# Simultaneity Factors of Public Electric Vehicle Charging Stations Based on Real-World Occupation Data

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## Abstract

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## 1. Introduction

- Cost efficiency:
- Vehicles optimize their charging behaviour to charge during the hours of the day when electricity is available at the cheapest price;

- Limiting power demand from the grid:
- Vehicles reduce their demand for charging power during times of high grid usage in order to avoid overburdening the electricity grid;

- Usage of intermittent renewable energy:
- Vehicles try to satisfy their energy demand, as much as possible, through the use of intermittent renewable energies such as PV and wind.

- Increasing the system’s flexibility:
- Increase the flexibility of the system, for example, via frequency control, power quality management, or use of backup power.

#### 1.1. Literature Review

#### 1.1.1. Simultaneity Factor (SF)

_{vehicles}is the SF defined in terms of vehicles; P

_{max}is the instantaneous maximum power recorded; P

_{sum,vehicles}is the sum of the charging power of all observed vehicles.

_{sum,connectors}) as shown in formula below. As can be seen, a wide gap exists between connectors with and without flexible energy tariffs. Understanding this difference is a key topic of this paper. Unfortunately, to the authors’ best knowledge, there is no other publication performing this type of calculation, even though it is crucial for grid planning.

#### 1.1.2. Impact on Electricity Prices and Emission Intensity

_{2}emissions, particularly for PV-based systems.

#### 1.1.3. Our Contribution

- Calculation of SF using real-world charging station occupation data;
- Comparison of the grid impacts of various EV recharging strategies;
- Energy cost comparison when employing these strategies;
- Comparison of emission intensities when employing these strategies.

## 2. Data

_{2}intensity of the German electricity grid [33]. These two datasets are visualised in Figure 6. Figure 6a,b show how the two variables behaved over the time observed in this study and on a weekly average, respectively. Figure 6c displays the correlation between the two variables. It can be seen that the two were correlated, which was to be expected, since photovoltaics and wind power are both free of emissions and have marginal costs of 0.

## 3. Methodology

_{2}intensity of the electricity mix to form strategies for when actual recharging should happen when a vehicle is connected to a station.

#### 3.1. Optimization Algorithms

#### 3.1.1. Naive Algorithm

#### 3.1.2. Price-Optimisation Algorithm

_{i,ki}is the charging power in charge event i at time k

_{i}; λ

_{ki}is the cost of recharging at time k

_{i}; T is the optimization time step, chosen to be one hour; T

_{tot,i}is the duration of the charge event i; E is the energy consumption assumed per charge event; e is an error term that reduces E⋅n to compensate so that not all events are long enough to supply planned E.

- Sort the price time series by price in ascending order;
- Iterate through the sorted time series, and perform the following steps for each timestamp, ts:
- Obtain the charge events (CE) happening at ts;
- Obtain the energy already charged per CE;
- Calculate energy that still needs to be charged per CE;
- Iterate through the list found in (a), and charge each event by the maximum of the station power limit or the remaining energy found in (c).

#### 3.1.3. CO_{2}-Optimization Algorithm

_{2}-optimization algorithm is almost identical to the price-optimisation algorithm, with the key difference being that instead of price, the hourly CO

_{2}emissions are used as the target. The time series was consequently sorted by grid CO

_{2}intensity instead of energy prices, and the least emission-intense hours were used where possible to perform recharging. Due to the similar approach, a detailed explanation is omitted.

#### 3.1.4. Peak Power Reduction Algorithm

_{max}. The criterion is, however, a weak condition and may be violated in specific hours if no solution is otherwise found.

- Create an empty list list
_{ts}of timestamps, ts; - While the length of list
_{ts}does not contain all ts do the following:- (a)
- Find the ts with the highest power flow;
- (b)
- If the power flow is less than the power limit, terminate the algorithm;
- (c)
- Obtain CEs occurring at ts;
- (d)
- For each CE, check if the charging process can also be performed at another moment in time. If this is possible, shift the charging to the least critical moment in time, starting with the cheapest option;
- (e)
- If there is no option to perform the charging at another moment in time or ts has been attempted n times already, add ts to list
_{ts}.

