Ahmed M. Zobaa

Corona discharge has been recognized for centuries, with sailors reporting the bluish glow of St. Elmo’s fire on ship masts during storms. In the early development of high-voltage engineering, researchers such as Townsend and Peek described the physical basis of this phenomenon as the ionization of air around a conductor when the electric field exceeds the strength of the surrounding medium. The result is a partial discharge that produces visible light, hissing sounds, ozone, and other reactive gases, while also creating radio interference and ultraviolet radiation. In modern transmission systems, these effects appear as wasted power, accelerated wear of insulators, shortened equipment lifetime, and environmental concerns. Although corona has been studied for decades, it continues to challenge the reliable and economical operation of high-voltage networks, particularly under changing weather conditions. This study investigates the phenomenon by analyzing its causes, effects, and mitigation strategies through a combination of theoretical modelling, simulation, and statistical analysis. Using MATLAB Simulink and Python, simulations were conducted under varying environmental conditions—including temperature, humidity, and pressure—as well as electrical parameters such as voltage and conductor design, using observed data to ensure practical relevance. Comparable data sources may be used in other national or regional contexts. Key statistical techniques, including linear and multiple regression, analysis of variance (ANOVA), t-tests, and Monte Carlo simulations, were applied to determine the most influential factors affecting corona discharge losses. Results confirmed that higher voltage levels and unfavorable environmental conditions significantly increase corona loss, while increased conductor spacing and the use of corona rings emerged as the most effective mitigation strategies. An economic analysis based on probabilistic modelling estimated potential annual savings of up to 455 million Egyptian pounds (EGP) for the Egyptian grid, serving as a representative case study. The analytical framework is general and can be applied to other national transmission systems with appropriate data. The findings offer data-driven insights for improving transmission efficiency, minimizing power losses, and enhancing the overall reliability and cost-effectiveness of high-voltage power systems.

This work presents an improved modelling approach for wind turbine power curves (WTPCs) using fractional differential equations (FDE). Nine novel FDE-based models are presented for mathematically modelling commercial wind turbine modules’ power–velocity (P-V) characteristics. These models utilize Weibull and Gamma probability density functions to estimate the capacity factor (CF), where accuracy is measured using relative error (RE). Comparative analysis is performed for the WTPC mathematical models with a varying order of differentiation (α) from 0.5 to 1.5, utilizing the manufacturer data for 36 wind turbines with capacities ranging from 150 to 3400 kW. The shortcomings of conventional mathematical models in various meteorological scenarios can be overcome by applying the Riemann–Liouville fractional integral instead of the classical integer-order integrals. By altering the sequence of differentiation and comparing accuracy, the suggested model uses fractional derivatives to increase flexibility. By contrasting the model output with actual data obtained from the wind turbine datasheet and the historical data of a specific location, the models are validated. Their accuracy is assessed using the correlation coefficient (R) and the Mean Absolute Percentage Error (MAPE). The results demonstrate that the exponential model at α=0.9 gives the best accuracy of WTPCs, while the original linear model was the least accurate.