Research on Possibilities for Increasing the Penetration of Photovoltaic Systems in Low-Voltage Distribution Networks in Slovakia

Abstract

With the increasing penetration of photovoltaic systems in low-voltage distribution networks, new operational challenges arise for distribution system operators. This article focuses on a comprehensive analysis of the impact of single-phase and three-phase photovoltaic systems on voltage magnitude, voltage unbalance, and currents flowing through distribution lines. The steady-state operation was calculated using EA-PSM simulation software, and the assessment of the impact of photovoltaic systems on the network was carried out using the international standard EN 50160. Simulation results show that a high penetration of photovoltaic systems causes significant changes in the network’s voltage profile. The study also includes a proposal of measures aimed at mitigating the adverse effects of decentralized generation in photovoltaic systems on the distribution network. Among the most effective measures is the selection of an appropriate conductor cross-section for distribution lines. The results also indicate that, in terms of negative impact on the network, it is preferable to prioritize three-phase connection over single-phase connection, because for the same impact on the network, three-phase photovoltaic systems can inject several times more power into the network compared to single-phase systems. These and other findings may be beneficial, especially for distribution system operators in planning the operation and development of networks.

1. Introduction

We are currently in a decisive phase of the global response to the climate and biodiversity emergency [1]. Among the leaders in climate protection worldwide is the European Union (EU). In 2019, the European Commission, in response to climate change and environmental degradation, introduced the European Green Deal, whose main goal is to reduce greenhouse gas emissions produced by EU member states by at least 55% by 2030 compared to 1990 and to achieve climate neutrality by 2050 [2]. To increase the likelihood of reaching the 2030 target, the EU adopted a legislative package in 2023 known as “Fit for 55” [3]. Specific measures in this package include, for example, increasing the energy efficiency of buildings, raising the share of renewable energy sources (RES) in total energy consumption, reducing energy consumption or developing electromobility [4,5].

In the EU, the main source of greenhouse gases is the energy sector, which includes electricity generation, heating, and transport, accounting for more than ¾ of total greenhouse gas emissions produced by member states. According to the EU, the key to significantly reducing emissions in the energy sector and achieving climate neutrality by 2050 is the development of RES [6]. The current EU goal is to increase the share of energy from renewables in gross final energy consumption in the EU to 42.5% by 2030, with member states encouraged to strive for 45% [5,7]. In 2023, renewables accounted for 24.5% of the EU’s gross final energy consumption, representing about 50% progress toward the 2030 target [8]. In recent years, RES have experienced the greatest expansion in electricity generation, with their share in production more than doubling since 2004. According to the latest available data, RES accounted for approximately 45% of net electricity generation in the EU in 2023. They were followed by fossil fuels with about 32% and nuclear energy with approximately 23% [9,10]. The fastest-growing renewable energy source in the EU is solar energy, which has many advantages making it suitable for addressing the current energy challenges of the EU. Therefore, starting from 2030, it will be mandatory to install solar systems on all new residential buildings, provided it is technically suitable and economically and functionally feasible [11].

For households, solar energy is the most accessible renewable energy. Electricity generation from solar radiation is carried out through photovoltaic (PV) systems, which have undergone significant development over the past decade (the costs of PV systems decreased by approximately 82% between 2010 and 2020). Installations of PV systems can protect end electricity consumers from high electricity prices and increase their independence from conventional power supply [12,13]. Households are powered from low-voltage (LV) distribution systems, with PV systems most commonly installed on their roofs. The capacity of these PV systems typically ranges in the order of kilowatts [14], and depending on the rules of distribution companies, PV systems can be connected to the grid either single-phase or three-phase. Comparison of the characteristics of single-phase and three-phase PV systems is shown in

Table 1. Comparison of the traits of single-phase and three-phase PV systems.

Trait	Single-Phase PV System	Three-Phase PV System
Typical application	Residential buildings, small installations	Larger residential buildings, commercial and industrial buildings
Grid connection	Two wires (phase, PEN conductor)	Five wires (phase A, B and C, PE, N)
Power output capacity	Limited, lower capacity	Higher capacity, suitable for larger installations
Output voltage	230 V	230/400 V
Cost	Lower initial investment	Higher costs due to more complex installation
Impact on electricity grid	May cause voltage unbalance	More stable voltage and power quality
Installation complexity	Less wiring, simpler design	More cables and careful phase balancing needed

.

PV systems in households are most often operated as on-grid, where the PV system works in parallel with the distribution system, and in case of surplus production at the consumption point, the excess electricity is fed into the distribution system. Thus, PV systems influence the operation of the distribution system in which they are installed.

Several studies have been conducted in the past to identify the consequences of integrating distributed electricity sources into LV distribution networks [15,16,17,18,19,20,21,22]. According to [15], one of the most significant consequences of integrating PV systems into LV distribution networks is the change in the network’s voltage profile and the impact on power flow within the network. According to [16], voltage rise is one of the most serious problems related to voltage when connecting distributed electricity sources in small residential areas that share a common distribution transformer. This study examined the impacts of PV systems on LV distribution networks, identifying reverse power flow, voltage rise and fluctuations, reactive power fluctuations, and increased losses as the main problems. In [18], changes in network behavior caused by the integration of PV systems were analyzed using a comprehensive assessment tool. The analysis showed that during midday, at maximum PV system production, the voltage profile can improve in phases with high load while losses in these phases decrease. However, on the other hand, voltage may rise above the allowable limit in phases with low load, and reverse power flow can also occur in these phases. A large number of PV systems installed in LV distribution networks can cause not only voltage rise but also transformer and line overloads due to increased active and reactive power flow [23,24]. According to [25], single-phase PV systems may contribute to worsening voltage unbalance in the distribution network, resulting in current flow through the neutral conductor and increased power losses.

