A Block-Coordinate-Descent Robust Approach to Incentive-Based Integrated Demand Response in Managing Multi-Energy Hubs with Must-Run Processes

This article presents a new robust incentive-based integrated demand response (IDR) model for energy hub systems (EHSs). The considered incentive-based demand response (IBDR) schemes are interruptible/curtailable service and capacity market program. The proposed IDR model integrates the arbitrage ability of EHS storages as well as energy conversion into the IDR model. The objective of the IDR optimization problem is to maximize/minimize the allocated incentives/penalties in targeted time periods by IBDR schemes while supplying must-run processes with no interruption. Uncertainties of load and energy prices are considered through user-defined polyhedral uncertainty sets. A trilevel robust optimization (RO) is developed, which includes a trilevel min-max-min problem. To solve the trilevel adaptive robust model, the column-and-constraint generation technique is employed by means of a decomposition methodology recasting the trilevel model into a single-level min problem and a bilevel max-min problem. Unlike previous RO models that solve the inner max-min problem by duality theory, a block-coordinate-descent (BCD) methodology is used to solve the max-min problem by means of the first-order Taylor series in this study. The use of the BCD technique instead of duality theory enables a recourse-based characterization of integer variables, such as EHS storage status, which was not applicable in previous models (due to the use of duality theory). Moreover, Lagrange multipliers are eliminated as no duality is conducted. A postevent analysis is conducted to justify the long-term performance of the robust solutions and determine the optimal settings of the BCD robust approach. Results indicate that the IDR model significantly reduces the EHS input electricity in targeted time periods (four hours per day) by IBDR schemes and covers the required electricity with must-run processes by combined heat and power unit, using natural gas. This implies a 2.13% reduction in the operation cost as incentives are obtained through IBDR schemes.