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Cited by 18Electric Vehicles and InfrastructureOptimal Power Flow DistributionElectric Power System Optimization

Integration of Electric Vehicles in Low-Voltage Distribution Networks Considering Voltage Management

Open access
Carrión, Miguel, Zárate-Miñano, Rafael, Domínguez, Ruth·2020·Energies
DOI 10.3390/en13164125
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Abstract

The expected growth of the number of electric vehicles can be challenging for planning and operating power systems. In this sense, distribution networks are considered the Achilles’ heel of the process of adapting current power systems for a high presence of electric vehicles. This paper aims at deciding the maximum number of three-phase high-power charging points that can be installed in a low-voltage residential distribution grid. In order to increase the number of installed charging points, a mixed-integer formulation is proposed to model the provision of decentralized voltage support by electric vehicle chargers. This formulation is afterwards integrated into a modified AC optimal power flow formulation to characterize the steady-state operation of the distribution network during a given planning horizon. The performance of the proposed formulations have been tested in a case study based on the distribution network of La Graciosa island in Spain.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper proposes mixed-integer optimization models to decide the maximum number of three-phase high-power domestic EV charging points in a low-voltage distribution network while allowing chargers to provide decentralized reactive power voltage support. In a La Graciosa case study, reactive power support increased installed charging points by up to 8.3% for 11 kVA chargers and 10.7% for 22 kVA chargers.

Key findings

  • In the illustrative example, without the reactive power droop curve no charging points could be installed; with the droop curve, three charging points were installed at buses 1, 2, and 3.
  • In the La Graciosa case study, considering reactive power injections increased the number of installed charging points by up to 8.3% and 10.7% for 11 and 22 kVA chargers, respectively.
  • With the reactive power droop curve and line set Z1, installed charging points were 26 for 11 kVA chargers and 21 for 22 kVA chargers; with Z2, they were 21 and 15, respectively.
  • Over 30-day simulations, voltage magnitudes were always greater than the lower limit of 218.5 V, and no voltage violations were observed; total reactive injection was 382.8 kvarh in case 11 kVA-E1, averaging 14.7 kvarh per charger, increasing 25.2% in 22 kVA-E1 and 56.1% in 11 kVA-E2.

Methods

  • Two optimization models are formulated: (P1) a mixed-integer nonlinear problem maximizing the number of accepted three-phase domestic charging point requests under worst-case simultaneity factor 1, and (P2) a modified AC optimal power flow minimizing voltage deviations to simulate steady-state operation over a planning horizon.
  • The reactive power–voltage magnitude droop curve is modeled with binary variables and linearized constraints; chargers inject reactive power when nodal voltage is low.
  • The case study uses the La Graciosa distribution network: a 400-kVA transformer, 26 buildings and 26 lines, 44 charging point requests, 11 and 22 kVA chargers, line parameter sets Z1 and Z2, and 30-day simulations with 10-min periods; 34,560 instances of (P2) were solved using GAMS and Dicopt 12.6.111.

Limitations

  • The paper states these limitations: an existing low-voltage residential distribution network is considered; previous operation limitations are not overcome; distribution asset upgrades are not modeled; only three-phase high-power chargers are considered; only domestic chargers are considered; charger power factor is constant; coordinated charging and vehicle-to-grid are not considered.
  • The paper states that a single-phase equivalent analysis is adopted, though it says the procedure can be modified for three-phase modeling.
  • The illustrative example parameters are stated not to be representative of a realistic network; the case study is based on one specific island district, so the numerical results are context-specific.

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

Integrity signals

Registry

Crossref · 10.3390/en13164125

Cites

41 of 41 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

1 of 8 cited sources checked · 0 supported · 0 flagged · accuracy not yet measured

  • Findingown data

    In general, voltages decreased as the rate power of the charger and the energy charged increased.

    “In general, voltages decreased as the rate power of the charger and the energy charged increased.”
    Quote in the paperNot a substantial claim
  • Findingown data

    Figure 8b shows that the charge of the vehicles usually started in the middle part of the day.

    “Figure 8a indicates that the average daily energy charged per vehicle was less than 10 kWh, whereas Figure 8b shows that the charge of the vehicles usually started in the middle part of the day.”
    Quote in the paperNot a substantial claim
  • Findingown data

    No charging points could be installed without violating voltage limits when the reactive power droop curve was not considered.

