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).
Electrical gridAn electrical grid is an interconnected network for electricity delivery from producers to consumers. Electrical grids vary in size and can cover whole countries or continents. It consists of: power stations: often located near energy and away from heavily populated areas electrical substations to step voltage up or down electric power transmission to carry power long distances electric power distribution to individual customers, where voltage is stepped down again to the required service voltage(s).
Electric power qualityElectric power quality is the degree to which the voltage, frequency, and waveform of a power supply system conform to established specifications. Good power quality can be defined as a steady supply voltage that stays within the prescribed range, steady AC frequency close to the rated value, and smooth voltage curve waveform (which resembles a sine wave). In general, it is useful to consider power quality as the compatibility between what comes out of an electric outlet and the load that is plugged into it.
Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
MicrogridA microgrid is a local electrical grid with defined electrical boundaries, acting as a single and controllable entity. It is able to operate in grid-connected and in island mode. A 'Stand-alone microgrid' or 'isolated microgrid' only operates off-the-grid and cannot be connected to a wider electric power system. A grid-connected microgrid normally operates connected to and synchronous with the traditional wide area synchronous grid (macrogrid), but is able to disconnect from the interconnected grid and to function autonomously in "island mode" as technical or economic conditions dictate.
Primary schoolA primary school (in Ireland, India, the United Kingdom, Australia, New Zealand, Trinidad and Tobago, Jamaica, and South Africa), elementary school, or grade school (in North America and the Philippines) is a school for primary education of children who are 4 to 10 years of age (and in many cases, 11 years of age). Primary schooling follows pre-school and precedes secondary schooling.
Distributed generationDistributed generation, also distributed energy, on-site generation (OSG), or district/decentralized energy, is electrical generation and storage performed by a variety of small, grid-connected or distribution system-connected devices referred to as distributed energy resources (DER). Conventional power stations, such as coal-fired, gas, and nuclear powered plants, as well as hydroelectric dams and large-scale solar power stations, are centralized and often require electric energy to be transmitted over long distances.
Smart gridA 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.
Marginal stabilityIn the theory of dynamical systems and control theory, a linear time-invariant system is marginally stable if it is neither asymptotically stable nor unstable. Roughly speaking, a system is stable if it always returns to and stays near a particular state (called the steady state), and is unstable if it goes farther and farther away from any state, without being bounded. A marginal system, sometimes referred to as having neutral stability, is between these two types: when displaced, it does not return to near a common steady state, nor does it go away from where it started without limit.
Primary educationPrimary education or elementary education is typically the first stage of formal education, coming after preschool/kindergarten and before secondary school. Primary education takes place in primary schools, elementary schools, or first schools and middle schools, depending on the location. The International Standard Classification of Education considers primary education as a single-phase where programmes are typically designed to provide fundamental reading, writing, and mathematics skills and establish a solid foundation for learning.
