Sync Machine Load

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A 100 MVA synchronous machine on a stiff 13.8 kV bus, exporting into a local PQ load.

One-line view: a near-ideal 13.8 kV source (1 mΩ series) and a 100 MVA round-rotor machine share a bus that also carries a 40 MW $+j10$ MVAr constant-impedance load. Nothing regulates the machine — field voltage $E_{\mathrm{fd}}$ and shaft torque $T_m$ are held at fixed values, so this is the open-loop operating point the controls sample builds on.

A round-rotor machine sits on a bus that a near-ideal source holds at 13.8 kV, with a constant-impedance load on the same bus. Nothing regulates the machine: its field voltage is pinned at efd0 = 1.05 pu and its shaft torque at tm0 = 0.4 pu, so the operating point is whatever those two numbers imply. The scope follows rotor angle delta next to the filtered Pgen and Qgen.

The first second is the machine's fluxes settling out of the file's hand-seeded initial condition rather than any physical event — Pgen overshoots to 109 MW at 29 ms, dips below zero near 0.19 s, and delta swings down to 6.4° before recovering. After that, real power locks on: Pgen holds 39.7 MW against the 40 MW load for the rest of the run. What keeps moving is the field flux. Steady power transfer across the synchronous reactance goes roughly as (Efd / Xd)·sin δ = 0.58·sin δ pu, so carrying 0.4 pu of torque needs an angle near 40°, and the machine walks there as the d-axis flux decays with its 8 s open-circuit time constant: delta passes 28.6° at 2 s, 37.1° at 8 s, and arrives at 39.8° by 20 s. Qgen slides the other way, from +9 MVAr down to −12.7 MVAr, because a 1.05 pu field behind a 1.8 pu reactance is under-excited at that angle — the machine ends up absorbing vars from the bus rather than supplying them.

Raise tm0 to 0.62 pu and the machine will carry 61.7 MW, but it needs more than 70° of angle to do it and takes far longer to get there: the P–δ curve flattens as you approach pull-out, so each extra megawatt costs more angle and more settling time. Raise efd0 to 1.3 pu instead and Qgen climbs from −12.7 MVAr through zero to +4.6 MVAr while the angle drops to 31.1° — a stronger field both exports vars and buys back rotor angle. That second lever is the one an AVR pulls automatically in the generator controls sample. The run is 20 s at a 50 µs step, long enough for the field transient to finish; a shorter window stops mid-pull-in and makes a converging machine look like a drifting one.