Synchronous generator laboratory
Design an experiment, check the numerical solution and report reproducible results.
Before you begin: lessons 16–19 and numerical error assessment.
After this lesson you can: check equilibrium and convergence and export a reproducible experiment.
Work through the explanation, examples, practical experiment and independent exercises.
Record the experiment
Record E, V, X, H, D, f₀, Sb, Ub and P₀, the mechanical-power step, residual voltage, dip duration and simulation end time. Every disturbance starts at 1 s. The stable initial angle is calculated automatically; initial speed deviation is zero.
Begin with E = 1.2, V = 1, X = 0.6, H = 4, D = 2 and P₀ = 0.8. First remove the disturbance, then change one factor at a time.
Solver and switching events
Classical RK4 uses steps no larger than 0.002 s. Steps are shortened to land exactly at switching times. Repeat with 0.001 s and compare angles at common times. A no-disturbance experiment should preserve δ₀ and Δω = 0 to roundoff accuracy. With D = 0, check an energy integral after the disturbance ends.
dW/dt = −D(2πf₀)Δω²
This is a normalized integral of the swing equation, not the complete machine energy in joules. It applies on intervals of constant Pm and V and need not be conserved across an external switch.
What to include in the report
Export CSV containing experiment parameters and time histories of angle, rotor-field frequency deviation, active power, reactive power and current. Show the initial state, extrema, voltage recovery time and step-size comparison. Do not call rotor-field frequency grid frequency: the infinite-bus frequency is fixed.
Run three cases: a small power step, a short deep voltage dip, and a long dip with angle drift. Explain the power balance in each. State what cannot be transferred to a real machine without excitation dynamics and operating limits.
Independent exercises
1. What should Pe equal before the disturbance when initialization is correct?
Show solution
Pe = P₀ = Pm and Δω = 0. Both state derivatives vanish.
2. Why does a smaller step not compensate for a missing excitation regulator?
Show solution
It reduces numerical error, not structural model error. Excitation requires additional states and parameters.
Practical work
Run all three cases, export CSV and select “Check step size”. Compare the maximum angle difference for an ordinary and a near-boundary case. State the observation duration, assumptions and numerical accuracy in your conclusion.
Key takeaways
Trust a calculation after checking units, initial equilibrium, event handling and convergence. Separate finite-time observations from a proof of stability.
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