CoChat
Sign Up
Cited by 26Optimal Power Flow DistributionPower Quality and HarmonicsThermal Analysis in Power Transmission

Stochastic Approach for Increasing the PV Hosting Capacity of a Low-Voltage Distribution Network

Open access
Bendík, Jozef, Cenký, Matej, Cintula, Boris, Beláń, Anton, Eleschová, Žaneta, Janiga, Peter·2022·Processes
DOI 10.3390/pr11010009
Open this paper in CoChat — free accountOpen PDF

Abstract

In recent years, the emerging fear of an energy crisis in central Europe has caused an increased demand for distributed energy resources (DER), especially small photovoltaic rooftop installations up to 10 kWp. From a technical point of view, distributed PV in low-voltage networks is associated with the risk of power quality violation, overvoltage, voltage unbalance, harmonics, and violation of the thermal limit of phase conductors, neutral conductors, and transformers. Distribution system operators (DSO) are currently in a position to determine the amount of installed PV power for which reliable and safe network operation is ensured, also known as the photovoltaic hosting capacity (PVHC). The presented study describes a stochastic methodology for PVHC estimation and uses it to analyze a typical LV rural network in the Slovak Republic. Detailed and precise calculations are performed on the 4-wire LV model with accurate results. In this study, we, thus, profoundly analyze the problems with voltage violation, unbalanced voltage energy losses, and the thermal loading effect of increasing PV penetration. The results show that overvoltage events are the main factor limiting the PVHC in LV systems. This conclusion is in accordance with the experience of the DSO in the Slovak and Czech Republic. Subsequently, the study focuses on the possibilities of increasing PVHC using those tools typically available for DSO, such as changes in PV inverter power factors and no-load tap changer transformers. The results are compared with those derived from similar analyses, but we ultimately find that the proposed solution is problematic due to the high variability of approaches and boundary conditions. In conclusion, the paper discusses the issue of the acceptable risk of overvoltage violation in the context of PVHC and lowering losses in LV networks.

AI snapshot

Written from the paper’s full text.

TL;DR

This paper develops a stochastic PV hosting capacity (PVHC) methodology for a real rural Slovak low-voltage 4-wire network and finds overvoltage is the limiting factor. It estimates base PVHC at 13.6% (79.9 kW) under 1% overvoltage risk, rising to 21.4% with PV power factor 0.95 or 31.5% with a −2.5% DETC tap.

Key findings

  • Overvoltage was the main PVHC limitation. In the basic scenario V0, PVHC with 1% overvoltage tolerance was 13.6%, equal to 79.9 kW of small PV systems, and implementing this PV reduced line and transformer losses by 8.2% on average. Thermal limits and other quantities did not reach their limits; voltage-unbalance violation probability was below 0.1%.
  • Absorbing reactive power increased PVHC: PF 0.95 gave 21.4% PVHC (127.7 kW, +57.35% over V0), PF 0.9 gave 26.4% (155 kW), PF 0.85 gave 33.3% (195.7 kW), and PF 0.8 gave 43.2% (253.4 kW, +217.65%). At DPI 0.3, losses decreased by 9.04% on average for PF 0.95 versus 15.6% in V0, while PF 0.80 increased losses by 1.9% on average.
  • Changing the DETC tap from −5% to −2.5% increased PVHC to 31.5% (185.1 kW, +131.62% over V0) and reduced losses by 15.5% on average. Tap 0% gave PVHC 0 due to undervoltages below 0.85 Un. With a 5% overvoltage tolerance, PVHC values were higher, e.g., 24.4% for PF 1 and 50.6% for tap −2.5%.
  • Increasing DPI did not significantly influence voltage unbalance αVUF; the probability of limit violation was below 0.1%, and increasing DPI even lowered αVUF due to random single-phase PV placement.

