CN114966194A - ADC-based low-frequency metering three-phase electric energy meter - Google Patents

Abstract

The invention discloses a low-frequency metering three-phase electric energy meter based on an ADC (analog to digital converter). The invention comprises a low-frequency signal conditioning unit, a data processing unit and a data management unit; the three-phase power grid voltage and current analog signals are respectively conditioned through a resistance voltage division sampling circuit and a zero-flux current transformer sampling circuit to obtain unipolar alternating current signals, the unipolar alternating current signals are sent to an ADC (analog-to-digital converter) to carry out A/D (analog-to-digital) conversion on sampling data, and the sampling data are output to a data processing unit; after digital low-pass filtering, direct-current offset correction, and correction of specific difference and angular difference of the sampled data, a data processing unit completes construction of a discrete four-item three-order Nuttall window, and Nuttall window fast FFT interpolation algorithm processing and a multi-refractive-index calibration compensation algorithm are performed to obtain accurate voltage, current, frequency and power. The invention is not limited by the performance and function of a special metering chip, and can accurately and quantitatively measure the electrical performance parameters in the flexible low-frequency power system and realize the electric energy metering with higher accuracy.

Description

ADC-based low-frequency metering three-phase electric energy meter

Technical Field

The invention belongs to the field of electric energy meters, and particularly relates to a low-frequency metering three-phase electric energy meter based on an ADC (analog to digital converter).

Background

Flexible low frequency transmission is a novel efficient alternating current transmission technology based on full-control power electronic devices, reduces 50Hz power frequency to about 20Hz low frequency through a high-voltage large-capacity alternating current-alternating current converter, reduces line impedance, reduces charging reactive power of cable lines, and realizes promotion of system power transmission capability and flexible regulation and control capability through potential excavation of frequency dimensions.

Compared with power frequency alternating current power transmission and direct current power transmission, the flexible low-frequency power transmission has the following technical characteristics: 1) the flexible power support can be carried out on the power grid; 2) the transmission capacity of a line can be improved, and the voltage loss can be reduced; 3) the alternating current networking capability is strong; 4) the construction and operation and maintenance costs can be reduced. Flexible low frequency transmission requires a three-phase electric energy meter that can be reliably metered at a frequency of 20 Hz. A common three-phase electric energy meter generally adopts a special metering chip, is suitable for electric energy metering under the frequency of 50Hz, and the sampling frequency of the special metering chip can not be matched with the 50Hz to cause metering errors due to the change of fundamental frequency caused by voltage and current distortion in a power grid, so that the common three-phase electric energy meter cannot be applied to a 20Hz flexible alternating current power transmission system.

The 20Hz fundamental wave electric energy metering detection technology generally comprises the following steps: (1) the FFT method based on frequency domain analysis is characterized in that when the frequency of a power grid fluctuates, a fence effect and frequency spectrum leakage can occur when non-whole-cycle wave truncation (namely asynchronous sampling) occurs, and the metering precision is influenced; (2) the filter harmonic detection method is characterized in that ideal frequency characteristics are difficult to obtain, the data processing efficiency is high under the condition of setting power grid parameters, the filter coefficient cannot be adjusted according to all running conditions, and the flexibility of a metering algorithm is low; (3) the method based on the instantaneous reactive power theory is characterized by large calculation amount and complex processing; (4) the method based on the neural network theory and the wavelet transform is characterized by large calculation amount, high power consumption requirement and difficult realization in an embedded low-power meter.

The fundamental wave electric energy algorithm based on FFT is realized on a digital signal processor, and is a harmonic analysis method which is most widely applied at present. In an electric power system, fundamental wave frequency changes caused by distortion of voltage and current of a power grid, and due to the fact that asynchronous sampling causes the problems of frequency spectrum leakage, fence effect and the like of an FFT (fast Fourier transform) algorithm, the accuracy of fundamental wave and harmonic wave detection is affected, the frequency spectrum leakage and fence effect influence of the FFT algorithm are reduced, and the difficulty in electric measurement signal analysis and electric energy quality management is to improve the detection accuracy of the fundamental wave and each harmonic wave in electric measurement.

