Optimal design of single-tuned filters for industrial power systems to reduce harmonic distortion using forest algorithm

ABSTRACT

This paper presents a novel optimization algorithm for designing single-tuned filters in industrial power systems to reduce harmonic distortion. Single-tuned filters are cost-efficient, simple, and easy to maintain. We formulate the filter design as an optimization problem, minimizing costs while incorporating harmonic limits and system constraints. Our solution algorithm simulates tree growth, proliferation, and death based on the forest algorithm to generate optimal solutions. This enables both local and global searches for fast convergence and feasible designs. Unlike traditional approaches, we account for variations in filter components and system parameters caused by factors like manufacturing tolerances, operating temperature, and frequency variations. Our study contributes by designing adaptive filters that match practical systems. We validate our method against previous publications and other techniques like simulated annealing and teaching-learning-based optimization. Simulation results demonstrate the effectiveness of our approach in minimizing costs, satisfying operation constraints, and accounting for component variations in this complex problem.

CO EDITOR-IN-CHIEF:

• Kuo, Cheng-Chien

ASSOCIATE EDITOR:

• Jeng, Yeau-Ren

KEYWORDS:

• Forest algorithm
• industrial power system
• optimization
• passive harmonic filters
• power quality

Nomenclature

C	=	capacitance (farad, F)
L	=	inductance (henry, H)
Lmax	=	maximum length of branches
Lmin	=	minimum length of branches
Lp	=	lengths of its parents
L0	=	length a branch
Q	=	capacity of filter
R	=	resistance (ohm, Ω)
THD	=	total harmonic distortion
V	=	vitality of tree
$\bar{V}$	=	average vitality of all trees
VR	=	voltage variation
X	=	reactance
Z	=	impedance (ohm, Ω)
h	=	order of the filter tuning harmonics
hr	=	resonance point
k1	=	unit cost of capacitance
k2	=	unit cost of inductance
k3	=	unit cost of filter capacity
rand	=	random value in [0 1]
α	=	threshold of the tree’s vitality
δ	=	growth factor
ρ	=	cost coefficient for installation space
σ	=	mutation rate
${\omega }_h$	=	resonance frequency

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the National Science and Technology Council [MOST 109-2622-E-152-001]. The authors express their gratitude to the National Science and Technology Council and Leegood Automation Systems Inc. for providing research funding.