Transient stability constrained optimal power flow applied to distribution systems with synchronous generators
Keywords:
Active and reactive power dispatch, distributed synchronous generators, distribution systems, transient stability, transient stability constrained optimal power flowAbstract
This paper proposes a Transient Stability Constrained Optimal Power Flow (TSC-OPF) formulation in order to calculate the optimum operating point of synchronous generators in distribution networks, in terms of dispatch of their active and reactive powers. However, the problem is complex due to the high number of constraints and variables, as well as, the presence of nonlinear constraints. To circumvent these adversities, an optimization problem is proposed in this paper with the application of a set of mathematical approximations in the constraints of the active and reactive power balance equations. In addition, an approximation is explored in the swing equation of synchronous generators belonging to a group of coherent machines, particularly regarding the active power injection from the generators. The proposed TSC-OPF is tested in a 31-bus radial distribution system with two and four generators. The results show that the running time to solve the proposed optimization problem with approximations becomes smaller when compared to the time to solve it without approximations.
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COPEL, "NTC 905100: Acesso de geração distribuída ao sistema da COPEL (com comercialização de energia)," Curitiba- PR, 2017.
S. Abhyankar, G. Geng, M. Anitescu, X. Wang and V. Dinavahi, "Solution techniques for transient stability-constrained optimal power flow – Part I," IET Generation, Transmission & Distribution, vol. 11, no. 12, pp. 3177-3185, 2017.
Y. Oubbati, S. Arif and M. Abido, "Improved PSO Applied to the Optimal Power Flow with Transient Stability Constraints," Journal of Electrical Systems, vol. 12, pp. 672-686, December 2016.
U. Kilic and K. Ayan, "Transient stability constrained optimal power flow solution of ac-dc systems using genetic algotithm," 3rd International Conference on Electric Power and Energy Conversion Systems, pp. 1-6, October 2013.
Y. Yang, W. Liu, J. Deng, H. Liu, H. Wei and T. Wang, "A parallel approach for multi-contingency transient stability constrained optimal power flow," 2017 IEEE Power & Energy Society General Meeting, 1-5 2017.
P. Ledesma, I. A. Calle, E. D. Castronuovo and F. Arredondo, "Multi-contingency TSCOPF based on full-system simulation," IET Generation, Transmission & Distribution, vol. 11, no. 1, pp. 64-72, 2017.
P. F. Liu, H. Wei, B. Li and B. Zhou, "Transient stability constrained optimal power flow using 2-stage diagonally implicit Runge-Kutta method," 2013 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC), pp. 1-5, 2013.
X. Xia and H. Wei, "Transient Stability Constrained Optimal Power Flow Based on Second-Order Differential Equations," Procedia Engineering, vol. 29, pp. 874-878, 2012.
K. Fuchs, R. Kuiava and T. S. P. Fernandes, "Optimal operation of distribution networks with synchronous generators via transient stability constrained optimal power flow," 2015 IEEE Power & Energy Society General Meeting, pp. 1-5, 2015.
K. Fuchs, R. Kuiava, T. S. P. Fernandes, P. A. B. Block and R. A. S. Benedito, "Flow Based on Multi-time Scale Power System Models," Journal of Control, Automation and Electrical Systems, vol. 28, pp. 418-427, 2017.
P. L. C. Wieler, R. Kuiava and W. F. S. Souza, "Transient stability constrained optimal power flow based on trajectory sensitivity for power dispatch of distributed synchronous generators," IEEE Latin America Transactions, vol. 18, no. 7, pp. 1247-1254, 2020.
R. Podmore, "Identification of Coherent Generators for Dynamic Equivalents," IEEE Transactions on Power Apparatus and Systems, Vols. PAS-97, no. 4, pp. 1344-1354, 1978.
X. Tu, L. Dessaint and I. Kamwa, "Fast approach for transient stability constrained optimal power flow based on dynamic reduction method," IET Generation, Transmission & Distribution, vol. 8, no. 7, pp. 1293-1305, 2014.
P. K. Naik, A. Qurechi and N. K. Nair, "Identification of coherent generator groups in power system networks with windfarms," AUPEC, pp. 1-5, 2011.
S. Chittora and S. N. Singh, "Coherency based dynamic equivalencing of electric power system," 2014 Eighteenth National Power Systems Conference (NPSC), pp. 1-6, 2014.
R. S. Rashedur, H. M. Yeakub and A. M. Sekendar, "A new approach to coherency identification in large multi-machine power system," 2012 7th International Conference on Electrical and Computer Engineering, pp. 587-590, 2012.