The specific impact of PV systems on the LV distribution network depends on various factors unique to each distribution area, such as load concentration, technology used for PV systems, line length, PV penetration in the distribution network, local consumption, and voltage level at the connection point [23].

Based on the long-term goals of the EU, it can be assumed that PV penetration in LV distribution networks has not yet reached its maximum and that the integration of PV systems will continue to grow rapidly in the future. This creates new challenges for distribution system operators (DSOs) that must be addressed [26].

There are several studies related to determining the hosting capacity of the distribution system [27,28,29,30], i.e., the maximum possible penetration of PV systems in the distribution network, at which the operational safety and reliability of the distribution system are not endangered. The hosting capacity of the distribution network is affected by many factors. Some are determined by the operational rules of the network, while others are determined by the physical limits of the various components forming the distribution network [31]. To increase the hosting capacity of the distribution system, various technical measures can be adopted. In study [23], such technical measures are divided into three categories: solutions on the side of the PV system operator, solutions on the side of the DSO, and interactive solutions requiring collaboration between both parties. Solutions on the side of the DSO do not require interaction with network users and can be deployed solely based on the decision of the distribution system operator. Such solutions include, for example:

• use of MV/LV transformers with on-load tap changers, which can contribute to active voltage control in LV distribution networks,
• use of SVC devices, which can immediately inject or absorb reactive power at a specific node in the network, thereby influencing the voltage profile of the network,
• use of LV/LV booster transformers—these transformers are autotransformers and can be used for voltage control along the line, which can also reduce losses in the line. These transformers can be used to limit the voltage magnitude caused by high PV system production.
• use of battery storage, which can support the flexibility of the distribution network operation. Battery storage can supply energy during peak load periods and store excess energy during periods of low consumption and high PV production, enabling voltage regulation within the network.
• reinforcement of the network, for example, by using parallel cable lines or increasing the conductor cross-section of the lines.

Solutions on the side of the PV system operator include the operation of devices installed at the consumption points of network users, which, for example, can adjust the supply or consumption of energy without intervention by the DSO. Such measures include, for example:

• use of energy storage, which can store excess energy during periods of surplus PV production and cover the load during high consumption, thereby contributing to more stable voltage in the network,
• limitation of energy supply to the network, where in case a certain defined threshold of supplied energy is exceeded, the PV system is disconnected,
• control of active power using an inverter, where the power injected into the network is automatically controlled based on the voltage at the connection point of the consumption point to the system,
• control of reactive power using an inverter, where the increase in voltage caused by PV production can be limited by adjusting the power factor of the PV system.

Interactive solutions require cooperation between the DSO and PV system operators, which usually necessitates the establishment of a communication infrastructure. Such measures include, for example:

• load management, where the DSO can remotely connect or disconnect certain loads at the users’ consumption points to increase the reliability of distribution system operation,
• control of active or reactive power of the inverter, where the DSO would have the ability to remotely control these parameters based on network conditions,
• comprehensive voltage management in the network, where the DSO simultaneously controls multiple devices within the system (e.g., transformer with on-load tap changer, active and reactive power of inverters of PV systems, SVC devices, etc.) [23,32,33,34,35,36,37,38,39,40,41,42,43].

Although the above-mentioned measures technically address problems related to integrating PV systems into low-voltage distribution networks, most of them require certain investment costs that could be unacceptable for DSOs given the number of low-voltage distribution networks. Therefore, most of these measures are not immediately practical or economically feasible. However, the growing number of PV systems in LV distribution networks is a current issue that requires solutions that can be implemented immediately or in the near future. Therefore, further research and development of practical solutions are necessary to help DSOs integrate the highest possible amount of renewable energy into distribution networks without compromising system operability.

The aim of this work is therefore to clearly define the impacts of distributed generation through single-phase and three-phase PV systems on the power quality parameters in the distribution network, and to propose practical measures that DSOs can immediately implement, for example, by changing the technical conditions for connecting devices to the distribution network or by modifying the principles of distribution network development planning. The main contributions of this work include:

• creation of a LV distribution network model with transformer, lines, loads, and PV systems typical for distribution networks in Slovakia in the EA-PSM simulation software, and asymmetric steady-state power flow calculation for 4 modeled scenarios,
• comprehensive three-phase analysis of the impact of single-phase and three-phase PV systems on voltage magnitude and unbalance at various points in the distribution network in accordance with the EN 50160 standard [44],
• detailed three-phase analysis of the impact of operating single-phase and three-phase PV systems on the currents flowing through the distribution network lines,
• defining the relationships between PV system operation and its impact on the power quality parameters in the distribution network,
• proposal of measures (both ex post and ex ante), on the part of the DSO as well as the PV system operator, to mitigate the impact of single-phase and three-phase PV systems on the distribution network and to increase PV penetration in LV distribution networks, with verification of their effectiveness on a modeled network.

The strengths of this study compared to other studies include:

• simultaneous examination of the impact of single-phase and three-phase PV systems on multiple distribution system variables (voltage magnitudes, voltage unbalance, relative voltage changes, and currents). Many existing studies focus only on single-phase or three-phase PV systems and their impact on selected network parameters (e.g., voltage magnitude or voltage unbalance). This study, however, offers a comprehensive view of the impact of both single-phase and three-phase PV systems simultaneously on multiple network parameters.
• performing simulations of an asymmetric network, which allows for a comprehensive assessment of the impact of single-phase and three-phase PV systems on all three phases of the distribution network and the PEN conductor. Many studies simplify the analysis by assuming a symmetrical network. Such studies do not reflect real conditions, since LV distribution networks, in particular, are characterized by significant asymmetry.
• the modeling does not assume perfect grounding of the PEN conductor in the distribution network, where it would be 0 V along its entire length. This simplification is often applied but does not reflect conditions in real LV distribution networks. Therefore, the distribution network model used in this study better corresponds to real LV networks from this perspective as well.
• proposal of possible measures to mitigate the adverse impacts of PV systems on the LV distribution network separately for single-phase and three-phase PV systems. When proposing measures, conditions of effectiveness, and immediate practical applicability were considered. Many studies explore options for reducing the impacts of PV integration into LV distribution networks, but many of the proposed measures face obstacles (technical or economic challenges) in their practical application. This study therefore proposes measures that meet the chosen conditions, and the study clearly demonstrates their effectiveness.

