The adaptive optimal control approach for the isolated and interconnected power systems, AGC scheme using PI technique is presented in this research. Due to the policy evaluation and policy improvement phases, which analyze and update the cost and control policy, the PI approach can provide adaptive optimal control without using all system states. This is possible through policy evaluation and improvement. An adaptive optimal control strategy based on the PI methodology may be model-free. To complete this work, a comparison of the PI-based and LQR-based schemes efficiency is needed. The adaptive optimum control approach's efficiency has also been studied following several parameter change scenarios. Simulations show that the PI-based adaptive optimum control approach surpasses the LQR-based framework in effectiveness