## Low Voltage Control Tool
### Description of the LVC Algorithm
#### 2.2.1 Voltage Regulation in LV Networks  
In LV networks with no DG, voltage control has traditionally been achieved by local compensation or by adjusting OLTC tap settings. However, with the advent of microgeneration, new methodologies are being developed in order to effectively tackle the voltage control problem at lower voltage levels in the distribution system. Since LV lines tend to be highly resistive as previously mentioned, traditional voltage control based only on reactive power management is ineffective [31; 32].  
In order to understand the influence of LV networks' characteristics, consider the example system presented in Figure 2.  
The expressions that determine the power flow in the LV line represented in Figure 2 (neglecting shunt admittances) are:  
\[P_{12}=\frac{RV_{1}^{2}-RV_{1}V_{2}\cos(\theta_{12})+XV_{1}V_{2}\sin(\theta_{1 2})}{R^{2}+X^{2}}, \tag{1}\]  
\[Q_{12}=\frac{XV_{1}^{2}-XV_{1}V_{2}\cos(\theta_{12})-RV_{1}V_{2}\sin(\theta_{ 12})}{R^{2}+X^{2}}, \tag{2}\]  
with  
\[\theta_{12}=\theta_{1}-\theta_{2}, \tag{3}\]  
where:  
\(V_{i}\): is the voltage magnitude at bus \(i\): \(\theta_{i}\): is the voltage angle at bus \(i\): \(S_{ij}\): is the apparent power flow in the branch connecting bus \(i\) to bus \(j\): \(P_{ij}\): is the active power flow in the branch connecting bus \(i\) to bus \(j\): \(Q_{ij}\): is the reactive power flow in the branch connecting bus \(i\) to bus \(j\): \(Z\): is the impedance of the branch connecting bus \(1\) to bus \(2\): \(R\): is the resistance of the branch connecting bus \(1\) to bus \(2\): \(X\): is the reactance of the branch connecting bus \(1\) to bus \(2\):  
Figure 2: Example system.  
Considering that in LV networks, the line resistance is usually much greater than the line reactance (i.e., \(R\gg X\)), the following expressions for active and reactive power flows can be derived from Equation (1) and Equation (2):  
\[P_{12}=\frac{V_{1}^{2}-V_{1}V_{2}\cos(\theta_{12})}{R}, \tag{4}\]  
\[Q_{12}=\frac{V_{1}V_{2}\sin(\theta_{12})}{R}. \tag{5}\]  
According to Equation (4), it can be seen that, in order to be able to inject active power from bus 2 to bus 1 in a resistive network, voltage should be higher at the bus 2 than at bus 1 (i.e., \(V_{2}>V_{1}\)). This shows that, contrary to the transmission system or even at some voltage levels of the distribution system, controlling reactive power flow is not as effective as real power for voltage control in LV networks. In LV networks, situations where the active power injection largely exceeds consumption--such as peak solar production coinciding with low load demand--can lead to overvoltages that violate the admissible limits. Similarly, consumption peaks derived, for instance, from simultaneous EV charging, can lead to undervoltages that can also violate the admissible limits. Furthermore, it is expected that LV networks will in the future accommodate large amounts of microgeneration units. Given that at the LV level both loads and microgeneration units are usually single-phase, given their small power rating, LV networks may suffer from phase unbalance, contrary to what happens at the MV or HV levels of the distribution system, for instance.