## 3 Results and Discussion
### Imbalance of Network Voltage Values between Phases  
This section analyses the imbalance or disequilibrium in voltage values among the three phases at each of the PCCs of the different PV installations analysed in this work, based on the grid voltage data recorded by the plants' inverters. The voltage imbalance factor, that will depend on how the solar PVs and loads are distributed in different phases of the LV distribution network, have also been mentioned as one of the significant problems with high levels of PV penetration into LV distribution networks [8]. Imbalance can result in overheating and derating of induction motors, transformers and of small three-phase generators and can significantly affect the effectiveness of voltage regulation in the system [9]. To analyse the possible effect of the production of the PV plants on this imbalance, the disequilibrium, in absolute value, of the voltage in each of the phases (i), \(\Delta V_{grid\_phase\_i}\) versus the mean value of the voltages of the three phases \(V_{grid\_phase\_i}\), with \(i\) = 1, 2 and 3, was calculated by the Equation (1)  
\[\Delta V_{grid\_phase\_i}=\left|V_{grid\_phase\_i}-(\frac{\sum_{i=1}^{3}V_{ grid\_phase\_i}}{3})\right| \tag{1}\]  
The result obtained have been represented in the form of colour maps. Some examples are shown below throughout the section. Figure 24a shows the voltage imbalance in phase 2 measured by the inverters in PV installation 1. It can be seen in this case that the maximum imbalance between the voltages of this phase with respect to the average value of the three phases barely exceeds 4 V, but these higher values only occur very rarely. These maximum values of imbalance found are even lower than the variations in the voltage values that have been seen to exist in the phases themselves throughout the day. Analysing Figure 24b, which represents a histogram of the values represented in Figure 24a, it can be seen that the highest incidence of these imbalance corresponded to values lower than 1.5 V, but mostly those that predominate were the values very close to zero. In installation 1 to which this Figure 24 corresponds, the inverters are three-phase and, as previously indicated, they measure the voltage value in the grid 24 h a day. During the hours when the installation was not operating, it can be seen that the imbalance was around 1 V, and during production hours, when the inverters distribute the generated energy equally among the three phases, the imbalances were even lower, so that in this case, it can be observed that the operation of the three-phase generator may serve to reduce any existing phase voltage imbalance in the PCC [46]. In the rest of the inverters and phases of this installation, the results were within the same order of magnitude, and present the same behaviour. [PERSON] et al. [9] indicate that the impact of PV to the system imbalance is sensitive to changes in the network configuration and to the existing imbalance of customers' connection and consumption, and the voltage disequilibrium can be even reduced by increasing PV penetration. In the case of this installation, its high nominal power, and the balancing potential that the three-phase inverters can provide, could be contributing to this improvement in the balance between the three phases when there is production in the PV installation. In Figure 25a, it is shown the imbalance of one of the phases, phase 3, determined from the data recorded by the two three-phase inverters of installation 2. The histogram of these values is shown in Figure 25b. It can be seen that the phase disequilibrium, which in this case was somewhat higher than that found in installation 1, was generally not directly related to the production of the PV plant, and the largest or smallest imbalance occurred at any time of the day. In the other two phases, as well as in the values recorded by the other inverter of this installation, the results were similar.