(365i) Multiperiod Generalized Disjunctive Programming Optimization in Idaes: Simultaneous Design and Operation of an Integrated Energy System

Increase in variable renewable energy penetration in the electrical grid has required fossil-based generators to be more flexible, while maintaining their thermal efficiency. One approach to increase the flexibility of these generators is the integration with thermal energy storage (TES) systems [Li et al., 2019], which offer the opportunity to save energy (charge) and use stored energy (discharge) during periods of low and high electricity prices, respectively. The integration of TES systems to fossil-based generators adds complexity to the already challenging thermal-generator model, since this integration represents the addition of more units to the flowsheet, increasing the difficulty of the optimization problem to determine the optimal design and operation of the generator and storage system given an electricity price signal. Currently, these integrated systems are operated and designed by evaluating the performance of the charge and discharge systems independently, which can lead to sub-optimal designs and scheduling of the TES system since there is a limited capability to evaluate the performance of the system as a whole.

To address this problem, in this work, we propose a multiperiod Generalized Disjunctive Programming (GDP) model of an integrated ultra-supercritical power plant (USCPP) to determine the optimal hourly operating design and schedule of the TES systems under a price taker assumption. The objective is to maximize total profit over a given time horizon, taking into account operating and capital costs. To perform the simultaneous design and operation optimization in the USCPP multiperiod GDP model, we consider two types of variables in the model: operational variables, to determine the operating conditions of the USCPP and storage systems, and design variables, to select the storage system to integrate with the USCPP and its design parameters (area of heat exchangers). To determine the storage system to integrate with the USCPP, we included three different operation modes to the USCPP model: no storage mode, which represents the USCPP superstructure without any storage, and charge and discharge mode, which integrate a charge and discharge heat exchanger, respectively, with the USCPP superstructure to an optimal fixed location. The selection of the operation mode is formulated using a disjunction, where each operation mode is included to the USCPP model as a discrete decision using a GDP formulation; if a particular operation mode is selected, a set of units, variables, and constraints for the respective mode are to be included to the global model equations. The USCPP GDP model is built using IDAES (Institute for the Design of Advanced Energy Systems Integrated Platform), an open-source platform that enables the design and optimization of integrated energy systems [Lee et al., 2021]. IDAES, built on Pyomo [Hart et al., 2017], supports the use of advanced solvers such as GDPopt, a solver that allows users to solve nonlinear Generalized Disjunctive Programming models in a reduced space using a variety of decomposition algorithms, including logic-based outer approximation [Chen et al., 2021]. To construct the multiperiod GDP model, we consider a steady-state USCPP GDP model for each time period, including coupling variables to link each time step. In our case study, two linking variables are considered: the optimal dispatch of the thermal power plant and the amount of storage material available at the end of each time period. The charge and discharge storage systems are subject to nonanticipativity constraints, which state that the design area of the storage heat exchangers and the hot temperature of the storage material in each time period must take equal values. In this case study, we use Solar salt as the storage material in the TES systems.

In our results, we show that with the proposed multiperiod GDP price-taker analysis, we were able to explore the use of discrete decisions to obtain an optimal schedule and design of the charge and discharge TES systems integrated with the USCPP while maximizing profit. For a 12 hour period, we observe that we increase the flexibility of the plant by dispatching the maximum power capacity of the USCPP and discharge storage system at high-electricity price periods, while satisfying the ramping limits of the boiler in the USCPP. While maintaining a boiler efficiency of about 85% to 95% in the explored time periods, both TES systems areas are obtained along with the hot solar salt temperature, which reaches the maximum temperature value of the Solar salt of 853.15 K, maximizing the use of its heat capacity. Since the multiperiod GDP model involves discrete decisions for the USCPP operation mode selection at each time period, it is combinatorially explosive, leading to approximately 3¹² possible alternatives. The optimal schedule of the integrated USCPP is obtained using the reduced integer cut decomposition strategy in GDPopt after 100 master iterations using a commercial laptop.

Disclaimer
Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

Acknowledgments
This work was conducted as part of the Institute for the Design of Advanced Energy Systems (IDAES) and Design and Optimization Infrastructure for Tightly Coupled Hybrid Systems (DISPATCHES) with support through (1) Simulation-Based Engineering, Crosscutting Research Program within the U.S. Department of Energy's Office of Fossil Energy and Carbon Management and (2) the Grid Modernization Laboratory Consortium, a strategic partnership between DOE and the national laboratories to bring together leading experts, technologies, and resources to collaborate on the goal of modernizing the nation's grid.

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