A method for calculating the DC component of a signal

Abstract

This invention discloses a method for calculating the DC component of a signal, aiming to filter out excess harmonic components from a sampled signal. First, a sampling time is selected based on the number of harmonic components to be filtered out. A set of computational equations related to the DC component and the harmonic components to be filtered out is constructed using the sampled signal. The coefficient matrix of the computational equations is then transformed into a Vandermonde matrix to reduce the complexity of the inversion operation. Finally, the DC component of the sampled signal is calculated based on the Vandermonde matrix. This method is suitable for signal processing applications.

Description

Technical Field

[0001] The invention relates to a method for calculating a direct current component of a signal, and belongs to the fields of electrical engineering and signal processing. Background Art

[0002] With the advancement of motor control technology, various motors are widely used in industrial production fields such as transportation, aerospace, and household appliances. To achieve efficient and reliable control of motors, precise measurement and processing of the motor's internal electrical signals are required to achieve higher dynamic performance. However, during the motor manufacturing process, due to the immaturity of the motor manufacturing process, dimensional errors in the silicon steel laminations are inevitable. These errors cause asymmetry between the motor and the load shaft, resulting in the presence of mechanical frequency and its multiple harmonics in various electrical signals such as voltage, current, power, and torque.

[0003] Harmonic components in electrical signals can interfere with the sampling and processing of electrical signals, resulting in reduced observation accuracy and poor control performance. To eliminate these specific frequency harmonics from electrical signals, low-pass filters or notch filters are often used. Low-pass filters filter out all high-frequency signals above a certain frequency point. However, as the cutoff frequency decreases, the filtering delay time increases. Notch filters can quickly attenuate the input signal at a specific frequency point to achieve a filtering effect that prevents the passage of signals at this frequency. Although notch filters are easy to implement, the step response delay becomes more significant when the mechanical frequency of the motor and its multiple harmonic components have low frequencies, which can reduce the dynamic performance of data processing. Summary of the Invention

[0004] To address the delay issues associated with traditional notch filters when filtering harmonics, this paper proposes a method for calculating the DC component of a signal with a shorter delay. Based on the sampled signal, the method constructs a set of equations related to the DC component and the harmonic components to be filtered, thereby solving for the effective DC component in the electrical signal.

[0005] In order to solve the above problems, the technical solution adopted by the present invention is:

[0006] Step 1: Sampling is performed at the current sampling moment and the moments before and after it that are N, 2N, 3N, ..., nN times the sampling period, respectively, to obtain m electrical signals as sampling signals; wherein m = 2n + 1, and n is the number of harmonic components to be filtered out in the sampling signal; the sampling signals may specifically be: direct-axis voltage, quadrature-axis voltage, direct-axis current, quadrature-axis current, active power, reactive power, or electromagnetic torque;

[0007] Step 2: Construct a set of calculation equations related to the DC component and the harmonic components to be filtered out using m sampling signals;

[0008] Step 3: To simplify the calculation, transform the coefficient matrix of the equation group into a Vandermonde matrix;

[0009] Step 4: Based on the Vandermonde matrix, solve the DC component in the electrical signal.

[0010] In the above technical solution, further, in step 1, the discrete expression form of the sampling signal is:

[0011]

[0012] In the above equation, X(k) is the sampling signal at the kth sampling moment; x0 is the DC component of the sampling signal; x i 、ω i 、 (i=1,2,3,…n) corresponds to the amplitude, frequency and phase of the i-th harmonic component to be filtered out; T s is the sampling period.

[0013] Furthermore, in step 2, before constructing the calculation matrix, it is necessary to preprocess the sampled signal values ​​at all sampling moments. The specific method is to calculate the average value F of the sampled signal values ​​at the jth time interval before and after the kth sampling moment. j (k):

[0014]

[0015] In the above equation, j = 0, N, 2N, 3N, ... nN; X(k+j) is the sampling signal at the k+jth sampling moment; the amplitude

[0016] Based on the mean F j (k) Construct a set of calculation equations related to the DC component and the harmonic components to be filtered out, specifically:

[0017]

[0018] In the above equation, b i =NT s ω i .

