourier transform algorithm, digital signal sequences of each harmonic are generated respectively;

[0008] The digital signal sequence is superimposed according to harmonic parameters to generate a composite signal sequence containing multiple harmonic components;

[0009] An adaptive filtering algorithm is used to optimize the composite signal sequence in real time.

[0010] Based on preset waveform accuracy indicators, the parameters of each harmonic are dynamically adjusted to correct waveform errors and generate high-precision multi-harmonic superposition waveforms.

[0011] Preferably, the harmonic parameters include harmonic order, amplitude, phase, frequency, and initial phase offset.

[0012] Preferably, the step of generating digital signal sequences for each harmonic based on the discrete Fourier transform algorithm includes:

[0013] Convert the time-domain parameters of each harmonic into a frequency-domain representation;

[0014] The complex amplitude at each frequency point is calculated using the discrete Fourier transform formula;

[0015] A corresponding digital signal sequence is generated based on the complex amplitude.

[0016] Preferably, the real-time optimization of the composite signal sequence using an adaptive filtering algorithm includes:

[0017] First, non-Gaussian noise in the composite signal is initially suppressed by particle filtering, and then the residual noise is finely filtered using the LMS / RLS algorithm.

[0018] The filter coefficients are dynamically adjusted based on the current input signal.

[0019] The filtering effect is optimized by minimizing the mean square value of the error signal.

[0020] Preferably, the dynamic adjustment of each harmonic parameter includes: introducing an adaptive BFO-PSO hybrid optimization algorithm, wherein the adaptive BFO-PSO hybrid optimization algorithm uses each harmonic parameter as an optimization particle and the deviation between the waveform accuracy index and the target value as the fitness function; global parameter search is achieved through particle swarm optimization (PSO), while incorporating the directional operation and migration mechanism of the bacterial foraging algorithm (BFO) to finely adjust local parameters;

[0021] In this process, the inertia weights of particle swarm optimization employ a nonlinear adaptive adjustment strategy, dynamically balancing global and local search capabilities based on the relationship between the current fitness value and the average fitness of the population. This improves the convergence speed and accuracy of parameter adjustment.

[0022] Preferred options also include:

[0023] Signal resampling is performed after generating the composite signal sequence;

[0024] The contribution weight of each harmonic signal in the composite sequence is calculated. When the contribution weight of a certain harmonic component is lower than a preset threshold, the digital signal sequence of that harmonic is resampled and updated. By supplementing high-contribution particles (signal samples), the expressiveness of weak harmonic components is enhanced, avoiding the component degradation problem during signal superposition.

[0025] Preferably, a multi-harmonic superposition waveform generation system includes:

[0026] The parameter customization module is used to customize and set harmonic parameters;

[0027] The digital signal sequence generation module is used to generate digital signal sequences of each harmonic based on the discrete Fourier transform algorithm.

[0028] The superposition module is used to superimpose the digital signal sequence according to harmonic parameters to generate a composite signal sequence containing multiple harmonic components.

[0029] The optimization module is used to perform real-time optimization of the composite signal sequence using an adaptive filtering algorithm;

[0030] The waveform generation module is used to dynamically adjust the harmonic parameters according to the preset waveform accuracy index to correct waveform errors and generate high-precision multi-harmonic superposition waveforms.

[0031] As can be seen from the above technical solutions, compared with the prior art, this invention discloses a method and system for generating multi-harmonic superposition waveforms. It improves waveform accuracy through a BFO-PSO hybrid optimization and self-calibration mechanism; employs a two-stage filtering architecture to suppress Gaussian and non-Gaussian noise, enhancing anti-interference capabilities; improves parameter optimization convergence speed; and introduces a signal resampling mechanism to reduce system resource occupancy. It solves problems such as high-order harmonic attenuation, waveform distortion, and low parameter optimization efficiency, achieving high-precision synthesis of multi-harmonic components. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0033] Figure 1 This is a schematic diagram of a method for generating multi-harmonic superposition waveforms provided by the present invention.

