Analytical optimisation of solid-round-wire windings conducting dc and ac non-sinusoidal periodic currents

In this study, an analytical optimisation of solid-round-wire windings conducting both the dc and ac non-sinusoidal periodic currents is performed. A closed-form analytical equation is derived for the normalised solid-round-wire diameter to achieve the minimum power loss for inductors conducting ac non-sinusoidal periodic currents superimposed on the dc component. The low- and medium-frequency normalised winding ac resistance for the nth harmonic frequency is derived and used to obtain the normalised total-power-valley diameter at the local minimum of the winding dc and ac power losses. Additionally, an equation for the local minimum of the winding dc and ac power losses is derived. A high-frequency approximation of Dowell's equation at the nth harmonic frequency is used to derive the normalised total-power-critical wire diameter at which the total winding power loss (dc and ac) is equal to the total winding power loss at the local minimum. A design procedure of the inductor with an optimised winding diameter operating in pulsewidth-modulated dc-dc buck converter in discontinuous conduction mode is presented. Experimental verification of the presented theory and comparison of the total winding power loss of the inductors with different solid-round-wire gauge are performed.