Characterization of Equilibrium and Stability in Power Systems

Study Of Transient Stability By Transient Energy Function

“…The equations describing the behaviour of the synchronous machines are formulated with respect to a fictitious inertial centre (in contrast to the usual situation where the machine's equations are formulated with respect to a synchronously moving frame of reference). The importance of this formulation is in clearly focusing on the motion that tends to separate one or more machines from the rest of the system, and in removing a substantial component of the system transient energy that does not contribute to instability, namely, the energy that accelerates the inertial centre [8,9].With this formulation, the forces tending to separate some machines from the rest of the system, and the energy components associated with their motion, can be easily identified [4,5,9].…”

On Angle References in Long-Term Time-Domain Simulations

“…T HE dynamic model of a power system considered in stability studies can be written in compact form as [1] (1) (2) Equations (1) relate to the network, whose response is assumed instantaneous under the phasor approximation. They are usually derived from the bus admittance matrix relations , where (resp. )…”

“…This is the idea underlying the center-of-inertia (COI) reference frame, which has been used in direct transient stability analysis methods [2] and in industrial simulation software (e.g., [3]). The COI angle and its time derivative are defined, respectively, as (7) (8) where is the total inertia and is an arbitrary constant.…”

An improved technique to determine the controlling unstable equilibrium point in a power system

“…In 1972 Tavora and Smith [8] dealt with the transient energy of a multimachine system and examined equilibrium points. They used the classical model with zero transfer conductances as well as the center of angle (now referred to as center of inertia) formulation for the swing equations.…”

“…6 UEP data for Case 7 160 Table 7.7 Transient stability assessment results for Cases 1 through 7 163 Table 7. 8 Criterion for the evaluation of the corrected kinetic energy for the 50-generator case 164 Table 7.9 Case description for the 161-generator system 164 Table 7.10 Number of cycles for each case for the 161-generator system 166 Table 7.11 UEP data for Case 8 and Case 9 167 Table 7.12 Transient stability assessment results for Case 8 and Case 9 172 Table B.l Machine data for the 3-machine system 206 …”