Methods

  • Stochastic PVHC model: probabilistic power flow for increasing DER penetration index (DPI), defined as the energy ratio of PV production to PoC consumption, varied from 0 to 0.5 in steps of 0.1. Each DPI used multiple model variations generated by Monte Carlo for PV position, size, type, and phase; calculations used OpenDSS with a COM interface and Python, with steady-state time-series calculations for one year at 1-h steps.
  • Case study: real rural LV 0.4 kV Slovak network, 4-wire, with 139 PoC in eight tariff categories, 163 overhead lines plus two cable lines, and a 22/0.4 kV 250 kVA DETC transformer with ±5% tap regulation in 2.5% steps and default tap −5%. Loads had yearly shapes, Pmax split among phases at 2:3:5, and random lagging PF 0.9–1; PV systems ranged from 0.2 to 10 kW per PoC, with meteorological measurements, maximum measured irradiation 906 W/m², and calculated yearly production of 1080 kWh per 1 kWp.
  • PVHC was calculated by comparing cumulative distribution functions of voltage violation from probabilistic power flow against EN-50160-based limits: max phase-neutral voltage 253 V with 1% overvoltage probability, min −207 V with 5% probability, −195.5 V with 0% probability, and voltage unbalance 2% with 5% probability. Thermal limits were deterministic and not violated; harmonics were excluded.

Limitations

  • The paper states that harmonics are not included due to lack of information; the methodology’s limitation is only the quality of the data on which the model is based; comparison with other studies is problematic due to high variability of approaches and boundary conditions; there is no consensus on acceptable risk; DSOs often do not control inverter PF and cannot order small customers to change PF; DETC tap cannot be changed while energized, so it remains static most of the year; further tap increase causes permanent undervoltages below 0.85 Un.
  • The paper states future improvements: include all deterministic parameters as probabilities defined by mean and standard deviation for specific time steps, use a smaller time step such as 10 min, increase the number of model variations per probabilistic power flow, and implement parallel processing due to current computational ability and code effectiveness.
  • Evident from the text: results are for one rural Slovak LV network and one year of hourly simulation; scenario V3 for BESS is listed but no results are reported; harmonics and supraharmonics are not modeled, and supraharmonic distortion limits have not yet been established.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.3390/pr11010009

Cites

56 of 56 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

11 of 45 cited sources checked · 2 supported · 0 flagged · accuracy not yet measured

  • Premisecitation

    Traditional deterministic models are not reliable for modeling systems with a high level of unpredictability.

    “Traditional deterministic models are not reliable for modeling systems with a high level of unpredictability.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [26] Zain ul Abideen, M., Ellabban, O., and Al-Fagih, L. (2020). A Review of the Tools and Methods for Distribution Networks’ Hosting Capacity Calculation. Energies, 13. source

      Section 3.1.1 (Constant Generation Method; page unavailable) says that this method is simplistic, can only estimate hosting capacity, and may underestimate it under worst-case assumptions. Section 3.2 (Stochastic Method; page unavailable) explains that stochastic techniques account for unknown variables in DER integration. These passages support limitations of one deterministic approach in distribution-network analysis, but not the broader assertion that traditional deterministic models are unreliable for all highly unpredictable systems. (LLM, conf=0.85)

      Experimental — accuracy not yet measured
  • Premisecitation

    The probability limitations chosen for analysis are significantly more conservative than the commonly used limit.

    “The probability limitations chosen for analysis are significantly more conservative than the commonly used limit.”
    Quote in the paperSubstantial claim1 of 4 sources checked
    • cites [41] Klonari, V., Toubeau, J.F., Lobry, J., and Vallee, F. (2022, January 27–29). Photovoltaic Integration in Smart City Power Distribution— A Probabilistic Photovoltaic Hosting Capacity Assessment based on Smart Metering Data. Proceedings of the 5th International Conference on Smart Cities and Green ICT Systems-SMARTGREENS, Rome, Italy.

      Not checked in the free run.

    • cites [42] Koirala, 2022, Hosting capacity of photovoltaic systems in low voltage distribution systems: A benchmark of deterministic and stochastic approaches, Renew. Sustain. Energy Rev. source
    • cites [60] Dubey, 2017, On Estimation and Sensitivity Analysis of Distribution Circuit’s Photovoltaic Hosting Capacity, IEEE Trans. Power Syst. source
    • cites [61] Navarro, A., Ochoa, L.F., and Randles, D. (2013, January 21–25). Monte Carlo-based assessment of PV impacts on real UK low voltage networks. Proceedings of the 2013 IEEE Power & Energy Society General Meeting, Vancouver, BC, Canada. source

      Section C (Impact Assessment; page not provided) describes the EN50160 voltage criterion, including its 95% requirement, and Section IV reports probabilities of voltage problems. Neither section says that the probability limits chosen for the analysis are more conservative than a commonly used limit. Searches for conservative probability thresholds and a comparison with the 95% criterion found no such statement in our copy. (LLM, conf=0.73)

      Experimental — accuracy not yet measured
  • Premisecitation

    Stochastic approaches combining probabilistic definitions of unpredictable parameters and the Monte Carlo method on unknown parameters must be applied to problems with a high level of unpredictability.

