*Article* **Fractional-Order Control of Grid-Connected Photovoltaic System Based on Synergetic and Sliding Mode Controllers**

**Marcel Nicola 1,\* and Claudiu-Ionel Nicola 1,2,\***


**\*** Correspondence: marcel\_nicola@yahoo.com or marcel\_nicola@icmet.ro (M.N.);claudiu@automation.ucv.ro(C.-I.N.)

**Abstract:** Starting with the problem of connecting the photovoltaic (PV) system to the main grid, this article presents the control of a grid-connected PV system using fractional-order (FO) sliding mode control (SMC) and FO-synergetic controllers. The article presents the mathematical model of a PV system connected to the main grid together with the chain of intermediate elements and their control systems. To obtain a control system with superior performance, the robustness and superior performance of an SMC-type controller for the control of the *udc* voltage in the DC intermediate circuit are combined with the advantages provided by the flexibility of using synergetic control for the control of currents *id* and *iq*. In addition, these control techniques are suitable for the control of nonlinear systems, and it is not necessary to linearize the controlled system around a static operating point; thus, the control system achieved is robust to parametric variations and provides the required static and dynamic performance. Further, by approaching the synthesis of these controllers using the fractional calculus for integration operators and differentiation operators, this article proposes a control system based on an FO-SMC controller combined with FO-synergetic controllers. The validation of the synthesis of the proposed control system is achieved through numerical simulations performed in Matlab/Simulink and by comparing it with a benchmark for the control of a grid-connected PV system implemented in Matlab/Simulink. Superior results of the proposed control system are obtained compared to other types of control algorithms.

**Keywords:** photovoltaic system; grid; sliding mode control; synergetic control; fractional-order control
