Unbalanced and Reactive Currents Compensation in Three-Phase Four-Wire Sinusoidal Power Systems

[EN] In an unbalanced linear three-phase electrical system, there are inefficient powers that increase the apparent power supplied by the network, line losses, machine malfunctions, etc. These inefficiencies are mainly due to the use of unbalanced loads. Unlike a three-wire unbalanced system, a four-wire system has zero sequence currents that circulate through the neutral wire and can be compensated by means of compensation equipment, which prevents it from being delivered by the network. To design a compensator that works with unbalanced voltages, it is necessary to consider the interactions between it and the other compensators used to compensate for negative-sequence currents and positive-sequence reactive currents. In this paper, through passive compensation, a new method is proposed to develop the zero sequence current compensation equipment. The method does not require iteration algorithms and is valid for unbalanced voltages. In addition, the interactions between all compensators are analyzed, and the necessary modifications in the calculations are proposed to obtain a total compensation. To facilitate the application of the method and demonstrate its validity, a case study is developed from a three-phase linear four-wire system with unbalanced voltages and loads. The results obtained are compared with other compensation methods that also use passive elements.This work is supported by the Spanish Ministry of Science, Innovation and Universities (MICINN) and the European Regional Development Fund (ERDF) under grant RTI2018-100732-B-C21.Montoya-Mira, R.; Blasco Espinosa, PA.; Diez-Aznar, J.; Montoya Villena, R.; Reig-Pérez, MJ. (2020). Unbalanced and Reactive Currents Compensation in Three-Phase Four-Wire Sinusoidal Power Systems. Applied Sciences. 10(5):1-23. https://doi.org/10.3390/app10051764S123105Sainz, L., Caro, M., & Caro, E. (2009). Analytical Study of the Series Resonance in Power Systems With the Steinmetz Circuit. IEEE Transactions on Power Delivery, 24(4), 2090-2098. doi:10.1109/tpwrd.2009.2028790Emanuel, A. E. (1993). On the definition of power factor and apparent power in unbalanced polyphase circuits with sinusoidal voltage and currents. IEEE Transactions on Power Delivery, 8(3), 841-852. doi:10.1109/61.252612Willems, J. L. (2004). Reflections on Apparent Power and Power Factor in Nonsinusoidal and Polyphase Situations. IEEE Transactions on Power Delivery, 19(2), 835-840. doi:10.1109/tpwrd.2003.823182Pillay, P., & Manyage, M. (2006). Loss of Life in Induction Machines Operating With Unbalanced Supplies. IEEE Transactions on Energy Conversion, 21(4), 813-822. doi:10.1109/tec.2005.853724Poblador, M. L. A., & Lopez, G. A. R. (2013). Power calculations in nonlinear and unbalanced conditions according to IEEE Std 1459-2010. 2013 Workshop on Power Electronics and Power Quality Applications (PEPQA). doi:10.1109/pepqa.2013.6614957IEEE Recommended Practice for Monitoring Electric Power Quality. (s. f.). doi:10.1109/ieeestd.2019.8796486Blasco, P. A., Montoya-Mira, R., Diez, J. M., Montoya, R., & Reig, M. J. (2019). Compensation of Reactive Power and Unbalanced Power in Three-Phase Three-Wire Systems Connected to an Infinite Power Network. Applied Sciences, 10(1), 113. doi:10.3390/app10010113San-Yi Lee, & Chi-Jui Wu. (1993). On-line reactive power compensation schemes for unbalanced three phase four wire distribution feeders. IEEE Transactions on Power Delivery, 8(4), 1958-1965. doi:10.1109/61.248308Otto, R. A., Putman, T. H., & Gyugyi, L. (1978). Principles and Applications of Static, Thyristor-Controlled Shunt Compensators. IEEE Transactions on Power Apparatus and Systems, PAS-97(5), 1935-1945. doi:10.1109/tpas.1978.354690Origa de Oliveira, L. C., Barros Neto, M. C., & de Souza, J. B. (s. f.). Load compensation in four-wire electrical power systems. PowerCon 2000. 2000 International Conference on Power System Technology. Proceedings (Cat. No.00EX409). doi:10.1109/icpst.2000.898206Li, E., Sheng, W., Wang, X., & Wang, B. (2011). Combined compensation strategies based on instantaneous reactive power theory for reactive power compensation and load balancing. 2011 International Conference on Electrical and Control Engineering. doi:10.1109/iceceng.2011.6057765Leon-Martinez, V., & Montanana-Romeu, J. (2014). Representation of load imbalances through reactances. Application to working standards. 2014 16th International Conference on Harmonics and Quality of Power (ICHQP). doi:10.1109/ichqp.2014.6842894Czarnecki, L. S., & Haley, P. M. (2015). Unbalanced Power in Four-Wire Systems and Its Reactive Compensation. IEEE Transactions on Power Delivery, 30(1), 53-63. doi:10.1109/tpwrd.2014.2314599Czarnecki, L. S. (1989). Reactive and unbalanced currents compensation in three-phase asymmetrical circuits under nonsinusoidal conditions. IEEE Transactions on Instrumentation and Measurement, 38(3), 754-759. doi:10.1109/19.32187Czarnecki, L. S. (1988). Orthogonal decomposition of the currents in a 3-phase nonlinear asymmetrical circuit with a nonsinusoidal voltage source. IEEE Transactions on Instrumentation and Measurement, 37(1), 30-34. doi:10.1109/19.2658Pană, A., Băloi, A., & Molnar-Matei, F. (2018). From the Balancing Reactive Compensator to the Balancing Capacitive Compensator. Energies, 11(8), 1979. doi:10.3390/en1108197

