# Low Current Ripple Parameter-Free MPCC of Grid-Connected Inverters for PV Systems
## 4 Results
### Steady-State Performance  
To highlight the advantage of steady-state performance in the proposed strategy, contrast experiments have been conducted with the condition of 4A current commanded. Figures 10 and 11 illustrate the results of grid voltage and grid-connection current in the manner of conventional MPCC. It can be seen that the grid-connection currents are sinusoidal and in the same frequency and phase as the grid voltage. Nevertheless, the current prediction error is unavoidable because of the limitation of eight vectors, reflected in the low-order current harmonics. The THD of current is 6.8% and ill-suited to meet government standards. Instead, as shown in the results of the proposed MPCC in Figures 12 and 13, the phase-A voltage of the grid is in line with the same phase of current, namely, the power factor is unity. Meanwhile, the expanded control vector sets are permissible when accompanied by the triangle candidate strategy, so that more accurate predictive currents and lower current ripples can be obtained. The THD value of the proposed MPCC is reduced to 1.59%, superior to the counterpart of conventional MPCC. \begin{table}
\begin{tabular}{c c} \hline
**Items** & **Specifications** \\ \hline DC-link voltage \(U_{dc}\) & 350 V \\ DC-link capacitance C & 4700 \(\mu\)F \\ Filter inductance \(L\) & 2 mH \\ Resistance \(R\) & 0.5 \(\Omega\) \\ Switching Frequency & 10 kHz \\ \hline \end{tabular}
\end{table} 
Table 3: Experimental prototype parameters. Figure 9: Experimental setup. Figure 11: Experimental results of THD in traditional MPCC. Figure 12: Experimental results of grid voltage and grid-connected currents in proposed MPCC. Figure 10: Experimental results of grid voltage and grid-connected currents in traditional MPCC. To analyze the current tracking performance of a proposed MPCC convincingly, the current prediction error is introduced by  
\[error=(i_{s}{}^{ref}-i_{s})/i_{s}{}^{ref}\times 100\% \tag{21}\]  
Figure 14 presents \(dq\)-axes current prediction error results of the traditional MPCC and the proposed control. As seen in Figure 14a, the \(q\)-axis current prediction error is obviously less than 0 for a long time and the current prediction error ripple is large. As mentioned above, because the control vector sets are limited, sometimes the vector found by rolling optimization is not optimal or suboptimal, which may result in the deteriorating control performance, for example, the current quality decreases and even distorts. However, under the same operating condition, the proposed strategy can pull the \(dq\)-axes current prediction error back to 0, and the current prediction error ripple is reduced within 0.1. On the other hand, the strong robustness against the inverter parameter variation is successfully verified as displayed in Figure 15. When actual inverter parameters are inconsistent with ideal values according to the special operating environment, traditional MPCC suffers from large harmonics of grid-connected current and severe deterioration of steady-state performance. It is detrimental to the normal and safe operation of photovoltaic systems. Luckily, the grid-connected current is not affected by the model mismatch at all in the proposed MPCC, and the THD of the current is small enough to achieve grid-connected standards. This is because the future behaviors of the current are merely dependent on the sampling information, instead of inverter parameters. The strong robustness assists the stable operation of the system. Figure 14: \(dq\)-axes current prediction error results: **(a)** conventional MPCC; **(b)** proposed MPCC. Figure 13: Experimental results of THD in proposed MPCC. To be specific, the root mean square errors (RMSE) of the \(d\)-axis current obtained by (22) under different command currents, are summarized in Figure 16. Obviously, the RMSE of the \(d\)-axis current under the proposed MPCC stays below 1.0 at different given currents, lower than that under conventional MPCC. All thanks to the appropriate candidate VVs in the proposed strategy.