A tri-level stochastic framework for planning integrated electricity, gas, and heating networks with enhanced resilience and renewable integration

In this work, a new tri-level stochastic optimization formulation is developed for the capacity expansion (CE) planning of an integrated multi-carrier energy system comprising electricity, natural gas, and district heating (DH) networks that explicitly captures the trade-off between economic optimality and system resilience in the face of extreme events. When prior works on the (dis)integration of energy vectors often consider energy vectors independently or overlook disrupted system recovery dynamics, the present research develops an integrated multi-carrier framework that simultaneously determines long-term investment decisions, short-term operational dispatch, and emergency reconfiguration measures. The problem is formulated in a hierarchical manner: the upper level searches for optimal capacity expansion for lines, pipelines, and conversion technologies (CHP, P2G, heat pumps), the middle level solves minimum operational cost problem under ordinary stochastic conditions, and the lower-level deals with maximum load restoration in N-k contingencies by a quantitative resiliency measure. To make the difficult mixed-integer problem computationally tractable, we employ an iterative Column-and-Constraint Generation (C&CG) algorithm. A numerical example of a coupled test system over a ten-year time period displays the feasibility of the presented approach. It is shown that the combined resilience-oriented design planning decreases the total expected costs as well as the resilience cost penalty by ca. 8.4% over the single-energy-system design and even surpasses the performance of deterministic methods considering system resilience, although with increasing costs. Critically, the framework features an endogenous, quantifiable resilience metric that is co-optimized with economic objectives, transforming resilience from a passive design constraint into an active driver of investment decisions. In addition, the framework enables a significant increase in renewables penetration (from18% to 54%) through exploiting multi-carrier flexibility to buffer intermittency. These results can help guide policy makers on the importance of cross-sectoral coupling to increase infrastructure robustness and demonstrate that such resilience-focused investments are instrumental in enabling deep decarbonization of the energy system.