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.

One of the negative effects of the rapid increase in the number and capacity of photovoltaic power sources distributed in consumption areas by connecting to existing low-, medium-, and high-voltage distribution networks is the increased risk of amplifying the non-sinusoidal steady-state condition caused by high-power inverters. This amplification occurs if the peak values of harmonic impedance in the sections of the respective grid zone, which depend on the values of the equivalent shunt capacitances present in the grid, correspond to frequency values that coincide with or are close to the frequencies of the harmonic currents injected by the distributed sources. The risk is particularly high in cases of malfunction or failure of the filters within the installations associated with these sources. High shunt capacitance values are not only caused by the capacitive compensators used to increase the power factor of consumers or to improve the voltage level in the grid, but also by long power lines, particularly long underground lines. Risks increase as the proportion of underground power lines in the network area with sources of harmonic currents rises. This article refers to a real high-voltage grid area where the distribution operator plans to install high-power photovoltaic sources, the connection of which requires grid expansion through the construction of new substations and high-voltage power lines (110 kV). Based on the designer’s intention for the new high-voltage power lines to be underground and of relatively long lengths—which implies the presence of high natural capacitances—the authors conduct two case studies to predictively evaluate the harmonic impedance in the network sections resulting from the expansion, with the aim of identifying the frequencies at which parallel resonances may occur. The authors use two software tools for numerical analysis, Mathcad 14.0 and MATLAB–Simulink 2025A, and compare the results obtained for two design variants of the new high-voltage lines: overhead and underground, respectively. Using the mathematical model of long lines in steady state with uniformly distributed parameters, the analysis highlights that the highest values of harmonic impedance correspond to the overhead line design variant. The use of this design variant increases the risk of parallel resonances, not only by increasing the harmonic impedance values but also by widening the frequency ranges for which the impedance has high values. In both the overhead line and underground line variants, increasing the load leads to a reduction in the maximum values. Compared to the design variant using overhead lines, the variant with underground lines increases the risk of parallel resonances by increasing the number of frequency intervals for which the harmonic impedance has high values, but this increase is limited by narrowing these frequency intervals and reducing the harmonic impedance values. An important contribution of the article lies in arguing the need to extend the conventional node-based evaluation of harmonic impedance by treating harmonic impedance as a continuous spatial frequency characteristic of the transmission network. The impedances seen at nodes become the impedances seen in particular sections/sections of the network, identified by the value of the variable that specifies their position in space, more precisely the distance from the end of one of the feeders on which they are located.