#### 3.1.5. Comparison to Algorithms in Literature

#### 3.2. Strategies

- Naive strategy: corresponds to the naive algorithm outlined in Section 3.1.1;
- Price-optimisation strategy: corresponds to price-optimisation algorithm in Section 3.1.2;
- Emission reduction strategy: usage of the price-optimisation algorithm with CO
_{2}intensity instead of day-ahead prices as optimisation target; - Peak minimisation strategy: combination of price-optimisation algorithm (Section 3.1.2 and peak power reduction algorithm Section 3.1.4).

## 4. Results

_{2}intensity, and SF.

#### 4.1. Power Demand Shape

#### 4.2. Peak Power Germany

- The naive charging strategy led to only moderate peak power requirements of 2 MW for the observed 1562 connectors if 20 kWh were charged per charging process. If this number is extrapolated to the planned one million public connectors [37] planned for 2030, this would result in approximately 1.28 GW of additional power;
- Depending on the charged amount of energy, the peak power when using the unidirectional price-optimisation strategy or the CO
_{2}emission reduction strategy rises by a factor of 3 to 4 compared to the naive charging strategy. This was caused by the fact that all connectors where a vehicle is connected will charge at the cheapest/least emission intense timestamp, thereby causing a power peak. This effect was almost identically strong for both strategies; - The peak power limitation strategy was able to flatten the power consumption during most observed hours. The peak power, however, did not change dramatically. Note that for the peak optimization algorithm, since the price-optimisation was run first, the peak power was above the peak power of the naive approach. This was the result of the optimization terminating as outlined in Section 3.1.4. The energy transferred during the peak hour, however, only represented <0.2% of the total energy transferred in all cases. It would consequently not cause great damage if a hard cap was introduced for that critical hour, since only few vehicles would be unserved. Additionally, it must be noted here that the data collection process from public sources was not free of faults. It was not unlikely that the peak was a result of a data gap, where for some time new arriving vehicles were not detected and then were all counted as arriving at one instance in time. Correcting this would require better data quality, which unfortunately was not available for this study.

#### 4.3. Cost Comparison

- The price differences between the naive strategy and the price-optimised strategy are smaller than 1 EURcent per kWh for the observed timeframe and all calculated amounts of energy per charge event;
- The electricity purchase cost per kWh is largely independent of the amount of energy charged per process. For all strategies, the price difference between the 8 kWh scenario and the 60 kWh scenario was less than 2%;
- Small price fluctuations exist for low power limits shown in Figure 16, as the optimization terminated due to the long runtime. Prices for a power limit of 0 kW were lower than for 704 kW, because each stricter power limit takes the results of the previous run as starting point. Since the optimization for 704 kW was eventually stopped, the new run had room left for improvement. The slight differences of less than 0.1 EURcent/kWh, however, did not change the overall picture;
- All in all, while the power increased by a factor of 3 between the naive and the price-optimizes strategy, the considered costs only decreased by 20%.

#### 4.4. CO_{2} Intensity

_{2}intensity was calculated in a similar fashion compared as the electricity costs by replacing hourly electricity costs with grid CO

_{2}intensity taken from [33]. Figure 17 shows how the different strategies perform in terms of CO

_{2}intensity. We do not include local renewable generation in our calculation which is nowadays already frequently combined with charging infrastructure [38]. This is due to the fact that the generation would otherwise be fed into the grid and replace flexible generators such as gas or coal fired power plants. Some key results that can be concluded from Figure 17 are:

- Price-optimisation already reduced CO
_{2}emissions compared to the naive base case. This is likely a result of the correlation already shown in Figure 6c. Renewable generators reduce the wholesale electricity price since their variable costs are often 0 €. Optimising for price consequently means optimising for renewable, CO_{2}-free electricity in many cases; - The CO
_{2}intensity was overall much lower than the time-weighted average in Germany of 324.20 g CO_{2}/kWh and the consumption-weighted average of 326.37 g CO_{2}/kWh; - The CO
_{2}intensity optimisation was able to reduce the CO_{2}intensity of charge electricity by ~6.6%.