    “Zain et al. have shown that stochastic approaches combining the probabilistic definitions of unpredictable parameters and the Monte Carlo method on unknown parameters must be applied to these problems [26].”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [26] Zain ul Abideen, M., Ellabban, O., and Al-Fagih, L. (2020). A Review of the Tools and Methods for Distribution Networks’ Hosting Capacity Calculation. Energies, 13. source

      Section 3.2, “Stochastic Method” (page not provided), describes using probabilistic power flow to account for unknown variables in distribution-network hosting-capacity calculations and identifies Monte Carlo simulation as the most common way to generate random scenarios. It says using stochastic techniques is reasonable, not that combining them with Monte Carlo is mandatory for all highly unpredictable problems; it also lists other methods. (LLM, conf=0.87)

      Experimental — accuracy not yet measured
  • Premisecitation

    In all examined studies, the permissible violation probability was 5% or more.

    “In the criteria of all examined studies, the permissible violation probability was 5% or more [41,42,60,61].”
    Quote in the paperSubstantial claim1 of 4 sources checked
    • cites [41] Klonari, V., Toubeau, J.F., Lobry, J., and Vallee, F. (2022, January 27–29). Photovoltaic Integration in Smart City Power Distribution— A Probabilistic Photovoltaic Hosting Capacity Assessment based on Smart Metering Data. Proceedings of the 5th International Conference on Smart Cities and Green ICT Systems-SMARTGREENS, Rome, Italy.

      Not checked in the free run.

    • cites [42] Koirala, 2022, Hosting capacity of photovoltaic systems in low voltage distribution systems: A benchmark of deterministic and stochastic approaches, Renew. Sustain. Energy Rev. source
    • cites [60] Dubey, 2017, On Estimation and Sensitivity Analysis of Distribution Circuit’s Photovoltaic Hosting Capacity, IEEE Trans. Power Syst. source
    • cites [61] Navarro, A., Ochoa, L.F., and Randles, D. (2013, January 21–25). Monte Carlo-based assessment of PV impacts on real UK low voltage networks. Proceedings of the 2013 IEEE Power & Energy Society General Meeting, Vancouver, BC, Canada. source

      The Impact Assessment section states that EN50160 requires voltage to remain within 0.9–1.1 p.u. for at least 95% of weekly measurements, allowing up to 5% outside that range. That is a tolerance for measurements over time, not an explicit permissible probability of violations across Monte Carlo simulations; the section also specifies limits that must never be exceeded. This paper cannot establish the criterion used by the other cited studies. (LLM, conf=0.82)

      Experimental — accuracy not yet measured
  • Findingreasoning

    In all cases, increasing PV penetration does not significantly influence voltage unbalance α VUF in the analyzed system.

    “In all cases, increasing PV penetration does not significantly influence voltage to unbalance α VUF in the analyzed system.”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim. 27
  • May combine two claims. 20

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    PVHC is extremely variable and depends not only on the aforementioned factors but also on the definitions and limiting factors.

    “These extensive reviews concluded that PVHC is extremely variable and depends not only on the aforementioned factors but also on the definitions and limiting factors.”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites [31] Fatima, S., Püvi, V., and Lehtonen, M. (2020). Review on the PV Hosting Capacity in Distribution Networks. Energies, 13. source
    • cites [42] Koirala, 2022, Hosting capacity of photovoltaic systems in low voltage distribution systems: A benchmark of deterministic and stochastic approaches, Renew. Sustain. Energy Rev. source
    • cites [62] Fatima, S., Püvi, V., Arshad, A., Pourakbari-Kasmaei, M., and Lehtonen, M. (2021). Comparison of Economical and Technical Photovoltaic Hosting Capacity Limits in Distribution Networks. Energies, 14. source

  • Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

    Premisecitation

    Improvement of the PVHC has a regional character and cannot be solved with a set of universal precautions; a detailed simulation should be carried out for each case.

