Risk-Constrained Scheduling of Energy Hubs: A Stochastic $p$-Robust Optimization Approach
Afshin Najafi-Ghalelou, Mohsen Khorasany, Reza Razzaghi
Abstract
This article proposes a two-stage risk-constrained energy scheduling approach for an energy hub (EH) model that can trade electricity and thermal energies, in the day-ahead and real-time markets. The scheduling problem of the EH is considered to maximize the expected profit and minimize the risk level or maximum relative regret level at a preferable level of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{CO}_2$</tex-math></inline-formula> emission, considering various uncertainties. In the proposed approach, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> -constraint method is used to model the economic and environmental factors at the same time, and the stochastic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula> -robust approach is used to manage the relative regret or risk level in the studied EH model. Furthermore, the techniques for order preference by similarity to an ideal solution method is employed to prioritize the Pareto optimal curve composed of the expected profit, risk level or maximum relative regret level, and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{CO}_2$</tex-math></inline-formula> emission. Extensive simulations are conducted to verify the effectiveness of the proposed risk-constrained scheduling approach and the comparison with downside risk constraint, conditional value at risk, and robust optimization approaches are provided. The results indicate remarkable improvements in the robustness of the studied model with a slight reduction in the expected profit at the preferable level of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{CO}_2$</tex-math></inline-formula> emission.