Katrin Witting

Optimal energy management for a hybrid energy storage system combining batteries and double layer capacitors

Many mobile vehicular applications like hybridelectrical cars and autonomous rail vehicles require an onboard energy storage for operation. High demands concerning power and energy density, small volume and weight at the same time cannot be satisfied solely by batteries or double layer capacitors. A suitable approach is to combine storage technologies with complementary characteristics as a hybrid energy storage system. Thus, long term storage like batteries featuring high energy density can be combined with short term storage like double layer capacitors offering high power density and high cycliability. To control the power flows of the system, we propose the use of self-optimization methods involving multi-objective and discrete optimization to design an operating strategy which is able to adapt the system behavior to different conditions not only by adapting its parameters but also its objectives, offering an optimal operation in different situations.

Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems

In many applications, it is required to optimize several conflicting objectives concurrently leading to a multobjective optimization problem (MOP). The solution set of a MOP, the Pareto set, typically forms a (k-1)-dimensional object, where k is the number of objectives involved in the optimization problem. The purpose of this chapter is to give an overview of recently developed set oriented techniques - subdivision and continuation methods - for the computation of Pareto sets \(\mathcal{P}\) of a givenMOP. All these methods have in common that they create sequences of box collections which aim for a tight covering of \(\mathcal{P}\). Further, we present a class of multiobjective optimal control problems which can be efficiently handled by the set oriented continuation methods using a transformation into high-dimensionalMOPs. We illustrate all the methods on both academic and real world examples.

A new approach for online multiobjective optimization of mechatronic systems

We present a new concept for online multiobjective optimization and its application to the optimization of the operating point assignment for a doubly-fed linear motor. This problem leads to a time-dependent multiobjective optimization problem. In contrast to classical optimization where the aim is to find the (global) minimum of a single function, we want to simultaneously minimize k objective functions. The solution to this problem is given by the set of optimal compromises, the so-called Pareto set. In the case of the linear motor, there are two conflicting aims which both have to be maximized: the degree of efficiency and the inverter utilization factor. The objective functions depend on velocity, force and power, which can be modeled as time-dependent parameters. For a fixed point of time, the entire corresponding Pareto set can be computed by means of a recently developed set-oriented numerical method. An online computation of the time-dependent Pareto sets is not possible, because the computation itself is too complex. Therefore, we combine the computation of the Pareto set with numerical path following techniques. Under certain smoothness assumptions the set of Pareto points can be characterized as the set of zeros of a certain function. Here, path following allows to track the evolution of a given solution point through time.

Multiobjective optimization for transistor sizing of CMOS logic standard cells using set-oriented numerical techniques

The design of resource efficient integrated circuits (IC) requires solving a minimization problem of more than one objective given as measures of available resources. This multiobjective optimization problem (MOP) can be solved on the smallest unit, the standard cells, to improve the performance of the entire IC. The traditional way of sizing the transistors of a standard logic cell does not focus on the resources directly. In this work transistor sizing is approached via an MOP and solved by set-oriented numerical techniques. A comparison of the Pareto optimal designs to elements of a commercial standard cell library indicates that for some gates the performance can even be significantly improved.

Design and implementation of a hybrid energy supply system for railway vehicles

An energy supply system based on a hybrid energy storage unit combined of batteries and ultracapacitors for a railway vehicle is studied. In order to optimize the energy supply system architecture and to manage the energy distribution the power electronic converters connecting ultracapacitors, batteries and the DC-link are investigated together with control strategies comprising a multiobjective continuous and a discrete optimization. The prospective goal of applying latter optimization techniques via a so-called operator controller module is a self-optimizing energy supply system. Simulated and measured results are presented, revealing that the separation of the dynamic load from batteries yield improvements in lifecycle, availability and long term costs, while the novel control facilitates prospectively large energy savings and obeying set constraints.

A variational approach to define robustness for parametric multiobjective optimization problems

In contrast to classical optimization problems, in multiobjective optimization several objective functions are considered at the same time. For these problems, the solution is not a single optimum but a set of optimal compromises, the so-called Pareto set. In this work, we consider multiobjective optimization problems that additionally depend on an external parameter

Energy transfer via linear doubly-fed motor in different operating modes

{\lambda \in \mathbb{R}}

Methods for the Design and Development

, so-called parametric multiobjective optimization problems. The solution of such a problem is given by the λ-dependent Pareto set. In this work we give a new definition that allows to characterize λ-robust Pareto points, meaning points which hardly vary under the variation of the parameter λ. To describe this task mathematically, we make use of the classical calculus of variations. A system of differential algebraic equations will turn out to describe λ-robust solutions. For the numerical solution of these equations concepts of the discrete calculus of variations are used. The new robustness concept is illustrated by numerical examples.