Systems, methods, and computer program products for providing an inertial response by a wind power system to power fluctuations in an electrical grid. The system includes a synthetic inertial response generator configured to generate a power offset in response to fluctuations in grid voltage. The power offset signal is generated by determining a quadrature component the grid voltage using an internal reference voltage having an angular frequency and phase angle that is synchronized to the electrical grid by a control loop. The quadrature component is used to determine a synchronous power level. A control loop error signal is produced by the difference between the synchronous power level and the wind turbine system power output. Changes in the grid frequency produce an error signal that is added to the power set point of wind turbine system output controllers to provide a power system inertial power output response.