Robust estimation of risks from small samples

Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited, but the impact of estimation errors may be very large. This paper presents a robust nonparametric Bayesian method to infer possible underlying distributions. The method obtains rigorous error bounds even for small samples taken from ill-behaved distributions. The approach taken has a natural interpretation in terms of the intervals between ordered observations, where allocation of probability mass across intervals is well-specified, but the location of that mass within each interval is unconstrained. This formulation gives rise to a straightforward computational resampling method: Bayesian Interval Sampling. In a comparison with common alternative approaches, it is shown to satisfy strict error bounds even for ill-behaved distributions.Comment: 13 pages, 3 figures; supplementary information provided. A revised version of this manuscript has been accepted for publication in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Science

A Machine-learning based Probabilistic Perspective on Dynamic Security Assessment

Probabilistic security assessment and real-time dynamic security assessments (DSA) are promising to better handle the risks of system operations. The current methodologies of security assessments may require many time-domain simulations for some stability phenomena that are unpractical in real-time. Supervised machine learning is promising to predict DSA as their predictions are immediately available. Classifiers are offline trained on operating conditions and then used in real-time to identify operating conditions that are insecure. However, the predictions of classifiers can be sometimes wrong and hazardous if an alarm is missed for instance. A probabilistic output of the classifier is explored in more detail and proposed for probabilistic security assessment. An ensemble classifier is trained and calibrated offline by using Platt scaling to provide accurate probability estimates of the output. Imbalances in the training database and a cost-skewness addressing strategy are proposed for considering that missed alarms are significantly worse than false alarms. Subsequently, risk-minimised predictions can be made in real-time operation by applying cost-sensitive learning. Through case studies on a real data-set of the French transmission grid and on the IEEE 6 bus system using static security metrics, it is showcased how the proposed approach reduces inaccurate predictions and risks. The sensitivity on the likelihood of contingency is studied as well as on expected outage costs. Finally, the scalability to several contingencies and operating conditions are showcased.Comment: 42 page

Realising transition pathways for a more electric, low-carbon energy system in the United Kingdom: challenges, insights and opportunities

The United Kingdom has placed itself on a transition towards a low-carbon economy and society, through the imposition of a legally-binding goal aimed at reducing its ‘greenhouse gas’ emissions by 80% by 2050 against a 1990 baseline. A set of three low-carbon, socio-technical transition pathways were developed and analysed via an innovative collaboration between engineers, social scientists and policy analysts. The pathways focus on the power sector, including the potential for increasing use of low-carbon electricity for heating and transport, within the context of critical European Union developments and policies. Their development started from narrative storylines regarding different governance framings, drawing on interviews and workshops with stakeholders and analysis of historical analogies. The quantified UK pathways were named Market Rules, Central Co-ordination and Thousand Flowers; each reflecting a dominant logic of governance arrangements. The aim of the present contribution was to use these pathways to explore what is needed to realise a transition that successfully addresses the so-called energy policy ‘trilemma,’ i.e. the simultaneous delivery of low carbon, secure and affordable energy services. Analytical tools were developed and applied to assess the technical feasibility,social acceptability, and environmental and economic impacts of the pathways. Technological and behavioural developments were examined, alongside appropriate governance structures and regulations for these low-carbon transition pathways, as well as the roles of key energy system ‘actors’ (both large and small). An assessment of the part that could possibly be played by future demand side response was also undertaken in order to understand the factors that drive energy demand and energy-using behaviour, and reflecting growing interest in demand side response for balancing a system with high proportions of renewable generation. A set of interacting and complementary engineering and technoeconomic models or tools were then employed to analyse electricity network infrastructure investment and operational decisions to assist market design and option evaluation. This provided a basis for integrating the analysis within a whole systems framework of electricity system development, together with the evaluation of future economic benefits, costs and uncertainties. Finally, the energy and environmental performance of the different energy mixes were appraised on a‘life-cycle’ basis to determine the greenhouse gas emissions and other ecological or health burdens associated with each of the three transition pathways. Here, the challenges, insights and opportunities that have been identified over the transition towards a low-carbon future in the United Kingdom are described with the purpose of providing a valuable evidence base for developers, policy makers and other stakeholders