Disclosure of Invention

The invention aims to overcome the defects in the prior art and provide a low-frequency metering three-phase electric energy meter based on an ADC (analog to digital converter), so that the frequency spectrum leakage and barrier effect influence caused by an FFT (fast Fourier transform) algorithm are reduced, and the detection precision of fundamental waves and harmonic waves in electric measurement is improved.

Therefore, the invention adopts the following technical scheme: a low-frequency metering three-phase electric energy meter based on an ADC (analog to digital converter) comprises a low-frequency signal conditioning unit, a data processing unit and a data management unit;

the low-frequency signal conditioning unit comprises an ADC (analog to digital converter), a resistance voltage division sampling circuit and a zero-flux current transformer sampling circuit; the three-phase power grid voltage and current analog signals are respectively conditioned through a resistance voltage division sampling circuit and a zero-flux current transformer sampling circuit to obtain unipolar alternating current signals, the unipolar alternating current signals are sent to an ADC (analog-to-digital converter) to carry out A/D (analog-to-digital) conversion on sampling data, and the sampling data are output to a data processing unit;

after digital low-pass filtering, direct-current offset correction, specific difference and angular difference correction are carried out on the sampled data, a data processing unit completes construction of a discrete four-item three-order Nuttall window, Nuttall window fast FFT interpolation algorithm processing and a multi-refractive-index calibration compensation algorithm are carried out, accurate voltage, current, frequency and power are obtained, and the processed data are sent to a data management unit for storage, communication and display processing.

Further, the Nuttall window fast FFT interpolation algorithm is used, namely under the asynchronous sampling condition, the deviation exists between discrete spectral lines and real frequency spectral lines, a practical interpolation calculation formula is obtained by searching three peak spectral lines near a real frequency point and adopting a polynomial fitting method, and therefore the frequency value, the amplitude value and the initial phase at the real spectral lines are obtained.

Further, the process of the Nuttall window fast FFT interpolation algorithm is as follows:

assume that the input signal voltages and currents are as follows:

wherein f is ₀ Denotes the sampling frequency, A _i And theta _i Respectively representing the corresponding amplitude and phase angle in each harmonic, x (t) representing the voltage and current of the input signal; at a sampling frequency f ₀ On the basis, x (t) is subjected to discrete sampling to obtain x (n), and then x (t) is subjected to truncation by using an H-order maximum sidelobe attenuation window w (n) to obtain x _w (N), N represents the number of truncation points, N is 0,1,., N-1, N, and fourier transform is performed on the basis of ignoring negative frequencies, so that:

wherein k represents the number of points subjected to FFT after truncation, v _i Indicates the number of frequency domain truncation point correspondences, X _w The method is characterized by comprising the following steps of representing a frequency domain signal obtained by cutting an original sampling value signal x (t) through windowing, | W (H) | represents a Fourier transform expression of an H-order maximum sidelobe attenuation window w (n), and the corresponding expression is as follows:

the performance of inhibiting the side lobe energy leakage of the four-term third-order Nuttall window is the most excellent, and each coefficient is b ₀ ＝0.338946，b ₁ ＝0.481973，b ₂ ＝0.161054，b ₃ 0.018027; m is the number of windowing truncation points, and M is 0,1,2,3 … … M;

due to the influence of asynchronous sampling and the fence effect, where v _i By v _i ＝k _i +δ _i Instead, k _i The position of the maximum spectral line is represented and can be obtained through maximum spectral line searching; delta _i Delta is more than or equal to-0.5 _i In the interval less than or equal to 0.5, the data is obtained by interpolation algorithm operation

Substituting the formula (2) and the formula (3) into the formula (4), and simplifying to obtain the final product

In the formula, H represents a four-term third-order Nuttall window;

get it solved

Thus, the frequency f of the i-th harmonic _i Is composed of

In the formula (f) _s Representing a signal sampling frequency;

amplitude and phase angle of

θ _i ＝Phase{X _w (k _i )}-πδ _i +π/2 (9)

Wherein H is 0,1,2,3, … … H;

the voltage amplitude and the phase angle under the ith harmonic are respectively U by using Fourier transform _i And theta _Ui The current amplitude and phase angle are respectively I _i And theta _Ii Then the electrical energy corresponding to the ith harmonic is:

P _i ＝U _i I _i cos(θ _Ui -θ _Ii ) (10)

and f, U and theta of each harmonic are calculated by using the formula, so that the electric energy metering is completed.

