Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Single-wire earth returnSingle-wire earth return (SWER) or single-wire ground return is a single-wire transmission line which supplies single-phase electric power from an electrical grid to remote areas at lowest cost. Its distinguishing feature is that the earth (or sometimes a body of water) is used as the return path for the current, to avoid the need for a second wire (or neutral wire) to act as a return path. Single-wire earth return is principally used for rural electrification, but also finds use for larger isolated loads such as water pumps.
Earth potential riseIn electrical engineering, earth potential rise (EPR) also called ground potential rise (GPR) occurs when a large current flows to earth through an earth grid impedance. The potential relative to a distant point on the Earth is highest at the point where current enters the ground, and declines with distance from the source. Ground potential rise is a concern in the design of electrical substations because the high potential may be a hazard to people or equipment.
Spark gapA spark gap consists of an arrangement of two conducting electrodes separated by a gap usually filled with a gas such as air, designed to allow an electric spark to pass between the conductors. When the potential difference between the conductors exceeds the breakdown voltage of the gas within the gap, a spark forms, ionizing the gas and drastically reducing its electrical resistance. An electric current then flows until the path of ionized gas is broken or the current reduces below a minimum value called the "holding current".
Symmetrical componentsIn electrical engineering, the method of symmetrical components simplifies analysis of unbalanced three-phase power systems under both normal and abnormal conditions. The basic idea is that an asymmetrical set of N phasors can be expressed as a linear combination of N symmetrical sets of phasors by means of a complex linear transformation. Fortescue's theorem (symmetrical components) is based on superposition principle, so it is applicable to linear power systems only, or to linear approximations of non-linear power systems.
Arcing hornsArcing horns (sometimes arc-horns) are projecting conductors used to protect insulators or switch hardware on high voltage electric power transmission systems from damage during flashover. Overvoltages on transmission lines, due to atmospheric electricity, lightning strikes, or electrical faults, can cause arcs across insulators (flashovers) that can damage them. Alternately, atmospheric conditions or transients that occur during switching can cause an arc to form in the breaking path of a switch during its operation.
James Clerk MaxwellJames Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist with broad interests and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and light as different manifestations of the same phenomenon. Maxwell's equations for electromagnetism have been called the "second great unification in physics" where the first one had been realised by Isaac Newton.
Lattice towerA lattice tower or truss tower is a freestanding vertical framework tower. This construction is widely used in transmission towers carrying high voltage electric power lines, in radio masts and towers (a self-radiating tower or as a support for aerials) and in observation towers. Its advantage is good shear strength at a much lower weight than a tower of solid construction would have as well as lower wind resistance. In structural engineering the term lattice tower is used for a freestanding structure, while a lattice mast is a guyed mast supported by guy lines.
