Mixed Integer Programming Based Energy Storage Sizing for a Community Considering Switchable Loads and Utility Dynamic Price

In this project, the size of an energy storage system for a community will be determined based on fixed cost of using the battery, rate of the battery power, utility price and incoming power limit, local load profile, and switchable load penetration. A 24-hour operation problem to minimize the total cost in the perspective of the community will be used to determine the size of the battery. While there is no constraint imposed for the energy size and maximum power size of the battery, the fixed cost of using battery and the rate of battery power will be used as penalty function in the objective function. Without those penalty costs, the size of the battery can of course go infinity. The operation of the battery will show how the battery will be operated given the typical local load profile, external utility price for 24 hours, and limited transfer capacity from the utility. From the battery’s operation for 24 hours, energy size and maximum power can then be determined.  In addition to local load profile and utility aspect, the local switchable load penetration is also considered for the second operation problem. To facilitate such consideration, the cost function now considers the penalty cost of switching off a load. The switchable loads are assumed to have the same size and the number of them determines the penetration of switchable loads in the community. The main contribution of this paper is two-fold: i) Linear mixed integer programming problems addressing 24 hour operation are formulated considering the above mentioned four aspects of considerations including switchable loads. Techniques to replace nonlinear objective functions and nonlinear constraints by linear objective functions and linear constraints are demonstrated in model formulation. Such formulation makes the large-scale problem solving feasible as linear mixed integer programming can be handled by commercial solvers with very fast speed. ii) Sensitivity analysis are conducted to demonstrate the effect on battery size of utility price, transmission constraints, cost of battery operation, penetration of switchable load and the granularity of the switchable unit. This research can answer the following questions for a community: What size of the energy storage device is most cost effective? If the switchable load penetration is 10%, how much size reduction can be achieved for the battery? How much penetration of switchable load can create most benefits? Finally how much cost saving can be achieved by the battery and/or switchable loads?

Keywords

Demand response, Mixed Integer Programming, Energy Storage, Switchable Loads