Further, in order to increase the FFT computation speed, an FFT fast computation algorithm is used, the process is as follows:

because the voltage and the current are synchronously sampled, the amplitude and the phase of each harmonic of the voltage and the current are simultaneously calculated by adopting a complex sequence FFT, and the algorithm is as follows:

the complex sequence of the structure is set as follows:

x(n)＝u(n)+j*i(n) (11)

then x (n) complex sequence FFT is

X(K)＝FFT[u(n)]+j*FFT[i(n)]＝u(K)+j*i(K)

X(K)＝FFT[x(n)]＝XR(K)+j*XI(K) (12)

According to the periodicity and conjugate symmetry of FFT, obtaining the corresponding frequency spectrums of u (n) and i (n) as follows:

u (n) denotes the real part of a signal, i (n) denotes the imaginary part of a signal, u (k), xr (k) denote FFT-transformed spectra for the real part, i (k), xi (k) denote FFT-transformed spectra for the imaginary part;

the FFT adopts radix-2 complex operation of extraction according to time, and comprises two parts of indexing and L-level recursive computation.

Further, the process of the multi-refractive index calibration compensation algorithm is as follows in sequence: the method comprises the following steps of direct current calibration, voltage and current gain calibration, voltage and current imbalance calibration, active and reactive gain calibration, active and reactive imbalance calibration and phase calibration.

Further, the purpose of the offset calibration is to ensure that at 0 input, the output is also 0; the purpose of gain correction is to establish a proportional correspondence between the calculated value and the actual value; the phase calibration is to ensure the synchronism of data acquisition.

Furthermore, in the multi-refractive index calibration compensation algorithm,

1) DC calibration

The direct current calibration is calculation for removing direct current components, wherein the whole collected data is firstly collected into n points, then the n points are accumulated, and then the accumulated points are divided by the value of n to obtain the direct current components, wherein n is a positive number, and the formula is as follows:

2) gain and phase calibration

The electric meter sends standard voltage and current signals through an external data source sending module before leaving a factory, acquires pulses sent by the electric meter, converts the pulses into actual theoretical power, and compares the actual theoretical power with standard power acquired and calculated through an AD sampling circuit, so that the gain and the angular difference of the electric meter are calibrated;

the calculation formula of the pulse converted power is shown in formula 15:

wherein: r _sum The number of the collected ammeter pulses is counted; t is _ime For collecting R emitted by electric meter _sum Time required for one pulse, P _ulse Is a table pulse constant; p is _st Is the standard power, in units of w.

Furthermore, in the amplitude birefringence calibration compensation algorithm, the principle of amplitude birefringence calibration is as follows:

set the value as S _et (i) Output value of O _ut (i) The standard table measured value is R _eal (i) The original amplitude calibration coefficient is K ₁ The current amplitude calibration coefficient is K ₂ As shown in equation 16:

Q _out ＝K ₁ *S _et (i)

finally make K ₁ ＝K ₂ And (4) finishing.

Furthermore, in the phase birefringence calibration compensation algorithm, the principle of phase birefringence calibration is as follows:

set the value as S _et (i) Output value of O _ut (i) The standard table measured value is R _eal (i) The original phase calibration coefficient is Q ₁ Now the phase alignment coefficient is Q ₂ As shown in formula 17:

O _ut (i)＝S _et (i+Q ₁ )

finally make Q ₁ ＝Q ₂ And (4) finishing.

Furthermore, in the multi-refractive-index calibration compensation algorithm, the calibration formula is designed as follows:

1) the gain calibration equation is shown in equation 18

C _alipst Actual power at power factor 1.0, C _alipmean Theoretical power is handled as a power factor of 1.0; l is _amada Is a gain calibration factor;

2) the power angle difference formula is shown in formula 19

C _alipmean0.5l Theoretical active power is handled for a power factor of 0.5L; c _alipmean0.5c Theoretical reactive power is handled for a power factor of 0.5C; c _aliqmean0.5l Theoretical reactive power is handled for a power factor of 0.5L; c _aliqmean0.5c Theoretical reactive power is handled for a power factor of 0.5C; c _alipst0.5l The actual active power is at the power factor of 0.5L; c _alipst0.5c Is the actual reactive power at a power factor of 0.5C.

