## 2 BCC--From Load Balancing to Power Flow Balancing
 \tag{14}\]  
Regarding the reactive power flow, on each phase of the BCC results in a reactive power equal and of the opposite sign to that on the homologous phase of the load, so that the load-BCC assembly works at a unit power factor on each phase:  
\[ \begin{split} Q_{a}^{comp}&=-Q_{a}^{load}\\ Q_{b}^{comp}&=-Q_{b}^{load}\\ Q_{c}^{comp}&=-Q_{c}^{load}\\ Q_{a}^{s}&=Q_{a}+Q_{a}=0\\ Q_{b}^{s}&=Q_{b}+Q_{b}=0\\ Q_{c}^{s}&=Q_{c}+Q_{c}=0\end{split}  \tag{15}\]  
The analysis of sequence components (symmetrical) allows us to understand the mechanism of compensation of the unwanted components of the load sequence currents. The relations for the currents on the respective load phases of the BCC, written in terms of the symmetrical components of the load currents, are:  
\[ \begin{split}\begin{bmatrix}l_{a}^{load}\\ l_{b}^{load}\\ l_{c}^{load}\end{bmatrix}&=\begin{bmatrix}1\\ a^{2}\\ a\end{bmatrix}\cdot l^{load+}&+\begin{bmatrix}1\\ a\\ a^{2}\end{bmatrix}\cdot l^{load-}\\ \begin{bmatrix}l_{a}^{comp}\\ l_{b}^{comp}\\ l_{c}^{comp}\end{bmatrix}&=\begin{bmatrix}1\\ a^{2}\\ a\end{bmatrix}\cdot l^{comp+}&+\begin{bmatrix}1\\ a\\ a^{2}\end{bmatrix}\cdot l^{comp-}&=-j\begin{bmatrix}1\\ a^{2}\\ a\end{bmatrix}\cdot lm\left(l^{load+}\right)-\begin{bmatrix}1\\ a\\ a^{2}\end{bmatrix}\cdot l^{load-}\\ \end{split}  \tag{16}\]  
So, for the currents on the source phases results:  
\[ \begin{split}\begin{bmatrix}l_{a}^{s}\\ l_{b}^{s}\\ l_{c}^{s}\\ l_{c}^{s}\end{bmatrix}&=\begin{bmatrix}l_{a}^{load}+l_{a}^{comp}\\ l_{b}^{load}+l_{b}^{comp}\\ l_{c}^{load}+l_{c}^{comp}\end{bmatrix}&=\begin{bmatrix}1\\ a^{2}\\ a\end{bmatrix}\cdot\text{Re}\left(l^{load+}\right)\end{split}  \tag{17}\]  
Therefore, BCC fully compensates for the negative sequence component and the imaginary (reactive) part of the positive sequence component of the load currents. During the phases of the load-BCC assembly, the currents form a set of positive sequences, containing only the real (active) component. The result is therefore the perfect balancing of the active powers and the total elimination of the reactive power taken from the source. In practice, in a large part of the situations, the active and reactive powers unbalances on the phases of the loads are not excessive, so by applying the (6)-(9) for the equivalent susceptances of the BCC, negative values are obtained. They will therefore have a capacitive character and will be realized practically only by single-phase capacitor banks. For the three susceptances of the compensator to be negative (or zero), from (8) the condition of simultaneous fulfilment of the following three conditions is deduced:  
\[Q_{a}^{load}+Q_{b}^{load} \geq Q_{c}^{load}\] \[Q_{b}^{load}+Q_{c}^{load} \geq Q_{a}^{load} \tag{20}\] \[Q_{c}^{load}+Q_{a}^{load} \geq Q_{b}^{load}\]  
If at least one of the (20) is not satisfied, the perfect load balancing, simultaneously with the total compensation of its reactive power by using a BCC, can only be obtained by a capacitive overcompensation. This capacitive overcompensation is sometimes necessary, for example when there is a two-way power transfer through the connection node of the compensator. When there are no other requirements, capacitive overcompensation, if accepted, should in most cases be minimized. In order not to change the negative sequence component of the currents on the compensator phases, the values obtained with (8) will be corrected with the same, negative value, which means the increase in the compensation capacitive-reactive power on the positive sequence. This value will be proportional to that of the susceptance components involved in the positive sequence current flow:  
\[B_{ab}^{comp+}=B_{bc}^{comp+}=B_{ca}^{comp+}=-\frac{Q_{t}^{load}}{9\cdot U^{2} }=-\frac{Q_{av}^{load}}{3\cdot U^{2}} \tag{21}\]  
where \(Q_{t}^{load}\) and \(Q_{av}^{load}\) are total inductive-reactive power and average reactive power absorbed by the load.