Traditionally, a P-Q Capability Chart is usually used to specify the safe operation boundary for a synchronous generator. With the increased development of inverter-based resources (IBRs) and interconnection of IBRs to the grid, IBR P-Q Capability Charts are also developed and proposed by the power industry to assure IBR operation efficiency and reliability. This thesis presents an evaluation about IBR control relation with the IBR P-Q capability, development of the IBR output active and reactive power models for IBR control in dq vector framework considering different filtering mechanisms and development of algorithms for computing IBR P-Q capability considering constraints that are specific to an IBR inverter and different from those for a synchronous generator. The proposed study considers the impact of different IBR grid-connected filters, IBR vector control implementation in the dq reference frame, and different pulse-width modulation methods applied to IBR inverters. The models and algorithms developed for the P-Q capability analysis have considered distinct IBR constraints that are different from those for a traditional synchronous generator. Also, this thesis presents a comprehensive evaluation of IBR P-Q capability curves under different conditions and P-Q capability theoretical evaluation for L-filter IBR. Both theoretical study for a special case and complete simulation evaluation are conducted to obtain IBR P-Q capability characteristics that are important for IBR control, operation and management, and for the development of international standards for interconnecting IBRs to the transmission and sub-transmission grids, such as IEEE P2800. In addition, this thesis present and derivate the equation for IBR P-Q capability curve with L-filter, that can work in most different perimeters to help the IBR P-Q capability curve can work in different condition in industry.