[0034] Figure 2 This is a schematic diagram of a multi-harmonic superposition waveform generation system provided by the present invention. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] This invention discloses a method for generating multi-harmonic superposition waveforms, such as... Figure 1 As shown, it includes:

[0037] Customize harmonic parameters;

[0038] Based on the discrete Fourier transform algorithm, digital signal sequences of each harmonic are generated respectively;

[0039] The digital signal sequence is superimposed according to harmonic parameters to generate a composite signal sequence containing multiple harmonic components;

[0040] An adaptive filtering algorithm is used to optimize the composite signal sequence in real time.

[0041] Based on preset waveform accuracy indicators, the parameters of each harmonic are dynamically adjusted to correct waveform errors and generate high-precision multi-harmonic superposition waveforms.

[0042] Specifically, the harmonic parameters include harmonic order, amplitude, phase, frequency, and initial phase offset.

[0043] Specifically, the process of generating digital signal sequences for each harmonic based on the discrete Fourier transform algorithm includes:

[0044] Convert the time-domain parameters of each harmonic into a frequency-domain representation;

[0045] The complex amplitude at each frequency point is calculated using the discrete Fourier transform formula;

[0046] A corresponding digital signal sequence is generated based on the complex amplitude.

[0047] Specifically, the real-time optimization of the composite signal sequence using an adaptive filtering algorithm includes:

[0048] First, non-Gaussian noise in the composite signal is initially suppressed by particle filtering, and then the residual noise is finely filtered using the LMS / RLS algorithm.

[0049] The filter coefficients are dynamically adjusted based on the current input signal.

[0050] The filtering effect is optimized by minimizing the mean square value of the error signal.

[0051] The LMS (Least Mean Square) algorithm or the RLS (Recursive Least Squares) algorithm is used as the adaptive filtering algorithm. Combining the adaptability of particle filtering to non-Gaussian noise with the real-time performance of the LMS / RLS algorithm, the non-Gaussian noise in the composite signal is initially suppressed by particle filtering during the filtering process, and then the LMS / RLS algorithm is used to finely filter the residual noise. At the same time, the weight ratio of the two algorithms is dynamically switched based on the signal noise characteristics. When the proportion of non-Gaussian noise exceeds 30%, the weight of particle filtering is increased, and vice versa.

[0052] Specifically, particle filtering is first used to initially suppress non-Gaussian noise in the composite signal, and then the LMS / RLS algorithm is used to finely filter the residual noise, including:

[0053] Particle filtering suppresses non-Gaussian noise:

[0054] The amplitude and phase state of the composite signal are encoded into a particle set: x k (i)=[A 复合 φ 复合 (i = 1, 2, ..., M, where M is the number of particles, ranging from 500 to 1000). Based on historical noise suppression data, the particles are initialized with prior probability to ensure that the particle distribution covers the normal fluctuation range of the signal.

[0055] According to signal model x k =H k-1 x k-1 +θ k-1 Predicting particle states (H k-1 Let θ be the state transition matrix. k-1 To handle process noise (adapted to non-Gaussian noise characteristics), generate a prediction particle set x. k∣k-1 (i).

[0056] Using the sum of squared signal errors as the fitness function ρ 实际 For the measured signal, ρ 预测 σ represents the predicted particle value, and σ represents the mean square error of the non-Gaussian noise.

[0057] Calculate particle weights and normalize them; when the number of effective particles is less than the effective particle threshold, resample the particles and reset the weights to 1 / M to avoid particle degradation.

[0058] The output filtering result yields a preliminary denoised signal, reducing the proportion of non-Gaussian noise.

[0059] LMS / RLS algorithm for fine-tuning residual noise:

[0060] Filter initialization: A 32nd-order FIR filter is used, with an initial step size of μ0 = 0.01 for the LMS algorithm and a forgetting factor of λ = 0.98 for the RLS algorithm.

[0061] Adaptive coefficient update:

[0062] For the LMS algorithm, according to ω k =ω k-1 +2μe(k)x(k) update coefficients;

[0063] Let z(k) be the error signal, and z(k) be the particle filter output.

[0064] A variable step size strategy μ(k) = μ0 / (1+α|e(k)|) is introduced; α = 0.1, which reduces steady-state error while ensuring convergence speed.

[0065] For the RLS algorithm, through P k =P k-1 -P k-1 x(k)x T (k)P k-1 / (λ+x T (k)P k-1 x(k)) updates the covariance matrix, improving the ability to track time-varying residual noise.

