Stochastic Optimization for Energy Efficient Outpost Modeling

OBJECTIVE The objective of this work is to support the Office of Naval Research (ONR) in the development of the Energy Resource Planning Tool (ERPT) as part of the Energy Efficient Outpost Modeling Consortium (EEOMC) effort. The PI will provide the following support to ONR: Task 1: Develop initial feasible solutions for the ERPT. Complex optimization models can often suffer from lengthy run-times. Developing a sound, initial feasible solution is one method of decreasing those model run-times. The PI will focus on creating an automated, initial feasible solution for the ERPT so that solutions are achieved as quickly as possible. The PI will lead this effort, and collaborate closely with the colleagues at the Colorado School of Mines (CSM) and the National Renewable Energy Laboratory (NREL). Task 2: Assume lead in modeling photovoltaics (PV) in the ERPT. PV resource availability will be modeled in the ERPT using NREL’s PVWatts model as the default tool. However, PVWatts (and other PV models) require solar irradiance data to accurately determine power supplied by a PV system. Especially challenging is determining solar irradiation in parts of the world that are of interest to the Department of Defense (DoD) that may not have reasonable historical PV data. The PI will gather solar irradiance data from across the world (focusing on geographic areas likely to be of interest to DoD), assess the likely accuracy of such data, and develop a capability to create a reasonable solar irradiance profile based on a user-input latitude/longitude coordinates and time of year. Locations already contained in the EnergyPlus model will be the default starting point for this assessment. Task 3: Model solution assessment. An optimal solution identified by the ERPT may not be the optimal solution. It is the optimal solution for the given parameters and data associated with a particular model run, however, some of the data will be varied stochastically in subsequent model runs to capture naturally occurring variation. Electrical load data and PV resource availability are two examples of “known” data that must be varied in multiple model runs to account for the uncertainty and variability associated with real-world experience. Varying these data may result in different solutions obtained by the ERPT. The PI will adopt techniques that minimize the number of scenarios assessed in the ERPT, to include the following: • Assessing solution quality: The goal is to be able to make a statement similar to the following: “We are ‘X’% confident that the proposed system design is suboptimal by at most ‘Y’%.” The PI will seek to prove a result that allows us to make a claim of this nature in reference to the solution under uncertainty of load and/or PV availability. • Variance reduction techniques: Well-designed sampling of scenarios can reduce the sampling variance, which reduces the width of a confidence interval associated with both the expected cost of operation and the optimality gap associated with a solution to a stochastic program like the one mentioned above. Effective techniques include the use of common random numbers, antithetic variates, stratified sampling techniques and Latin hypercube sampling (LHS). The PI will explore different sampling techniques and assess the best means to reduce the variance associated with the expected cost and optimality gap. These variance reduction techniques also typically allow us to improve the quality of the system design decision we obtain when solving a Monte Carlo sampling-based approximation of the stochasti