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Kron reduction methods for plug-and-play control of AC islanded microgrids with arbitrary topology

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Initial topology

In general topology and related areas of mathematics, the initial topology (or induced topology or weak topology or limit topology or projective topology) on a set with respect to a family of functions on is the coarsest topology on that makes those functions continuous. The subspace topology and product topology constructions are both special cases of initial topologies. Indeed, the initial topology construction can be viewed as a generalization of these.

Electric power transmission

Electric 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.

Network topology

Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network. Network topology can be used to define or describe the arrangement of various types of telecommunication networks, including command and control radio networks, industrial fieldbusses and computer networks. Network topology is the topological structure of a network and may be depicted physically or logically. It is an application of graph theory wherein communicating devices are modeled as nodes and the connections between the devices are modeled as links or lines between the nodes.

Computer terminal

A computer terminal is an electronic or electromechanical hardware device that can be used for entering data into, and transcribing data from, a computer or a computing system. The teletype was an example of an early-day hard-copy terminal and predated the use of a computer screen by decades. Early terminals were inexpensive devices but very slow compared to punched cards or paper tape for input, yet as the technology improved and video displays were introduced, terminals pushed these older forms of interaction from the industry.

Transmission line

In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmission must be taken into account. This applies especially to radio-frequency engineering because the short wavelengths mean that wave phenomena arise over very short distances (this can be as short as millimetres depending on frequency).

Flexible AC transmission system

A flexible alternating current transmission system (FACTS) is a system composed of static equipment used for the alternating current (AC) transmission of electrical energy. It is meant to enhance controllability and increase power transfer capability of the network. It is generally a power electronics-based system. FACTS is defined by the Institute of Electrical and Electronics Engineers (IEEE) as "a power electronic based system and other static equipment that provide control of one or more AC transmission system parameters to enhance controllability and increase power transfer capability".

Surge protector

A surge protector (or spike suppressor, surge suppressor, surge diverter, surge protection device (SPD) or transient voltage surge suppressor (TVSS) is an appliance or device intended to protect electrical devices from voltage spikes in alternating current (AC) circuits. A voltage spike is a transient event, typically lasting 1 to 30 microseconds, that may reach over 1,000 volts.

Attractor

In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed. In finite-dimensional systems, the evolving variable may be represented algebraically as an n-dimensional vector. The attractor is a region in n-dimensional space.

Railway signal

A railway signal is a visual display device that conveys instructions or provides warning of instructions regarding the driver’s authority to proceed. The driver interprets the signal's indication and acts accordingly. Typically, a signal might inform the driver of the speed at which the train may safely proceed or it may instruct the driver to stop. Application of railway signals Originally, signals displayed simple stop or proceed indications. As traffic density increased, this proved to be too limiting and refinements were added.

Electric power distribution

Electric power distribution is the final stage in the delivery of electricity. Electricity is carried from the transmission system to individual consumers. Distribution substations connect to the transmission system and lower the transmission voltage to medium voltage ranging between 2kV and 33kV with the use of transformers. Primary distribution lines carry this medium voltage power to distribution transformers located near the customer's premises.