    “Improvement of the PHVC has always had a regional character and, therefore, cannot be solved with a set of universal precautions.Instead, a detailed simulation should be carried out for each case [50,51].”
    Quote in the paperNot a substantial claim2 of 2 sources checked
    • cites [50] Hashemi, 2017, Methods and strategies for overvoltage prevention in low voltage distribution systems with PV, IET Renew. Power Gener. source

      The indexed Abstract discusses methods for increasing PV hosting capacity, but does not say that improvements are region-specific, that universal precautions cannot work, or that each case requires detailed simulation. Searches for those terms and for case-specific network analysis found no passage addressing the claim. (LLM, conf=0.73)

      Experimental — accuracy not yet measured
    • cites [51] Zhang, D., Jiang, S., Liu, J., Wang, L., Chen, Y., Xiao, Y., Jiao, S., Xie, Y., Zhang, Y., and Li, M. (2022). Stochastic Optimization Operation of the Integrated Energy System Based on a Novel Scenario Generation Method. Processes, 10. source

      Section 4.3 describes simulations of stochastic operation in an integrated energy microgrid, and Section 4 identifies the particular microgrid studied. Neither passage addresses whether improving photovoltaic hosting capacity is region-specific, whether universal precautions are inadequate, or whether every case requires detailed simulation. Searches for hosting capacity and region-specific simulation found no passage making those points. (LLM, conf=0.76)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    A 2016 study on an LV network in Denmark estimated 40% PVHC.

    “A study in 2016 [67] performed on an LV network in Denmark with estimation of 40% PVHC.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [67] Hu, 2016, Coordinated voltage control of a decoupled three-phase on-load tap changer transformer and photovoltaic inverters for managing unbalanced networks, Electr. Power Syst. Res. source

  • May combine two claims.

    Premisecitation

    Reactive power control by PV is a cost-effective solution, but it has limited potential for increasing the PVHC.

    “Reactive power control by PV is a cost-effective solution, but it has limited potential for increasing the PVHC [53,54].”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites [53] Pecenak, Z.K., Kleissl, J., and Disfani, V.R. (2017, January 16–20). Smart inverter impacts on california distribution feeders with increasing pv penetration: A case study. Proceedings of the 2017 IEEE Power & Energy Society General Meeting, Chicago, IL, USA. source

      The Maximum Voltage section reports that Volt/VAr control mitigated overvoltage at 150% PV penetration on the studied feeder, but violations remained at higher penetration because the inverters lacked sufficient reactive-power capacity. This supports a limit on increasing hosting capacity in that setting. The paper does not establish that reactive-power control is cost-effective; its Introduction instead notes the high cost of retrofitting existing systems. Page numbers are unavailable in our copy. (LLM, conf=0.88)

      Experimental — accuracy not yet measured
    • cites [54] Dvoracek, J., Klusacek, J., Drapela, J., and Topolánek, D. (2022, January 8–10). Dispatch Reactive Power Sharing Concept for Power Generating Plants in Medium Voltage Distribution Systems. Proceedings of the 2022 22nd International Scientific Conference on Electric Power Engineering (EPE), Kouty nad Desnou, Czech Republic. source

  • May combine two claims.

    Premisecitation

    Increasing PV in LV networks does not always lead to increased conductor currents and TR loading; if the PoC consumes most of the generated power, line and transformer losses decrease.

    “Increasing PV in LV networks does not always lead to increased conductor currents and TR loading.If the PoC is capable of consuming most of the generated power, then the opposite is true, and line and transformer losses decrease [30,47].”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites [30] Ismael, 2019, State-of-the-art of hosting capacity in modern power systems with distributed generation, Renew. Energy source

      Section 3.2, “Overloading and power loss problems” (page unavailable), says DG connected close to the load can reduce feeder losses and the loading of feeding transformers. It supports the claim that more local generation need not increase loading, but does not specifically establish that transformer losses decrease when the point of connection consumes most of the PV output. (LLM, conf=0.84)

      Experimental — accuracy not yet measured
    • cites [47] Bendík, J., Cenký, M., Eleschová, Z., Beláň, A., Cintula, B., and Janiga, P. (2022, January 8–10). Stochastic Concept for Modeling Distributed Energy Resources in Power Systems. Proceedings of the 2022 22nd International Scientific Conference on Electric Power Engineering (EPE), Kouty nad Desnou, Czech Republic. source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Centralized BESS are an efficient means to improve the PVHC in remote areas.

