## 2 BCC--From Load Balancing to Power Flow Balancing  
SVC-type equipment has found a very efficient application from a technical-economic point of view in three-phase network power flow balancing. According to a series of studies previously published by authors of this article, in a wide variety of situations, three-phase unbalanced loads can be perfectly balanced, simultaneously maximizing the power factor, by unbalanced shunt capacitive compensation [29; 30; 31], by using a BCC. Such a compensator offers, in addition to the advantage of a low cost, by eliminating the coils, the easy possibility to obtain a dynamic compensation, which follows the load variation, by automatically switching the steps of single-phase capacitor banks (ABCC--Adaptive Balancing Capacitive Compensator) [30; 31]. In the case of three-phase three-wire networks, the compensator contains three batteries of single-phase capacitors in a delta connection (Figure 1). In addition to the usual functions of voltage regulation or power factor improvement, the compensator can perform the balancing of active and reactive powers consumed per phase. The mathematical model associated with the load-compensator assembly, expressed in phase components, shows that the energy balancing mechanism consists of the redistribution of active and reactive powers between the phases. By using positive-negative-zero sequence components, it is demonstrated that the compensator causes the negative sequence current flow, equal and sign opposite to the negative sequence currents of the load [23; 24; 25]. The following paragraphs briefly present the relationships for calculating the equivalent susceptances of the reactive elements of the respective compensator to illustrate the energy mechanism of load balancing, which will then allow the load balancing function to be extended to that of power flow balancing. According to [26], the values of the three equivalent susceptances of the single-phase sides of the BCC can be calculated using the relationships derived based on a simplified mathematical model, in which it is considered that the three-phase assembly formed by the unbalanced equivalent load and the BCC, is connected to a source with a sufficiently large short-circuit power so that the asymmetries of the three-phase sets of the phase to ground voltages and the phase to phase voltages can be neglected. The unbalanced load, real or equivalent, can be modelled by a triangle of three equivalent admittances:  
\[ \begin{bmatrix}\Sigma_{ab}^{load}\\ \Sigma_{bc}^{load}\\ \Sigma_{ca}^{load}\end{bmatrix} = \begin{bmatrix}1&0&0\\ 0&1&0\\ 0&0&1\end{bmatrix}\begin{bmatrix}G_{ab}^{load}\\ G_{ca}^{load}\\ G_{ca}^{load}\end{bmatrix} -j\cdot \begin{bmatrix}1&0&0\\ 0&1&0\\ 0&0&1\end{bmatrix}\begin{bmatrix}B_{ab}^{load}\\ B_{ca}^{load}\\ B_{ca}^{load}\end{bmatrix}  \tag{1}\]As with any delta-connected circuit, the zero-sequence component of the load phase currents is zero:  
\[\underline{l}^{load-}\
eq 0,\ \ \underline{l}^{load0}=0, \tag{2}\]  
Those in (2) are also valid for the currents on the BCC phases, which also is in delta connection:  
\[\underline{l}^{comp-}\
eq 0,\ \ \underline{l}^{comp0}=0, \tag{3}\]  
For the symmetrical components of the phase currents absorbed from the source by the load-BRC assembly, relations (4) are valid:  
\[ \begin{split}&\underline{l}^{s+}=\underline{l}^{load+}+ \underline{l}^{comp+}\\ &\underline{l}^{s-}=\underline{l}^{load-}+\underline{l}^{comp- }\\ &\underline{l}^{s0}=\underline{l}^{load0}+\underline{l}^{comp0}= 0\end{split}  \tag{4}\]  
The sizing of the three BCC susceptances is performed with the aim of total compensation of the negative sequence currents from the currents on the load phases. In addition, the condition of total compensation of the reactive power absorbed from the source is imposed on the positive sequence (\(\cos\varphi^{s+}=1\)). The expressions for calculating the susceptances are determined by solving a system of three independent first-degree Equation (5):  
\[