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In this study, a space-vector pulse-width modulation (SVPWM) method is presented for a Z-source six-phase inverter using the neural network (NN) classification. The Z-source inverter is a new generation of inverters with buck and boost features. Using an L-C network placed between the power supply and the switches, this modulation method can result in unique features which are not achieved through traditional inverters. NN classification can help in reducing the complexity of calculations for the SVPWM method in a six-phase inverter. NN classification reduces the required computational efforts and makes it possible to increase switching frequency. In addition, the method results in a smaller system in terms of hardware and software, and generates more precise pulses. The modulation method presented in this study uses the minimum number of switching vectors. Here, 14 switching vectors are employed instead of 64. In fact, only large vectors in a plane are selected. Moreover, an additional vector, called 'shoot through', is considered for creating buck and boost features in the six-phase Z-source inverters. Therefore using 15 switching vectors, it is possible to achieve minimum switching in the six-phase Z-source inverters with buck and boost capabilities. Practical and simulation results for this type of inverter connected to a six-phase induction motor are also presented.