The remainder of the article is organized as follows. Section 2 describes the methodology chosen for the simulations, processing of results, and their evaluation. Section 3 provides a detailed description of the selected LV distribution network model used in the simulations, characterizes the individual modeled scenarios, and lists the monitored parameters along with their limit values. Section 4 presents the simulation results and their comprehensive analysis. Section 5 focuses on proposing measures to eliminate the negative impact of distributed generation on the distribution network and quantifies their effectiveness.

2. Methodology

This study is conducted using a classical deterministic approach, which provides clear results for various operating scenarios and network configurations. The analysis is performed for specific, predefined operating states of the network, such as maximum photovoltaic generation and average load values. In line with the standard procedure for deterministic analysis, the focus is primarily on so-called worst-case scenarios, which represent the potentially most adverse operating conditions for the network.

The steady-state calculation can be performed in various ways, including the use of numerical methods such as the Newton-Raphson method [45], the Gauss-Seidel method, or the Backward/Forward Sweep method [46], as well as by using different simulation software. For analyzing the impact of electricity generation from PV systems connected to LV distribution networks, study [34] utilized PowerFactory DIgSILENT software, study [24] employed NEPLAN, study [35] used the OPENDSS-EPRI simulator, and study [47] applied Matpower for simulations.

The case study presented in this article is carried out using the EA-PSM software (version 22.05.02), which, according to available literature, has not yet been used for modeling the impact of PV systems on LV distribution networks. This software enables modeling and calculation of symmetrical as well as asymmetrical transmission, distribution, and industrial networks of various voltage levels with integrated PV systems, making it suitable for use in this study. The key features of the EA-PSM program are:

• Power flow analysis—this function allows determining the current flows in the network, power flows (active and reactive), voltages at nodes, voltage drops on lines, losses, power factor, and more.
• Short circuit calculation—this function enables finding short circuit current values for different types of faults. All calculations are performed in accordance with IEC 60909-0 standard [48].
• Harmonic flow analysis—this function allows evaluating the impact of nonlinear loads on the electrical network. The harmonic flow analysis checks whether harmonic voltages and currents are within acceptable levels.
• Relay coordination and protection tracking—the user can design a network protection system and find optimal parameters for protective devices to ensure selectivity and to clear faults as quickly as possible. Users can add various types of protection, such as overcurrent protection, undervoltage protection, ground fault protection, thermal overload protection, and others.
• DC calculations—this feature provides DC calculations that include power flows, time-dependent power flows, and short circuit analysis. You can model schemes using various types of elements such as DC cables, photovoltaic panels, DC batteries, AC/DC inverters, and DC circuit breakers.
• Parallel line modeling—this function allows users to analyze transmission networks with parallel lines, create custom models of towers with phase, ground, and lightning protection conductors as well as wire conductors.
• and more [49,50,51].

However, a drawback of the EA-PSM software, similar to other simulation programs, is that the calculated voltage values at individual network nodes are referenced to the slack bus and therefore do not directly provide information about the voltages between the phase conductors and the neutral conductor at the individual network nodes. To determine the impact of PV system operation on the phase voltage magnitude at the PV connection point in the network, it is necessary to calculate the phase-to-neutral voltages at all monitored nodes based on the simulation software results. Due to the large amount of data, this calculation is performed in MATLAB (version 9.13).

The EA-PSM program also does not provide data on voltage unbalance at individual network nodes, and therefore voltage unbalance must be calculated additionally. Voltage unbalance can be calculated using several computational methods, with the most well-known definitions of voltage unbalance being the IEEE definition, NEMA definition, and IEC definition [52,53,54]. The most comprehensive of the mentioned definitions is the IEC definition, which takes into account not only the magnitudes of the voltages but also their angles in the calculation. Therefore, this method will be used to calculate voltage unbalance.

The definition of voltage unbalance according to IEC is also referred to as the true definition, and the formula for the calculation is defined as the ratio of the negative U₍₂₎ to the positive U₍₁₎ phase sequence voltage as follows [55,56]:

$${VU}_{\mathrm{IEC}} (\%) ={\displaystyle \frac{U_{\left(2\right)}}{U_{\left(1\right)}}}·100$$

(1)

This definition is based on the theory of decomposing an unbalanced system into symmetrical components (positive, negative, and zero phase sequence) [57]. A three-phase unbalanced system can be decomposed into three symmetrical components using Fortescue’s method [58,59]. With the known magnitudes of voltages and their angles in the individual phases of an unbalanced three-phase system, it is possible to obtain the symmetrical components of the voltage as follows [60,61]:

$$\left[\begin{array}{c}{\dot{U}}_{\left(0\right)}\\ {\dot{U}}_{\left(1\right)}\\ {\dot{U}}_{\left(2\right)}\end{array}\right]={\displaystyle \frac{1}{3}}·\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right]·\left[\begin{array}{c}{\dot{U}}_{\mathrm{A}}\\ {\dot{U}}_{\mathrm{B}}\\ {\dot{U}}_{\mathrm{C}}\end{array}\right]$$

(2)

where ${\dot{U}}_{\left(0\right)}$, ${\dot{U}}_{\left(1\right)}$ and ${\dot{U}}_{\left(2\right)}$ are the zero, positive and negative sequence voltages, respectively, ${\dot{U}}_{\mathrm{A}}$, ${\dot{U}}_{\mathrm{B}}$ and ${\dot{U}}_{\mathrm{C}}$ are the phase voltages in phases A, B and C, respectively, $a$ is a complex operator, where it holds that $a=e^{ j 120°}$ and $a^2=e^{ j 240°}=e^{- j 120°}$.

