Research of Metering Arithmetic for Distortion Power

Under the condition of voltage and current waveform distortion, in order to make the metering fair and rational, this paper proposed measurement model of fundamental wave plus harmonics wave and the distortion power algorithm. Studied and compared two measurement models, namely fundamental wave and full wave, a mixed measurement model of fundamental wave plus harmonic wave is proposed. Then, the distortion power calculation formula and algorithm are proposed based on the definitions recommended in IEEE Std 1459-2010, and analyzed the feasibility of the proposed method in combination with the existing smart meter technology. By field measuring data validated that, the proposed distortion power metering is necessary and the algorithm is practical.


Introduction
The electrical energy metering, as the main evidence of economic accounting in power grid, its accuracy and rationality is related to the economic benefits of power supply and demand [1,2].With the development of power electronics technology, more and more nonlinear load were connected to power grid and produced a large number of harmonic,that has an passive affect on the rationality of smart meter which is designed for using in the traditional sinusoidal fundamental frequency [3][4][5].Therefore, it is necessary to study the power measurement algorithm of nonlinear load, and the key point is the distortion power metering algorithm.
At present, a lot of researches have been carried out on the definition and metering of distortion power, but still have some controversy.IEEE Std 519-2014 [6] specifies maximum limits for the harmonic current and harmonic voltage magnitudes, but can not meter distortion power accurately just by these values.Budeanu described distortion power as the remaining quantity of apparent power, active power and reactive power [7], the definition of distortion power meet power conservation relationship, but do not possess the attributes which can be related to the power phenomena in circuits with nonsinusoidal waveforms [8].Fryze proposed a definition of current component [9], which is clear and correct in physical and mathematical, but not revealing all the details of the instantaneous power and not representing the true mechanism of energy transfer to the load.Depenbrock improved on Fryze's method, creating a more detailed current component [10], he defined distortion current equal difference between wattles current and fundamental reactive current, but not gave complete physical explanation.Czarnecki's model is more complete, can explain the power flow in detail [11], but the complexity of the decomposition method also make it difficult to implement in practical project.
Based on the recommended definitions of distortion power in IEEE Std 1459-2010 [12], which meet the electromagnetic distortion energy flow physics laws when voltage and current occur distortion, this paper proposed the distortion power metering algorithm, and analyzed the feasibility in combination with the existing smart meter technology.As a case study, field recorded dada in one iron and steel plant is used to validate the proposed distortion power metering algorithm.

Measurement model
Established a single-phase circuit with nonlinear load and linear load, as shown in Figure 1.AC represent a sine alternating current source, which amplitude is 100 V.The ideal rectifier diode D series resistance R 3 is used to represent the nonlinear load.The value of R 1 , R 2 and R 3 equal 2 Ω , 10 Ω and 10 Ω , respectively.Perform Fast Fourier Transform (FFT) on the voltage and current data of linear and nonlinear loads as follows The results are showed in Table 1.Using the data of Table 1, calculated power value of linear and nonlinear load in the measurement model of fundamental wave and full wave, respectively.The results are showed in Table 2.Where As it can be seen from Table .2, under the measurement model of full wave, linear load absorb fundamental and harmonic power and they are in the same direction, thus metering result is greater than fundamental power; nonlinear load absorb fundamental power and inject harmonic power, the metering is lesser than fundamental power.In other words, nonlinear load inject harmonic that pollute power grid, at the same time, the metering result is lesser.Therefore, the measurement model is unfair.Under the measurement model of fundamental wave, linear and nonlinear load both only be metered fundamental wave.It is fair for linear load, but neglect the harmonic pollution that nonlinear load produced.
In conclusion, the rationality of the measurement model of full wave and fundamental wave both exist shortcoming, cannot satisfy requirement of metering.Thus, the measurement model of fundamental wave plus harmonic wave is another choice, but still need study distortion power definition and metering algorithm.

