Energy Modelling
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Energy Modelling
Energy modeling or energy system modeling is the process of building computer models of energy systems in order to analyze them. Such models often employ scenario analysis to investigate different assumptions about the technical and economic conditions at play. Outputs may include the system feasibility, greenhouse gas emissions, cumulative financial costs, natural resource use, and energy efficiency of the system under investigation. A wide range of techniques are employed, ranging from broadly economic to broadly engineering. Mathematical optimization is often used to determine the least-cost in some sense. Models can be international, regional, national, municipal, or stand-alone in scope. Governments maintain national energy models for energy policy development. Energy models are usually intended to contribute variously to system operations, engineering design, or energy policy development. This page concentrates on policy models. Individual building energy simulati ...
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Computer Model
Computer simulation is the running of a mathematical model on a computer, the model being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions. Computer simulations are realized by running computer programs that can be either small, running almost instantly on small devices, or large-scale p ...
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Fossil Fuel
A fossil fuel is a flammable carbon compound- or hydrocarbon-containing material formed naturally in the Earth's crust from the buried remains of prehistoric organisms (animals, plants or microplanktons), a process that occurs within geological formations. Reservoirs of such compound mixtures, such as coal, petroleum and natural gas, can be extracted and burnt as fuel for human consumption to provide energy for direct use (such as for cooking, heating or lighting), to power heat engines (such as steam or internal combustion engines) that can propel vehicles, or to generate electricity via steam turbine generators. Some fossil fuels are further refined into derivatives such as kerosene, gasoline and diesel, or converted into petrochemicals such as polyolefins ( plastics), aromatics and synthetic resins. The origin of fossil fuels is the anaerobic decomposition of buried dead organisms. The conversion from these organic materials to high-carbon fossil fuels is ty ...
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Market Clearing
In economics, market clearing is the process by which, in an economic market, the supply of whatever is traded is equated to the demand so that there is no excess supply or demand, ensuring that there is neither a surplus nor a shortage. The new classical economics assumes that in any given market, assuming that all buyers and sellers have access to information and that there is no "friction" impeding price changes, prices ''constantly'' adjust up or down to ensure market clearing. Mechanism and examples A market-clearing price is the price of a good or service at which the quantity supplied equals the quantity demanded, also called the equilibrium price. The theory claims that markets tend to move toward this price. Supply is fixed for a one-time sale of goods, so the market-clearing price is simply the maximum price at which all items can be sold. In a market where goods are produced and sold on an ongoing basis, the theory predicts that the market will move toward a price wh ...
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Long Run And Short Run
In economics, the long-run is a theoretical concept in which all markets are in equilibrium, and all prices and quantities have fully adjusted and are in equilibrium. The long-run contrasts with the short-run, in which there are some constraints and markets are not fully in equilibrium. More specifically, in microeconomics there are no fixed factors of production in the long-run, and there is enough time for adjustment so that there are no constraints preventing changing the output level by changing the capital stock or by entering or leaving an industry. This contrasts with the short-run, where some factors are variable (dependent on the quantity produced) and others are fixed (paid once), constraining entry or exit from an industry. In macroeconomics, the long-run is the period when the general price level, contractual wage rates, and expectations adjust fully to the state of the economy, in contrast to the short-run when these variables may not fully adjust. History The ...
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CMA-ES
Covariance matrix adaptation evolution strategy (CMA-ES) is a particular kind of strategy for numerical optimization. evolution strategy, Evolution strategies (ES) are stochastic, Derivative-free optimization, derivative-free methods for numerical optimization of non-Linear map, linear or non-Convex function, convex continuous optimization problems. They belong to the class of evolutionary algorithms and evolutionary computation. An evolutionary algorithm is broadly based on the principle of biological evolution, namely the repeated interplay of variation (via recombination and mutation) and selection: in each generation (iteration) new individuals (candidate solutions, denoted as x) are generated by variation of the current parental individuals, usually in a stochastic way. Then, some individuals are selected to become the parents in the next generation based on their fitness or objective function value f(x). Like this, individuals with better and better f-values are generated ove ...
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Genetic Programming
Genetic programming (GP) is an evolutionary algorithm, an artificial intelligence technique mimicking natural evolution, which operates on a population of programs. It applies the genetic operators selection (evolutionary algorithm), selection according to a predefined fitness function, fitness measure, mutation (evolutionary algorithm), mutation and crossover (evolutionary algorithm), crossover. The crossover operation involves swapping specified parts of selected pairs (parents) to produce new and different offspring that become part of the new generation of programs. Some programs not selected for reproduction are copied from the current generation to the new generation. Mutation involves substitution of some random part of a program with some other random part of a program. Then the selection and other operations are recursively applied to the new generation of programs. Typically, members of each new generation are on average more fit than the members of the previous gene ...
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Nonlinear Programming
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear. Definition and discussion Let ''n'', ''m'', and ''p'' be positive integers. Let ''X'' be a subset of ''Rn'' (usually a box-constrained one), let ''f'', ''gi'', and ''hj'' be real-valued functions on ''X'' for each ''i'' in and each ''j'' in , with at least one of ''f'', ''gi'', and ''hj'' being nonlinear. A nonlinear programming problem is an optimization problem of the form : \begin \text & f(x) \\ \text ...
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Linear Programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear function#As a polynomial function, linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the mathematical optimization, optimization of a linear objective function, subject to linear equality and linear inequality Constraint (mathematics), constraints. Its feasible region is a convex polytope, which is a set defined as the intersection (mathematics), intersection of finitely many Half-space (geometry), half spaces, each of which is defined by a linear inequality. Its objective function is a real number, real-valued affine function, affine (linear) function defined on this polytope. A linear programming algorithm finds a point in the po ...
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Operations Research
Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and decision-making. Although the term management science is sometimes used similarly, the two fields differ in their scope and emphasis. Employing techniques from other mathematical sciences, such as mathematical model, modeling, statistics, and mathematical optimization, optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlapped with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the Maxima and minima, maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in ...
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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 ...
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Capital (economics)
In economics, capital goods or capital are "those durable produced goods that are in turn used as productive inputs for further production" of goods and services. A typical example is the machinery used in a factory. At the macroeconomic level, "the nation's capital stock includes buildings, equipment, software, and inventories during a given year." The means of production is as a "... series of heterogeneous commodities, each having specific technical characteristics ..." "capital goods", are one of the three types of intermediate goods used in the production process, the other two being land and labour. The three are also known collectively as "primary factors of production". This classification originated during the classical economics period and has remained the dominant method for classification. Capital can be increased by the use of a production process (see production function and factors of production). Outputs of the production process are normally classif ...
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