Chapter 5

Energy Function Theory and Direct Methods

5.1 INTRODUCTION

Power system stability analysis is concerned with whether the postfault trajectory will settle to an acceptable operating condition. Direct methods for stability analysis use algorithmic procedures to assess, without integrating the postfault system, the stability property of the postfault trajectory by comparing the system energy at the initial state of the postfault trajectory to a critical energy value. Direct methods not only avoid the time-consuming procedure of numerical integration of the postfault system, but they also provide a quantitative measure of the degree of system stability. Given a power system transient stability model with specified fault-on systems and a specified postfault system, direct methods for transient stability analysis are composed of the following steps:

Step 1. Numerically simulate the fault-on trajectory.

Step 2. Compute the initial point of the postfault system.

Step 3. Construct an energy function for the postfault power system.

Step 4. Compute the energy function value at the initial point of the postfault system.

Step 5. Compute the critical energy for the fault-on trajectory.

Step 6. Perform direct stability analysis by comparing the system energy at the initial state of the postfault system (computed at Step 4) with the critical energy (computed at Step 5). If the former is smaller than the latter, then the postfault trajectory will be stable; otherwise, it may ...

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