We present a probabilistic assessment of power distribution systems resilience under different weather conditions. It is based on Monte Carlo simulation considering failures and repairs models obtained in previous studies for the used power distribution system allowing consideration of different weather scenarios during the resilience estimation. Our main contribution is the methodology for assessing power distribution systems under different weather scenarios, which integrates time-to-event models to estimate resilience. The assessment is carried out on distribution networks of a Brazilian power company, and using two resilience perspectives: structural, considering networks connectivity and service, quantifying energy delivered. An investigation of which features are related to the resilience loss in extreme weather is also performed. Results show that all the networks are resilient to a normal weather condition in both perspectives and weather adversities reduce their structural resilience, mainly in large networks. At the same time, service resilience loss is not linearly related to network size, but with how electricity flows over the networks, as the average load passing through vertices and the presence of lateral branches. These findings can support decision making about management and planning of such systems as resilience-oriented modifications, resources allocation, and expansion planning.

This paper presents a three-phase Distribution System State Estimator (DSSE) based on a Bayesian inference approach to manage different sampling rates of typical sources of information present in distribution networks. Such information comes from smart meters, supervisory control and data acquisition (SCADA) measurements, phasor measurement units and typical load profiles from pseudo measurements. The temporal aspect of the measurement set is incorporated in the estimation process by using a sampling layer concept, dealing separately with each group of measurements according to the respective updating rate. A Bayesian information fusion procedure provides the final estimation. The proposed DSSE consists in a multiple stage estimator that combines a prior model for the state variables, updated by new observations from measured values in each sampling layer, through Maximum a Posteriori estimation. This work also introduces an orthogonal method for the information fusion numerical solution, to tackle the severe ill-conditioning associated with practical distribution systems. Simulations with IEEE distribution test feeders and a Brazilian real distribution feeder illustrate the features of the proposed DSSE and its applicability. By exploring the concept of credibility intervals, the method is able to detect events on the grid, such as subtle load variation and contingencies, while maintaining accuracy.

Entropy is a concept that emerged in the 19th century. It used to be associated with heat harnessed by a thermal machine to perform work during the Industrial Revolution. However, there was an unprecedented scientific revolution in the 20th century due to one of its most essential innovations, i.e., the information theory, which also encompasses the concept of entropy. Therefore, the following question is naturally raised: “what is the difference, if any, between concepts of entropy in each field of knowledge?” There are misconceptions, as there have been multiple attempts to conciliate the entropy of thermodynamics with that of information theory. Entropy is most commonly defined as “disorder”, although it is not a good analogy since “order” is a subjective human concept, and “disorder” cannot always be obtained from entropy. Therefore, this paper presents a historical background on the evolution of the term “entropy”, and provides mathematical evidence and logical arguments regarding its interconnection in various scientific areas, with the objective of providing a theoretical review and reference material for a broad audience.

Cyber‐physical systems result from the integration of information and communication technologies into physical systems. A particular case are cyber‐physical power systems, which use communication technologies to perform real‐time monitoring and operations, impacting on systems' characteristics, such as their reliability. In addition, it is known that failures of the communication network are just as relevant as the electrical network failures in terms of cyber‐physical power distribution systems (CPPDS) reliability. However, some of the operators’ performances, such as response time and decision quality, during CPPDS contingencies have not been investigated yet. In this study, the authors introduce a model to the operator response time, present a sequential Monte Carlo simulation methodology that incorporates the response time in CPPDS reliability indices estimation, and evaluate the impact of such response time in CPPDS reliability indices. The method is tested on a CPPDS using different values for operators' average response time. The results show that the operators' response time affects the reliability indices related to failures duration, indicating that a fast decision directly contributes to the system performance. The authors conclude that the improvement of CPPDS reliability is not only dependent on the electric and communication components, but also dependent on operators' performance.