Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

Control and Simulation of Photovoltaic Power Plants in OpenModelica

As solar generation increases globally, there exists a need for innovation and increased operational flexibility. In Photovoltaic Power Plants (PVPPs) and Large Scale Photovoltaic Power Plants (LS-PVPPs) the challenges increase due to the necessity to integrate them into the electrical system. To ensure the stability and reliability in the electricity supply, power systems require complex dynamic analysis. Therefore, to carry out these analysis, modelling and simulation tools are needed. This thesis focuses on the control and operation of PVPPs in OpenModelica, a free and open-source modelling and simulation environment based on Modelica language. In the later part, OpenModelica potential in large-scale power systemoriented models is investigated. These issues are addressed by a literature review concerning photovoltaic power systems and OpenModelica functionality, a theoretical analysis of a photovoltaic inverter and a LS-PVPP, and detailed simulations. The models are tested under variations in the active and reactive power requirements. The results show an optimal dynamic response and the capacity to perform independent active and reactive power controls. As an outcome, OpenModelica is a promising tool for power system modelling and simulation even though existing barriers and difficulties must be overcome

JModelica---an Open Source Platform for Optimization of Modelica Models

Optimization is becoming a standard methodology in many engineering disciplines to improve products and processes. The need for optimization is driven by factors such as increased costs for raw materials and stricter environmental regulations as well as a general need to meet increased competition. As model-based design processes are being used increasingly in industry, the prerequisites for optimization are often fulfilled. However, current tools and languages used to model dynamic systems are not always well suited for integration with state of the art numerical optimization algorithms. As a result, optimization is not used as frequently as it could, or less efficient, but easier to use, algorithms are employed. This paper reports a new Modelica-based open source project entitled JModelica, targeted towards dynamic optimization. The objective of the project is to bridge the gap between the need for high-level description languages and the details of numerical optimization algorithms. JModelica is also intended as an extensible platform where algorithm developers, particularly in the academic community, may integrate new and innovative methods. In doing so, researchers gain access to a wealth of industrially relevant optimization problems based on existing Modelica models, while at the same time facilitating industrial use of state of the art algorithms. The JModelica project rests upon three pillars, namely a language extension of Modelica for optimization entitled Optimica, software tools, and applications. In this paper, these three topics will be highlighted

Dynamic Optimization on Quantum Hardware: Feasibility for a Process Industry Use Case

The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model predictive control where rapid and reliable computations are critical. Conventional methods can struggle to surmount the complexities of such tasks. Quantum computing and quantum annealing emerge as avant-garde contenders to transcend conventional computational constraints. We convert a dynamic optimization problem, characterized by a system of differential equations, into a Quadratic Unconstrained Binary Optimization problem, enabling quantum computational approaches. The empirical findings synthesized from classical methods, simulated annealing, quantum annealing via D-Wave's quantum annealer, and hybrid solver methodologies, illuminate the intricate landscape of computational prowess essential for tackling complex and high-dimensional dynamic optimization problems. Our findings suggest that while quantum annealing is a maturing technology that currently does not outperform state-of-the-art classical solvers, continuous improvements could eventually aid in increasing efficiency within the chemical process industry.Comment: 17 pages, 5 figure