# Current Sensorless MPPT Control for PV Systems Based on Robust Observer
## 1 Introduction
Nevertheless, this approach efficiency is obviously dependent on the accuracy of the local website data about the PV system location. Further, because of its inaccurate forecasting of temperatures, it may lead to operate at a point far from the maximum power point. The unscented Kalman filter and Extended Kalman filter are implemented to estimate the inductor current in a boost converter based PV system obtaining an accurate estimation [14; 15]. However, both techniques are computationally intensive due to the use of non-linear transformations and linearization procedures [16; 17]. A current sensorless method based on finite control set model predictive control (MPC) with auto-tuning is developed in [18]. MPC is a powerful technique, but its applicability is limited because of its complexity of implementation, mainly in small scale PV systems. The sliding modes technique has been used to design robust observers to estimate voltages and currents in PV systems with good results against different perturbations and operating conditions [19; 20]. However, the main drawback of this technique is the chattering problem which reduces the life of components. The high gain observers are another alternative used for robust current estimation in PV systems. As shown in [21] a high gain observer is designed to estimate voltage and current in a pumping system supplied by a PV generator. Although a precise estimation is performed, the disadvantages of this approach are the sensitivity to measurement noise and the peaking phenomenon [22]. In [23], a Luenberger observer is proposed to estimate the current and this estimation is used in a PO scheme for MPPT, the proposal is effective and easy to implement but lacks robustness since there is no consideration about system uncertainties or external perturbations at the output. Due to its effectiveness and ease of implementation, a Luenberger observer is a good alternative for current estimation but requires a robust design to improve its efficiency under disturbance scenarios. The Attractive Ellipsoid Method (AEM) is a tool used for synthesis of robust feedback controllers with respect to a wide class of uncertainties contained in the system's model. This methodology guarantees system stability by finding appropriate controller gains obtained through the definition and solution of an optimization problem in terms of Linear Matrix Inequalities (LMI) or Bilinear Matrix Inequalities (BMI) [24]. System motion stabilization to zero is not always possible when external disturbances, uncertainties or nonlinearities are present in a system, in such cases only boundedness of trajectories within some compact set is guaranteed. This boundedness is commonly obtained through invariant sets. Ellipsoidal sets possess such invariant condition and can be obtainedusing the invariant ellipsoid method, called attractive ellipsoid method if this condition is ensured for any initial conditions [24]. These ellipsoidal sets can be designed to obtain certain minimal properties related to ellipsoid size, volume, among others, which may be used for design of robust observers/controllers for several applications [25; 26]. The optimization problems based on LMI/BMI derived from application of AEM can be solved using semi-definite programming or specialized BMI solvers. Therefore, this paper proposes the design of a robust Luenberger state observer based on AEM which allows a current sensorless operation that improves the reliability at the same time that reduces the overall system cost. Such proposed robust observer guarantees a low estimation error that ensures the proper application of MPPT algorithms which requires PV current measurement. Furthermore, this observer is robust against output disturbances and parameter uncertainties on the PV system components which contributes to obtain a more accurate estimation under such conditions. In order to demonstrate the effectiveness of the proposed robust observer a simulation of an INC-MPPT sensorless scheme is performed in Simulink under the european standard EN-5060.