TY - GEN

T1 - A method for proving the global stability of a synchronous generator connected to an infinite bus

AU - Natarajan, Vivek

AU - Weiss, George

N1 - Publisher Copyright:
© Copyright 2015 IEEE All rights reserved.

PY - 2014

Y1 - 2014

N2 - We consider a grid connected synchronous generator (SG), having a constant field current and driven by a prime mover with constant torque. The grid is regarded as an "infinite bus", i.e., a three-phase AC voltage source. The problem of interest is verifying if, for a given set of SG parameters, the angular velocity of the SG rotor converges to the angular velocity of the grid, irrespectively of the SG initial conditions. We pose this problem as a question of almost global asymptotic stability of a fourth order nonlinear system. In a recent work, we derived an integro-differential equation, which resembles the forced pendulum equation, and showed that the fourth order system is almost globally asymptotically stable if and only if the same holds for this equation. In this paper, it is shown that this equation is almost globally asymptotically stable if a real-valued nonlinear map defined on a finite interval is a contraction. For any given set of SG parameters, it is straight forward to check numerically if this map is a contraction. An example demonstrating our results is included.

AB - We consider a grid connected synchronous generator (SG), having a constant field current and driven by a prime mover with constant torque. The grid is regarded as an "infinite bus", i.e., a three-phase AC voltage source. The problem of interest is verifying if, for a given set of SG parameters, the angular velocity of the SG rotor converges to the angular velocity of the grid, irrespectively of the SG initial conditions. We pose this problem as a question of almost global asymptotic stability of a fourth order nonlinear system. In a recent work, we derived an integro-differential equation, which resembles the forced pendulum equation, and showed that the fourth order system is almost globally asymptotically stable if and only if the same holds for this equation. In this paper, it is shown that this equation is almost globally asymptotically stable if a real-valued nonlinear map defined on a finite interval is a contraction. For any given set of SG parameters, it is straight forward to check numerically if this map is a contraction. An example demonstrating our results is included.

UR - http://www.scopus.com/inward/record.url?scp=84941249033&partnerID=8YFLogxK

U2 - 10.1109/EEEI.2014.7005745

DO - 10.1109/EEEI.2014.7005745

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AN - SCOPUS:84941249033

T3 - 2014 IEEE 28th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2014

BT - 2014 IEEE 28th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2014

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 28th IEEE Convention of Electrical and Electronics Engineers in Israel, IEEEI 2014

Y2 - 3 December 2014 through 5 December 2014

ER -