Lyapunov-based Transient Stability Analysis

The paper presents an analytical control solution to the problem of transient stabilization of lossy multi-machine power systems. Firstly, a new form of control Lyapunov function candidates with a flexible potential-energy-like term is proposed. This is achieved mainly by introducing an auxiliary state that contributes to the derivation of a cross-term. Based on the Lyapunov function candidates, a new control law ensuring asymptotic stability of the desired closed-loop operating equilibrium is proposed. Finally, a case study on the model of a two-machine system to illustrate the effectiveness of the proposed control solution is presented.

I. Introduction

Transient stability analysis of power systems is a longstanding challenge because of several intrinsic complex characteristics, such as the nonlinear dynamic behaviours of the synchronous generators (SGs), the network discontinuity caused by faults or switching operations and the saturation effects due to limited feasible operating ranges, see e.g. [1]–[4]. 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]. To assess the transient stability of a post-fault power system, time domain simulations (TDS) offer one of the most widely accepted methods [1], [3]. This is usually achieved through the numerical integration of the model of the considered post-fault power system. However, since the scale of power systems has been ever increasing, TDS methods have become computationally expensive and therefore not well-suited for real-time implementations [3]. Compared to TDS methods, direct methods have a distinct advantage in that they allow assessing transient stability of a post-fault trajectory without time-consuming numerical integration [1], [3]. This is achieved mainly by using a suitable Lyapunov or energy function to analyze the stability properties of the desired post-fault operating equilibrium, and to check whether the initial post-fault state is inside the region of attraction of the desired post-fault operating equilibrium [3]. Therefore, direct methods are expected to offer a promising solution to the problem of real-time transient stability analysis of power systems [1], [3].