A general model for energy hub economic dispatch Soheil Derafshi Beigvand a , Hamdi Abdi a,⇑ , Massimo La Scala b a Electrical Engineering Department, Engineering Faculty, Razi University, Kermanshah, Iran b Electrical and Electronic Department (DEE), Polytechnic School of Bari (Politecnico di Bari), Bari, Italy highlights  Modeling the economic dispatch of energy hubs.  Proposing a new optimization algorithm namely SAL-TVAC-GSA.  Considering electricity, gas, heat, cool, and compressed air as energy carriers.  Including the valve-point loading effect and prohibited zones of electrical power-only units. article info Article history: Received 6 October 2016 Received in revised form 11 December 2016 Accepted 27 December 2016 Keywords: Economic dispatch Energy hub Energy hub economic dispatch Gravitational search algorithm Self-adoptive learning with time varying acceleration coefficient-gravitational search algorithm Optimization abstract This paper proposes a new optimization algorithm, namely Self-Adoptive Learning with Time Varying Acceleration Coefficient-Gravitational Search Algorithm (SAL-TVAC-GSA), to solve highly nonlinear, non-convex, non-smooth, non-differential, and high-dimension single- and multi-objective Energy Hub Economic Dispatch (EHED) problems. The presented algorithm is based on GSA considering three funda- mental modifications to improve the quality solution and performance of original GSA. Moreover, a new optimization framework for economic dispatch is adapted to a system of energy hubs considering differ- ent hub structures, various energy carriers (electricity, gas, heat, cool, and compressed air), valve-point loading effect and prohibited zones of electric-only units, as well as the different equality and inequality constraints. To show the effectiveness of the suggested method, a high-complex energy hub system con- sisting of 39 hubs with 29 structures and 76 energy (electricity, gas, and heat) production units is pro- posed. Two individual objectives including energy cost and hub losses are minimized separately as two single-objective EHED problems. These objectives are simultaneously minimized in the multi- objective optimization. Results obtained by SAL-TVAC-GSA in terms of quality solution and computa- tional performance are compared with Enhanced GSA (EGSA), GSA, Particle Swarm Optimization (PSO), and Genetic Algorithm (GA) to demonstrate the ability of the proposed algorithm in finding an operating point with lower objective function. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction Future vision of energy networks including several energy car- riers in the form of multi-carrier systems [1] (also, called multiple energy carrier networks [2] or hybrid systems [3]), allows more flexibility in the integrated network operation and optimization [4,5]. In fact, various infrastructures can affect each other in terms of energy flow, storage, etc. In the meantime, energy hubs play an essential role in the connection points between different infras- tructures allowing energy flow through various networks. Combi- nation of several converters in hubs provides necessary motivations to integrate multiple energy carriers [3]. Some con- verters such as CHP devices [6–9] and tri-generations [10–13] in the hubs are two attractive cases which can establish more effec- tive energy conversion between different carriers [1,3,4,6]. In this regards, other elements (such as heater exchangers) may operate with a single carrier. In this view point, various carriers can be con- sumed by different hub structures to provide different forms of energy at the output port. Proposing the different optimization problems for electrical sys- tems will be lead to introduce two problems, namely Multi-Carrier System Optimal Power Flow (MCSOPF) and Energy Hub Optimal Dispatch (EHOD), for hybrid systems. The first one, optimizes the energy flow through various networks based on a desirability e.g. energy cost, emission cost, energy loss, and etc. [1,2,4]. So, the sys- tem condition in terms of all control and state variables, energy flows and the other quantities can be determined. Due to different http://dx.doi.org/10.1016/j.apenergy.2016.12.126 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: hamdiabdi@rai.ac.ir (H. Abdi). Applied Energy 190 (2017) 1090–1111 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy