# Load Frequency Optimal Active Disturbance Rejection Control of Hybrid Power System
## 1 Introduction
The integration of power systems across multiple regions and variations in tie-line power also requires a greater level of accuracy in control. As renewable energy sources like hydroelectric generators, Photovoltaic Generators (PVGs), and Wind Turbine Generators (WTGs) are gradually being integrated, traditional LFC methods encounter difficulties in maintaining efficient control. This is primarily attributed to the inherent occasionally and uncertainty associated with WTG and PVG [16]. Therefore, it is imperative to implement an appropriate LFC strategy to ensure the stability of the power system. Since the variable nature and stochastic nature of wind and sunlight, the output powers of a WTG or PVG change indeterminately. Thus, the LFC mechanism of an electric power system with penetration of renewables should be reacted with electrical loads and outputs of generators [17]. In the context of a hybrid energy power system, the incorporation of the WTG and PVG introduces increased variability and unpredictability to the power system, thereby posing challenges to the LFC method. Previous research endeavors have also made attempts to address this matter [18; 19; 20; 21; 22; 23; 24; 25]. A hybrid control strategy, consisting of a Linear Quadratic Regulator (LQR) and a generalized predictive controller, is introduced in reference [18]. The load variations were employed as quantifiable disturbances to attain frequency stability in hydroelectric power systems. The analysis failed to account for fluctuations in the load within the generating units themselves. A decentralized control strategy was proposed for the LFC task in the presence of renewable energy sources [19]. Their strategy of using the LQR with an ESO is utilized. However, the system failed to consider the feedback of errors, resulting in a notable increase in the frequency overshoot. For a microgrid, the case of delayed electric vehicle aggregators and renewable energy sources, including photovoltaic, wind, and fuel cells, was examined [20]. A novel approach for implementing a linear ADRC method, which is based on the ESO and a nonlinear feedback control law (NLFCL). This method demonstrated its effectiveness in reducing the impact of load disturbances and uncertainties arising from renewable energy sources. For a more complex multi-area interconnected hybrid power system, WTG [21] or PVG [22; 23] will be introduced separately. In this study, an LFC strategy of a hybrid power system with hydroelectric generators, WTGs, and PVGs with thermal generators is studied. It is more challenging work than the above-mentioned systems. The LQR shows good stability for uncertain systems [24], and ADRC shows strong disturbance rejection features [25]. In this research, a novel LFC mechanism for hybrid power systems is presented based on the optimal ADRC, which is a combination of an improved LQR with the ADRC. Since the complexity of a multi-area interconnected hybrid power system, the state space model of the LFC target of the hybrid power system is established at first. Then, an LQR controller with the output weightings is designed as an optimal controller. Finally, the ADRC technique estimates the disturbances of plants and adjusts the power flows on the tie-line. This compensation is achieved without adding complexity to the designed model. Compared with the LQR with ESO, the relative errors of the maximum peaks of frequency deviation of the three regions of the established hybrid power system are reduced by 96%, 95%, and 96%, respectively, by using the proposed strategy. The relative errors of the maximum peaks of tie-line exchange power of the three regions of the established hybrid power system are reduced by 83%, 54%, and 76%, respectively, by using the proposed strategy. The framework of this research is arranged as follows: The structure of the LFC strategy and the linearized models of LFC components in a multi-area interconnected hybrid power system are introduced in Section 2. The controller design of the proposed optimal ADRC is described in Section 3.