# ComputeIncrementalMatrixInductanceForNonMeshedCoilsMagnetoStatic.PFM

## Introduction

This document deals how to use the ComputeIncrementalMatrixInductanceForNonMeshedCoilsMagnetoStatic.PFM macro. The goal is to be able to compute matrix of incremental inductance with non-meshed coils in 3D magneto-static projects. This macro intends to create automatically an output excel file which includes the incremental inductance matrix data.

## Goal of this macro

This macro intends to create automatically an output excel file which includes the incremental inductance matrix data. For every case (with and without magnets in the project), the incremental inductance is evaluated.

The computation principle is given below:

The first computation will be done for the reference values of the coil currents i.e the values set for the non-meshed coils in the given project will be considered as the reference values. And the incremental inductance matrix will be calculated on this operating point $\left({I}_{1},{I}_{2}\right)$ .

Then the coil currents will be incremented with a $\u2206I$ and the flux through each coil will be computed on each step. This procedure could be explained as below:

- First computation
- Reference coil current values : ${I}_{10},{I}_{20}\to {\u0424}_{10},{\u0424}_{20}$

- Second computation
- Increment ${I}_{1}$ with respect to the current variation, ${I}_{2}$ set to the reference value. ${I}_{10}*\left(1+\%\u2206I\right),{I}_{20}\to {\u0424}_{11},{\u0424}_{21}$

- Third computation
- Increment ${I}_{2}$ with respect to the current variation, ${I}_{1}$ set to the reference value. ${I}_{10},{I}_{20}*\left(1+\%\u2206I\right)\to {\u0424}_{12},{\u0424}_{22}$

The incremental inductance matrix can be expressed as:

${\left[\begin{array}{cc}\u2206{L}_{1}=\frac{{\u0424}_{11}-{\u0424}_{10}}{\u2206{I}_{1}}& \u2206{M}_{12}=\frac{{\u0424}_{12}-{\u0424}_{10}}{\u2206{I}_{2}}\\ \u2206{M}_{21}=\frac{{\u0424}_{21}-{\u0424}_{20}}{\u2206{I}_{1}}& \u2206{L}_{2}=\frac{{\u0424}_{22}-{\u0424}_{20}}{\u2206{I}_{2}}\end{array}\right]}_{{I}_{1},{I}_{2}}$

## Parameters

- Set the variation of coil currents in % with respect to the reference values. This value is set to 1% by default.
- Select if you want to save the intermediate files or not which will represent the .FLU files for each increment.
- Select the name for the excel output file which will contain the resulting inductance matrix.

**What the macro will do ?**

- The first computation with the reference values;
- Saves the initial file
- Creates the sensors for each coil to compute the flux
- Solves the first scenario with the reference values of coil currents

- For each increment;
- Sets the coil current values
- Creates the corresponding scenario an solves
- Computes and stores the flux through the coils

- Once the process is done, it calculates the incremental inductance matrix from the data stored during the above steps
- Displays the results on the console
- Export the result to an excel file