Transient stabilization of multimachine power systems with nontrivial transfer conductances

Abstract

Abstract-In this paper, we provide a solution to the long-standing problem of transient stabilization of multimachine power systems with nonnegligible transfer conductances.More specifically, we consider the full 3 -dimensional model of the -generator system with lossy transmission lines and loads and prove the existence of a nonlinear static state feedback law for the generator excitation field that ensures asymptotic stability of the operating point with a well-defined estimate of the domain of attraction provided by a bona fide Lyapunov function. To design the control law we apply the recently introduced interconnection and damping assignment passivity-based control methodology that endows the closed-loop system with a port-controlled Hamiltonian structure with desired total energy function. The latter consists of terms akin to kinetic and potential energies, thus has a clear physical interpretation. Our derivations underscore the deleterious effects of resistive elements which, as is well known, hamper the assignment of simple "gradient" energy functions and compel us to include nonstandard cross terms. A key step in the construction is the modification of the energy transfer between the electrical and the mechanical parts of the system which is obtained via the introduction of state-modulated interconnections that play the role of multipliers in classical passivity theory.

Lyapunov-based Transient Stability Analysis

“…By applying the Implicit Function Theorem, [5] has proved the existence of a cross-term λ such that any C 1 function is assignable for ψ. Moreover, the CLF in (4) guarantees asymptotic stability of the desired operating equilibrium x * .…”

“…Moreover, the CLF in (4) guarantees asymptotic stability of the desired operating equilibrium x * . However, neither an explicit form of ψ nor an explicit control law has been suggested for n-machine models in [5], which is mainly due to the difficulty in the explicit computation of the cross-term.…”

“…Transient stability is mainly concerned with the ability of the power system to maintain synchronism when subject to large disturbances such as a fault on the transmission facilities [1]. The fault modifies the network topology, therefore driving the state away from the pre-fault operating equilibrium; after the fault is cleared, the question becomes whether the state trajectory converges back to a desired post-fault operating equilibrium [1], [5]. Typically, if the post-fault rotor angular separations between all SGs remain within certain bounds, the system maintains synchronism; otherwise, the system is deemed to be transient unstable and corrective actions have to be undertaken [1], [3], [4].…”

“…The main obstacle to the task of constructing an explicit control Lyapunov function (CLF) stems from the deleterious effects of resistive elements that hamper the assignment of the potential-energy-like term [5]. To address this problem, [5] has proposed a nonstandard cross-term that modifies the energy transfer and therefore improves the general form of traditional CLFs. By applying the Implicit Function Theorem, [5] has proved the existence of a CLF for the transient stability analysis of lossy multi-machine models.…”

“…To address this problem, [5] has proposed a nonstandard cross-term that modifies the energy transfer and therefore improves the general form of traditional CLFs. By applying the Implicit Function Theorem, [5] has proved the existence of a CLF for the transient stability analysis of lossy multi-machine models. However, neither an explicit form of CLFs nor a feasible control law has been suggested.…”