Assessment of the Impact of PV Systems on the LV Distribution Network

Electricity is a product that, like any other product, must meet certain quality criteria. The level of electricity quality in the LV distribution system is the responsibility of the DSO [62]. The DSO is obligated to ensure that the quality of electricity at the user’s supply terminals in the public electrical network is at the required level under normal operating conditions, i.e., in accordance with the EN 50160 standard. This standard defines the power quality parameters in public electrical networks along with specified limit values. The basic voltage quality parameters listed in the standard, which can be used to monitor the impact of the operation of PV systems on the distribution network, are:

(a)

voltage magnitude—according to the EN 50160 standard, 95% of the ten-minute average effective (RMS) voltage values during any one-week period must be within the range of U_n ± 10%, and all ten-minute average effective voltage values must be within the range of U_n + 10%/−15%. The nominal voltage U_n of the public LV network in four-wire three-phase systems is 230 V between the phase and neutral conductor [44,63].

(b)

voltage unbalance—according to the EN 50160 standard, 95% of the ten-minute average effective values of the negative phase sequence of the voltage must be within 2% of the positive phase sequence of the voltage during each one-week period [44].

The EN 50160 standard defines requirements for power quality in public electrical networks, for which the operator is responsible. However, power quality in the distribution system is mainly influenced by the operation of users’ electrical equipment connected to the system. To maintain the required power quality in the system, DSOs in Slovakia have defined the maximum permissible adverse impacts that users’ electrical equipment may have on the system. If the operation of any electrical equipment exceeds the defined limits of its impact on the system, then the DSO may refuse to permit the operation of this equipment in the system.

One of the conditions for the successful connection of electrical equipment to LV distribution systems in Slovakia is that the connection of a user’s electrical equipment to the distribution network must not cause a voltage change at the point of connection of more than ±3% compared to the voltage value before the equipment was connected [64]. The formula for calculating the voltage change is as follows:

$$\mathsf{\Delta }u (\%) ={\displaystyle \frac{U_{\mathrm{after}} - U_{\mathrm{before}}}{U_{\mathrm{before}}}}·100$$

(3)

where $U_{\mathrm{before}}$ is the voltage at the point of electrical equipment connection before connection, $U_{\mathrm{after}}$ is the voltage at the point of electrical equipment connection after connection.

3. Case Study

3.1. Description of the Modeled Network

Figure 1 shows the general topology of the modeled network, which consists of four lines originating from node n1, supplied by transformer MV/LV (TR). The voltage at node n0, i.e., the voltage on the primary side of the transformer, is 22.66 kV. The individual lines are made of cables of different types and cross-sections. The parameters of the transformer and the individual lines are listed in

Table 2. Parameters of transformer.

Parameter	Sn [kVA]	U1n [kV]	U2n [kV]	uk12 [%]	Pk [kW]	P0 [kW]	Winding Connection	X/R [−]
Parameter value	400	22	0.42	4	3.9	0.4	Dyn1	10

and

Table 3. Parameters of lines.

Line	Type	R [Ω/km]	X [Ω/km]	In [A]
l1	NFA2X 4x95	0.32	0.083	240
l2	NFA2X 4x120	0.25	0.082	280
l3	NAYY-J 4x150	0.206	0.08	254
l4	NAYY-J 4x240	0.129	0.08	332

.

Each line is 600 m long and contains 12 nodes evenly distributed along the entire length of the line, i.e., every 50 m. Two consumption points are connected to each node, where a three-phase load with a power consumption of 3.464 kW and a power factor (PF) cos φ = 1 is installed. Depending on the modeled state, single-phase or three-phase PV systems are installed in the consumption points in addition to the loads.

3.2. Overview of the Modeled Scenarios

A total of four scenarios were modeled, one of which is the reference scenario (A0), where the consumption points in the distribution system do not contain PV systems, only loads. The remaining scenarios include connection of only single-phase PV systems, connection of only three-phase PV systems, and also connection of a mix of single-phase and three-phase PV systems. An overview of the modeled scenarios and their designations can be found in

Table 4. Modeled scenarios.

Modeled State	Description
A0	in the consumption points, only loads are connected (i.e., no PV systems are connected)
B1	in each consumption point, a single-phase PV system (P = 3.68 kW, cos φ = −0.97) connected to phase A is installed
B2	in each consumption point, a three-phase PV system (P = 11 kW, cos φ = −0.97) is connected
B3	at each node of the distribution system, in one consumption point a single-phase PV system (P = 3.68 kW, cos φ = −0.97) connected to phase A is installed, and in the second consumption point a three-phase PV system (P = 11 kW, cos φ = −0.97) is connected

Note 1: The power values of single-phase and three-phase PV systems correspond to the maximum permissible capacities of PV systems that can be connected to the LV distribution networks in Slovakia. Note 2: The operating power factor (cos φ) of the PV systems is chosen based on the operating rules for PV systems specified by DSOs in Slovakia.

.

3.3. Monitored Parameters and Their Limits

The monitored parameters are:

• the phase voltage magnitude at the consumption point connection to the distribution system, which shall be within the range of 230 V ± 10%, i.e., between 207 V and 253 V,
• voltage unbalance at the point of connection, defined as the percentage ratio of the negative phase sequence voltage to the positive phase sequence voltage, which shall be within the range of 0% to 2%,
• relative voltage change caused by the connection of a PV system to the distribution system, which shall not exceed ±3% at the point of connection compared to the voltage value before the PV system connection, i.e., Δu ≤ ±3%.

