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XXIV Symposium Electromagnetic Phenomena in Nonlinear Circuits June 28 - July 1, 2016 Helsinki, FINLAND ______________________________________________________________________________________________________ COMPENSATION FOR NON-ACTIVE CURRENT COMPONENTS AT MAINS SUPPLY VOLTAGE UNBALANCE Atef S. Al-Mashakbeh*, Mykhaylo Zagirnyak, Andrii Kalinov and Mariia Maliakova * Tafila Technical University, Electrical Engineering Department, P.O. Box 179, Tafila, 66110, Jordan, e-mail: [email protected] Kremenchuk Mykhailo Ostrohradskyi National University, Institute of Electromechanics, Electric Machines and Apparatus Department Pershotravneva str. 20, Kremenchuk, 39600, Ukraine, e-mail: [email protected] Abstract - Analytical research of compensation for nonactive current components in a three-phase three-wire power-supply system has been carried out with the use of cross-vector theory of instantaneous power in frequency domain. The obtained results allowed us to propose a method of improvement the compensation for non-active current components under supply voltage unbalance by means of the use of mains supply voltage signals balancing block. The results of numerical modeling of the processes of compensation for non-active current components under the conditions of supply voltage unbalance have revealed the advantages of the proposed method in comparison with the classical one. I. INTRODUCTION It is commonly known, that in most cases the real load of power-supply systems is characterized by both nonlinearity of its characteristics and unsymmetry of its parameters by phases. This leads to appearance of higher harmonics in current and voltage signals and also to amplitude and angle unsymmetry of voltages and currents in the system. This means that in load currents the non-active components appears. In accordance with works [1-2] the active current is only a main harmonic component of the current signal, and it has sinusoidal waveform and flows co-phased with the mains voltage. All the rest components of load current, conditioned by unsymmetrical load, are non-active. The flow of nonactive current components in power-supply systems leads to increase the losses in transformers, power lines, capacitors of reactive power compensators, etc. To compensate these currents the power active filters (APF) are used [1, 3, 5-6]. However, in the author’s opinion [1], the use of p-q theory of instantaneous power (IP) for calculation of APF compensation currents in the system with non-sinusoidal and unbalanced supply voltage is doubtful. It can be explained by the fact that interpretation of power components according to p-q IP theory, as well as of other theories, does not answer the question: what is the reason of non-sinusoidality and unbalance – the load or the mains. It is shown in paper [1] that APF operation on the basis of p-q IP theory at distorted mains voltages may cause still bigger distortions of current signals. The purpose of the paper is the improvement of methods of compensation for non-active current components under the conditions of unbalance of supply voltage in order to increase the efficiency of operation of power-supply system. II. MATERIAL AND RESULTS OF THE RESEARCH A. Research of compensation processes in an analytical form in frequency domain Processes of compensation for nonactive current components in a three-phase three-wire system, caused by amplitude unbalance of loads current, are considered in frequency domain in an analytical form. In this case it was assumed that there is no currents influence on mains voltage distortion, i.e. power of the power-supply system is unlimited. Output orthogonal cosine and sine components of current in three-phase three-wire mains were 3 1 I1 m ; I A b1 = − I1m ; 4 4 1 1 3 = ε B I1m ; I C a1 = − εC I1m ; I C b1 = − εC I1m , 2 4 4 presented in frequency domain: I A a1 = I B a1 = 0 ; I B b1 where ε B , εC – coefficients of amplitude unbalance of phase В and phase С, respectively; shear angle of the first harmonic component of current