Evaluation of hosting capacity of the power grid for electric vehicles – A case study in a Swedish residential area

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Introduction
Electric vehicles (EVs) are gaining in popularity.The global sale of EVs doubled in 2021 compared to the previous year and compared to vehicles with internal combustion engines the EVs have lower net greenhouse gas emissions [1].In fact, environmental reasons were the main motivation for choosing an EV according to early adopters in Sweden [2].However, from an electric power grid perspective, the deployment of EVs comes with both positive and negative impacts [3,4].Positive impacts are for example that EVs can act as dynamic energy storage devices to facilitate the integration of intermittent renewable energy sources [5].Furthermore, by utilizing the so-called vehicle-to-grid (V2G) technology, EVs can deliver energy back to the grid [6].By doing so, the active and reactive energy from the EV battery can regulate voltage levels and the frequency in the grid and keep them within their permitted limits [3].The negative impacts include voltage deviation, overloading of power system equipment, harmonics injection, increased peak demand [3,4], increased power losses and phase unbalance [4], etc.However, by employing controlled charging or smart charging, these negative effects can be mitigated [3].
Charging behaviour is central when investigating the impact of EVs on the power grid.Existing studies have analysed EV charging behaviour [7,8] and some have created different models to simulate EV charging behaviour [9][10][11][12][13].Leemput et al. used a mobility profile generator to create charging load profiles for EVs based on statistical data on transportation behaviour [9].A probability density function forecasting approach was developed by Jahromi et al. to predict the residential EV charging profile [10].Quirós-Tortós et al. created EV charging load profiles with the use of travel surveys and by mathematical model and curve fit against real-life EV charging data ( [14,15]) [11].By the use of a model developed by Shepero and Munkhammar [12], data from five Swedish charging stations in combination with Swedish travel surveys were used to create a spatial EV charging model [16].Another Swedish study used synthetic low voltage grids in combination with tracking data from combustion vehicles and assumptions of EV characteristics to study the impact of different charging strategies on a national level [17].The ability of a power grid to integrate new loads, such as EV charging, is called the hosting capacity (HC).It can be defined as "the maximum amount of electricity consumption or generation that can be integrated into the power system, while still maintaining its performance within acceptable limits" [18].The HC is determined by different performance indices (PIs), such as voltage drop and overloading of power system equipment.When the limit of a PI is reached, the HC is obtained.It is important for the distribution system operator (DSO) to know the capacities of their power grids and to plan for what measures to make for continuing a satisfactory operation of the grid when load conditions change [19].Studies show that the resulting HC is dependent on what risk the DSO is willing to take: the higher risk, the larger the HC [20,21].There is a trade-off between the risk of bad voltage quality caused by too little investment in the grid and over-dimensioning of the grid, i.e., too much investment [20].Measures to improve the HC in a power grid are for example to reinforce or reconfigure the grid, to use on-load tap changing transformers, reactive power control, energy storage or demand response [22].
There are several approaches to estimate the HC of a grid for EVs: deterministic method, stochastic method, and time-series method [23].The deterministic method can be applied to assess the mean or maximum power consumption, and the stochastic and time-series models can consider uncertainties associated with EV charging and its grid impacts [24].Time series approaches use load/generation profiles to account for the dynamic nature of the load or generation, and load flow calculations are performed for the time steps in the data set [25].The stochastic approach estimates multiple scenarios to account for uncertainties [22].The unknown variables are applied with various values, and repeated load flow calculations are performed to capture the uncertainty in the results by generating a wide range of outcomes [25].
