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Cost Minimization of Charging Stations with Photovoltaics: An Approach with EV Classification

Wayes Tushar, Chau Yuen, Shisheng Huang, David Smith, H. Vincent Poor

arXiv:1507.07994v1eess.SY

TL;DR

This paper addresses the limited attention given to minimizing operational costs in PV-powered charging stations across time slots. It proposes an EV classification and energy-trading scheme, finding that greater green-EV participation reduces charging-station costs, with stronger green-EV contributions in winter.

  • Problem

    PV-powered charging stations need implementable methods to minimize operational costs from managing electricity across different time slots.

  • Method

    The paper classifies EVs as premium, conservative, or green and designs distinct charging, discharging, and pricing rules using mixed integer programming.

  • Results

    Greater green-EV participation significantly reduces total charging-station cost, while green-EV contributions are greater in winter than summer.

  • Takeaways & Limitations

    Green EV batteries can serve as distributed storage, allowing the charging station to buy more energy from green EVs instead of the higher-priced grid.

Abstract

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This paper proposes a novel electric vehicle (EV) classification scheme for a photovoltaic (PV) powered EV charging station (CS) that reduces the effect of intermittency of electricity supply as well as reducing the cost of energy trading of the CS. Since not all EV drivers would like to be environmentally friendly, all vehicles in the CS are divided into three categories: 1) premium, 2) conservative, and 3) green, according to their charging behavior. Premium and conservative EVs are considered to be interested only in charging their batteries, with noticeably higher rate of charging for premium EVs. Green vehicles are more environmentally friendly, and thus assist the CS to reduce its cost of energy trading by allowing the CS to use their batteries as distributed storage. A different charging scheme is proposed for each type of EV, which is adopted by the CS to encourage more EVs to be green. A basic mixed integer programming (MIP) technique is used to facilitate the proposed classification scheme. It is shown that the uncertainty in PV generation can be effectively compensated, along with minimization of total cost of energy trading to the CS, by consolidating more green EVs. Real solar and pricing data are used for performance analysis of the system. It is demonstrated that the total cost to the CS reduces considerably as the percentage of green vehicles increases, and also that the contributions of green EVs in winter are greater than those in summer.

NOMENCLATURE

The nomenclature defines the time horizon, solar-generation variables, EV and battery parameters, energy prices, and binary flow-direction variables used in the model.

  • The model uses T time slots indexed by t, with solar intensity Ilight(t), K panels, panel area A, and efficiency κ.
  • EV notation includes N vehicles, arrival and leaving times, battery capacity bn, state of charge sn(t), and target SOC sn,r.
  • Premium, conservative, and green EVs use distinct charging-rate variables, while green EVs additionally have a discharging-rate variable.
  • The notation distinguishes charging and discharging prices for EVs from grid buying and selling prices, with CS markup and predefined pricing parameters.
  • Binary variables yn(t) and x(t) determine energy-flow direction for green EVs and the grid, respectively.

I. INTRODUCTION

The introduction motivates coordinating EV charging with renewable generation and presents a three-category EV scheme with MIP-based scheduling to reduce charging-station costs.

  • Electricity and transportation together contribute approximately 64% of global CO2 production, motivating combined deployment of EVs and renewable energy.
  • Renewable-powered EV charging can reduce emissions, but unregulated charging risks grid overloading, power losses, voltage deviations, and supply uncertainty.
  • Prior work has paid little attention to optimally managing energy in PV-powered charging stations to minimize operational cost across time slots.
  • The proposed scheme classifies EVs as premium, conservative, or green according to environmental friendliness and expected charging rate.
  • Premium and conservative EVs permit charging only, whereas green EVs permit battery discharge to compensate for PV-production uncertainty.
  • A basic MIP scheduler models objectives and constraints, and extensive numerical results using real data evaluate the scheme.

II. STATE-OF-THE ART

The paper situates its PV charging-station problem within coordinated EV and renewable-energy research, then specifies the station, time slots, solar model, and grid-trading setup.

