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## Core settings |

This dialog box enables the user to modify the way the core is modeled in ATP. The dialog is primarily for testing purposes and for the program developers.

Frolich equation:

The fluxlinkage as a function of current is assumed to follow the Frolich equation. The original and default equation is with two parameters a and b. Some improvements were found by added the parameter c (buth this requires more than two open circuit Urms/Irms points from the test report).

The Frolich equation is the fundament for the optimization of the core model.

Final slope:

In addition to the 3 Frolich equation parameter comes the final slope of the core inductance, La. This is the inductance when the core fully saturates and behaves as a medium with permeability mu_zero. This is a cruisal parameter for inrush current calculations.

The value here really requires design data and is equal to:

La=mu_zero*N^2*A_leg/l_leg [H] where mu_zero=4*Pi*1e-7, N is the number of turns of the inner winding, a_leg is the absolute area of the leg and l_leg is the absolute length of the leg. The final slope is automatically scaled for the yoke and legs based on relative dimensions.

The estimate option will approximate N^2*A_leg/l_leg by 6/a where 'a' is found in the optimization and 6 is the typical 'a' value for type M4 material.

#points in saturation:

The user can choose how many points the final l-i characteristic will consist of. Based on the Frolich equation the required piecewise characteristic is sampled at fixed currents points. Behavior in extreme saturation is emphasized so a large number of points is required to obtain a good result around rated voltage. The priority is n={0, 5, -1, 1, -2, 2, -3, 3, 4} with the current defined as Im=Im-rated * 2^n. If 5 points are requested, the sequence of current becomes Im-rated*(1/4, 1/2, 1, 2, 32).

Type of nonlinearity:

ATP supports three types of nonlinear inductances; type 98, 93 and 96.

Investigations have revealed the type 98 as the most stable one.

Type 93 and 96 both give numerical problems at least for 5-legged cores (and delta coupled windings). Type 96 give residual flux at de-energization, but is generally not recommended for transient studies. In type 96 half the core losses is included as hysteresis losses by assuming a constant width of the hysteresis loop. A Steinmetz coefficient of 2 is used to scale the hysteresis losses. A main problem with the implementation is that it becomes difficult to obtain the steady state operation point (the internal setting CURR=8888 is assumed) and this results in offset problems. Ramping up the source voltage with a control system helps (a small steady-state source must be kept in parallel).

Zero sequence inductance:

A 3-legged core (also assumed as default for typical cores) will have noe return path for the zero sequence flux. This flux is thus forced into oil/tank resulting in a low zero sequence inductance. This inductance shows up as an effective outer leg inductance, L0. More research is required on the quantity of this value when test report data are unavailable. The user can anyhow choose the zero sequence inductance here. If a value zero is specified or the Omit if no test report the zero sequence inductance will be set to 1 micro Henry.

Core resistance:

At the moment the core loss resistance is fixed at the rated value (100 % excitation) even if core loss at several voltage points is given in the test report.

The fitting of losses is complicated (more research required) for 5-legged transformers as there will be harmonics in the fluxes in yokes and outer legs.

Damping resistance:

Some small resistors should be inserted in the core model to damp possible oscillations. These are added between Leg-A and Leg-B and between Leg-B and Leg-C. This also separates the core-winding terminals at the A-matrix. If Base on final slope is checked the resistance is set to dl/di/(w*100), where dl/di is the final slope (large current) of the magnetization of the leg. The theory is that the resistance should be much less than the possibly lowest reactance in the leg. A value of 1E-6 has been used successfully in the MTU reports.