For existing studies, HC analysis was performed in a time series framework by the use of synthetic EV load profiles created in profile generators (e.g., Refs.[9,16]) and by considering the impact of different charging strategies (e.g., Refs.[9,17]).However, uncertainties in the location of EV integration in the power grid or different EV penetration levels were not considered.Stochastic approaches with Monte Carlo (MC) simulations have previously been applied in Refs.[20,21,26].This method includes uncertainties in EV location by multiple simulations, however, the correlation of different loads over time is lacking.Some literature assesses the HC in a stochastic and time series framework, but the used EV charging profiles are synthetic and derived from a limited sample of EV data, which may not represent reality (e.g., Ref. [27]).Moreover, the impacts of different EV charging strategies on the grid HC using a combination of stochastic and time series HC assessments are not considered in the existing studies.The above-mentioned stochastic method can effectively deal with the uncertainty in EV charging.However, as there is a lack of real-life information, the simulated results have a significant level of uncertainty and thus the obtained conclusions become less informative.Furthermore, the EV usage behaviour and electricity demand patterns differ in different countries, caused by the different cultures.The findings and conclusions obtained using data from other countries cannot be directly applied in Sweden.
There are yet several studies involving EV charging impacts on the power grid in the Swedish context, (e.g., Refs.[16,17,20,21]).For instance, a stochastic approach was developed in Ref. [20] for estimating the single-phase and three-phase HC for EV charging uncertainty such as EV number, charging locations, and charging patterns in two networks in Sweden.In Ref. [21], a tool was developed for estimating the HC of two low-voltage networks for customers with PV panels or with EVs.However, the combination of HC assessment methods together with different EV penetration levels and charging strategies used in this study has not been found in previous studies.
To bridge the gap, this study proposes a study to investigate the HC of EVs in a Swedish residential area in a combined stochastic and time series framework based on different charging strategies and different EV penetration levels.MC simulation will be conducted considering the uncertainty in the EV charging loads and the location of EV charging load integration into the grid.The aim is to comprehensively evaluate the HC of EVs in a residential area under different future scenarios and see how different charging strategies can affect the HC considering various uncertainty.Note that the main focus of this study is to compare three completely different strategies based on the same charging data, rather than finding an optimal charging solution to maximize the HC.Results that can indicate problematic areas in the grid and how it is affected by the charging strategy are desirable.A case study is performed based on real-life data from a local power grid in combination with reallife data on home charging behaviour.The generated results will reflect reality in the Swedish conditions.Note there are many similar residential areas in Sweden, and the results from this study in terms of trends by the use of different charging strategies are expected to apply to other places.
To summarize, the contribution of this paper is as follows: • HC case study reflecting real-life conditions in the Swedish context.The scenario analyses are based on real-life power grid data, real-life residential electricity load profiles and real-life data on EV charging behaviour (collected from a large number of chargers).• A combination of a stochastic framework using MC simulations and time series analysis to consider both uncertainties in EV charging and the correlation of different loads over time.• The impacts of EV charging on a power grid are analysed from the perspectives of EV charging strategies and EV penetration levels.
This paper is structured as follows: Section 2 presents the full method of this study, including the studied system information and the simulation method.The case study results are presented in Section 3. Section 4 discusses the results and the strengths and limitations of this study.A conclusion is given in Section 5.