    “At the same time, centralized BESS are an efficient means to improve the PVHC in remote areas [55].”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [55] Gong, Q., Fang, J., Qiao, H., Liu, D., Tan, S., Zhang, H., and He, H. (2019). Optimal Allocation of Energy Storage System Considering Price-Based Demand Response and Dynamic Characteristics of VRB in Wind-PV-ES Hybrid Microgrid. Processes, 7. source

      The Introduction says energy storage can improve clean-energy consumption, and the Abstract describes a BESS configuration intended to maximize absorption of photovoltaic and wind power. The paper does not establish improved photovoltaic hosting capacity specifically, nor does it assess centralized BESS in remote areas. (LLM, conf=0.82)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Findingown data

    Thermal limits of conductors and TR were considered in the analysis; their values are strictly deterministic and have no violation of line ratings, and the TR power limit (250 kVA) is permissible.

    “Thermal limits of conductors and TR were also considered in the analysis.However, their values are strictly deterministic and have no violation of line ratings, Table 1, and the TR power limit (250 kVA) is permissible.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    In scenario V2, increasing DPI does not significantly influence α VUF, the probability of limit violation was below 0.1%, and currents in lines and TR loading did not reach their limits.

    “Similarly, as in the V0 scenario, increasing the DPI does not significantly influence α VUF .The probability of limit violation was below 0.1%.Currents in lines and TR loading did not reach their limits.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    In scenario V1, the biggest problem is overvoltage; the lower voltage limit was not exceeded, increased DPI does not significantly influence α VUF, the probability of limit violation was below 0.1%, and currents and TR loading did not reach their limitations.

    “From the results, we can state that the biggest problem in scenario V1 is overvoltage, Figure 11.The lower voltage limit was not exceeded in any calculation.Similarly, as in the V0 scenario, increased DPI does not significantly influence α VUF .The probability of limit violation was below 0.1%.The currents in lines and TR loading did not reach their limitations.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In scenario V2, the limitations are overvoltage and undervoltage below 0.85 U n.

    “From the results, we can state that the limitations in scenario V2 are overvoltage, Figure 13, and undervoltage below 0.85 U n , Table 3.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    The 2% voltage unbalance limit was violated in every case in scenario V0, but the probability of limit violation was below 0.1%, and increasing DPI even lowers the probability.

    “The 2% limit was violated in every case, but this is a result of load distribution.The probability of limit violation was below 0.1%, and increasing DPI even lowers the probability.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The tap position had negligible influence on total power loss compared with V0; the reduction in power losses remains at 15.5% on average for DPI 0.3.

    “The tap position had negligible influence on the total power loss compared with the V0 scenario.The reduction in power losses remains at 15.5% on average for DPI 0.3.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    In the particular network of scenario V0, the biggest problem is overvoltage; all other quantities did not reach their limits, and currents remained below the maximum current carrying capacity of the lines.

    “From the results, we can state that the biggest problem in this particular network is overvoltage.All other quantities did not reach their limits.Although there has been a significant increase in currents, the values are still below the maximum current carrying capacity of the lines.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Increasing PV penetration causes significant reverse power flow, but the TR power limit was not violated even for high DPI.

    “Increasing PV penetration causes significant reverse power flow.However, the TR power limit was not violated even for high DPI.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    In scenario V1, PF helps to increase PVHC significantly, at the price of decreased PV efficiency and increased losses.

    “In our study, PF helps to increase PVHC (Table 2), significantly.The price for this increase is a decrease in PV efficiency and increased losses, Figure 12.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In tap position -2.5%, there are significant undervoltages below 1.1 U n, but their probability was lower than 0.01%.

