(240b) Economics and Dynamic Flexibility of Concentrated Solar Power Technologies
Beyond economics, cooling system water usage is increasing in importance. CSP systems, in particular, operate in water-sparse areas and thus water conservation is priority if the technology is to be competitive. Cooling systems influence overall system efficiency both due to primary thermal (Rankine cycle) efficiency impacts and parasitic loading associated with cooling system operation, which in turn impact system economics. Most CSP optimization literature, however, focuses only on economic metrics and does not consider water usage.
Compressive analysis of market-based revenue potential and water usage for CSP systems is especially complex because it depends on the selected operating policy. In several studies, revenue estimation is formulated as an optimization problem: manipulate the operational policy (e.g., mass and energy flows) to maximize market revenue subject to physical constraints [3 - 5]. Broadly speaking, CSP operational methods may be classified into two categories: in revenue-focused studies (e.g., [3 - 5]), emphasis is placed on capturing market rules and start-up and shutdown physical restrictions (e.g., minimum up/down times). Simplified correlations (e.g., piecewise linear approximations) are commonly used to model the solar collector and Rankine cycle, and 1 hour time discetizations are considered. In contrast, control focused studies (e.g., [6 - 8]) use much finer time discretizations (e.g., minutes) and consider nonlinear (partial) differential algebraic equation models to capture CSP system physics. These studies neglect market rules and start-up/shutdown limitations, and typically seek to maximize solar energy production or similar metrics. As such, neither of these approaches are capable of analyzing revenue opportunities available at multiple timescales from day-ahead (hour frequency) and real-time markets (minutes frequency).
We present a unified framework that considers market rules, start-up/shutdown restrictions and detailed system physics to analyze multiple CSP performance metrics, especially profits and water usage. The electricity market mathematical model is sufficiently detailed to evaluate revenues from selling/providing both energy and ancillary services, including regulation and (non)-spinning reserve capacity, in the California day-ahead and real-time markets. The CSP physics models include mass and energy balances and nonlinear equipment performance correlations. They are sufficiently complex to resolve temperature profiles in the thermal storage tanks and study the impact of storage dynamics on system performance. Revenue estimation and operational policy determination are formulated as mixed integer nonlinear programs (optimization problems). We present a decomposition strategy that uses physics inspired relaxations to efficiently find approximate solutions that are feasible for all of constraints and locally optimal with respect to a fixed start-up/shut-down schedule. The framework is implemented in Julia/JuMP (an open-source programming language/modeling environment) and leverages large-scale and efficient numerical optimization solvers such as IPOPT and Gurobi.
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