#### 4.5. Simultaneity Factor

_{n}with 1000 elements was created by randomly selecting n connectors each and ensuring that each set is unique.

- Already for groups of 10 connectors, the SFs reduce to about 50% compared to the value for a single connector;
- For individual connectors, the SF is 1 in virtually all cases. All connectors were consequently used at least once in the observed period;
- The amount of energy required has a large impact on the SF of larger sets of connectors, particularly for the naive and the peak-power strategy. In these two, larger amounts of energy required lead to overall longer charging times which in turn increases the likelihood of overlaps between charging processes;
- In terms of SF, there is little difference between price- and CO
_{2}-optimised strategy. This was to be expected since both optimisation function in a very similar fashion; - For the price- and CO
_{2}-optimised strategy, the SF does not change as strongly between the different amounts of energy charged. This is because the peak power occurs at the time step with the lowest price or lowest CO_{2}-intensity. The optimiser will move as much charging as possible to this critical hour. This process therefore unaffected by the length of the individual charging processes; - Even in the extreme cases of vehicles recharging much energy or the simplified bidirectional charging, large sets of connectors seldom exceed an SF of 40%;
- The difference between the price-optimised and non-price-optimised strategies is particularly prominent for 8 kWh of recharged energy and for smaller sets of less than 100 connectors;
- For the largest number of connectors considered, the SF varies around 20% for the naive strategy. This shows, that the EVs are not going to cause dramatic grid overloads by simultaneity.

## 5. Discussion

#### Limitations

- Hourly resolution
- All calculations in this paper were performed with an hourly resolution and only for the average power consumption observed during each hour. Most charging processes took significantly longer than 1 h [2], and it is therefore acceptable to use this resolution. For very short processes, an inaccuracy was introduced. This might slightly lower peak power demand as reported in Section 4.1 and SF for larger sets as reported in Section 4.5. If two short processes occur in the same hour but do not overlap, they would appear as overlapping in this study.

- Simplified vehicle charging model
- Since no information about the arriving vehicles was present in this study, the assumption was made that the vehicle was able to charge at the power level dictated by the charging station. Many car models today are not yet able to charge at 22 kW.

## 6. Conclusions

#### 6.1. SFs for Public Charging Infrastructure Were Found

#### 6.2. Naive Charging Is Challenging Only on the Distribution Grid Level

#### 6.3. Price-Optimisation Can Cause Local Hotspots

#### 6.4. Wholesale Electricity Price Optimisation Did Not Reduce Electricity Purchase Costs Significantly

#### 6.5. Local Storage Units Need to Be Used Intelligently

_{2}intensity, their combined effect could be detrimental for grid stability.

#### 6.6. The Introduced Algorithms Are Fast and Efficient

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Connector, C | A socket or cable at a charging station to which an electric vehicle can be connected |

Charge event, CE | A charge event starts when an electric vehicle is connected to a connector and ends once it is disconnected again |

Power limit | The power limit is the power available globally for all connectors |

Power capacity | The rated power of a connector |

EV | Electric vehicle |

SF | Simultaneity factor |

## Appendix A. Pseudo Code

## Appendix B. Simultaneity Factor for the Different Scenarios and Strategies

**Figure A3.**Coincidence factor assuming 8 kWh per CE for (

**a**) naive charging; (

**b**) price-optimised charging; (

**c**) CO

_{2}intensity optimised charging; (

**d**) peak power optimised charging. Note that peak power was optimised for all C simultaneously. Optimizing for each set in (

**d**) for a low simultaneity factor likely results in significantly lower values. For the larger sets, the difference is minor. The blue line shows the mean across the randomly selected sets, and the orange and green lines the upper and lower boundaries of the standard deviation. Each randomly selected set was of the size shown on the x-axis.

