## 3 Hierarchical State-of-the-Art Control
### Power Sharing for Primary Control
#### 3.2.1 Droop-Based Control  
The droop-based control method is the most widely applied method to control DG units, as distinguished in the literature [3; 9; 72; 73; 74; 75; 76; 77]. The well-established control method is frequency and voltage droop. The main advantage of droop-based control is that it is solely based on local information. Hence, it offers a higher degree of operation in terms of flexibility and reliability. However, the conventional droop control experiences various constraints that could affect the power sharing accuracy among the parallel DG units. These are due to several factors, such as (i) voltage amplitude and frequency deviations, (ii) slow transient response, as it requires low-pass filters (LPF), (iii) vulnerability to nonlinear loads or unbalanced conditions, which introduce circulating currents (harmonic currents), and (iv) the mismatch on the inverter output impedance. Therefore, various research efforts have been presented to counter the inherent limitations of the conventional droop control scheme. * _Virtual output impedance (VI)_: VI is widely applied to advance the power sharing capability and stability of the system under line mismatch. The inverter output impedance would be in resistive and inductive behaviors. The conventional droop approach in large power systems is entirely operating in inductive line impedance. However, when applied in power electronics, the output impedance relies upon the control strategy used by the inner control loop. In [78], the study demonstrates a robust performance of the inverter with resistive output impedance against \begin{table}
\begin{tabular}{c c c} \hline \hline
**Controller** & **Advantages** & **Shortcomings** \\ \hline PI & Straightforward implementation. & Performance degrades under distorted condition. \\
[43] & A zero steady-state error in the \(4g\) reference frame. & Display steady-state error in an unbalanced system. \\ PR & Robust performance during disturbances. & Frequency variation sensitivity. \\
[50] & No excessive computational required. & Harmonics regulation difficulty. \\
[50] & Relatively zero steady-state error. & \\ \multirow{2}{*}{DB} & Accurate current reference tracking within zero error. & \multirow{2}{*}{Vulnerable to model uncertainties and parameter mismatch.} \\  & Closed-loop stability compensation. & High THD in nonlinear load. \\  & Fast transient response with lower THD. & \\ H & Fast transient response. & \\
[55; 57] & A robust operation against load variations. & \\  & Straightforward implementation. & \\ P & Obtains a swift transient response. & \\
[67; 68] & Involes less switching frequency. & \\  & Provides accurate tracking with low THD. & \\ SMC & A robust and dynamic response. & \\
[62; 69] & Decent performance in adaptively under parameter changes. & \\
[62; 69] & Excellent disturbance rejection. & \\ \multirow{2}{*}{\(H_{\infty}\)} & Robust performance in both linear and nonlinear loads. & \\  & Fast response with deficient THD issues. & \\
[70] & Reduced tracking error. & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The advantages and shortcomings of the inner-loop controllers’ scheme. numerical errors, disturbances, feeder impedance and parameter mismatch by compensating the voltage drop at the load effect and the droop effect itself. As for inductive impedance [79], adaptive droop control is achieved through a self-adjusted VI to provide the decoupling of active and reactive powers, thus guaranteeing accurate power sharing as well as reliable voltage assistance throughout the voltage compensator. A single line-current feedforward control at the voltage reference is widely applied in the conventional VI approach. An enhancement method is presented in [80] to provide VI at both the fundamental and harmonic frequencies by controlling via the DG current loop and the feedforward PCC voltage, respectively.