Synchronous Machine — Parameter Conversion (XT ↔ RL)

A SYNC_MACH record can be entered using one of two equivalent parameter formats, selected by the TYPE_MOD keyword:

• RL — the Park-model inductances and resistances are supplied directly.
• XT — characteristic reactances and open-circuit time constants are supplied; STEPSS/RAMSES converts them internally.

Both formats describe the same machine. XT is convenient when data comes from manufacturer datasheets or Kundur-style standard parameters. This page documents exactly how that conversion is done, so it can be reproduced by hand or cross-checked against external simulators (e.g. Typhoon HIL EMT).

Common pitfalls

Two details that break hand calculations against STEPSS:

1. Open-circuit time constants are normalised to radians by $t_b = 1/(2\pi f_{nom})$ before use in the resistance formulas.
2. The field circuit base is tied to IBRATIO via $p_{uf} = R_f / \text{IBRATIO}$; a wrong assumption here corrupts $M_d$, $L_{\ell f}$, and $R_f$ after per-unit → Henry conversion.

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Authoritative field order

From the RAMSES source (sync.f90, get_sync_mach):

SYNC_MACH NAME BUS FP FQ P Q SNOM PNOM H D IBRATIO
  RL  LL MDU  LLF  LLD1 MQU LLQ1 LLQ2 M N RA RF   RD1  RQ1  RQ2
  XT  LL XD   XPD  XSD  XQ  XPQ  XSQ  M N RA TPD0 TSD0 TPQ0 TSQ0
  EXC <model> ... TOR <model> ... ;

A rotor circuit the machine does not have is skipped with * in both its reactance/inductance and its resistance/time-constant field.

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Conversion algorithm (XT → RL)

All parameters are in per unit; time constants are entered in seconds and normalised internally.

Time base

$$t_b = \frac{1}{2\pi f_{nom}}$$

All time constants (TPD0, TSD0, TPQ0, TSQ0) are divided by $t_b$ before entering the resistance formulas.

Unsaturated mutuals

$$M_d^u = X_d - L_\ell, \qquad M_q^u = X_q - L_\ell$$

d axis — two rotor circuits (field + damper, XSD/TSD0 present)

$$T'_d = T'_{d0}\frac{X'_d}{X_d}, \qquad T''_d = \frac{X''_d \, T'_{d0} \, T''_{d0}}{X_d \, T'_d}$$ $$a = \frac{X_d T'_d T''_d - L_\ell T'_{d0} T''_{d0}}{X_d - L_\ell}, \quad b = \frac{X_d(T'_d + T''_d) - L_\ell(T'_{d0} + T''_{d0})}{X_d - L_\ell}$$ $$c = \frac{X_d(T'_{d0} T''_{d0} - T'_d T''_d)}{(X_d - L_\ell)^2}, \quad d = \frac{X_d(T'_{d0} + T''_{d0} - T'_d - T''_d)}{(X_d - L_\ell)^2}$$ $$T_f = \frac{b + \sqrt{b^2 - 4a}}{2}, \qquad T_{d1} = b - T_f$$ $$R_{d1} = \frac{T_f - T_{d1}}{c - d \, T_{d1}}, \qquad R_f = \frac{-R_{d1}}{1 - d \, R_{d1}}$$ $$L_{\ell f} = T_f R_f, \qquad L_{\ell d1} = T_{d1} R_{d1}$$

d axis — single rotor circuit (XSD/TSD0 skipped)

$$L_{ff} = \frac{(M_d^u)^2}{X_d - X'_d}, \qquad L_{\ell f} = L_{ff} - M_d^u, \qquad R_f = \frac{L_{ff}}{T'_{d0}}$$

q axis is fully symmetric to the d axis. Two circuits (XPQ/TPQ0 and XSQ/TSQ0) use the same quadratic with $X_q, L_\ell, T'_{q0}, T''_{q0}, X'_q, X''_q$. Single-circuit fallbacks:

