A power conversion device is provided, and includes a major circuit part and a control device; the major circuit part includes a power conversion part converting, into AC power, power that is input, and a filter circuit causing the AC power output from the power conversion part to approach a sine wave; the control device controls power conversion by the major circuit part by controlling an operation of the power conversion part; the control device includes an overcurrent suppression controller; the overcurrent suppression controller calculates instantaneous value voltage output command values of the phases of the AC power output from the power conversion part to suppress an overcurrent at the output end of the major circuit part. Accordingly, a power conversion device and a control device of the power conversion device are provided in which the generation of an overcurrent can be suppressed even when a voltage-controlled operation is performed.