Numerical method for EMTP solution: RK or Difference Eqn

[electricpete]

I am under the (naïve?) impression that a single general purpose integration method for time domain solution of ordinary differential equations is generally satisfactory. In particular Runge-Kutta variable step size algorithm seems omnipresent in programs such as Matlab.

But I was skimming the book “Power Systems Electromagnetic Transients Simulation” by Watson and Arrillaga and I was surprised to see how much of the discussion focuses on numerical solution methods and their errors and stability (Chapter 2 continuous and discrete analysis, Chapter 4 numerical integrator substitution method, Chapter 5 root matching method, Appendix C – Numerical Integration, Appendix E – Developing Difference Equations.

It leaves me with the general impression that more than Runge-Kutta or other general purpose “integration methods” is needed and that specialized difference equations are required. Is this the case….or will Runge Kutta work for analyzing transients such as switching transients?

Is there something different about EMTP analysis from other ODE applications that would demand approaches like developing a specialized discrete difference equation using order matching method, rather than using general purpose integration method like Runge Kutta?

Main Question: What is used in the off-the-shelf programs like ATP?
Runge Kutta (or similar integration methods) or difference equations?


=====================================
(2B)+(2B)' ?

 

[electricpete]

I guess the various models of transmission line may not exactly match the typical form dx/dt(t0) = f(x(t0),t0) where x is vector of state variables. Even if modeled as a simple delay, then it depends on the time history.

=====================================
(2B)+(2B)' ?

 

[ijl]

ATP uses basically the trapezoidal rule.