Uncertainty Quantification for Capacity Expansion Planning

Capacity Expansion Planning (CEP) is a resource allocation problem in which decisions are made and represented as a binary variable. CEP often refers to the planning of expansion decisions, which represent different types, sizes, and locations of electricity-generating sources to meet demand. Industry professionals, scientists, researchers, and engineers use CEP to make decisions regarding what technologies, e.g., wind, solar, natural gas, nuclear, etc., to build to meet demand and satisfy regulatory or reliability conditions. There are two types of variables associated with expansion and dispatch decisions, and for each, there are costs associated with installing new generating capacity and dispatching generators. In contrast, Production Cost Modeling (PCM) involves simulating the operation of an electric grid and focuses on dispatch decisions. Often, computational models are formed of an electric grid and an optimization problem is solved which seeks to minimize the costs of expanding the system. In this work, we numerically study an electric grid whose expansions costs are on the order of hundreds of millions of dollars ($ U.S.D.) and operations costs are on the order of tens of millions of dollars. The Scalable Power-System Economic Expansion Dispatch (SPEED) model is used in this work as a stochastic approach to study CEP and PCM. Simulations yield expansion decisions in the form of either natural gas or wind generators, of different sizes, at different locations, over ten years, using data for a hypothetical electric grid overlapping parts of California, Nevada, and Arizona. Relevant Quantities of Interest (QoIs) are identified as 1) expansion cost, 2) operations cost, 3) maximum installed gas capacity, and 4) maximum installed wind capacity, resulting from any given SPEED simulation. The key uncertain model input parameters we study are capacity reserve margin for expansion, cost of loss of load, cost of excess load, natural gas price, wind installation cost, and transmission capacity. Simulations are performed utilizing the modified Institute of Electrical and Electronics Engineers' (IEEE) Reliability Test System (RTS) provided by the Grid Modernization Lab Consortium (GMLC). The resulting data is post-processed and two different approaches are considered to quantify the uncertainty in the model, sparse Polynomial Chaos Expansions (PCEs) and Active Subspace analysis. Five global sensitivity metrics, which explicitly quantify uncertainty by measuring an input parameter's influence on the variance of the QoIs and provide a measure of explainable uncertainty, are reported. PCE surrogate models were constructed and exploited to generate rich posterior distributions of the SPEED model output QoIs. To better understand the uncertainty associated with unit commitment (UC), we conducted two independent numerical experiments holding all modeling conditions equal except for the integer modeling assumption regarding the dispatch decision variables, which has a significant impact on the model complexity. Our results support the following conclusions: The global sensitivity metrics indicate that all four QoIs are relatively insensitive to the input parameters cost of loss of load, cost of excess load, and cost of natural gas, while they are sensitive to reserve capacity margin, cost of wind, and transmission capacity. The global sensitivity metrics indicate that all four QoIs are influenced by cost of loss of load, cost of excess load, and cost of natural gas only through their interactions with other terms, if at all. Among the uncertainties considered, expansion cost and maximum installed wind capacity in this model are driven primarily by cost of wind and secondarily by reserve capacity margin. Among the uncertainties considered, operation cost in this model is driven primarily by cost of wind, secondarily by transmission availability, and slightly by reserve capacity margin. Among the uncertainties considered, maximum installed gas capacity in this model is driven primarily by reserve capacity margin, secondarily by cost of wind, and slightly by transmission availability. When considering relaxed vs. binary UC, the posterior distributions of the expansions cost, operations cost, and maximum installed gas capacity predicted by the PC surrogates are similar, while the distribution of maximum installed wind capacity differs significantly, The mean values of each QoI, approximated by the PCEs, are similar for both relaxed and binary UC. However, we report larger standard deviations of expansion cost, operations cost, and max installed wind capacity for relaxed UC compared to the binary UC model assumption. In contrast, the standard deviation for max installed gas capacity was smaller for relaxed UC compared to binary.