Control of Transmission Lines
This problem was provided by Göttlich, Potschka, and Teuber [Goettlich2018]Author: G{\"o}ttlich, Simone; Potschka, Andreas; Teuber, Claus
Institution: University of Mannheim
Note: Optimization Online 6312
Title: A partial outer convexification approach to control
transmission lines
Url: http://www.optimization-online.org/DB_HTML/2017/11/6312.html
Year: 2018
. It is governed by a 2x2-system of conservation laws based on the telegraph equations for single transmission lines, which are then connected to form a network. The objective is to minimize the quadratic deviation of the load delivered to customer nodes from their demand by continuously controlling the power inflow to the network at the energy producer nodes and by discrete but time-varying switches at the coupling nodes inside the network.
Contents
Mathematical formulation
The dynamics on the -th transmission line with spatial variable , temporal variable , and state variable containing the characteristic variables for right-traveling and left-traveling components are given by the hyperbolic PDE system
with a diagonal 2x2-matrix and a symmetric matrix . We combine all single line states to a large state vector to obtain the system
and formulate the coupling between the lines and the continuously controlled power inflow as boundary conditions involving distribution matrices , which depend on a discrete switching signal , and constant distribution matrices of size according to
The continuous control is subject to simple bounds.
The objective is to track the given demands of consumers, which can be formulated as
where is the set of consumer nodes and is the set of all lines adjacent to vertex .
Parameters
Discretization
Reference Solution
Source Code
References
[Goettlich2018] | G{\"o}ttlich, Simone; Potschka, Andreas; Teuber, Claus (2018): A partial outer convexification approach to control transmission lines. University of Mannheim. |