The lifestyle of today leads to a substantial growth in the demand for energy in residential areas. To fulfill this increasing demand, it is inevitable that there is a need to increase the generation capacity of the current energy grid. Economic and environmental benefits of distributed generation (DG) with the priority on renewable energy resource usage makes it a much better alternative compared to building expensive and polluting fossil fuel power plants that are then far away from many consumers. However, despite all the economic and environmental benefits that come with DG, it also adds more complexity to the already sophisticated and complex power system. One of the main challenges is to provide consumers with the same level of reliability and power quality that traditional power systems offer. Microgrids, which are used to divide the big bulky energy grid into smaller, more manageable units, proved to be good candidates to tackle this issue [1
]. In this paper we assume that microgrids are always still connected to the overall grid; i.e., the paper assumes a grid-connected microgrid. However, for reasons of simplicity we will only use the term microgrid from now on.
Research on all aspects of microgrids has become very popular in the recent past. In this review we will concentrate on optimization objectives in microgrids only since this is the topic of this paper.
] presents a review of existing optimization objectives, tools, and solution approaches used in microgrid energy management. In [6
], a summary of various uncertainty quantification methods along with a comparative analysis on utilized communication technologies are presented. An energy management solution based on a Bayesian optimization algorithm (BOA) is proposed by [7
] in which the optimization problem is formulated without a closed-form objective function expression, and solved using a BOA-based data-driven framework. In [8
], a two-layer predictive energy management system (EMS) for microgrids was proposed. The upper layer reduces the total operational cost and the lower layer try to remove the forecast fluctuations. In [9
], an optimal scheduling of a standalone microgrid under system uncertainties is proposed. This model uses a dynamic programming method to solve a single-objective optimization problem to reduce the operation and emission costs.
Flexibility and cooperative behavior of multi-agent systems (MASs) make them appropriate candidates for energy management in Smart grids [10
]. There have been numerous studies utilizing benefits of MAS-based solution approaches in control and energy management of microgrids [11
]. A MAS-based game theoretic optimization approach consisting of a double-auction mechanism for the day-ahead market and reverse auction model for the hour-ahead and real-time markets is proposed in [13
]. In [14
], a game theoretic non-cooperative distributed coordination control (NCDCC) scheme is suggested, trying to address multi-operator energy trading for microgrids. There is some MAS research utilizing fuzzy-logic controllers to mitigate the effects of unpredictability in microgrid energy management which can be found in comprehensive reviews [15
]. Optimal operation of energy storage systems has also gained popularity in microgrid management [17
]. Authors in [18
] proposed three different storage strategies for a battery agent in a PV-based microgrid. In their MAS framework, since long-term data of the grid is not available for agents, they perform a rolling horizon scheduling by collaborating to each other to reach global cost reduction.
Recent developments in communication technology put the practicality of demand response programs (DRPs) to the center of attention [19
]. In [20
], a game theoretic demand-side management (DSM) model is proposed which can reduce the peak-to-average ratio and flattens the load profile. They suggest using blockchain technologies to implement the decentralized DSM. In [21
] various types of DRPs, based on price elasticity and customer benefit are compared considering the effect of uncertainties in the microgrid operation. They concluded that emergency DRP (EDRP) is the best performer in terms of maximizing consumer benefits, and real-time pricing (RTP) has the lowest operation costs among different incentive-based and time-based programs. However, the impact of demand response programs on the consumer’s level of convenience is not considered in the investigated models. Authors in [22
] addressed this issue by proposing an MAS-based DSM approach for a microgrid, in which the level of consumer convenience is considered as an important factor in decision-making.
1.2. Artificial Intelligence (AI) Techniques in Microgrid Energy Management
The utilization of nature-inspired techniques in microgrid management systems has become very popular. Most of these algorithms fit into two main categories, namely, swarm intelligence (SI) approaches and evolutionary algorithms (EA).
SI systems (cf. http://www.scholarpedia.org/article/Swarm_intelligence
(accessed July 2019)) are composed of many individuals that coordinate their behaviors and actions in a way that results in achievements that are bigger than the sum of all individuals. In order to achieve this, they rely on decentralized control, emergence and self-organization. Examples of such are colonies of ants and termites, schools of fish, flocks of birds, but also particle swarm optimization (PSO). The latter is a population-based stochastic optimization technique for the solution of continuous optimization problems. It is inspired by social behaviors in flocks of birds and schools of fish. A set of software agents, called particles, search for good solutions to a given continuous optimization problem. Each particle is a solution of the considered problem and uses its own experience and the experience of neighbor particles to choose how to move in the search space.