[0066] After LMS / RLS processing, the residual noise power is reduced, ensuring a smaller overall distortion of the composite signal and providing a high-precision signal basis for subsequent harmonic parameter adjustment.

[0067] In conjunction with practical application scenarios (such as harmonic error verification of electricity meters), the proportion of non-Gaussian noise is monitored in real time through noise characteristic analysis. When the proportion is ≤30%, the LMS / RLS weight is increased to 80% to accelerate processing (to meet the efficiency requirements of batch verification); conversely, the particle filter weight is increased to 70% to prioritize the suppression effect of non-Gaussian impulse noise (such as switching interference).

[0068] Specifically, the dynamic adjustment of each harmonic parameter includes: introducing an adaptive BFO-PSO hybrid optimization algorithm, which uses each harmonic parameter as an optimization particle and the deviation between the waveform accuracy index and the target value as the fitness function; achieving global parameter search through particle swarm optimization (PSO), while integrating the directional operation and migration mechanism of the bacterial foraging algorithm (BFO) to finely adjust local parameters;

[0069] In this process, the inertia weights of particle swarm optimization employ a nonlinear adaptive adjustment strategy, dynamically balancing global and local search capabilities based on the relationship between the current fitness value and the average fitness of the population. This improves the convergence speed and accuracy of parameter adjustment.

[0070] Specifically, the adaptive BFO-PSO hybrid optimization algorithm includes:

[0071] Particle initialization: Encode harmonic parameters (amplitude, phase, frequency) into particle state vectors:

[0072] x k (i)=[A1,φ1,f1,A2,φ2,f2,...,A m ,φ m ,f m ];

[0073] Where i is the particle number and m is the harmonic order;

[0074] Based on historical calibration data, M initial particle sets are generated with prior probability, and the particle value range is matched to adjust the accuracy.

[0075] Fitness function: The sum of squared deviations between the waveform accuracy index and the target value is used as the fitness function.

[0076]

[0077] Where ΔA, Δφ, and Δf are the amplitude, phase, and frequency deviations between the actual and target values, respectively, and σ is a constant set to 0.002.

[0078] PSO Global Search: Updates particle velocity and position according to the following formula:

[0079] v k (i)=ηv k-1 (i)+c1r1(pbest k-1 (i)-x k-1 (i))+c2r2(gbest k-1 -x k-1 (i));

[0080] x k (i)=x k-1 (i)+v k (i);

[0081] Where c1 and c2 are learning factors; random numbers r1 and r2 ∈ [0,1]; the inertia weight η is adjusted nonlinearly and adaptively.

[0082]

[0083] Among them, f min f max These represent the minimum and average fitness values ​​of the population particles, respectively.

[0084] Here, η is the inertia weight, whose magnitude significantly affects the search capability of PSO. A larger η indicates a stronger global search capability of PSO, while a smaller η indicates a stronger local search capability. Therefore, this invention comprehensively measures the search capability of PSO and uses a nonlinear adaptive inertia weight η for dynamic adjustment.

[0085] BFO local optimization:

[0086] Trending operation: Initialize the number of trending iterations N c =10, swimming step length G c =0.01, according to x n (i)=x n-1 (i)+G c ·R c (i) Adjust the particle position; if the new position has better fitness, keep it; otherwise, backtrack. R c (i) is a random direction vector.

[0087] Migration operation: Move the 50% of particles with the lowest fitness to the next highest fitness with a migration probability p. ed =0.2 Reinitialize to avoid local optima.

[0088] Particle weights and resampling:

[0089] Calculate particle weight ω k (i)=ω k-1 (i)·f(x k (i));

[0090] Calculate the particle weights, and after normalization, we get:

[0091]

[0092] Calculate the number of effective particles

[0093] When the calculated number of effective particles is less than the effective particle threshold, the particles are resampled and the weight is reset to 1 / M.

[0094] Specifically, this also includes: resampling the signal after generating the composite signal sequence;

[0095] The contribution weight of each harmonic signal in the composite sequence is calculated. When the contribution weight of a certain harmonic component is lower than a preset threshold, the digital signal sequence of that harmonic is resampled and updated. By supplementing high-contribution particles (signal samples), the expressiveness of weak harmonic components is enhanced, avoiding the component degradation problem during signal superposition.