[0019] Furthermore, in step 3, the coefficient matrix of the calculation equation group is transformed into a Vandermonde matrix. The calculation equation group after the transformation into the Vandermonde matrix is:

[0020]

[0021] In the above equation, c i =cosb i; Output of the calculation equation group after transformation into Vandermonde matrix h i (k) is:

[0022]

[0023] Furthermore, in step 4, based on the Vandermonde matrix, the expression of the DC component x0 of the electrical signal obtained by solution is:

[0024] x0=v0h0(k)+v1h1(k)+v2h2(k)+v3h3(k)+…+v n h n (k)

[0025] In the above equation, the coefficient v i for:

[0026]

[0027] Among them, p1, p2, ... p n-i is the coefficient v i The sum of the numerators corresponds to the subscripts of the 1st, 2nd, ... ni factors. q is the coefficient v i The coefficient subscript of the denominator of the product term, c q =cosb q =cosNT s ω q .

[0028] The inventive principle of the present invention is:

[0029] 1. In view of the characteristics of traditional notch filters that only filter out harmonics at specific notch frequencies and produce response delays when the harmonic frequencies are low, the present invention samples electrical signals within different time intervals, constructs a full-rank coefficient matrix of separation conditions based on the number of existing mechanical frequencies and their multiple harmonics, and finally constructs a set of calculation equations related to the DC component and the harmonic components to solve and separate the required DC component.

[0030] 2. Because solving the inverse matrix from the coefficient matrix of the equation is too complex during calculation, the present invention constructs a one-to-one correspondence between signal values ​​at different sampling intervals and the solution components by converting the coefficient matrix into a Vandermonde matrix. Each column of the Vandermonde matrix is ​​a power of the number of nodes, making it easy to invert the matrix, greatly reducing the amount of calculation and significantly improving computational efficiency.

[0031] The beneficial effects of the present invention are:

[0032] 1. The sampling time is selected according to the number of harmonic components to be filtered out, and a set of linearly related equations is constructed to separate the effective DC component from the electrical signal containing multiple harmonic components. This improves the problem of delayed response of low-pass filters and notch filters in filtering out low-frequency harmonic components. The present invention can effectively filter out the motor mechanical frequency and its multiple harmonics at the same time within a relatively short sampling time.

[0033] 2. Taking advantage of the fact that the Vandermonde matrix is ​​easy to solve the inverse matrix, by converting the coefficient matrix into a Vandermonde matrix, the complexity of the operation is reduced and the dynamic performance of data processing is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Different normalized delay time t d_n The gain attenuation of the method of the present invention for harmonics of different frequencies is shown below;

[0035] Figure 2 A comparison diagram of the effects of the method of the present invention, a low-pass filter, and a notch filter. DETAILED DESCRIPTION

[0036] The present invention is further described below with reference to the accompanying drawings and specific embodiments.

[0037] Figure 1 For different normalized delay times t d_n The following is the gain attenuation of the present invention for different frequency harmonics. d_n is the normalized delay, defined as t d_n =t d / T0;t d is the decay time; T0 is the period of the target harmonic filter; f0 is the frequency of the target harmonic filter; f is the frequency of different harmonics. The normalized delay time selected by the present invention is t d_n =0.6, the corresponding sampling spacing N selection rule is N=0.1 / T s f0.

[0038] Figure 2 The following figure compares the effects of the proposed method with those of a low-pass filter and a notch filter. Using the reactive power signal processing in a motor as an example, the three methods' filtering and dynamic response performance are compared under different current and speed conditions. The proposed method for calculating the DC component of the signal has a shorter delay than traditional notch filters and filters harmonic components better than low-pass filters.

[0039] This invention will be combined with an implementation example to specifically describe how to use the DC component calculation method. In this implementation example, a reactive power signal is used as the electrical signal to be processed. It is assumed that the harmonics in the reactive power signal to be processed include three harmonics of different frequencies: the fundamental mechanical frequency, the third mechanical frequency harmonic, and the sixth mechanical frequency harmonic. The specific implementation steps of the proposed invention are as follows:

[0040] Step 1: Select 7 reactive power signals at the current sampling moment and the moments before and after it that are N, 2N, and 3N times the sampling period as sampling signals;

[0041] Step 2: Use the reactive power signals at 7 sampling moments to construct a set of calculation equations related to the DC component and the fundamental wave, third harmonic, and sixth harmonic of the mechanical frequency;

[0042] Step 3: To simplify the calculation, transform the coefficient matrix of the equation group into a Vandermonde matrix;

[0043] Step 4: Based on the Vandermonde matrix, solve the DC component in the reactive power signal.

