General Analytic Solution of the Telegrapher’s Equations and the Resulting Consequences for Electrically Short Transmission Lines

Based on classical circuit theory, this article develops a general analytic solution of the telegrapher’s equations, in which the length of the cable is explicitly contained as a freely adjustable parameter. For this reason, the solution is also applicable to electrically short cables. Such a model has become indispensable because a few months ago, it was experimentally shown that voltage fluctuations in ordinary but electrically short copper lines move at signal velocities that are significantly higher than the speed of light in a vacuum. This finding contradicts the statements of the special theory of relativity but not, as is shown here, the fundamental principles of electrical engineering. Based on the general transfer function of a transmission line, the article shows mathematically that an unterminated, electrically short cable has the characteristics of an ideal delay element, meaning that an input signal appears at the output with a slight delay but remains otherwise unchanged. Even for conventional cables, the time constants can be so small that the corresponding signal velocities can significantly exceed the speed of light in a vacuum. The article also analyses the technical means with which this effect can be conveyed to very long cables.

An Exact Solution of Telegraph Equations for Voltage Monitoring of Electrical Transmission Line

Telegraph equations are derived from the equations of transmission line theory. They describe the relationships between the currents and voltages on a portion of an electric line as a function of the linear constants of the conductor (resistance, conductance, inductance, capacitance). Their resolution makes it possible to determine the variation of the current and the voltage as a function of time at each point of the line. By adopting a general sinusoidal form, we propose a new exact solution to the telegraphers’ partial differential equations. Different simulations have been carried out considering the parameter of the 12/20 (24) kV Medium Voltage Cable NF C 33,220. The curves of the obtained solution better fit the real voltage curves observed in the electrical networks in operation.

Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method

We introduce a new integral scheme namely improved Kudryashov method for solving any nonlinear fractional differential model.Specifically,we apply the approach to the nonlinear space-time fractional model leading the wave to spread in electrical transmission lines(s-tfETL),the time fractional complex Schrödinger(tfcS),and the space-time M-fractional Schrödinger-Hirota(s-tM-fSH)models to verify the effectiveness of the proposed approach.The implementing of the introduced new technique based on the models provides us with periodic envelope,exponentially changeable soliton envelope,rational rogue wave,periodic rogue wave,combo periodic-soliton,and combo rational-soliton solutions,which are much interesting phenomena in nonlinear sciences.Thus the results disclose that the proposed technique is very effective and straight-forward,and such solutions of the models are much more fruitful than those from the generalized Kudryashov and the modified Kudryashov methods.

Reducing Greenhouse Gas Emissions through Improving the Life Span of Wooden Power Electric Poles of Eucalyptus saligna

The present work deals with reducing greenhouse gas emissions through improving the life span of wooden power electric poles of Eucalyptus saligna. Indeed, in Sub-Saharan African countries, Cameroon in particular, most of the power line networks are made of wooden supports and according to the Cameroon energy distribution company, wooden poles represent 32% of the causes of death linked to the state of the network. The company’s 2019 annual report indicates that 40,000 wooden poles were in critical condition and should be replaced. A significant number of mechanical failures affecting these supports have been observed. For example, on the HVA/LV power line “D17 Nko- abang” in Yaoundé in Cameroon, less than three years old, 10 (ten) cases of poles falling and/or breaking, due to their mechanical loading, were observed over a period of fewer than nine months, causing an average service stoppage for more than 11 hours and affecting an average of 3280 customers. These incidents lead to questions about how the supports are dimensioned and what load capacities they are designed to support. The aim of this work is, therefore, to suggest a method of dimensioning wooden poles hence reducing green- house gas emissions due to the deforestation by reducing the number of woo- den poles at risk to be replaced on Cameroon’s electricity distribution network. And more specifically, to reduce the number of mechanical failures affecting the wooden supports observed by analyzing the current wooden supports with their loads and to make proposals for improving the actual dimensioning me- thods. From the study carried out, it appears that 449 out of 845 supports, i.e., 53% needed to be replaced or monitored because they support the nominal forces ranging from 85% to 150% of their admissible limit and proposals have been made to improve their dimensioning.

The double auxiliary equations method and its application to space-time fractional nonlinear equations

This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differential equation.The proposed scheme has been successfully applied on two very important evolution equations,the space-time fractional differential equation governing wave propagation in low-pass electrical transmission lines equation and the time fractional Burger’s equation.The obtained results show that the proposed method is more powerful,promising and convenient for solving nonlinear fractional differential equations(NFPDEs).To our knowledge,the solutions obtained by the proposed method have not been reported in former literature.