Modelling and Simulation of Long-Term Dynamics in Power Systems

A reliable and cost-effective operation of power systems involves different tasks over different time horizons ranging from tens of milliseconds (protection) to years (planning). Generally, power system operators routinely check the effectiveness of these tasks separately (depending on time constants) through computer studies based on mathematical models. While the modelling and simulation of short-term dynamics of power systems (e.g. electromagnetic and transient simulation) have received tremendous attention in the literature, that is not the case for long-term dynamics. In this context, this thesis aims to assist power system operators in addressing the modelling and simulation of long-term dynamics in modern power systems (minutes to years). To do so, the thesis presents novel mathematical and software tools that allow studying the long-term impact interactions between different short-term electricity markets models and power systems, and the impact of energy policy incentives on the evolution of Renewable Energy Sources (RESs) technologies, particularly that of solar Photovoltaics (PVs). Short-term electricity markets are essential tools to guarantee the reliable operation of the power system. They are moving closer to real-time and using finer time resolutions (e.g. 5 minutes) in response to the large-scale integration of variable RESs. This means that their dynamics evolve with a timescale similar to some long-term power system dynamics, e.g. the Automatic Generation Control (AGC). Consequently, assessing the impact interactions between such markets and the dynamic response of the power grid becomes increasingly important. The contributions on this topic are as follows: (i) Investigate the effect of real-time electricity markets modelled as a sort of discrete AGC or Market-based Automatic Generation Control (MAGC) on power system dynamics. In particular, a thorough analysis using Time Domain Simulations (TDSs) is provided. (ii) Propose a short-term dynamic electricity market model that includes the memory effect of market participants. Particularly, the effect of the memory of suppliers on the decision-making (generator schedules) and dynamic response of the grid is discussed. (iii) Investigate the impact interactions between sub-hourly deterministic Unit Commitment (d-UC) and stochastic Unit Commitment (s-UC) and the power grid. Furthermore, the thesis also proposes a dynamic model based on nonlinear delay Differential-Algebraic Equations (DAEs) able to predict the evolution of PV installations for different countries. This model is a valuable tool that can help policymakers in the decision-making process, such as the definition of the Feed-in Tariff (FiT) price and the duration of the incentives. Finally, the proposed models and tools are duly validated throughout the thesis by means of numerical tests based on benchmark test systems.