Maximum Tolerated Number of Simultaneous BEV Charging Events in a Typical Low-Voltage Grid for Urban Residential Area

Abstract

In this paper, we determine the maximum number of battery electric vehicles (BEVs) that can be charged simultaneously at full power during peak load hour without overloading transformer and lines or causing an unacceptable voltage drop in the low-voltage (LV) grid. In order to predict the BEVs charging demand, an application that takes into account the random user’s arrival time and the initial battery state of charge (SOC) was developed using the C++ programming language and the Qt toolkit. The network analysis was then carried out using the Quasi-Dynamic Simulation (QDS) toolbox in DIgSILENT PowerFactory on a typical German LV grid for a metropolitan urban area. The simulation findings indicate that the value of simultaneity factor (SF) plays an important role in identifying the most robust and weakest grid’s bottlenecks. There is currently no immediate threat of electromobility pushing the parameters of the grid to their unacceptable limits; however, it is essential to examine the LV grid’s bottlenecks and gradually prepare them for the ramp-up of BEVs. In the short term, the bottlenecks can be removed using conservative planning and operating principles; however, employing novel approaches will be crucial in the longer term.

1. Introduction

The German government is making significant financial investments in the electrification of the transportation sector as part of its effort to achieve carbon neutrality by 2045 [1], given that it contributes 20% of the country’s overall emissions [2]. For this purpose, 15 million registered electric vehicles (EVs) are expected to be on the road by 2030, according to German policymakers [3]. The electrical grid may experience a considerable increase in the load demand as a result of charging a large number of EVs; however, the stochastic behavior of the users prevents the charging operations from taking place simultaneously. Therefore, when designing and planning the distribution grid, the SF for EVs charging, as well as the other group of loads, must be taken into consideration to calculate the maximum simultaneous power. As a consequence, by not overestimating the grid load, additional expenditures associated with the procurement and installation of high-capacity electrical components are avoided. Furthermore, it is essential to assess typical LV network topologies for any potential vulnerabilities that can appear during EV charging processes and to identify when grid bottlenecks go beyond their standard limits.

The influence of EV charging on the electrical grid has been the subject of many research studies from around the world [4,5,6,7,8], and multiple strategies have been proposed to minimize its negative impacts [9,10,11,12]. Similarly, several studies in this field have recently been undertaken using real or typical German LV grids, as highlighted in [13,14,15,16,17,18].

Gauglitz et al. [13] suggested a method for estimating the number and distribution of home charging stations in the city of Wiesbaden in order to examine their effects on voltage and transformer/line loadings. The realistic worst-case scenarios for the grid were defined using the SF. Gemassmer et al. [14] examined the impacts of three different charging methods on the voltage and line/transformer loadings of LV grids for urban and rural regions in Berlin and Brandenburg; simulations were carried out with 0.1% of the anticipated number of vehicles in 2040. Hecht et al. [15] analyzed SF, peak power, CO₂ intensity, and electricity prices under four different charging methods using real data from public charging stations in Germany. However, the other challenges in the LV grid, such as voltage stability and line/transformer loadings, have not been studied. Held et al. [16] assessed the effects of EV penetration in a residential area on line loading, voltage stability, and the unbalance of a typical German distribution grid while taking SF into account. However, transformer loading, random arrivals, and the random initial SOC of EVs have not been addressed. Held et al. [17] employed load flow calculations to evaluate the transformer/line loadings and voltage values for typical German LV grids in campestral, suburban, and rural regions with the integration of EVs; however, urban grids have not been considered. Two scenarios for daily EV recharging and one scenario dependent on driving distance were presented. Spitzer et al. [18] investigated how coordinated and uncoordinated EV charging at a residential area affected the voltage stability and unbalances of a semi-urban European LV grid, but line/transformer loadings have not been covered.

In this study, we investigate the impact of BEV charging processes on the voltage and loadings of the transformer and line. The contributions of the paper are summarized as follows:

• The definition of a typical LV grid in a German metropolitan urban area, including associated bottlenecks;
• The definition of the worst-case grid scenarios, as well as determining the maximum number of BEVs that can be charged simultaneously without exceeding the voltage and transformer/line loadings restrictions;
• The calculation of the actual number of BEVs in the LV network whose charging demands cause the grid’s parameters to be violated.

The remainder of the paper is organized as follows: Section 2 describes the grid configuration, the modeling of BEVs, the objective, and the constraints. Section 3 presents two case studies and simulation results, followed by a discussion in Section 4. Finally, conclusions are given in Section 5.

2. Materials and Methods

2.1. Grid Topology

A representative metropolitan urban grid was developed by statistically analyzing typical network characteristics using grid data from Syna GmbH (Frankfurt am Main, Germany) and the regional statistical spatial typology (RegioStaR) of the German Federal Ministry of Transport and Digital Infrastructure (BMVI) [19]. RegioStaR provides a useful way to distinguish between regions and can be used to assign each municipality to a particular typology; it is organized hierarchically, starting with RegioStaR 2, a general regional type (urban and rural regions), moving through RegioStaR 4, a regional type that is divided into 4 regions, and ending with 17 spatial types (RegioStaR 17). In this respect, 306 municipalities in the German states of Rhineland-Palatinate, Hesse, Bavaria, and Baden-Württemberg are assessed based on the RegioStaR classification to identify the frequency distribution of the following grid characteristics:

• The total number of LV feeders per transformer;
• The total length of LV lines (km), as well as their classification based on overhead lines and underground cables;
• The total number of transformers and their rated power (kVA);
• The total number of house connections, including allocated electric meter, consumer types, and the predicted yearly consumption (kWh).

