TY - CONF
T1 - A bound on the minimum rank of solutions to sparse linear matrix equations
T2 - 2016 American Control Conference (ACC)
Y1 - 2016/08//
SP - 6501
EP - 6506
A1 - Raphael Louca
A1 - Subhonmesh Bose
A1 - Eilyan Bitar
KW - RM14-002
AB - We derive a new upper bound on the minimum rank of matrices belonging to an affine slice of the positive semidefinite cone, when the affine slice is defined according to a system of sparse linear matrix equations. It is shown that a feasible matrix whose rank is no greater than said bound can be computed in polynomial time. The bound depends on both the number of linear matrix equations and their underlying sparsity pattern. For certain problem families, this bound is shown to improve upon well known bounds in the literature. Several examples are provided to illustrate the efficacy of this bound.
JF - 2016 American Control Conference (ACC)
PB - IEEE
CY - Boston, MA, USA
DO - 10.1109/ACC.2016.7526693
ER -
TY - CONF
T1 - Variability and the Locational Marginal Value of Energy Storage
T2 - 2014 IEEE 53rd Annual Conference on Decision and Control (CDC)
Y1 - 2014/12//
SP - 3259
EP - 3265
A1 - Subhonmesh Bose
A1 - Eilyan Bitar
KW - energy storage
KW - Locational marginal value
KW - reliability and markets
KW - RM11-006
AB - Given a stochastic net demand process evolving over a transmission-constrained power network, we consider the system operator's problem of minimizing the expected cost of generator dispatch, when it has access to spatially distributed energy storage resources. We show that the expected benefit of storage derived under the optimal dispatch policy is concave and non-decreasing in the vector of energy storage capacities. Thus, the greatest marginal value of storage is derived at small installed capacities. For such capacities, we provide an upper bound on the locational (nodal) marginal value of storage in terms of the variation of the shadow prices of electricity at each node. In addition, we prove that this upper bound is tight, when the cost of generation is spatially uniform and the network topology is acyclic. These formulae not only shed light on the correct measure of statistical variation in quantifying the value of storage, but also provide computationally tractable tools to empirically calculate the locational marginal value of storage from net demand time series data.
JF - 2014 IEEE 53rd Annual Conference on Decision and Control (CDC)
PB - IEEE
CY - Los Angeles, CA, USA
SN - 978-1-4799-7746-8
DO - 10.1109/CDC.2014.7039893
ER -