The input current of a VFD has harmonic distortion. In effect it is the sum of a 50/60 Hz fundamental current and harmonic currents at various multiples of line frequency. The displacement power factor is calculated as the input watts divided by the input VA where only the line frequency (fundamental) part of the current is used in calculating the VA. The displacement power factor of a VFD is about .98, so installing a VFD would improve the displacement power factor. The new power factor of an existing motor would be improved by adding a VFD and the overall power factor of the plant would be improved by adding a VFD or a VFD and motor.
The total power factor is calculated as the input watts divided by the input VA where the total RMS current including harmonic currents is used to calculate VA. The level of harmonics is determined by the source impedance at the drive input terminals. If the source impedance is low (available fault current is high), the harmonic current will be high and the power factor will be low. If the source impedance is high (available fault current low), the harmonic current will be low and the power factor will be high. The total power factor of a VFD might be lower than the power factor of a motor without a VFD.
Even if the total power factor of the VFD is lower than the power factor of a motor without a VFD, adding a VFD may not reduce the total power factor of the plant. The total power factor of the plant must be calculated as the plant watts divided by the total plant VA including harmonics currents. When harmonic current is included, the total current is the square root of the sum of the square of the fundamental current plus the square of the harmonic current.