The excessive computational burden encountered in power market analysis has necessitated the need for obtaining reduced equivalent networks that preserve flows along certain selected lines called tie lines in a larger power system. In this context, the concept of PTDF (Power Transfer Distribution Factors) matrix was introduced and studied using the DC flow model. On the other hand, the concept of modified circuit matrix of a multi-port resistance network was introduced by Thulasiraman and Murti. In this paper we draw attention to certain limitations of the approach by Cheng and Overbye to determine an equivalent that preserves a PTDF matrix. We then show the equivalence of the concept of modified circuit matrix of a multi-port resistance network and the concept of the PTDF matrix under the DC flow model. We then present a generalized theory of flow preserving equivalence that is not constrained by these limitations. We give a methodology to generate a flow preserving equivalent network and demonstrate its feasibility through simulations.
References
[1]
U.S. Energy Information Administration: Energy Explained. http://www.eia.gov/energy_in_brief/article/power_grid.cfm
[2]
Sharma, D., Thulasiraman, K., Wu, D. and Jiang, J.N. (2019) A Network Science-Based k-Means++ Clustering Method for Power Systems Network Equivalence. ComputationalSocialNetworks, 6, Article No. 4. https://doi.org/10.1186/s40649-019-0064-3
[3]
Dimo, P. (1975) Nodal Analysis of Power Systems. Routledge.
Srinivasan, S., Sujeer, V. and Thulasiraman, K. (1964) A New Equivalence Technique in Linear Graph Theory. Journal of the Institution of Engineers (India), 44, No. 12.
[6]
Srinivasan, S., Sujeer, V.N. and Thulasiraman, K. (1966) Application of Equivalence Technique in Linear Graph Theory to Reduction Process in a Power System. Journal of the Institution of Engineers (India), 46, 528-554.
[7]
Housos, E., Irisarri, G., Porter, R. and Sasson, A. (1980) Steady State Network Equivalents for Power System Planning Applications. IEEETransactionsonPowerApparatusandSystems, 99, 2113-2120. https://doi.org/10.1109/tpas.1980.319789
[8]
Tinney, W.F. and Bright, J.M. (1987) Adaptive Reductions for Power Flow Equivalents. IEEETransactionsonPowerSystems, 2, 351-359. https://doi.org/10.1109/tpwrs.1987.4335132
[9]
Wang, H., Murillo-Sanchez, C.E., Zimmerman, R.D. and Thomas, R.J. (2007) On Computational Issues of Market-Based Optimal Power Flow. IEEETransactionsonPowerSystems, 22, 1185-1193. https://doi.org/10.1109/tpwrs.2007.901301
[10]
Duran, H. and Arvanitidis, N. (1972) Simplifications for Area Security Analysis: A New Look at Equivalence. IEEETransactionsonPowerApparatusandSystems, 91, 670-679. https://doi.org/10.1109/tpas.1972.293253
[11]
Cheng, X. and Overbye, T.J. (2005) PTDF-Based Power System Equivalents. IEEETransactionsonPowerSystems, 20, 1868-1876. https://doi.org/10.1109/tpwrs.2005.857013
[12]
Shi, D. and Tylavsky, D.J. (2015) A Novel Bus-Aggregation-Based Structure-Preserving Power System Equivalent. IEEETransactionsonPowerSystems, 30, 1977-1986. https://doi.org/10.1109/tpwrs.2014.2359447
[13]
Doyle, P. and Snell, J. (1984) Random Walks and Electric Networks. American Mathematical Society. https://doi.org/10.5948/upo9781614440222
[14]
Thulasiraman, K. and Murti, V. (1969) The Modified Circuit Matrix of an N-Port Network and Its Applications. IEEETransactionsonCircuitTheory, 16, 2-7. https://doi.org/10.1109/tct.1969.1082879
[15]
Swamy, M. and Thulasiraman, K. (1981) Graphs, Networks and Algorithms. Wiley.
[16]
U.S. Electricity Industry Primer. https://www.energy.gov/sites/prod/files/2015/12/f28/united-states-electricity-industry-primer.pdf
[17]
Hogan, W.W. (1997) A Market Power Model with Strategic Interaction in Electricity Networks. TheEnergyJournal, 18, 107-141. https://doi.org/10.5547/issn0195-6574-ej-vol18-no4-5
