An approach for determining the subsystem experiencing and producing a bifurcation in a power system dynamic model

Abstract

This paper presents a method for determining reduced-order subsystems called bifurcation subsystems, that experience bifurcation, and produce the bifurcation in the full power system dynamic model. The bifurcation subsystem is generally a subset of the center manifold subsystem. The bifurcation subsystem is in fact the singular perturbation determined slow subsystem within the center manifold dynamics that actually experiences and produces the bifurcation in the center manifold dynamics. The test procedure used to determine a bifurcation subsystem is described in this paper and does not require performing a nonlinear transformation required to determine the center manifold. The theory provides two singular perturbation based test conditions for existence of bifurcation subsystems. Examples that demonstrate the systematic use of this test procedure are presented for saddle-node and Hopf bifurcations in a single-machine-infinite-bus-model. Results when the test procedure for finding a bifurcation subsystem is applied to the large dominant elements of the tight eigenvector and the participation factor of a bifurcating eigenvalue are compared.

Ferroresonance in Voltage Transformer ConsideringLinear and Nonlinear Core Losses Effect

“…Linear and Nonlinear Core Losses Effect 4pu can theoretically gained in worst case conditions. The magnetizing characteristic of a typical 100VA VTs can be presented by 7 order polynomial [19]. These VTs fed through circuit breaker grading capacitance, and studied using nonlinear dynamics analysis and packages such as Rung kutta Fehlberg algorithm and MATLAB SIMULINK.…”

“…Fig. 1 shows the single line diagram of the most commonly encountered system arrangement that can give rise to VT ferroresonance [19]. [13] In Fig.…”

“…However, for very high currents the iron core might be driven into saturation and the flux-current characteristic becomes highly nonlinear, here the 1are chosen for the best fit of the saturation region that was obtained by the comparison between different approximations of the saturation regions against the true magnetization characteristic that was obtain by dick and Watson [5]. It was found that for adequate representation of the saturation characteristics of a voltage transformer core, the exponent q may acquire value 7 [19]. Fig.…”

“…In Mathematical analysis of equivalent circuit by applying KVL and KCL has been done and equations of system can be presented as below: where, ω is supply frequency, and E is the rms supply phase voltage, C series is the circuit breaker grading capacitance and C shunt is the total phase-to-earth capacitance of the arrangement and in equation (1) a=3.4 and b=0.41 are the seven order polynomial sufficient [19].…”

“…An approach for determining the subsystem experiencing and producing a bifurcation in a power system dynamic model has been reported in [18]. Effect of circuit breaker shunt resistance on chaotic ferroresonance in voltage transformer has been done in [19]. In all previous studies, possibility of occurring ferroresonance and nonlinear phenomena in power system had been studied, also the effects of nonlinear core losses on VT ferroresonance in the deeper case has not been investigated.…”