A fundamental wave complex number estimation method and system based on Goertzel

Abstract

The present application relates to a kind of fundamental wave complex estimation method and system based on Goertzel, belong to digital signal processing technical field.The present application utilizes the output of the designed digital quadrature oscillator as the frequency conversion sequence in first-order Goertzel algorithm, adopts linear AGC method to adjust the gain value in digital quadrature oscillator in real time, so that the output of digital quadrature oscillator can be stabilized around 1, the gain value is multiplied with the output of digital quadrature oscillator at previous time to obtain the output of digital quadrature oscillator, which can greatly enhance the stability of oscillator, and the frequency conversion sequence of first-order Goertzel algorithm realized by superheterodyne scheme is replaced by the output of stable digital quadrature oscillator, and then the accuracy of fundamental wave vector size and phase calculation can be improved.

Description

TECHNICAL FIELD

[0001] The application relates to a Goertzel-based fundamental wave complex number estimation method and system and belongs to the technical field of digital signal processing. BACKGROUND

[0002] Power quality refers to the quality of alternating voltage supplied to users after power generation, transmission and distribution. Ideal power quality refers to constant three-phase grid voltage frequency, equal effective values and 2pi / 3 phase difference. In fact, any link from power generation, transmission to power transformation and distribution may affect power quality. In a three-phase four-wire low-voltage distribution network power supply system, whether the three-phase load of a distribution transformer is balanced is an important factor affecting the power quality of the distribution network. Load imbalance will affect the symmetry and sinusoidal nature of the three-phase current of the distribution network, increase the line and system loss, reduce the active power output of the distribution transformer, seriously affect the normal operation of the equipment in the network, and even threaten the safety of the entire public power grid.

[0003] In a low-voltage distribution network, three-phase imbalance is increasing, which is not conducive to the normal and orderly operation of the power grid system. In order to provide theoretical and data support for effective management of three-phase imbalance, it is the first prerequisite to quickly and accurately find three-phase imbalance. The International Electrotechnical Commission (IEC) defines the degree of three-phase imbalance by the ratio of the negative sequence component effective value of voltage to the positive sequence component effective value of voltage. At present, this method is more commonly used in engineering. This method needs the size and phase of three-phase vectors to perform phase sequence decomposition to obtain positive and negative sequence components.

[0004] Three-phase imbalance analysis is all selected for single fundamental wave (50Hz) frequency analysis. Using FFT to obtain the size and phase of the fundamental wave frequency will cause redundant calculation. Therefore, the first-order Goertzel algorithm with higher efficiency is used for calculation. However, in fixed-point data format, the superheterodyne frequency conversion sequence e -j2πm / N The amplitude factor deviates from 1 due to different quantization bit widths and m, which causes errors in the calculation of the size and phase of the fundamental wave vector, and finally affects the estimation of the degree of imbalance. SUMMARY

[0005] The application aims to provide a Goertzel-based fundamental wave complex number estimation method and system to solve the problem that the first-order Goertzel algorithm causes errors in the calculation of the fundamental wave due to the deviation of the superheterodyne frequency conversion sequence amplitude from 1.

[0006] The application provides a Goertzel-based fundamental wave complex number estimation method, which comprises the following steps:

[0007] 1) design a digital quadrature oscillator, which can make ejθ The amplitude is 1; where θ = 2πm / N, m = f i *N / f s , N is the number of sampling points, f i is the fundamental frequency, f s is the sampling frequency; the AGC method is used to adjust the digital quadrature oscillator gain value so that e jθ The amplitude of is always 1;

[0008] 2) Using the output of the digital quadrature oscillator as a frequency conversion sequence for the first-order Goertzel algorithm;

[0009] 3) Use the output of the digital orthogonal oscillator and the first-order Goertzel algorithm to calculate the fundamental complex number.

[0010] The present invention utilizes the output of a designed digital orthogonal oscillator as the frequency conversion sequence in the first-order Goertzel algorithm. The stable output of the digital orthogonal oscillator makes the amplitude of the frequency conversion sequence of the first-order Goertzel algorithm stable in a fixed-point format, thus avoiding the problem of the superheterodyne frequency conversion sequence in the first-order Goertzel algorithm in a fixed-point data format. -j2πm / N The amplitude will deviate from 1 due to the difference in quantization bit width and m, which will cause errors in the calculation of the size and phase of the fundamental wave vector, thereby improving the accuracy of the calculation of the size and phase of the fundamental wave vector.

[0011] Furthermore, the output of the digital quadrature oscillator designed in step 1) is:

[0012] y i (n)-jy q (n) = G(n)*(y i '(n-1)-jy' q (n-1))

[0013] y i '(n-1)=y i (n-1)*cos(θ)-y q (n-1)*sin(θ)

[0014] y' q (n-1)=y q (n-1)*cos(θ)+y i (n-1)*sin(θ)

[0015]

[0016] where y i (n), y q (n) are the in-phase and quadrature outputs of the digital quadrature oscillator, G(n) is the gain value, y i(n-1), y q (n-1) are the in-phase and quadrature outputs of the digital quadrature oscillator at the previous moment.

