Energy Measurement Technology of Low-frequency 20 Hz Intelligent Energy Meter

A high-speed and high-precision voltage and current acquisition scheme suitable for 20 Hz low-frequency energy metering, and an energy meter suitable for low-frequency transmission scenarios was designed in this paper. A high-precision energy metering algorithm based on low-frequency metering for three-phase energy meters, using the four-term third-order Nuttall window algorithm to address the impact of asynchronous sampling on metering was proposed in this paper. Equipped with sampling and metering algorithms suitable for low-frequency transmission, the designed meter achieves seamless calibration of diagonal difference and stable power calculation. Adopting an A/D+DSP metering scheme, a 24-bit A/D chip is selected as the signal sampling unit, and a 32-bit high-speed DSP is used as the signal processing unit to achieve the sampling and processing function of 20 Hz signals, completing the low-frequency transmission scenario electricity metering.


Introduction
Flexible low-frequency transmission is a new and efficient AC transmission technology based on fully controlled power electronic devices.It reduces the 50 Hz power frequency to about 20 Hz low-frequency through high-voltage and high-capacity AC converters, reduces line impedance, and reduces reactive power during cable line charging [1][2] .By tapping into the potential of frequency dimensions, the system's power transmission ability and flexible regulation ability are improved.Compared with power frequency AC transmission and DC transmission, flexible low-frequency transmission can provide flexible power support for the power grid, improve line transmission capacity and reduce voltage loss.It has strong AC networking ability, which can reduce construction and operation costs, and is suitable for low-speed motors such as wind power [3][4] .
Flexible low-frequency transmission requires a three-phase energy meter that can reliably measure at a frequency of 20 Hz.Ordinary three-phase energy meters generally use dedicated metering chips, which are suitable for energy metering at a 50 Hz frequency.The fundamental frequency changes caused by voltage and current distortion in the power grid can cause metering errors due to the mismatch between the sampling frequency of the dedicated metering chip and 50 Hz, making it unsuitable for use in flexible AC transmission systems at 20 Hz.
The 20 Hz fundamental wave electric energy measurement and detection technology is mainly based on the FFT method of frequency domain analysis.Its characteristic is that when the frequency of the power grid fluctuates, integer wave truncation (i.e., non-synchronous sampling) will occur, resulting in fence effect and spectrum leakage, affecting the measurement accuracy [5] .Reducing the spectrum leakage and fence effect of the FFT algorithm, and improving the detection accuracy of fundamental and various harmonics in electrical measurement, are challenges in signal analysis and power quality management of electrical measurement [6][7][8] .
Based on the shortcomings of the existing technologies mentioned above, this article designs an ADCbased low-frequency metering three-phase energy meter to reduce the spectral leakage and barrier effect caused by the FFT algorithm and improve the accuracy of fundamental and harmonic detection in electrical measurement.