Besides the above-mentioned parameters, the study also examines the impact of PV system operation on the magnitudes of currents flowing through sections of individual lines and evaluates the current loading of conductors with respect to their rated current.

4. Case Study Results

4.1. Analysis of the Impact of PV Systems on Voltage Magnitude

Figure 2 shows the phase voltages at the individual nodes of the distribution system for all modeled scenarios with the marked limits within which the voltage magnitude should remain.

From Figure 2, it can be seen that the phase voltages in all phases at all nodes are within the allowable limits only in scenario A0. In scenarios B1 and B3, when single-phase PV systems (all connected to phase A) are connected to the distribution system, voltage unbalance occurs at every node of the distribution system where the voltage magnitudes in individual phases differ. According to the simulation results, after connecting the PV system at the consumption point to phase A, the voltage in phase B increases. This phenomenon is caused by the presence of asymmetry at the consumption point. In the case of asymmetry, current flows through the PEN conductor which causes a voltage drop across the PEN conductor’s impedance. As a result, the PEN conductor at the consumption point acquires a potential relative to the transformer’s grounded node. Therefore, the phase voltage at the consumption point is given by the difference between the voltage in the specific phase and the voltage of the PEN conductor at that consumption point. A graphical representation of this phenomenon is shown in Figure 3 which shows the phasor diagram of voltages at node n1-12 in scenario B1 where ${\dot{U}}_{\mathrm{A}1\text{-}12}$, ${\dot{U}}_{\mathrm{B}1\text{-}12}$ and ${\dot{U}}_{\mathrm{C}1\text{-}12}$ are the voltages in phases A, B and C, ${\dot{U}}_{\mathrm{PEN}1\text{-}12}$ is the voltage of the PEN conductor relative to the transformer node, and ${\dot{U}}_{\mathrm{A}\mathrm{PEN}1\text{-}12}$, ${\dot{U}}_{\mathrm{BPEN}1\text{-}12}$ and ${\dot{U}}_{\mathrm{CPEN}1\text{-}12}$ are the voltages of phases A, B and C relative to the PEN conductor at that node.

From Figure 2, it can also be seen that in scenarios B1 and B3, after connecting the PV system to phase A, the voltage in phase B increases to such an extent that in no node is the voltage magnitude in phase B within the allowed limits. In scenario B2, where only three-phase PV systems are installed in the distribution network, no asymmetry occurs, so voltages at all nodes have the same magnitude in all phases. However, Figure 2 also shows that operation of three-phase PV systems caused the voltage in most network nodes to rise above the permissible limit, which is a consequence of excess generation in the system.

The voltage rise is positively influenced by the conductor cross-section of the line (the larger the cross-section, the smaller the voltage increase). Under the same operating conditions, on the line with the smallest conductor cross-section (95 mm²), the voltage exceeds the allowed values in 11 out of 12 nodes, whereas on the line with the largest cross-section (240 mm²), the voltage exceeds the allowed values in only 6 out of 12 nodes.

4.2. Analysis of the Impact of PV Systems on Relative Voltage Change

Figure 4 shows the relative voltage changes in the individual phases at the network nodes in scenario B1 to B3 compared to state A0, with the marked limits.

From Figure 4, it can be seen that in scenario B1, when only single-phase PV systems are connected to the distribution network, all connected to the same phase (phase A), significant relative voltage changes occur in phases B and C, exceeding the allowed limits at all network nodes. The presence of single-phase PV systems connected to the same phase also caused relative voltage changes in phase B to exceed the limit at all network nodes in scenario B3. The voltage changes in phase C are smaller in scenario B3 compared to scenario B1 due to the lower number of single-phase PV systems connected to the network.

In scenario B2, when only three-phase PV systems are connected to the distribution network, the relative voltage changes at individual nodes are equal across all three phases. However, due to the high penetration of PV systems in the network, relative voltage changes exceed the allowed limits at most nodes.

From Figure 4, it can also be observed that the larger the conductor cross-section of the line, the smaller the relative voltage changes at the nodes along the line after connecting the PV systems.

4.3. Analysis of the Impact of PV Systems on Voltage Unbalance

Figure 5 shows the voltage unbalance values at all network nodes for each modeled scenario, with the indicated limit that the voltage unbalance should not exceed.

From Figure 5, it can be seen that in scenario B1, the cumulative effect of single-phase PV systems connected to the same phase (phase A) is so intense that the voltage unbalance exceeds the maximum permissible limit at all network nodes. In scenario B3, the resulting voltage unbalance is lower compared to scenario B1 due to the smaller number of connected single-phase PV systems, although it still exceeds the maximum allowable value in almost all network nodes. In scenario B2, where only three-phase PV systems are installed in the distribution network, no unbalance occurs, and thus the voltage unbalance value is zero in all network nodes. From Figure 5, it also follows that the value of voltage unbalance is positively affected by the conductor cross-section of the line. The larger the cross-section of the line conductors, the smaller the voltage unbalance that arises at the nodes along the line.

4.4. Analysis of the Impact of PV Systems on Current Loading of Lines

Operation of PV systems also affects the currents flowing through sections of individual lines. The magnitudes of currents flowing through the sections of the modeled network lines are shown in Figure 6.

From Figure 6, it can be seen that the highest number of overloaded sections in the distribution system occurs in scenario B1. This scenario is characterized by voltage unbalance, which causes currents to flow through the PEN conductors of individual lines. Since the voltage unbalance in scenario B1 reaches significant values, the currents flowing through the PEN conductors in some sections reach levels that exceed their current-carrying capacity. In scenario B3, where only half the number of single-phase PV systems is installed in the distribution network compared to scenario B1, overloading of the PEN conductors does not occur. The connection of single-phase PV systems to phase A in scenarios B1 and B3 affects not only the current flowing through the PEN conductor, but also the magnitudes of currents flowing through the individual phases. The data obtained indicate that the operation of a PV system has the greatest impact on the current of the phase to which the PV system is connected. From the data for scenarios B1 and B3 shown in Figure 6, it can be seen that in both cases, due to the presence of single-phase PV systems connected to phase A, the conductors for phase A become overloaded in some line sections, especially those at the beginnings of the lines.

