This study formulated a bi-level mixed integer non-linear optimization planning and operation model for the optimal configuration (location, capacity, and power ratings) of energy storage systems (ESSs) in power transmission networks. The model was formulated with consideration for independent and correlated wind farms. The single objective function in the inner layer of the bi-level model includes the difference between the total daily expected operational cost of conventional generators and the energy arbitrage benefits derived when considering the operational strategies of ESSs. The outer layer is a multi-objective function composed of three objective functions to be minimized. The objective functions encompass the total daily expected planning and operational cost, total daily expected emission, and the maximum expected voltage deviation. Wind power uncertainties in independent and correlated wind farms were also examined. Multivariate model-based Clayton copulas, which represent joint power distribution amongst correlated wind farms, were discretized using a developed five-point estimation method based on the discretization. A hybrid non-dominating sorted genetic algorithm and multi-objective particle swarm optimization were used to minimize the outer layer objective function, whilst fast Tabu search that considers the probabilistic load flow represented by wind power uncertainties and the operational strategies of ESSs was adopted to minimize the inner layer objective function. An IEEE 57-bus system was subjected to a case study using the proposed two-stage model. The simulation results confirmed the advantage of considering the benefits of a peak shaving operational strategy from economic, technical, and environmental points of view.