Lyapunov stabilityVarious types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).
Demand curveIn a demand schedule, a demand curve is a graph depicting the relationship between the price of a certain commodity (the y-axis) and the quantity of that commodity that is demanded at that price (the x-axis). Demand curves can be used either for the price-quantity relationship for an individual consumer (an individual demand curve), or for all consumers in a particular market (a market demand curve). It is generally assumed that demand curves slope down, as shown in the adjacent image.
DemandIn economics, demand is the quantity of a good that consumers are willing and able to purchase at various prices during a given time. The relationship between price and quantity demand is also called the demand curve. Demand for a specific item is a function of an item's perceived necessity, price, perceived quality, convenience, available alternatives, purchasers' disposable income and tastes, and many other options. Innumerable factors and circumstances affect a consumer's willingness or to buy a good.
HydroelectricityHydroelectricity, or hydroelectric power, is electricity generated from hydropower (water power). Hydropower supplies one sixth of the world's electricity, almost 4500 TWh in 2020, which is more than all other renewable sources combined and also more than nuclear power. Hydropower can provide large amounts of low-carbon electricity on demand, making it a key element for creating secure and clean electricity supply systems.
Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
Electric power systemAn electric power system is a network of electrical components deployed to supply, transfer, and use electric power. An example of a power system is the electrical grid that provides power to homes and industries within an extended area. The electrical grid can be broadly divided into the generators that supply the power, the transmission system that carries the power from the generating centers to the load centers, and the distribution system that feeds the power to nearby homes and industries.
Power engineeringPower engineering, also called power systems engineering, is a subfield of electrical engineering that deals with the generation, transmission, distribution, and utilization of electric power, and the electrical apparatus connected to such systems. Although much of the field is concerned with the problems of three-phase AC power – the standard for large-scale power transmission and distribution across the modern world – a significant fraction of the field is concerned with the conversion between AC and DC power and the development of specialized power systems such as those used in aircraft or for electric railway networks.
Cross elasticity of demandIn economics, the cross (or cross-price) elasticity of demand measures the effect of changes in the price of one good on the quantity demanded of another good. This reflects the fact that the quantity demanded of good is dependent on not only its own price (price elasticity of demand) but also the price of other "related" good. The cross elasticity of demand is calculated as the ratio between the percentage change of the quantity demanded for a good and the percentage change in the price of another good, ceteris paribus:The sign of the cross elasticity indicates the relationship between two goods.
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.
Electrical networkAn electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, current sources, resistances, inductances, capacitances). An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Thus all circuits are networks, but not all networks are circuits (although networks without a closed loop are often imprecisely referred to as "circuits").
