Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
A rotary converter is a type of electrical machine which acts as a mechanical rectifier, inverter or frequency converter. Rotary converters were used to convert alternating current (AC) to direct current (DC), or DC to AC power, before the advent of chemical or solid state power rectification and inverting. They were commonly used to provide DC power for commercial, industrial and railway electrification from an AC power source. The rotary converter can be thought of as a motor-generator, where the two machines share a single rotating armature and set of field coils.
A high-voltage direct current (HVDC) electric power transmission system (also called a power superhighway or an electrical superhighway) uses direct current (DC) for electric power transmission, in contrast with the more common alternating current (AC) transmission systems. Most HVDC links use voltages between 100 kV and 800 kV. However, a 1,100 kV link in China was completed in 2019 over a distance of with a power capacity of 12 GW. With this dimension, intercontinental connections become possible which could help to deal with the fluctuations of wind power and photovoltaics.
In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.
A power inverter, inverter or invertor is a power electronic device or circuitry that changes direct current (DC) to alternating current (AC). The resulting AC frequency obtained depends on the particular device employed. Inverters do the opposite of rectifiers which were originally large electromechanical devices converting AC to DC. The input voltage, output voltage and frequency, and overall power handling depend on the design of the specific device or circuitry. The inverter does not produce any power; the power is provided by the DC source.
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
A smart grid is an electrical grid which includes a variety of operation and energy measures including: Advanced metering infrastructure (of which smart meters are a generic name for any utility side device even if it is more capable e.g. a fiber optic router) Smart distribution boards and circuit breakers integrated with home control and demand response (behind the meter from a utility perspective) Load control switches and smart appliances, often financed by efficiency gains on municipal programs (e.g.
A voltage regulator is a system designed to automatically maintain a constant voltage. A voltage regulator may use a simple feed-forward design or may include negative feedback. It may use an electromechanical mechanism, or electronic components. Depending on the design, it may be used to regulate one or more AC or DC voltages. Electronic voltage regulators are found in devices such as computer power supplies where they stabilize the DC voltages used by the processor and other elements.
Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function is equivalent to the minimization of the function . Given a possibly nonlinear and non-convex continuous function with the global minima and the set of all global minimizers in , the standard minimization problem can be given as that is, finding and a global minimizer in ; where is a (not necessarily convex) compact set defined by inequalities .
In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa). Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem.
