Module lcc 

The steady state of a line-commutated (LCC) two-terminal DC line at its AC terminal voltages.

A two-terminal DC line read from PSS/E keeps its converter records (psse_dc_* extras), and those, with the AC voltage at each converter bus, fix the converters’ firing and extinction angles, their commutation overlap, and the reactive power each one draws from its AC bus. The Hvdc record states no converter reactive power (qf = qt = 0), so a calculation that wants the converters’ physical demand computes it here.

The model is the classic six-pulse bridge equations PSS/E states for its two-terminal lines. With NB bridges in series, commutating resistance RC and reactance XC per bridge (ohms), and the converter transformer’s primary base voltage EBAS (kV), ratio TR, and tap TAP, the valve-side line-to-line voltage at AC magnitude V (per unit) is E = V·EBAS·TR/TAP, and each converter’s angle θ (firing angle α at the rectifier, extinction angle γ at the inverter) satisfies

Vd/NB = (3√2/π)·E·cos θ − (3·XC/π + 2·RC)·Id
cos(θ + μ) = cos θ − √2·XC·Id/E
Q = P·(2μ + sin 2θ − sin 2(θ + μ)) / (cos 2θ − cos 2(θ + μ))

with P = Vd·Id. The DC operating point comes from the record’s schedule: the scheduled compounded voltage VSCHD holds Vd_inverter + RCOMP·Id, the rectifier sits RDC·Id above the inverter, and SETVL states the power (at the rectifier, or at the inverter when negative) or, under MDC 2, the current.

A converter whose angle reaches 90 degrees or more, or whose DC voltage is not positive, has a power factor at or below zero: the schedule does not describe a rectifier or inverter at these voltages, so no operating point is returned and a caller keeps the line’s stated reactive powers.

Known inconsistency with the PSS/E reader

The two-terminal reader on main prices a power schedule at the rectifier as Id = SETVL / VSCHD, as if VSCHD were the rectifier voltage, and stores pf = SETVL and pt = SETVL - RDC·Id². The bridge model here follows PSS/E: VSCHD is the inverter voltage plus the compounding drop RCOMP·Id, so the rectifier sits RDC·Id above it and Id solves (VSCHD + (RDC - RCOMP)·Id)·Id = SETVL. For SETVL 1000 MW, VSCHD 500 kV, RDC 10 Ω, and RCOMP 0, the reader has Id = 2.0 kA and pt = 960 MW, the bridge model Id = 1.9258 kA and 962.9 MW at the inverter. The stated-state balance uses this model’s current only for the converters’ reactive power and keeps the reader’s pf and pt for the active power; aligning the reader changes conversion output and is separate work.

Structs

LccConverterState

One converter of an LCC line at an operating point.

LccOperatingPoint

Both converters of an LCC line at an operating point.