# Predictive Control for Current Distortion Mitigation in Mining Power Grids
## 1 Introduction
The authors of [15] proposed an MPC for hybrid AC/DC microgrids that finds a balance between the power quality and efficiency of the system in order to control the power exchange between the microgrids. In [16], the authors proposed a dual PWM technique to reduce the grid flickering and aliasing distortion caused by low-frequency oscillations that emerge in the power grid when torque disturbances occur in adjustable frequency drives. Model predictive control (MPC) was also used in this approach [17; 18; 19; 20]. In [17; 18], finite control set MPC applications were reported considering power quality objectives, by minimizing unbalanced and harmonics components, respectively. In [17], unbalances compensation is made through the computation of positive and negative sequences of active and reactive powers, whereas the harmonics detection strategy in [18] uses synchronous reference frames rotating at harmonics frequencies. The authors of [19] proposed an MPC that maintains low current distortion, which is based on dividing the operating regions of the space vector diagram and compensating for absent vectors. Similarly, reference [20] proposed a multi-vector MPC to reduce the current distortion, where the volt-second balance is achieved when three optimal vectors are adopted to synthesize the desired voltage. In these approaches, model predictions are one step ahead and the cost function is computed for each switch's combination. The second approach states the integration of passive and active filters along the microgrid or power system area, usually close to sensitive nodes; however, it implies the integration of additional hardware. A deep analysis of the selection and design of passive filters for high-power applications in mining is presented in [10]. The authors conclude that C-type filters, and second-order high-pass filters could be used appropriately in mining applications because of their low-order current harmonics attenuation and reactive power compensation properties. On the other hand, active filtering is a widely used technique in the industry to compensate for the pollution caused by unbalances and harmonics. This technique is based on measuring power components from the load to supply and compensating the undesired ones, reducing higher order harmonics at the PCC. The most common frameworks used to state the value of the compensation components are selective harmonics compensation, instantaneous power theory [21], and conservative power theory [22]. Applications of active filtering using instantaneous power and conservative power (CPT) theories have been reported in [23; 24], respectively. A remarkable advantage of these techniques is the decomposition of power in direct and oscillatory components, where the latter is controlled to a zero reference; thus, simple controllers, such as proportional integral (PI) controllers, can be used. However, a drawback of such techniques is the low bandwidth of PI controllers, which may not meet the high bandwidth required for controlling the oscillatory components. In this sense, this solution is classified into the primary control level in microgrids or power systems. In contrast, the selection of harmonics to compensate them by injecting a counter-phase current increases the computational burden required for total distortion mitigation but improves the system frequency response. In [25], sliding discrete Fourier transform allows distortion mitigation, by proportional control of each voltage harmonic, as a complementary objective in the primary level of distributed generators. In [26], a set of second-order band-pass filters are defined for harmonics filtering in the \(\alpha\beta\) domain, and then compensation components are computed at the primary level as well. Conversely, approaches based on consensus theory to share imbalances [27] and harmonic distortion [28] have been reported. For instance, in reference [27] three-phase MGs are controlled as three single-phase subsystems, where droop reactive power-voltage controllers are employed to share imbalances.