Measurement of power consumption parameters in the presence of high harmonics

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The paper presents the study of high harmonics influence on power metering by static meters for active and reactive energy. The review and analysis of manufacturer’s documents and standards in the field of electricity meters testing was conducted and mathematical models for calculating active and reactive energy were identified.

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International Journal of Mechanical Engineering and Technology (IJMET) Volume 10, Issue 03, March 2019, pp. 1204–1209, Article ID: IJMET_10_04_122 Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=3 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed MEASUREMENT OF POWER CONSUMPTION PARAMETERS IN THE PRESENCE OF HIGH HARMONICS Y.E Shklyarskiy, A.N. Skamyin, O.S. Vasilkov Chair of General Electrotechnic, Saint-Petersburg Mining University, St. Petersburg, Russia ABSTRACT The paper presents the study of high harmonics influence on power metering by static meters for active and reactive energy. The review and analysis of manufacturer’s documents and standards in the field of electricity meters testing was conducted and mathematical models for calculating active and reactive energy were identified. Various electronic meters were tested at the experimental stand. As a result, the errors of active and reactive energy metering in the presence of high harmonics were determined. It is shown that the implemented in static meters equations for the active and reactive energy calculation can lead to unfair payments for electrical energy in the presence of high harmonics. Key words: Power consumption, reactive energy, THD, mathematical model, harmonic distortion, active power, reactive power Cite this Article: Y.E Shklyarskiy, A.N. Skamyin, O.S. Vasilkov, Measurement of Power Consumption Parameters in the Presence of High Harmonics, International Journal of Mechanical Engineering and Technology 10(3), 2019, pp. 1204–1209. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=3 1. INTRODUCTION Reorganization of Russian electrical energy structure which was finished at 2008 led to the separation of vertically integrated companies into independent generating, grid companies, power sales companies and operational dispatch control subjects. So since one large company split into several independent companies, solving organizational matters of power quality managing is not easy these days. Responsibility for the inadequate power quality between the electricity market subjects is determined by Russian federal law [1] and Resolutions of the Russian Government No. 442 and 861. However, the disturbances of the Russian standard requirements for the power quality [2] are massive and systematic in many power systems. The facility responsible for the deterioration of the power quality is not subject to appropriate measures and does not pay any fines and surcharges to the electricity tariff. Russian regulatory documents set the required values of the reactive power ratio for electric power consumers [3]. But in fact, in recent years, the mechanism of discounts and surcharges to the electricity tariff for unsatisfactory values of the reactive power ratio has been destroyed. The analysis of power supply contracts and parameters of power consumption at a number of St. Petersburg industrial enterprises confirms these conclusions. In addition, currently there are no approved methods to identify the source of high harmonics at the point of comsumers common coupling (PCC). Very often, consumers who do not distort the supply voltage, receive electrical energy with distortion due to the operation of a powerful non-linear load of third-party power facilities connected to the PCC. This is mainly observed http://www.iaeme.com/IJMET/index.asp 1204 editor@iaeme.com
Y.E Shklyarskiy, A.N. Skamyin, O.S. Vasilkov in electrical networks supplying an alternating current electrified railway, aluminum plants and large metallurgical enterprises [4, 5]. For many industrial enterprises, their energy costs are fundamental to the cost structure of a product [6, 7, 8]. Power consumption at the electrical input of enterprise in the presence of high harmonics can be both more and less in comparison with the power at the fundamental frequency [9, 10]. This is primarily determined by the phase shift at high harmonics between voltage and current. A number of studies have shown that the additive in terms of power consumption due to the presence of high harmonics can reach tens of kilowatts [11, 12], which can be expressed as several million rubles a year. As a rule, payment for electrical energy is made taking into account the active and reactive component of the consumed energy. Therefore, measurement of active and reactive energy is required. In case of sinusoidal voltage and current, different electronic static meters provide comparable readings for active and reactive energy in accordance with their precision class. Electric power meters tested for sinusoidal conditions are currently used at non-sinusoidal currents and voltages. In this conditions various power meters can give different readings. Therefore, the aim of the work is to study the effect of high harmonics on the power consumption parameters recorded by static energy meters. First of all, it is the consumption of apparent, active and reactive power. 