P. Kundur, J. Paserba, V. Ajjarapu, G. Andersson and A. Bose, "Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions," IEEE Transactions on Power Systems, vol. 19, no. 3, pp. 1387-1401, August 2004.
P. Kundur, Power System Stability and Control, New York - NY: McGraw, 1994.
N. G. Bretas and L. F. C. Alberto, Estabilidade Transitória em Sistemas Eletroenergéticos, 1ª ed., São Carlos, SP: EESC/USP Projeto REENGE, 2000.
K. Fuchs, R. Kuiava, T. S. P. Fernandes, P. A. B. Block and R. A. S. Benedito, "Transient Stability Constrained Optimal Power Flow Based on Multi-time Scale Power System Models," J Control Autom Electr Syst, vol. 28, pp. 418-427, 2017.
F. Arredondo, E. DanielCastronuovo, P. Ledesma and Z. Leonowicz, "Comparative Implementation of Numerical Integration Methods for Transient Stability Constrained Optimal Power Flow," 2018 IEEE International Conference on Environment and Electrical Engineering and 2018 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe), pp. 1-6, 2018.
R. Zarate-Minano, T. Van Cutsem , F. Milano and A. J. Conejo, "Securing Transient Stability Using Time-Domain Simulations Within an Optimal Power Flow," IEEE Transactions on Power Systems, vol. 25, no. 1, pp. 243-253, 2010.
A. J. Monticelli, Fluxo de carga em redes de energia elétrica, São Paulo: Edgard Blucher, 1983.
D. K. Molzahn and I. A. Hiskens, "A Survey of Relaxations and Approximations of the Power Flow Equations," Now Foundations and Trends, 2019.
H. Yuan, F. Li, Y. Wei and J. Zhu, "Novel Linearized Power Flow and Linearized OPF Models for Active Distribution Networks With Application in Distribution LMP," IEEE Transactions on Smart Grid, vol. 9, no. 1, pp. 438-448, January 2018.
J. Machowski, "Dynamic equivalents for transient stability studies of electrical power systems," International Journal of Electrical Power & Energy Systems, vol. 7, no. 4, pp. 215-224, 1985.
K. Verma and K. R. Niazi, "A coherency based generator rescheduling for preventive control of transient stability in power systems," International Journal of Electrical Power & Energy Systems, vol. 45, no. 1, pp. 10-18, 2013.
M. H. Haque, "Hybrid method of determining the transient stability margin of a power system," IEEE Generation, Transmission and Distribution, vol. 143, no. 1, pp. 27-32, 1996.
M. H. Haque, "Novel method of finding the first swing stability margin of a power system from time domain simulation," IEE Proceedings - Generation, Transmission and Distribution, vol. 143, no. 5, pp. 413-419, 1996.
R. H. Salim, R. Kuiava, R. A. Ramos and N. G. Bretas, "Impact of power factor regulation on small-signal stability of power distribution systems with distributed synchronous generators," European Transactions on Electrical Power, vol. 21, pp. 1923-1940, 2011.
IEEE, "IEEE Standard for Cylindrical-Rotor 50 Hz and 60 Hz Synchronous Generators Rated 10 MVA and Above," IEEE Std C50.13-2014 (Revision of IEEE Std C50.13-2005), pp. 1-63, 2014.
IEEE, "IEEE Standard for Salient-Pole 50 Hz and 60 Hz Synchronous Generators and Generator/Motors for Hydraulic Turbine Applications Rated 5 MVA and Above," IEEE Std C50.12-2005 (Previously designated as ANSI C50.12-1982), pp. 1-45, 2006.
IEEE, "IEEE Guide for Synchronous Generator Modeling Practices and Parameter Verification with Applications in Power System Stability Analyses," 2020.
F. J. Lachovicz et al., "Ponderação de Critérios de Otimização Utilizados em Fluxo de Potência Ótimo Dinâmico que Realiza Despacho de Geração Hidrotérmico Mensal Discretizado por Patamares de Carga," Sociedade Brasileira de Automática, vol. 1, n° 1, 2020.
M. N. Faqiry, L. Edmonds e H. Wu, “Distribution LMP-based Transactive Day-ahead Market with Variable Renewable Generation”. Cornell University, 2019.
B. Wang et al., “Three-phase DLMP model based on linearized power flow for distribution with application to DER benefit studies”. International Journal of Electrical Power and Energy Systems, volume 130, 2021.
D. M. B. de Siqueira, Otimização da operação de geradores síncronos distribuídos em redes de distribuição via fluxo de potência ótimo com restrições de estabilidade transitória angular. Universidade Federal do Paraná (UFPR). Dissertação de mestrado. 2021.
