Probabilistic weather forecasting for dynamic line rating studies

This paper aims to describe methods to determine short term probabilistic forecasts of weather conditions experienced at overhead lines (OHLs) in order to predict percentiles of dynamic line ratings of OHLs which can be used by a system operator within a chosen risk policy with respect to probability of a rating being exceeded. Predictive probability distributions of air temperature, wind speed and direction are assumed to be normal, truncated normal and von Mises respectively. Predictive centres are estimated as a sum of residuals predicted by a univariate auto-regressive model or a vector auto-regressive model and temporal trends fitted by a Fourier series. Conditional heteroscedasticity of the predictive distribution is modelled as a linear function of recent changes in residuals within one hour for air temperature and wind speed or concentration of recent wind direction observations within two hours. Parameters of the probabilistic models are determined to minimize the average value of continuous ranked probability score which is a summary indicator to assess performance of probabilistic models. The conditionally heteroscedastic models are shown to have appropriate sharpness and better calibration than the respective homoscedastic models

A short-term electricity price forecasting scheme for power market

Electricity price forecasting has become an important aspect of promoting competition and safeguarding the interests of participants in electricity market. As market participants, both producers and consumers intent to contribute more efforts on developing appropriate price forecasting scheme to maximize their profits. This paper introduces a time series method developed by Box-Jenkins that applies autoregressive integrated moving average (ARIMA) model to address a best-fitted time-domain model based on a time series of historical price data. Using the model’s parameters determined from the stationarized time series of prices, the price forecasts in UK electricity market for 1 step ahead are estimated in the next day and the next week. The most suitable models are selected for them separately after comparing their prediction outcomes. The data of historical prices are obtained from UK three-month Reference Price Data from April 1st to July 7th 2010

Probabilistic real-time thermal rating forecasting for overhead lines by conditionally heteroscedastic auto-regressive models

Conventional approaches to forecasting of real-time thermal ratings (RTTRs) provide only single point estimates with no indication of the size or distribution of possible errors. This paper describes weather based methods to estimate probabilistic RTTR forecasts for overhead lines which can be used by a system operator within a chosen risk policy with respect to probability of a rating being exceeded. Predictive centres of weather conditions are estimated as a sum of residuals predicted by a suitable auto-regressive model and temporal trends fitted by Fourier series. Conditional heteroscedasticity of the predictive distribution is modelled as a linear function of recent changes in residuals within one hour for air temperature and wind speed or concentration of recent wind direction observations within two hours. A technique of minimum continuous ranked probability score estimation is used to estimate predictive distributions. Numerous RTTRs for a particular span are generated by a combination of the Monte Carlo method where weather inputs are randomly sampled from the modelled predictive distributions at a particular future moment and a thermal model of overhead conductors. Kernel density estimation is then used to smooth and estimate the percentiles of RTTR forecasts which are then compared with actual ratings and discussed alongside practical issues around use of RTTR forecasts

Transient-state real-time thermal rating forecasting for overhead lines by an enhanced analytical method

The majority of published approaches to real-time thermal rating (RTTR) deal with continuous or steady-state ratings for overhead lines. Less attention has been given to short-term or transient-state RTTRs, partly due to the increased computation time required. This paper describes a fast-computational approach to providing a transient-state RTTR in the form of percentiles based on the predictive distributions modelled for the measured weather variables that are combined with Monte Carlo simulation. An analytical method developed in IEEE Standard 738 calculates the transient-state conductor temperature after a step change in line current only and additionally requires the conductor to be in thermal equilibrium before the step occurs. The IEEE analytical method is enhanced here through inference of an equivalent steady-state initial line current from the initial conductor temperature and weather conditions over a specified time period. Numerous transient-state RTTR forecasts for a particular span are estimated via weather inputs randomly sampled from predictive distributions for a number of time steps ahead combined with the secant method to find the transient-state RTTR. Along with an enhanced analytical method, this yields a maximum allowable conductor temperature for a specified time period under each set of weather samples. The percentiles of transient-state RTTR forecasts are then determined from their sampled values using kernel density estimation. The approach developed here considers variations in weather forecasts at each 10-min time step

Influence of Statistical Distributions on Availability and Inspection Interval of Protective Devices

Protective devices are designed to protect people, the environment and material assets under emergency situations. If protective devices do not work well, serious consequences may be resulted. It is critical to pay special attention to their maintenance. For this reason, many availability models have been developed to obtain an optimal inspection interval and to maximize their availability. However, few attention have been paid to the relationship between the statistical distributions used to describe the lifetime of protective devices and their optimal inspection interval and maximum availability. Furthermore, the problem that might occur when the normal distribution takes negative values has not been considered yet in protective device maintenance. This thesis aims to calculate the optimal inspection interval and maximum availability for the Weibull, normal, truncated normal and exponential distributions. Also, the relationship between these statistical distributions, and the availability and the inspection interval is studied. Finally, this thesis intends to study the problem that arises when the normal distribution might take negative values. To meet these objectives, an existing availability model, which considers constant time between inspections, is adapted to the Weibull, normal, truncated and exponential distributions. After adapting the model to each distribution, the effects of each distribution’s parameters on the optimal inspection interval and maximum availability are analyzed. It is not recommended to use the normal distribution if it has a large number of negative values while the truncated normal distribution is suggested as a possible approach to replace the normal distribution. This analysis help us to have a understanding on what is the performance and limitations of each of the four distributions.Outgoin

Metodología para la predicción de ampacidad en líneas eléctricas aéreas a partir de medidas directas y predicciones meteorológicas.

155 p.En los últimos años, la demanda de energía eléctrica ha aumentado de forma considerable, pero las redes eléctricas no están preparadas para integrar un mayor flujo de energía. Las líneas más cortas de una red, como las que conectan parques eólicos, o las líneas de distribución, están limitadas térmicamente. La ampacidad se define como la corriente máxima que puede conducir un conductor de manera continuada, cumpliendo los criterios de diseño y seguridad de la línea en la que se utiliza, y en conductores aéreos depende de las condiciones meteorológicas. Las compañías eléctricas calculan un límite térmico estático, asumiendo unas condiciones meteorológicas constantes durante todo el año, o durante toda una estación. Pero el límite estático desaprovecha parte de la capacidad térmica de las líneas y no está exento de riesgos. Una posible solución consiste en estimar la ampacidad de forma dinámica, conforme varían las condiciones ambientales. Estimar la ampacidad en tiempo real presenta ventajas en operación, pero los mercados eléctricos comercializan la energía con uno o varios días de antelación, por lo que es igualmente ventajosa su predicción.En la tesis se ha desarrollado una metodología que, combinando medidas directas en la línea ypredicciones meteorológicas, permite predecir la ampacidad de líneas aéreas. Los dispositivos de medición proporcionan medidas locales, pero las predicciones meteorológicas se obtienen a partir de modelos de la atmósfera a una escala mayor, lo que hace necesario su adaptación a la localización de la línea. La predicción puntual de la ampacidad no permite gestionar adecuadamente el nivel de riesgo derivado de una temperatura excesiva de los conductores, por lo que se hacen necesarias predicciones probabilísticas. Adicionalmente, se ha establecido una metodología para la evaluación de las predicciones, definiendo una serie de indicadores que permiten evaluar las predicciones tanto desde el punto de vista de la seguridad, como desde el punto de vista de aprovechamiento de la línea eléctrica. Aunque los conductores de la línea piloto para los que se ha validado la metodología son de tipo ACSR, esta también se ha validado para conductores HTLS, de alta temperatura y flecha reducida