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Electric Vehicle Charging Station Placement Method for Urban Areas

Qiushi Cui, Yang Weng, Chin-Woo Tan

arXiv:1808.09660v1eess.SYcs.SY

TL;DR

Urban EV charging placement must account for practical electrical-network costs, while existing optimization approaches may not guarantee a global optimum. This paper incorporates those costs and convexifies constraints; its results show that protection upgrades can be a meaningful share of total cost and influence placement.

  • Problem

    Urban charging-station planning must address practical network factors, and existing approaches that do not convexify constraints cannot guarantee a global optimum.

    Source: §I · pp. 1–2

  • Method

    The paper combines station, distribution-expansion, voltage-regulation, and protection-upgrade costs in an optimization model and convexifies constraints while preserving convexity.

    Source: §I · p. 2, §III · p. 6, §VI · p. 12

  • Results

    Protection cost may reach 8% of total cost, and convex preservation is reported to guarantee a global minimum while reducing computational time.

    Source: B. Results Without Considering the… · p. 12, §VI · p. 12

  • Takeaways & Limitations

    Protection-device upgrade cost is not negligible in urban charging-station planning and can alter station placement.

    Source: B. Results Without Considering the… · p. 12, §VI · p. 12

Abstract

from arXiv · show

For accommodating more electric vehicles (EVs) to battle against fossil fuel emission, the problem of charging station placement is inevitable and could be costly if done improperly. Some researches consider a general setup, using conditions such as driving ranges for planning. However, most of the EV growths in the next decades will happen in the urban area, where driving ranges is not the biggest concern. For such a need, we consider several practical aspects of urban systems, such as voltage regulation cost and protection device upgrade resulting from the large integration of EVs. Notably, our diversified objective can reveal the trade-off between different factors in different cities worldwide. To understand the global optimum of large-scale analysis, we add constraint one-by-one to see how to preserve the problem convexity. Our sensitivity analysis before and after convexification shows that our approach is not only universally applicable but also has a small approximation error for prioritizing the most urgent constraint in a specific setup. Finally, numerical results demonstrate the trade-off, the relationship between different factors and the global objective, and the small approximation error. A unique observation in this study shows the importance of incorporating the protection device upgrade in urban system planning on charging stations.

I. INTRODUCTION

The paper addresses urban EV charging placement by combining practical network costs with optimization methods intended to preserve convexity and guarantee a global optimum.

I. INTRODUCTION

  • Limited charging availability is a barrier to large-scale EV adoption, while prior placement approaches do not convexify constraints and therefore cannot guarantee a global optimum.Urban planning also involves factors such as land and labor costs, voltage effects, and infrastructure upgrades.Source: §I · pp. 1–2
  • The paper incorporates voltage regulation and protective-device upgrade costs into the placement objective and analyzes sensitivity before and after convexification.The authors also describe the approach as applicable across different cities and countries.Source: §I · p. 2

A. Objective Function and Constraints

  • The objective minimizes charging-station, distribution-expansion, voltage-regulation, and protection-upgrade costs subject to operational constraints.The problem is formulated as a mixed-integer nonlinear optimization problem.Source: A. Objective Function and Constraints · pp. 2–3

B. Explanations of the Objective Function

The objective combines charging-station, distribution, voltage-regulation, and protective-device costs, making their trade-offs part of both planning and operation.

B. Explanations of the Objective Function

  • The objective treats the four cost components as a planning and operational trade-off, visualized as a cost decomposition over the electrical network.The components are station construction, distribution expansion, voltage regulation, and protective-device upgrade.Source: B. Explanations of the Objective… · p. 4, Figure 2 · p. 4
  • Station cost covers building a new station or adding a spot, while distribution cost reflects line length and total line capacity.The total capacity includes original and expanded capacity; expanded capacity is estimated proportional to new charging spots.Source: B. Explanations of the Objective… · p. 4
  • Voltage-regulation cost evaluates squared bus-voltage deviations from reference values as an equivalent cost of station impacts on the voltage profile.The passage links reactive-power compensation to bus voltage and uses squared voltage deviation in the cost term.Source: B. Explanations of the Objective… · p. 4
  • Protective-device upgrade cost includes acquisition, installation, uninstallation, and maintenance, assumed constant within each operating-current range.The model represents device upgrades by type and capacity; it assumes no relocation during an upgrade because relay reach likely determined the original recloser placement.Source: B. Explanations of the Objective… · pp. 4–5

C. Explanations of the Constraints

The constraints require adequate charging service and ensure that EV integration respects electrical-network operating limits and any applicable budget.

