With the increasingly high penetration of renewable energy into the power system, the inertia level of the power system is gradually decreasing, and the frequency stability issue has become more prominent than ever before. This paper proposes a supplementary control strategy to improve the frequency stability of the renewable energy integrated power system, which estimates the unbalanced power of the system by detecting the rate of change of frequency in the center of system inertia (COI) as well as the equivalent inertia level of the system, and adjusts the referenced power of the converter to provide inertia support for ac grids. The proposed unbalanced power estimating method includes two parts:rate of change of COI frequency detection and system equivalent inertia calculation. Since the COI frequency curve passes through the zero points of the second derivative of the local measurement frequency curve, the COI frequency curve can be approximated by the piecewise linear curve connected by the second derivative zero points. The system equivalent inertia considering the effective inertia of the non-synchronized components in the system can be obtained by counting the synchronous inertia of the system, change of active power of generators, and the total unbalanced power. Subsequently, an additional control method is proposed to compensate for unbalanced power based on the proportion of the capacities of renewable energies. The referenced power value of the renewable energy station will be quickly adjusted to suppress system frequency fluctuations when a frequency event occurs. PSCAD/EMTDC simulation verifies the effectiveness of the proposed additional control strategy.