    “In this tap position, there are significant undervoltages below 1.1 U n .However, their probability was lower than 0.01%.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Compared with V0 at DPI 0.3, power losses decreased on average by 9.04% for PF 0.95 instead of 15.6%; for PF 0.80, there was an even increase in losses, by 1.9% on average.

    “Compared with V0 at DPI, 0.3 power losses decreased on average by 9.04% for PF 0.95 instead of 15.6%.For PF 0.80, there was an even increase in losses, by 1.9% on average.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisecitation

    In most studies, the 5% probability of exceeding limit values is the benchmark and standard.

    “In most of the studies, the 5% probability of exceeding the limit values is the benchmark and standard [42] from which we deviated in the first step.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [42] Koirala, 2022, Hosting capacity of photovoltaic systems in low voltage distribution systems: A benchmark of deterministic and stochastic approaches, Renew. Sustain. Energy Rev. source

  • Classified as probably not a substantial claim. May combine two claims.

    Study design and conductnone given

    The model is built on real topology, grid parameters, PoC characteristics, and meteorological data measured at the location of the network and small source PV probability distribution characteristics provided by DSO.

    “The model is built on real topology, grid parameters, PoC characteristics, and meteorological data measured at the location of the network and small source PV probability distribution characteristics provided by DSO.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisereasoning

    Using the stochastic approach, PVHC limits can be expressed with probabilities of violation.

    “Using the stochastic approach, PVHC limits can also be expressed with probabilities of violation.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Overvoltages were the PVHC limitation identified in the 2010 rural European study.

    “Overvoltages were also the PVHC limitation identified in this study.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [65] Stetz, T., Yan, W., and Braun, M. (2010, January 6–10). Voltage control in distribution systems with high level PV-penetration. Proceedings of the 25th European PV Solar Energy Conference, Valencia, Spain.

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Premisecitation

    The limit for voltage unbalance is 2% according to EN-50160:2010 and 3% for ANSI C84.1.

    “The limit for voltage unbalance is 2% according to EN-50160:2010 [39], and 3% for ANSI C84.1 [40].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [39] (2010). Voltage Characteristics of Electricity Supplied by Public Electricity Networks. Standard No. EN 50160:2010.

      Not checked in the free run.

    • cites [40] (2011). American National Standard for Electric Power Systems and Equipment—Voltage Ratings (60 Hertz). Standard No. ANSI C84.1-2011.

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    A 2007 study calculated 30% PVHC, with voltage limitation, in an LV of a United Kingdom network.

    “A study in 2007 [57] in which 30% PVHC was calculated, with voltage limitation, in an LV of a United Kingdom network.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [57] Thomson, 2007, Impact of widespread photovoltaics generation on distribution systems, IET Renew. Power Gener. source

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    Power quality standards and thermal limits are crucial for LV networks.

    “Hereafter, we focus only on power quality standards and thermal limits, which are crucial for LV networks [36].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [36] Martin, W., Stauffer, Y., Ballif, C., Hutter, A., and Alet, P.J. (2018, January 21–25). Automated Quantification of PV Hosting Capacity In Distribution Networks Under User-Defined Control and Optimisation Procedures. Proceedings of the 2018 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe), Sarajevo, Bosnia and Herzegovina. source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In the 2019 study, changing PF to 0.895 increased PVHC up to 32.3%.

    “By changing PF to 0.895, the PVHC was increased up to 32.3%.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [68] Atmaja, W.Y., Lesnanto, M.P., and Pramono, E.Y. (2019, January 12–14). Hosting Capacity Improvement Using Reactive Power Control Strategy of Rooftop PV Inverters. Proceedings of the 2019 IEEE 7th International Conference on Smart Energy Grid Engineering (SEGE), Oshawa, ON, Canada. source

  • Classified as probably not a substantial claim. May combine two claims.

    Study design and conductreasoning

    The number of generated and calculated VR for each DPI is an essential calculation parameter; more VR analyzed means more grid configurations examined and more realistic results.

    “The number of generated and calculated VR for each DPI is an essential calculation parameter.The more VR that have been analyzed, the larger the number of possible grid configurations examined and the more realistic the results.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given

    This approach can be applied to any level of model detail.

    “This approach can be applied to any level of model detail.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    From the point of view of the safety and functionality of the devices, overvoltage conditions are much riskier than undervoltage conditions.

