Abstract
Monitoring an electrical network is an important and challenging task. Phasor measurement units are measurement devices that can be used for a state estimation of this network. In this paper we consider a PMU placement problem without conventional measurements and with zero injection nodes for a full observability of the network. We propose two new approaches to model this problem, which take into account a propagation rule based on Ohm’s and Kirchoff’s law. The natural binary linear programming description models an iterative observability process. We remove the iteration by reformulating its fixed point conditions to a bilevel program, which we then further reformulate to a single-level mixed-integer linear program. We also present a bilevel algorithm to solve directly the proposed bilevel model. We implemented and tested our models and algorithm: the results show that the bilevel algorithm is better in terms of running time and size of instances which can be solved.
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Acknowledgments
This work was carried out as part of the SOGRID project (www.so-grid.com), co-funded by the French agency for Environment and Energy Management (ADEME) and developed in collaboration between participating academic and industrial partners.
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Toubaline, S., Poirion, PL., D’Ambrosio, C., Liberti, L. (2015). Observing the State of a Smart Grid Using Bilevel Programming. In: Lu, Z., Kim, D., Wu, W., Li, W., Du, DZ. (eds) Combinatorial Optimization and Applications. Lecture Notes in Computer Science(), vol 9486. Springer, Cham. https://doi.org/10.1007/978-3-319-26626-8_27
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DOI: https://doi.org/10.1007/978-3-319-26626-8_27
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