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Voltage Control in Active Distribution Networks Under Uncertainty in the System Model: A Robust Optimization Approach

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Voltage divider

In electronics, a voltage divider (also known as a potential divider) is a passive linear circuit that produces an output voltage (Vout) that is a fraction of its input voltage (Vin). Voltage division is the result of distributing the input voltage among the components of the divider. A simple example of a voltage divider is two resistors connected in series, with the input voltage applied across the resistor pair and the output voltage emerging from the connection between them.

Distribution transformer

A distribution transformer or service transformer is a transformer that provides the final voltage transformation in the electric power distribution system, stepping down the voltage used in the distribution lines to the level used by the customer. The invention of a practical efficient transformer made AC power distribution feasible; a system using distribution transformers was demonstrated as early as 1882. If mounted on a utility pole, they are called pole-mount transformers.

Optimal control

Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.

Adaptive control

Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain.cite journal|author=Chengyu Cao, Lili Ma, Yunjun Xu|title="Adaptive Control Theory and Applications", Journal of Control Science and Engineering'|volume=2012|issue=1|year=2012|doi=10.1155/2012/827353|pages=1,2|doi-access=free For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions.

Transmission system operator

File:Electricity grid simple- North America.svg|thumb|380px|right|Simplified diagram of AC electricity grid from generation stations to consumers in North America rect 2 243 235 438 [[Power station]] rect 276 317 412 556 [[Transformer]] rect 412 121 781 400 [[Electric power transmission]] rect 800 0 980 165 [[Transformer]] desc bottom-left A transmission system operator (TSO) is an entity entrusted with transporting energy in the form of natural gas or electrical power on a national or regional level, using fixed infrastructure.

Mixed reality

Mixed reality (MR) is a term used to describe the merging of a real-world environment and a computer-generated one. Physical and virtual objects may co-exist in mixed reality environments and interact in real time. Mixed reality that incorporates haptics has sometimes been referred to as Visuo-haptic mixed reality. In a physics context, the term "interreality system" refers to a virtual reality system coupled with its real-world counterpart.

Virtual reality headset

A virtual reality headset (or VR headset) is a head-mounted device that provides virtual reality for the wearer. VR headsets are widely used with VR video games but they are also used in other applications, including simulators and trainers. VR headsets typically include a stereoscopic display (providing separate images for each eye), stereo sound, and sensors like accelerometers and gyroscopes for tracking the pose of the user's head to match the orientation of the virtual camera with the user's eye positions in the real world.

Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, 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.

Power-flow study

In power engineering, the power-flow study, or load-flow study, is a numerical analysis of the flow of electric power in an interconnected system. A power-flow study usually uses simplified notations such as a one-line diagram and per-unit system, and focuses on various aspects of AC power parameters, such as voltages, voltage angles, real power and reactive power. It analyzes the power systems in normal steady-state operation. Power-flow or load-flow studies are important for planning future expansion of power systems as well as in determining the best operation of existing systems.

Uncertainty quantification

Uncertainty quantification (UQ) is the science of quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known. An example would be to predict the acceleration of a human body in a head-on crash with another car: even if the speed was exactly known, small differences in the manufacturing of individual cars, how tightly every bolt has been tightened, etc.