C. Explanations of the Constraints

  • Charging serviceability must meet a predetermined charge count in an area, calculated by summing the serviceability function across charging locations.The model identifies station availability at each bus as binary and the number of spots as an integer decision variable.Source: C. Explanations of the Constraints · p. 5
  • Electrical constraints require power-flow feasibility, line current below its rated maximum, bus voltages within 0.95–1.05, and compliance with budget limits when applicable.The voltage interval is the range recommended in this study.Source: C. Explanations of the Constraints · p. 5

D. Sensitivity Analysis of the Problem

The sensitivity analysis compares how charging-station, distribution, voltage-regulation, and protection-cost terms respond to placement and cost parameters.

D. Sensitivity Analysis of the Problem

  • Distribution-expansion cost varies with its coefficients, and the distribution term includes a station-count component that depends on the optimized number of stations.The compared distribution-cost terms include coefficients for line and substation expansion.Source: D. Sensitivity Analysis of the Problem · p. 5
  • Voltage-regulation cost can grow relatively faster when its coefficient is large, and squared voltage deviation makes it relevant to placements that boost bus voltages.Source: D. Sensitivity Analysis of the Problem · p. 5
  • Protection-cost terms depend mainly on the assumed current-cost relationship, so placements with high current absorption increase this cost.These terms do not increase as fast as the term proportional to the total number of charging spots.Source: D. Sensitivity Analysis of the Problem · p. 5

III. PROBLEM CONVEXIFICATION

The paper convexifies nonlinear terms while preserving a globally optimal solution, accepting approximation errors that are later assessed. It treats station counts, substation expansion, and the voltage-power relation through different constraint formulations.

III. PROBLEM CONVEXIFICATION

  • Convexification introduces some optimization error but guarantees a global minimum in small and large electric systems.The paper evaluates the resulting approximation error separately.Source: §III · p. 6

1) Constraint (3):

  • The station-count constraint is a linear combination of station and spot counts, so it is convex.Source: 1) Constraint (3) · p. 6

2) Constraint (4):

  • The substation-expansion constraint becomes linear above 1 MW of surplus capacity, corresponding to about 23 downstream spots in the toy example.The paper notes this is not a strict requirement in a larger system.Source: 2) Constraint (4) · p. 6

3) Constraint (5):

  • AC power-flow linearization makes the relation between charging variable x and non-slack bus voltage linear, yielding a convex constraint with a guaranteed global optimum.The optimization variable x_i is linearly related to net active power injection, while voltage V_i is nonlinear in x_i before linearization.Source: 3) Constraint (5) · p. 6

4) Constraint (6):

The paper approximates protective-device step costs with fitted lines and examines errors from convexifying constraints. It reports small overall errors and little effect on problem sensitivity under the stated conditions.

4) Constraint (6):

  • The protection cost sums acquisition, installation, uninstallation, and maintenance step functions, approximated by three fitted linear lines.The figure depicts the device cost functions and their estimated and linearized forms for four capacity levels.Source: 4) Constraint (6) · p. 6, Figure 3 · p. 7

B. Convexification Error Analysis

C. Sensitivity Analysis

  • The maximum voltage approximation error is 0.26% when the voltage regulator keeps bus voltage between 0.95 and 1.05; overall, the errors have little influence on sensitivity.The paper also reports no error for the linear constraint and no large cost change between adjacent protective-device current ranges.Source: C. Sensitivity Analysis · p. 7

IV. NUMERICAL RESULTS

The numerical-results section evaluates how constraints affect station placement using realistic cost assumptions and small- and large-system studies. Its setup uses a modified IEEE 4-bus toy system and an IEEE 123-bus large system.

IV. NUMERICAL RESULTS

  • The numerical results examine how each objective-function constraint affects placement in small and large systems using realistic data.Source: §IV · p. 7

A. Cost Parameters and Systems Under Study

B. Numerical Results of a Toy Example

The toy example adds placement constraints incrementally to show how each changes the solution; the large-system results test whether convexification preserves cost evaluation while guaranteeing a global minimum.

