## 2 PV Systems and LV Network Context in Europe
### Voltage Unbalance from PV Penetration in LV Networks  
A high line resistance over reactance ratio (R/X) and an unbalanced in nature are typical features of LV distribution networks. For historical reasons, the sector was mostly seen as a vertical value chain, i.e., from generation at the top, to transmission, distribution, and consumption at the bottom. Together with such a high R/X ratio, they are generally planned to have a unidirectional power flow from high voltage to low voltage. The unbalance in power systems is mainly due to asymmetry in load currents and feeder impedances producing uneven voltage levels in each phase. As a result, LV distribution networks may encounter some technical challenges, with high numbers of PV systems installed at a residential level, which can degrade the situation, leading to poor power quality. The challenges and impacts of integrating many distributed generation resources in LV distribution networks is a well-covered topic in the literature [5; 16; 17; 18; 19; 20; 25; 26; 27; 28]. There are three main approaches to the calculation of voltage unbalance [29], as can be seen from Equations (2)-(4). The first according to National Equipment Manufacturer's Association (NEMA) is defined as the line voltage unbalance rate (LVUR) and is given by:  
\[\%\text{LVUR}=\frac{\text{max voltage deviation from the avg line voltage}}{\text{avg line voltage}}\times 100\% \tag{2}\]  
The NEMA definition assumes that the average voltage is always equal to the rated value, which is 400 V for the three-phase systems, and since it works only with magnitudes, phase angles are not included. A definition by IEEE: The IEEE definition of voltage unbalance, also known as the phase voltage unbalance rate (PVUR), is given by \(\%\text{PVUR}\):  
\[\%\text{PVUF}=\frac{\text{max voltage deviation from the avg phase voltage}}{\text{avg phase voltage}}\times 100\% \tag{3}\]  
The IEEE uses the same definition of voltage unbalance as NEMA, the only difference being that the IEEE uses phase voltages rather than line-to-line voltages. Here again, phase angle information is lost, since only magnitudes are considered. A third definition states that voltage unbalance is defined as the ratio of negative sequence to positive sequence voltage components and is represented in percentage terms as the voltage unbalance factor [29]. \[\%\text{VUF}=\frac{\text{negative sequence voltage component}}{\text{positive sequence voltage component}}\times 100\% \tag{4}\]  
The EN 50160 [30] standard states the limits for voltage unbalance as up to 2% for 95% of the week, with a mean of 10 min root mean square (rms) values, and even up to 3% in some locations. Voltage unbalance is viewed as a power quality issue of huge worry in LV distribution networks [31]. Even though the voltages are quite well balanced at the generator and transmission levels, the voltages at the consumption level can be unbalanced. This phenomenon is mostly due to unequal system impedances and the unequal distribution of single-phase loads. Voltage unbalance in LV distribution networks may also be caused by unbalanced solar generation and the intermittent nature of PV [18; 32] itself. The increase in voltage unbalance can result in overheating and low of all induction motor types and also distribution transformers [33]. Voltage unbalance likewise relieson upon the area and rating of disseminated PV. Voltage unbalance tends to increase with uneven loading [18], and the worst condition seems to be with high load demand and no PV installed. On the other hand, voltage unbalance is enhanced significantly when levelling the feeder loads with the combination of moderate loads and moderate PV generation. Simulations with scenarios exploring high-load demand with moderate PV generation or moderate load demand with high PV generation also report voltage unbalance problems. The present study only considers the magnitude of the voltages; hence the NEMA definitions, as it is not pertinent to consider the angles for the purpose of this analysis, and given its easiness to use.