**Figure A4.**Coincidence factor assuming 20 kWh per CE for (

**a**) naive charging; (

**b**) price-optimised charging; (

**c**) CO

_{2}intensity optimised charging; (

**d**) peak power optimised charging. Note that peak power was optimised for all C simultaneously. Optimizing for each set in (

**d**) for a low simultaneity factor likely results in significantly lower values. For the larger sets, the difference is minor. The blue line shows the mean across the randomly selected sets, and the orange and green lines the upper and lower boundaries of the standard deviation. Each randomly selected set was of the size shown on the x-axis.

**Figure A5.**Coincidence factor assuming 40 kWh per CE for (

**a**) naive charging; (

**b**) price-optimised charging; (

**c**) CO

_{2}intensity optimised charging; (

**d**) peak power optimised charging. Note that peak power was optimised for all C simultaneously. Optimizing for each set in (

**d**) for a low simultaneity factor likely results in significantly lower values. For the larger sets, the difference is minor. The blue line shows the mean across the randomly selected sets, and the orange and green lines the upper and lower boundaries of the standard deviation. Each randomly selected set was of the size shown on the x-axis.

**Figure A6.**Coincidence factor assuming 60 kWh per CE for (

**a**) naive charging; (

**b**) price-optimised charging; (

**c**) CO

_{2}intensity optimised charging; (

**d**) peak power optimised charging. Note that peak power was optimised for all C simultaneously. Optimizing for each set in (

**d**) for a low simultaneity factor likely results in significantly lower values. For the larger sets, the difference is minor. The blue line shows the mean across the randomly selected sets, and the orange and green lines the upper and lower boundaries of the standard deviation. Each randomly selected set was of the size shown on the x-axis.

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**Figure 1.**Number of publications found via Scopus

^{®}per year for the search terms shown in the legend. Note that not all of the publications submitted in 2020 will likely have been accepted yet, leading to a slightly lower actual value for 2020 [4].

**Figure 2.**SFs reported in the literature by Junge et al. [12] (three scenarios) and by Bründlinger et al. [18] for electric vehicle charging. An SF of 100% was equivalent to all observed vehicles charging simultaneously at one moment in time. For a description of the individual scenarios, please refer to the linked studies.

**Figure 3.**SFs reported in the literature [16] for electric vehicle charging stations. An SF of 100% is equivalent to all observed charging stations having a vehicle charging at full power at one moment in time.

**Figure 4.**Locations of the connectors used in this study. Created with [31].

**Figure 5.**Share of the charging station connectors that were occupied at each moment in time by power rating. For each power rating, the number of connectors marked as occupied was divided by the sum of the connectors for which the status was known: (

**a**) the occupation rate over the entire observed period; (

**b**) aggregated on a weekly level; (

**c**) aggregated on a daily level. Note that the peak on 23 January 2020 as well as the small peaks at approximately 2:10 in the morning were reported by the observed websites but likely represent a fault in the IT system on the remote end. The data and their description are a direct copy from our previous publication and repeated here for the reader’s convenience [2] (This article was published in eTransportation, volume 6, Hecht, C.; Das, S.; Bussar, C.; Sauer, D.U., Representative, empirical, real-world charging station usage characteristics and data in Germany, 100079, Copyright Elsevier 2020).

**Figure 6.**Emission factor [33] and day-ahead prices [32] used in this paper: (

**a**) the full analysed period; (

**b**) the average over a week; (

**c**) the relationship between the two factors. In the scatter plot in (

**c**), each dot reflects one hour, where the x- and y-axis values are defined by the mentioned prices and emission factors.

**Figure 7.**Example of the price-optimisation algorithm. The prices are illustrative only. Iterations 1 to 3 show the charging power that the algorithm would assign to each hour assuming that the vehicle was connected for 24 h, required 60 kWh, and was able to recharge at 22 kW. Charging was first assigned to hour 13, as the price was the lowest. The next-lowest price was at hour 3, and the algorithm decided to also charge with full power during that hour. Since 44 kWh were already charged, only 16 remained to be charged at the next-cheapest hour, 24.

