Candidate
Alfredo Vaccaro
Title
Affine Arithmetic for Power and Optimal Power Flow Analyses in the Presence of Uncertainties
Supervisor
Claudio Canizares
Abstract
Optimal power system operation requires intensive numerical analysis to study and improve system security and reliability. To address this issue, Power Flow (PF) and Optimal Power Flow (OPF) analyses are important tools, since they are the foundation of many power engineering applications. For the most common formalization of these problems, the input data are specified using deterministic variables resulting either from a snapshot of the system or defined by the analyst based on several assumptions about the system under study. This approach provides problem solutions for a single system state, which is deemed representative of the limited set of system conditions corresponding to the data assumptions. Thus, when the input conditions are uncertain, numerous scenarios need to be analyzed.
To address the aforementioned problem, this thesis proposes novel solution method- ologies based on the use of Affine Arithmetic (AA), which is an enhanced model for self- validated numerical analysis in which the quantities of interest are represented as affine combinations of certain primitive variables representing the sources of uncertainty in the data or approximations made during computations. In particular, AA-based techniques are proposed to solve uncertain PF and OPF problems. The adoption of these approaches allows to express the uncertain power system equations in a more convenient formalism compared to the traditional and widely used linearization frequently adopted in interval Newton methods. The proposed techniques allow to reliably estimate the PF and OPF solution hull by taking into account the parameter uncertainty inter-dependencies, as well as the diversity of uncertainty sources.
A novel AA-based computing paradigm aimed at achieving more efficient computational processes and better enclosures of PF and OPF solution sets is conceptualized. The main idea is to formulate a generic mathematical programming problem under uncertainty by means of equivalent deterministic problems, defining a coherent set of minimization, equal- ity and inequality operators. Compared to existing solution paradigms, this formulation presents greater flexibility, as it allows to find partial solutions and inclusion of multiple equality and inequality constraints, and reduce the approximation errors to obtain better PF and OPF solution enclosures.
Finally, formal methods for knowledge discovery from large quantity of data as an enabling methodology for reducing the complexity of the PF and OPF problem, and for the optimal identification of the affine forms describing their uncertain parameters are proposed. In particular, a knowledge-based paradigm for PF and OPF analysis is used to extract from operation data-sets complex features, hidden relationships and useful hy- potheses potentially describing regularities in the problem solutions. This is realized by designing a knowledge-extraction process based on Principal Components Analysis (PCA). The structural knowledge extracted by this process is then used to define a mathematical kernel, which transforms the PF and OPF equations into a domain in which these equa- tions can be solved more effectively. In this new domain, the cardinality of the PF and OPF problem is sensibly reduced and, consequently, a more efficient algorithm can be used to obtain PF and OPF solutions: also it is possible to define a formal connection between the principal components and the noise symbols of the uncertain parameters, which furnish an effective method for the optimal identification of the affine forms.
Detailed numerical results are presented and discussed using a variety of test systems, demonstrating the effectiveness of the proposed methodologies and comparing it to existing techniques for uncertain PF and OPF analysis.