[0096] In one specific embodiment of the present invention, such as Figure 2 As shown, a multi-harmonic superposition waveform generation system includes:

[0097] The parameter customization module is used to customize and set harmonic parameters;

[0098] The digital signal sequence generation module is used to generate digital signal sequences of each harmonic based on the discrete Fourier transform algorithm.

[0099] The superposition module is used to superimpose the digital signal sequence according to harmonic parameters to generate a composite signal sequence containing multiple harmonic components.

[0100] The optimization module is used to perform real-time optimization of the composite signal sequence using an adaptive filtering algorithm;

[0101] The waveform generation module is used to dynamically adjust the harmonic parameters according to the preset waveform accuracy index to correct waveform errors and generate high-precision multi-harmonic superposition waveforms.

[0102] In a specific embodiment of the present invention, during the factory calibration of a three-phase energy meter, a multi-harmonic superimposed waveform conforming to the standard JJG1106-2015 needs to be generated to test the metering accuracy of the energy meter under complex harmonic environments. The target waveform requirements are: fundamental wave (50Hz) voltage 220V, current 5A, superimposed with 3rd (150Hz), 5th (250Hz), and 7th (350Hz) harmonics, where the 3rd harmonic voltage content is 5% (11V) and current content is 10% (0.5A), the 5th harmonic voltage content is 3% (6.6V) and current content is 6% (0.3A), and the 7th harmonic voltage content is 2% (4.4V) and current content is 4% (0.2A). The total harmonic distortion (THD) is ≤2%, and the waveform must meet the accuracy requirements of fundamental wave 0.02 and harmonic wave 0.2.

[0103] S100, Customize harmonic parameters by configuring parameters through the system parameter customization module;

[0104] The system automatically matches the sampling rate to 10kHz (meeting the 28-fold sampling requirement of the 7th harmonic 350Hz) and pre-configures the initial parameters for BFO-PSO optimization (50 particles, 10 trend iterations).

[0105] S200: Generates digital signal sequences of each harmonic;

[0106] Time-domain to frequency-domain conversion: In this embodiment of the invention, the third harmonic voltage is used as an example, and the time-domain parameter is the amplitude. Phase θ is converted to complex amplitude in the frequency domain:

[0107]

[0108] The discrete signal sequence is generated using Fast Fourier Transform (FFT). The time-domain signal of the third harmonic voltage is as follows: Where n is the sampling point number.

[0109] Apply the Blackman-Harris window function to suppress spectral leakage.

[0110] S300, Composite Signal Superposition and Resampling

[0111] The three-phase voltage and current signals are weighted and superimposed according to parameters to generate a composite sequence:

[0112] u 复合 (n)=u1(n)+u3(n)+u5(n)+u7(n);

[0113] i 复合 (n)=i1(n)+i3(n)+i5(n)+i7(n).

[0114] Real-time monitoring of the energy proportion of each harmonic.

[0115] Resampling trigger: If the weight of a certain harmonic is lower than the preset threshold, the resampling mechanism is activated: by supplementing high amplitude sample points (adding sample points in the peak region of the harmonic), the weight of the harmonic is increased, so as to avoid it being masked by the fundamental wave during superposition.

[0116] S400, adaptive filtering optimization, to verify the presence of non-Gaussian noise and circuit thermal noise introduced by the power amplifier in the testing environment.

[0117] Particle filter preprocessing: Initialize 300 particles, with the particle state defined as the joint vector of signal amplitude and phase, through the state transition equation x. k =H k-1 x k-1 +θ k-1 Predict the state, θ k-1 This is to filter out process noise; the particle weights are updated using the observation equation to initially filter out non-Gaussian noise.

[0118] LMS algorithm for refined filtering: The variable step size LMS algorithm (step size factor 0.01) is adopted, the filter order is 32, and the mean square value of the error signal is minimized.

[0119] S500, Adaptive BFO-PSO Parameter Optimization

[0120] Particle encoding: The voltage amplitude, current amplitude, and phase of the 3rd, 5th, and 7th harmonics are used as optimized particles with a dimension of 9.

[0121] Fitness function: the sum of squared errors between the actual waveform and the target waveform. For fitness, the objective is to minimize J; y s Represents the actual value, y m This represents the target value.