1) The Constraint Added:

  • With charging-station cost alone, the toy example places all 30 spots at either bus 2 or bus 3, with none at the other bus.The two optimal placements are (0, 30) and (30, 0).Source: 1) The Constraint Added · p. 8

2) The Constraint Added:

  • Adding distribution-expansion cost leaves the bus placements unchanged because that cost depends on total spots; station capacity can still affect total cost.Building fewer stations is more economical when station capacity is not violated.Source: 1) The Constraint Added · p. 8, 2) The Constraint Added · p. 8

3) The Constraint Added:

  • Adding voltage-regulation cost favors the end of the feeder, placing all 30 spots at bus 3 to minimize voltage violation.The voltage-regulation cost can overwhelm other costs.Source: 3) The Constraint Added · p. 8

4) The Constraint Added:

  • Adding protection-upgrade cost shifts all 30 spots to bus 2, since placing them at the feeder end requires more protective-device upgrades along the feeder.Expensive urban land can instead make land cost outweigh voltage-regulation and protection costs.Source: 4) The Constraint Added · p. 8

1) The Benefits of Problem Convexification:

  • 19.8% of nonconvex cases failed to find a global minimum, while all convexified cases succeeded, with 0.51% total-cost error at 5185 EVs/h and a 25-spot station limit.Convexified computation time was comparable to the nonconvex cases, while cases finding a local minimum took significantly longer.Source: Table IV · p. 9, 1) The Benefits of Problem… · p. 9

2) Sensitivity Validation With Respect to Optimization Variables:

The 123-bus analysis examines how voltage regulation and protection costs steer placement, and how EV flow and local cost coefficients affect station counts and total cost. The discussion illustrates how different city and country costs can change which constraints dominate.

2) Sensitivity Validation With Respect to Optimization Variables:

  • With voltage regulation absent, buses 33–37 need 4 spots; as its coefficient rises from 1e4 to 5e5, spots there increase from 21 to 50, and voltage regulation can dominate even without protection constraints.The regional placements reach their bus capacities as the voltage-regulation coefficient increases.Source: Table V · p. 9, 2) Sensitivity Validation With Respect… · p. 9
  • Voltage-regulation constraints push stations toward the feeder end, while protective-device upgrade costs are lower when stations are near the feeder trunk.These large-system observations align with the toy-example sensitivity analysis.Source: 2) Sensitivity Validation With Respect… · p. 10

V. DISCUSSIONS

  • Cost coefficients vary with local land, labor, and equipment prices, so different cities or countries can have different dominant constraints.The objective remains total-cost minimization across locations.Source: A. Applicability in Different Cities… · p. 10

3) Sensitivity Validation With Respect to Different Cost Components:

A. Applicability in Different Cities and Countries

  • In the U.S. example, labor can account for 60% of EV supply-equipment installation cost, making station and distribution-expansion costs dominant.The paper attributes this to comparatively high labor costs.Source: A. Applicability in Different Cities… · p. 12
  • For Beijing, lower station and distribution-expansion costs could make voltage regulation the dominant constraint, especially in smaller Chinese cities.The listed cost coefficients use an assumed USD/CNY exchange rate of 6.35.Source: A. Applicability in Different Cities… · p. 12

B. Results Without Considering the Protection Cost

Protection costs can materially affect EV charging-station placement, while the planning method preserves sensitivity after convexification and supports added constraints with a global optimum guarantee.

B. Results Without Considering the Protection Cost

C. Expandability of the Planning Strategy

VI. CONCLUSIONS

  • The conclusion formulates station siting and sizing as mixed-integer linear programming and includes distribution expansion, station, voltage-regulation, and protection-device costs.Source: §VI · p. 12
  • Sensitivity is preserved after convexification, computation time decreases, and voltage-regulation and protection costs favor different station locations.Voltage-regulation cost favors branch ends, whereas protection-device upgrades cost less with more stations on the feeder main line; protection costs are not negligible overall.Source: §VI · p. 12

APPENDIX A PROTECTIVE DEVICE COSTS

Appendix A presents protective-device costs by cost type. Appendix B describes an AC power-flow linearization using nodal currents, voltages, and load representations.

APPENDIX A PROTECTIVE DEVICE COSTS

APPENDIX B DERIVATION OF THE AC POWER FLOW LINEARIZATION

  • Nodal currents are expressed using the admittance matrix and nodal voltages, and each current is related to voltage through the ZIP model.Source: Appendix B · p. 13
  • The linearization expresses non-slack bus voltage as a function of power injected in closed rectangular form, with constant-impedance, constant-current, and constant-power load injections identified.Source: Appendix B · p. 13
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