Mathematical models for power system dynamic analysis including the dynamics of the protective system are presented. The formulation of the equations is based on establishing explicit relations between the protection system and the rest of system dynamic elements through the node admittance matrix Ysus.This relationship is achieved by representing the circuit breakers of interest as part of the transmission network elements. The protective relays, reclosing relays and circuit breakers are modeled as dynamic devices for tracking the dependence of these devices on the voltage and current inputs using the phasor state variables. A simple example illustrates the concepts. As a direct consequence of the analytical model, the concept of a protection success region is introduced and the implications for stability analysis, relay coordination, adaptive relaying and cascade tripping are discussed.The objective of the electric power system is to generate and to distribute power to its customers in a 1) stable (sustaining small disturbances), 2) viable (currents, voltages, angles and frequencies within tolerances) and 3) optimal fashion (economy): For this operation to be secure, it is also necessary that the system can withstand certain major disturbances such as line faults or sudden loss of equipments without severe consequences. This motivates the notion of transient stability which is essentially the ability of the system operation to recover its stable operating point without major break-ups after a specified set of first contingencies. The system, with suitable degrees of local stability, viability and transient stability, can then be considered to be secure and additional conditions on optimality imply economic operation [I]. The evolution of system operation after major disturbances such as faults depends on the interaction b e tween two principal factors, namely the protection subsystem consisting mainly of relays and circuit breakers 94 WM 191-7 PWRS by the IEEE Power System Engineering Committee of the IEEE Power Engineering Society for presentation at the IEEE/PES A paper recommended and approved and the dynamics governed by generators, loads and control devices. The operating time of the system protection is typically in the range of 3-10 cycles [2] and the variation of the voltage and current magnitudes caused by system dynamics during this period can usually be ignored from the system protection view-point. However there are circumstances when the relay operation can be much slower (such as the second and third zones of distance relays) where the system dynamics has a direct role to play. The system protection is designed 1) to protect the system components such as lines and machines from excessive currents or voltages and 2) to selectively isolate the "faulty" portion of the system from the rest so that the fault can be cleared for resumption of normal service. Setting the relay parameters for proper detection and clearing of faults is a complex operation in general and typically relay coordination is based...