A method is presented to enhance solar penetration of a hybrid solar-combined cycle power plant integrated with a packed-bed thermal energy storage system. The hybrid plant is modeled using Simulink and employs systems-level automation. Feedback control regulates net power, collector temperature, and turbine firing temperature. A base-case plant is presented, and plant design is systematically modified to improve solar energy utilization. A novel recycling configuration enables robust control of collector temperature and net power during times of high solar activity. Recycling allows for improved solar energy utilization and a yearly solar fraction over 30%, while maintaining power control. During significant solar activity, excessive collector temperature and power setpoint mismatch are still observed with the proposed recycling configuration. A storage bypass is integrated with recycling, to lower storage charging rate. This operation results in diverting only a fraction of air flow to storage, which lowers the storage charging rate and improves solar energy utilization. Recycling with a storage bypass can handle larger solar inputs and a solar fraction over 70% occurs when following a drastic peaking power load. The novel plant configuration is estimated to reduce levelized cost of the plant by over 4% compared to the base-case plant.