Compositional Transient Stability Analysis of Multimachine Power Networks

Abstract

Abstract. During the normal operation of a power system all the voltages and currents are sinusoids with a frequency of 60 Hz in America and parts of Asia, or of 50Hz in the rest of the world. Forcing all the currents and voltages to be sinusoids with the right frequency is one of the most important problems in power systems. This problem is known as the transient stability problem in the power systems literature.The classical models used to study transient stability are based on several implicit assumptions that are violated when transients occur. One such assumption is the use of phasors to study transients. While phasors require sinusoidal waveforms to be well defined, there is no guarantee that waveforms will remain sinusoidal during transients. In this paper, we use energy-based models derived from first principles that are not subject to hard-to-justify classical assumptions. In addition to eliminate assumptions that are known not to hold during transient stages, we derive intuitive conditions ensuring the transient stability of power systems with lossy transmission lines. Furthermore, the conditions for transient stability are compositional in the sense that one infers transient stability of a large power system by checking simple conditions for individual generators.

Almost global attractivity of a synchronous generator connected to an infinite bus

“…We make some standard assumptions on the SG [22], [23], which are also used in [10], [14], [15]. First, the rotor is round, the machine has one pole pair per phase, there are no damper windings and no saturation effects as well as no Eddy currents.…”

“…Furthermore, and perhaps more importantly, the geometric tools employed to establish the results in [14], [15], don't seem to be applicable to a multimachine power system. In [10] a scenario similar to that of the SGIB system is analyzed. However, the analysis in [10] is conducted under very stringent assumptions on the specific form of the infinite bus voltage, as well as the steady-state values of the mechanical torque.…”

“…In [10] a scenario similar to that of the SGIB system is analyzed. However, the analysis in [10] is conducted under very stringent assumptions on the specific form of the infinite bus voltage, as well as the steady-state values of the mechanical torque.…”

Optimal power dispatch in networks of high-dimensional models of synchronous machines

“…acts as a local storage function for proving passivity in a neighborhood of a steady statex of (12), provided that the Hessian of H evaluated atx (denoted as ∇ 2 H(x)) is positive definite 4 . Proposition 2: Letū be a constant input and suppose there exists a corresponding steady statex to (12) (12) is passive in a neighborhood ofx with respect to the shifted external portvariablesũ := u −ū,ỹ := y −ȳ whereȳ := g T ∇H(x).…”

“…However, the full-order model of the synchronous machine as derived in many power engineering books like [2], [6], [8] is difficult to analyze, see e.g. [5] for a port-Hamiltonian approach, especially when considering multi-machine networks [4], [9]. Moreover, it is not necessary to consider the full-order model when studying electromechanical dynamics [8].…”