Method
The method used in this paper is presented in this chapter and can roughly be divided into three steps according to the flowchart in Fig. 1.In Step 1, the power grid model of the case residential community is constructed, and simulation time is selected based on the availability of historical load data.In Step 2, three EV charging profile pools are created based on a real-life EV charging dataset and assumptions on when the actual charging of EVs occurs.In Step 3, the HC of the grid is estimated based on the developed power grid model, the load profiles (obtained from Step 1), the different penetration levels and the charging profiles (obtained from Step 2).The details about each step are explained in the following sections.
2.1.System information for the analysis 2.1.1.Grid information 2.1.1.1.General information of the studied power grid.Borlänge Energi, the DSO owning the power grid in this study, is located in the central part of Sweden and feeds approximately 30,000 customers with electricity.A part of the grid located in a residential area is used for analysis.The customers are mainly detached single-family households with some multi-family houses, and there are a few companies and schools.The area has district heating, which was designed at the planning stage of the construction of the residential area in late 1970 [28].Thus, the electricity grid does not need to cover the heating load.The area was chosen since it mainly consists of residential buildings and it is rather isolated from the rest of the power grid, with only one outgoing 10 kV cable feeding another area further out in the grid (an area that is not included in the case study).The analysed power grid consists of two main feeding underground cables fed from a 130/10 kV station, which feeds twelve 10/0.4 kV substations.From the substations, underground cables are feeding 1321 customers with electricity in 3-phase connections with a nominal phase-to-phase voltage of 0.4 kV.In total, the analysed grid consists of 1299 cables.There are a total of 1278 buses (customer connection points, cable cabinets and cable joints) of which 1028 are customer connection points.
M. Sandström et al. 2.1.1.2.Power grid data and historical load data.Information on the grid structure, performance data of the grid components and its current settings were extracted from the network information system used by Borlänge Energi.The transformers in the substations have a fixed ratio between the primary and secondary side of the transformer, i.e., no onload tap changers.The 130/10 kV transformer has an on-load tap changer which is set to run at a voltage between 10.5 and 10.7 kV on the secondary side.The secondary side of this transformer served as a slack bus in the power grid model.For simplicity, the voltage level was set at a fixed value of 10.6 kV in the model and the phase angle was set to zero.Extracted data for the power cables consisted of the cables impedances, rated current, its length and to and from which bus the cable was connected.
Historical load data was available from July 2021 to mid-January 2022.To shorten the computation time, a two-week period containing the highest hourly aggregated power load was used in the simulation (Monday 29th of November to Sunday December 12, 2021).This is to be considered a worst-case scenario because the grid is already heavily loaded.The data consisted of the total three-phase load for hourly active and reactive energy consumption and production (kWh/h, kVAR/h).Hourly data was available from 1305 meters.For the remaining 16 meters and the outgoing 10 kV cable, static loads were used based on the Velander constant.The outgoing 10 kV cable was simulated as a static load of 257 kWh/h, which corresponds to the total load of the other area not included in the HC case study.The aggregated active load distribution from the 1305 hourly meters is shown in Fig. 2.