Distortion power metering algorithm 3.1 The recommended definitions in IEEE Std 1459-2010
Under stationary conditions, voltage and current that occur distortion can be decomposed into power frequency component and the rest of the component, be represented by v 1 , i 1 , v h and i h , respectively.Power frequency voltage components as reference, then Where:

sin( )
With the root mean square (RMS) value can be represented as: ; ; According to type ( 9) and (10), apparent power can be decompose as follows Where DI, DV and SH are defined as current distortion power, voltage distortion power and harmonic apparent power, respectively.In the type (11), harmonic apparent power can be decomposed into two component, namely active harmonic power PH and distortion power DH, respectively. Where Total harmonic voltage and current distortion is defined as: According to type ( 12) to ( 14), distortion power can be calculated as follows

Distortion power metering in smart meter
The common smart meter is composed of measurement, data processing, communication and other units.The electric energy metering chip can measure and store the real-time voltage and current data.In the case of RN 83208 metering chip, can chose sample frequency 6.4 kHz, and it will meet the needs of harmonic analysis in the scope of 64 harmonic frequency spectrum, according to the Nyquist sampling theorem.The chip can store data of voltage, current, fundamental apparent power and apparent power.
According to type (13), calculate distortion power D H need known the value of fundamental apparent power S 1 , total harmonic voltage distortion THD v , and total harmonic current distortion THD I .Therefore, smart meter only need to perform FFT on the voltage and current data, and then acquisition amplitude and phase of voltage and current in each frequency spectrum.After calculate THDv, THD I and P H, get further calculate distortion power D H according to type (15).The distortion power algorithm flow as shown in Figure 3.

Field test verification
In this section, the practical of the proposed distortion power algorithm is evaluated by using the actual field recorded dada.The field measurement was carried out at a refining furnace in one iron and steel plant in 2 hours, the sample frequency is 1000 Hz.Considering the recommended in IEC Std 61000-4-30 [13], data processing per 200 ms, calculate and record the full wave and fundamental wave apparent power.According to Figure 3, the FFT is applied to acquisition amplitude and phase of voltage and current in each frequency spectrum, total 36,000 groups of data.The value of THD V and THD I as shown in Figure 4. Refining furnace is arc load and is the main harmonic source in iron and steel plant.The result show that the maximum of THD v and THD I is 4.09% and 92%, respectively.Using the calculated data of THD V and THD I , included the measurement data of the full wave and fundamental wave apparent power, calculated distortion power DH according to type(15).The Result of full wave and fundamental wave apparent power and distortion power are showed in Table .3.
As it can be seen from Table 3, the maximum of distortion power D H is 38.41 kW in the test period, and the average value is 11.35 kW.Assumed the refining furnace work 5000 hours in a year, calculate by the average value in the test period, then the distortion energy of the refining furnace is 56772 J. Illustrates that it will cause unfair metering and economic loss if neglect distortion energy.
From Figure 3, this paper proposed the distortion power algorithm based on IEEE Std 1459-2010 is clear and easy to implement just need to improve exist smart meter.

Conclusion
(1) By simulation a simple system model with linear and nonlinear load, proved that the irrationality of the measurement model of fundamental wave and full wave, and then proposed a measurement model named "fundamental wave plus harmonic wave", and the distortion power metering is the key; (2) According to the recommended definitions of distortion power in IEEE Std 1459-2010, considered the existing smart meter technology, this paper proposed the distortion power metering algorithm.(3) Through field test validated that, the proposed distortion power metering algorithm is reasonable and feasible.

Figure 1 .
Figure 1.Single phase circuit model including linear and nonlinear loads

Figure 3 .
Figure 3.The algorithm flow chart of distortion power

Figure 4 .
Figure 4.The trend chart of THD V and THD I

Table 1 .
Current and voltage dataU

Table 2 .
Power values

Table 3 .
POWER VALUES FOR FURNACE