    “From the point of view of the safety and functionality of the devices, overvoltage conditions are much riskier than undervoltage conditions.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In 48% of all networks, the PVHC is limited by voltage violations, mostly overvoltages due to reverse power flow.

    “According to [31], the PVHC in 48% of all networks is limited by voltage violations, mostly overvoltages due to reverse power flow in the network.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [31] Fatima, S., Püvi, V., and Lehtonen, M. (2020). Review on the PV Hosting Capacity in Distribution Networks. Energies, 13. source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductown data

    In all CDF calculations, the residual sum of squares (RSS) is below 0.002.

    “In all CDF calculations, the residual sum of squares (RSS) is below 0.002.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Study design and conductreasoning

    A sufficient number of VR represents the stabilization of defined global network parameters, such as overvoltage probability in each incremental step.

    “A sufficient number of VR represents the stabilization of defined global network parameters, such as overvoltage probability in each incremental step.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning

    Comparing the results of other studies with ours is problematic due to the large variance in PVHC.

    “Comparing the results of other studies with ours is problematic due to this large variance, which is due to the large number of variables that are often specific to individual studies, such as:”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductreasoning

    Limitations due to harmonics are not included in this study due to the lack of information.

    “Limitations due to harmonics are not included in this proposed study due to the lack of information.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning

    There are very few studies with which we can compare our results.

    “Because of this, there are very few studies with which we can compare our results.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Study design and conductnone given

    The limitation of the presented methodology is only the quality of the data on which the model is based.

    “The limitation of the presented methodology is only the quality of the data on which the model is based.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    A 2016 study on a rural system with rooftop PV calculated 13% PVHC, with overvoltages estimated as the limitation source.

    “A study in 2016 [66] performed on a rural system with rooftop PV installations with a calculation of 13% PVHC, with overvoltages estimated as the limitation source.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [66] Heinrich, C., Fortenbacher, P., Fuchs, A., and Andersson, G. (2016, January 4–8). PV-integration strategies for low voltage networks. Proceedings of the 2016 IEEE International Energy Conference (ENERGYCON), Leuven, Belgium. source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    This stochastic approach has been widely adopted in recent years by several research groups.

    “This approach has been widely adopted in recent years by several research groups [15,24,[27][28][29].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [15,24,[27][28][29]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    EN-50160:2010 sets the limit for voltage total harmonic distortion (THD) at 8%.

    “EN-50160:2010 sets the limit for voltage total harmonic distortion (THD), defined by IEEE-519 [44], at 8%.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [39] (2010). Voltage Characteristics of Electricity Supplied by Public Electricity Networks. Standard No. EN 50160:2010.

      Not checked in the free run.

    • cites [44] (2014). IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems. Standard No. IEEE Std 519-2014.

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    A 2010 study on a rural European network calculated a maximum installed power of 3.5 kWp per PoC.

    “A study in 2010 [65] performed on a rural European network, with a calculated maximum installed power of 3.5 kWp per PoC.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [65] Stetz, T., Yan, W., and Braun, M. (2010, January 6–10). Voltage control in distribution systems with high level PV-penetration. Proceedings of the 25th European PV Solar Energy Conference, Valencia, Spain.

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given

    Stochastic studies with highly specific and realistic input values for particular regions, such as the typical Slovak Republic, are rare.

    “We found that stochastic studies with highly specific and realistic input values for particular regions, such as the typical Slovak Republic, are rare.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In a 2020 study in a suburban area of Finland, 233.5% PVHC was estimated.

    “In another study conducted in 2020 in a suburban area of Finland, 233.5% PVHC was estimated [64].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [64] Ferdowsi, 2020, Assessing distribution network sensitivity to voltage rise and flicker under high penetration of behind-the-meter solar, Renew. Energy source
41 of 41

  • The paper relies on this without support.

    In the Slovak Republic, stochastic methods for PVHC remain in the background.

    “In the region of the Slovak Republic, however, stochastic methods remain in the background.”

  • The paper relies on this without support.

    The default tap position of -5% is typical in LV networks to avoid undervoltage at the end of long feeders.

    “This is the typical tap position used in LV networks to avoid undervoltage at the end of long feeders.”