EV data 2.1.2.1. EV charging data.
In this study, real-life EV charging data was obtained from the Swedish EV charging product supplier CTEK [29].The cleaned dataset contained approximately 159000 charging sessions from approximately 900 different chargers.The data contained the following information: • Date and time for plug-in and plug-out of the EVs (in minute resolution) • Total energy used in the charging session (active energy, kWh) • Charger-ID for each session The dataset contains data from a time period of one year (2020-10-29 to 2021-10-29).However, all the chargers were not active during the whole time period.The specific locations of the chargers are unknown with the concern of privacy, but all chargers are installed in Sweden and categorized as home chargers (i.e., chargers at either single-or multifamily houses).

Creation of the EV charging profile pools.
The EV charging dataset was used to create charging profiles.To match the time period used for the historical load data, only Holliday free winter weeks were selected, resulting in data from nine different two-week periods.
The charging profiles were created based on the energy consumed during the session and a rounded time duration in a 15-min resolution.A simplification was made as the charging was set as only three-phase charging with a power factor of 1. Three-phase charging was used considering the fact that the amount of pure battery EVs is increasing dramatically in Sweden, and the majority registered in the year 2021 accept three-phase power [30][31][32] and thus is a likely future scenario.
Three different charging strategies/cases were considered, as summarized in Table 1.Case 1 uses the assumption that the charging starts immediately after the EV was plugged in.Case 2 uses the assumption that the charging is evened out through the complete plug-in session, giving a constant average charging power from start to stop in the session.Case 3 uses the assumption that the EVs are charging when the spot price is lowest within the plug-in session.Spot price data from SE3 was used [33].
The maximum charging power was set to 11 kW because the majority of the newly registered battery EVs in Sweden year 2021 have on-board  chargers with a maximum capacity of 11 kW [31,32].
For each case, a charging profile pool was created according to the process illustrated in Fig. 3.
For each time period, the plug-in sessions with the same charger ID were filtered.For each charging session, charging profiles were created using Policy (1) and Policy (2) (for Case 1 and Case 3) or Policy (3) (for Case 2).Policy (1) and Policy (2) handle overlapping sessions due to chargers with two outlets and restricts the charging power to 11 kW.ts is the time step, P exist is the existing power value for that ts due to an overlapping session, P ts,overlapping is the power from the same ts in an overlapping session.P 15 is the power required for 15 min to achieve the remaining energy of the session, E ses is the total energy used in the plugin session, P max is the maximum allowed charging power, P ts is the assigned power for the time step, P used is the share of P 15 that is used in the time step.P mean is the average power used in the session.
For Case 3, between Policy (1) and Policy (2) the spot price is assigned to its corresponding time step, and the session is then sorted based on ascending spot price instead of having it ordered by time.In other words, the hours are first sorted in price order and then the EV charging loads are assigned to each hour following the price order.After that, the hours are restored to follow the time sequence, with the evaluated charging demand of EVs.
Eq. ( 1) (for Case 1 and Case 3) and Eq. ( 2) (Case 2) were used to merge all session profiles with the same charger ID.All charging profiles from different IDs and time periods then resulted in the charging profile pool.

P ts = max (P ts session n, P ts session n + 1)
Eq. ( 1) where n is the specific session.

Simulation method
The assessment method of the HC used in this study is a combination of a time series approach and a stochastic approach in which EV loads are added at pre-defined penetration levels.The time series approach was used for household loads and EV charging loads.Uncertainties in the location of EV chargers and individual charging behaviour (in terms of what charging profile is used) were handled with a stochastic approach using MC simulations.
The power system analysis tool Pandapower was used to build a power grid model for the considered case district and to perform the simulations.It is an open-source tool that is validated and tested against commercial software [34].The tool has a Newton-Raphson power flow solver and is based on Python programming language [35].

Investigated PIs and PI limits used in the simulation
Many different PIs can be used in HC analysis.In this study, three PIs were investigated with the consideration of data availability, namely voltage deviation, cable loading and transformer loading.
The HC is dependent on what PI limit is used.In the voltage characteristic standard EN 50160 [36] and the Swedish regulation EIFS 2013:1 [37], it is stated that the 10 min rms (root mean square) value of the voltage should not exceed ±10 % of the nominal voltage.However, in this study a stricter limit of ±5 % is used.This is because the DSO owning the power grid wants to keep the voltage at stricter limits to avoid any disturbances to the customers.The nominal phase-to-phase voltage at the low voltage grid is 0.4 kV, hence the limit of the voltage drop is set as 0.02 kV.The PI limit of the transformers was set to 100 % of its rated power.The PI limit for cables was set to 80 % of its rated current since the DSO in this study usually uses a lower fuse to limit the time of fault currents.

HC simulation steps
To consider the randomness and uncertainty of the EV charging loads, MC simulations were performed.The simulations were performed following the processes in Fig. 4.
The processes of the MC simulation in Fig. 4 are explained below: a.The power grid model was constructed by importing data from the power grid components.Load profiles of the historical load data for the selected time period were assigned to their corresponding connection point and served as a base load.b.A penetration level of EV chargers was chosen.c.The number of charging profiles corresponding to the number of households with a charger (NHC) was randomly selected from a charging profile pool.The same number of households were randomly selected for receiving a charger.The selection of EV Fig. 3. General process of creating charging profile pools from the charging sessions.
M. Sandström et al. charging profiles and households were assumed to follow uniform distribution, i.e., all charging profiles and households had an equal chance of being picked.No charging profile or household was picked more than once in the same simulation set.d.If a household was chosen to have a charger, the charging profile load was added to the household load profile.e.If the total load of a time step (tot.load (ts)) exceeded the maximum power (Pmax), which was set to 17 kW, the power for that particular ts was changed to Pmax.The remaining power of the ts, Pdiff was added to the existing power in the next time step, P(ts+1).In this way the main fuse was limited to 25 A (see section 2.2.3).f.Power flow calculations were performed for the ts.If a PI limit was violated the violated component was registered.g.Time series power flow calculations were performed for each ts in the period (1344 time steps, 14 days × 24 h x 4 quarters).h.The process was iterated for 200 simulation sets, i.e., 200 times repeated simulations in which the EVs have different charging locations (randomly selected from the map) and charging profiles (randomly selected from the created charging profile pool).
The process in Fig. 4 was repeated for different penetration levels of EV chargers and the different cases.The penetration levels started from 0 % and were increased by 25 % intervals up to a penetration level of 100 %.In this paper, a 100 % penetration level means that every household has one EV charger.

