# Current Sensorless MPPT Control for PV Systems Based on Robust Observer
## 5 Results  
To verify the performance of the designed robust observer, simulations are developed in Matlab/Simulink environment using the toolbox Simscape/Power Systems which contains specialized functions to model power converter components and PV systems. The parameters of the selected PV module used in simulation are presented in Table 1 and the ones corresponding to boost converter are shown in Table 2.  
The simulation is based on a small scale system which is composed only by 1 PV panel, its corresponding P-V and I-V curves showing the maximum power point are illustrated in Figure 4 and Figure 5, respectively. \begin{table}
\begin{tabular}{l l l} \hline
**Parameter** & **Description** & **Value** \\ \hline \(P_{max}\) & Maximum power & 239.68 W \\ \(V_{oc}\) & Open circuit voltage & 37.1 V \\ \(I_{sc}\) & Short-circuit current & 8.58 A \\ \(V_{mpp}\) & Voltage at MPP & 29.7 V \\ \(I_{mpp}\) & Current at MPP & 8.07 A \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of PV panel 1 Soltech 1 STH-240-WH. Figure 3: Flow chart of INC algorithm. The proposed observer gain matrix \(L\) and ellipsoid size matrix \(P\) obtained by solving the optimization problem (30) with a parameter uncertainty equal to 10% of the nominal component value (for \(R\),\(L_{b}\),\(C_{b}\)) are  
\[L= \begin{bmatrix}1.8522\\ 0.1190\end{bmatrix} \times 10^{4}\ \ P_{1}= \begin{bmatrix}1.1489&0.1031\\ 0.1031&0.6071\end{bmatrix} \times 10^{5},\]  
\[P_{2}= \begin{bmatrix}4.4802&-5.0986\\ -5.0986&165\end{bmatrix} \times 10^{-4},\]  
\[\alpha=31.6248\ \,\ \ \tau_{1}=1.5180\times 10^{-4}\ \,\ \ \tau_{2}=131.7717\ \.\]  
The first simulation scenario is for two fixed values of solar irradiation at 800 W/m\({}^{2}\) and 1000 W/m\({}^{2}\) as shown in Figure 6.  
The PV current is depicted in Figure 7 where \(x_{1}\) and \(x_{1e}\) stands for the ideal measured state and estimated state, respectively. The estimated current fol  
Figure 4: P-V curve for PV module 1 Soltech 1 STH-240-WH. Figure 5: I-V curve for PV module 1 Soltech 1 STH-240-WH. Figure 6: Irradiation profile for fixed values. with high speed and an acceptable precision for both irradiation levels but decreases for higher current values. A similar situation is observed in Figure 8 for the output voltage \(x_{2}\). The error signal for both states is illustrated in Figure 9 where is observed an error value lower than 2% for both irradiation conditions which verifies an efficient estimation under the proposed parameter variation. This result indicates that the estimated current can be a good alternative for current based MPPT techniques as Incremental Conductance algorithm, allowing a current sensorless operation. The second simulation corresponds to the application of the designed observer to achieve MPPT using a conventional current based technique as the INC algorithm. The INC algorithm depends on measures of PV voltage and current, then the current sensor is substituted for the designed robust observer. An irradiation profile based on the European standard EN50530 is constructed which contains oscillations of different period between two values located approximately in the middle section of PV module operating range. This irradiation profile is depicted in Figure 10.  
Figure 8: Output voltage. Figure 7: PV current. Figure 9: The error of estimation. The estimation of PV current and output voltage for the MPPT test is shown in Figure 11 and Figure 12, respectively. A good tracking of the actual values is observed for both states, but some small oscillations are present due to the constant solar irradiation changes introduced as input for the PV system in the test profile. In Figure 13, the estimation error for the MPPT test is presented. It can be seen that the estimation error has a low value for both states which confirms an appropriate performance of the designed observer for a changing irradiation situation.