ϕ I 1 = −30 el. deg. Numerical values of coefficients of unbalance were taken ε B = 0.8 , εC = 1.2 , respectively. Analytical expressions of variable components of instantaneous active and reactive power and their root-mean-square (RMS) values were obtained: (1) P2rms = 1 / 4 U1m I1m 1 + εB2 + εC 2 −εC εB −εC −εB ; Q2rms = 3 / 4 U1 m I1 m 1 + ε B 2 + εC 2 − εC ε B − εC − ε B . (2) Compensation currents in frequency domain were calculated according to cross-vector theory: I A b1 = − (1 / 4 ) I1m ; I A a1 = − 3 / 12 I1m −2 + ε B + εC ; ( =( I B a1 = I C a1 ( ) ) 3 / 24 ) I 3 / 24 I1m 1 + ε B + εC ; 1m I B b1 = (1 / 8 ) I1m 3ε B − 1 − εC ; 1 + ε B − 5εC ; I C b1 = (1 / 8 ) I1m 1 + ε B − εC . Correctness of the obtained orthogonal components of compensating current is confirmed by the fact that provided ε B = εC = 1 expressions of variable components of instantaneous active and reactive power and their RMS values P2rms , Q2rms acquire zero values. The analysis performed in an analytical form made it possible to come to the conclusion that compensation for non-active current components is possible without taking into account the unbalanced components of supply voltage in the algorithm of generation of compensation currents. B. Mathematical modeling of compensation system operation To confirm the results of analytical research a mathematical model of a section of power-supply mains was created. It consists of balanced/unbalanced linear load, active-inductive resistances of the mains, blocks of currents and voltages measurement, APF, APF control system, separation block (SB), as well as voltage signal balancing block (VSBB). VSBB (Fig. 1) is meant for balancing of supply voltage signals before their feed to APF control system. Amplitude values of voltage in every phase were determined in VSBB by means of Fourier transform (FT) (Fig. 1, block I). ______________________________________________________________________________________________________ 135 power at the mains active resistances ∆P efficiency η of the supply mains. TABLE I INDICES OF APF OPERATION AT UNBALANCED SUPPLY VOLTAGE AND BALANCED LOAD Fig. 1. Supply mains VSBB The obtained numerical values were added up and then averaged (Fig. 1, block II). Coefficients KA, KB, KC were determined by division of the obtained values by initial amplitude (Fig. 1, block III). These coefficients are necessary to balance voltage amplitudes in every phase (Fig. 1, block IV). After that a voltage signal without components caused by voltage unbalance was fed to the system of compensator control. Unbalanced supply voltage – balanced load. During research of compensator operation under the conditions of supply voltage unbalance the amplitude unbalance was introduced into phase А by the value of coefficient ε A = 0.885 (Fig. 2, I). This value of amplitude undalance corresponds to voltage reciprocal sequence coefficient K 2U = 4 %, which is twice as big as the boundary value in accordance with European Standard EN 50160 [4]. In such a system unbalance of supply voltage causes current unbalance at the supply terminal (Fig. 2, I). iA(t), iB(t), iC(t), A 400 I III II 200 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 t, c 200 400 600 Fig. 2. Mains currents before (I) and after (II) connection of a classical compensator, and also after connection of compensator with VSBB and SB (III) In this case the work of classical compensator (Fig. 2, II) was characterized by decrease of voltage unbalance coefficient ( K 2U =1.76 %), but considerable total harmonic distortion (THD) of current with THDI = 9 % was observed (Fig. 2, II). It is caused by the fact that a voltage signal distorted (THDU = 11 %) due to incorrect operation of APF control system under the conditions of supply voltage unbalance was fed to compensator control system. SB described in papers [5-6] was proposed to be used for correct APF operation under the conditions of harmonic distortions of supply voltage. Transfer to frequency domain was performed and voltage harmonic composition was determined at the point of APF connection