2. STANDARDS AND CALCULATION METHODS The existing Russian standards in the field of testing the active energy static meters sets the requirements for accurcy checking in the presence of high harmonics [13, 14]. The existing standards in the field of testing the reactive energy static meters applies to their operation with sinusoidal voltages and currents [15]. It should be noted that the previous standard contained verification of the reactive energy meters accuracy in the presence of third current harmonics with an amplitude of 10%, but in the replaced standard this type of test was canceled. Manufacturers of electronic static energy meters produce their devices with high-precision integrated circuits. The analog part of the microchip includes an analog-to-digital converter and a reference voltage source. All further signal transformations, such as multiplication and filtering, are carried out in digital domain. A functional block diagram of static energy meter is presented on figure 1. Figure 1. Functional block diagram. The active power calculation is derived from the instantaneous power signal. The instantaneous power signal is generated by a direct multiplication of the current and voltage signals. To extract the active power component (that is, the DC component), the instantaneous power signal is low-pass filtered. The considered approach correctly calculates active power for nonsinusoidal current and voltage waveforms. All voltage and current signals in practical applications have some harmonic component. Using the Fourier Transform operation, instantaneous voltage and current waveforms can be expressed in terms of their harmonic content. Therefore the active power can be expressed in terms of its fundamental active power and harmonic active power. 𝑃 = 𝑃1 + 𝑃𝐻 , (1) 𝑃1 = 𝑉1 𝐼1 cos𝜑1 , 𝜑1 = 𝛼1 − 𝛽1, (2) http://www.iaeme.com/IJMET/index.asp 1205 editor@iaeme.com
Measurement of Power Consumption Parameters in the Presence of High Harmonics 𝑃𝐻 = ∑∞ ℎ≠1 𝑉ℎ 𝐼ℎ cos𝜑ℎ , 𝜑ℎ = 𝛼ℎ − 𝛽ℎ , (3) where Vh is the rms value of voltage harmonic h, αh is the phase angle of voltage harmonic, Ih is the RMS value of current harmonic h, βh is the phase angle of current harmonic. As we can see from the equation (3), the harmonic component of active power is determined by all harmonics, provided that the harmonic is represented in both the current signal and the voltage signal. Reactive power is defined as the product of the voltage and current waveforms when one of these signals is phase-shifted by 90° [16]. The resulting waveform is called the instantaneous reactive power signal. Equation (4) gives an expression for the instantaneous reactive power signal in an AC system when the phase of the current channel is shifted by +90°. 𝑉(𝑡) = √2𝑉sin(𝜔𝑡 + 𝜃), 𝐼(𝑡) = √2𝐼sin(𝜔𝑡), 𝐼`(𝑡) = √2𝐼sin(𝜔𝑡 + 𝜋/2), (4) 𝑞(𝑡) = 𝑉(𝑡)𝐼`(𝑡) = 𝑉𝐼sin(𝜃) + 𝑉𝐼sin(2𝜔𝑡 + 𝜃), (5) where θ is the phase difference between the voltage and current channel, V is the rms voltage, I is the rms current. The average reactive power over an integral number of lines (n) is given in equation (6). 1 𝑛𝑇 𝑄 = 𝑛𝑇 ∫0 𝑞(𝑡)d𝑡 = 𝑉𝐼sin(𝜃), (6) where T is the line cycle period, q is referred as the reactive power. Block diagram for reactive energy metering is presented on figure 2. In addition, the phase shifting filter has a nonunity magnitude response. Because the phase shifted filter has a large attenuation at high frequency, the reactive power is primarily for calculation at line frequency. The effect of harmonics is largely ignored in the reactive power calculation. Figure 2. Block diagram for reactive energy metering. Some energy meters can compute the total reactive power which includes all fundamental and harmonic components of the voltages and currents. Reactive power is defined as the product of the voltage and current waveforms when all harmonic components of one of these signals are phase shifted by 90°. The total reactive power is equal to: 𝑄 = ∑∞ 𝑘=1 𝑉𝑘 𝐼𝑘 sin(𝜑𝑘 − γ𝑘 ), (7) where Vk, Ik are the rms voltage and current, respectively, of each harmonic; φk, γk are the phase delays of each harmonic. Electrical energy in some electronic energy meters can be computed as the difference of squares between the total and active powers. 𝑄 = √𝑆 2 − 𝑃2 . (8) The reactive power is calculated based on the measurement of active and apparent power. In case of sinusoidal voltage and current, all these expressions give the same values. Therefore, in accordance with the standard for reactive energy meters all these methods for calculating reactive power can be applied. Obviously, that mentioned calculation methods can lead to different results in the presence of high harmonics. 3. EXPERIMENTAL STUDIES http://www.iaeme.com/IJMET/index.asp 1206 editor@iaeme.com
