Abstract
Energy hub system (EHS) incorporating multiple energy carriers, storage, and renewables can efficiently coordinate various energy resources to optimally satisfy energy demand. However, the intermittency of renewable generation poses great challenges on optimal EHS operation. This article proposes an innovative distributionally robust optimization model to operate EHS with an energy storage system (ESS), considering the multimodal forecast errors of photovoltaic (PV) power. Both battery and heat storage are utilized to smooth PV output fluctuation and improve the energy efficiency of EHS. This article proposes a novel multimodal ambiguity set to capture the stochastic characteristics of PV multimodality. A two-stage scheme is adopted, where 1) the first stage optimizes EHS operation cost, and 2) the second stage implements real-time dispatch after the realization of PV output uncertainty. The aim is to overcome the conservatism of multimodal distribution uncertainties modeled by typical ambiguity sets and reduce the operation cost of EHS. The presented model is reformulated as a tractable semidefinite programming problem and solved by a constraint generation algorithm. Its performance is extensively compared with widely used normal and unimodal ambiguity sets. The results from this article justify the effectiveness and performance of the proposed method compared to conventional models, which can help EHS operators to economically consume energy and use ESS wisely through the optimal coordination of multienergy carriers.

Abstract
Electricity-distribution network operators face several operational constraints in the provision of safe and reliable power given that investments for network area reinforcement must be commensurate with improvements in network reliability. This paper provides an integrated approach for assessing the impact of different operational constraints on distribution-network reliability by incorporating component lifetime models, time-varying component failure rates, as well as the monetary cost of customer interruptions in an all-inclusive probabilistic methodology that applies a time-sequential Monte Carlo simulation. A test distribution network based on the Roy Billinton test system was modelled to investigate the system performance when overloading limits are exceeded as well as when preventive maintenance is performed. Standard reliability indices measuring the frequency and duration of interruptions and the energy not supplied were complemented with a novel monetary reliability index. The comprehensive assessment includes not only average indices but also their probability distributions to adequately describe the risk of customer interruptions. Results demonstrate the effectiveness of this holistic approach, as the impacts of operational decisions are assessed from both reliability and monetary perspectives. This informs network planning decisions through optimum investments and consideration of customer outage costs.

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