  • II. STATE-OF-THE ART: Existing EV studies address grid losses, voltage deviation, network capacity, generation costs, ancillary services, renewable intermittency, and frequency regulation.
  • II. STATE-OF-THE ART: Solar-charging research has examined parking-lot chargers, PV sizing, large-scale deployment, and the technical feasibility of on-site solar charging.
  • II. STATE-OF-THE ART: The paper identifies limited prior attention to minimizing PV charging-station operating costs and calls for easily implementable solutions using existing techniques.
  • III. MODEL AND EV CLASSIFICATION: The system contains a single roof-top-solar charging station connected to EVs and the main grid, with grid purchases available during energy deficiency.
  • III. MODEL AND EV CLASSIFICATION: Scheduling spans 11 hours from 7 am to 6 pm and is divided into T = 22 half-hour time slots.
  • III. MODEL AND EV CLASSIFICATION: PV generation is computed from measured solar radiation, panel efficiency, panel area, and panel count, while the station uses generation for charging and may trade with the grid.
  • III. MODEL AND EV CLASSIFICATION: Vehicles have individual arrival and leaving times, battery capacities, SOC values, and target SOCs, while the station trades energy using time-varying rates.
  • III. MODEL AND EV CLASSIFICATION: The classification allows different charging behavior and pricing for premium, conservative, and green vehicles.

A. Premium vehicles

Premium EVs are charged at the maximum available rate and do not permit battery discharge, prioritizing the highest possible charging rate before departure.

  • A. Premium vehicles: Premium EVs charge at the maximum available charging rate.The feasible solution assumes charging at the EV’s rated capacity, en,max.
  • A. Premium vehicles: Premium EVs do not allow the CS to discharge their batteries.This restriction applies even when considering early departure from the CS.
  • A. Premium vehicles: Premium EVs are charged at the premium price per unit of energy.The premium rate and premium pricing distinguish this category from conservative vehicles.

B. Conservative vehicles

Conservative EVs charge only at a chosen average rate sufficient to reach their desired state by departure, with pricing tied to that rate.

  • B. Conservative vehicles: Conservative EVs charge their batteries at an average rate determined by their desired state and available stay duration.Arrival and leaving times vary across vehicles, so the resulting charging rate differs between conservative EVs.
  • B. Conservative vehicles: The CS sets each conservative EV’s price per unit of energy based on its charging rate.The pricing relationship is illustrated for different values of the predetermined parameter γ.
  • B. Conservative vehicles: Lower-rate charging is rewarded through a lower charging price than the premium rate.The conservative charging price functions as a reward for charging more slowly than premium EVs.
  • B. Conservative vehicles: A conservative EV whose charging rate exceeds the designated condition is treated as a premium EV and charged at the maximum rate.In that case, the premium price per unit of energy applies.
  • B. Conservative vehicles: Conservative EVs do not allow the CS to discharge their batteries.If they leave early, their battery SOC may remain below the required SOC.

C. Green vehicles

Green EVs permit both charging and discharging, allowing the CS to use their batteries for energy trading while providing charging discounts and discharge payments under SOC constraints.

  • C. Green vehicles: Green EVs allow the CS to both charge and discharge their batteries.Their batteries can accumulate and release energy at different times during the vehicles’ stay.
  • C. Green vehicles: Green EVs receive a charging discount and payment for energy sold to the CS.Their charging price is discounted by η, while their discharge price is linked through the design parameter ϵ.
  • C. Green vehicles: The parameter ϵ connects green-EV charging and discharging prices and can be set to 1 for price-balanced transactions.The choice may reflect solar intensity, grid price, and the CS’s urgency to buy electricity.
  • C. Green vehicles: Green EVs may experience SOC below their required departure level after early departure, depending on other EV demand and PV generation.They allow discharge only after reaching a specified minimum SOC through charging, while battery safety requires SOC to remain above sn,min.
  • C. Green vehicles: Green EVs maintain an emergency SOC requirement that supports reaching the nearest charging facility after early departure.The requirement applies before the predefined leaving time and can vary across green EVs.
  • C. Green vehicles: The CS manages energy trading among the grid and all three EV categories across time slots.Grid buying prices are lower than grid selling prices, creating a trading-management setting for the scheduler.