Y.E Shklyarskiy, A.N. Skamyin, O.S. Vasilkov Experimental studies consisted in the creation of various harmonic signals on voltage and current, which were fed to the energy meters with subsequent fixation of the readings. Three electronic energy meters of different manufacturers were tested and their readings were compared with an power quality analyzer. The accuracy class of the tested electricity meters is 1.0 for active energy and 2.0 for reactive energy. A simplified electrical circuit diagram of the experimental stand for measurements is presented in figure 3. Figure 3. Single-line diagram of the experimental stand. Power supply of the stand is carried out through the transmission line TL of 220 V. The installation consists of a three-phase laboratory autotransformer T, an asynchronous motor M (rated power is 1.5 kW) with a load in the form of a DC generator, a capacitor banks CB with an antiharmonic reactor (rated power is 2.5 kvar) and an uncontrolled three-phase rectifier as a source of harmonics HS with a load in the form of active resistance (rated power is 1.0 kW). Measurement of electrical energy using the tested electricity meters was made for different modes of electrical equipment operation. The readings of active, reactive and apparent powers were recorded. In the first mode, an electric motor at idling speed and an uncontrolled three-phase rectifier with a load in the form of active resistance are connected to the stand. Mode 2 corresponds to mode 1 with an additionally connected capacitor banks (power factor ratio is about 0.94, inductive mode). Mode 3 corresponds to mode 2 with reactive power overcompensation (power factor ratio is about 0.92, capacitive mode). Modes 4, 5, 6 correspond to modes 1, 2, 3 with the loaded asynchronous motor respectively. For modes 5 and 6, the power factors are about 0.94 and 0.88 respectively. The measured values for the different load modes are shown in Table 1, where P, Q, S are measured in W, var, VA respectively. Table 1. Consumed active, reactive and apparent powers. Name of Energy meter 1 Energy meter 2 Energy meter 3 PQ analyser mode P Q S P Q S P Q S P Q 1 728 1554 1738 733 1569 1752 729 1583 1754 729 1550 2 772 183 818 771 260 822 771 263 821 773 240 3 785 -285 854 787 -322 857 784 -315 850 787 -340 4 1408 1293 1913 1404 1332 1925 1407 1326 1923 1409 1330 5 1420 480 1505 1420 522 1506 1420 523 1510 1421 500 6 1442 -776 1640 1441 -780 1644 1442 -779 1632 1444 -790 The percentage error of the measured values was calculated relative to the values measured by the power quality analyzer. In addition, the reactive power values were calculated using the above- mentioned calculations to identify the measuring energy meters equation. 4. RESULTS AND DISCUSSION http://www.iaeme.com/IJMET/index.asp 1207 editor@iaeme.com
Measurement of Power Consumption Parameters in the Presence of High Harmonics As a result of the experimental studies, relative errors of active and reactive power were obtained. For all modes THDU was about 2%, and THDI changed within the range from 15 to 30%. Static energy meters completely adequately repeat the mathematical model of active power in accordance with its accuracy class. Reactive power errors are presented in figure 4. E, % 15,0 10,0 5,0 Mode 1 0,0 Mode 2 -5,0 Mode 3 -10,0 Mode 4 -15,0 Mode 5 -20,0 Mode 6 -25,0 -30,0 Energy Meter 1 Energy Meter 2 Energy Meter 3 Figure 4. Relative errors for reactive power of different electricity meters. As we can see, the relative error in metering reactive power when capacitor banks are switched on significantly increases, which is associated with an increase in THDI. The error reaches the 24% for the first energy meter and it does not exceed 10% for the second and third energy meters. So switching on capacitor banks without an antiharmonic reactor will result in even greater errors. There is also a trend to increase the relative error of reactive power measurement with an increase in the network power factor. The analysis of the correlation between measured and calculated by mathematical models values has shown that energy meters 2 and 3 calculate the value of reactive power by equation (8). The first energy meter gives a maximum error