The invention has the following beneficial effects: the invention is not limited by the performance and function of a special metering chip, can reduce the frequency spectrum leakage and the fence effect influence brought by an FFT algorithm based on an excellent algorithm, accurately and quantitatively measure the dynamic characteristics of fundamental voltage current and harmonic voltage current in a flexible power transmission system with the frequency of 20Hz, and realize higher harmonic analysis and higher-accuracy electric energy metering. The invention has high reliability, accurate measurement, strong environmental interference resistance and good application value.

Drawings

FIG. 1 is a schematic diagram of the structure of the present invention;

FIG. 2 is a flow chart of a multi-index calibration compensation algorithm of the present invention;

fig. 3 is a schematic diagram of the phase birefringence calibration of the present invention.

Detailed Description

The embodiments of the invention will be described in detail below with reference to the accompanying drawings: the present embodiment is implemented on the premise of the technical solution of the present invention, and detailed embodiments and processes are given, but the scope of the present invention is not limited to the following embodiments.

The embodiment is a low-frequency metering three-phase electric energy meter based on an ADC, which includes a low-frequency signal conditioning unit, a data processing unit, and a data management unit, as shown in fig. 1.

The low-frequency signal conditioning unit comprises an ADC (analog to digital converter), a resistance voltage division sampling circuit and a zero-flux current transformer sampling circuit; three-phase power grid voltage and current analog signals with 20Hz rated values of 57.7V and 1A in the system are respectively conditioned through a resistance voltage division sampling circuit and a zero-flux current transformer sampling circuit to obtain unipolar 5V alternating current signals, the unipolar 5V alternating current signals are sent to a high-precision 8-channel ADC (analog-to-digital converter) to carry out A/D (analog-to-digital) conversion on sampling data, and the sampling data are output to a data processing unit through an SPI (serial peripheral interface).

After digital low-pass filtering, direct-current offset correction, specific difference and angular difference correction are carried out on the sampled data, a data processing unit completes construction of a discrete four-item three-order Nuttall window, Nuttall window fast FFT interpolation algorithm processing and a multi-refractive-index calibration compensation algorithm are carried out, accurate voltage, current, frequency and power are obtained, and the processed data are sent to a data management unit for storage, communication and display processing.

The data management unit comprises an MCU chip, a real-time clock, an SDRAM (synchronous dynamic random access memory) and FLASH memory, a communication interface circuit and a segment code liquid crystal, and the MCU is used as a core to manage fundamental wave electric energy calculation and each electric parameter calculation.

The data processing unit is a general digital signal processor and is connected with the MCU chip by adopting an SPI interface; the MCU chip is externally connected with a real-time clock, an SDRAM (synchronous dynamic random access memory) and a FLASH memory, a communication interface circuit and a segment code liquid crystal at the same time, and is controlled by the MCU chip to complete the work.

The chip model of the ADC converter with the high-precision 8-channel is ADS131E08, and the chip model of the general digital signal processor is ADSP-BF 516. The MCU chip model is STM32F207, and the maximum number of times of harmonic detection is 50.

The ADC converter is ADS131E08 produced by TI company, ADS131E08 is a high-precision and high-performance analog-to-digital converter with 8 channels and 24 bits and up to 32KHz sampling rate, and is very suitable for a harmonic wave electric energy data acquisition system with high performance requirements, low power consumption and multiple analog channels.

The working principle of the invention is as follows: ADC converter and general digital signal processor adopt the SPI interface to link to each other in the 20Hz low frequency three-phase electric energy meter based on ADC, and general digital signal processor and MCU chip adopt the SPI interface to link to each other, and MCU chip outside connects real-time clock, SDRAM and FLASH memory, communication interface circuit and section code liquid crystal simultaneously, is accomplished work by MCU chip control.

The Nuttall window is a cosine combined window function with a narrow main lobe and excellent side lobe performance, under the condition of asynchronous sampling, the FFT operation without window has serious frequency spectrum leakage and barrier effect, and the detection precision is low; the frequency spectrum leakage and the fence effect of the Nuttall window fast FFT interpolation algorithm can be obviously reduced, the detection precision of fundamental waves and harmonic waves can be effectively improved, and the design is flexible to realize.

