Efficient global assessment of power system resilience under uncertainty using an enhanced polynomial chaos expansion method

Climate change has resulted in increasing frequency and intensity of extreme weather events, such as blizzards and wind storms.These extreme events pose a severe risk to the safe and secure operation of power systems, which has motivated recent interest in assessing power system resilience to extreme weather.The random nature of these extreme events and the corresponding power system failures mandates resilience assessment in probabilistic frameworks.However, state-of-the-art probabilistic methods struggle to efficiently assess resilience across all possible failure scenarios (i.e., globally), presenting a significant barrier to practical resilience assessment.To overcome this, this thesis develops a novel method leveraging polynomial chaos expansion (PCE) models to efficiently assess power system resilience.Firstly, this thesis models a power system's response to an extreme weather event.An efficient resilience event model capable of modelling many failure mechanisms is presented: applying fragility curves to model component failures and the AC cascading failure model to simulate the system's response.The developed model is then applied to assess power system resilience.To improve computational efficiency and globally assess resilience, this thesis leverages PCE models, which approximate the system's resilience with a polynomial function computed from a small set of system response samples.However, issues in PCE stability (i.e., the reliable computation of PCE models with different sample sets) pose a significant barrier to this method's applicability.Therefore, this thesis proposes a novel experiment design method, the Maximin-Latin hypercube sampling (MmLHS) method, that improves stability by uniformly selecting the samples used in PCE model computation.A PCE-based method for resilience assessment is then proposed that leverages MmLHS to construct stable PCE models and efficiently assess resilience.To validate the proposed method case studies are performed on the IEEE 39-Bus and 118-Bus systems using real-world data.Numerical studies on the IEEE 39-Bus system demonstrate the improved stability obtained by the MmLHS method while further studies on the IEEE 39-Bus and 118-Bus systems demonstrate the proposed PCE-based method's accuracy and efficiency and showcase its application to Scaled-MAD of a random variable.T V (P, Q) Total variation between PDFs P and Q. Polynomial Chaos ExpansionsTo efficiently assess the global probabilistic behaviour of complex system's the polynomial chaos expansion (PCE) method [29] has gained popularity.This method, first proposed by Wiener in 1938 [30], approximates a model's response using a polynomial function computed from a small number of model evaluations.The polynomial function's (hereafter "PCE model ") coefficients can be used to directly compute mean and variance, and the PCE model

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