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Frequency response performance in power systems is becoming vulnerable due to the transition toward the higher penetration of renewable energy such as achieving carbon neutrality. In particular, reducing power system inertia energy as the asynchronous generation increases could result in violating the frequency stability constraint when a disturbance occurs in the power systems. In order to control the rapidly fluctuating frequency of the power system with low inertia, it is necessary to introduce fast frequency response resources such as a Battery Energy Storage System (BESS). This paper proposes a method to calculate the required capacity of BESS for compensating the frequency control performance of the power system using inertia energy. For calculating the required capacity of BESS, the inertia energy in the critical power system, where frequency control performance marginally satisfies frequency stability constraint, should be calculated. Also, the inertia energy in the evaluated power system having deficit inertia energy should be calculated. By comparing power systems that respond with different dynamics when the same disturbance occurs, the proposed calculation corresponds to the ratio of inertia energy deficiency based on critical power system inertia energy within the power imbalance. Through various case studies employing Korean power systems, the effectiveness of the inertia energy-based calculation method for the required BESS is verified by the fact that the BESS integrated power system marginally satisfies the frequency stability constraint. In these study cases, it is found that the instant response of BESS is very effective for compensating the frequency control performance of the low inertia power system. By applying the proposed method, it is also found that about 840 MW of BESS can achieve carbon neutrality in the Korean power system. [ABSTRACT FROM AUTHOR]