The Nuttall window fast FFT interpolation algorithm is that under the condition of asynchronous sampling, a discrete spectral line and a real frequency spectral line have deviation, a practical interpolation calculation formula is solved by searching three peak spectral lines near a real frequency point and adopting a polynomial fitting method, and therefore a frequency value, an amplitude value and an initial phase at the real spectral line are solved.

The process of the Nuttall window fast FFT interpolation algorithm is as follows:

assume that the input signal voltages and currents are as follows:

wherein f is ₀ Denotes the sampling frequency, A _i And theta _i Respectively representing the corresponding amplitude and phase angle in each harmonic, x: (t) represents the voltage and current of the input signal; at a sampling frequency f ₀ On the basis, x (t) is subjected to discrete sampling to obtain x (n), and then x (t) is subjected to truncation by using an H-order maximum sidelobe attenuation window w (n) to obtain x _w (N), N represents the number of truncation points, N is 0,1,., N-1, N, and fourier transform is performed on the basis of ignoring negative frequencies, so that:

wherein k represents the number of points subjected to FFT after truncation, and v _i Indicates the number of frequency domain truncation point correspondences, X _w The method is characterized by comprising the following steps of representing a frequency domain signal obtained by cutting an original sampling value signal x (t) through windowing, | W (H) | represents a Fourier transform expression of an H-order maximum sidelobe attenuation window w (n), and the corresponding expression is as follows:

the performance of inhibiting the side lobe energy leakage of the four-term third-order Nuttall window is the most excellent, and each coefficient is b ₀ ＝0.338946，b ₁ ＝0.481973，b ₂ ＝0.161054，b ₃ 0.018027; m is the number of cut-off points for windowing, which is 1600 in this embodiment, M is 0,1,2,3 … … M;

due to the influence of asynchronous sampling and the fence effect, where v _i By v _i ＝k _i +δ _i Instead of, k _i The position of the maximum spectral line is represented and can be obtained through maximum spectral line searching; delta _i Delta is more than or equal to-0.5 _i In the interval less than or equal to 0.5, the data is obtained by interpolation algorithm operation

Substituting the formula (2) and the formula (3) into the formula (4), and simplifying to obtain the final product

In the formula, H represents a four-term third-order Nuttall window;

get it solved

Thus, the frequency f of the i-th harmonic _i Is composed of

In the formula (f) _s Represents the signal sampling frequency, which is 8000Hz in this example;

amplitude and phase angle of

θ _i ＝Phase{X _w (k _i )}-πδ _i +π/2 (9)

Wherein H is 0,1,2,3, … … H;

the voltage amplitude and the phase angle under the ith harmonic are respectively U by using Fourier transform _i And theta _Ui The current amplitude and phase angle are respectively I _i And theta _Ii Then the electrical energy corresponding to the ith harmonic is:

P _i ＝U _i I _i cos(θ _Ui -θ _Ii ) (10)

and f, U and theta of each harmonic are calculated by using the formula, so that the electric energy metering is completed.

In order to increase the FFT calculation speed, an FFT fast calculation algorithm is adopted, and the process is as follows:

because the voltage and the current are synchronously sampled, the amplitude and the phase of each harmonic of the voltage and the current are simultaneously calculated by adopting a complex sequence FFT, and the algorithm is as follows:

the complex sequence of the structure is set as follows:

x(n)＝u(n)+j*i(n) (11)

then x (n) complex sequence FFT is

X(K)＝FFT[u(n)]+j*FFT[i(n)]＝u(K)+j*i(K)

X(K)＝FFT[x(n)]＝XR(K)+j*XI(K) (12)

According to the periodicity and conjugate symmetry of FFT, obtaining the corresponding frequency spectrums of u (n) and i (n) as follows:

u (n) denotes the real part of a signal, i (n) denotes the imaginary part of a signal, u (k), xr (k) denote FFT-transformed spectra for the real part, i (k), xi (k) denote FFT-transformed spectra for the imaginary part;

the FFT adopts a radix-2 time-decimating complex operation, which comprises two parts of indexing and L-level recursive computation.

The process of the multi-refractive index calibration compensation algorithm is as follows in sequence: direct current calibration, voltage and current gain calibration, voltage and current offset calibration, active and reactive gain calibration, active and reactive offset calibration, and phase calibration, as shown in fig. 2.

