# Predictive Control for Current Distortion Mitigation in Mining Power Grids
## 4 System Implementation and Results
### Analysis  
Four different cases were presented to evidence the proposed MPC capabilities related to low-frequency harmonics compensation. Although the computational burden of MPC applications is recognized, the proposed scheme allows the integration of power quality constraints referred to the IEEE std 1547.  
Cases 1 and 2 showed the capabilities of the proposed scheme, i.e., selective harmonics and THD compensation, respectively. Each one of these cases demonstrated that the system currents were, individually, in the expected range, due to the power Constraints (14) (case 1) and (18) (case 2). The controller was able to properly compensate for harmonics and  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Period** & \(\mathbf{I_{1}}\) & \(\mathbf{I_{2}}\) & \(\mathbf{I_{3}}\) & \(\mathbf{I_{4}}\) \\ \hline
1 & 8 & 0.3 & 0.129 & 0.2 \\  & 100\% & 3.75\% & 1.612\% & 2.5\% \\ \hline  & \(P_{0}^{\text{\tiny{OC}}}=2\) & & \(THD^{\text{\tiny{VCC}}}=7.86\%\) & \\ \hline
2 & 7 & 0.0665 & 0.103 & 0.06 \\  & 100\% & 0.95\% & 1.471\% & 0.857\% \\ \hline  & \(P_{0}^{\text{\tiny{OC}}}=3\) & & \(THD^{\text{\tiny{VCC}}}=3.278\%\) & \\ \hline \(\lambda_{u}[1/W^{2}]\) & \(\lambda_{0}[1/W^{2}]\) & \(\lambda_{p}[1/W^{2}]\) & \(\lambda_{c}[1/W^{2}]\) & \(\lambda_{T}\) \\ \hline
1 & 1 & 1e4 & 1e8 & 1e3 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Measured currents and weighting factors.  
Figure 8: Power and currents delivered by the PCC and the DG for case 4: (**a**) time–domain PCC and DG active power signals, (**b**) total power supplied by the DG, (**c**) no saturated and (**d**) saturated measurements at the PCC.  
Figure 9: Power delivered by the DG for harmonics compensation.  
current distortion. In the same way, case 3 presents the results when both aforementioned constraints were settled according to the IEEE std 1547. In this case, the second current harmonic was close to its maximum value, but the third and the fourth harmonics were lower to preserve \(THD^{\text{PCC}}\leq 5\%\), as the standard requires.  
Similarly, case 4 showed the system performance when the DG was saturated. In this case, the saturation was due to an over-rated active power reference. The results showed that power quality objectives were prioritized over active power transference. This is because active power used for mining activities is mainly supplied by third-party power purchase agreements; therefore, generation is not the main topic in the mining industry. In contrast, promoting high power quality requirements in mining power systems reduces not only operational expenditures but also power system failures.  
The four cases analyzed demonstrated that the proposed MPC scheme is able to compensate for harmonics and current distortion effects without adding additional power converters. Instead, these capabilities are embedded in the control system of the DGs. This is of great importance, as implementation costs are reduced and no hardware intervention is needed. Moreover, the MPC strategy fulfils the requirements of the IEEE 1547 standard, while the maximum power ratings of the DGs are respected. The proposed MPC strategy presents a better solution than PI-based approaches, as with these approaches it is hard to include constraints in the controlled variables and to achieve multiple objectives at the same time. Finally, note that the four cases analyzed were validated via hardware-in-the-loop experiments.