## 4 Matrix Converters in the Connection of Renewable Energies to the Grid
### Matrix Converter Applications in Wind Energy Conversion Systems  
The European Wind Energy Association predicts that wind energy will represent 30% of the European union electricity generation by 2030, and 50% by 2050 [78]. Indeed, the growth of installed capacity of wind energy conversion systems (WECS) in the last 2 decades determined not only on the increase in size and rated power of individual WECS but also changed the role that such systems represent to the grid. Nowadays WECS act as active contributors and stabilizers to the electrical grid by providing support on the grid frequency stabilization and voltage regulation providing fault ride through (FRT) capability [78]. Figure 12: Proposed grid-tied PV array with Indirect matrix converter. Figure 13: Experimental results of integrating a PV array into the smart grid (SG) with indirect matrix converter (IMC) and power quality (PQ) compensation. (**a**) Shunt current compensation with a 250 W non-linear load: grid line current \(i_{a}\) shunt converter ac line current \(i_{a}^{\prime}\) and load line current \(i_{n1,a}\) [5 A/div]. (**b**) Series voltage compensation with a 15% sag: grid line-to-ground voltage \(v_{a}\) series compensation line-to-line voltage \(v_{\text{ser,ab}}\) and load line-to-ground voltage \(v_{a}\) [125 V/div]. Currently, the majority of WECS are based on wind turbines coupled through a gearbox to a dual-fed induction generator (DFIG) with its stator connected to the grid while its rotor is supplied by a B2B converter, as shown in Figure 14a [79]. This topology allows the power converter to process only about one third of the power delivered to the grid but relies on bulky and failure-prone electrolytic DC-link capacitors. A DMC-based alternative to this B2B is given in Figure 14b. The replacement of the B2B by matrix converter-based topologies for Induction Generators based WECS has been approached in the literature. In [80] a grid connected WECS based on a squirrel cage Induction generator fed by a DMC is analyzed with special care given to stability issues related to the design of the filter and its damping coefficient for the whole WECS power and speed range. The authors of [81] proposed an improved direct torque control (DTC) scheme with grid reactive power control capability for a DMC-fed DFIG WECS. The researchers in [82] introduced a method for finding the DFIG optimum stator reactive power reference in order to maximize the active power injected to the grid at a given wind speed and grid power factor. They also derived the active and reactive power diagrams for DMC-fed DFIG WECS. In [83] a model-based predictive rotor current controller for an IMC fed DFIG WECS is implemented achieving a fast dynamic response. WECS gearboxes and its bearings are among the major causes of WECS downtime [84]. Among electrical machines universe, DFIGs are expected to require a high level of maintenance due to the brushes that allow the supply of its rotor windings. For these reasons, there is a growing interest in direct drive WECS based on permanent magnet generators (PMGs) with high number of poles, resulting in gearless and brushless WECS [85]. This concept is further developed in [86] by supplying the PMG through a DMC. The authors introduce a control methodology that allows power factor variation on the machine side to improve the grid-side maximum achievable power factor regulation for the entire rated range of the WECS speed and power. The high number of poles required due to the low and small speed range of PMG in gearless WECS may result in wider machines with lower voltage ratings. In [87] the authors analyze two variants of ultrasparse matrix-based topologies that feature a Z-source network as an intermediate stage for voltage boost from the PMG side to the grid, presented in Figure 15a,b. Even though the analyzed converters only allow unidirectional power flow  
Figure 14: Wind energy conversion systems (WECS) based on dual-fed induction generator (DFIG).