The purpose of the offset calibration is to ensure that at 0 input, the output is also 0; the purpose of gain correction is to establish a proportional correspondence between the calculated value and the actual value; the phase calibration is to ensure the synchronism of data acquisition.

In the multi-refractive index calibration compensation algorithm,

1) DC calibration

The direct current calibration is calculation for removing direct current components, wherein the whole collected data is firstly collected into n points, then the n points are accumulated, and then the accumulated points are divided by the value of n to obtain the direct current components, wherein n is a positive number, and the formula is as follows:

2) gain and phase calibration

The electric meter sends standard voltage and current signals through an external data source sending module before leaving a factory, the electric meter collects pulses sent by the electric meter and converts the pulses into actual theoretical power, and the actual theoretical power is compared with standard power collected and calculated through an AD sampling circuit, so that the gain and the angular difference of the electric meter are calibrated;

the calculation formula of the pulse converted power is shown in formula 15:

wherein: r _sum The number of the collected ammeter pulses is counted; t is _ime For collecting R emitted from electric meter _sum The time required for one pulse; p _ulse Is a table pulse constant; p is _st Is standard power in units of w.

In the amplitude birefringence calibration compensation algorithm, the principle of amplitude birefringence calibration is as follows:

set the value as S _et (i) Output value of O _ut (i) The standard table measured value is R _eal (i) The original amplitude calibration coefficient is K ₁ The current amplitude calibration coefficient is K ₂ As shown in equation 16:

Q _out ＝K ₁ *S _et (i)

finally make K ₁ ＝K ₂ And (4) finishing.

In the phase birefringence calibration compensation algorithm, the principle of phase birefringence calibration is shown in fig. 3:

set the value as S _et (i) (X (t) in FIG. 3), the output value is O _ut (i) (Y (t) in FIG. 3), and the standard table has a measurement value of R _eal (i) The original phase calibration coefficient is Q ₁ The current phase calibration coefficient is Q ₂ As shown in formula 17:

O _ut (i)＝S _et (i+Q ₁ )

finally make Q ₁ ＝Q ₂ And (4) finishing.

In the multi-refractive index calibration compensation algorithm, a calibration formula is designed as follows:

1) the gain calibration equation is shown in equation 18

C _alipst Actual power at power factor 1.0, C _alipmean Theoretical power is handled as a power factor of 1.0; l is _amada Is a gain calibration factor;

2) the power angle difference formula is shown in formula 19

C _alipmean0.5l Theoretical active power is handled for a power factor of 0.5L; c _alipmean0.5c Theoretical reactive power is handled for a power factor of 0.5C; c _aliqmean0.5l Theoretical reactive power is handled for a power factor of 0.5L; c _aliqmean0.5c Theoretical reactive power is handled for a power factor of 0.5C; c _alipst0.5l The actual active power is at the power factor of 0.5L; c _alipst0.5c Is the actual reactive power at a power factor of 0.5C.

The invention relates to a 20Hz low-frequency electric energy meter based on a Nuttall window fast FFT interpolation algorithm, wherein the adopted interpolation FFT algorithm means that under the condition of asynchronous sampling, a discrete spectral line has deviation with a real frequency spectral line, a practical interpolation calculation formula is worked out by searching three peak spectral lines near a real frequency point and adopting a polynomial fitting method, so that the frequency value, the amplitude value and the initial phase position of the real spectral line are worked out, and meanwhile, a multi-refractive index calibration compensation algorithm is provided for compensating the ratio difference and the angle difference, so that higher metering precision is obtained.

While the present invention has been described in detail by the above embodiments, it should be appreciated that the above description should not be construed as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (10)

1. A low-frequency metering three-phase electric energy meter based on an ADC (analog to digital converter) is characterized by comprising a low-frequency signal conditioning unit, a data processing unit and a data management unit;

the low-frequency signal conditioning unit comprises an ADC (analog to digital converter), a resistance voltage division sampling circuit and a zero-flux current transformer sampling circuit; the three-phase power grid voltage and current analog signals are respectively conditioned through a resistance voltage division sampling circuit and a zero-flux current transformer sampling circuit to obtain unipolar alternating current signals, the unipolar alternating current signals are sent to an ADC (analog-to-digital converter) to carry out A/D (analog-to-digital) conversion on sampling data, and the sampling data are output to a data processing unit;

after digital low-pass filtering, direct-current offset correction, specific difference and angular difference correction are carried out on the sampled data, a data processing unit completes construction of a discrete four-item three-order Nuttall window, Nuttall window fast FFT interpolation algorithm processing and a multi-refractive-index calibration compensation algorithm are carried out, accurate voltage, current, frequency and power are obtained, and the processed data are sent to a data management unit for storage, communication and display processing.

