**1. Introduction**

With the increasing need for electricity and the problems associated with centralized fossil fuel power plants—such as environmental pollution, exorbitant construction and maintenance costs, etc.—the use of MEMGs is a good solution; they allow the extensive utilization of renewable energies, distributed energy resources (DERs), and participation of consumers in the optimal management of power system operation, and using these systems can play a vital role in optimal energy consumption, system stability, and system reliability [1–4]. Furthermore, renewable energy sources have high uncertainty and an intermittent nature [5–8]. One solution to this problem is the micro-grid, which facilitates the response to load demand [9–12].

In terms of operation, micro-grid energy management systems (MEMSs) can be divided into centralized and decentralized (distributed) perspectives [13]. In centralized approaches, a central agent, which can process large amounts of data, is needed in order to gather information from other agents [14]. In multi-carrier micro-grids with distributed energy management, the privacy of agents is preserved. Moreover, each independent

**Citation:** Faghiri, M.; Samizadeh, S.; Nikoofard, A.; Khosravy, M.; Senjyu, T. Mixed-Integer Linear Programming for Decentralized Multi-Carrier Optimal Energy Management of a Micro-Grid. *Appl. Sci.* **2022**, *12*, 3262. https://doi.org/ 10.3390/app12073262

Academic Editors: Davide Astiaso Garcia and Rodolfo Dufo López

Received: 9 January 2022 Accepted: 15 March 2022 Published: 23 March 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

agent can optimize its costs in a parallel or sequential manner [15]. Providing an optimal approach to planning of system components is very important. The network used in this research consisted of micro-turbines, waste power plants, fuel cells, wind turbines, boilers, anaerobic reactors, inverters, rectifiers, and some energy storage units. It is also possible to exchange information between different levels of the system. This feature increases the reliability of the system and, compared with non-participating systems, achieves a better result. In this research, we sought to find the optimal performance strategy for system components, while meeting the electrical and thermal needs of customers. The micro-grid system is capable of exchanging electricity with high energy levels, as well as daily component performance scheduling.

The rest of this paper is organized as follows: In Section 2, a review of the related work, along with a description of the proposed methodology of this research, is provided. Section 3 presents the proposed MEMG structure. In Section 4, agents are modeled. In Section 5, the simulation of the proposed method to achieve optimal performance of MEMG agents is performed. Section 6 presents the simulation results, and we review the obtained results with different criteria and compare them with other methods in order to validate the proposed method.

### **2. Literature Review**

In energy management systems with a single energy carrier, optimal performance and calculations are simpler, due to the lack of independence among energy carriers. Some research has been done to optimize the performance of such systems based on time-series analysis, factor-based optimization algorithms, etc. [16–19]. However, in a few cases, uncertainty in load demand is included in optimizing system performance. For example, in [20], the effect of the presence of DERs in optimizing the performance of energy management systems is investigated.

In multi-carrier energy management systems, computing and optimizing system performance is more complex. In [21], a model for optimizing the performance of the Poly Generation micro-grid of the University of Geneva is presented, showing that MEMGs can have economic and environmental benefits if they use the optimal strategy. Furthermore, in [22], an optimization model for a PG micro-grid in the presence of renewable energy sources is proposed. In [23], a real-time operational optimization method is presented. In [24–26], the problems of optimizing the performance of multi-carrier energy systems with centralized approaches, and from top to down, were investigated. On the other hand, in a few cases—such as [27,28]—the problems of optimal planning of the performance of the multi-carrier energy systems with decentralized and distributed approaches have been investigated.

Load demand is not considered in energy management systems with multiple energy carriers. The reasons for this include computational complexity, performance optimization of energy carriers, uncertainties in renewable energy production, and continuous fluctuation.

Hence, the authors of [27,28] could not consider the uncertainties. Considering uncertainties makes it difficult to provide an optimal approach but, on the other hand, it makes the optimal approach more efficient and reduces the operating costs of the system. In [29], optimization was achieved using PSO and GA to solve the problem of MEMG operational planning. Meanwhile, [30] used a stochastic model for electricity and natural gas pricing and load demand in real time. In [31], a micro-grid management approach is presented, considering random load and predicting the demand. In [26], a new method for a multi-agent system (MAS) is presented, which is a combination of ANFIS and GA.

In [15], deep learning is used to model uncertainties. In [32], optimization of the performance of the system is achieved using the gray wolf optimization method. In [33], the evolutionary vertical sequencing protocol is used to model coordination between high-level agents, and a two-layer MLIP is used for low-level uncertainty. In [34], microgrid energy management with a decentralized approach is achieved using reinforcement

learning. In [35], a game-theory-based optimization model is presented to configure the capacity of energy carrier agents.

In multi-carrier systems, providing an optimal approach is complex because, in such systems, uncertainties related to energy production in renewable sources, fluctuations in load demand, and uncertainty in market price exist. Reviewing the related work in energy management of multi-carrier energy networks indicates that such systems can reduce costs and pollution if optimally operated. Due to the importance of the optimal performance of MEMGs, studies in this field have been considered. However, most of these studies have not considered demand response programs and uncertainties related to the output of renewable energy. To overcome these limitations, this study presents a multi-carrier system (MCS) for planning the optimal performance of MEMG agents, considering uncertainties related to renewable energy production and energy demand fluctuations. The effect of using demand response programs is also presented, with the two objectives of minimizing operational and environmental costs. The efficiency of the proposed method is to simplify the complex MEMG model and reduce the calculations so as to apply uncertainty in the relationships of MG agents.
