# Optimal Non-Integer Sliding Mode Control for Frequency Regulation in Stand-Alone Modern Power Grids
## 1 Introduction  
Over the past decade, the reduction of conventional fossil fuel reserves, along with the environmental concerns about their burning, have led to the paradigm change toward the development of renewable energy sources (RESs), such as photovoltaic (PV) and wind turbine generator (WTG) systems penetrating into the power grid [1; 2; 3]. The planning and exploitation of RESs through distributed generators (DGs) offers the benefits of local generation according to the needs of consumers, with a consequent minimization in the transmission loss. The DGs can be potentially implemented for improving power quality and service reliability [4; 5; 6; 7; 8]. A microgrid is regarded as a regulated entity in the power plant and consists of various DGs such as microsources, energy reserve devices, and loads which are locally integrated into the grid for the profit of the customers. Normally, microgrids (MGs) can work in the stand-alone mode as independent islands or grid-connected modes in conjunction with the main electrical grid [9; 10; 11]. In the grid-connected mode, the main utility generators are responsible for power balance management in connection with new demands. In the isolated operation, the DGs are exposed to the load variationsand randomness characteristics of renewable sources, which threaten the grid's stability. The inherent weakness of the integrated power plants may be somewhat shorted out by the installation of backup systems such as microturbines and energy storage systems (ESSs) [12; 13]. Since load frequency control (LFC) capacity is not sufficient to meet all of the control objectives of the microgrid, employing a supplementary regulator in a secondary loop is obligatory. To deal with the secondary LFC control of an islanded MG, the conventional proportional integral derivative (PID) controllers and their variants are capable of restoring frequency deviations in normal operation; however, they cannot work appropriately as operation points of the grid vary remarkably during a daily cycle. To improve the efficiency of the LFC, some suitable control strategies including Hoe control theory [7], adaptive control [14], robust control [15], and model predictive control (MPC) [16] have been applied to the DGs of the hybrid MG. In this regard, an MPC-based coordinated control of the blade pitch angles of the wind turbine (WT), and the plug-in hybrid electric vehicle (PHEV), has been developed in [16] for the LFC issue. The authors in [17] proposed a robust controller using linear matrix inequalities to control the frequency in an integrated form of the MG and multi-MG with different DG units. A model-free intelligent proportional integral (PI) controller is suggested in [18] for several configurations of the isolated hybrid RESs/ESSs. The influence of the increased penetration of WTs and MGs on frequency control is investigated in [19], and an advanced hierarchical control methodology is established for the optimal control of the whole system. The sliding mode control (SMC) is recognized as a prominent model-based approach to handle disturbances, since this design scheme has inherent insensitivity features against the dynamical system uncertainty. The advantages of the SMC are ease of use, quick convergent velocity, and robustness. Up to now, several published works have been done to boost the strength of the SMC by combining it with Hoe control theory [20], fuzzy logic [21] and neural network [22], etc. However, implementing such sophisticated hybrid methodologies is a challenging duty for controller designers. Most recently, similar to the uses of the fractional calculus (FC) concepts in other conventional methodologies [23; 24], the fractional order is incorporated for extension of the simple classic version of the SMC, so that the degree of flexibility is enhanced. A few types of studies have been published for the application of the fractional order SMC (FOSMC) in engineering applications [25; 26].