Optimal design of a cascade controller for frequency stability of photovoltaic-reheat thermal power systems considering nonlinearities

Automatic generation control (AGC) is essential for raising living standards because it enhances power supply quality. However, due to the constraints and challenges experienced in practice, an effective and computationally economical control method is necessary to improve AGC performance, particularly in the presence of renewable energy. Therefore, this study introduces a novel cascade controller (CC) of a proportional-integral-derivative (PIDn) controller followed by a proportional-integral (PI) controller, forming a PIDn-PI CC. This controller is used in a two-area model comprising a reheat thermal generator and a photovoltaic unit. The gains of the PI, PIDn, and PIDn-PI controllers are adjusted using the recently introduced chaos game optimization (CGO), which minimizes the objective function integral time multiplied absolute error. The CGO relies on chaos theory principals, wherein the organization of fractal geometry is perceived through the chaotic game and the fractals' self-similarity properties are considered. At first, the CGO based PIDn controller is employed, to check the suitability of CGO in dealing with AGC problems. Furthermore, several scenarios are used to confirm the effectiveness of the CGO:PIDn-PI scheme when subjected to a high load disturbance and uncertainty, which can change system parameters by +/- 50%. A random load pattern is used to ascertain the proposed method's efficacy. Finally, nonlinearities, such as generation rate constraint and time delay, which have a significant impact on AGC performance, are considered. Compared with relevant current research, the suggested approach outperforms them in terms of settling time, frequency, and tie-line power deviations.