Hierarchical genetic optimization of a fuzzy logic system for energy flows management in microgrids

Highlights

• A Fuzzy-Genetic Algorithm paradigm for power flow management in a microgrid is proposed.

• The microgrid is connected to the main grid and it is equipped with renewable energy sources and a Battery Management System.

• A Hierarchical Genetic Algorithm is adopted for tuning the Rule Base of a suitable Fuzzy Inference System.

Abstract

Bio-inspired algorithms like Genetic Algorithms and Fuzzy Inference Systems (FIS) are nowadays widely adopted as hybrid techniques in improving goods and services. In this paper we present an interesting application of the fuzzy-GA paradigm to the problem of energy flows management in microgrids, concerning the design, through a data driven synthesis procedure, of an Energy Management System (EMS). The main aim consists in performing decision making for power flow management tasks in the proposed microgrid model, equipped by renewable sources and an energy storage system, aiming to maximize the accounting profit in energy trading with the main-grid. In particular this study focuses on the application of a Hierarchical Genetic Algorithm (HGA) for tuning the Rule Base (RB) of a Fuzzy Inference System (FIS), trying to discover a minimal fuzzy rules set as the core inference engine of an an EMS. The HGA rationale focuses on a particular encoding scheme, based on control genes and parametric genes, applied to the optimization of the FIS parameters, allowing to perform a reduction in the structural complexity of the RB. A performance comparison is performed with a simpler approach based on a classic fuzzy-GA scheme, where both FIS parameters and rule weights are tuned, while the number of fuzzy rules is fixed in advance. Experiments shows how the fuzzy-HGA approach adopted for the synthesis of the proposed controller outperforms the classic fuzzy-GA scheme, increasing the accounting profit by 67% in the considered energy trading problem, yielding at the same time a simpler RB.