An analysis of 4020 local substations revealed that transformers with a rated power of 630 kVA are the most frequently used in metropolitan urban areas. Typically, there are 8 ± 2 feeders at the 0.4 kV level; each feeder has a main line that is 0.25 ± 0.04 km long and serves 8 ± 1 house connections. To reflect the worst-case scenario, the longest main line length, as well as the greatest number of feeders and house connections resulting from the average values plus deviations, were utilized in this study.

The evaluation of the network data indicates that each house connection in a metropolitan urban area consists of three residential units, with a total yearly consumption of 13,500 kWh. The modeling of house connection loads is based on the household’s load profile (H0) from the BDEW (Bundesverband der Energie- und Wasserwirtschaft) standard [20], which is a component of the DIgSILENT PowerFactory library [21], as well as the anticipated annual consumption.

According to a statistical analysis of the grid data, the aluminum cable type NAYY 4 × 150 mm² is often used as the main cable type in LV grids. A cross-section of 240 mm² was used for lines that supply a high load. On the other hand, depending on the number of connected residential units, the cable types NAYY 4 × 35 mm² or NAYY 4 × 50 mm² were utilized for house connection cables. Figure 1 depicts a single-line diagram of a representative metropolitan urban grid based on the aforementioned grid characteristics. It consists of a 630 kVA MV/LV transformer, with 10 feeders with 9 house connections (i.e., 27 residential units) on each. Each feeder has a 0.29 km line length.

2.2. BEV Load Modeling

In this study, we developed an application using the C++ programming language and the Qt toolkit [22] to predict the demand for BEV charging. The SOC and user arrival time were regarded as random variables owing to the stochastic behavior of BEV owner. We assumed that arrival time followed a uniform distribution $U(a,b)$ with the lower and upper bounds of $a=16:00$ and $b=18:00$, respectively, since the VDE FNN study [23] indicates that the majority of BEV charging processes in residential areas begin within this time frame; thus, the highest SF becomes effective in the evening hours. In terms of SOC, users were expected to accept a lower SOC value due to the availability of wallbox charging stations at home and the awareness that BEV charging would undoubtedly be possible once they arrive. The initial SOC was assumed to follow normal distribution $N(\mu ,{\sigma }^2)$ with a mean and standard deviation of $\mu =25\%$ and $\sigma =10\%$, respectively [24]. To determine the charging rate, the SOC is calculated for each step size as follows:

$${SOC}_{t+1}={SOC}_t+\frac{P_{wb}\times ∆t\times 100}{C_{bat}\times 3600}$$

(1)

where ${SOC}_{t+1}$ indicates the SOC level (%) at next time step $\left(t+1\right)$, ${SOC}_t$ is the actual SOC (%), $∆t$ is the simulation step size (s), $C_{bat}$ is the battery capacity (kWh), and $P_{wb}$ is the power of the wallbox (kW). We made the assumption that $P_{wb}$ is set to 11 kW, and $C_{bat}$ is 64 kWh in accordance with the dataset in [25] that indicates the average useable battery capacity of BEVs in the current market.

The charging procedure would be completed once the BEV battery SOC level reaches 80%. The assumption was made that the BEV is only charged once each day.

Since Digsilent PowerFactory was utilized to carry out the grid calculations, an interface was developed between this application and PowerFactory to complete the BEV load modeling, as detailed below:

• Create a text file from the Qt-application’s output, which indicates the BEV charging power over time;
• Model the BEV in PowerFactory using LV load;
• Define the time characteristic parameter of the LV load using the text file.

2.3. The Objective and Constraints

The aim of this paper is to examine the robustness of a typical German metropolitan urban grid given the simultaneous charging of BEVs under the worst grid conditions (Section 3.1.2). The following main questions will be answered in this study:

• To what extent can the existing LV grid be reliably used for the development of the charging infrastructure?
• What correlations exist between charging procedures, other loads, and the grid operational parameters?
• To what extent should electromobility be incorporated into the current planning and operating principles of distribution networks? What strategy can be recommended in this circumstance?

When evaluating the robustness of the LV grid, a particular focus should be given to the network bottlenecks [26]:

• The transformer;
• The first segment of the line, through which most of the current flows;
• The voltage at the feeder’s last connection point.

The maximum short-term overloads for the transformer and lines were assumed to be 120% and 100%, respectively, based on empirical values of aging processes and typical planning and operating principles for urban distribution networks [26]. The voltage deviation at the LV level was restricted to ±5% of the nominal voltage to ensure that the voltage band was maintained, even in the worst-case scenario, i.e., when a local substation uses a transformer with a fixed voltage ratio.

3. Results

The network calculation software DIgSILENT PowerFactory Version 2019, which provides a wide variety of computation features for network planning, was used to simulate the metropolitan urban grid. In this work, the QDS toolbox was utilized to perform a set of load flow calculations to monitor the desired variables for elements that are time-dependent. For this purpose, the QDS was executed on 1 July 2022, a typical summer day, with a time resolution of 5 min. Two scenarios were defined in order to observe the required findings.

3.1. Case Studies

The following case studies were taken into consideration to examine the grid’s capacity and quantify the effects of BEV demand on the grid’s parameters:

3.1.1. Scenario #1: Initial Scenario

The initial calculation scenario only took into account the base load of residential units without the penetration of wallbox charging stations in order to subsequently assess the effects of charging operations on the LV grid. Here, the peak hour in the feeder’s load profile was determined as a starting point for the worst-case scenario.

3.1.2. