# Modelling Electric Vehicle Charge Demand: Implementation for the Greek Power System

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## Abstract

**:**

## 1. Introduction and State of the Art

_{2}emissions rate of the electricity mix per hour and investigating the optimal charging hours that would minimise the total emissions in a Life Cycle Assessment of BEVs. The study monitored five EVs for an annual period and showed that the test vehicles were charged mostly during the daytime, from 08:00 to 22:00. It was assumed that the users opportunistically charged their EVs continuously at work and, later on, they might plug the EV in immediately after coming home.

## 2. Input Parameters and Data Analysis

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- Vehicle categories;
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- Battery capacity (kWh);
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- Consumption of EVs (kWh/km);
- -
- Charging location/strategy;
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- Charging rate (kW);
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- Departure/arrival time;
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- Daily distance travelled (km).

- L7e: Small four-wheeled EVs weighing up to 400 kg (excluding the load and battery) or up to 550 kg for vehicles intended to carry goods.
- M1: Typical passenger cars with a maximum of nine seats.
- N1: EVs for the carriage of goods up to 3.5 tonnes (without cargo). This category includes semi-trucks and light commercial vehicles.

**Type of Day:**Every day of the year is characterised as a weekday or weekend and is modelled so that the hourly traffic volume of the fleet is compatible with the generic profiles of Figure 1. Holidays are considered to be weekends, and the seasonal effect is also incorporated, as will be described later.

**Time Step:**The time step for this study was set to 15 min in order to facilitate an accurate simulation. During a time step, the external environment is considered unchanged, so any event (start/end of charging session, arrival and departure time) is only studied for integer multiples of this time step. In other words, each day is divided into intervals i = 1, …, 96.

**Driving Schedules:**Reference values were set for the weekday and weekend driving schedule of each EV (see Figure 2). This schedule includes the departure time and arrival time from/to home, work, or another destination and distances covered (km). Random deviation is added to the above values, and seasonal changes are incorporated into the time schedules.

**Battery Capacities:**Table 1 presents data for the minimum and maximum values of the battery capacities in the EVs of the fleet, depending on class and type. A distribution of values was formulated using all available statistical data. Battery capacities were also chosen to match the driving schedules of the EVs.

**Consumption:**Typical values for consumption (in kWh/km) are provided in Table 2 and were distributed and utilised for the simulation.

**State of Charge (SoC):**This variable is monitored for each time step of the simulation. Discharging is based on the assessments for the driving schedule and the consumption rate of each EV, while charging considers the appropriate charging rates at home, work, or public locations and incorporates a typical charging curve. For each EV, a random initial value was set for the SoC at the beginning of the annual simulation.

**Charging Rates:**According to Greek legislation (Hellenic Ministry of Environment and Energy decision no. 4743, 2021 on Law 4495/2017), the charging levels considered in the simulation were 3.7 kW (residential), 7.2–22 kW (at work), and 22–150 kW (fast commercial charging).

**Charging Schedule:**Various charging habits were considered utilising all the available knowledge retrieved from the previous research. The charging sessions per day were adjusted to the driving schedules. The time schedule was different for domestic charges, charges at work, and fast charges.

## 3. The EV Charging Model

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- The EV parameters were loaded (category, battery capacity in kWh, consumption in kWh/km, reference departure and arrival times, charging location/strategy, and reference daily distance in km). All EVs were considered to have access to home charging, while 15% of them were marked as having access to charging at work. The above-mentioned reference values were provided separately for weekdays and weekends.
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- The daily parameters were loaded per EV. This means that, based on a Monte Carlo approach and depending on the type of day (weekday or weekend), different parameters were produced, slightly deviating from the reference values. This refers to departure and arrival times and daily distance. Additionally, the seasonal effect was considered, which introduces a systematic variation of reference values, as will be detailed later.
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- Thus, a certain driving schedule was formulated for certain EVs on a certain day, while the SoC of the vehicle, based on its previous status, was sequentially monitored and updated.
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- Depending on the above, the charging needs were considered, and plug-in time and charging mode (fast/slow, home/work) were decided.
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- The duration and the end of the charging session were calculated based on the charging curve of the battery and the EV driving schedule (the latter means that the charging may be interrupted before reaching 100% of SoC). The load demand time series (for the specific vehicle and day) were produced with a 15 min step.
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- The above process was followed for each of the 10,000 EVs independently, and the aggregated load demand was extracted.
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- The incorporation of additional issues, e.g., residual charges, will be detailed later. A comprehensive block diagram of the simulation is presented in Figure 4.

**Frequency of charging sessions:**The aggregated results for an annual simulation of 10,000 EVs suggest that 99.1% of the vehicles are charged less than once per day, while 35% are only charged once per week (see Figure 5).

**Home charging:**During weekdays, according to our modelling, home charging begins immediately after the completion of the day’s final journey if the battery charge status (SoC) is less than or equal to 50%. This is reflected in Figure 6. Charging may last until the time of departure of the EV the next morning. Statistics show that the median home charge lasts 2.5 h, and only 5% of them last more than 7 h (see Figure 7). These durations refer to both regular and residual charging sessions.