[0017] The digital quadrature oscillator designed by the present invention can provide a stable output.

[0018] The present invention uses a linear AGC method to adjust the gain value G in real time, and multiplies the gain value G with the oscillator's output at the previous moment to obtain the oscillator output, which can greatly enhance the stability of the oscillator and thereby improve the accuracy of fundamental wave vector size and phase calculation.

[0019] Furthermore, in step 2), the calculation formula for calculating the fundamental frequency of the first-order Goertzel algorithm using the digital orthogonal oscillator output as the frequency conversion sequence is:

[0020] y(n)=x(n)[G(n)*(y i '(n-1)-jy' q (n-1))]+y(n-1)

[0021] Where x(n) is the input data sequence, y(n) is the output of the first-order Goertzel algorithm, and y(n-1) is the output of the first-order Goertzel algorithm at the previous moment.

[0022] The present invention also provides a fundamental complex number estimation system based on Goertzel, which includes a first-order Goertzel algorithm module and a digital orthogonal oscillator. The output of the digital orthogonal oscillator is a frequency conversion sequence of the first-order Goertzel algorithm. The first-order Goertzel algorithm module is used to estimate the fundamental complex number by using the output of the digital orthogonal oscillator as the frequency conversion sequence; the digital orthogonal oscillator is adjusted by a gain adjustment module. jθ The amplitude is stable at 1, where θ = 2πm / N, m = f i *N / f s , N is the number of sampling points, f i is the fundamental frequency, f s The sampling frequency is the gain adjustment module, and the gain value of the digital quadrature oscillator is adjusted by the AGC method.

[0023] The present invention utilizes the output of a designed digital orthogonal oscillator as the frequency conversion sequence in the first-order Goertzel algorithm. The stable output of the digital orthogonal oscillator stabilizes the amplitude of the frequency conversion sequence in the first-order Goertzel algorithm, thereby avoiding the problem of the superheterodyne frequency conversion sequence in the first-order Goertzel algorithm in the fixed-point data format. -j2πm / NThe amplitude will deviate from 1 due to the difference in quantization bit width and m, which will cause errors in the calculation of the size and phase of the fundamental wave vector, thereby improving the accuracy of the calculation of the size and phase of the fundamental wave vector.

[0024] Furthermore, the output of the digital quadrature oscillator is:

[0025] y i (n)-jy q (n) = G(n)*(y i '(n-1)-jy' q (n-1))

[0026] y i '(n-1)=y i (n-1)*cos(θ)-y q (n-1)*sin(θ)

[0027] y' q (n-1)=y q (n-1)*cos(θ)+y i (n-1)*sin(θ)

[0028]

[0029] where y i (n), y q (n) are the in-phase and quadrature outputs of the digital quadrature oscillator, G(n) is the gain value, y i (n-1), y q (n-1) are the in-phase and quadrature outputs of the digital quadrature oscillator at the previous moment.

[0030] The digital quadrature oscillator designed by the present invention can provide a stable output.

[0031] The present invention uses a linear AGC method to adjust the gain value G in real time, and multiplies the gain value G with the oscillator's output at the previous moment to obtain the oscillator output, which can greatly enhance the stability of the oscillator and thereby improve the accuracy of fundamental wave vector size and phase calculation.

[0032] Furthermore, the calculation formula for the first-order Goertzel algorithm module to calculate the fundamental wave vector is:

[0033] y(n)=x(n)[G(n)*(y i '(n-1)-jy' q (n-1))]+y(n-1)

[0034] Where x(n) is the input data sequence, y(n) is the output of the first-order Goertzel algorithm, and y(n-1) is the output of the first-order Goertzel algorithm at the previous moment. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a principle diagram of the fundamental complex number estimation method based on Goertzel of the present invention. DETAILED DESCRIPTION

[0036] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0037] Example of Goertzel-based fundamental complex number estimation method

[0038] Currently, the first-order Goertzel algorithm is implemented using a superheterodyne solution. The specific calculation formula is as follows:

[0039] y(n)=x(n)*e -j2πnm / N +y(n-1)