**Figure 8.**Example of the peak power reduction algorithm. Legend entries starting with “Sum” show the sum of the power demand of the three observed connecters for each iteration. Labels starting with “Availability” show the difference between the sum of the charging power of all connected vehicles and the already scheduled recharges at that instance.

**Figure 9.**Power demand using the naive charging strategy for the 1562 connectors with a total power of ~34 MW observed in this study: (

**a**) the power flow over the entire simulated timeframe; (

**b**) the average of (

**a**) over a week; (

**c**) the average of (

**a**) over a day. The plot is structurally very similar to Figure 5.

**Figure 11.**Sorted summed connector power when employing the naive strategy. For example, if during each charging process 40 kWh is to be charged, during ~800 h of the observed 1921 h, the chargers consumed 500 kW or less.

**Figure 12.**Sorted summed connector power when employing the price optimization strategy. For example, if during each charging process 40 kWh should be charged, during ~1400 h of the observed 1921 h, the chargers consumed 1000 kW or less.

**Figure 13.**Sorted summed connector power when employing the CO

_{2}optimisation strategy. For example, if during each charging process 40 kWh should be charged, during ~200 h of the observed 1921 h, the chargers feed in power at a rating of 4000 kW or more.

**Figure 14.**Sorted summed connector power when employing the peak minimization strategy. For example, if during each charging process 40 kWh should be charged, during ~400 h of the observed 1921 h, the chargers consumed 500 kW or less.

**Figure 15.**Costs in EURcent per kWh for the charged energy used assuming the energy recharged per charge event and charging strategies.

**Figure 16.**Costs in EURcent per kWh net recharged energy as a function of the global power limit for the power limits defined in Section 3.2. The left end is the same as “peak minimisation” and the right end is almost identical to the “price optimised” in Figure 15 as a little peak minimisation is required with a power limit of over 7040 kW.

**Figure 17.**CO

_{2}intensity of the electricity charged from the grid using assumed energy recharged per charge event and charging strategies.

**Figure 18.**Summary of the simultaneity factors assuming for (

**a**) naive charging; (

**b**) price-optimised charging; (

**c**) CO

_{2}intensity optimised charging; (

**d**) peak power optimised charging. The plots summarise the information given in Figure A3, Figure A4, Figure A5 and Figure A6. For each combination of number of connectors per set and energy per charge event, 1000 sets were randomly created, and the results displayed in the box and whiskers plots in this figure. For example, when applying the CO

_{2}-optimisation strategy, a random selection of 100 connectors lead to a median simultaneity factor of 30% if a 20 kWh per charge event were assumed with outliers ranging from 20% to 42%.

**Table 1.**Short-term impact of EV charging on the selected key performance indicators. BAU = Business as usual; V1G = smart unidirectional charging; V2G = bidirectional charging; MaaS = mobility as a service. Taken from [3].

Curtailment | Δ Peak Load (%) | Δ Marginal Cost (%) | Δ in CO_{2} Emissions (%) | |
---|---|---|---|---|

BAU | 2% | |||

V1G | 1% | −3% | −1% | −1% |

V2G | −4% | −13% | −2% | |

MaaS | 8% | −8% | 14% |

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**MDPI and ACS Style**

Hecht, C.; Figgener, J.; Sauer, D.U.
Simultaneity Factors of Public Electric Vehicle Charging Stations Based on Real-World Occupation Data. *World Electr. Veh. J.* **2022**, *13*, 129.
https://doi.org/10.3390/wevj13070129

**AMA Style**

Hecht C, Figgener J, Sauer DU.
Simultaneity Factors of Public Electric Vehicle Charging Stations Based on Real-World Occupation Data. *World Electric Vehicle Journal*. 2022; 13(7):129.
https://doi.org/10.3390/wevj13070129

**Chicago/Turabian Style**

Hecht, Christopher, Jan Figgener, and Dirk Uwe Sauer.
2022. "Simultaneity Factors of Public Electric Vehicle Charging Stations Based on Real-World Occupation Data" *World Electric Vehicle Journal* 13, no. 7: 129.
https://doi.org/10.3390/wevj13070129