We propose two algorithms for the solution of the Optimal Power Flow (OPF) problem to global optimality. The algorithms are based on the spatial branch and bound framework with lower bounds on the optimal objective function value calculated by solving either the Lagrangian dual or the semidefinite programming (SDP) relaxation. We show that this approach can solve to global optimality the general form of the OPF problem including: generation power bounds, apparent and real power line limits, voltage limits and thermal loss limits. The approach makes no assumption on the topology or resistive connectivity of the network. This work also removes some of the restrictive assumptions of the SDP approaches [5]. We present the performance of the algorithms on a number of standard IEEE systems, which are known to have a zero duality gap. We also make parameter perturbations to the test cases that result in solutions that fail to satisfy the SDP rank condition and have a non-zero duality gap. The proposed branch and bound algorithms are able to solve these cases to global optimality. Allerton Confernce on Communication, Control and Computing (Allerton)This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. [5]. We present the performance of the algorithms on a number of standard IEEE systems, which are known to have a zero duality gap. We also make parameter perturbations to the test cases that result in solutions that fail to satisfy the SDP rank condition and have a non-zero duality gap. The proposed branch and bound algorithms are able to solve these cases to global optimality.

No abstract

No abstract

In this work, we extend the algorithm proposed in [1] to solve multi-period optimal power flow (MOPF) problems to global optimality. The multi-period version of the OPF is time coupled due to the integration of storage systems into the network, and ramp constraints on the generators. The global optimization algorithm is based on the spatial branch and bound framework with lower bounds on the optimal objective function value calculated by solving a semidefinite programming (SDP) relaxation of the MOPF. The proposed approach does not assume convexity and is more general than the ones presented previously for the solution of MOPF. We present a case study of the IEEE 57 bus instance with a time varying demand profile. The integration of storage in the network helps to satisfy loads during high demands and the ramp constraints ensure smooth generation profiles. The SDP relaxation does not satisfy the rank condition, and our optimization algorithm is able to guarantee global optimality within reasonable computational time. American Control Conference (ACC)This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Abstract-In this work, we extend the algorithm proposed in [1] to solve multi-period optimal power flow (MOPF) problems to global optimality. The multi-period version of the OPF is time coupled due to the integration of storage systems into the network, and ramp constraints on the generators. The global optimization algorithm is based on the spatial branch and bound framework with lower bounds on the optimal objective function value calculated by solving a semidefinite programming (SDP) relaxation of the MOPF. The proposed approach does not assume convexity and is more general than the ones presented previously for the solution of MOPF. We present a case study of the IEEE 57 bus instance with a time varying demand profile. The integration of storage in the network helps to satisfy loads during high demands and the ramp constraints ensure smooth generation profiles. The SDP relaxation does not satisfy the rank condition, and our optimization algorithm is able to guarantee global optimality within reasonable computational time.

This paper addresses industrial gases supply chains involving multiple products at multiple plants that must be coordinated with multiple depot-truck-routes in order to satisfy customer demands. The full-space optimization problem corresponds to a large-scale mixed-integer linear programming model (MILP). To solve large-scale industrial problems, this paper proposes a rolling horizon approach with two aggregation strategies for solving the smaller subproblems. The first one relies on the linear programming (LP) relaxation for which the binary variables (complicating variables) of the distribution problem are treated as continuous, while the second one uses a novel tailored model for the distribution side constraints that leads to improved solutions. A real case study of an industrial gases supply chain has been addressed obtaining good results in both objective value and with lower computational effort compared with the full-space solution. The extension to longer time horizons through a receding horizon is also considered.