In scenario B2, where only three-phase PV systems are present in the distribution network, no currents flow through the PEN conductors, and the magnitudes of the sectional currents are the same in all phases. In scenario B2, only a single section in the entire network experiences an overload problem, specifically the section at the beginning of the line with the smallest conductor cross-section.

5. Options for Mitigating the Impact of PV Systems on the Distribution System

This study also includes a proposal of measures to mitigate the negative effects caused by the operation of PV systems on the monitored parameters in the distribution network. The proposal of measures is implemented for scenario B1, where only single-phase PV systems are connected to the distribution network, and scenario B2, where only three-phase PV systems are connected to the network. The proposal of measures for scenario B3 is not carried out, as the negative effects of single-phase and three-phase PV systems in this scenario can be mitigated by combining the measures for scenarios B1 and B2.

5.1. Proposed Measures for Scenario B1

Table 5. Level of PV systems impact in scenario B1 before the application of measures.

Line	U = 230 V ± 10%	VUIEC ≤ 2%	Δu ≤ ±3%	Current Loading
l1	✖ (298 V)	✖ (7.61%)	✖ (26.6%)	✖ (394 A)
l2	✖ (293 V)	✖ (6.78%)	✖ (23.2%)	✖ (388 A)
l3	✖ (290 V)	✖ (6.28%)	✖ (21.1%)	✖ (385 A)
l4	✖ (286 V)	✖ (5.54%)	✖ (17.9%)	✖ (379 A)

Note: The specific values of the monitored parameters presented in the table represent the highest values of the respective parameters on the line before the implementation of the measures.

expresses the level of impact of single-phase PV systems on the monitored parameters in scenario B1 before the application of measures. If the assessed parameter is outside the allowable range in at least one phase at any node or section on the given line, then the table shows the symbol ✖. If the level of impact is within permissible limits, the symbol ✔ is shown in the table.

5.1.1. Symmetrization of Single-Phase PV System Connections

Since scenario B1 is characterized by a high level of voltage unbalance (a consequence of connecting all single-phase PV systems to only one phase), the first proposed measure is the even redistribution of single-phase PV system connections across all three phases. The redistribution of single-phase PV system connections is carried out as follows:

• single-phase PV systems at nodes nx-1, nx-4, nx-7, and nx-10 are connected to phase A,
• single-phase PV systems at nodes nx-2, nx-5, nx-8, and nx-11 are connected to phase B,
• single-phase PV systems at nodes nx-3, nx-6, nx-9, and nx-12 are connected to phase C.

Table 6. Level of impact of single-phase PV systems after symmetrization.

Line	U = 230 V ± 10%	VUIEC ≤ 2%	Δu ≤ ±3%	Current Loading
l1	✔ (from 298 V to 249 V)	✔ (from 7.61% to 0.48%)	✖ (from 26.6% to 6.0%)	✔ (from 394 A to 39 A)
l2	✔ (from 293 V to 249 V)	✔ (from 6.78% to 0.38%)	✖ (from 23.2% to 4.5%)	✔ (from 388 A to 39 A)
l3	✔ (from 290 V to 249 V)	✔ (from 6.28% to 0.32%)	✖ (from 21.1% to 3.7%)	✔ (from 385 A to 39 A)
l4	✔ (from 286 V to 248 V)	✔ (from 5.54% to 0.22%)	✔ (from 17.9% to 2.2%)	✔ (from 379 A to 39 A)

Note: The specific values of the monitored parameters presented in the table represent the highest values of the respective parameters on the line before and after the implementation of the measures.

shows that by evenly redistributing single-phase PV systems across all three phases, the impact of the PV systems is limited to a level where all assessed parameters, except for the relative voltage changes on lines l1 to l3, remain within permissible limits. After symmetrization, the relative voltage changes at all nodes along the lines are within the allowable range only for line l4. Since the values of relative voltage changes on lines l1 to l3 still exceed the permissible limit, it is necessary to adopt additional measures alongside the symmetrization. Possible supplementary measures include:

• changing the mode of operation of the PV systems (adjusting the PF),
• reducing the number of consumption points with installed PV systems connected to the individual lines.

Combination of Connection Symmetrization and PF Adjustment of Single-Phase PV Systems

In the individual modeled scenarios, it is assumed that the PV systems operate with a PF of cos φ = −0.97, meaning they draw reactive power from the grid. By reducing the PF, it is possible to positively influence the relative voltage changes at the nodes of the individual lines. To ensure that on the line with the smallest cross-section, i.e., line l1, the relative voltage changes at all nodes remain within the required level, all PV systems on this line need to operate with a PF of cos φ = −0.74.

The larger the cross-section of the line, the smaller the reduction in the PF of the PV systems connected to that line is needed to achieve relative voltage changes within permissible limits at all nodes. As shown in Table 6, it is not necessary to reduce the PF of the PV systems connected to line l4, the line with the largest cross-section, since symmetrization alone is sufficient to limit the impact of the PV systems connected to this line to the desired level. This implies that an additional complementary measure to the symmetrization of PV system connections is the appropriate selection of the line cross-section.

However, reducing the PF is limited by the inverter’s PQ diagram and the fact that lowering the PF increases the current flowing through the lines, which leads to higher losses and may cause conductor overloads.

Changing the PF alone, without symmetrizing the connection of single-phase PV systems across the individual lines, cannot limit the impact of PV systems on the monitored parameters to the required level in scenario B1.

