Abstract
In this chapter, a hybrid bare bones fireworks algorithm (HBBFWA) is proposed and its application in solving the load flow problem of islanded microgrid is demonstrated. The hybridization is carried out by updating the positions of generated sparks with the help of grasshopper optimization algorithm (GOA) mimicking the swarming behavior of grasshoppers. The purpose of incorporating GOA with bare bones fireworks algorithm (BBFWA) is to enhance the global searching capability of conventional BBFWA for complex optimization problems. The proposed HBBFWA is applied to perform the load flow analysis of a modified IEEE 37-Bus system. The performance of the proposed HBBFWA is compared against the performance of BBFWA in terms of computational time, convergence speed, and number of iterations required for convergence of the load flow problem. Moreover, standard statistical analysis test such as the independent sample t-test is conducted to identify statistically significant differences between the two algorithms.
TopIntroduction
Metaheuristic optimization algorithms have gained much popularity over the years in solving complex optimization problems. These algorithms work in stochastic manner which implies that there is inherent randomness in the optimization process of these algorithms. Evolutionary and swarm intelligence-based algorithms such as genetic algorithm (GA) (Holland, 1992), simulated annealing (SA) (Kirkpatrick, Gelatt, & Vecchi, 1983), particle swarm optimization (PSO) (Eberhart & Kennedy, 1995), ant colony optimization (ACO) (Dorigo & Birattari, 2010), imperialist competitive algorithm (ICA) (Atashpaz-Gargari & Lucas, 2007), grasshopper optimization algorithm (GOA) (Saremi, Mirjalili, & Lewis, 2017) etc. are categorized under the class of metaheuristic algorithms. Most of these algorithms are inspired from some sort of biological or natural phenomenon. Similarly, inspired by observing fireworks explosion, a novel swarm intelligence-based algorithm, named fireworks algorithm (FWA) was proposed in (Tan & Zhu, 2010). Since its inception, several modified versions of the fireworks algorithm have been proposed by different researchers over the years. The bare bones fireworks algorithm (BBFWA) is one of the modified versions of the conventional fireworks algorithm where only the essential explosion operation is kept and remaining less significant operations, i.e. mutation operations are eliminated (Li & Tan, 2018). This results in an algorithm which is easier to implement, dependent on a smaller number of parameters, and computationally less expensive. However, the absence of the mutation operator reduces the global searching capability of this algorithm. Thus, to compensate the absence of the mutation operator, the focus of this chapter will be to include the searching process involved in the grasshopper optimization algorithm (GOA) within the working steps of the BBFWA forming a hybrid bare bones fireworks algorithm (HBBFWA). This hybrid algorithm will then be applied to perform the load flow analysis of islanded microgrid considering the modified IEEE-37 bus system as a case study system. Due to the absence of slack bus, the conventional methods of load flow solution are not applicable for an islanded microgrid. Metaheuristic optimization algorithms can be good alternatives to the conventional algorithms used for load flow analysis. Considering this fact, the proposed HBBFWA will be employed to perform load flow analysis of islanded microgrids. Additionally, this will also justify the applicability of this algorithm in solving complex optimization problems. The following sub-sections include background study on the evolution of fireworks algorithm, a brief literature review on the load flow analysis of islanded microgrid and the main focus of this chapter.
Key Terms in this Chapter
Objective Function: The function whose value is intended to be minimized or maximized through the optimization process.
Optimum Solution: The set of decision variables for which the value of given objective function is minimum or maximum.
Droop Controller: It is an autonomous approach for controlling frequency and voltage level of a generating unit, utilizing the real power – frequency and reactive power – voltage relationships.
Metaheuristic Optimization: Optimization technique where it is not required to calculate the derivative of the objective function. Rather, the optimization technique is associated with several stochastic components and the optimum solution is obtained by trial and error.
Global Optimum: Global optimum solution of an optimization problem is the solution which provides the optimum (either minimum or maximum) value of the objective function compared to all possible solution sets.
Islanded Microgrid: Islanded microgrid system is disconnected from the main grid and all the distributed generator units are collectively responsible for supplying power to different loads.
Load Flow Analysis: It is a computational tool essential to determine steady state operating points of any power system. The complex voltages at all the buses, power flows from different buses and through the transmission lines can be obtained through load flow analysis.
Local Optimum: Local optimum solution of an optimization problem is the solution for which the value of the objective function is optimum (either minimum or maximum) within a small range of nearby possible solution sets.
Optimization: Optimization refers to a mathematical technique of obtaining the minimum or maximum value of a given function dependent on several variables. These variables depend on several constraints.