Equivalent circuit and calculation of unbalanced power in three-wire three-phase linear networks

[EN] For analysis of three-wire three-phase linear systems, the transformations wye-delta and delta-wye from theorem of Kennelly are used. These transformations can be applied to balanced systems but not to unbalanced systems. This is due to the fact that zero-sequence voltages or zero-sequence currents are present in these types of connections. This modifies the value of the unbalance power in the load with respect to the generator. These zero-sequence voltages and currents that appear in generators and loads are not transferred over the network. The zero-sequence voltage in a delta-connected load and the zero-sequence current that is obtained using theorem of Kennelly in a star-connected load, or vice versa, cause different imbalance effects. Here, the equivalent circuit for any point of the system is developed. The impedances of the equivalent circuit in any node are calculated using line-to-line voltages and line currents. This equivalent circuit incorporates all energetic phenomena, including the unbalance of all downstream loads. For its verification, the phasor unbalance power is used.Montoya-Mira, R.; Diez-Aznar, J.; Blasco Espinosa, PA.; Montoya Villena, R. (2018). Equivalent circuit and calculation of unbalanced power in three-wire three-phase linear networks. IET Generation Transmission & Distribution. 12(7):1466-1473. https://doi.org/10.1049/iet-gtd.2017.0670S14661473127Emanuel, 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:10.1109/61.252612Jeon, S.-J. (2005). Definitions of Apparent Power and Power Factor in a Power System Having Transmission Lines With Unequal Resistances. IEEE Transactions on Power Delivery, 20(3), 1806-1811. doi:10.1109/tpwrd.2005.848658Czarnecki, L. S. (1994). Misinterpretations of some power properties of electric circuits. IEEE Transactions on Power Delivery, 9(4), 1760-1769. doi:10.1109/61.329509Willems, 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:10.1109/61.772313Jayatunga, U., Ciufo, P., Perera, S., & Agalgaonkar, A. P. (2015). Deterministic methodologies for the quantification of voltage unbalance propagation in radial and interconnected networks. IET Generation, Transmission & Distribution, 9(11), 1069-1076. doi:10.1049/iet-gtd.2014.0661Von Jouanne, A., & Banerjee, B. (2001). Assessment of voltage unbalance. IEEE Transactions on Power Delivery, 16(4), 782-790. doi:10.1109/61.956770Viswanadha Raju, G. K., & Bijwe, P. R. (2008). Efficient reconfiguration of balanced and unbalanced distribution systems for loss minimisation. IET Generation, Transmission & Distribution, 2(1), 7. doi:10.1049/iet-gtd:20070216Kersting, 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.2005.853724Emanuel, A. E. (1998). The Buchholz-Goodhue apparent power definition: the practical approach for nonsinusoidal and unbalanced systems. IEEE Transactions on Power Delivery, 13(2), 344-350. doi:10.1109/61.660900Leon-Martinez, V., Montanana-Romeu, J., & Palazon-Garcia, J. M. (2011). Unbalance Compensator for Three-Phase Industrial Installations. IEEE Latin America Transactions, 9(5), 808-814. doi:10.1109/tla.2011.6030993Reginatto, R., & Ramos, R. A. (2014). On electrical power evaluation in dq coordinates under sinusoidal unbalanced conditions. IET Generation, Transmission & Distribution, 8(5), 976-982. doi:10.1049/iet-gtd.2013.0532Diez, J. M., Blasco, P. A., & Montoya, R. (2016). Formulation of phasor unbalance power: application to sinusoidal power systems. IET Generation, Transmission & Distribution, 10(16), 4178-4186. doi:10.1049/iet-gtd.2016.0730Marzband, M., Moghaddam, M. M., Akorede, M. F., & Khomeyrani, G. (2016). Adaptive load shedding scheme for frequency stability enhancement in microgrids. Electric Power Systems Research, 140, 78-86. doi:10.1016/j.epsr.2016.06.03

A probabilistic method for the operation of three-phase unbalanced active distribution networks

YesThis paper proposes a probabilistic multi-objective optimization method for the operation of three-phase distribution networks incorporating active network management (ANM) schemes including coordinated voltage control and adaptive power factor control. The proposed probabilistic method incorporates detailed modelling of three-phase distribution network components and considers different operational objectives. The method simultaneously minimizes the total energy losses of the lines from the point of view of distribution network operators (DNOs) and maximizes the energy generated by photovoltaic (PV) cells considering ANM schemes and network constraints. Uncertainties related to intermittent generation of PVs and load demands are modelled by probability density functions (PDFs). Monte Carlo simulation method is employed to use the generated PDFs. The problem is solved using ɛ-constraint approach and fuzzy satisfying method is used to select the best solution from the Pareto optimal set. The effectiveness of the proposed probabilistic method is demonstrated with IEEE 13- and 34- bus test feeders