    “no charging points could be installed without violating voltage limits (x k = 0, ∀k ∈ {1, • • • , 4})”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The distribution network has to be capable of operating under normal operation limits when households consume the contracted peak power and all electric vehicles are simultaneously charging.
  • Findingown data

    This value corresponded to an average value of 14.7 kvarh per charger.

    “This value corresponded to an average value of 14.7 kvarh per charger.”
    Quote in the paperNot a substantial claim
  • Findingown data

    It has been verified through 30-day simulations that the voltage magnitudes resulting from the model including reactive power injections are greater than the specified lower voltage limit.

    “It has been verified through 30-day simulations that the voltage magnitudes resulting from the model including reactive power injections are greater than the specified lower voltage limit.”
    Quote in the paperSubstantial claim
  • May combine two claims. 14
  • Classified as probably not a substantial claim. 8

  • May combine two claims.

    Premisecitation

    If a large number of electric vehicles is charged in a non-coordinated manner, undervoltage phenomena can happen, jeopardizing the stability of distribution networks.

    “If a large number of electric vehicles is charged in a non-coordinated manner, undervoltage phenomena can happen, jeopardizing the stability of the distribution networks, [2].”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [2] Graham, R.L., Francis, J., and Bogacz, R.J. (2017). Challenges and Opportunities of Grid Modernization and Electric Transportation. source

      The Advances section says that maintaining distribution-system reliability as PEV numbers and charging infrastructure grow is critical, and discusses managed charging. It does not say that uncoordinated EV charging causes undervoltage; its discussion of voltage fluctuations concerns variable renewable generation. The specific undervoltage mechanism is therefore unsupported. (LLM, conf=0.84)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Findingown data

    In the case without the reactive power droop curve, the voltage magnitude in the transformer network bus was 240.7 V, greater than the nominal value of 230.0 V.

    “the voltage magnitude in the transformer network bus was greater than the nominal value, 240.7 > 230.0V”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    It was verified that voltage magnitudes were always greater than the lower limit, 218.5 V, and none voltage violations have been observed in the analyzed cases.

    “It was verified that voltage magnitudes were always greater than the lower limit, 218.5 V, and none voltage violations have been observed in the analyzed cases.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    This value increased 25.2% and 56.1% in cases 22 kVA-E1 and 11kVA-E2, respectively.

    “This value increased 25.2% and 56.1% in cases 22 kVA-E 1 and 11kVA-E 2 , respectively.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    In the illustrative example, only bus 1 had a voltage magnitude greater than V(2)n, so y(1)1dt = y(2)1dt = 0 and qEV,S kdt = 0.

    “Observe that only bus 1 had a voltage magnitude greater than V (2) n , which results in y (1) 1dt = y (2) 1dt = 0 and q EV,S kdt = 0 by constraints ( 6)-( 14).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    From case 11kVA-E1 to case 22kVA-E1, the average minimum voltage decreased 0.3 V, whereas this difference was 0.2 V if cases 11 kVA-E1 and 11 kVA-E2 were compared.

    “For instance, from case 11kVA-E 1 to case 22kVA-E 1 , the average minimum voltage decreased 0.3 V, whereas this difference was 0.2 V if cases 11 kVA-E 1 and 11 kVA-E 2 were compared.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    In the illustrative example, voltages in buses 2 and 3 were lower than Vn, resulting in y1dt = 1, y(1)1dt = 0 and qEV,S kdt = -QEV,max k = -2.18 kvar.

    “On the other hand, voltages in buses 2 and 3 were lower than V n , which resulted in y 1dt = 1, y(1) 1dt = 0 and q EV,S kdt = -Q EV,max k = -2.18kvar.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The total energy consumed by the house, without considering electric vehicles, was 8.9 kWh, whereas the sum of the energy charged by two electric vehicles was only 3.5 kWh.

    “The total energy consumed by the house, without considering electric vehicles, was 8.9 kWh, whereas the sum of the energy charged by two electric vehicles was only 3.5 kWh.”
    Quote in the paperNot a substantial claim

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

    Findingown data

    As indicated in Table 5, two electric vehicle chargers were installed in bus 10.

    “As indicated in Table 5, two electric vehicles chargers were installed in bus 10.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    For Z2, the number of installed charging points was lower and equal to 21 for an 11 kVA charger and 15 for a 22 kVA charger.