2. The ADC-based low-frequency metering three-phase electric energy meter according to claim 1, wherein the adopted Nuttall window fast FFT interpolation algorithm means that under the asynchronous sampling condition, a discrete spectral line and a real frequency spectral line have deviation, a practical interpolation calculation formula is obtained by searching three peak spectral lines near a real frequency point and adopting a polynomial fitting method, and therefore the frequency value, the amplitude value and the initial phase at the real spectral line are obtained.

3. The ADC-based low-frequency metering three-phase electric energy meter according to claim 1 or 2, wherein the Nuttall window fast FFT interpolation algorithm is as follows:

assume that the input signal voltages and currents are as follows:

wherein f is ₀ Denotes the sampling frequency, A _i And theta _i Respectively representing the corresponding amplitude and phase angle in each harmonic, x (t) representing the voltage and current of the input signal; at a sampling frequency f ₀ On the basis, x (t) is subjected to discrete sampling to obtain x (n), and then x (t) is subjected to truncation by using an H-order maximum sidelobe attenuation window w (n) to obtain x _w (N), N represents the number of truncation points, N is 0,1,., N-1, N, and fourier transform is performed on the basis of ignoring negative frequencies, so that:

wherein k represents the number of points subjected to FFT after truncation, and v _i Indicates the number of frequency domain truncation point correspondences, X _w The method is characterized by comprising the following steps of representing a frequency domain signal obtained by cutting an original sampling value signal x (t) through windowing, | W (H) | represents a Fourier transform expression of an H-order maximum sidelobe attenuation window w (n), and the corresponding expression is as follows:

the performance of inhibiting the side lobe energy leakage of the four-term third-order Nuttall window is the most excellent, and each coefficient is b ₀ ＝0.338946，b ₁ ＝0.481973，b ₂ ＝0.161054，b ₃ 0.018027; m is to carry out windowingThe number of cut points, M is 0,1,2,3 … … M;

due to the influence of asynchronous sampling and the fence effect, where v _i By v _i ＝k _i +δ _i Instead, k _i The position of the maximum spectral line is represented and can be obtained through maximum spectral line searching; delta _i Delta is more than or equal to-0.5 _i In the interval less than or equal to 0.5, the data is obtained by interpolation algorithm operation

Substituting the formula (2) and the formula (3) into the formula (4), and simplifying to obtain the final product

In the formula, H represents a four-term third-order Nuttall window;

get it solved

Thus, the frequency f of the i-th harmonic _i Is composed of

In the formula (f) _s Representing a signal sampling frequency;

amplitude and phase angle of

θ _i ＝Phase{X _w (k _i )}-πδ _i +π/2 (9)

Wherein H is 0,1,2,3, … … H;

the voltage amplitude and the phase angle under the ith harmonic are respectively U by using Fourier transform _i And theta _Ui The current amplitude and phase angle are respectively I _i And theta _Ii Then the electrical energy corresponding to the ith harmonic is:

P _i ＝U _i I _i cos(θ _Ui -θ _Ii ) (10)

and calculating the frequency f, the voltage amplitude U and the phase angle theta of each harmonic by using the formula, thereby completing the electric energy metering.

