SMIB dynamics

Learning goals¶

Write classical SMIB swing equations in consistent units
Relate inertia and damping to post-disturbance trajectories
Name prefault, fault-on, and postfault stages for teaching experiments

Reading¶

Swing equations and transient stability framing Kundur & Malik, 2022
Lab 1 — reference simulation uses this model

Classical swing model (teaching form)¶

A common classical-machine SMIB model (per-unit power, radian angles) is:

\begin{aligned} \dot{\delta} &= \omega - \omega_0, \\ \frac{2H}{\omega_0}\dot{\omega} &= P_m - P_e(\delta) - D\,(\omega - \omega_0), \end{aligned}

(1)

with electrical power of the form $P_e = \frac{E V}{X}\sin\delta$ (details and bases documented in the lab notebook).

Teaching estimands in Lab 3: inertia $H$ and damping $D$ . Keep units and the per-unit base in the dataset manifest.

Event stages¶

Stage	Network / driving	Typical use
Prefault	Intact network, equilibrium	Initial condition
Fault-on	Reduced $P_e$ capability (e.g. bolted fault)	Energy input / acceleration
Postfault	Cleared topology	Stability vs loss of synchronism

Critical clearing time (CCT) later asks: how long can fault-on last before postfault trajectories are unstable under a stated rule? See Stability and CCT.

Worked example¶

For fixed $H$ , plot qualitative $\delta(t)$ after a short fault vs a long fault. Which parameter mainly scales the “inertia” of the swing?

Lab¶

Lab 1 — Reference simulation

Common misconceptions¶

Calling every fitted coefficient “physical inertia” without a model map
Mixing SI and per-unit in the same residual without conversion
Using converter $(M_v, D_v, m_p)$ language in classical SMIB labs without an explicit elective flag

References¶

Kundur, P., & Malik, O. P. (2022). Power System Stability and Control (Second). McGraw-Hill Education. https://openlibrary.org/isbn/9781260473544
Kundur, P., Paserba, J., Ajjarapu, V., Andersson, G., Bose, A., Canizares, C., Hatziargyriou, N., Hill, D. J., Stankovic, A., Taylor, C., Van Cutsem, T., & Vittal, V. (2004). Definition and Classification of Power System Stability IEEE/CIGRE Joint Task Force on Stability Terms and Definitions. IEEE Transactions on Power Systems, 19(3), 1387–1401. 10.1109/TPWRS.2004.825981

Learning goals¶

Reading¶

Classical swing model (teaching form)¶

Event stages¶

Worked example¶

Lab¶

Further reading¶

Common misconceptions¶