Essays on market design and regulation in electricity systems

This thesis discusses market design and regulation in electricity systems, focusing on the information exchange of the regulated grid firm and the generation firms as well as the regulation of the grid firm. In the first chapter, an economic framework is developed to consistently analyze different market designs and the information exchange between the grid firm and the generation firms. Perfect competition between the generation firms and perfect regulation of the grid firm is assumed. A numerical algorithm is developed and its feasibility demonstrated on a large-scale problem. The effects of different market designs for the Central Western European (CWE) region until 2030 are analyzed. In the second chapter, the consequences of restricted grid expansion within the current market design in the CWE region until 2030 are analyzed. In the third chapter the assumption of efficient markets is modified. The focus of the analysis is then, whether and how inefficiencies in information availability and processing affect different market designs. For different parameter settings, nodal and zonal pricing are compared regarding their welfare in the spot and forward market. In the fourth chapter, information asymmetries between the regulator and the regulated firm are analyzed. The optimal regulatory strategy for a firm, providing one output with two substitutable inputs, is defined. Thereby, one input and the absolute quantity of inputs is not observable for the regulator. The result is then compared to current regulatory approaches.

Algebro-Geometric Aspects of the Classical Yang-Baxter Equation

In this thesis we consider algebro-geometric aspects of the Classical Yang-Baxter Equation and the Generalised Classical Yang-Baxter Equation. In chapter one we present a method to construct solutions of the Generalised Classical Yang-Baxter Equation starting with certain sheaves of Lie algebras on algebraic curves. Furthermore we discuss a criterion to check unitarity of such solutions. In chapter two we consider the special class of solutions coming from sheaves of traceless endomorphisms of simple vector bundles on the nodal cubic curve. These solutions are quasi-trigonometric and we describe how they fit into the classification scheme of such solutions. Moreover, we describe a concrete formula for these solutions. In the third and final chapter we show that any unitary, rational solution of the Classical Yang-Baxter Equation can be obtained via the method of chapter one applied to a sheaf of Lie algebras on the cuspidal cubic curve.