Power System Analysis

6

Numerical Integration of ODEs

CHAPTER OUTLINE

6.1 System of Differential Equations: Some Observations

6.2 Classification of Numerical Integration Algorithms

6.3 Accuracy and Stability of Numerical Integration Methods

6.4 Demonstration of Some Numerical Integration Methods

6.5 Example: Solution of Swing Equation

In this chapter, numerical integration techniques to obtain time–domain solution of ordinary differential equations (ODE) are reviewed from fundamentals. Accuracy and stability performances of numerical integration methods are introduced by using typical methods such as Forward Euler, Backward Euler, Trapezoidal, and Runge Kutta methods. In addition, some features of Dormand-Prince, a variable-step method, are discussed.

In order ...