In ARTEMiS, a different approach is used that modifies the current injection curves by including the linear part of the magnetization curve inside the state space equations describing the system.

**The modifications are as follows:**

- The first segment of the phi=f(i) characteristic is included in the linear part of the state-space system described by ABCD matrices.
- This linear part is extracted from the original phi=f(i) characteristic.
- The flux across the branch is computed from its linear part phi_linear=L_linear*I_linear
- A current injection in parallel to the linear inductive branch is used to model the saturation.

The method can be viewed as follows: in normal mode (non-saturated), the magnetization branch is part of the ABCD state-space system and the branch flux phi is equal to L*i. When saturation occurs, it is like connecting another inductance in parallel to the first one. The voltage across these two inductances is the same, so is the total flux that would be obtained by the integration of the voltage across the branch.

**The differences with SPS native models are the following:**

- The ARTEMiS saturable transformer model requires a non-infinite 1 segment slope so that a state can exist in the ABCD matrices. If not, ARTEMiS will add a very large one.
- Residual flux can be specified even if the first segment does not has an infinite slope. The implication of this is that the flux will move from the start of the simulation but in a very slow manner because of the very high inductance. The model is therefore adapted to transformer re-energization tests.

**Advantages of the Approach**

The main advantage of the ARTEMiS model is that it can provide accurate fixed-step simulation results without algebraic loops. In SPS, this algebraic loop is caused by the usage of a discrete-integrator (trapezoidal method) in the transformer itself. In ARTEMiS, this flux is computed in the linear part of the state-space system.

**Limitations of the Approach**

When testing cases with inrush current caused by residual flux, the approach can cause a small flux decay due to the non-infinite linear part of the transformer core inductance.