Hybrid power plants (HPPs) support decarbonization and enhance grid stability by integrating renewable generation with complementary energy storage technologies. This study introduces a hybrid power plant controller (HPPC) for storage-oriented active power dispatch between a high-power storage technology (HIPST) and a high-energy storage technology (HIEST). The HIEST setpoint is determined based on the HIPST state of charge, preserving HIPST energy reserves and reducing cycling stress on HIEST. The controller operates in two modes: constant setpoint tracking and an adaptive smoothing mode using exponential moving average (EMA), which improves responsiveness under variable wind conditions. Time-domain simulations using realistic wind generation profiles from DTU CorRES, calibrated to the Lem Kær wind farm configuration, ensure practical relevance. Results highlight the critical role of tuning droop parameters and EMA settings to balance smoothing quality with efficient storage utilization. The proposed HPPC provides a practical solution for hybrid power plants, optimizing the operational roles of HIPST and HIEST while maintaining stable power delivery under dynamic conditions.