of 32% in comparison with the calculations on the equation (8). But it also gives an error not exceeding 5% in comparison with the calculations by equation (6). Consequently, it is most likely that the calculations are carried out according to the equation (6). This explains the significant metering errors of the first energy meter compared to the readings of the power quality analyzer, which calculates the reactive power by the equation (8). The results lead to interesting conclusions. It is known that the harmonic active powers have a negative value when they are caused by the nonlinear electrical load`s operation of the consumers. And vice versa, the harmonic active powers is summed up with the fundamental active power when the distortions appear from the utility side. Thus, a consumer who does not distort the voltage and current pays more for active energy, and a consumer who distorts the voltage and current pays less. This applies to active power. Measurement of reactive power is possible by different mathematical equations. Reactive power is determined on the basis of the active power measurement in calculations by equation (8). Therefore, the distorting consumer will pay more for the reactive energy. The expression (6) gives the reactive power value corresponding to the consumption on the fundamental frequency. So in case of harmonics generation from the consumer`s side the value of reactive power is underestimated in comparison with the equation (8), as evidenced by the conducted studies. 5. CONCLUSIONS The paper identifies mathematical models for the calculation of active and reactive power, which describe the operation of electronic static meters in the presence of high harmonics. It is shown that the meter readings can differ significantly from each other in the presence of high harmonics, as well as from the measured energy (power) values on the fundamental frequency. http://www.iaeme.com/IJMET/index.asp 1208 editor@iaeme.com
Y.E Shklyarskiy, A.N. Skamyin, O.S. Vasilkov The equation for calculating the active power in the presence of high harmonics is the same for all tested meters. However, it is questionable from the viewpoint of fairness in the payment of electricity bills to distorting and non-distorting consumers. The usage of different computational equations for reactive power may lead to disagreements between power suppliers and consumers due to differences in the payments for the same electrical energy consumption. ACKNOWLEDGMENTS This research has been conducted with financial support from Russian Science Foundation grant (project No. 18-79-00127). REFERENCES [1] Russian Federal law of 26.03.2003 N 35 “On electric power industry” [2] Russian Standard 32144-2013. Electric energy. Electromagnetic compatibility of technical equipment. Power quality limits in public power supply systems [3] Normative document of the Russian Ministry of Energy N 380 from 23.06.2015 Available: https://www.pravo.gov.ru [4] Shklyarskiy Y. E. and Pirog S. 2016 Journal of Mininig Institute 222 858-863 [5] Artyukhov I. I., Bochkareva I. I., Molot S V at al. 2017 Proceedings of the 9th International Scientific Symposium on Electrical Power Engineering, ELEKTROENERGETIKA, 44-49 [6] Zhukovskiy Y. L., Korolev N. A., Babanova I S and Boikov A V 2017 IOP Conference Series: Earth and Environmental Science 87(3) ID: 032055 [7] Abramovich B. N. and Sychev Y. A. 2016 International Conference on Actual Problems of Electron Devices Engineering (APEDE), 1-7 [8] Semykina I. and Skrebneva E. 2017 Advances in Intelligent Systems and Computing, 495 113-122 [9] Belsky A. A. and Dobush V. S. 2015 International Conference on Mechanical Engineering, Automation and Control Systems (MEACS), 1-4 [10] Korotkov A. and Frolov V. 2016 Proceedings of the 2016 IEEE North West Russia Section Young Researchers in Electrical and Electronic Engineering Conference EIConRus ID: 7448254 601-603 [11] Kovernikova L. and Shamonov R. 2017 E3S Web Conf. 25 ID: 04001 [12] Dvorkin D., Palis S., Silaev M. and Tulsky V. 2017 IEEE 58th International Scientific Conference on Power and Electrical Engineering of Riga Technical University (RTUCON), 1-4 [13] Standard 31819.21-2012 (IEC 62053-21:2003). Electricity metering equipment (а. с). Particular requirements. Part 21. Stаtiс meters for active energy (classes 1 and 2) [14] Standard 31819.22-2012 (IEC 62053-21:2003). Electricity metering equipment (a.c.). Particular requirements. Part 22. Static meters for active energy (classes 0,2 S and 0,5 S) [15] Standard 31819.23-2012 (IEC 62053-21:2003). Electricity metering equipment (a. c). Particular requirements. Part 23. Static meters for reactive energy [16] Filipski P. S. and Labaj P. W. 1992 IEEE Trans. Power Deliv. 7(4) 1793–1799 http://www.iaeme.com/IJMET/index.asp 1209 editor@iaeme.com