Calculation of induction heating setup power consumption

[hxianc]

TL;DR Summary

This thread is for asking for help from professionals about opinions regarding the calculation of total power consumption of an induction heating setup (solenoid structure)

Hi everyone!
I am trying to calculate the total power consumption of an induction heating setup, where ferromagnetic material is placed inside a conductive coil-formed solenoid, and alternating current is passed through the solenoid by a certain power supplier.
My questions are:
1. Under such circumstances, will the total power consumption P_total = P_by_Hysteresis+P_by_EddyCurrent+P_Anomalous_loss?
2. How to quantify the Anomalous_loss term?
Any suggestion would be appreciated!

 

[berkeman]

Welcome to PF.

Can you post links to the reading you've been doing about inductive heating so far? Thanks.

 

[hxianc]

Welcome to PF.

Can you post links to the reading you've been doing about inductive heating so far? Thanks.

Thanks for replying. Please check the following DOI: https://doi.org/10.1016/j.cattod.2019.05.005. There is a Pin defined on page 3.

 

[berkeman]

Please check the following DOI: https://doi.org/10.1016/j.cattod.2019.05.005. There is a Pin defined on page 3.

I didn't try to download the full PDF (paywall?), but the summary of the input power looks reasonable to me:

 

[hxianc]

I didn't try to download the full PDF (paywall?), but the summary of the input power looks reasonable to me:

View attachment 355801

Thank you for your quick response and confirmation. Sorry for the reference confusion, I was referring to the equation in "Modelling" section.
I have two follow-up questions that:
1. please see the attached material from another reference2(https://doi.org/10.1016/j.cej.2023.147205) In their paper they define P_in = P_reaction+P_elec+P_surrounding which is similar to reference1. However, reference2 calculates P_in by P_in=IV of the power supplier (Ohm's law), which is used in reference1 for the calculation of P_coil (eddy current conduction loss). I am confused are they both right that V,I (R) in the two references are different(reference1 refers to VI(R) of solenoid in induction setup and reference2 refers to VI(R) of power supplier) or one of the definitions is wrong?
2. Is there a general way of defining the P_rest?

 

[Ivan Nikiforov]

Electrical power is equal to the product of current and voltage: P =UxI. You know the supply voltage. The question boils down to determining the current strength in the circuit. The current in the circuit is equal to the ratio of voltage to resistance: I=U/Z, where Z is the total resistance, which is defined as the sum of active resistance and inductive resistance: Z=R+XL. The active resistance R of the circuit can be measured or calculated by the length, cross-section and material of the wire. Inductive resistance XL = 2nfL, where N = 3.14, f is the mains frequency, and L is the circuit inductance. It is important to keep in mind that the inductance of your circuit will vary, as a unique body is introduced into the coil each time