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As electrical measurement and test instruments manufacturer, hope to share some technical articles with our experience and knowledge.Welcome your comments and ideas or send email through support@gfuve.com
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■ Easy to install and remove with power on;
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Sunday, May 31, 2015
Analysis about effects of DC ripple on DC energy meter
Preface
The measurement and traceability of DC energy meter has no reference standard at present. One approach is to use a DC voltmeter and a DC ampermeter measuring the RMS and then multiply to obtain the DC power then compute energy. Another option would be to sample the value of voltage and current at the same time, accumulate the instantaneous power electricity to obtain energy. If no ripple DC signal, that is, no superposition any ac signal, both way are accurate in theory, so the traceability of DC energy can also be simplified as raising the level of the dc voltage and dc current to a separate source. But the reality is superposition of ac signal inside some of the dc signal is unavoidable, so whether the above two methods have error for the measurement of the dc watt-hour meter and what they are, let`s analyze the errors in the following, so as to provide reference for dc traceability and dc measurement.I. Error analysis----multiply value of voltage and current to obtain energy
For dc power, there is no reactive power, so there should be only active power. But due to the dc superimposed ac signal, actually reactive power will occur. So when analyzing the error, we introduce many concepts in order to understand standard calculation formula of active power easier.![]() |
| 1-1 |
![]() |
| 1-2 |
For dc signal superimposed ripple, any continuous periodic signal can be made of Fourier series. So dc current or voltage with ripple can be shown in formula 1-3, 1-4
![]() |
| 1-3 |
![]() |
| 1-4 |
![]() |
| 1-5 |
![]() |
| 1-6 |
![]() |
| 1-7 |
![]() |
| 1-8 |
Insert formula 1-3 and 1-4 into formula 1-1, we can get the following active power:
![]() |
| 1-9 |
![]() |
| 1-10 |
![]() |
| 1-11 |
![]() |
| 1-12 |

But,

Let alone,

Therefore, for the case of dc energy with dc ripple, if we only multiply the RMS, it will cause more active energy and the result is inevitable. The excess energy can be calculated in the following way:
![]() |
| 1-13 |
, we can obtain maximum
, which is![]() |
| 1-14 |
can`t always appear. Because the mathematical expression of
is not very intuitive, it is difficult to evaluate the largest error of
from the formula. However, based on formula 1-14, we can estimate the relative error,![]() |
| 1-15 |
If the convergence of the ripple is the h-th wave, the ratio of ripple and dc current and voltage is

.
The power factor angle
of h-th harmonic wave is ranging from 0° to 360°.The range of
is 0-100%.The distribution diagram of simulation error through mat-lab is listed as follows:
![]() |
| Chart 1-1 the distribution diagram of energy error |
From the mat-lab simulation, it indicates that when harmonic power factor angle is near 180, and UhIh is close to 100%, error
will be very big. because true value of P is close to zero, the denominator is very small,besides, there is no more accurate simulation, When the power factor Angle equals to 180° and Uh = 100%, its error is infinity.When the range is 0-10%, through mat-lab simulation error distribution diagram is as follows![]() |
| Chart 1-2 the distribution diagram of energy error |
From chart 1-2, it shows that once the harmonic wave content decreases, the P value of
reduces slightly, the denominator is very large, the error fluctuate a little. To sum up, when the upper limit of harmonic wave content is 10%, the error is less than 2%.When the range of
is 0-1%, the error distribution error is listed as chart 1-3,![]() |
| Chart 1-3 the distribution diagram of energy error |
As is shown above, once the harmonic wave content decreases,when the upper limit of harmonic wave content is 1%, the error is less than 0.02% to 1% of the installation type dc watt-hour meter as long as the voltage and current ripple is less than 1%, its error, the error of using the RMS of current and voltage to multiply , is negligible.
II. Error analysis- Synchronous sampling to measure DC energy
The hardware of dc energy meter can be simplified as chart 2-1. Generally, it is made up of voltage converter, current transformer, Low-pass filter, AD sampling and CPU.Based on the approach of accumulating instantaneous power, this part mainly analyzes the effects of the hardware filter and AD non synchronous sampling on dc energy. At the same time, suppose the cut-off frequency of LPF filter is less than sampling rate Fs/2 (to guarantee no superimposed Frequency spectrum) .
![]() |
Chart 2-1 design diagram---dc measuring the hardware
|
![]() |
| 2-1 |
: Simulate front-end low-pass filter transfer function(butter-worth stands for simulation second low-pass filter)
: AD sampling time-lapse transfer function
Y(S): AD final collected voltage or current data
Thus, the error is,
![]() |
| 2-2 |
error formula will be complemented in the subsequent development.Make quantitive analysis to filter wave and synchronous time-lapse through mat-lab simulation.
Mat-lab simulation error analysis when using hi-speed AD
Adopting hi-speed chip in AD circuit, the sampling frequency is 100KHZ(similar to ADS 2374 regardless of the sampling principle)The ripple frequency spectrum of input signal is focused on 10-50KHZ (chart 2-2)
The cut-off frequency of voltage channels using second low-pass filter is 10KHZ.
The cut-off frequency of current channels using second low-pass filter is 1KHZ-10KHZ.
Sampling time-lapse of voltage channel is 0
Sampling time-lapse of current channel is 0-1/fs
Error via mat-lab simulation
![]() |
Chart 2-2 simulation wave
|
When the ripple content is 10%, the error distribution diagram
![]() |
Chart 2-3 error distribution diagram--100K sampling ripple content is 10%
|
Error distribution diagram--ripple content is 1% (hi-speed AD)
![]() |
| Chart 2-4 100K sampling frequency when ripple content is 1% |
Mat-lab simulation error analysis--when using low-speed AD
Adopting low-speed chip in AD circuit, the sampling frequency is 100KHZ(similar to ADS 7793 regardless of the sampling principle)The ripple frequency spectrum of input signal is focused on 10-50KHZ
The cut-off frequency of voltage channels using second low-pass filter is 20KHZ.
The cut-off frequency of current channels using second low-pass filter is 10KHZ-40KHZ.
Sampling time-lapse of voltage channel is 0
Sampling time-lapse of current channel is 0-1/fs
Error via mat-lab simulation
Error distribution diagram--when ripple content is 10% (low speed AD)
![]() |
| Chart 2-5 error distribution diagram-- 100K sampling frequency when ripple content is 1% |
Error distribution diagram--when ripple content is 1% (low speed AD)
![]() |
| Chart 2-6 error distribution diagram-- 100K sampling frequency when ripple content is 1% |

