[0044] First, in step 1, the discrete expression of the reactive power signal is:

[0045]

[0046] In the above equation, Q(k) is the reactive power signal at the kth sampling moment; q0 is the DC component of the reactive power signal, q i 、ω i 、 Corresponding to the amplitude, frequency and phase of the fundamental wave, 3rd harmonic and 6th harmonic of the mechanical frequency respectively; T s is the sampling period;

[0047] Secondly, in step 2, before constructing the calculation matrix, the reactive power signal values ​​at the 7 sampling moments need to be preprocessed. The specific method is to calculate the average value F of the reactive power signal values ​​with the same time interval before and after. j (k):

[0048]

[0049] In the above equation, j = 0, N, 2N, 3N; X(k+j) is the sampling signal at the k+jth sampling moment; the amplitude

[0050] Then, based on the average value F j (k) Construct a set of calculation equations related to the DC component and the fundamental wave, third harmonic, and sixth harmonic of the mechanical frequency, which are specifically:

[0051]

[0052] In the above equation, b i =NT s ω i ;

[0053] Convert the coefficient matrix of the computational equations into a Vandermonde matrix:

[0054]

[0055] In the above equation, h0(k)=F0(k); h1(k)=F N (k); h2(k)=[F0(k)+F 2N (k)] / 2; h3(k)=[3F N (k)+F 3N (k)] / 4;c i =cosb i ;

[0056] Finally, the expression of the effective DC component q0 in the reactive power signal is solved as follows:

[0057] q0=v0h0(k)+v1h1(k)+v2h2(k)+v3h3(k)

[0058] In the above equation, the coefficient v i for:

[0059]

Claims

1. A method for calculating the DC component of a signal, characterized in that: The following steps are involved: Step 1: Select the current sampling moment and the moments before and after it that are N, 2N, 3N, ... nN times the sampling period, and perform sampling to obtain m electrical signals as sampling signals; where m = 2n + 1, and n is the number of harmonic components to be filtered out in the sampling signal; Step 2: Construct a set of calculation equations related to the DC component and the harmonic components to be filtered out using m sampling signals; Step 3: To simplify the calculation, transform the coefficient matrix of the equation group into a Vandermonde matrix; Step 4: Based on the Vandermonde matrix, solve the DC component of the electrical signal; In step 1, the discrete expression of the sampling signal is: ， In the above equation, X(k) is the sampling signal at the kth sampling moment; x0 is the DC component of the sampling signal; x i 、ω i 、φ i Corresponding to the amplitude, frequency and phase of the i-th harmonic component to be filtered out, i=1, 2, 3, …n; T s is the sampling period; The step 2 is specifically as follows: First, calculate the average value F of the sampled signal values ​​in the jth time interval before and after the kth sampling moment j (k): ， Where, j=0, N, 2N, 3N, …nN; X(k+j) is the sampling signal at the k+jth sampling moment; the amplitude a i =x i cos(kT s ω i +φ i ); Then, based on the average value F j (k) Construct a set of calculation equations related to the DC component and the harmonic components to be filtered out, specifically: ， Among them, b i =NT s ω i .

2. A method for calculating a DC component of a signal according to claim 1, characterized in that: In step 3, the coefficient matrix of the calculation equation group is transformed into a Vandermonde matrix. The calculation equation group after the transformation into the Vandermonde matrix is: ， Among them, c i =cosb i ; Output h of the calculation equation group after transformation into Vandermonde matrix i (k) is: 。 3. The signal DC component calculation method according to claim 2, characterized in that: In step 4, based on the Vandermonde matrix, the DC component x0 of the electrical signal is obtained: ， Coefficient v i for: ， Among them, p1, p2, …p n-i is the coefficient v i The sum of the numerators corresponds to the subscripts of the 1st, 2nd, …ni factors, c p1 =cosb p1 =cosNT s ω p1 , c p2 =cosb p2 =cosNT s ω p2 , …c pn-i =cosb pn-i =cosNT s ω pn-i ;q is the coefficient v i The coefficient subscript of the denominator of the product term, c q =cosb q =cosNT s ω q .

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