Introduction

The world wide power grid can be considered one of the greatest masterpiece of engineering that human being has ever made. Moreover, starting from the First Industrial Revolution, Smart Grids (SGs) are one of the most important breakthrough that science and engineering fields are carrying out. Currently, the Smart Grid concept is founded on a paradigmatic revolution that will permeate many aspects of human life. From the power system point of view, SGs can be considered as a way to transform the electric energy infrastructures from a centralized, producer-controlled network, into a distributed and consumer-interactive system, leveraging the same concepts and technologies that enabled the emergence and spread of the Internet [1]. SGs vision promises a power grid infrastructure with increased automation of the grid operations and “self-healing” capabilities. SGs integrate the renewable energy production, seamlessly balancing energy supply and demand, and can be considered as a key technology for facilitating the spread of electric mobility. To achieve that vision, the current power grid has to be thought as a technological ecosystem that needs a strong injection of distributed intelligence [2]. G.K. Venayagamoorthy argues that the current power grid can be considered a spatially and temporally complex, nonlinear and non-stationary system with a lot of uncertainties [3]. Accordingly, the SG can be examined for all intents and purposes as a Complex System, and Computational Intelligence (CI) and Soft Computing (SC) techniques [4], [5], [6], [7], are widely adopted to face a plethora of applications and problems arising in the SG context. The main CI paradigms for SG related problem solutions are: neuro-fuzzy, neuro-swarm, fuzzy-PSO, fuzzy-GA, neuro-Genetic [3], [8], [9], [10]. In fact, in MG related tasks, such as flows management and control, the presence of uncertainty and non-linearity, for example in the power demand profile of a large amount of users or in the power produced by solar or wind sources, makes related problems extremely challenging. Hence, SC techniques can help managing the complexity of problems offering reliable solutions, especially in presence of non-linearity [11] and in presence of storage devices that increase the solution space of the unit commitment problem [12]. Consequently, since linear techniques cannot be considered adequate in solving problems whose nature is nonlinear and even stochastic, SC techniques offer a suitable framework introducing learning capabilities in the design of the MG controllers, especially in presence of renewable energy sources and storage. The current research follows our previous work [13] concerning an application of what we call classic fuzzy-GA paradigm to the problem of Energy Flows Management System Optimization in a Microgrid (MG). The MG can be thought as a sub-network of the SG characterized by the presence of autonomous (often renewable) energy sources buffered by some type of Battery Energy Storage System (BESS) and locally controlled in order to achieve smart energy flows management. It is important to underline that the problem we are facing is related to the synthesis of an EMS, able to take decisions in real time in operative conditions (i.e. able to show a generalization capability when operating on data different from the ones used at learning stage), which is a much more challenging task compared to just optimizing the behavior of an EMS on given and predefined data (known in advance). The flow control task is carried out by an EMS whose behavior is defined by two Fuzzy Inference Systems (FISs) of Mamdani type. FISs, relaying on approximated reasoning based on Fuzzy Logic (FL), are in charge to take decisions concerning energy flows, trying to maximize the overall accounting profit in energy trading operations with the main-grid. The current work is focused on two main objectives: (i) to improve the MG model, in particular the BESS model, (ii) to optimize the Rule Base (RB) of the EMS in charge of managing power flows in the MG. As concerns the first goal we move on from an ideal battery adopted in [13] by considering an energy storage device based on a real-world model with realistic efficiency parameters. For the second objective, we designed an optimization method based on a suited Genetic Algorithm (GA) that is in charge of adapting the FIS parameters, optimizing at the same time both the accounting profit in energy trading and the cardinality of the fuzzy RB. The adopted optimization algorithm is known as Hierarchical Genetic Algorithm (HGA) aiming to perform at the same time a fine tuning of the fuzzy Membership Functions (MFs) and the structural optimization of the FISs – in the following we will refer to this paradigm as “fuzzy-HGA paradigm”. In fact, while in our previous work the FIS structure is constrained to be fixed, with a predefined number of antecedent and consequent terms and, thereby, with an immutable number of fuzzy rules, the adopted HGA scheme allows to relax these constraints. Moreover, the standard GA approach deals with a chromosome of fixed length, whose encoding scheme leads to a lower flexibility in the RB tuning. A GA algorithm able to emulate a variable length chromosome with a suitable encoding scheme of the FIS is ideal for optimizing the number of rules in the given RB. Finally, the fuzzy rule optimization can lead to an improved performance of the FIS, discarding pre-defined low performing rules. The idea behind HGAs is based on the biological inspired gene structure of a chromosome formed in a hierarchical fashion, emulating the encoding approach of the deoxyribonucleic acid (DNA). In Nature the genes can be classified into two different types: regulatory sequences and structural genes. One of the regulatory sequences found in DNA is called the “promoter” with the task of activating or deactivating structural genes. Therefore the presence of active and inactive genes in the structural genes leads to the idea of a hierarchical structure formulation of the chromosome that consists of control genes and parametric genes. The activation of the parametric genes is governed by the value of the control genes. Accordingly, the strategy suggested by Nature can be modeled for solving a number of engineering problems, such as those involving mix integer programming methods [14] or fuzzy control applications demanding the joint optimization of both FISs parameters and RBs [15]. In the last case the novelty of a hierarchical coding scheme is based on the definition of suitable genetic operators moving from standard GA algorithms to more advanced ones. The hierarchical encoding scheme allows to code the FISs parameters, more precisely MF parameters, as parametric genes and, at the same time, control genes can be used to activate and deactivate MFs composing a given fuzzy RB, thus tuning the overall number of fuzzy rules. The work is organized as follows.

Section 2 is a literature review about FISs for energy flows management in microgrids and the fuzzy-GA paradigm as an effective approach for EMS synthesis. In Section 3 we introduce the optimization problem and the MG model. Section 4 clarifies the level of abstraction of the problem, introducing the adopted notation and explaining how the EMS works. The fuzzy control scheme for a MG, together with the classic fuzzy-GA and fuzzy-HGA paradigms are treated in Section 5 and related subsections. In Section 6, soon after the introduction of the examined MG scenarios and the algorithm settings, the main results are reported and discussed. Finally, conclusions are drawn in Section 7, while feature works are discussed in Section 8.