# Double-Consensus Based Distributed Optimal Energy Management for Multiple Energy Hubs
## 1 Introduction  
The energy crisis and environmental pollution are regarded as a major challenge all over the world. To address these issues, multiple energy systems, aiming at integrating conventional independent energy service networks such as power and natural gas systems, could provide a promising solution [1, 2]. As one type of multiple energy system, the concept of the energy hub has gained significant attention recently [3, 4]. An energy hub focuses on feeding different energy loads through multiple energy inputs and outputs, acting as an interface between various energy producers and consumers. It could provide the desired effects of reconstructing traditional decoupled energy supplies, adding operational flexibility of energy services, improving overall efficiency and reliability, reducing pollutant emissions, etc. The EMP is a fundamental and key topic in different energy and building systems. [PERSON] et al. [5] made an outstanding contribution in reviewing and analyzing the works related to energy management, from models to technologies, such as the effects of different components [6], cost and performance analysis [7, 8], technology evolution [9], etc. In this paper, we focus on investigating EMP within the context of energy hub-based multiple energy systems, which is typically formulated as an optimization problem. Several research works have been reported on this topic, which can be classified into two categories. The first mainly aims at achieving the internal resource management of individual energy hubs, with the objective of maximizing the energy allocation profits or minimizing the energy cost [10, 11, 12]. To further enhance the system robustness and energy efficiency, the other tries to investigate the cooperative energy management problem of multiple energy hubs, where the energy hubs interact with each other to determine the global optimal operations. For instance, a multiagent genetic algorithm was proposed in [13] to solve the economic dispatch problem for multi-hubs with the consideration of uncertain renewable energy resources. In [14], a probabilistic optimizationapproach was introduced for renewable-based residential energy hubs, in which the interactions between the electricity and natural gas were taken into consideration. In [15], a self-adaptive learning with time varying acceleration coefficient-gravitational search algorithm was proposed to address multi-objective economic dispatch problem for energy hubs. Moreover, the underlying energy flow optimization [16; 17], and the reliability of energy demands [18] and criteria [19] have been further taken into consideration and studied in the energy management problem. It is worth noting that the approaches mentioned above for solving the energy management of energy hubs are implemented centrally. However, as the scale of the system expands, centralized approaches may face several challenges, which can be summarized as follows:  
1. The centralized approaches rely on a powerful central controller to process a huge mass of data and require two-way and high-bandwidth communication to work on the information gathered for the whole system [20; 21]. Thus, solutions based on centralized approaches are costly to implement and are prone to single-point failures and modeling errors. 2. Despite the plug-and-play and peer-to-peer nature of distributed energy resources, both the physical and associated communication topologies tend to be subject to topology variabilities, which may undermine the efficacy of the centralized approaches [22; 23]. As an alternative, the distributed approaches, which have some advantages compared to centralized approaches, e.g., enhanced reliability and robustness [24], fast computation and reduction in communication [25], are more suitable for accommodating a mass of units. Not surprisingly, only a small number of results have been documented. In [26], the authors proposed the concept of smart energy hubs and formulated the interaction among smart energy hubs as a noncooperative game.