Power system planning is the process of forecasting load demand and ensuring sufficient generation and reserve capacities over some planning horizon. This process includes investigation of steady-state and dynamic operation of power system of interest. This paper addresses the transient stability (also known as large-signal stability) analysis of power systems for offshore wind power plant integration planning studies. In particular, this study develops a comprehensive practical methodology to assess transient stability of power systems, including rotor angle stability, voltage stability and frequency response for all fault types for large scale power systems. This methodology considers variability of the offshore wind power plants as well as the type of any faulted components present and is applicable to the study of both short term and long term faults, though only short term faults are considered here (long term faults are treated sequentially in a companion paper). Furthermore, this paper considers the integration of offshore wind power plants into existing power systems and demonstrates the utility of this methodology through the examination of the specific case of integrating 1,000MW of offshore wind power into the FirstEnergy/PJM service territory using a realistic model of 63k-bus test system that represents the U.S. Eastern Interconnection.