[0040] In the formula, x(n) is the input data sequence, y(n) is the output of the Goertzel algorithm, y(n-1) is the output of the previous moment, and e -j2πnm / N is a frequency conversion sequence, n is the signal time domain index, m is the frequency point to be obtained, N is the data length, when n=N, y(N) is the spectrum value of frequency point m. -j2πnm / N Multiplication modulates the signal frequency to zero frequency, but due to e -j2πnm / N In the fixed-point implementation of the value, there will be a loss of precision in quantization. As time n increases, e -j2πnm / N The amplitude may increase or decrease, that is, the superheterodyne frequency conversion sequence e in the first-order Goertzel algorithm -j2πm / N The amplitude deviates from 1 due to the difference in quantization bit width and m, which in turn affects the accuracy of subsequent fundamental wave calculation. To this end, the present invention provides a fundamental wave complex number estimation method based on Goertzel, which designs a digital orthogonal oscillator to convert e -j2πnm / N The value is replaced by the stable digital orthogonal oscillator output, and the linear AGC method is used to adjust the gain value G of the digital orthogonal oscillator in real time. The gain value G is multiplied by the output of the digital orthogonal oscillator at the previous moment to obtain the digital orthogonal oscillator output, which can greatly enhance the stability of the oscillator and thus improve the accuracy of the fundamental wave complex number size and phase calculation. The implementation principle of this method is as follows Figure 1 As shown, the specific steps include the following steps.

[0041] 1. Design a digital quadrature oscillator so that when the digital quadrature oscillator is in fixed-point digital format, e jθ The amplitude is stable at 1.

[0042] In floating point data format, according to y i (n)-jy q (n)=[y i (n-1)-jy q (n-1)]e jθ The calculated digital orthogonal oscillator can have a stable output, but in chip design, the data format is fixed-point format. Depending on the length of the binary number and θ, e jθ It is difficult to achieve that the amplitude of θ is 1 at any value of θ. The oscillator output amplitude may increase or decrease. Therefore, it is necessary to adjust the e in fixed-point format. jθ The value is adjusted using a linear AGC method. The specific implementation idea of ​​the adjustment is:

[0043] The expected gain is defined as:

[0044]

[0045] Where: P des is the power of the desired output signal, P act =(abs(e jθ )) 2 =y i '(n-1) 2 +y' q (n-1) 2 is the power of the actual output signal, and the error factor E is P act With P des The difference between them. Taylor series expansion of the above equation yields G(n)=a0+a1E, let a0=1, available:

[0046]

[0047] Due to the expected jθ The amplitude is 1, so P des is 1, the formula for G(n) is as follows:

[0048]

[0049] y i '(n-1)=y i (n-1)*cos(θ)-y q (n-1)*sin(θ)

[0050] y' q (n-1)=y q (n-1)*cos(θ)+y i (n-1)*sin(θ)

[0051] Finally, the output of the stable digital quadrature oscillator is:

[0052] y i (n)-jy q (n) = G(n)*(y i '(n-1)-jy' q (n-1))

[0053] Where θ = 2πf i / f s , f i is the fundamental frequency, f s is the sampling rate.

[0054] The output of the digital quadrature oscillator at the previous moment is used to calculate the in-phase and quadrature outputs at the next moment. In the fixed-point digital format, e jθ The amplitude of will deviate from 1 according to the quantization bit width and the value of θ, and may increase or decrease with time. To solve this problem, the gain value G(n) can be adjusted in real time by the linear AGC method mentioned above so that e jθ The magnitude is always 1.

[0055] 2. Use the output of the digital orthogonal oscillator as the frequency conversion sequence of the first-order Goertzel algorithm.

[0056] The calculation formula of the first-order Goertzel algorithm implemented by the superheterodyne solution is as follows:

[0057] y(n)=x(n)*e -j2πnm / N +y(n-1)

[0058] where e -j2πnm / N is a frequency conversion sequence, n is the signal time domain index, m is the frequency point to be obtained, N is the data length, θ=2πm / N, m=f i *N / f s .

[0059] The present invention converts the output y of the digital quadrature oscillator i (n)-jy q (n) as the frequency-varying sequence of the first-order Goertzel algorithm, i.e., e -j2πnm / N By y i (n)-jy q (n) Replace.

[0060] 3. Use the output of a digital quadrature oscillator and the first-order Goertzel algorithm to calculate the fundamental complex number.

[0061] Since the present invention will -j2πnm / N The value is replaced by the stable digital quadrature oscillator output, that is, e -j2πnm / N =yi (n)-jy q (n), and bring it into the first-order Goertzel algorithm to get:

[0062] y(n)=x(n)[G(n)*(y i '(n-1)-jy' q (n-1))]+y(n-1)

[0063] If the number of sampling points is N, the loop iterates N times and sets the initial condition y i (n-1)=1,y q (n-1)=0, and the final output y(N) is the fundamental wave complex output.