  • The paper relies on this without support.

    There is currently no consensus on the permissible risk of limit violation, and it is up to DSO to define it.

    “There is currently no consensus on the permissible risk, and it is up to DSO to define it.”

  • The paper relies on this without support.

    The tap of a DETC transformer cannot be changed if energized.

    “The problem with DETC TR is that its tap cannot be changed if energized.”

  • The paper relies on this without support.

    Voltage unbalance in the LV network increases with the extent of unequal load and generation distributed among phases.

    “Voltage unbalance in the LV network increases with the extent of unequal load and generation distributed among phases.”

  • The paper relies on this without support.

    Overvoltage conditions are much riskier than undervoltage conditions from the point of safety and functionality of devices.

    “From the point of the safety and functionality of devices, overvoltage conditions are much riskier than undervoltage conditions.”

  • The paper relies on this without support.

    DSO often does not have control over the PF inverters, and in the current legislative setting, it cannot order small customers to change the PF.

    “It is also important to mention that DSO often does not have control over the PF inverters, and in the current legislative setting, it cannot even order small customers to change the PF.”

  • The paper relies on this without support.

    DSO does not allow permanent undervoltages lower than 0.85 U n.

    “Further tap increase will cause permanent undervoltages lower than 0.85 U n , and this is not allowed by DSO.”
8 of 8

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Undervoltages are described as below the overvoltage threshold

    Minor

    The paper identifies 1.1 times nominal voltage as its overvoltage threshold, but calls voltages below that threshold "undervoltages" with a probability below 0.01%. These are not the same limit or event.

  • Conclusion gives power factor as 0.95% rather than 0.95

    Minor

    The conclusion attributes a PVHC of 21.4% to a power factor of 0.95%, whereas Table 2 attributes that result to a power factor of 0.95. Those power-factor values differ by a factor of 100.

  • Scenario V1 includes a power factor outside its stated range

    Minor

    Scenario V1 says the PV power factor varies only down to 0.85, yet its results include PF 0.80.

3 of 3

Cites

Flagged first, then by citations

Research works printed but not linked: 4

  1. IEA (2021). Global Energy Review 2021, IEA.
  2. Rylander, M., and Smith, J. (2012, January 28–30). Stochastic approach for distribution planning with distributed energy resources. Proceedings of the CIGRE Grid of the Future Symposium, Kansas City, MO, USA.
  3. Rylander, M., and Smith, J. (2012, January 13–15). Comprehensive Approach for Determining Distribution Network Hosting Capacity for Solar PV. Proceedings of the 2nd International Workshop on Integration of Solar Power Into Power Systems, Lisbon, Portugal.
  4. Stetz, T., Yan, W., and Braun, M. (2010, January 6–10). Voltage control in distribution systems with high level PV-penetration. Proceedings of the 25th European PV Solar Energy Conference, Valencia, Spain.

Cited by

Sorted by citations

Related

Authors
Bendík, J., Cenký, M., Cintula, B., Beláń, A., Eleschová, Ž., & Janiga, P.
Affiliations
  • Slovak University of Technology in Bratislava (SK)
  • Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Ilkovičova 3, 81 219 Bratislava, Slovakia
Corresponding author
Bendík, Jozef
ORCID
Venue
Processes
Publisher
MDPI AG
Published
2022-12-21
Volume
11
Issue
1
Pages
9
ISSN
2227-9717 (ISSN-L)
DOI
10.3390/pr11010009
OpenAlex
W4313502099
Cited by
26
References
55
Citations by year
2026: 2 · 2025: 6 · 2024: 7 · 2023: 11
FWCI
1.61
Type
journal article
Language
en
Open access
Licence
Locations
Processes (publishedVersion, cc-by)
Funders
Operational Program Integrated Infra-structure (313021W404)
Topics
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Optimal Power Flow Distribution
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Power Quality and Harmonics
  • Physical Sciences › Engineering › Control and Systems Engineering › Thermal Analysis in Power Transmission
Keywords
photovoltaic hosting capacity, low-voltage distribution networks, stochastic modeling, overvoltage, voltage unbalance, power quality, photovoltaic penetration, energy loss, rural distribution networks

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-28.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-28.

Cited sources are checked by gpt-6-sol.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review