In this paper comprehensive space vector model of a thirteen-phase voltage source inverter (VSI) is reported. The paper also discusses the space vector Pulse Width Modulation (SVPWM) of a thirteen-phase voltage source inverter (VSI) with the aim of producing sinusoidal output waveform. Generalized space vector theory is used to achieve the SVPWM. As per the general inverter switching theory there are 213 = 8192 switching states possible that yield 8190 active space voltage vectors and two zero voltage vectors at the origin. Out of the total 8190 active voltage vectors, 156 voltage vectors are utilized for the implementation of SVPWM considering the constraint of sinusoidal output voltage. The sinusoidal voltage is obtained by controlling the duty cycle the voltage space vectors of d-q plane when voltage space vectors of other five x-y planes are set to zero. The theoretical results are verified by simulation and experimental results with R-L load.