This article takes an integrated view of optimized capacity design and operation of islanded energy hubs. We consider energy hubs that incorporate emerging distributed energy resources as well as energy storage devices and fully support electricity and heat demand of an islanded installation. Both battery and hydrogen storage are incorporated. To explicitly account for the stochasticity in renewable energy generation and load, the energy hub capacity design problem is first expressed as a chance-constrained optimization problem and then reformulated as a robust counterpart problem, where battery charging/discharging responds to stochastic renewable energy generation and load realizations through a control policy. In particular, an affine policy is considered, enabling a linear program formulation of the problem. To reduce conservativeness of the design, an iterative algorithm is proposed, where the interaction between a chance-constrained design problem and a validation problem is achieved through a scalar auxiliary variable. The design result demonstrates a balanced tradeoff between robustness and cost efficiency. After the energy hub has been designed, we propose a bi-level operating strategy, where a day-ahead schedule is optimized at the higher level and model predictive control is used for tracking the schedule in real time at the lower level. Finally, we discuss the potential for increasing the reliability of energy hub systems while decreasing operational cost by sharing energy between multiple energy hubs through networking.

Trajectory sensitivity analysis has been widely used to analyze the dynamic behaviour of complex systems such as power system. It is common to use first-order sensitivities, which have been fully described for hybrid dynamical system. However, second-order trajectory sensitivities have only been analyzed for continuous systems. This paper derives the jump conditions describing the behaviour of second-order trajectory sensitivities at switching and reset events. This enables second-order sensitivity analysis of general hybrid dynamical systems. The jump conditions are illustrated using a simple power system example and the results are compared with first-order sensitivities. It is shown that incorporating second-order sensitivity increases the accuracy of trajectory approximation.