    “For Z 2 , the number of installed charging points was lower and it was equal to 21 for a 11 kVA charger, and 15 for a 22 kVA charger.”
    Quote in the paperNot a substantial claim

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

    Findingown data

    In Figure 10c, one vehicle started the charging at 8:10 am, and the other at 11:40 am.

    “As observed in Figure 10c, one vehicle started the charging at 8:10 am, and the other at 11:40 am.”
    Quote in the paperNot a substantial claim

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

    Findingown data

    When the reactive power droop curve was considered, three charging points were installed at buses 1, 2 and 3.

    “In this case, three charging points were installed (buses 1, 2 and 3).”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The distribution network has to be capable of operating under normal operation limits when households consume the contracted peak power and all electric vehicles are simultaneously charging.
    • The authors state this as an assumption: Electric vehicle chargers have a leading power factor (cos φ_k < 1, φ_k < 0) and are able to inject reactive power as shown in Figure 1.

  • Classified as probably not a substantial claim.

    Interpretationreasoning

    It was expected that the voltage droop along the lines in case Z2 would be higher than that in case Z1.

    “In this manner, it was expected that the voltage droop along the lines in case Z 2 would be higher than that in case Z 1 .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationnone given

    The modeling of voltage control by means of a reactive power-voltage droop curve is mathematically non-convex and requires the usage of additional binary variables.

    “Additionally, the modeling of voltage control by means of a reactive power-voltage droop curve is mathematically non-convex and requires the usage of additional binary variables.”
    Quote in the paperNot a substantial claim

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

    Interpretationreasoning

    For a typical electric vehicle consumption rate of 0.2 kWh/km, the daily distance driven in case 11 kVA-E1 was 42.5 km.

    “As an example, the average energy charged per vehicle and day in case 11 kVA-E 1 was 8.5 kWh resulting, for a typical electric vehicle consumption rate of 0.2 kWh/km, in a daily distance driven equal to 42.5 km.”
    Quote in the paperNot a substantial claim

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

    Premisecitation

    The mathematical formulation of piecewise functions using mixed-integer linear expressions has been typically used in different power system problems.

    “The mathematical formulation of piecewise functions using mixed-integer linear expressions has been typically used in different power system problems, [38,39].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [38] Arroyo, 2000, Optimal response of a thermal unit to an electricity spot market, IEEE Trans. Power Syst. source
    • cites [39] Conejo, 2002, Self-scheduling of a hydro producer in a pool-based electricity market, IEEE Trans. Power Syst. source

  • May combine two claims.

    Interpretationreasoning

    The voltage control mechanism by electric vehicle chargers is totally decentralized and does not require changing the charging preferences of electric vehicle users.

    “Observe that this voltage control mechanism is totally decentralized and it is not required to change the charging preferences of electric vehicle users.”
    Quote in the paperSubstantial claim

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

    Premisecitation

    The linearization of the product of a continuous and a binary variable has been previously done.

    “The linearization of the product of a continuous and a binary variable has been previously done, for instance, in [40].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [40] Dvorkin, 2018, Primary Frequency Response in Capacity Expansion with Energy Storage, IEEE Trans. Power Syst. source

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

    Study design and conductnone given

    The parameter values selected for the case study are not meant to be representative of a realistic network and are only used for illustrative purposes.

    “the values of the parameters selected for this case study are not meant to be representative of a realistic network and they are only used for illustrative purposes.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    The reactive power-voltage magnitude control is activated locally and does not require the presence of a central operator.

    “Therefore, the reactive power-voltage magnitude control is activated locally and it does not require the presence of a central operator.”
    Quote in the paperSubstantial claim
20 of 20

  • The authors state this as an assumption.

    The distribution network operator has to decide the maximum number of charging points that can be installed from a list of charging point requests ensuring a reliable operation of the network.

    “It is assumed that the distribution network operator has to decide the maximum number of charging points that can be installed from a list of charging point requests ensuring a reliable operation of the network.”

  • The authors state this as an assumption.

    Charging points are private and installed in residential buildings.

    “We assume that charging points are private and they are installed in residential buildings.”

  • The authors state this as an assumption.

    The distribution network has to be capable of operating under normal operation limits when households consume the contracted peak power and all electric vehicles are simultaneously charging.

    “it is assumed that the distribution network has to be capable of operating under normal operation limits when households consume the contracted peak power and all electric vehicles are simultaneously charging.”

  • The authors state this as an assumption.

