Kenya is experiencing a fast increase in grid-connected intermittent renewable energy sources (RESs) to meet its increased power demand, and at the same time be able to fulfill its Paris Agreement obligations of abating greenhouse gas emissions. For instance, Kenya has 102 MW of grid-tied solar power and 410 MW of grid-tied wind power. However, these sources are very intermittent with low predictability. Thus, after their installation and integration into the grid, they impose a new challenge for the secure, reliable, and economic operation of the system. To mitigate these and to ensure proper planning of the system operations, accurate and faster prediction of the generation output of the wind energy resources and optimal design and sizing of storage for the large-scale wind energy integration into the grid are of paramount importance. Artificial intelligence (AI) and metaheuristic techniques have proven to be efficient and robust in offering solutions to complex nonlinear prediction and optimization problems. Therefore, this study aims to utilize backpropagation neural network (BPNN) algorithm to conduct hourly prediction of the generation output of Lake Turkana Wind Power Plant (LTWPP), a 310 MW plant connected to the Kenyan power grid, and optimally size its battery energy storage system (BESS) using genetic algorithm (GA) to guarantee its dispatchability. The historical weather data, namely wind speed, ambient temperature, relative humidity, wind direction, and generation output from LTWPP, are employed in the training, testing, and validation of the neural network. LTWPP and BESS are modelled in MATLAB R2016a software. Thereafter, the developed BPNN and GA algorithms are applied to the modelled systems to predict the wind output and optimize the storage system, respectively. BESS optimization with neural prediction reduces the BESS capacity and investment costs by 59.82%, while the overall dispatchability of LTWPP is increased from 73.36% to 90.14%, hence enabling the farm to meet its allowable loss of power supply probability (LPSP) index of 0.1 while guaranteeing its dispatchability.