Compensation of Reactive Power and Unbalanced Power in Three-Phase Three-Wire Systems Connected to an Infinite Power Network

[EN] The compensation of an electrical system from passive compensators mainly focuses on linear systems where the consumption of charges does not vary significantly over time. In three-phase three-wire systems, when the network voltages are unbalanced, negative-sequence voltages and currents appear, which can significantly increase the total apparent power supplied by the network. This also increases the network losses. This paper presents a method for calculating the compensation of the positive-sequence reactive power and unbalanced powers caused by the negative-sequence line currents using reactive elements (coils and/or capacitors). The compensation is applied to three-phase three-wire linear systems with unbalanced voltages and loads, which are connected to an infinite power network. The method is independent of the load characteristics, where only the line-to-line voltages and line currents, at the point where compensation is desired, need to be known in advance. The solution obtained is optimal, and the system observed from the network behaves as one that only consumes the active power required by a load with a fully balanced current system. To understand the proposed method and demonstrate its validity, a case study of a three-phase three-wire linear system connected to an infinite power network with unbalanced voltages and currents is conducted.This work is supported by the Spanish Ministry of Science, Innovation and Universities (MICINN) and the European Regional Development Fund (ERDF) under Grant RTI2018-100732-B-C21.Blasco Espinosa, PA.; Montoya-Mira, R.; Diez-Aznar, J.; Montoya Villena, R.; Reig-Pérez, MJ. (2019). Compensation of Reactive Power and Unbalanced Power in Three-Phase Three-Wire Systems Connected to an Infinite Power Network. Applied Sciences. 10(1):1-17. https://doi.org/10.3390/app10010113S117101Emanuel, A. E. (1993). On the definition of power factor and apparent power in unbalanced polyphase circuits with sinusoidal voltage and currents. IEEE Transactions on Power Delivery, 8(3), 841-852. doi:10.1109/61.252612Willems, J. L. (2004). Reflections on Apparent Power and Power Factor in Nonsinusoidal and Polyphase Situations. IEEE Transactions on Power Delivery, 19(2), 835-840. doi:10.1109/tpwrd.2003.823182Emanuel, A. E. (1999). Apparent power definitions for three-phase systems. IEEE Transactions on Power Delivery, 14(3), 767-772. doi:10.1109/61.772313Czarnecki, L. S. (1994). Misinterpretations of some power properties of electric circuits. IEEE Transactions on Power Delivery, 9(4), 1760-1769. doi:10.1109/61.329509Kersting, W. H. (2001). Causes and effects of unbalanced voltages serving an induction motor. IEEE Transactions on Industry Applications, 37(1), 165-170. doi:10.1109/28.903142Pillay, P., & Manyage, M. (2006). Loss of Life in Induction Machines Operating With Unbalanced Supplies. IEEE Transactions on Energy Conversion, 21(4), 813-822. doi:10.1109/tec.2005.853724Poblador, M. L. A., & Lopez, G. A. R. (2013). Power calculations in nonlinear and unbalanced conditions according to IEEE Std 1459-2010. 2013 Workshop on Power Electronics and Power Quality Applications (PEPQA). doi:10.1109/pepqa.2013.6614957Langella, R., Testa, A., & Emanuel, A. E. (2012). Unbalance Definition for Electrical Power Systems in the Presence of Harmonics and Interharmonics. IEEE Transactions on Instrumentation and Measurement, 61(10), 2622-2631. doi:10.1109/tim.2012.2209909Kukačka, L., Zissis, G., Kolář, M., Dupuis, P., & Kraus, J. (2016). Review of AC power theories under stationary and non-stationary, clean and distorted conditions. IET Generation, Transmission & Distribution, 10(1), 221-231. doi:10.1049/iet-gtd.2015.0713Chicco, G., Postolache, P., & Toader, C. (2007). Analysis of Three-Phase Systems With Neutral Under Distorted and Unbalanced Conditions in the Symmetrical Component-Based Framework. IEEE Transactions on Power Delivery, 22(1), 674-683. doi:10.1109/tpwrd.2006.887095Paap, G. C. (2000). Symmetrical components in the time domain and their application to power network calculations. IEEE Transactions on Power Systems, 15(2), 522-528. doi:10.1109/59.867135Czarnecki, L. S. (1992). Minimisation of unbalanced and reactive currents in three-phase asymmetrical circuits with nonsinusoidal voltage. IEE Proceedings B Electric Power Applications, 139(4), 347. doi:10.1049/ip-b.1992.0041San-Yi Lee, & Chi-Jui Wu. (1993). On-line reactive power compensation schemes for unbalanced three phase four wire distribution feeders. IEEE Transactions on Power Delivery, 8(4), 1958-1965. doi:10.1109/61.248308Czarnecki, L. S. (1994). Supply and loading quality improvement in sinusoidal power systems with unbalanced loads supplied with asymmetrical voltage. Archiv für Elektrotechnik, 77(3), 169-177. doi:10.1007/bf01573892Sainz, L., Caro, M., & Caro, E. (2009). Analytical Study of the Series Resonance in Power Systems With the Steinmetz Circuit. IEEE Transactions on Power Delivery, 24(4), 2090-2098. doi:10.1109/tpwrd.2009.2028790Otto, R. A., Putman, T. H., & Gyugyi, L. (1978). Principles and Applications of Static, Thyristor-Controlled Shunt Compensators. IEEE Transactions on Power Apparatus and Systems, PAS-97(5), 1935-1945. doi:10.1109/tpas.1978.354690Czarnecki, L. S. (1989). Reactive and unbalanced currents compensation in three-phase asymmetrical circuits under nonsinusoidal conditions. IEEE Transactions on Instrumentation and Measurement, 38(3), 754-759. doi:10.1109/19.32187Czarnecki, L. S. (1988). Orthogonal decomposition of the currents in a 3-phase nonlinear asymmetrical circuit with a nonsinusoidal voltage source. IEEE Transactions on Instrumentation and Measurement, 37(1), 30-34. doi:10.1109/19.2658Willems, J. L. (2007). Current compensation in three-phase power systems. European Transactions on Electrical Power, 3(1), 61-66. doi:10.1002/etep.4450030110Origa de Oliveira, L. C., Barros Neto, M. C., & de Souza, J. B. (s. f.). Load compensation in four-wire electrical power systems. PowerCon 2000. 2000 International Conference on Power System Technology. Proceedings (Cat. No.00EX409). doi:10.1109/icpst.2000.898206Jeon, S.-J., & Willems, J. L. (2011). Reactive power compensation in a multi-line system under sinusoidal unbalanced conditions. International Journal of Circuit Theory and Applications, 39(3), 211-224. doi:10.1002/cta.629Leon-Martinez, V., & Montanana-Romeu, J. (2014). Representation of load imbalances through reactances. Application to working standards. 2014 16th International Conference on Harmonics and Quality of Power (ICHQP). doi:10.1109/ichqp.2014.6842894Czarnecki, L. S., & Haley, P. M. (2015). Unbalanced Power in Four-Wire Systems and Its Reactive Compensation. IEEE Transactions on Power Delivery, 30(1), 53-63. doi:10.1109/tpwrd.2014.231459

