1. Introduction

The availability and use of electrical power in the society is crucial in the development and growth of the society. Power generated from power stations is transmitted using high voltage transmission lines. The transmission of power from the point of generation to the point of use requires complex network of high voltage lines, systems and components [1]. High voltage conductors are usually subjected to vibration and the vulnerabilities of the power lines to vibration can lead to fatigue failure. Thus, power loading determination and control on the power grid can influence the integrity of the transmission network. High voltage conductor vibration is very difficult to model due to the fact that the responses exhibit a non-linear

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behaviour. There has been concerted effort to try and predict the conductor response as a result of aeolian vibration. Evaluations of conductor vibration caused by aeolian forces have been investigated be several researchers [2–6].

Recent researches developed models to investigate wind-induced vibration using nonlinear time history, expert systems, the concept of principal modes, aero-elastic and bending stiffness [7–17]. The investigation of vortex formation and the phenomenon of wind-induced vibration was done using the concept fluid–solid dynamic excitation [18–20]. The models were used to determine how wind loading influenced the oscillation of transmission lines. This form of investigation was done by experimental studies carried out in a wind tunnel [21, 22]. The outcomes of these experiments were used to determine conductor input loading. Several models developed by various researchers can be used to determine conductor damping and also the placement of vibration absorbers on the line conductors to curtail the effect of cable mechanical oscillation [23–27]. Based on the various models that have been developed by researchers as indicated in the first and second paragraphs, there is a need to further analyze wind-induced vibration using finite element method (FEM) in MATLAB.

The design, construction and maintenance of power transmission network requires adequate understanding of the system dynamics that occurs when subjected to vortex induced vibration [28]. Various analysis can be conducted using techniques that suit certain objectives. System integrity in high voltage transmission lines is of paramount importance. MATLAB is a multimodel simulation environment used for numerical computing. It can be integrated with physical hardware or systems in order to determine real-time performance, characteristics and behavior. MATLAB also provides a platform for special hardware in loop simulations [29]. These functionalities amongst others are vital in determining various characteristics and behaviors in high voltage transmission lines.

High voltage transmission lines and grid can experience vulnerabilities such as vibration, electromagnetic transients, fatigue, transmission loss, switching surges, conductor sag fluctuation [30, 31]. When the conductor experiences vibration, the transmission lines experience high amplitudes of vibrations from wind forces and can lead to fatigue of the transmission lines [1]. The use of systems simulation and analysis provides the platform to understand the response of the transmission conductor. The responses considered in the chapter include transmission line excitation through wind loading, conductor properties such as damping and damper placement used in mitigating the vibration.

The chapter discussed the development and implementation of a wind-induced high voltage transmission line vibration using finite element method (FEM) in MATLAB. The sections in the chapter discussed the development of transmission line equation of motion, the solution to the equation of motion, free and forced vibration of the transmission line, dampers and conductor self-damping, FEM MATLAB setup and implementation, simulation of FEM models. The chapter also discussed results from FEM models, simulation and experimental investigation. The chapter is focused towards the development of a finite element method and its implementation on the MATLAB software. The developed finite element method (FEM) was based on the concept of the simply supported beam model and it was used in modeling the transverse vibration of power line conductors. The results from the FEM were then compared with results from the analytical model and results obtained from experimental studies documented in [1]. The results from MATLAB simulations from the finite element models and experimental results were compared in order to determine the accuracy of the models. The developed FEM was then used as the means to verify the effect of varying the conductor axial tension on the natural frequencies of the conductors.
