## 2 Review of PV Inverter Efficiency
### Types of Inverter Weighted Efficiency  
Currently, the most widely used weighted efficiency is the \(\eta_{EURO}\). Its formulation is based on an hourly irradiance dataset gathered from a town called Trier, Germany [12; 13]. In general, \(\eta_{EURO}\) represents the inverter installed in regions that receive moderate irradiance penetration [14; 15]. Its formula is given as  
\[\eta_{EURO}=0.03\cdot\eta_{5\%}+0.06\cdot\eta_{10\%}+0.13\cdot\eta_{20\%}+ 0.10\cdot\eta_{30\%}+0.48\cdot\eta_{50\%}+0.20\cdot\eta_{100\%} \tag{4}\]  
Since \(\eta_{EURO}\) was developed before the existence of IEC 61724 and IEC 61683 Standards, it does not conform to the maximum of a 15 min sampling interval requirement. Instead, it was based on hourly irradiance sampling, which was manually recorded every three hours [12; 13]. Recently, several researchers revisited the computation of \(\eta_{EURO}\) using one second sampling time. However, the difference in the outcome was only 0.2% and thus, the finding is not considered to be significant [13]. The \(\eta_{EURO}\) formula is characterized by six pre-determined levels of operation: i.e., 5%, 10%, 20%, 30%, 50%, and 100%. The ranges for \(P_{dc}\)/\(P_{dc\_rated}\) that form the level of operation is shown in Table 1. For each level, a group of \(P_{dc}\)/\(P_{dc\_rated}\) is assigned; for instance, level 20% comprises of \(P_{dc}\)/\(P_{dc\_rated}\) that fall between 15% and 25%. Furthermore, the associated weightages are also shown. The heaviest weightage of 0.48 occurs at level of operation that equals 50%. This means that for nearly half of the operational time (\(T\)/\(T_{W}\)), the inverter is operating at approximately 50% of its rated power. On the other extreme, the lowest weightage is 0.03, which occurs when level of operation equals 5%. This implies that for 3% of the operational time, the inverter operates at approximately 5% of its capacity. In the case of \(\eta_{EURO}\), it is unclear how the weightage is determined. This most likely occurs is through trial and error. The California Energy Commission weighted efficiency (\(\eta_{CEC}\)) is based on one second sampling of the irradiance data, collected from Sacramento, California [16]. It has become a popular indicator to quantify the performance of the inverter in a region with high irradiance [13]. Similar to \(\eta_{EURO}\), it also has six levels of operation. However, the efficiency at each level of operation assumes a different value. Furthermore the weightage differ as follows:  
\[\eta_{CEC}=0.04\cdot\eta_{10\%}+0.05\cdot\eta_{20\%}+0.12\cdot\eta_{30\%}+ 0.21\cdot\eta_{50\%}+0.53\cdot\eta_{75\%}+0.05\cdot\eta_{100\%} \tag{5}\]  
By comparing (4) and (5), it can be observed that the \(\eta_{CEC}\) is more balanced in terms of the range of efficiency distribution that the inverter operates in. In contrast, the \(\eta_{EURO}\) pays more attention towards the range under 50% of PV inverter efficiency. Besides \(\eta_{CEC}\) and \(\eta_{EURO}\), there were other attempts to formulate the weighted efficiency according to respective local climates. The Izmir Efficiency (\(\eta_{IZM}\)) is based on a one minute sampling of irradiance data of Izmir, Turkey [17]. The formulation of \(\eta_{IZM}\) is done using the PV array simulator at the Austrian Institute of Technology (AIT), Vienna. The resulting equation, i.e., (6), resembles the simplified version of \(\eta_{CEC}\), but with the omission of weightages at levels of operation equal to 20% and 100%. Moreover, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Level of Operation (LO) (\%)** & **Range for \(P_{dc}\)/\(P_{dc\_rated}\) (\%)** & **Weightage (WT)** \\ \hline
5 & 0–7.5 & 0.03 \\
10 & \(>\)7–5.15 & 0.06 \\
20 & \(>\)15–25 & 0.13 \\
30 & \(>\)25–40 & 0.10 \\
50 & \(>\)40–75 & 0.48 \\
100 & \(>\)75 & 0.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The ranges for \(P_{dc}\)/\(P_{dc\_rated}\) and weightage for each level of operation for \(\eta_{EURO}\). the power level efficiency at 75% was changed to 70%. These similarities are no coincidence.