A Comparison Study of Multi-Objective Bonobo Optimizers for Optimal Integration of Distributed Generation in Distribution Systems

Abstract

In this paper, the three newly published Multi-Objective Bonobo Optimizer (MOBO) variants are assessed and evaluated using statistical analysis for solving the multi-objective optimization of Distributed Generation (DG) into distribution systems. The main objectives of the study are to minimize system loss and enhance voltage profile. While the first variant, MOBO1, depends on the sort and grid-index approach, the second variant, MOBO2, relies on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) algorithm technique. The last variant, MOBO3, is inspired by the Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D). The three MOBO algorithms are compared to themselves and to other algorithms solving the same optimization problem. These algorithms include the MOJAYA, Multi-Objective Artificial Ecosystem-Based Algorithm (MOAEO), Multi-Objective Gravitational Search Algorithm (MOGSA), and Multi-Objective Particle Swarm Optimization (MOPSO). The 33-bus and 85-bus radial distribution systems are used test systems for solving the optimal allocation of single- and three-DG units operating at unity power factor. In order to find the best compromise solution, the Pareto Optimal front method is adopted with the help of a fuzzy-based function. The obtained results show the effectiveness of the MOBO variants compared with other algorithms in terms of different statistical parameters and multi-objective performance metrics such as diversity, hypervolume, spacing, and set coverage. While the MOBO algorithm reduces power loss and TVD by 39.59 and 68.31% for a single DG, they are reduced to 58.13 and 88.44% for three DG units allocated to the 33-bus distribution system, respectively. On the other hand, the MOBO algorithm reduces power loss and TVD by 37.28 and 66.84% for a single DG, respectively, they are decreased to 46.35 and 82.53% for three DG units assigned to the 85-bus distribution system. Among the three MOBO variants, it is found that the MOBO1 is superior for a single-DG allocation, while the MOBO3 is the best for the allocation of three-DG units.

Reduction of Emission Cost, Loss Cost and Energy Purchase Cost for Distribution Systems With Capacitors, Photovoltaic Distributed Generators, and Harmonics

“…In the promiscuous and restrictive mating strategies, pp is compared with a random number (𝑟𝑑 1 ) between zero and one, if pp is greater than or equal to 𝑟𝑑 1 then a new bonobo is produced by applying Eq. ( 16) as given below [34,44]:…”

Optimal sizing and location of grid-interfaced PV, PHES, and ultra capacitor systems to replace LFO and HFO based power generations

“…Several variants of this method are available, including a version that integrates a distance sorting approach and non-dominated crowding (MOBO-II) 77 . This algorithm has been employed to address a wide range of optimization issues, particularly as documented in references 78 – 82 . The variation employed in this work is the proposed one, which incorporates distance sorting and a non-dominated crowding approach.…”

Multi-objective optimal allocation of multiple capacitors and distributed generators considering different load models using Lichtenberg and thermal exchange optimization techniques

“…Compared to PSO and ASO techniques, the MOAOA is the best technique for the current optimization problem. The authors in [30] introduced the application of the three new versions of the MO Bonobo Optimizer (MOBO) for solving the optimal installation of DG Type-I on the 33-bus and 85-bus distribution systems to minimize only the voltage deviation summation and power loss. The POF obtained using the MOBO versions was compared with other well-known multi-objective optimization techniques such as MOPSO, MOAEO, MOGSA, and MOJAYA using MO indicators.…”

“…The V i and V j denote the voltage at the sending and receiving end buses, respectively. Now, the current ðI ij Þ through the line between two nodes i and j is a function of the demand ðS j Þ at bus j and is given by the following expression, as follows [30]:…”