This is a three part series paper, where the novel idea of representing flyback transformer losses as loss functions has been presented with scientific proof.Thirteen calculations for each transformer have been tabulated and used to derive mathematical loss function using hyperbolic secant spline interpolation which is subjected to Lyapunov method to predict core saturation and instability in the control loop. For scientific validity, 72 working transformers at thirty-six wattage’s which are being internationally used, have been examined to check, whether such proposition is valid or not.The definiteness of matrix,singular value decomposition,Lyapunov exponents are also tabulated. Then each of these transformers are simulated with non-linearies of Li-ion battery namely state of charge (SoC), self-discharge resistance, temperature-dependent leakage resistance,five time-constant dynamics, deterioration of battery performance over repeated charge and discharge cycles. The coefficients in the Jiles-Atherton model have been altered with fractional perturbations to obtain hysteresis curves.Various interesting comparisons in Bm,Bp,AC flux densities, effect on varying the coefficients in JA, residual errors, Lyapunov exponents, switching frequency vs MOSFET and transformer losses, reflected voltages, are tabulated and plotted.