Saturation Model Synchronous Machine pu Fundamental

Hi, everyone,

Based on the (if, vt) data from the no-load test, how can I calculate the ifd_sat (y-axis) of the look-up table inside the sturation model?

The look-up table x-axis values are equal to the vt values (since the flux is equal to the voltage in pu). But I cannot find en expression for ifd_sat.

Please help me to understand this model and if you have the reference which MATLAB is based on please share it.

Answer 1

[Sameer]

Hi @Jose

The "ifd_sat" values in the Saturation Model are derived from the relationship between the air-gap flux (Φ, in pu) and the field current (Ifd) obtained from your no-load test.

In per-unit form, for the synchronous machine:

1. From your no-load test data (If, Vt), first convert Vt to per-unit and note that in steady-state flux ≈ voltage (pu).

• This gives you Φsat = Vt(pu).

2. The look-up table uses "Φsat" on the x-axis. The y-axis (ifd_sat) is the equivalent unsaturated field current needed to produce that Φ.

• MATLAB computes this internally as:

where:

Lmd = unsaturated mutual inductance (pu)

Lmsatd = saturated mutual inductance (pu)

These inductance curves are also stored in the SM structure.

3. In practice:

• Fit a curve "Ifd(Φsat)" from your measured points (linear interpolation is fine).
• This curve directly becomes your ifd_sat vector.

4. MATLAB’s model follows the approach in standard synchronous machine modeling references, e.g., P. Kundur, Power System Stability and Control and the IEEE Synchronous Machine Model documentation, where ifd_sat is just the field current vs. air-gap flux characteristic obtained from the open-circuit test.

Hope this helps!