**Residual Charging:**This term refers to domestic partial charging and covers up to 17% of all charging sessions. This is a rather undesired case which also featured in other research and occurs for the following reasons:

- (a)
- A scheduled full charging remains incomplete because the owner of the EV has to depart.
- (b)
- The owner decides to charge, even though SoC is above 50%.
- (c)
- Most of the residual charging sessions differ from the usual home charges because they start during the morning or the afternoon.

**External fast charging:**Fast charging occurs at rest areas, malls, gas stations, etc., usually when the EV has an extended travel schedule. It turns out that fast/public charges cover 16% of all charging sessions.

**External/work charging:**It was estimated that one-seventh of the Evs have access to charging at work. These chargers are, in general, faster than household ones (e.g., 7.4 or 11 kW). The respective charging sessions occur mostly on weekdays, and yet it is considered that a quarter of the above EVs also charge at work during weekends.

**Daily distance:**The daily distance profile (for weekdays and weekends) follows the distribution curve in Figure 2. For 85% of the cases, travel distances do not exceed 100 km on weekdays. The average distance of all EVs is around 45.3 km on weekdays (median is 24 km) and 37 km on weekends and holidays (median is 18 km). These statistics do not include days/cases of EV immobility.

**Departure/arrival time:**Two of the most important implicated parameters are the departure and arrival time-stamps, as they define the daily travelling profile of the EV and eventually determine the charging process, its type, start time, and duration. A different profile was set for each EV in the data set, incorporating all available data from the literature. The data for an annual simulation are summarised in Figure 8, where the distribution curves for departure and arrival times are presented using a time step of 15 min. The departure times are usually determined by working hours. It should be emphasised that the arrival times (which present a wider range) strictly refer to the last daily arrival at home.

- i = 1, …, 365 is the day of the year.
- j = 1, …, 10,000 is the number of EVs.
- dep
_{jref}is the reference departure time for each EV (in hours). - dep
_{ij}is the actual departure time for each day of the year and each EV, after the seasonal effect and the daily effect is added (in hours). - arr
_{X}are respective terms for arrival time. - rand
_{j}(0, 1) is a uniform distribution between [0, 1]; it constitutes a constant random effect per EV, representing the driver’s low or high seasonal deviation from the reference schedule. - rand
_{i}(0, 1) is a uniform distribution between [0, 1]; it represents a random daily deviation from the reference schedule of each driver. As implied in Equations (1) and (2), the departure or arrival time can have an additional daily deviation of ±5%. Thus, for a departure time at 8 a.m. and arrival time at 8 p.m., this means a deviation of ±20 min and ±1 h, respectively.

## 4. Results and Statistics of Charging Demand Modelling

## 5. EVs and PV Energy Communities

## 6. Conclusions and Discussion

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Distribution curve of reference daily distances for weekdays and weekends in the fleet of 10,000 EVs.

**Figure 6.**Distribution of plug-in time. The number refers to the total number of charging sessions per year in the fleet, commencing at specific 15 min time steps during the day.

**Figure 7.**Distribution curve of charging duration. The number refers to the total number of charging sessions per year of a specific duration across the fleet. This curve includes all types of charges (fast/slow, regular, residual, at home, work, or public).

**Figure 9.**Scatter diagram of charging duration vs. plug-in time for each type of charging (home, residual, work, fast).

**Figure 10.**Scatter diagram of energy stored vs. plug-in time for each type of charging (home, residual, work, fast).

**Figure 11.**Distribution function of plug-in times for each type of charging (home, residual, work, fast).

**Figure 12.**Aggregated charging load for each type of charging (home, residual, work, fast) for a random day.

**Figure 13.**Aggregated charging load for each type of charging (home, residual, work, fast) for a random week.

**Figure 14.**Depiction of seasonal effect. Load demand series for a random winter and a random summer week.

Vehicle Class | Average Capacity | Min Capacity | Max Capacity |
---|---|---|---|

L7e | 5.7 | 3 | 10 |

M1 | 39 | 20 | 100 |

N1 | 44.2 | 20 | 80 |

Vehicle Class | Average Consumption | Min Consumption | Max Consumption |
---|---|---|---|

L7e | 0.13 | 0.06 | 0.18 |

M1 | 0.18 | 0.12 | 0.21 |

N1 | 0.21 | 0.14 | 0.24 |

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**MDPI and ACS Style**

Mitrakoudis, S.G.; Alexiadis, M.C.
Modelling Electric Vehicle Charge Demand: Implementation for the Greek Power System. *World Electr. Veh. J.* **2022**, *13*, 115.
https://doi.org/10.3390/wevj13070115

**AMA Style**

Mitrakoudis SG, Alexiadis MC.
Modelling Electric Vehicle Charge Demand: Implementation for the Greek Power System. *World Electric Vehicle Journal*. 2022; 13(7):115.
https://doi.org/10.3390/wevj13070115

**Chicago/Turabian Style**

Mitrakoudis, Stavros G., and Minas C. Alexiadis.
2022. "Modelling Electric Vehicle Charge Demand: Implementation for the Greek Power System" *World Electric Vehicle Journal* 13, no. 7: 115.
https://doi.org/10.3390/wevj13070115