# Inductance calculation

For induction heating professionals, visual temperature distribution and hardened profile examination are only half of the whole amount of information required. Simulations carried out with CENOS gives not only visual results, but **energy statistics** as well, which can be used to calculate important simulation parameters, such as inductor inductivity.

**You can calculate inductivity of an inductor from CENOS simulation data**, and there is more than one way of how to do this.

## How to calculate inductance of an inductor?

You can obtain the inductance value **L** in two ways - using *magnetic energy* or *complex power*. Simply take the needed values of **one time step**, insert them into one of two formulas, and calculate inductance!

The formulas used by each of these calculation approaches are as follows:

**MAGNETIC ENERGY**

**COMPLEX POWER**

$$ L = \frac{2 \sum_{i} W_i}{I_{RMS}^2}$$

$$ L = \frac{\sqrt{S^2 - P^2}}{2 \pi f I_{RMS}^2}$$

where

Symbol: | Unit name: |
---|---|

L | Inductance [H] |

W | Magnetic Energy [J] |

S | Apparent Power [VA] |

P | Active Power [W] |

f | Frequency [Hz] |

$$ I_{RMS} $$ | Induced Current.RMS [A] |

**IMPORTANT:** Using *magnetic energy* approach, the **sum of magnetic energy is over all domains** at one time step. Using *complex power* approach, the **active power is the sum of active power over all domains (workpiece + inductor)**.

## Where to find required values

CENOS post-processing with .csv file gives access to all the required values for inductance calculations, including active power, apparent power, voltage and magnetic energy - .csv file can be accessed through *Note* button under *Visualization* block.

Within it are the energy statistics for each domain which can be used to carry out the inductance calculations mentioned above.

## Theoretical basis

### Using magnetic energy

Magnetic energy is defined as:

$$ W=\frac{1}{2} \int B H dV $$

On the other hand, it is also known that

$$ W=\frac{1}{2} L I_{RMS}^2 $$

If sum of magnetic energy *in all domains* is known, one can obtain inductance

$$ L = \frac{2 \sum_{i} W_i}{I_{RMS}^2}$$

**IMPORTANT**: Here sum of magnetic energy is **over all domains**.

### Using complex power

** Apparent power** S is defined as

$$ S = \sqrt{P^2 + Q^2} = I_{RMS}^2 Z $$

where P is ** active power**, Q is reactive power, V is voltage, Z is impedance:

$$ Z = \sqrt{R^2 + X^2} $$

where R is resistance, X is reactance. Resistance is

$$ R = \frac{P}{I_{RMS}^2} $$

Neglecting capacitive reactance, X is purely inductive:

$$ X_L = 2 \pi f L $$

where L is inductance. Using all the above, formula for inductance can be obtained:

$$ L = \frac{\sqrt{S^2 - P^2}}{2 \pi f I_{RMS}^2}$$

**IMPORTANT**: Here active power is sum of active power **over all domains**.