# Smart Inverters for Microgrid Applications: A Review
## 2 Smart Inverters
### Cooperativeness
#### 2.5.1 Reactive Power and Harmonic Current Sharing  
The problem of reactive power sharing inaccuracy in conventional droop methods is derived from the fact that it depends on the impedance of DG feeders and out-put side impedance of L-C-L filters. This contrasts with the active power sharing control, which is always accurate. In order to overcome this problem, several techniques have been proposed. The first group of methods are based on introducing a virtual impedance loop in order to compensate for the inverter output and line impedance unbalances and therefore improving the reactive power sharing. Several approaches based on this idea can be found in the literature, and their sole drawback is due to the possible large value of the virtual impedance. This may degrade the voltage quality particularly in weak islanded microgrids [19; 107; 108; 109]. The concept of virtual impedance loop can be described by the following equations:  
\[\vartheta_{0}=\vartheta_{0}^{*}-i_{0}Z_{0}(s), \tag{5}\]  
where \(\vartheta_{0}\) is the voltage reference provided for inner control loops, \(\vartheta_{0}^{*}\) is the voltage reference calculated by the droop control loop and \(Z_{0}(s)\) is the virtual impedance transfer function. Same as the \(m\) and \(n\) droop coefficient calculations in Equations (3) and (4), \(Z_{0}\) values for different units are calculated according to their power ratings:  
\[Z_{01}\ S_{1}=Z_{02}S_{2}=\cdots, \tag{6}\]  
Considering Equations (5) and (6) it can be understood that the virtual impedance implementation method generates a new voltage reference for inner control loops of the inverter by modifying the initial references set by the droop algorithms. Many approaches are conducted to empower the virtual impedance shaping technique. By using communication, the feeder impedance can be actively compensated, and this improves the reactive power sharing quality [8; 13]. Modifying the droop method is another method to improve reactive current sharing Over the years, many improved techniques have been proposed and implemented [110; 111]. In [110], an enhanced droop method has been proposed. In this method, the reactive power sharing is improved by the sharing error reduction operation. However, this procedure will cause an output voltage reduction which is regulated separately. Signal injection techniques can be mentioned as an example of other methods proposed for this purpose [112].  
The sharing of harmonic currents generated because of the presence of non-linear loads, such as rectifiers, have not been addressed by conventional droop methods [107; 113; 114; 115]. This presence of harmonics can affect the voltage and current wave-forms, cause overheating problems and add to losses, and lead to stability problems, therefore needed to be shared accurately [116; 117]. In [108] a modification in the virtual impedance loop was proposed. This method provides the resistive output impedance for higher order current harmonics by subtracting the voltages corresponding to current harmonics from the reference voltage:  
\[\vartheta_{0}=\vartheta_{0}^{*}-i_{01}.sL_{D}-\sum_{\begin{array}{c}h=3\\ odd\end{array}}^{11}i_{oh}R_{h}, \tag{7}\]where \(i_{01}\) is the output current, \(L_{D}\) is the virtual impedance and \(R_{h}\) is the resistive coefficient corresponding to each of the harmonic terms, \(i_{ol}\) By using Equation (7), a new voltage reference is generated for the inner loops, covering effects of both linear and non-linear loads.