[0122] Optimization process:

[0123] PSO Global Search: Inertia weights are dynamically adjusted according to the following formula:

[0124]

[0125] Among them, f min f max These represent the minimum and average fitness values ​​of the population particles, respectively.

[0126] Here, η is the inertia weight, whose magnitude significantly affects the search capability of PSO. A larger η indicates a stronger global search capability of PSO, while a smaller η indicates a stronger local search capability. Therefore, this invention comprehensively measures the search capability of PSO and uses a nonlinear adaptive inertia weight η for dynamic adjustment.

[0127] BFO Local Optimization: Perform a tendency operation to reinitialize the bottom 40% of particles with a 15% probability (migration operation) until the harmonic accuracy requirements are met.

[0128] The multi-harmonic superposition waveform generated in this embodiment meets the harmonic error verification requirements of three-phase energy meters. By integrating adaptive filtering and intelligent optimization algorithms, it adapts to the metering accuracy detection requirements of energy meters in complex harmonic environments.

[0129] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0130] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for generating multi-harmonic superposition waveforms, characterized in that, include: Customize harmonic parameters; Based on the discrete Fourier transform algorithm, digital signal sequences of each harmonic are generated respectively; The digital signal sequence is superimposed according to harmonic parameters to generate a composite signal sequence containing multiple harmonic components; An adaptive filtering algorithm is used to optimize the composite signal sequence in real time. Based on the preset waveform accuracy index, the parameters of each harmonic are dynamically adjusted to correct waveform errors and generate a multi-harmonic superposition waveform.

2. The method for generating multi-harmonic superposition waveforms according to claim 1, characterized in that, The harmonic parameters include harmonic order, amplitude, phase, frequency, and initial phase offset.

3. The method for generating multi-harmonic superposition waveforms according to claim 1, characterized in that, The algorithm based on Discrete Fourier Transform generates digital signal sequences for each harmonic, including: Convert the time-domain parameters of each harmonic into a frequency-domain representation; The complex amplitude at each frequency point is calculated using the discrete Fourier transform formula; A corresponding digital signal sequence is generated based on the complex amplitude.

4. The method for generating multi-harmonic superposition waveforms according to claim 1, characterized in that, The real-time optimization of the composite signal sequence using an adaptive filtering algorithm includes: First, non-Gaussian noise in the composite signal is initially suppressed by particle filtering, and then residual noise is filtered out using the LMS / RLS algorithm. The filter coefficients are dynamically adjusted based on the current input signal. The filtering effect is optimized by minimizing the mean square value of the error signal.

5. The method for generating multi-harmonic superposition waveforms according to claim 1, characterized in that, The dynamic adjustment of each harmonic parameter includes: introducing an adaptive BFO-PSO hybrid optimization algorithm, which uses each harmonic parameter as an optimization particle and the deviation between the waveform accuracy index and the target value as the fitness function; achieving global parameter search through particle swarm optimization, while integrating the directional operation and migration mechanism of the bacterial foraging algorithm to finely adjust local parameters; Among them, the inertial weight of particle swarm optimization adopts a nonlinear adaptive adjustment strategy, which dynamically balances the global and local search capabilities based on the relationship between the current fitness value and the average fitness of the population.

6. The method for generating multi-harmonic superposition waveforms according to claim 1, characterized in that, Also includes: Signal resampling is performed after generating the composite signal sequence; Calculate the contribution weight of each harmonic signal in the composite sequence. When the contribution weight of a certain harmonic component is lower than a preset threshold, resample and update the digital signal sequence of that harmonic.

7. A multi-harmonic superposition waveform generation system, characterized in that, include: The parameter customization module is used to customize and set harmonic parameters; The digital signal sequence generation module is used to generate digital signal sequences of each harmonic based on the discrete Fourier transform algorithm. The superposition module is used to superimpose the digital signal sequence according to harmonic parameters to generate a composite signal sequence containing multiple harmonic components. The optimization module is used to perform real-time optimization of the composite signal sequence using an adaptive filtering algorithm; The waveform generation module is used to dynamically adjust the harmonic parameters according to the preset waveform accuracy index to correct waveform errors and generate a multi-harmonic superimposed waveform.

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