Maximum load restrictions
If the total load (historical load + EV charging load) at one customer exceeded 17 kW, the EV load was decreased, and the excess power was moved to the next time step.The reason why a maximum of 17 kW is used is that it corresponds to a fuse of 25 A. Although most of the households in the investigated grid have a fuse smaller than 25 A (16 A), they can easily upgrade these fuses to 25 A without the need of changing connection cables.Furthermore, two simplifications were made.
o Simplification-1: For sessions with high average charging power, the duration of the charging sessions was extended to respect the maximum total load.o Simplification-2: For the price-based case (i.e., Case 3).When the total power is larger than 17 kW, the remaining charging power is moved to the next time step following temporal sequence, instead of the next cheapest time step in the session.
Both of these simplifications are of small significance in the total result since few sessions are affected.As a reference, approximately 0.2 % of the charging session in the charging profile pools had an average power larger than 11 kW and 0.07 % of the load hours for meters categorized as households had a power larger than 6 kW.

EV charging profile pools
Each charging profile pool contains 4557 different charging profiles from 855 different chargers.The mean time for a plug-in session was approximately 13 h and the mean energy consumed during a session was approximately 10 kWh.On average, a charger had approximately 11 plug-in sessions in a two-week period.Table 2 shows statistics from all two-week periods used in the charging profile pools.Med and Std are abbreviations of median and standard deviation.
Fig. 5 illustrates an example of how the charging profiles differ in the three cases for one charger in a period.In Case 1, there is a large charging load at the start of each charging session.In Case 2, the charging load is evenly distributed across the whole charging session.While in Case 3, the charging load is in the period with low electricity prices.
To see trends and differences between the charging profile pools, aggregated results were visualized.Fig. 6 (a) shows the aggregated load from all charging profiles in the pool divided by the total amount of charging profiles in the pool, giving an average charging profile per charger.Fig. 6 (b) illustrates a zoomed-in plot of the first Monday in the period.Note these illustrations show averaged profiles, and thus the power is lower than the individual profile.The peak load in Case 3 is much higher than the other two cases, as the EVs shift their charging loads into the same low electricity-price period.In Case 1, as the EVs have a different charging start time (i.e., different arrival times), the peak charging loads are flatter compared to Case 3. Fig. 7 shows how the load of the EV chargers for the three different cases coincides with the household load.The EV charger load is the average charging profile per charger and the household load is the average of the hourly metered household loads.
For Case 1, the peak average charging load coincides with the peak household load, while it does not in the other two cases.The peak average total load is however highest in Case 3 due to the fact that all chargers react to the low price signal.
Fig. 8 (a) shows what percentage of all chargers in the profile pools have EV plugged in based on the two-week periods.Fig. 8 (b) illustrates a zoomed-in plot of the first Monday in the period.Approximately twice as many chargers are plugged in at midnight compared to midday.