Analysis of Low-Frequency Measurement Algorithm for Intelligent Energy Meters
By analyzing the error variation characteristics of low-frequency electric energy meters under different movie noise levels and environmental impact levels, a high-precision metering compensation method based on an adaptive compensation coefficient is proposed.A high-precision electric energy metering algorithm based on low-frequency metering for three-phase electric energy meters is proposed, and a four-term third-order Nuttall window algorithm is used to solve the impact of asynchronous sampling on metering.The sampled data is processed through digital low-pass filtering, DC bias correction, and ratio and angle difference correction.The data processing unit completes the construction of a discrete fourterm third-order Nuttall window, performs fast FFT interpolation algorithm processing and multirefractive index calibration compensation algorithm for Nuttall window, obtains accurate voltage, current, frequency, and power, and sends the processed data to the data management unit for storage, communication, and display processing.
The use of the Nuttall window fast FFT interpolation algorithm refers to the deviation between discrete spectral lines and true frequency spectral lines in asynchronous sampling.By searching for three peak spectral lines near the true frequency point and using the polynomial fitting method, a practical interpolation calculation formula is obtained, and then the frequency value, amplitude, and initial phase at the true spectral line are obtained.
The input signal voltage and current are assumed as follows: where f 0 represents the sampling frequency, A i and θ i represent the corresponding amplitude and phase angle in each harmonic, and x(t) represents the voltage and current of the input signal; On the basis of sampling frequency f 0 , discrete sampling is performed on x(t) to obtain x(n).Then, the H-order maximum side lobe attenuation window w(n) is used to truncate x(n) to obtain x w (n), where n represents the number of truncation points, n =0,1... N-1, N and Fourier transform is performed without considering negative frequency to obtain: where k represents the number of FFT points after truncation, v i represents the number of frequency domain truncation points, X w represents the frequency domain signal of the original sampling value signal x(t) after windowing and truncation, |W(H)| represents the Fourier transform formula of the H-order maximum side lobe attenuation window w(n), and the corresponding expression is: (3) The fourth-order Nuttall window has the best performance in suppressing side lobe energy leakage, with coefficients of b0=0.338946,b1=0.481973,b2=0.161054, and b3=0.018027,respectively; M represents the number of window truncation points, which is 1600 for this project, m=0, 1, 2, 3... M.
Due to the influence of asynchronous sampling and fence effect, in the formula, v i is used as v i =k i +δ i instead, k i represents the position of the maximum spectral line, which can be obtained by searching the maximum spectral line search; -0.5≤ δ i ≤0.5, obtained through interpolation algorithm operation, by: 4) Formulas ( 2) and ( 3) are substituted into Formula (4), simplifying and obtaining: ) where H represents the fourth order Nuttall window.Solution: (6) Therefore, the frequency f i of the i-th harmonic is: where f s represents the signal sampling frequency, and this system is designed at 8000 Hz.The amplitude and phase angle are:   where h=0, 1, 2, 3, ... H. Using Fourier transform, the voltage amplitude and phase angle under the i-th harmonic are U i and θ Ui , the current amplitude and phase angle are I i and θ Ii , then the electrical energy corresponding to the i-th harmonic is: (10) Using the above formula, the f, U, and θ are calculated, And then the electricity metering is completed.

Gain and Phase Calibration of Low-frequency Intelligent Energy Meters
Before leaving the factory, the low-frequency smart meter sends standard voltage and current signals through the external data source sending module.The meter collects the pulses sent by itself and converts them into actual theoretical power, which is compared with the standard power calculated through the AD sampling circuit to calibrate the gain and angle difference of the meter itself.
The calculation method for pulse-converted power is: 3600 1000 where R sum is the number of collected meter pulses; T ime is the time required to collect R sum pulses emitted by the electricity meter; P ulse is the table pulse constant; P st is the standard power, in watts.
Using the amplitude multi-refractive index calibration compensation algorithm, when calibrating the amplitude multi -refractive index, the set value is S et (i), the output value is O ut (i), the measured value of the standard table is R eal (i), the original amplitude calibration coefficient is K 1 , and the current amplitude calibration coefficient is K 2 , then: In the phase multi-refractive index calibration compensation algorithm, if the set value is S et (i), the output value is O ut (i), the standard meter measurement value is R eal (i), the original phase calibration coefficient is Q 1 , and the current phase calibration coefficient is Q 2 , it can be expressed as: The system is designed with an ADC-based low-frequency metering three-phase electricity meter, which is characterized by the multi-refractive index calibration compensation algorithm.The calibration design is as follows: 1) The gain calibration method is: where  is the actual power at a power factor of 1.0;  is the theoretical power at a power factor of 1.0;  is the gain calibration coefficient; 2) The calculation method for power angle difference is: is the theoretical active power with a power factor of 0.5 L everywhere;  .

Conclusion
The low-frequency energy meter designed by this research institute is developed and designed for the measurement needs of low-frequency transmission energy.It is the first AC energy meter in China with a reference frequency of 20 Hz, filling the technical gap in the field of low-frequency measurement instruments and effectively supporting the commercial operation of low-frequency transmission projects such as offshore wind power grid connection.Low-frequency electricity meters can support the entire process management of core marketing businesses such as "business expansion", "metering", and "verification and collection" of State Grid Corporation, achieving functions such as an automatic collection of electricity information, abnormal measurement detection, power quality detection, electricity analysis and management, distributed energy monitoring, and information exchange of intelligent electricity equipment.

Figure 4 .
Figure 4. Software architecture diagram of low-frequency electric energy meter