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Unit Commitment Problem In Electrical Power Production
The unit commitment problem (UC) in electrical power production is a large family of mathematical optimization problems where the production of a set of electrical generators is coordinated in order to achieve some common target, usually either matching the energy demand at minimum cost or maximizing revenue from electricity production. This is necessary because it is difficult to store electrical energy on a scale comparable with normal consumption; hence, each (substantial) variation in the consumption must be matched by a corresponding variation of the production. Coordinating generation units is a difficult task for a number of reasons: * the number of units can be large (hundreds or thousands); * there are several types of units, with significantly different energy production costs and constraints about how power can be produced; * generation is distributed across a vast geographical area (e.g., a country), and therefore the response of the electrical grid, itself a highly c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
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 of sorts 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. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydraulic Head
Hydraulic head or piezometric head is a specific measurement of liquid pressure above a vertical datum., 410 pages. See pp. 43–44., 650 pages. See p. 22. It is usually measured as a liquid surface elevation, expressed in units of length, at the entrance (or bottom) of a piezometer. In an aquifer, it can be calculated from the depth to water in a piezometric well (a specialized water well), and given information of the piezometer's elevation and screen depth. Hydraulic head can similarly be measured in a column of water using a standpipe piezometer by measuring the height of the water surface in the tube relative to a common datum. The hydraulic head can be used to determine a ''hydraulic gradient'' between two or more points. "Head" in fluid dynamics In fluid dynamics, ''head'' is a concept that relates the energy in an incompressible fluid to the height of an equivalent static column of that fluid. From Bernoulli's principle, the total energy at a given point in a f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scenario Optimization
The scenario approach or scenario optimization approach is a technique for obtaining solutions to robust optimization and chance-constrained optimization problems based on a sample of the constraints. It also relates to inductive reasoning in modeling and decision-making. The technique has existed for decades as a heuristic approach and has more recently been given a systematic theoretical foundation. In optimization, robustness features translate into constraints that are parameterized by the uncertain elements of the problem. In the scenario method, a solution is obtained by only looking at a random sample of constraints (heuristic approach) called ''scenarios'' and a deeply-grounded theory tells the user how “robust” the corresponding solution is related to other constraints. This theory justifies the use of randomization in robust and chance-constrained optimization. Data-driven optimization At times, scenarios are obtained as random extractions from a model. More oft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust Optimization
Robust optimization is a field of mathematical optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty that can be represented as deterministic variability in the value of the parameters of the problem itself and/or its solution. History The origins of robust optimization date back to the establishment of modern decision theory in the 1950s and the use of worst case analysis and Wald's maximin model as a tool for the treatment of severe uncertainty. It became a discipline of its own in the 1970s with parallel developments in several scientific and technological fields. Over the years, it has been applied in statistics, but also in operations research, electrical engineering, control theory, finance, portfolio management logistics, manufacturing engineering, chemical engineering, medicine, and computer science. In engineering problems, these formulations often take the name of "Robust Design Optimization", ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operating Reserve
In electricity networks, the operating reserve is the generating capacity available to the system operator within a short interval of time to meet demand in case a generator goes down or there is another disruption to the supply. Most power systems are designed so that, under normal conditions, the operating reserve is always at least the capacity of the largest supplier plus a fraction of the peak load. Types of operating reserve The operating reserve is made up of the spinning reserve as well as the non-spinning or supplemental reserve: * The spinning reserve is the extra generating capacity that is available by increasing the power output of generators that are already connected to the power system. For most generators, this increase in power output is achieved by increasing the torque applied to the turbine's rotor. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phasor
In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude (''A''), angular frequency (''ω''), and initial phase (''θ'') are time-invariant. It is related to a more general concept called analytic representation,Bracewell, Ron. ''The Fourier Transform and Its Applications''. McGraw-Hill, 1965. p269 which decomposes a sinusoid into the product of a complex constant and a factor depending on time and frequency. The complex constant, which depends on amplitude and phase, is known as a phasor, or complex amplitude, and (in older texts) sinor or even complexor. A common situation in electrical networks powered by time varying current is the existence of multiple sinusoids all with the same frequency, but different amplitudes and phases. The only difference in their analytic representations is the complex amplitude (phasor). A linear combination of such functions can be represented as a linear co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirchhoff's Circuit Laws
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for network analysis. Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits. Kirchhoff's current law This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy Forecasting
Energy forecasting includes forecasting demand ( load) and price of electricity, fossil fuels (natural gas, oil, coal) and renewable energy sources (RES; hydro, wind, solar). Forecasting can be both expected price value and probabilistic forecasting. Background When electricity sectors were regulated, utility monopolies used short-term load forecasts to ensure the reliability of supply and long-term demand forecasts as the basis for planning and investing in new capacity. However, since the early 1990s, the process of deregulation and the introduction of competitive electricity markets have been reshaping the landscape of the traditionally monopolistic and government-controlled power sectors. In many countries worldwide, electricity is now traded under market rules using spot and derivative contracts. At the corporate level, electricity load and price forecasts have become a fundamental input to energy companies’ decision making mechanisms. The costs of over- or undercontractin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intermittent Energy Source
Variable renewable energy (VRE) or intermittent renewable energy sources (IRES) are renewable energy sources that are not dispatchable due to their fluctuating nature, such as wind power and solar power, as opposed to controllable renewable energy sources, such as dammed hydroelectricity or biomass, or relatively constant sources, such as geothermal power. The use of small amounts of intermittent power has little effect on grid operations. Using larger amounts of intermittent power may require upgrades or even a redesign of the grid infrastructure. Options to absorb large shares of variable energy into the grid include using storage, improved interconnection between different variable sources to smooth out supply, using dispatchable energy sources such as hydroelectricity and having overcapacity, so that sufficient energy is produced even when weather is less favourable. More connections between the energy sector and the building, transport and industrial sectors may also help. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geothermal Energy
Geothermal energy is the thermal energy in the Earth's crust which originates from the formation of the planet and from radioactive decay of materials in currently uncertain but possibly roughly equal proportions. The high temperature and pressure in Earth's interior cause some rock to melt and solid mantle to behave plastically. This results in parts of the mantle convecting upward since it is lighter than the surrounding rock. Temperatures at the core–mantle boundary can reach over 4000 °C (7200 °F). Geothermal heating, using water from hot springs, for example, has been used for bathing since Paleolithic times and for space heating since ancient Roman times. More recently geothermal power, the term used for generation of electricity from geothermal energy, has gained in importance. It is estimated that the earth's geothermal resources are theoretically more than adequate to supply humanity's energy needs, although only a very small fraction is currentl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Run-of-the-river Hydroelectricity
Run-of-river hydroelectricity (ROR) or run-of-the-river hydroelectricity is a type of hydroelectric generation plant whereby little or no water storage is provided. Run-of-the-river power plants may have no water storage at all or a limited amount of storage, in which case the storage reservoir is referred to as pondage. A plant without pondage is subject to seasonal river flows, thus the plant will operate as an intermittent energy source. Conventional hydro uses reservoirs, which regulate water for flood control, dispatchable electrical power, and the provision of fresh water for agriculture. Concept Run-of-the-river, or ROR, hydroelectricity is considered ideal for streams or rivers that can sustain a minimum flow or those regulated by a lake or reservoir upstream. A small dam is usually built to create a headpond ensuring that there is enough water entering the penstock pipes that lead to the turbines, which are at a lower elevation. Projects with pondage, as opposed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
