Due to the non-linear load characteristics in the domestic three-phase grid system, the quality of power transmission is a challenge for researchers. In this paper, the harmonics injected in a three-phase grid system due to the non-linear loads and a solution for harmonics minimisation using the hysteresis current controller (HCC) is presented. The proposed work consists of switched dc loads such as personal computers, SMPS, etc., connected to the three-phase grid system through the rectifier unit. These loads connected with other AC loads inject harmonics in the power lines. The total harmonic distortion (THD) at the power line is therefore increased. A ZETA embedded three-phase inverter using an artificial neural network-based HCC (ANN-HCC) is used to minimise the voltage and the current THDs. To ease the power consumption, a solar photovoltaic system (SPV) is used to power the ZETA embedded three-phase inverter. The output of the SPV is regulated using the ZETA dc/dc converter. However, the hysteresis bands (Uupper and Ulower) are selected using the ANN with respect to the actual value compared with the calculated current error. The vector shifts to the next based on the previous vector applied, and thereby the process repeats following the same pattern. The back propagation (BP)-based neural network is trained using the currents’ non-linear and differential functions to generate the current error. The neural structure ends when the value hits the hysteresis band. Simultaneously, the PWM control waveform is tracked by the neural network output. The proposed system is mathematically modelled using MATLAB/Simulink. An experimental setup of a similar prototype model is designed. The voltage and the current harmonics are measured using a Yokogawa CW240 power quality meter and the results are discussed.