Electrical faultIn an electric power system, a fault or fault current is any abnormal electric current. For example, a short circuit is a fault in which a live wire touches a neutral or ground wire. An open-circuit fault occurs if a circuit is interrupted by a failure of a current-carrying wire (phase or neutral) or a blown fuse or circuit breaker. In three-phase systems, a fault may involve one or more phases and ground, or may occur only between phases. In a "ground fault" or "earth fault", current flows into the earth.
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).
Prospective short-circuit currentThe prospective short-circuit current (PSCC), available fault current, or short-circuit making current is the highest electric current which can exist in a particular electrical system under short-circuit conditions. It is determined by the voltage and impedance of the supply system. It is of the order of a few thousand amperes for a standard domestic mains electrical installation, but may be as low as a few milliamperes in a separated extra-low voltage (SELV) system or as high as hundreds of thousands of amps in large industrial power systems.
Power system protectionPower system protection is a branch of electrical power engineering that deals with the protection of electrical power systems from faults through the disconnection of faulted parts from the rest of the electrical network. The objective of a protection scheme is to keep the power system stable by isolating only the components that are under fault, whilst leaving as much of the network as possible in operation. The devices that are used to protect the power systems from faults are called protection devices.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Earthing systemAn earthing system (UK and IEC) or grounding system (US) connects specific parts of an electric power system with the ground, typically the Earth's conductive surface, for safety and functional purposes. The choice of earthing system can affect the safety and electromagnetic compatibility of the installation. Regulations for earthing systems vary among countries, though most follow the recommendations of the International Electrotechnical Commission (IEC).
Protective relayIn electrical engineering, a protective relay is a relay device designed to trip a circuit breaker when a fault is detected. The first protective relays were electromagnetic devices, relying on coils operating on moving parts to provide detection of abnormal operating conditions such as over-current, overvoltage, reverse power flow, over-frequency, and under-frequency. Microprocessor-based solid-state digital protection relays now emulate the original devices, as well as providing types of protection and supervision impractical with electromechanical relays.
Wavelet transformIn mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space of square integrable functions.
Discrete wavelet transformIn numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time). Haar wavelet The first DWT was invented by Hungarian mathematician Alfréd Haar. For an input represented by a list of numbers, the Haar wavelet transform may be considered to pair up input values, storing the difference and passing the sum.
Transmission lineIn electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmission must be taken into account. This applies especially to radio-frequency engineering because the short wavelengths mean that wave phenomena arise over very short distances (this can be as short as millimetres depending on frequency).
Electric power transmissionElectric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation. The interconnected lines that facilitate this movement form a transmission network. This is distinct from the local wiring between high-voltage substations and customers, which is typically referred to as electric power distribution. The combined transmission and distribution network is part of electricity delivery, known as the electrical grid.
WaveletA wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second.
Time-domain reflectometerA time-domain reflectometer (TDR) is an electronic instrument used to determine the characteristics of electrical lines by observing reflected pulses. It can be used to characterize and locate faults in metallic cables (for example, twisted pair wire or coaxial cable), and to locate discontinuities in a connector, printed circuit board, or any other electrical path. A TDR measures reflections along a conductor. In order to measure those reflections, the TDR will transmit an incident signal onto the conductor and listen for its reflections.
Real-time locating systemReal-time locating systems (RTLS), also known as real-time tracking systems, are used to automatically identify and track the location of objects or people in real time, usually within a building or other contained area. Wireless RTLS tags are attached to objects or worn by people, and in most RTLS, fixed reference points receive wireless signals from tags to determine their location. Examples of real-time locating systems include tracking automobiles through an assembly line, locating pallets of merchandise in a warehouse, or finding medical equipment in a hospital.
Continuous wavelet transformIn mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the wavelets vary continuously. The continuous wavelet transform of a function at a scale (a>0) and translational value is expressed by the following integral where is a continuous function in both the time domain and the frequency domain called the mother wavelet and the overline represents operation of complex conjugate.
Transmission towerA transmission tower, also known as an electricity pylon or simply a pylon in British English and as a hydro tower in Canadian English, is a tall structure, usually a steel lattice tower, used to support an overhead power line. In electrical grids, they are generally used to carry high-voltage transmission lines that transport bulk electric power from generating stations to electrical substations before reaching its end consumers; utility poles are used to support lower-voltage subtransmission and distribution lines that transport power from substations to electric customers.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Overhead power lineAn overhead power line is a structure used in electric power transmission and distribution to transmit electrical energy across long distances. It consists of one or more uninsulated electrical cables (commonly multiples of three for three-phase power) suspended by towers or poles. Since most of the insulation is provided by the surrounding air, overhead power lines are generally the least costly method of power transmission for large quantities of electric energy.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
