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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 criteria, 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. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydraulic Head
Hydraulic head or piezometric head is a measurement related to liquid pressure (normalized by specific weight) and the liquid elevation above a vertical datum., 410 pages. See pp. 43–44., 650 pages. See p. 22, eq.3.2a. It is usually measured as an equivalent 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. Definition In fluid dynamics, the ''head'' at some point in an incompressible (constant density) flow is equal to the height of a static column of fluid whose pressure at ... [...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 constraint (mathematics), 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 (mathematics), 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 o ... [...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. It is related to, but often distinguished from, probabilistic optimization methods such as chance-constrained optimization. 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, Investment management, portfolio management logistics, manufacturing engineering, chem ... [...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 and initial phase are time-invariant and whose angular frequency is fixed. 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 application is in the steady-state analysis of an electrical network powered by time varying current where all signals are assumed to be sinusoidal with a common frequency. Phasor representation allows the analyst to represent the amplitude and phase of the signal using a single complex number. The only difference in their analytic rep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AC Power
In an electric circuit, instantaneous power is the time rate of flow of energy past a given point of the circuit. In alternating current circuits, energy storage elements such as inductors and capacitors may result in periodic reversals of the direction of energy flow. Its SI unit is the watt. The portion of instantaneous power that, averaged over a complete cycle of the AC waveform, results in net transfer of energy in one direction is known as instantaneous active power, and its time average is known as active power or real power. The portion of instantaneous power that results in no net transfer of energy but instead oscillates between the source and load in each cycle due to stored energy is known as instantaneous reactive power, and its amplitude is the absolute value of reactive power. Active, reactive, apparent, and complex power in sinusoidal steady-state For a simple alternating current (AC) circuit in steady-state; consisting of a source and a Linear circuit, linear T ... [...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 cur ... [...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 undercontract ... [...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 bioenergy, 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 h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geothermal Energy
Geothermal energy is thermal energy extracted from the crust (geology), crust. It combines energy from the formation of the planet and from radioactive decay. Geothermal energy has been exploited as a source of heat and/or electric power for millennia. Geothermal heating, using water from hot springs, for example, has been used for bathing since Paleolithic times and for space heating since Roman times. Geothermal power (generation of electricity from geothermal energy), has been used since the 20th century. Unlike wind and solar energy, geothermal plants produce power at a constant rate, without regard to weather conditions. Geothermal resources are theoretically more than adequate to supply humanity's energy needs. Most extraction occurs in areas near tectonic plate boundaries. The cost of generating geothermal power decreased by 25% during the 1980s and 1990s. Technological advances continued to reduce costs and thereby expand the amount of viable resources. In 2021, the US ... [...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, so 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 to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
