A GUI in MATLAB for fast uncertainty analysis with non-intrusive Polynomial ChaosCopyright: RWTH Aachen
In modern energy research, uncertainty plays a significant role. For example, a major factor is the increasing share of energy generated from renewable sources, of which many depend on the weather. Thus, future energy systems can no longer be treated as deterministic. The understanding of how uncertainty propagates through power systems provides the possibility of designing adequate control and operation strategies.
In systems with few random inputs, Polynomial Chaos (PC) theory is a fast concept of stochastic analysis. Classical PC consists of a representation of stochastic parameters which, inserted into the system equations, leads to a new set of deterministic equations. Non-intrusive Polynomial Chaos (NIPC) exploits the principle of PC, while preserving the original equations and therefore being applicable to black box simulations. In this way, NIPC can replace a Monte- Carlo simulation without change to the solver. For a distribution system with wind and solar generation, uncertain parameters are e.g. wind speed and irradiation. The system could be evaluated twenty-five times for each combination of parameter values of the two uncertainties. Finally, the results would be post-processed to assess the generated energy rather than repeating the simulation randomly many thousand times.
One of the main drawbacks to PC-based concepts is the depth of their mathematical foundation, involving advanced functional analysis, approximation theory and stochastics. The numerous adjustments which must be made for different types of random input are another downside. At ACS, we have developed a graphical user interface (GUI) in MATLAB which facilitates the application of NIPC.
The GUI consists of two parts. In the pre-processing interface, the user may choose the number of involved random variables and their distribution type, as well as some information on desired approximation orders. From this information, a text file is generated, which contains all combinations of parameter values which must be evaluated in the external solver of an arbitrary simulation platform. The results of these simulation runs are fed into the post-processing interface which allows the user to choose different time instants and histogram options for sampling.
In this way, stochastic simulations with few random parameters can be accelerated with little effort. The only necessary input is the knowledge of the parameter types of the system of interest, no longer the understanding of PC based methods.