HC simulation
In this section, figures and tables are used to illustrate the grid structure and the resulting number of violations of the PIs in three cases (as introduced in Section 2.1.2.2) under four penetration levels (i.e., 25 %, 50 %, 75 % and 100 %).The MC simulation was conducted with a repetition of 200 times, with 1344 simulation steps in each repetition.The average values of the results from the MC simulation are shown in this section.
In the result figures, triangles are customer connection points, cable  Fig. 9 and Table 3 show the result at a penetration level of 0 %, which is used as the start of analysis for the three cases.There is no EV charging load, and thus the results are only dependent on the historical load data.Table 3 gives the number of unique components that were violated in the simulation set and the average number of violations per violated component and simulation set.Components that were never violated are not included in the average.As shown in Table 3, there is one cable and two buses that got violated in every simulation.Hence, for this part of the grid, the HC is already reached without EV charging.Apart from these three components, there are no violations in the grid, and the HC is not reached for the other areas.
In Fig. 10, the results from the simulation of all penetration levels for the three cases are presented in maps of the grid.From the figure, problematic areas can be derived.It can be seen that Case 3 gives the highest number of violations, followed by Case 1, and Case 2. For a higher penetration level, both the number of areas that are affected and the number of times the components get violated are increasing.Table 4 shows the number of unique components that were violated for each case and penetration level when the PI limit for voltage drop is 5 %.Note, the statistics are based on 200 MC simulations (i.e.200 simulation sets).The values in parenthesis are the average number of times a unique component got violated per simulation set.
From the table one can get the exact number of the individual components that are violated.One can for example see that in Case 1 and Case 2, the HC is reached for relatively few numbers of cables compared to Case 3. The majority of the violated cables were 0.4 kV cables.Only Case 3, with 100 % EV penetration level, got violations for 10 kV cables, in which five of the 119 violated cables were 10 kV cables.
Between the Cases there is a large difference in how the grid is affected, for example, a penetration level of 100 % for Case 2 gives fewer violated components than the penetration level of 25 % for Case 1 and Case 3. Furthermore, for the penetration level of 100 %, the HC is reached for relatively small parts of the grid for Case 2 whereas for Case 3 it is reached for almost the whole grid.
The PI limit of the voltage drop was set to 5 % in this study.To get an Fig. 5. Charging profiles for one example charger in a 2-week period.understanding of how a change in the PI limit can affect the result, the performances of the buses were evaluated when PI limit of the voltage drop was set to 10 %.As can be seen in Table 5, much fewer buses are affected at a PI limit of 10 % compared to a limit of 5 %.
To examine if 200 MC simulations were enough, a sensitivity analysis was made.More details are presented in Appendix A.

Discussion of the results
Real-life data of when an EV is plugged in, the duration of the plug-in and energy used in the plugin session have been used together with assumptions of when the actual charging occurs to create the charging profiles.In this way, human behaviour is the same in the three cases, it is only the setting of when the charging occurs that differs.Nevertheless, EV owners do not always know for how long the EV is to be plugged in.It could therefore be hard to beforehand decide what settings to use for Case 2 and Case 3 since these cases are based on the duration of the plugin session.However, the analysis shows the potential of how the grid is utilized based on the same historical EV plug-in behaviour.
The results are based on a period of two weeks.For the household load, the two-week period with the highest aggregated energy consumption was used, giving a worst case in terms of load contribution from the households.The periods for the EV load were chosen to match the two-week period for the households.It was not investigated if these periods differed from periods in the summer seasons, however, colder temperatures lead to higher energy consumption of EVs [38].Hence, the  chosen periods and the HC analysis can be considered as a worst-case application.
Case 1 is the most common case when the EV owners do not have any incentives to postpone the charging or spread it out in time.The result from the average charging profile in combination with the average household load (Fig. 7), is comparable with results from a study [11] based on data for UK home charging behaviour [14].Both show that the average peak demand for households was approximately doubled with EV charging compared to without it.However, even though a large share of the charging occurred at the peak hour for household consumption, it gave less impact on the grid compared to Case 3.This is because of the variation in the time when the EVs are plugged in.For Case 3, the majority of the charging occurred at off-peak hours, but new peaks were created since many EVs started to charge at the same time.Similar results are shown in the study by Leemput et al. [9], a charging strategy based on off-peak tariff periods gave lower HC due to simultaneous EV loads compared to a strategy of charging directly after plugging in the EV.Moreover, other technologies could also be electrified and operate based on price signals and thereby potentially decrease the HC further.In a study by Marszal-Pomianowska et al. [39] it was shown that operating heat pumps and other residential equipment based on electricity price signals gave new peak loads, which caused power grid violations.
From a grid perspective, Case 2 is the most desirable.It utilizes the grid more efficiently, and thus fewer grid reinforcements are required.In Sweden, the most common form for the DSO to charge household customers is through a fuse-based tariff.In recent years, there is an increased interest in introducing power tariffs [40].With power tariffs, customers are charged based on their highest power consumption, giving them the incentive to avoid high power peaks.This could lead to charging strategies similar to Case 2 where the charging is spread out in time to avoid peaks.It would be interesting to investigate charging based on energy price signals and lower total power for individual households.The power peaks would then be lower but the aggregated load at low electricity prices could still be relatively high.
Results in this study cannot be directly transferred to other grids since different power grids have different designs and conditions.However, the overall method can be used and the general findings, in terms of which charging strategy is most grid friendly, are expected to apply to other residential grids.

