Optimal Resource Allocation Problems in Renewable Energy

This talk consists of two optimization problems in renewable energy.
First, we study the problem of finding an optimal schedule for running a generator coupled with a wind farm to meet a promised electrical load, with the aim of maximizing revenue. The goal is to design a so-called dispatchable system, which can provide firm energy to a day-ahead or an intra-day market. Highly reliable dispatch can be modeled using joint-chance constraints, but their non-convex nature poses significant computational challenges. We study integer programming formulations of these models motivated by extended variable approaches proposed in literature. As a case study, we present preliminary results based on the wind power data from Texas, USA.
Second, we consider a pumped storage for hydro-electric power generation. By pumping water to a higher elevation when energy prices are low, and releasing water to generate electricity via a hydro turbine when prices are high, the aim is to create revenue. We formulate a stochastic dynamic program to maximize expected revenue under a stochastic model for energy prices under the assumption that we can determine the pumping-and-generating schedule. However, in reality, a pumped-storage unit submits bids for energy-generation and energy purchase to a market. We develop a bidding strategy that allows us to track the desired generate-pump schedule. Thus, we solve a model that yields an optimal block-bidding policy in the sense of tracking the desired stochastic generate-pump policy.