    The distribution network planner has a request list of high-power three-phase electric vehicle chargers desired to be installed in the distribution network.

    “It is also assumed that the distribution network planner has a request list of high-power three-phase electric vehicles chargers that are desired to be installed in the distribution network.”

  • The authors state this as an assumption.

    The active power consumed by the charger is equal to the maximum value.

    “It is assumed that the active power consumed by the charger is equal to the maximum value”

  • The authors state this as an assumption.

    Electric vehicle chargers have a leading power factor (cos φ_k < 1, φ_k < 0) and are able to inject reactive power as shown in Figure 1.

    “it is assumed a leading power factor, {cos φ k < 1, φ k < 0}, and that electric vehicle chargers are able to inject reactive power as shown in Figure 1.”

  • The authors state this as an assumption.

    The power factor value of electric vehicle chargers is a constant value.

    “The power factor value of electric vehicle chargers is a constant value.”

  • The paper relies on this without support.

    Three-phase chargers do not cause additional unbalances between phases.

    “three-phase chargers do not cause additional unbalances between phases”

  • The paper relies on this without support.

    The analyzed distribution network operates properly under normal conditions.

    “an existing residential distribution network that operates properly under normal conditions is analyzed”

  • The paper relies on this without support.

    Distribution networks are traditionally associated with high resistance-reactance ratios.

    “distribution networks are traditionally associated with high resistance-reactance ratios”

  • The paper relies on this without support.

    Local reactive power injection mechanisms do not need the installation of additional devices and exploit the capability of the inverters used in electric vehicle charging points.

    “local reactive power injection mechanisms are typically used, since they do not need the installation of additional devices and exploit the capability of the inverters used in electric vehicle charging points.”
11 of 11

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.

  • Line-capacity constraint compares squared power with unsquared capacity

    Major

    Constraint (20) squares both power flows but bounds their sum by S L,max rather than its square. With the stated 100-kVA line capacity, the corresponding squared-power bound is 10,000 (kVA)2, not 100.

    Reported 100 · recomputed 10000

  • Vehicle count changes from 44 to 41

    Major

    The input-data section identifies 44 requested charging points as the number of electric vehicles, but the simulation section describes probability distributions for 41 electric vehicles.

  • Z2 resistance-to-reactance ratio is misstated

    Minor

    The stated impedance components give 0.716/0.089 = 8.04, not 8.6.

    Reported 8.6 · recomputed 8.044944

  • Leading power-factor angle gives the opposite sign for maximum reactive power

    Minor

    Equation (3) makes Q EV,max negative when the stipulated power-factor angle is negative, whereas the numerical example gives Q EV,max as positive 2.18 kvar. That sign also determines the direction of injection in the stated droop law.

4 of 4

Cites

Flagged first, then by citations

Research works printed but not linked: 2

  1. Gómez Expósito, A., Conejo, A.J., and Cañizares, C. (2009). Electric Energy Systems: Analysis and Operation, CRC Press.
  2. Carpentier, 1962, Contribution to the economic dispatch problem, Bull. Soc. Fr. Electr., 8, 431

Cited by

Sorted by citations

Related

Authors
Carrión, M., Zárate-Miñano, R., & Domínguez, R.
Affiliations
University of Castilla-La Mancha (ES)
Corresponding author
Carrión, Miguel
ORCID
Venue
Energies
Publisher
MDPI AG
Published
2020-08-10
Volume
13
Issue
16
Pages
4125
ISSN
1996-1073 (ISSN-L)
DOI
10.3390/en13164125
OpenAlex
W3048263835
Cited by
18
References
41
Citations by year
2025: 1 · 2024: 3 · 2023: 7 · 2022: 4 · 2021: 3
FWCI
1.20
Type
journal article
Language
en
Open access
Licence
Locations
  • Energies (publishedVersion, cc-by)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • Institutional Research Information System (Università degli Studi di Brescia) (submittedVersion)
Funders
  • Ministerio de Economía y Competitividad, Spain (Project DPI2015-71280-RMINECO/FEDER, UE)
  • Ministerio de Ciencia e Innovación, Spain (Project PID2019-111211RB-I00/AEI/10.13039/501100011033)
Topics
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Electric Vehicles and Infrastructure
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Optimal Power Flow Distribution
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Electric Power System Optimization
Keywords
electric vehicles, low-voltage distribution networks, voltage management, AC optimal power flow, distribution network planning

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