## 2 BCC--From Load Balancing to Power Flow Balancing
\[Q_{t}^{load}=Q_{a}^{load}+Q_{b}^{load}+Q_{c}^{load} \tag{22}\]  
\[Q_{av}^{load}=\frac{Q_{t}^{load}}{3} \tag{23}\]  
If noted with \(k_{Q}^{+}\) the proportionality factor applied to supplement the capacitive compensation on the positive sequence, the corrected values of the BCC susceptances will be:  
\[ \begin{bmatrix}B_{ab}^{comp*}\\ B_{b}^{b}\\ B_{ab}^{b}\\ B_{ab}^{b}\end{bmatrix} =-\frac{1}{3\cdot U^{2}}\left( \begin{bmatrix}1&1&-1\\ -1&1&1\\ 1&-1&1\end{bmatrix}\begin{bmatrix}Q_{a}^{load}\\ Q_{b}^{load}\\ Q_{c}^{load}\end{bmatrix} +k_{Q}^{+} \begin{bmatrix}1\\ 1\\ 1\end{bmatrix} Q_{av}^{load}\right) \tag{24}\]  
When the sum of the reactive powers flowing on the load phases is positive, the minimum value of the capacitive overcompensation that ensures the perfect load balancing by using a BCC, is obtained when:  
\[k_{Q}^{+}=\max(M_{1},\ M_{2},\ M_{3}) \tag{25}\]  
where:  
\[ \begin{bmatrix}M_{1}\\ M_{2}\\ M_{3}\end{bmatrix} =\frac{1}{Q_{av}^{load}}\cdot \begin{bmatrix}-1&-1&1\\ 1&-1&-1\\ -1&-1&1\end{bmatrix} \cdot \begin{bmatrix}Q_{a}^{load}\\ Q_{b}^{load}\\ Q_{c}^{load}\end{bmatrix}  \tag{26}\]  
The relationships presented above are part of a complex mathematical model, presented in detail in [26], except Equations (7), (8) and (10) and, respectively, (20)-(26), obtained by extending the same mathematical model and which were presented for the first time in this article. Both the relations for sizing the susceptances of the BCC (BRC) composition (6)-(9) and those for explaining the energy mechanism of the load balancing (10)-(19) were based on the conditions related to the three-phase load balancing. Among these relationships, those that use the active and reactive powers on the load phases allow us to obtain an important conclusion: they remain valid regardless of the flowing way of the active and reactive powers, which can even be simultaneously different on different phases. This conclusion transforms the BCC from a means of load balancing, to one of power flow balancing. The purpose of this article is to demonstrate the validity of the mathematical model presented above even in the case of two-way active and reactive power flow on the network phases, in the section controlled by the BCC. The best example for such a situation and at the same time the best application for a BCC, more precisely an ABCC with the function of power flow dynamic balancing in a three-phase three-wire network, is that of medium voltage distribution networks with a high concentration of distributed renewable sources of electricity. During periods of time with excess generated power, on different phases, the active and reactive powers can have both different values and different flowing ways. In addition, in the same phase, the way of the active power flow can be different from that of the reactive power (Figure 2). Capacitive balancing compensators can be used by consumers for load balancing, respectively, by the distribution operator for two-way power flow balancing on network sections (Figure 2). In the case of extended networks with high concentrations of distributed renewable sources, to benefit from the positive effects of power flow balancing on the network sections, this operation must be carried out in several sections of the network, depending on its complexity. The number and capacitive-reactive power installed in the compensators is determined by solving a technical-economic optimization problem. The expected effects of power flow balancing on the network sections are:  
* reducing the asymmetry of the three-phase voltages;
* placing the rms voltage values at the consumer terminals within the admissible limits by reducing the maximum voltage losses on the phases;
* avoiding thermal overloading of the current paths on the network sections;
* reducing the level of unbalance disturbances transferred to the main network.