4. The ADC-based low-frequency metering three-phase electric energy meter according to claim 1 or 2, wherein in order to increase the FFT calculation speed, an FFT fast calculation algorithm is adopted, and the process is as follows:

because the voltage and the current are synchronously sampled, the amplitude and the phase of each harmonic of the voltage and the current are simultaneously calculated by adopting a complex sequence FFT, and the algorithm is as follows:

the complex sequence of the structure is set as follows:

x(n)＝u(n)+j*i(n) (11)

then x (n) complex sequence FFT is

X(K)＝FFT[u(n)]+j*FFT[i(n)]＝u(K)+j*i(K)

X(K)＝FFT[x(n)]＝XR(K)+j*XI(K) (12)

According to the periodicity and conjugate symmetry of FFT, obtaining the corresponding frequency spectrums of u (n) and i (n) as follows:

u (n) denotes the real part of a signal, i (n) denotes the imaginary part of a signal, u (k), xr (k) denote FFT-transformed spectra for the real part, i (k), xi (k) denote FFT-transformed spectra for the imaginary part;

the FFT adopts a radix-2 time-decimating complex operation, which comprises two parts of indexing and L-level recursive computation.

5. The ADC-based low frequency metering three-phase electric energy meter according to claim 1 or 2, wherein the multi-refractive index calibration compensation algorithm is sequentially processed as follows: the method comprises the following steps of direct current calibration, voltage and current gain calibration, voltage and current imbalance calibration, active and reactive gain calibration, active and reactive imbalance calibration and phase calibration.

6. The ADC-based low frequency metering three-phase electric energy meter according to claim 5, wherein the purpose of the offset calibration is to ensure that when 0 is input, the output is 0; the purpose of gain correction is to establish a proportional correspondence between the calculated value and the actual value; the phase calibration is to ensure the synchronism of data acquisition.

7. An ADC-based low frequency metering three-phase electric energy meter according to claim 6, wherein in the multi-refractive index calibration compensation algorithm,

1) DC calibration

The direct current calibration is calculation for removing direct current components, wherein the whole collected data is firstly collected into n points, then the n points are accumulated, and then the accumulated points are divided by the value of n to obtain the direct current components, wherein n is a positive number, and the formula is as follows:

2) gain and phase calibration

The electric meter sends standard voltage and current signals through an external data source sending module before leaving a factory, acquires pulses sent by the electric meter, converts the pulses into actual theoretical power, and compares the actual theoretical power with standard power acquired and calculated through an AD sampling circuit, so that the gain and the angular difference of the electric meter are calibrated;

the calculation formula of the pulse converted power is shown in formula 15:

wherein: r _sum The number of the collected ammeter pulses is counted; t is _ime For collecting R emitted by electric meter _sum Time required for one pulse, P _ulse Is a table pulse constant; p _st Is standard power in units of w.

8. The ADC-based low frequency metering three-phase electric energy meter according to claim 6, wherein in the amplitude birefringence calibration compensation algorithm, the principle of amplitude birefringence calibration is as follows:

set the value as S _et (i) Output value of O _ut (i) The standard table measured value is R _eal (i) The original amplitude calibration coefficient is K ₁ The current amplitude calibration coefficient is K ₂ As shown in equation 16:

Q _out ＝K ₁ *S _et (i)

finally make K ₁ ＝K ₂ And (4) finishing.

9. The ADC-based low-frequency metering three-phase electric energy meter according to claim 6, wherein in the phase birefringence calibration compensation algorithm, the principle of phase birefringence calibration is as follows:

set the value as S _et (i) Output value of O _ut (i) The standard table measured value is R _eal (i) The original phase calibration coefficient is Q ₁ The current phase calibration coefficient is Q ₂ As shown in formula 17:

O _ut (i)＝S _et (i+Q ₁ )

finally make Q ₁ ＝Q ₂ And (4) finishing.

10. The ADC-based low-frequency metering three-phase electric energy meter according to claim 6, wherein in the multi-refractive-index calibration compensation algorithm, a calibration formula is designed as follows:

1) the gain calibration equation is shown in equation 18

C _alipst Actual power at power factor 1.0, C _alipmean Theoretical power is handled as a power factor of 1.0; l is _amada Is a gain calibration factor;

2) the power angle difference formula is shown in formula 19

C _alipmean0.5l Theoretical active power is handled for a power factor of 0.5L; c _alipmean0.5c Theoretical reactive power is handled for a power factor of 0.5C; c _aliqmean0.5l Theoretical reactive power is handled for a power factor of 0.5L; c _aliqmean0.5c Theoretical reactive power is handled for a power factor of 0.5C; c _alipst0.5l The actual active power is at the power factor of 0.5L; c _alipst0.5c Is the actual reactive power at a power factor of 0.5C.

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