IV. MIP APPROACH WITH EV CLASSIFICATION

The paper formulates a basic mixed integer programming approach to schedule CS energy trading under the proposed EV classification. The formulation uses linear equations and Boolean variables, provides an offline optimum, and assumes prior solar-generation information.

  • IV. MIP APPROACH WITH EV CLASSIFICATION: The MIP formulation minimizes the CS’s total energy-trading cost subject to operational constraints.Constraints apply to the CS, the main grid, and each EV during scheduling.
  • IV. MIP APPROACH WITH EV CLASSIFICATION: The approach represents the objective and constraints with linear equations and Boolean variables.This structure matches MIP’s suitability for linear objectives, linear constraints, and Boolean variables.
  • IV. MIP APPROACH WITH EV CLASSIFICATION: The method is positioned as a relatively simple way to capture the operational-cost effects of EV charging characteristics.The paper also notes that MIP is widely used for smart-grid energy-management design.
  • IV. MIP APPROACH WITH EV CLASSIFICATION: MIP provides an optimal offline energy-management solution for the proposed classification scheme.The solution can serve as a benchmark for more sophisticated online schemes under similar CS settings.
  • IV. MIP APPROACH WITH EV CLASSIFICATION: The proposed MIP requires prior information about solar generation.Statistical or incomplete-information extensions are mentioned but left beyond the paper’s scope.

A. Objective function

The charging station minimizes its daily energy-trading cost by choosing how much energy to exchange with each EV and the grid at each time slot. The objective accounts for trading prices, PV generation, EV demand, and green-EV discharging.

  • A. Objective function: The CS minimizes total daily energy-exchange cost by selecting energy traded with vehicles and the grid at each time slot.The objective covers trading over duration T.
  • A. Objective function: The objective includes payments and revenues from energy trading, PV generation, EV demand, and green-EV battery discharge rates.These factors determine the cost at each time slot.
  • A. Objective function: Positive terms in Γ represent costs, while negative terms represent revenues to the CS.The CS minimizes Γ by choosing relevant energy quantities.
  • A. Objective function: The CS controls green-EV charging and discharging through Γ, while premium and conservative charging follows their respective control procedures.EVs choose whether to participate as premium, conservative, or green during charging.

B. Constraints

The scheduling constraints enforce energy availability, SOC requirements and safety, vehicle charging limits, mutually exclusive charging or discharging, and grid power-flow limits. Green-EV constraints additionally support controlled battery discharge while preserving minimum mobility requirements.

  • B. Constraints: CS energy supplied to the grid and connected EVs cannot exceed energy available during each time slot.This constrains total supply during scheduling.
  • B. Constraints: Each EV’s SOC starts at plug-in, updates from the previous slot using charging or discharging energy, and ends within requested and capacity bounds.Battery efficiency μ enters the SOC update, with an extra term for green EVs because they may discharge.
  • B. Constraints: Vehicle SOC must remain above the manufacturer-specified minimum safety value during charging and discharging.This safety constraint applies throughout the vehicle’s stay.
  • B. Constraints: Green EVs can be discharged only after reaching a required minimum SOC that supports travel if they leave the station early.The stated example is reaching the next available battery exchange station.
  • B. Constraints: Green EV batteries may not charge and discharge simultaneously, and every vehicle’s charging or discharging rate is limited by rated maximum capacity.A binary variable determines whether a green EV is charging or discharging.
  • B. Constraints: Grid energy flow cannot exceed maximum power capacity or occur simultaneously in both directions.A binary variable indicates whether power flows into or out of the grid.

