With the increase of renewable energy sources (RES) in power systems, the number of traditional synchronous generators (SGs) declines gradually, which leads to a decrease in total inertia and frequency instability in extreme situations. The synchronous motor-generator pair (MGP) system was proposed as a new grid-connection method to improve the inertial response and frequency stability of grids. To study the effects of the MGP on the frequency stability and penetration rate of RES in power grids, first the frequency response equations of a single MGP in a single-machine infinite bus system are derived; then, the system frequency response (SFR) model for a multi-machine system with the MGP integrated is built. By comparing key critical indices of the frequency response after step disturbance with this model, we discover that the MGP system can increase the upper limit penetration rate of RES by quite a percentage. Furthermore, time domain simulations are used to compare the frequency characteristics of RES penetration rates of 25%, 50% and 75% with and without MGP. Finally, the MGP test bench is built for relevant experimental verification.