Decision-making for stochastic multi-objective dispatch of integrated electrical and heating systems

In the realm of modern energy systems, addressing the challenges of enhancing flexibility and efficiency under uncertain conditions is of paramount importance. This paper explores the stochastic multi-objective optimal multi-energy flow problem within the context of integrated electrical and heating systems (IEHS). First, the electrical network, the heating network, and the energy hubs were modeled in a completely linearized form. The linear weighted sum method with variable weights was used to transform the multi-objective problem into a single-objective problem and generate a large number of Pareto-optimal solutions. Second, the input stochastic variables were divided into multi-interval scenarios by employing the Cartesian product. For each interval scenario, the interval satisfaction degree level was proposed to convert the constraints involving interval numbers into deterministic ones. Third, a multiple attributes decision analysis (MADA) approach was proposed based on evidential reasoning theory. Six evaluation attributes, namely, the power purchase cost and pollution gas emissions of IEHS, the sum of power loss and sum of voltage deviation in the electrical system, the sum of temperature drop in the heating system, and the interval probability value of the multi-interval scenarios, were considered to rank the Pareto-optimal solutions collected from the multi-interval scenarios and determine the final dispatch solution (called the Utopia solution). Numerical simulations demonstrated that the Utopia solution can comprehensively evaluate various attributes, making it the most suitable option for meeting the operational requirements of IEHS.