Simulation analysis of energy metering error of non-vehicle charger

This paper studies three methods of DC energy measurement for non-vehicle chargers, namely, the average value method, effective value method, and time domain integration method, introduces the definition of ripple, and analyzes the characteristics of constant voltage, constant current charging mode and pulse charging mode of electric vehicles, providing an algorithm basis for the establishment of DC energy metering error model and simulation analysis. This paper studies high-power DC energy measurement algorithms with ripple parameters, analyzes the error characteristics of various algorithms, summarizes the relevant laws, and provides a theoretical basis for the design of a high-precision DC metering module under the influence of ripple.


Introduction
With the promotion of electric vehicles, China has rapidly built supporting charging facilities such as DC charging piles.DC watt-hour meters in charging piles are electric energy metering devices, and the metering accuracy of DC watt-hour meters is easily affected by temperature, ripple, and other factors [1], resulting in billing errors that bring unnecessary property losses to users and power supply companies.Therefore, it is necessary to analyze the influence of temperature, ripple, and other factors on the measurement accuracy of DC energy, and take measures to reduce the measurement error.
At present, there is no special chip for DC metering in the market, and the chip used in DC meter is a mixed AC and DC metering chip, which realizes DC metering by disabling the high-pass filter of its internal voltage and current acquisition channel.In [2], the DC ripple measurement of DC watt-hour meters was analyzed by studying the metrology algorithm, but there was little analysis of the bandwidth of the metering chip.In [3], the bandwidth action mechanism of the metering chip and the principle of the digital filtering algorithm were analyzed and a single-phase SOC metering chip was developed to solve the spectrum leakage caused by the metering algorithm.However, the chip was mostly applied to AC metering, and the ideal effect could not be achieved for DC metering.
Theoretically, there is no AC signal superposition in the output of the DC charging pile, but due to the limitations of relevant analog circuit processing, power battery performance, and interference of high-power charging environment [4], the output voltage of the charging pile inevitably carries ripple signals and the measurement of DC charging energy is mainly affected by ripple parameters.This paper will focus on the study of high-power DC energy measurement algorithms with ripple parameters, analyze the error characteristics of various algorithms, summarize the relevant laws, and provide the algorithm basis and theoretical basis for the design of a high-precision DC metering module under the influence of ripple.
In Equation ( 1), W 1 is the average measurement of electric energy; U ̂, I ̂, and P 1 are the average voltage, average current, and average power within t time, respectively.
The second scheme is the effective value method, and its operation expression is shown in Equation ( 2): In Equation ( 2), W 2 is the effective value method to measure electric energy; U  , I  , and P 2 are the voltage RMS, current RMS, and power RMS in t time, respectively.
The third scheme is the instantaneous power integration method, and its operation expression is shown in Equation ( 3 In Equation (3), W 3 represents the integrated energy of instantaneous voltage and current in unit period T, and P3 is the instantaneous power.
However, in actual power measurement, the collection of instantaneous power is not strictly continuous [5], it is usually necessary to set the sampling interval t, and the number of collection times is N within the unit period T. When the value of t is small enough and the number of collection times is large enough, the power calculation expression of the instantaneous power integration method can be reduced to Equation (4): Under ideal conditions, the results of the three calculation schemes are accurate and consistent, but the DC signal in the real environment often carries the ripple signal, so it is necessary to analyze the power metering error in the ripple environment.

Error calculation of electric energy measurement in ripple environment
DC ripple coefficient reflects the ripple content in the DC signal.In the standard of GBT 29318-2012 "Energy Measurement of Electric Vehicle Non-on-Board Charger", the DC ripple coefficient can be characterized as the ripple RMS coefficient and ripple peak coefficient [6], and the ripple RMS coefficient is defined as the ratio of the RMS value of the output AC component to the average DC output voltage.Its operation is shown in Equation ( 5).The ripple peak coefficient is defined as the ratio of the peak value of the output AC component to the average value of the DC output voltage, and its calculation equation is shown in Equation ( 6): In the equations, U DC is the average DC output voltage; U ms and X ms are the effective value and ripple effective value coefficients of the output AC component, respectively;   and   are the peak-peak value and ripple peak coefficient of the DC output AC component, respectively.
According to the Part 1: Non-vehicle charger provisions of the NB/T 33008.1 "Electric Vehicle Charging Equipment Inspection Test Specification", the output ripple RMS coefficient   should not exceed 1%, and the ripple peak coefficient   should not exceed 0.5% [7].
From the perspective of functional structure, the electric vehicle DC charging pile mainly includes the rectifier unit and the power conversion unit, the former realizes the three-phase AC input initial rectification to DC, and the latter changes the electric energy output mode in real time according to the charging characteristics and needs of the power battery.According to the different implementation principles of the rectifier unit, the DC charging pile has two design structures: phase-controlled type and high-frequency switching type [8], and its charging output performance is shown in Table 1 below.Therefore, compared with the ripple data shown in Table 1, the design of the DC charging pile should adopt a high-frequency switching rectifier scheme.The ideal DC power can be directly determined by the product of instantaneous voltage and instantaneous current.For DC signals with ripple components, it is necessary to introduce a correlation algorithm of AC power.In [9], the following conclusions were drawn after theoretical derivation, simulation verification, and field test of the harmonic of electric vehicle DC charging pile: Due to the characteristics of the three-phase full-bridge rectifier circuit, the output ripple of DC charging pile mainly includes 6k±1 harmonics based on power frequency, especially the 5, 7, 11 and 13 harmonics.In order to facilitate calculation and modeling analysis, it is advisable to temporarily determine that the DC ripple signal only has the harmonic of the relative power frequency (frequency  1 ), then the output voltage and current of the DC charging pile can be expressed as: 01 ( ) 2 cos( ) In the equation,  0 and  0 represent the DC voltage component and DC current component;  ℎ and  ℎ represent the effective voltage and current values of the h harmonic signal,  ℎ and h  are the initial voltage phase and initial current phase of the h harmonic component.

