Emerging Horizons in Scientific Research

With the world shifting towards the use of sustainable energy, solar photovoltaic (PV) and wind energy have become significant providers of electricity because they are environmentally friendly, they are abundant, and they are becoming cheaper. They are variable in nature, and this makes it difficult to have a consistent power supply and integrate them well into the current power grids. The mathematical modelling has been an essential tool to overcome these challenges so as to make precise predictions, optimise the system and hybridise.

Such a survey offers an inclusive perspective of mathematical methodologies that are utilised in photovoltaic systems and wind energy systems. Solar modelling includes geometric and empirical irradiance models, photovoltaic performance analysis via single-diode and equivalent-circuit models, and advanced machine-learning applications, including neural networks and support-vector regression to the accurate short- and long-term forecasting of energy output. The modelling of wind energy takes the use of the statistical distribution methods, mostly the Weibull distribution, alongside the aerodynamic power equations to predict the site-specific turbine performance. Energy yield, cost-effectiveness and system reliability are discussed as applications of optimisation strategies which include genetic algorithms, particle-swarm optimisation, linear programming, and mixed-integer programming.

A typical example of a hybrid campus-scale solar-wind system can be used as an illustrative case study to show how the analytical constructs can be executed in practice and how the problem of generating and storing, as well as operational efficiency, can be aligned to generate a balanced energy portfolio. The new technologies, such as Internet-of-Things-based monitoring, digital-twins resources, and probabilistic forecasting frameworks, are also emphasised as tools to support real-time supervision and enable the process of decision-making. This chapter highlights the necessity of mathematical modelling in designing, analysing, and optimising renewable energy systems, whose goal is to obtain reliable power delivery, efficient, and sustainable power delivery.