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  • Publication
    Impact of noise (auto)correlation on power system dynamic performance
    (University College Dublin. School of Electrical and Electronic Engineering, 2022) ;
    Non-deterministic loads and non-dispatchable renewable energy sources such as wind and photovoltaic are the major sources of random fluctuations and volatility in power systems. The techniques to account for the effects of random fluctuations on the transient behaviour of the power system have been developed and well-assessed in the literature. On the other hand, the analysis of impact of volatility on the power system short-term dynamic and transient behaviour has not been fully explored so far. For power system dynamic studies, volatility can be modelled as a fast-varying time-continuous stochastic process. Stochastic processes are formulated as Stochastic Differential Equations (SDEs). SDEs are then introduced into existing power system dynamic models to generate nonlinear Stochastic Differential Algebraic Equations (SDAEs). SDAEs are the fundamental tool, utilised in this thesis, to study the dynamic behaviour of the power system subjected to volatility. Stochastic processes have three distinct features, namely, drift, correlation, and diffusion. While the impact of the latter on the system dynamics has been studied widely that is not the case for the other two. The drift defines the variability of the process in time. Whereas the correlation is the degree of similarity between two processes. Thus, the question on what the impact of drift and correlation of the stochastic processes on the dynamic behaviour of the power system is and how to quantify it remains unanswered. This thesis aims at providing systematic and generalized methods based on data measurements to model correlation on stochastic processes and introduce them into power system dynamic studies. The thesis also provides a general technique to extract correlation from the measurement data. The methods provided in this thesis are independent of dimensions, timescales, drifts, and probability distributions of the processes. This allows for the inclusion of a wide range of sources of volatility into existing power system dynamic models and the study of their impact on power system dynamics without the need for any simplifications or modifications to the original system. On the other hand, the impact of the drift of the stochastic processes on the power system dynamic behaviour is studied through time- and frequency-domain analyses. The former involves the study of the impact of the drift of the stochastic processes on the power system variables in normal grid operation. Whereas the latter consists in the study of the dynamic interactions between the drift of the stochastic processes and the electro-mechanical oscillatory modes of the power system. The thesis also presents a direct method to assess the probability that a power system's physical limit is violated when modelling stochastic processes in normal grid operation. The accuracy and computational efficiency of the direct method is demonstrated using the bench-mark Irish system. Direct methods can only study a linearized system at stationary conditions. Whereas the detailed dynamic behaviour of the power system simulating stochastic processes, controller hard limits, saturations and system nonlinearities can only be studied using the nonlinear models, which do not have a closed form solution. For this reason, the analyses conducted in the entire thesis, except for the direct method, rely on time domain simulations. Several case studies utilising the Irish system are illustrated throughout the thesis to demonstrate the practical applications of the introduced methods to model and study the impact of correlated stochastic processes on the power system dynamic and transient security. As the modelling techniques presented in the thesis are general, based on measurement data and easy to implement in software tools. They are expected to be readily adopted by the system operators to ensure the security and stability of the power system in the presence of stochastic processes.
  • Publication
    Power system modelling as stochastic functional hybrid differential-algebraic equations
    This paper presents the software tools developed for the research project Advanced Modelling for Power System Analysis and Simulation (AMPSAS) funded by Science Foundation Ireland from 2016 to 2021. The main objective of AMPSAS was the development of novel analytical and computational tools to understand, efficiently design, and optimise ever-changing modern power systems and smart grids, through model-based approaches. In particular, the paper discusses (i) stochastic differential equations for modelling power systems, which are subject to large stochastic perturbations (e.g. wind and solar generation); (ii) the effect of controller and modelling imperfections, for example, delays, discontinuities, and digital signals, on both local and area-wide regulators in power systems; and (iii) the stability analysis and dynamic performance of power systems modelled through stochastic, delay and hybrid implicit differential-algebraic equations. The software tool developed during the execution of AMPSAS integrates areas of applied mathematics, automatic control, and computer science. Several implementation features and open challenges of this software tool are also discussed in the paper. A variety of examples that illustrates the features of this software tool are based on a dynamic model of the all-island Irish transmission system.
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