Advanced Matrix Techniques for the Steady-State Assessment of Large Power Systems

This dissertation systematically presents the research results related to the development of self-made computational models and matrix algorithms for the steady-state analysis of large electrical transmission grids. First, the steady-state matrix models of single devices (power lines, power transformers, loads, generators, reactive power compensators, etc.) of large AC/DC power systems are presented. These models are original and derive from self-made elaborations of concepts presented in technical and scientific literature. In particular, the development of a) single-phase, b) three-phase, and c) Multiconductor Cell Analysis (MCA) models is shown. These models are the three main layers giving a gradually ascending level of detail for the steady-state analyses. By using the models developed in the first part, the focus is then brought to the analysis of long HVDC and HVAC power lines, in order to study the impact of line length and loadability on the steady-state stability and power quality (voltage and current unbalance factors) of transmission grids. This study is carried out because long power lines, characterized by high power transmissions, are the crucial element for the expansion and construction of large power systems. An important result in this assessment, is the finding of the most precise analytical formulation, in scientific literature, of voltage collapse of any HVAC/HVDC power line. This formulation has been found by considering the Ossanna’s theorem and the uniformly distributed parameter modelling approach. A novel form of the capability charts for the study of the transmittable power by any line has been also developed, giving for them also an experimental validation by means of field measurements. Then detailed parametric MCA simulations on electrical lines are performed in order to assess the impact of line lengths and loadability on the power quality (unbalance factors) of transmission grids. Since power flow analysis is the most fundamental tool for steady-state power system assessment, two original power flow algorithms, suitable for AC large systems, are presented. The former is for the analysis of single-phase network models (PFPD) and the latter is for the analysis of three-phase network models (PFPD_3P). Both developed for the study of AC synchronous networks, their generalization for assessing AC/DC networks are then shown (so developing PFPD_ACDC and PFPD_3P_ACDC). Regarding the power flow problem for the steady-state analysis, two precise distributed slack bus power flow algorithms are then presented: a multi-area (PFPD_X) and a dynamic (PFPD_D) power flow algorithms. These two algorithms improve the solution accuracy of large power system analysis, since power losses are distributed among the generators. An important achievement in this regard, is the successful implementation of PFPD_X on the real ENTSO-E (21760 nodes) power system model. Finally, thanks to PFPD_3P and a new probabilistic matrix power flow (developed in this dissertation and named PFPD_PRB), steady-state analyses of the Italian grid model, with high penetration of renewable energy source scenarios are presented. Therefore, both uncertainties and voltage/current unbalances, as a consequence of the synchronous generation reduction in the Italian grid are studied. All the above-mentioned matrix algorithms developed in this dissertation are implemented in Matlab©, the suitable environment for matrix modelling. The results, analyses, observations and discussions are always performed on real and large networks, e.g., the Italian grid (7800 nodes) and the pan-European network (21760 nodes). From an epistemological standpoint, all the models and algorithms are original, self-made, and validated by means of result comparisons with reliable commercial/open-source power system software. Finally, where applicable, model validations are also performed by means of experimental measurements given by the Italian TSO Terna.