(537d) Accounting for Uncertainty Via Scheduling Informed Optimal Design: A Renewable Ammonia Case Study

The optimal design of systems with renewable energy generation requires taking into account decision making on the time scale of scheduling due to the time-varying nature of renewable energy availability. As a result, such optimization problems tend to be large as operating states at each time point over at least one year need to be tracked. Because of the innate size of the deterministic problem, it is extremely difficult to include nonlinear relations for capital cost and other phenomena, or further take into account uncertainty in parameters such as renewable energy availability using stochastic or robust programming, as such formulations of the problem quickly become intractable. However, uncertainty can play an important role in deciding on an optimal design, since a deterministic design may not include enough operating flexibility to manage uncertainty. As an example of this, consider a renewable energy powered chemical plant designed to run in the electricity market structure presented in [1], where day-ahead power exchange commitments must be made. Market parameters govern how much commitments in consecutive time periods can vary and how close a realized exchange must be to its commitment value to avoid paying a penalty, a scenario referred to as a “commitment violation.” Designing a plant in such a market structure necessitates considering operation under uncertainty, otherwise one would never design for the possibility of commitment violations due to imperfect forecasts.

In this work, we consider the case study of finding the optimal design of a wind-powered ammonia generation system operating in the aforementioned market structure. To keep the problem tractable, we propose a method where the optimization problems for scheduling and design are decoupled. To do so, we develop a receding horizon formulation for scheduling a system with a wind turbine which services a renewable ammonia plant as well as other uncertain but uncontrollable loads. These problems make hourly decisions about the operating state of the system to minimize operating cost based on uncertain forecasts of weather and power load over the next 48 hours. We then simulate many yearlong scheduling problems for wind-powered ammonia plants of various designs to obtain annual operating costs. From this data, we use a method similar to that described in [2] to identify a small number of key design parameters on which operating cost depends and develop simple correlations relating operating cost to these parameters. We repeat this analysis for different values of the electricity market parameters and obtain different sets of correlations for tight, loose, and no market parameters.

The correlations found by scheduling the renewable ammonia plant are then embedded in a design optimization problem attempting to find unit sizes which can meet a given power and ammonia demand at minimal net present cost. Because scheduling is embedded in the correlations for operating cost, the design optimization problem no longer needs to include variables for operating states, making the resulting optimization problem much smaller and allowing more accurate nonlinear capital cost functions to be included. Our results show how the optimal design of the ammonia system can change based on the market parameters, as a tight market structure where one cannot deviate much from their power exchange commitment requires a design that can be operated more flexibly than a loose market structure. We also compare our results with those obtained from attempting to design without taking into account uncertainty, and show that the deterministic optimal design is not as economical in the electricity market structure.

[1] Zachar, M. and Daoutidis, P. Microgrid/macrogrid energy exchange: A novel market structure and stochastic scheduling. IEEE Trans. Smart Grid (8), 2017, pp. 178-189.
[2] Allman, A. and Daoutidis, P. Optimal scheduling for wind-powered ammonia generation: Effects of key design parameters. Chem. Eng. Res. Des., 2017, in press.