Power calculation of DC energy metering algorithm
According to the AC power calculation method [10], the expression of active power P, reactive power Q, and apparent power S of the ripple DC output signal can be obtained: 00 cos( ) sin( ) By combining the calculation methods of average power  1 in Equation ( 1), effective power  2 in Equation ( 2), and instantaneous power 3 P in Equation ( 3), the following correspondence can be obtained: By comparison, the RMS power  2 in Equation ( 14) can be regarded as the apparent power under an AC signal, and the instantaneous integrated power 3 P in Equation (15) can be regarded as the active power under an AC signal.According to the AC power measurement theory, the instantaneous integrated power can be used as the standard power [9].Therefore, when analyzing the error of three kinds of DC energy measurement algorithms, the average value method, the effective value method and the instantaneous power integration method, the instantaneous integral power 3 P can be used as the reference standard to analyze the error relationship between  1 ,  2 , and 3 P .

Error calculation of DC energy measurement algorithm
The electric energy calculation error 31  of the average method can be equivalent to the relative error between the average power  1 and the instantaneous integrated power  3 , and its calculation expression is shown in equation ( 16): The energy calculation error 32  of the RMS method can be equivalent to the relative error between the RMS power 2 P and the instantaneous integral power 3 P , and its calculation expression is shown as follows: (ε is the phase difference between the current and voltage of the h harmonic component, meeting 0 ≤ ϕ ≤ 2π), Equations ( 16) and ( 17) can be simplified:

M M h h h h h h h h h h h h h h h h h h P P P U I U I U I
Through inequality relations, we can obtain: Therefore, if and only if a=b, the energy calculation error 31  of the average method and the energy calculation error 32  of the effective value method simultaneously reach the maximum value.

Error simulation and result analysis of electric energy metering algorithm
In Section 2 of this paper, the calculation results of the power calculation error 31  of the average method (such as Equation ( 18)) and the power calculation error 32  of the effective value method (such as Equation ( 19)) are obtained.In this section, the distribution of 31  and 32  will be simulated based MATLAB, and the advantages and disadvantages of the two measurement algorithms and their application occasions will be analyzed.

Distributed simulation in different cases
(1) When 0 ≤ = ab ≤0.005 and 0 ≤Φ≤ 2π, the distribution of electric energy error 31  by the average method is shown in Figure 1; (2) When 0 ≤ = ab ≤0.02 and 0 ≤Φ≤ 2π, the distribution of electric energy error 31  by the average method is shown in Figure 2; (3) When 0 ≤ = ab ≤0.005 and 0 ≤Φ≤ 2π, the distribution of electric energy error 32  by the RMS method is shown in Figure 3; (4) When 0 ≤ = ab ≤0.02 and 0 ≤Φ≤ 2π, the distribution of electric energy error 32  by the RMS method is shown in Figure 4; (5) In order to compare the error accuracy of the effective value method and the mean value method, the difference between the two methods is taken as the judging basis, 0 ≤ = ab ≤0.02 and 0 ≤Φ≤ 2π are set, and the distribution of    is centered on Φ180° and shows a decreasing trend to both sides, while 32  decreases first and then increases to a maximum value, at which time A happens to be in the minimum state.

Conclusion
This paper studies the measurement theory of DC charging electric energy, focuses on analyzing the calculation schemes of DC electric energy such as mean value method, effective value method, and pulse power integration method under ripple environment, uses MATLAB to simulate the measurement error, and analyzes the advantages and disadvantages of various algorithms and their application occasions.The best application of the three DC energy measurement algorithms, the average value method, the effective value method, and the instantaneous power integration method, is as follows: (1) When the ripple coefficient is lower than 2%, the error generated by the three measurement algorithms is less than 0.1%, and the accuracy level of charging piles on the market is Level 1 or Level 2, so the above three measurement algorithms can meet the verification needs; (2) When the ripple coefficient is higher than 2%, necessary measures should be taken to reduce the ripple content of the charging pile output to improve the measurement accuracy.The commonly used scheme is to use a polyphase rectifier circuit, design a superior-performance LC filter circuit, or increase the filter capacitance capacity; (3) When the voltage and current phase difference Φ is in the range of ±60°, the measurement accuracy of the effective value method is better, and the average measurement scheme that is easier to achieve is preferred in other cases.
According to the charging output performance of electric vehicle DC charging piles under different rectification modes, the ripple coefficient of high-frequency switching charging piles can be controlled within 0.5%.According to the above conclusions, any metering algorithm can be selected.Due to the limitations of the phase-controlled charging pile rectifier circuit, the ripple coefficient is often greater than 1%, and the above three measurement algorithms can be used to obtain more accurate results under the premise of good voltage regulation accuracy (ripple coefficient is less than 2%) or under the premise of taking certain ripple suppression measures.
11),   and   are voltage RMS and current RMS, respectively, and their calculation methods are shown in Equation (12): let a =  ℎ  0 ⁄ , b =  ℎ  0 ⁄ (a and b are the effective proportional coefficients of H-order ripple and DC, meet 0≤a, b≤1); =

Figure 1 .
Figure 1.Distribution of the average power error 31  .

Table 1 .
Charging Output Performance in Different Rectification Modes.