Combination of Symmetrization of Single-Phase PV System Connections and Reduction in the Number of Consumption Points with PV Systems Connected to the Lines

Reduction in the relative voltage changes on lines l1 to l3, which still exceed permissible values after the symmetrization of PV system connections, can also be achieved by reducing the number of consumption points with installed PV systems connected to these lines. To ensure that the relative voltage changes at all nodes on line l1 remain within the allowable range, it is necessary to disconnect sections l1–9 to l1–12, which results in reducing the number of installed PV systems on this line from 24 to 16. To reduce the relative voltage changes at all nodes on lines l2 and l3 to the required level, it is necessary to disconnect the last three sections of these lines, thereby reducing the number of PV systems connected to lines l2 and l3 from 24 to 18.

Without symmetrizing the connection of single-phase PV systems across the individual lines, it is not possible to reduce the impact of PV systems on the monitored parameters to the required level, even with a drastic reduction in the number of consumption points with installed PV systems connected to the lines (from 24 to 4).

5.1.2. Limiting the Power Rating of Single-Phase PV Systems

It is also possible to limit the impact of single-phase PV systems on the distribution network by reducing their power. The highest equal power of all PV systems connected to the modeled network in scenario B1, at which the impact of the PV systems remains within the required limits on all lines, is 0.4 kW. The level of impact of single-phase PV systems with a power rating of 0.4 kW on the distribution network in scenario B1 is summarized in

Table 7. Level of impact of single-phase PV systems with a power rating of 0.4 kW.

Line	U = 230 V ± 10%	VUIEC ≤ 2%	Δu ≤ ±3%	Current Loading
l1	✔ (250 V)	✔ (0.9%)	✔ (2.8%)	✔ (117 A)
l2	✔ (249 V)	✔ (0.8%)	✔ (2.5%)	✔ (116 A)
l3	✔ (249 V)	✔ (0.7%)	✔ (2.3%)	✔ (116 A)
l4	✔ (250 V)	✔ (0.6%)	✔ (1.9%)	✔ (115 A)

Note: The specific values of the monitored parameters presented in the table represent the highest values of the respective parameters on the line after the implementation of the measures.

.

5.2. Proposed Measures for Scenario B2

Table 8. Level of PV systems impact in scenario B2 before the application of measures.

Line	U = 230 V ± 10%	VUIEC ≤ 2%	Δu ≤ ±3%	Current Loading
l1	✖ (268 V)	✔	✖ (13.8%)	✖ (246 A)
l2	✖ (263 V)	✔	✖ (10.4%)	✔ (249 A)
l3	✖ (260 V)	✔	✖ (8.4%)	✔ (251 A)
l4	✖ (254 V)	✔	✖ (4.7%)	✔ (255 A)

Note: The specific values of the monitored parameters presented in the table represent the highest values of the respective parameters on the line before the implementation of the measures.

expresses the level of impact of PV systems on the distribution network in scenario B2 before the application of measures.

Since only three-phase PV systems are connected to the distribution network in scenario B2, which do not cause an increase in voltage unbalance in the network, the voltage unbalance values at all nodes on all lines are within the required limits. Moreover, the currents flowing through lines l2 to l4 are lower than the maximum current-carrying capacity of the conductors of these lines, meaning their operation is acceptable in terms of current load. However, other monitored parameters on lines l1 to l4 exceed the maximum allowable values, and line l1 also experiences current overloading.

5.2.1. PF Adjustment of Three-Phase PV Systems

Similarly to single-phase PV systems in scenario B1, three-phase PV systems can also influence the voltage magnitude and relative voltage changes at the nodes along the lines by adjusting their PF.

Table 9. Level of impact of three-phase PV systems after PF adjustment.

Line	U = 230 V ± 10%	VUIEC ≤ 2%	Δu ≤ ±3%	Current Loading
l1	✔ (from 268 V to 252 V)	✔	✖ (from 13.8% to 7.2%)	✖ (from 246 A to 342 A)
l2	✔ (from 263 V to 248 V)	✔	✖ (from 10.4% to 3.9%)	✖ (from 249 A to 347 A)
l3	✔ (from 260 V to 245 V)	✔	✖ (from 8.4% to 4.1%)	✖ (from 251 A to 350 A)
l4	✔ (from 254 V to 239 V)	✔	✖ (from 4.7% to 4.6%)	✖ (from 255 A to 355 A)

Note: The specific values of the monitored parameters presented in the table represent the highest values of the respective parameters on the line before and after the implementation of the measures.

shows how the monitored parameters are affected by changing the PV systems’ PF from cos φ = −0.97 to cos φ = −0.83, which is the change required to reduce the voltage magnitude at all nodes of the modeled network below the limit value of 253 V.

From Table 9, it can be seen that although this change in PF results in a decrease in voltage magnitudes at all network nodes to the desired level, the relative voltage changes still exceed the allowable limits, and moreover, this change in PF also leads to an increase in the currents flowing through the lines. When all PV systems in the modeled network operate with a PF of cos φ = −0.83, all four lines become overloaded.

5.2.2. Reduction in the Number of Consumption Points with PV Systems Connected to the Lines

Limiting the negative impact of PV systems on the monitored parameters can be achieved by reducing the number of consumption points with installed PV systems connected to the individual lines.

Table 10. Level of impact of three-phase PV systems after reduction in the number of consumption points with PV systems connected to the lines.