in SB with the use of FT. After that supply voltage harmonic components caused by mains distortions were determined with the use of the analysis of the sign of corresponding frequency component of active power. These voltage components were removed and did not participate in generation of signal at the transfer to the time domain. The obtained signals were fed to APF control system [5-6]. The following parameters were calculated for quantitative assessment of compensation (TABLE I): THDI and THDU, voltage drop at the mains resistances ∆U, reactive power constant component Q, coefficients of unbalance of current and voltage of reciprocal sequence K 2I and K 2U , respectively, loss Param. ∆U, THDU, THDI, Q, Mode V var % % Before comp. 27.84 0 0 1.22·105 After comp. 31.4 11 9 100 After comp. 24.25 0.2 0.005 -85 with VSBB and SB η, ∆P, W 1.965·104 1.386·104 % 92.45 94.69 , K 2I , % % 3.98 3.98 4.1 1.76 1.383·104 97.72 4.25 0.176 K 2U Unbalanced supply voltage-unbalanced load. In this case unbalance was introduced into phase А of supply voltage by the value of coefficient ε A = 0.885 and into load of phase С with level 10 % of the value of its active resistance. In this case the level of unbalance by coefficient of voltage reciprocal sequence K 2U made 4.03 %. In this case the same characteristics of APF operation as in the previous case were observed (TABLE II) – compensator with VSBB and SB enbled decrease of load current unbalance level to K 2 I = 0.17 % and maintain THDI and THDU at a practically zero level. TABLE II INDICES OF APF OPERATION AT UNBALANCED SUPPLY VOLTAGE AND UNBALANCED LOAD Param. ∆U, THDU, THDI, Q, ∆P, Mode V % % var W Before comp. 27.25 0 0 –1.18·105 1.9·104 After comp. 27.2 7.3 7.35 450 1.3621·104 After comp. 24.15 0.002 0.005 –93.5 1.35·104 with VSBB and SB η, % 92.05 94.7 , K 2I , % % 4.03 4.87 4.15 1.72 94.72 4.32 K 2U 0.17 III. CONCLUSIONS Use of the developed method with balancing and separation of supply voltage harmonics, as compared with the classical system of compensation, makes it possible to decrease the level of unbalance of current signals with reciprocal sequence coefficient by 1.3..1.5 %, reduce power line losses ∆P by 0.5..0.7 %, the value of reactive power after compensation Q by 15..23 %, voltage drop at the mains resistances ∆U by 0.5..23 %, improve the system efficiency by 0.3..2.5 %, achieve practically zero value of coefficient of current sinusoidality distortion THDI. REFERENCES [1] Czarnecki L.S., Samuel S. Pearce, “CPC-based comparison of compensation goals in systems with nonsinusoidal voltages and currents”, International School on Nonsinusoidal Currents and Compensation, Łagow, Poland pp. 27-36, 2010. [2] Peng F.Z., Tolbert L.M., Zhaoming Qian “Definition and compensation of non-active current in power systems”, Power Electronics Specialists Conference, 2002. pesc 02. 2002 IEEE 33rd Annual, Vol. 4, 23–27 June 2002, Cairns, Qld, pp. 1779–1784, 2002. [3] Akagi H., Kanazawa Y., Nabai A., “Generalized theory of the instantaneous reactive power in three-phase circuits”, Proceeding of Int. Power Electronic Conference, pp. 1375–1386, 1983. [4] European standard EN 50160 “Voltage characteristics of electricity supplied by public distribution systems”, CENELEC TC 8X, 2006. [5] Zagirnyak M., Maliakova M., Kalinov A., “Analysis of operation of power components compensation systems at harmonic distortions of mains supply voltage”, Proceedings 2015 ACEMP–OPTIM– Electromotion 2015 Joint Conference, 02–04 September, Side, Turkey, 978-1-4763-7239-8/15 IEEE, pp. 355–362, 2015. [6] Zagirnyak M., Maliakova M., Kalinov A., “Compensation of higher current harmonics at harmonic distortions of mains supply voltage”, Proceedings 2015 16th international conference on computational problems of electrical engineering (CPEE), 02–05 September, Lviv, Ukraine, IEEE Catalog Number CFP15A10-PRT, ISBN 978-617-607803-6, pp. 245–248, 2015. ______________________________________________________________________________________________________ 136 Proceedings of EPNC 2016, June 28 - July 1, 2016 Helsinki, FINLAND