Abstract: There exist several different reliability-and approximation-based methods to determine the contribution of solar resources toward resource adequacy. However, most of these approaches require knowing in advance the installed capacities of both conventional and solar generators. This is a complication since generator capacities are actually decision variables in capacity planning studies. In this paper, we study the effect of time resolution and solar PV penetration using a planning model that accounts for the full distribution of generator outages and solar resource variability. We also describe a modification of a standard deterministic planning model that enforces a resource adequacy target through a reserve margin constraint. Our numerical experiments show that at least 50 days worth of data are necessary to approximate the results of the full-resolution model with a maximum error of 2.5% on costs and capacity. We also show that the amount of displaced capacity of conventional generation decreases rapidly as the penetration of solar PV increases. We find that using an exogenously defined and constant capacity value based on time-series data can yield relatively accurate results for small penetration levels. For higher penetration levels, the modified deterministic planning model better captures avoided costs and the decreasing value of solar PV.

Abstract: Planning for new generation infrastructure in hydrothermal power systems requires consideration of a series of nonlinearities that are often ignored in planning models for policy analysis. In this article, three different capacity- planning models are used, one nonlinear and two linear ones, with different degrees of complexity, to quantify the impact of simplifying the head dependency of hydropower generation on investments in both conventional and renewable generators and system operations. It was found that simplified investment models can bias the optimal generation portfolios by, for example, understating the need for coal and combined-cycle gas units and overstating investments in wind capacity with respect to a more accurate nonlinear formulation, which could affect policy recommendations. It was also found that the economic cost of employing a simplified model can be below 10% of total system cost for most of the scenarios and system configurations analyzed, but as high as nearly 70% of total system cost for specific applications. Although these results are not general, they suggest that for certain system configurations both linear models can provide reasonable approximations to more complex nonlinear formulations. Uncertain water inflows were also considered using stochastic variants of all three planning models. Interestingly, if due to time or computational limitations only one of these two features could be accounted for, these results indicate that explicit modeling of the nonlinear-head effect in a deterministic model could yield better results (up to 0.6% of economic regret) than a stochastic linear model (up to 9.6% of economic regret) that considers the uncertainty of water inflows.