Analytical Energy-Based Approach for Frequency Nadir Estimation Under Increasing RESs

The increasing penetration of renewable energy sources (RESs) reduces system inertia and the availability of primary frequency response (PFR), leading to deeper frequency nadir (FN). Therefore, accurate estimation of the FN has become a key challenge in power system analysis. While traditional approaches have analyzed FN reduction with increasing RES penetration, they often rely on simplified or linearized models, which limit their accuracy under transient conditions. This study introduces an energy-based formulation in which the power imbalance between a disturbance and the frequency response is systematically analyzed in terms of energy. This formulation directly relates FN formation to the energy mismatch between the load demand and the energy supplied by generating units. Accordingly, the FN is estimated under varying RES penetration by incorporating inertia, PFR, and the energy mix. In addition, the formulation is applied to determine the extra frequency support required to maintain the FN above a secure level.