A linear compressor and methods of operation, for example, to detect polarity for the linear compressor are provided herein. The method may include supplying an initial time varying voltage to the motor of the linear compressor at an assumed polarity; estimating a first acceleration of the motor of the linear compressor when the motor is at a bottom dead center position; estimating a second acceleration of the motor of the linear compressor when the motor is at a top dead center position; comparing the first acceleration to the second acceleration; and determining whether the assumed polarity is correct based on the comparison.