Equilibrium-Independent Passivity of Power Systems: A Link Between Classical and Two-Axis Synchronous Generator Models
CoRR(2023)
摘要
We study the equilibrium-independent (EI) passivity of a nonlinear power
system composed of two-axis generator models. The model of our interest
consists of a feedback inter-connection of linear and nonlinear subsystems,
called mechanical and electromagnetic subsystems. We mathematically prove the
following three facts by analyzing the nonlinear electromagnetic subsystem.
First, a lossless transmission network is necessary for the EI passivity of the
electromagnetic subsystem. Second, the convexity of a strain energy function
characterizes the largest set of equilibria over which the electromagnetic
subsystem is EI passive. Finally, we prove that the strain energy function for
the network of the two-axis generator models is convex if and only if its flux
linkage dynamics is stable, and the strain energy function for the network of
the classical generator models derived by singular perturbation approximation
of the flux linkage dynamics is convex. Numerical simulation of the IEEE 9-bus
power system model demonstrates the practical implications of the various
mathematical results. In particular, we validate that the convex domain of the
strain energy function over which the electromagnetic subsystem is EI passive
is almost identical to the set of all stable equilibria. This result is also
generalized to lossy power systems based on our finding that the convexity of
the strain energy function is equivalent to the positive semidefiniteness of a
synchronizing torque coefficient matrix.
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关键词
power systems,passivity,equilibrium-independent,two-axis
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