39 research outputs found
Optimal Placement of Distributed Energy Storage in Power Networks
We formulate the optimal placement, sizing and control of storage devices in
a power network to minimize generation costs with the intent of load shifting.
We assume deterministic demand, a linearized DC approximated power flow model
and a fixed available storage budget. Our main result proves that when the
generation costs are convex and nondecreasing, there always exists an optimal
storage capacity allocation that places zero storage at generation-only buses
that connect to the rest of the network via single links. This holds regardless
of the demand profiles, generation capacities, line-flow limits and
characteristics of the storage technologies. Through a counterexample, we
illustrate that this result is not generally true for generation buses with
multiple connections. For specific network topologies, we also characterize the
dependence of the optimal generation cost on the available storage budget,
generation capacities and flow constraints.Comment: 15 pages, 9 figures, generalized result to include line losses in
Section 4
Equivalent relaxations of optimal power flow
Several convex relaxations of the optimal power flow (OPF) problem have
recently been developed using both bus injection models and branch flow models.
In this paper, we prove relations among three convex relaxations: a
semidefinite relaxation that computes a full matrix, a chordal relaxation based
on a chordal extension of the network graph, and a second-order cone relaxation
that computes the smallest partial matrix. We prove a bijection between the
feasible sets of the OPF in the bus injection model and the branch flow model,
establishing the equivalence of these two models and their second-order cone
relaxations. Our results imply that, for radial networks, all these relaxations
are equivalent and one should always solve the second-order cone relaxation.
For mesh networks, the semidefinite relaxation is tighter than the second-order
cone relaxation but requires a heavier computational effort, and the chordal
relaxation strikes a good balance. Simulations are used to illustrate these
results.Comment: 12 pages, 7 figure
Optimal Placement of Distributed Energy Storage in Power Networks
We formulate the optimal placement, sizing and control of storage devices in a power network to minimize generation costs with the intent of load shifting. We assume deterministic demand, a linearized DC approximated power flow model and a fixed available storage budget. Our main result proves that when the generation costs are convex and nondecreasing, there always exists an optimal storage capacity allocation that places zero storage at generation-only buses that connect to the rest of the network via single links. This holds regardless of the demand profiles, generation capacities, line-flow limits and characteristics of the storage technologies. Through a counterexample, we illustrate that this result is not generally true for generation buses with multiple connections. For specific network topologies, we also characterize the dependence of the optimal generation cost on the available storage budget, generation capacities and flow constraints