With the deployment of sensors in hardware equipment and advanced metering infrastructure, system operators have access to unprecedented amounts of data. Simultaneously, grid-connected power electronics technology has had a large impact on the way electrical energy is generated, transmitted, and delivered to consumers. Artificial intelligence and machine learning can help address the new power grid challenges with enhanced computational abilities and access to large amounts of data. This thesis discusses the fundamentals of neural networks and their applications in power systems such as load forecasting, power system stability analysis, and fault diagnosis. It extends application of neural networks to inverter-based resources by studying the implementation and performance of a neural network controller emulator for voltage-sourced converters. It delves into how neural networks could enhance cybersecurity of a component through multiple hardware and software implementations of the same component. This ensures that vulnerabilities inherent in one form of implementation do not affect the system as a whole. The thesis also proposes a comprehensive support vector classifier (SVC)--based submodule open-circuit fault detection and localization method for modular multilevel converters. This method eliminates the need for extra hardware. Its efficacy is discussed through simulation studies in PSCAD/EMTDC software. To ensure efficient usage of neural networks in power system simulation softwares, this thesis entails the step by step implementation of a neural network custom component in PSCAD/EMTDC. The custom component simplifies the process of recreating a neural network in PSCAD/EMTDC by eliminating the manual assembly of predefined library components such as summers, multipliers, comparators, and other miscellaneous blocks.