Hypercube matrix computation task

A major objective of the Hypercube Matrix Computation effort at the Jet Propulsion Laboratory (JPL) is to investigate the applicability of a parallel computing architecture to the solution of large-scale electromagnetic scattering problems. Three scattering analysis codes are being implemented and assessed on a JPL/California Institute of Technology (Caltech) Mark 3 Hypercube. The codes, which utilize different underlying algorithms, give a means of evaluating the general applicability of this parallel architecture. The three analysis codes being implemented are a frequency domain method of moments code, a time domain finite difference code, and a frequency domain finite elements code. These analysis capabilities are being integrated into an electromagnetics interactive analysis workstation which can serve as a design tool for the construction of antennas and other radiating or scattering structures. The first two years of work on the Hypercube Matrix Computation effort is summarized. It includes both new developments and results as well as work previously reported in the Hypercube Matrix Computation Task: Final Report for 1986 to 1987 (JPL Publication 87-18)

Vectorial formalism for analysis and design of polyphase synchronous machines

A vectorial formalism for analysis and design of polyphase synchronous machines without reluctance and saturation effects is described. We prove the equivalence of such a machine with a set of magnetically independent machines, which are electrically and mechanically coupled. Specific problems of polyphase machines can thus be favorably analyzed with this concept. Rules of conception and constraints on electric supply can be deduced. Moreover the vectorial approach, which generalizes the complex phasor method, can also be used to control n-leg Voltage Source Inverters. This methodology is applied to 3-phase and 6- phase synchronous machines