Strengths and limitations of the study
One strength of this study is that the results are illustrated in maps of the grid, giving the possibility to see where in the grid problems are likely to occur.The study is performed over a time period of two weeks, giving a larger spread in the result compared to if the simulation were made on only one time step.Repeated MC simulations are performed over the two-week period with different combinations of used charger profiles and assigned households with a charger, giving a further spread in the result.The MC simulations consider the randomness in reality where different EVs may charge in different locations.The identified results regarding cables, transformers, and buses with violations are more robust, compared to the deterministic analysis.Another strength is that the study is based on real-life data and simulations are performed on an existing grid, which gives results that reflect reality.The EV charging behaviour is based on a large number of chargers, giving a natural  spread in individual charging behaviour.However, the use of real-life data also comes with some limitations.For the charging profiles, the results are based on assumptions that the behavioural patterns are the same as those in the dataset.This leads to several implications.For example, all data used in this study is collected from periods when people were affected by the corona pandemic, behavioural patterns might therefore be different compared to before and after the pandemic.The battery sizes of the EVs can affect the behaviour of charging: if a car has a larger battery, it is possible to be charged less frequently compared to a small battery-sized EV.A development in EV car batteries could therefore change the behaviour derived from the data in this study.
The results are based on household data with an hourly resolution and EV data with a quarterly resolution.According to the standard EN 50160, the 10 % limit of the voltage drop is based on 10 min average data.With the lower resolution, there might be occasions with a 10 min average with a higher voltage drop.However, in this study a stricter limit of the voltage drop compared to the standard has been considered.
There are also some implications of the results connected to choices in the modelling process.The results are based on three-phase charging, which could give a more optimistic HC.Results from another case study on Swedish grids show that the HC is higher for three-phase charging compared to single-phase charging [20].

