Abstract: A method determines a power flow of a power grid by optimizing an objective function representing an operation of the power grid using a spatial branch and bound (BB) framework for determining iteratively upper and lower bounds of the objective function. During the optimization, the lower bounds are determined using a semi-definite programming (SDP) relaxation of an optimal power flow (OPF) problem.

Abstract: Power flow in an electric power network is optimized during multiple time periods of operation of the electric power network by solving an optimization problem represented by an objective function by first initializing variables and constraints of a branch and bound (BB) tree, wherein nodes in the BB tree represent feasible regions of the optimization problem. Upper and lower bounds on the objective function are solved using the BB tree. A lowest upper bound and a lowest upper bound are updated. If difference between the lowest lower bound and the lowest upper bound is less than a threshold, the power flow is outputted based on the lowest lower bound and the lowest upper bound.

Abstract: A power flow problem (OPF) in an electric power network is globally optimized using a branch and bound tree of nodes connected by edges. The BB initially includes at least a root node, and each node represents a feasible region of limits on voltages and powers. An upper bound on the OPF problem is solved for selected nodes using nonlinear programming, while a lower bound is solved using a convex relaxation. The lowest upper and lower bounds are updated using the current upper and lower bound. If a difference between the lowest upper and lowest lower bound is less than a threshold, then outputting the voltages and the powers for the electric power network as represented by the feasibility region for the selected node. Otherwise, the feasible region of the node is partitioned to replace the node. The process is repeated until the tree is empty.

Abstract: A method determines a power flow of a power grid by optimizing an objective function representing an operation of the power grid using a spatial branch and bound (BB) framework for determining iteratively upper and lower bounds of the objective function. During the optimization, the lower bounds are determined using a semi-definite programming (SDP) relaxation of an optimal power flow (OPF) problem.

Abstract: A power flow problem (OPF) in an electric power network is globally optimized using a branch and bound tree of nodes connected by edges. The BB initially includes at least a root node, and each node represents a feasible region of limits on voltages and powers. An upper bound on the OPF problem is solved for selected nodes using nonlinear programming, while a lower bound is solved using a convex relaxation. The lowest upper and lower bounds are updated using the current upper and lower bound. If a difference between the lowest upper and lowest lower bound is less than a threshold, then outputting the voltages and the powers for the electric power network as represented by the feasibility region for the selected node. Otherwise, the feasible region of the node is partitioned to replace the node. The process is repeated until the tree is empty.