• Transient only (XPQ/TPQ0): $L_{\ell q1} = M_q^u{}^2/(X_q - X'_q) - M_q^u$, $R_{q1} = (M_q^u{}^2/(X_q - X'_q))/T'_{q0}$
• Subtransient only (XSQ/TSQ0): same with $X''_q, T''_{q0}$, result assigned to $L_{\ell q2}, R_{q2}$

Field base scaling

$$p_{uf} = R_f \,/\, \text{IBRATIO}$$

The field current is then reconstructed internally as $i_f = (\psi_f - \psi_{ad}) \cdot (R_f/p_{uf}) / L_{\ell f}$.

Sanity check

If any of $R_f, R_{d1}, L_{\ell f}, L_{\ell d1}$ (or q-axis equivalents) turns out negative, the supplied reactances/time constants are physically inconsistent. STEPSS emits an “unrealistic Park inductances or resistances” warning.

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Reference Python implementation

A standalone Python port of the XT branch is available at Sync_mach_Octave (Octave) and as ramses_xt_to_park.py (attached below). It reproduces the algorithm above including the $t_b$ normalisation, the quadratic solve, the symmetric q axis, and puf = RF/IBRATIO. Pass None for any rotor circuit the machine does not have.

from ramses_xt_to_park import ramses_xt_to_park

p = ramses_xt_to_park(
    fnom=50.0, ibratio=1.0,
    ll=0.15,  ra=0.003,
    xd=1.81,  xpd=0.30, xsd=0.23, tpd0=8.0, tsd0=0.03,
    xq=1.76,  xpq=0.65, xsq=0.25, tpq0=1.0, tsq0=0.07)
# → llf=0.169902, lld1=0.166338, rf=0.000741, rd1=0.033390, ...

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Worked examples

Inputs (both cases, 50 Hz, IBRATIO = 1): $L_\ell = 0.15$, $R_a = 0.003$, $X_d = 1.81$, $X'_d = 0.30$, $X''_d = 0.23$, $T'_{d0} = 8.0$ s, $T''_{d0} = 0.03$ s, $X_q = 1.76$, $X'_q = 0.65$, $T'_{q0} = 1.0$ s. The round-rotor case adds $X''_q = 0.25$, $T''_{q0} = 0.07$ s.

Parameter	Round rotor (d2/q2)	Single q-damper (d2/q1)
$M_d^u$	1.660000	1.660000
$L_{\ell f}$	0.169902	0.169902
$L_{\ell d1}$	0.166338	0.166338
$M_q^u$	1.610000	1.610000
$L_{\ell q1}$	0.928153	0.725225
$L_{\ell q2}$	0.120461	n/a
$R_f$	0.000741	0.000741
$R_{d1}$	0.033390	0.033390
$R_{q1}$	0.009236	0.007433
$R_{q2}$	0.028210	n/a
$p_{uf}$	0.000741	0.000741

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Comparing with an EMT simulator

When cross-checking STEPSS (RMS/phasor) against an EMT tool such as Typhoon HIL:

1. Per unit vs physical units. STEPSS stays entirely in per unit. Converting to Henry/Ohm for the EMT tool requires a consistent per-unit base on the rotor side; use the same IBRATIO assumption on both sides.
2. Radians vs seconds. The $t_b$ normalisation is internal to STEPSS. Your hand calculation must divide every time constant by $t_b = 1/(2\pi f_{nom})$ before computing resistances.
3. Expected post-fault difference. STEPSS uses the phasor approximation and neglects stator transformer voltages ($d\psi_d/dt$, $d\psi_q/dt$), so it omits the DC-offset and high-frequency current components immediately after a short circuit. An EMT model retains them. Compare the slow post-fault envelopes first: envelope agreement with first-cycle differences indicates a modelling assumption, not a parameter error.

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See also

• Synchronous Machine Model — equations, per unit system, and SYNC_MACH record reference
• Octave reference implementation
• Phasor approximation
• Synchronous machine dynamics