[0064] Through the above process, the present invention utilizes the output of the designed digital quadrature oscillator as the frequency conversion sequence in the first-order Goertzel algorithm, adopts the linear AGC method to adjust the gain value in the digital quadrature oscillator in real time, so that the output of the digital quadrature oscillator can be stabilized near 1, and multiplies the gain value by the output of the digital quadrature oscillator at the previous moment to obtain the digital quadrature oscillator output, which can greatly enhance the stability of the oscillator. The frequency conversion sequence of the first-order Goertzel algorithm implemented by the superheterodyne scheme is replaced by the stable digital quadrature oscillator output, thereby improving the accuracy of the fundamental wave vector size and phase calculation.

[0065] An embodiment of a fundamental complex number estimation system based on Goertzel

[0066] The Goertzel-based fundamental complex number estimation system of the present invention includes a first-order Goertzel algorithm module and a digital orthogonal oscillator. The output of the digital orthogonal oscillator is a frequency conversion sequence of the first-order Goertzel algorithm. The first-order Goertzel algorithm module is used to estimate the fundamental complex number by using the output of the digital orthogonal oscillator as a frequency conversion sequence. The digital orthogonal oscillator can make e jθ The amplitude is stable at 1, where θ = 2πm / N, m = f i *N / f s , N is the number of sampling points, f i is the fundamental frequency, f s The specific implementation of the system has been described in detail in the method embodiment and will not be repeated here.

Claims

1. A fundamental complex number estimation method based on Goertzel, characterized in that: The method comprises the following steps: 1) Design a digital quadrature oscillator that can generate jθ The amplitude is 1; where θ = 2πm / N, m = f i *N / f s , N is the number of sampling points, f i is the fundamental frequency, f s is the sampling frequency; the AGC method is used to adjust the digital quadrature oscillator gain value so that e jθ The amplitude of is always 1; 2) Using the output of the digital quadrature oscillator as a frequency conversion sequence for the first-order Goertzel algorithm; 3) Use the output of the digital orthogonal oscillator and the first-order Goertzel algorithm to calculate the fundamental complex number.

2. The Goertzel-based fundamental complex number estimation method according to claim 1, characterized in that: The output of the digital quadrature oscillator designed in step 1) is: y i (n)-you q (n)=G(n)*(y i '(n-1)-you' q (n-1)) and i '(n-1)=y i (n-1)*cos(θ)-y q (n-1)*sin(θ) and' q (n-1)=y q (n-1)*cos(θ)+y i (n-1)*sin(θ) where y i (n), y q (n) are the in-phase and quadrature outputs of the digital quadrature oscillator, G(n) is the gain value, y i (n-1), y q (n-1) are the in-phase and quadrature outputs of the digital quadrature oscillator at the previous moment.

3. The Goertzel-based fundamental complex number estimation method according to claim 2, characterized in that: In the step 2), the calculation formula for calculating the fundamental wave vector of the first-order Goertzel algorithm using the digital orthogonal oscillator output as the frequency conversion sequence is: y(n)=x(n)[G(n)*(y i '(n-1)-you' q (n-1))]+y(n-1) Where x(n) is the input data sequence, y(n) is the output of the first-order Goertzel algorithm, and y(n-1) is the output of the first-order Goertzel algorithm at the previous moment.

4. A fundamental complex number estimation system based on Goertzel, characterized in that: The system includes a first-order Goertzel algorithm module and a digital orthogonal oscillator. The output of the digital orthogonal oscillator is a frequency conversion sequence of the first-order Goertzel algorithm. The first-order Goertzel algorithm module is used to estimate the fundamental complex number by using the output of the digital orthogonal oscillator as the frequency conversion sequence. The digital orthogonal oscillator is adjusted by the gain adjustment module. jθ The amplitude is stable at 1, where θ = 2πm / N, m = f i *N / f s , N is the number of sampling points, f i is the fundamental frequency, f s The sampling frequency is the gain adjustment module, and the gain value of the digital quadrature oscillator is adjusted by the AGC method.

5. The Goertzel-based fundamental complex number estimation system according to claim 4, characterized in that: The output of the digital quadrature oscillator is: y i (n)-you q (n)=G(n)*(y′ i (n-1)-you' q (n-1)) and' i (n-1)=y i (n-1)*cos(θ)-y q (n-1)*sin(θ) and' q (n-1)=y q (n-1)*cos(θ)+y i (n-1)*sin(θ) where y i (n), y q (n) are the in-phase and quadrature outputs of the digital quadrature oscillator, G(n) is the gain value, y i (n-1), y q (n-1) are the in-phase and quadrature outputs of the digital quadrature oscillator at the previous moment.

6. The Goertzel-based fundamental complex number estimation system according to claim 5, characterized in that: The calculation formula for the fundamental wave vector calculated by the first-order Goertzel algorithm module is: y(n)=x(n)[G(n)*(y′ i (n-1)-you' q (n-1))]+y(n-1) Where x(n) is the input data sequence, y(n) is the output of the first-order Goertzel algorithm, and y(n-1) is the output of the first-order Goertzel algorithm at the previous moment.

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