Nowadays, improving the power quality at the Point of Common Coupling (PCC) between the consumers’ installations and the distribution system operators’ installations depends more and more on the use of specialized equipment, able to intervene in the network to eliminate or diminish the disturbances. The reactive power compensators remain valid solutions for applications in consumer and electricity distribution, in those situations when the criterion regarding the costs of installing and operating the equipment is more important than the ones related to the reaction speed or the control accuracy. This is also the case of the equipment for power factor improvement and load balancing in a three-phase distribution network. The two functions can be achieved simultaneously by using an unbalanced static var compensator, known as an adaptive balancing compensator, achieved by adjusting the equivalent parameters of circuits containing single-phase coils and capacitor banks. The paper presents the mathematical model for the sizing and operation of a balancing reactive compensator for a three-phase four-wire network and then presents some resizing methods to convert it into a balancing capacitive compensator, having the same functions. The mathematical model is then validated by a numerical application, modelling with a specialized software tool, and by experimental laboratory determinations. The paper contains strong arguments to support the idea that a balancing capacitive compensator becomes a very advantageous solution in many industrial applications.

Developed to achieve the balancing of three-phase loads and improve their power factor, the BCC (Balancing Capacitive Compensator) is presented in this paper as having a broader capability, namely that of balancing the two-way power flow. BCCs are becoming useful in today’s distribution networks with a high content of DERs (Distributed Energy Resources), where unbalanced power transfers to the higher voltage network occur more and more frequently as a result of the excess power generated. The article contains a case study in which, by means of Matlab-Simulink 2021 modelling, such a network is studied by considering two regimes corresponding to the two-way power flow. The numerical analysis of phase components and sequence components confirms the validity of the mathematical model concerning the BCC and also for the case of changing the way of power flow in the section controlled by the compensator. This demonstrates the possibility of extending the load balancing function of the BCC to that of balancing the two-way power flow and is an additional argument in support of replacing, in the more or less near future, conventional shunt capacitive compensators with capacitive balancing compensators.

To increase the electrical power quality, in the last decades, an intense development in the last decades of high-performance equipment built as advanced power electronics applications, such as the compensators from Switching Power Converter category, has taken place. For all that, Reactive Power Compensators (RPC) based on passive circuit elements, such as Static var Compensators (SVCs), still occupy a wide range of applications in customer and installations of the distribution system installations. The functions of power factor (PF) improvement and load balancing in a three-phase distribution network can be achieved with an unbalanced SVC, known as the Adaptive Balancing Reactive Compensator (ABRC). Presenting first the mathematical model of the initial sizing and the working mechanism of a Balancing Reactive Compensator (BRC) for a three-phase four-wire network, this article develops a compensator resizing algorithm through an iterative change of the initial sizing to transform the compensator into a Balancing Capacitive Compensator (BCC), which keeps the same functions. By using two computational and modeling software tools, a case study on the application of the method was carried out, demonstrating the availability of the sizing problem solution and validating the unbalanced capacitive compensation as an efficient way to PF improving and load balancing in a PCC (Point of Common Coupling).

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.

The constructive asymmetry of the untransposed overhead lines of a high voltage alternating current is the cause of a great number of difficulties in their operation and modeling. In order to model the operating regimes of such lines, the symmetrical component method, based on constructive symmetry and thus the symmetry of the equivalent phase parameters, is inappropriate, which is why many research papers have been dedicated to either setting up improved modeling methods or to returning to phase coordinate modeling. This paper intends to justify a paradox found on some untransposed overhead lines of a high voltage alternating current during the no-load operating conditions by performing phase coordinate modeling. In such a situation, the transmission or distribution operators measured significant negative values for the active powers on one or two phases at the beginning of the lines. Considering the case of a real untransposed overhead line operating under no-load conditions, the paper starts from presenting the recorded electrical values. Then, the paper moves on to outlining the Carson’s simplified computing relations for calculating the series and shunt primitive equivalent parameters and Kron’s transformation relationships for calculating the phase equivalent parameters. After applying them to the real line, the calculation of the power flow for the no-load operating conditions, which is applied to an equivalent scheme of the line consisting of nine identical octopoles, is performed. Both the untransposed line and its transposed variant are studied here. The values of the electrical amounts obtained by the calculation for the untransposed line are basically similar to those obtained by measuring on the real line, which gives a mathematical confirmation of the so-called paradox. Its occurrence represents the effect of the asymmetry of the equivalent phase capacities, which causes a redistribution of the active powers between the phases of the network to which the overhead line operating in no-load conditions is connected.

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.