Conclusion
This study uses a stochastic time-series method to investigate the impacts of EV penetration levels and EV charging forms on the HC of a local residential electricity network.The uncertainty analysis based evaluation method can robustly identify the weak power grid areas, which need reinforcement for integrating more EVs in the future grid system.Power flow calculations have been performed over a two-week period with the highest average electricity demands.The study is based on real-life data from an electric power grid, historical electricity consumption and EV charging behaviour.It is performed as a case study of a Swedish residential power grid, considering three different charging strategies.
By comparing the three different charging strategies, the results show that when the actual charging occurs has a big impact on the HC.The case based on energy price signals resulted in most violations in the grid, followed by the case in which charging started immediately after the plug-in of the EV.The best case from a grid perspective was when the charging was spread out in time.This case resulted in a smaller number of affected components in the grid at a penetration level of 100 % compared to the other cases at a penetration level of 25 %.Hence, if the charging power can be kept at a lower level and spread out in time, the grid can host more EVs with less need for reinforcement.On the other hand, if many EV owners start to charge at the same time the grid could host much fewer EVs before violations occur.This implies the need for coordinated charging controls of EV fleets or diversified power tariffs to balance power on a large scale.Reinforcing the grid could however still be a necessary and relevant measure.As a continuation of this study, it would therefore be interesting to investigate the cause of the violated areas in the grid and investigate which approach is the most economical to mitigate such problems.
In this study, the control of EV charging load is relatively simple by forming the strategies as constant models.Future work will conduct more comprehensive studies by integrating intelligent EV charging controls into the model to form new strategies.Moreover, EVs can be used as a mobile energy storage system to store surplus renewable power.Future work will also investigate how such charging-discharging usage can change the HC of the existing grid.

Table 4
Number of unique components violated when the PI limit for voltage drop is 5 %.(In parenthesis the number of average violations per violated component and simulation set is given.The two buses and one cable that got violated in every simulation are not included in the average, to give it a more representative value.)Minor differences were found, as can be derived from Table A1.The number of violated cables is the same, and for transformers one more transformer got violated in the extended simulation, however it only got violated one time.More buses were violated for the extended MC simulation, but it is still a relatively low increase of 2.5 % for 100 additional simulation sets.The geographical distribution of the violations was also similar for both simulations, as can be seen in Fig. A1.Considering such marginal performance improvements at the expense of a significantly large computational load increase, 200 MC simulations were used for the analysis in this study.

Fig. 4 .
Fig. 4. Flowchart of the different steps in the MC simulation to estimate the HC.
cabinets and cable joints (so-called buses), circles are transformers, solid lines are connected cables, and dashed lines are disconnected cables.Components coloured in grey mean there is no violation of these components in any of the simulations.Components that are violated in any of the simulations are coloured according to the colour bar in the figures, indicating the average number of violations for the component per simulation set (average number of violations in the two-week period, with 1344 simulation steps).Components coloured in red are violated 100 or more times per simulation set.The result figures are produced based on violating limits of any of the three PIs, i.e., 100 % transformer loading, 80 % cable loading and a 5 % voltage drop at the buses.

Fig. 6 .
Fig. 6.Average charging profiles per charger, (a) for the two-week period; (b) for the first Monday in the period.

Fig. 7 .
Fig. 7. Average charging load per charger and the average household loads.

Fig. 8 .
Fig. 8. Percentage of all chargers in the profile pools that have EVs plugged into the charger, (a) for the two-week period; (b) for the first Monday in the period.

Fig. 9 .
Fig. 9. Grid illustration of the average number of violations per simulation set at an EV penetration level of 0 %.

Fig. 10 .
Fig. 10.Grid illustration of areas reaching the HC and the average number of violations per simulation set.For all cases and EV penetration levels of 25, 50, 75 and 100 %.

Fig. A. 1 .
Fig. A.1.Grid illustration of the result from the original simulation and the extended simulation.Results are for Case 1 and 25 % penetration level.

Table 1
Summary of the different Cases used in the analysis.
CaseAssumption of charging time point Maximum charging power 1 Immediately after the plug-in of the EV 11 kW 2 Spread out during the session Average power of the session 3 Cheapest spot price during the session 11 kW M. Sandström et al.

Table 2
Statistics of the charging sessions used in the profile pools.

Table 3
Statistics of the components violated for an EV penetration level of 0 %.

Table 5
Change in number of unique buses violated per simulation set when the PI limit for voltage drop changes from 5 % to 10 %.

Table A . 1
Comparison of number of unique components violated between the original and the extended simulation, for Case 1 and an EV penetration level of 25 %.In parenthesis the number of average violations per violated component and simulation set is given.The two buses and one cable that got violated in every simulation are not included in the average, to give it a more representative value.