Profit maximizing storage allocation in power grids

Abstract

Abstract-This work investigates the interaction between nodal price signals and the optimal allocation and operation of distributed energy storage systems (ESS) in alternating current (AC) power networks. We model a multi-period optimal power flow (OPF) problem with charge and discharge dynamics for energy storage collocated with load and/or generation. We then apply a convex relaxation based on semidefinite programming (SDP) and derive the storage subproblem from the Lagrangian dual. We use the storage subproblem to investigate the relationship between the storage variables and the locational marginal prices (LMPs), which are market-based price signals defined by the dual variables associated with the nodal active power flow balance. Our theoretical results prove that LMPs drive charging and discharging dynamics, and that storage is allocated and operated to maximize the storage operator's profits, i.e. minimize the system costs in a purely competitive market. We then use this framework to illustrate LMP-based storage dynamics.

Sensitivity analysis on locations of Energy Storage in power systems with wind integration

“…Ref [13] demonstrates that LMPs play a significant role in driving storage operation at low penetrations of ESS integration. In this work, we examine how LMPs are changed due to the addition of BES at different locations.…”

“…Reference [12] builds a reduced power flow model for the Pacific Northwest area to identify transmission line congestion and uses a sensitivity analysis method to find optimal locations of ESSs for reducing transmission congestion. Reference [13] applies a semidefinite programming relaxation of OPF problem to investigate the interaction between Locational Marginal Prices and location and operation of ESS in power networks with only conventional generators. According to this paper, LMP is a price parameter for resource investment and operation in competitive electricity markets, consisting of marginal unit cost, congestion cost, and cost due to losses.…”

Evaluation of Wind Power Curtailment in Active Network Management Schemes

“…Multi-period, or dynamic optimal power flow (DOPF) method was initially developed to analyze power systems dominated by hydrothermal generation [31], however this tool has been developed to analyze energy storage [32], [33] and elements of electricity markets [34]. DOPF extends the OPF to apply to multiple time periods to improve the use of energy storage in ANM systems.…”

Optimal Power flow Model with Storage and Renewable in IEEE 14 Bus test systems

“…Equation (10) captures the minimum and maximum capacity limits for storage; (11) is optionally used for setting the final value of the stored energy to a pre-specified value, which is commonly chosen equal to the initial value .EI (0) The problem given by (2)- (11) is a sparse mixed-integer linear program, where the binary variables ensure that storage operates exclusively either in the charge or discharge mode. In this respect, [13] showed that simultaneous charging and discharging will not occur at a bus if the locational marginal price (LMP) at this bus is strictly positive. Congested power networks could cause negative LMPs at some buses even if all offer curves are positive, in which case the operational cost will be reduced if consumers draw more power from the bus with the negative LMP; this is also known to appear in the classical transportation problem, where it is named the more-for-less-paradox [37].…”

“…Ref. [13] studied the relation between locational marginal prices and storage dynamics in the context of the multi-period SDP-OPF, and gave conditions under which simultaneous charging and discharging will not occur. In other multiperiod OPF applications, simultaneous charging and discharging was avoided by defining a predetermined cycle of charge/discharge per day [14]; further flexibility in scheduling the storage operation comes at the expense of solving a mixed-integer nonlinear programming formulation [15], [16], which is an NP-hard problem.…”