Within a disruptively changing environment, design of power systems becomes a complex task. Meeting multi-criteria requirements with increasing degrees of freedom in design and simultaneously decreasing technical expertise strengthens the need for multi-objective optimization (MOO) making use of algorithms and virtual prototyping. In this context, we present Gaussian Process Regression based Multi-Objective Bayesian Optimization (GPR-MOBO) with special emphasis on its profound theoretical background. A detailed mathematical framework is provided to derive a GPR-MOBO computer implementable algorithm. We quantify GPR-MOBO effectiveness and efficiency by hypervolume and the number of required computationally expensive simulations to identify Pareto-optimal design solutions, respectively. For validation purposes, we benchmark our GPR-MOBO implementation based on a mathematical test function with analytically known Pareto front and compare results to those of well-known algorithms NSGA-II and pure Latin Hyper Cube Sampling. To rule out effects of randomness, we include statistical evaluations. GPR-MOBO turnes out as an effective and efficient approach with superior character versus state-of-the art approaches and increasing value-add when simulations are computationally expensive and the number of design degrees of freedom is high. Finally, we provide an example of GPR-MOBO based power system design and optimization that demonstrates both the methodology itself and its performance benefits.

Parametric models allow to reflect system behavior in general and characterize individual system instances by specific parameter values. For a variety of scientific disciplines, model calibration by parameter quantification is therefore of central importance. As the time and cost of calibration experiments increases, the question of how to determine parameter values of required quality with a minimum number of experiments comes to the fore. In this paper, a methodology is introduced allowing to quantify and optimize achievable parameter extraction quality based on an experimental plan including a process and methods how to adapt the experimental plan for improved estimation of individually selectable parameters. The resulting parameter-individual optimal design of experiments (pi-OED) enables experimenters to extract a maximum of parameter-specific information from a given number of experiments. We demonstrate how to minimize variance or covariances of individually selectable parameter estimators by model-based calculation of the experimental designs. Using the Fisher Information Matrix in combination with the Cramer-Raó inequality, the pi-OED plan is reduced to a global optimization problem. The pi-OED workflow is demonstrated using computer experiments to calibrate a model describing calendrical aging of lithium-ion battery cells. Applying bootstrapping methods allows to also quantify parameter estimation distributions for further benchmarking. Comparing pi-OED based computer experimental results with those based on state-of-the-art designs of experiments, reveals its efficiency improvement. All computer experimental results are gained in Python and may be reproduced using a provided Jupyter Notebook along with the source code. Both are available under https://github.com/nicolaipalm/oed.INDEX TERMS Parametric models, parameter estimation, design of experiments, optimal experimental design, battery aging, computer experiment. I. DESIGN OF COST INTENSIVE EXPERIMENTS