Abstract
This article proposes a continuous-time modeling approach to calculate the spatio-temporal value of energy storage (ES) devices in power transmission networks. More specifically, this article formulates the dynamic operation of ES devices in power transmission networks as a continuous-time optimal control problem, where the Lagrange multiplier trajectories of nodal power balance constraints are defined as continuous-time locational marginal prices (LMPs). In addition, the adjoint functions associated with ES state equations are calculated in closed-form, which define the locational value of stored energy (LVSE) in ES devices. The notion of LVSE is, then, leveraged to define incremental charging utility and discharging cost rates of ES devices, which pass on the spatio-temporal values of ES devices to the continuous-time LMPs. The numerical results of implementing the proposed continuous-time model on a test 3-bus power system and the IEEE-Reliability Test System highlight its effectiveness in calculating the value of ES energy shifting and congestion relief services in transmission networks.
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