## 2 Control Strategies Description
### Active Power Drooping  
When high solar irradiance is present, DERs generate maximum power. If the penetration level of renewables is high, the excessive power production combined with less loading may lead to power quality problems like overvoltages and voltage unbalance. This will lead to temporarily disconnection of DERs so that safe operation of the LV grid is preserved. This is known as active power curtailment, and it will lead to some financial losses to the prosumer due to the lost renewable energy injection. An appropriate solution for this problem is the active power drooping. This solution relies on measurements at the inverter terminals like injected current and grid voltages as implemented in [26]. Based on these measurements, the active power drooping is calculated and some active power curtailment is applied. Although active power is curtailed, this solution is still able to keep the DER connected to the grid and renewable energy is being injected into it, but most importantly, the quality of the power is not deteriorated. Some of the outcomes of the project INCREASE [27] are published in [28] and the results showed that the droop-based active power curtailment is able to improve the annual energy production with almost 50% compared to the hard power curtailment. Therefore, the active power curtailment is a more desirable solution when overvoltages and maximising the penetration level of renewables is concerned. Furthermore, because of its effectiveness, simplicity, and reliability, the need of supervisory control like multi-agent systems and coordinated control can be omitted.  
The active power droop controller measures the root mean square (rms) values of the grid voltages \(v_{g}\) at the inverter terminals. If a three-phase inverter is used, the droop controller uses the maximum of the phase voltages to ensure a safe and reliable operation. The droop controller is presented in Figure 1 and the final value of the drooped power \(p_{\text{dc}}\) is described mathematically by the following piecewise linear function:  
Figure 1: Active power drooping based on the work in [29].  
\[p_{\text{dc}}=\begin{cases}0,\ \ \text{if}\ |\underline{v}_{\text{g}}|<v_{\text{g,min}} \\ p_{\text{dc}}^{\bullet},\text{if}\ |\underline{v}_{\text{g}}|\leq v_{\text{cpb}}\\ p_{\text{dc}}^{\bullet}\left(1-\frac{|\underline{v}_{\text{g}}|-v_{\text{cpb }}}{v_{\text{g,max}}-v_{\text{cpb}}}\right),\text{if}\ v_{\text{cpb}}<| \underline{v}_{\text{g}}|\leq v_{\text{g,max}}\\ 0,\ \ \text{if}\ |\underline{v}_{\text{g}}|>v_{\text{g,max}}\end{cases} \tag{1}\]  
where \(v_{\text{g,min}}\) and \(v_{\text{g,max}}\) are the minimum and maximum grid voltages, respectively. To comply with EN50160 [30], these parameters are set to \(v_{\text{g,min}}=\)0.9 and \(v_{\text{g,max}}=\)1.1 p.u. The constant power band is set by \(v_{\text{cpb}}\) and in this case equals to 1.06 p.u. In this work, it is assumed that the power electronic inverter has an efficiency of 100% and then the available power at the dc side is equal to the injected power at the ac side, hence, \(p_{\text{dc}}^{\bullet}=p_{\text{ac}}\). Index \"\(\bullet\)\" denotes the available power at the dc side, which can vary from 0 to the nominal power \(p_{\text{dc,nom}}\). The parameter \(p_{\text{dc,nom}}\) depends on the power ratings of the primary source (photovoltaic system, wind turbine, small combined heat and power (CHP), etc.). The conditioning algorithm that ensures maximum power harvesting called a maximum power point tracking algorithm is also neglected because it is out of the scope of this work.