The expansion and ongoing refinement of control solutions for three-phase microgrids are key enablers in the transition from conventional distribution networks to smart microgrids. By integrating distributed generation, a microgrid can operate in either grid-connected or island mode. One of the major technical challenges in microgrid operation is mitigating or eliminating phase power unbalances. Unbalanced single-phase loads, combined with unbalanced and intermittent single-phase generation, can produce adverse effects on both energy efficiency and power quality. Unlike conventional distribution networks, microgrids may exhibit bidirectional power flows, which can occur simultaneously on all phases or differ from phase to phase. This paper introduces new analytical expressions for sizing a balancing capacitive compensator (BCC) for three-phase four-wire systems and derives a simplified sizing algorithm. The approach is validated through a numerical study using a Matlab/Simulink model of a low-voltage three-phase microgrid with high penetration of single-phase loads and single-phase distributed sources. The BCC is installed at the point of common coupling (PCC) between the microgrid and the main grid. Three operating regimes (cases) of the microgrid were analyzed, considering three compensation scenarios (sub-cases) for each: 1—without compensation, 2—with balanced capacitive compensation (classical), and 3—with unbalanced capacitive compensation (with BCC). For each of the three regimes (cases), the use of the BCC determines, at the PCC, in addition to the cancellation of the reactive component of the positive sequence current, the cancellation of the negative- and zero-sequence currents. In other words, the BCC–microgrid assembly is seen from the main grid either as a perfectly balanced active power load or as a perfectly balanced active power source. Thus, the BCC prevents the propagation of the unbalance disturbance in the main grid; in the considered case study, this also results from the cancellation of the negative- and zero-sequence components of the phase voltages measured at the PCC. The results show that the load-balancing capability of the BCC can be extended to power-flow balancing in any network section, including cases where the phase power directions differ. Implemented as a BCC-type SVC or as an automatically adjustable variant (ABCC), the proposed unbalanced shunt capacitive compensation method is effective for mitigating or eliminating bidirectional phase power-flow unbalances.