C. Optimizing the scheduling

The station’s energy-trading problem is formulated as a basic mixed integer program with linear objectives, linear constraints, and integer variables. Random vehicle arrival and departure times are included, and Gurobi is used to solve the resulting optimization problem.

  • C. Optimizing the scheduling: Table II summarizes the parameters and variables used in the MIP formulation.The table is identified as “Parameters and variables for MIP.”
  • C. Optimizing the scheduling: The energy-trading model is formulated as a basic MIP to minimize the CS’s total cost Γ under practical scheduling constraints.The formulation includes integer variables such as x(t) and y(t).
  • C. Optimizing the scheduling: Vehicle arrival and departure times are modeled as random variables with suitable probability distributions.The optimization is subject to the stated constraints.
  • C. Optimizing the scheduling: The Gurobi optimizer solves the formulated MIP subject to constraints (8)–(16) and finds its optimal solution.The optimization problem is identified as (17).

V. CASE STUDY

The case study evaluates the classification scheme with PV, EV, pricing, and weather data, showing how green EVs support energy balancing and reduce costs for the charging station and participating drivers.

  • Case-study setup: The study models a 24-space charging station over 22 half-hour time slots, with equal numbers of premium, conservative, and green EVs unless otherwise stated.Roof-top PV sizing is tied to vehicle-space area, and solar data are averaged from measurements at the Australian National University in Canberra.
  • EV charging behavior: Premium EVs charge fastest, conservative EVs follow an average requested rate, and green EVs charge, store energy, and discharge before reaching their target SOC.In the illustrated case, green EV storage is used during time slots 7–14, followed by discharging during slots 15–17 and final charging at slot 18.
  • Energy trading: Green EVs supplement PV and grid energy when charging demand exceeds generation, while absorbing excess PV generation when the station has surplus energy.The case study reports green-EV support during time slots 4–6 and excess-energy storage during time slots such as 15 and 19.
  • PV sensitivity: Increasing the number of PV panels decreases grid purchases and increases energy sold to the grid, although installation inconvenience and changing conditions may affect implementation.The study keeps EV traffic conditions fixed while varying the number of panels.
  • Cost outcomes: The charging station’s total cost decreases as green-EV penetration and solar generation increase, converging toward the all-green fixed-price baseline in both seasons.The modeled cost can become negative, representing net revenue from energy sales; green-EV energy substitution is especially important when winter solar generation is lower.
  • EV cost outcomes: Green EVs have lower average daily charging costs than premium and conservative EVs, with summer reductions of about 44.6% versus conservative and 47.7% versus premium vehicles.The study reports similar reductions in winter and concludes that the classification benefits both the charging station and green EVs.

VI. CONCLUSION

The paper introduces an EV classification and charging framework for photovoltaic charging stations that accounts for owners who may not permit battery discharging. Green EVs can reduce the station’s energy-trading cost, while further extensions address penalties, uncertainty, and power quality.

  • The classification explicitly considers that some EV owners may not allow their vehicles’ batteries to discharge.This constraint motivates the proposed vehicle categories and their distinct operating rules.
  • The scheme classifies connected EVs as premium, conservative, or green according to charging behavior.It defines charging rules for all three categories and energy-discharging rules exclusively for green vehicles.
  • Real solar and pricing data show that introducing green vehicles can significantly reduce the charging station’s total energy-trading cost.The results compare the proposed scheme with a baseline approach.
  • As the number of green EVs increases, the proposed scheme’s total cost tends to converge toward the baseline cost.The paper quantifies the energy-trading difference as the green-vehicle percentage rises from 10% to 100%.
  • Future work includes penalties for late departures, alternative arrival and leaving-time models, real-time management under uncertainty, and power-quality analysis.The proposed extensions address vehicle timing, unknown future arrivals and departures, renewable generation, prices, and harmonic effects.
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