Module 4 — Transformers and rotating machines

Module status: outline

This is the detailed outline for Module 4. The fully written core of the course is Module 1; chapter prose here is in development.

Transformers and rotating machines are the magnetically coupled, often nonlinear heart of a power system. This module shows how each is brought into the time-domain network solution and how their nonlinearities (saturation) and the machine's mechanical dynamics are handled.

What you will learn

• How a multi-winding transformer becomes a coupled set of branches in the network, and how magnetizing saturation (a nonlinearity) is added.
• The structure of the synchronous machine model: the electrical (dq-axis) sub-model, the mechanical (rotor) sub-model, and the interface to the network.
• How the induction machine differs and where it is used.
• Why machines are usually initialized from a steady-state operating point so the simulation starts in balance rather than lurching at $t=0$.

Planned chapters

• 11. Transformer models. The ideal-plus-leakage representation, two- and three-winding configurations, and saturation via a nonlinear magnetizing branch; inrush as a worked phenomenon.
• 12. The synchronous machine. Park/dq-axis electrical model, the swing (rotor) equation, multimass shafts, and the machine-network interface; per-unit conventions.
• 13. The induction machine. Slip, the equivalent model, and typical start-up / loading studies.

Hands-on circuits

The transformer (single- and three-phase, two- and three-winding), synchronous machine, and induction machine components are all in the palette. Worked course samples will include transformer energization (inrush), a synchronous machine feeding a load, and an induction-motor start. Several of these components are developer-tier; the component reference lists each one's ports and parameters.

Practice themes

Expect problems on: deriving transformer leakage parameters from nameplate / test data; reading inrush current and relating it to the saturation curve; and interpreting a synchronous machine's response to a load step in terms of its time constants.

References

• H. W. Dommel, Electromagnetic Transients Program (EMTP) Theory Book, Bonneville Power Administration — transformers, the synchronous machine, and the universal machine.
• P. Kundur, Power System Stability and Control, McGraw-Hill — the definitive treatment of synchronous-machine modeling and per-unit conventions.
• J. Arrillaga and N. R. Watson, Power Systems Electromagnetic Transients Simulation, IET Power and Energy Series 39 — transformers and rotating plant.

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