Line	U = 230 V ± 10%	VUIEC ≤ 2%	Δu ≤ ±3%	Current Loading
l1	✔ (from 268 V to 253 V)	✔	✔ (from 13.8% to 2.6%)	✔ (106 A)
l2	✔ (from 263 V to 252 V)	✔	✔ (from 10.4% to 2.0%)	✔ (107 A)
l3	✔ (from 260 V to 252 V)	✔	✔ (from 8.4% to 2.2%)	✔ (128 A)
l4	✔ (from 254 V to 253 V)	✔	✔ (from 4.7% to 2.8%)	✔ (191 A)

Note: The specific values of the monitored parameters presented in the table represent the highest values of the respective parameters on the line before and after the implementation of the measures.

provides information about the impacts of PV systems on the distribution network in scenario B2 after sections l1–6 to l1–12 were disconnected on line l1, sections l2–6 to l2–12 on line l2, sections l3–7 to l3–12 on line l3, and sections l4–10 to l4–12 on line l4. The number of disconnected sections on each line represents the minimum number of sections that must be disconnected on that line to keep the monitored parameters within the required range for that line.

Data from Table 10 indicate that the larger the conductor cross-section of the line, the fewer sections need to be disconnected, which allows more consumption points with PV systems to remain connected to that line. For comparison, after the implementation of the measure, 10 consumption points with PV systems remain connected on the line with the smallest conductor cross-section (line l1), while 18 consumption points with PV systems remain connected on the line with the largest conductor cross-section (line l4) (originally, both lines had 24 consumption points with PV systems connected).

5.2.3. Limiting the Power Rating of Three-Phase PV Systems

Limiting the negative impact of three-phase PV systems on the distribution network is possible, similarly to single-phase PV systems, by reducing their power ratings. The maximum equal power of all three-phase PV systems in scenario B2, at which it is possible to ensure that all monitored parameters on all lines remain within allowable limits, is 2 kW. Level of impact of three-phase PV systems with a power rating of 2 kW on the distribution network in scenario B2 is shown in

Table 11. Level of impact of three-phase PV systems with a power rating of 2 kW.

Line	U = 230 V ± 10%	VUIEC ≤ 2%	Δu ≤ ±3%	Current Loading
l1	✔ (248 V)	✔	✔ (2.9%)	✔ (51 A)
l2	✔ (247 V)	✔	✔ (2.2%)	✔ (51 A)
l3	✔ (247 V)	✔	✔ (1.8%)	✔ (50 A)
l4	✔ (247 V)	✔	✔ (1.1%)	✔ (50 A)

Note: The specific values of the monitored parameters presented in the table represent the highest values of the respective parameters on the line after the implementation of the measures.

.

The chosen power of 2 kW is limited by line l1, which has the smallest conductor cross-section. However, the larger the conductor cross-section of the line, the higher the power of three-phase PV systems that can be connected to it while maintaining permissible impacts on the monitored parameters. For example, on the line with the largest conductor cross-section, i.e., line l4, it is possible to connect three-phase PV systems with a power of 6.2 kW, which is more than three times the power compared to line l1.

6. Conclusions

The aim of this study was to clearly define the impact of operating single-phase and three-phase PV systems on the low-voltage distribution network, and to propose technical measures to mitigate these impacts and enable the large-scale integration of PV systems into distribution networks.

The simulation results show that if every consumption point in the distribution system contains a PV system, their cumulative effect may cause the power quality in the distribution system to fall below the required level, which could threaten the reliability and safety of electricity supply. The most affected power quality parameters due to the operation of PV systems include voltage magnitude and voltage unbalance. The increase in voltage unbalance in the distribution network is caused by single-phase PV systems whose connections are unevenly distributed among the three phases of the distribution network. An interesting finding from the analysis is that connecting a single-phase PV system to phase A of a consumption point with a symmetrical load causes an increase in voltage on phase B.

To prevent the negative effects of both single-phase and three-phase PV systems on voltage magnitude, voltage unbalance, and currents flowing through distribution network lines, the study also includes the proposal and verification of measures to limit the impact of PV systems on the distribution network. The results show that although the operation of PV systems has a negative impact on the distribution network, this impact can be reduced by adopting appropriate measures. Effective measures include:

• selection of an appropriate conductor cross-section for the line (the larger the cross-section, the smaller the impact of PV system operation on the monitored power quality parameters),
• limiting the number of consumption points with PV systems connected to a single line,
• adjustment of the reactive power of PV systems (operating PV systems with an appropriate power factor),
• limiting the power output of PV systems,
• for single-phase PV systems, implementation of symmetrical connection of PV systems to all three phases of the distribution network.

By suitably combining these measures, the negative impacts of PV systems can be further reduced.

The results also indicate that, for the same impact on the distribution network, it is possible to connect approximately five times greater power through three-phase PV systems compared to single-phase PV systems. From this, it follows that wherever technically feasible, three-phase PV system connections should be preferred over single-phase connections in order to minimize the impact on the network.

The conclusions of this study can be especially valuable for distribution system operators, who may, based on the findings, modify the current way of operating distribution networks and adapt it to the growing trend of decentralized generation. The proposed technical measures to eliminate the impact of PV systems on distribution networks can be implemented immediately by changing the conditions for connecting and operating PV systems in distribution networks or by adjusting the planning of future distribution system development.

Although the proposed measures are effective, they can be considered passive, i.e., based on a “fit and forget” principle. Given the increasing dynamics in low-voltage networks, further research should therefore focus on more dynamic solutions to mitigate the negative impact of decentralized generation on the network, which can appropriately complement the proposed passive measures. Future research should therefore focus, for example, on the development of active network management strategies or the integration of intelligent inverters that enable dynamic response to voltage quality issues at the point of connection of the consumption point to the network.

The authors will focus in future work on creating a distribution network model that will be an accurate replica of a real distribution network in one of the villages in Slovakia. This network will include the real placement of consumption points within the network, the real method of connecting the consumption point to the system in terms of phase number and consumption size, and the real network structure. Various active measures will then be tested on this network, such as the use of battery storage or compensation SVC devices. The authors will also focus on comparing the cost-effectiveness of passive and active measures, which will determine the combination of solutions for the economically and technically optimal operation and development of low-voltage distribution networks with integrated distributed energy resources.