An EA (cf. Wikipedia on these topics (accessed July 2019)) is a generic population-based metaheuristic optimization algorithm. It uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions. Evolution of the population then takes place after the repeated application of the above operators. One popular type of EA is a genetic algorithm (GAs). Starting from a pool or a population of possible solutions to the given problem these solutions then undergo recombination and mutations (like in natural genetics), producing new children. This process is repeated over various generations. Each individual (or candidate solution) is assigned a fitness value (based on its objective function value) and the fitter individuals are given a higher chance to mate and yield more “fitter” individuals. This is in line with the Darwinian theory of “Survival of the Fittest”.
], a PSO of the cost function is proposed which aims to feed highly fluctuating industrial load using PV generation, wind farms, and conventional energy generation. In order to optimally maintain the state-of-charge in batteries, a multi-objective particle swarm optimization (MOPSO) algorithm is introduced by [25
] in an AC/DC microgrid based on renewable energy production. However, the most common drawbacks of swarm intelligence algorithms are that they may get trapped in local minima or they may converge too early.
The authors in [26
] propose an ant-lion optimizer (ALO) algorithm and recurrent neural network (RNN) for energy management within microgrids. In their model, demand response (DR) is done by utilizing the RNN. The economic dispatch issues are solved by deploying the ALO algorithm. An improved GA is proposed by [27
] that works based on a Tabu search that is analyzing the economic operation of a typical microgrid. [28
] proposes an improved quantum genetic algorithm to optimize a multi-objective model for a microgrid with an electric vehicle that serves as a generation and load unit at the same time. Despite the benefits of using various EA algorithms for the microgrid energy management issues, they still suffer from having a slow convergence rate despite requiring high computational power.
Taking uncertainties into consideration will increase the planning accuracy and lead to the better energy management methods. One of the uncertainty sources is climate change that affects the energy generation and the load estimation, as well as electricity prices [29
]. The production, the load, and the price of electricity in the energy management systems are estimated by several methods, and the error of this estimation creates a deviation from the optimal planning. In [30
], the power production grading is considered for the combined analysis of uncertainty. The Monte Carlo simulation for scenario generation and the PSO algorithm for optimization of an islanded microgrid are recommended. In [31
], authors try to compensate the uncertainty of the wind speed by using a battery and the charging/discharging management. In [32
], the optimal planning of a microgrid with low voltage renewable resources is provided, considering the uncertainty of electricity prices. The normal logarithmic probability distribution function is used for the variable price of the reserve and a two-level randomized programming approach is implemented using mixed integer non-linear programming (MINLP) in the GAMS software environment.
In this paper an innovative stochastic scenario-based MAS energy management approach for microgrids is proposed. For this purpose, a new weighted objective function based on scenarios is provided, in which, each scenario influences the objective function according to its probability of occurrence. To generate different scenarios, the probability density function of the variables and the roulette wheel (RW) mechanism are used. Also, a modified version of the lightning search algorithm is proposed to solve the optimization problem of energy management.
The specific contributions of this research are the following:
The wind and solar generation uncertainty, as well as the load uncertainty, and the interaction of the load and the generation are considered simultaneously in a multi-agent based microgrid energy management approach.
Weighted Objective Function
A new weighted objective function is proposed for the microgrid energy management in which each contingency influences the objective function in terms of its own probability coefficient obtained from the deployed Probability Density Function.
Metaheuristic Optimization Method
A modified version of the Lightning Search Algorithm is presented for the energy management problem. Having higher accuracy than its previous version, the modified algorithm permits a more precise energy management of a microgrid under uncertainty.
The rest of this paper is organized as follows: In Section 2
, the optimization problem is formulated, and the proposed objective function and constraints are defined. In Section 3
, the model of uncertainties, photovoltaic system, and wind turbine are mathematically expressed. A brief introduction of the Lightning Search Algorithm comes in Section 4
. The model of the underlying microgrid is presented in Section 5
. Section 6
presents and discusses the simulation results. Finally, Section 7
concludes the paper.