Application of the Moment-SOS Approach to Global Optimization of the OPF Problem
By Cédric Josz, Jean Maeght, Patrick Panciatici, Jean Charles Gilbert. IEEE Transactions on Power Systems, 2013
122 citations recorded by the source corpus.
Finding a global solution to the optimal power flow (OPF) problem is difficult due to its nonconvexity. A convex relaxation in the form of semidefinite programPming (SDP) has attracted much attention lately as it yields a global solution in several practical cases. However, it does not in all cases, and such cases have been documented in recent publications. This paper presents another SDP method known as the moment-sos (sum of squares) approach, which generates a sequence that converges towards a global solution to the OPF problem at the cost of higher runtime. Our finding is that in the small examples where the previously studied SDP method fails, this approach finds the global solution. The higher cost in runtime is due to an increase in the matrix size of the SDP problem, which can vary from one instance to another. Numerical experiment shows that the size is very often a quadratic function of the number of buses in the network, whereas it is a linear function of the number of buses in the case of the previously studied SDP method.
Subfields: Electrical and Electronic Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/29fe3d67073cd495b383abfe9bbe6cc842939da2
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In Electrical and Electronic Engineering
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In Numerical Analysis
Citations in the corpus
- A Successive Linear Programming Approach to Solving the IV-ACOPF (2016, background): “[34] propose moment relaxations in order to obtain tighter lower bounds.”
- Strong SOCP Relaxations for the Optimal Power Flow Problem (2015, methodology): “This approach is used in Josz et al. (2015) to globally solve small-size problems, and is also used in Molzahn and Hiskens (2015) to obtain tighter lower bounds for larger problems of 300-bus systems.”
- Bound Tightening for the Alternating Current Optimal Power Flow Problem (2016, background): “In cases with positive duality gap, more advanced techniques must be developed to search for global optimal solutions, such as higher moment relaxations [19], [20].”
- Conic relaxations of the unit commitment problem (2017, methodology): “[38] design a hierarchy of SDP-based models to find a globally optimal solution of the OPF problem.”
- Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow (2014, methodology): “In this case, an alternative approach would be to use an hierarchy for SDPs [13] as suggested in [14].”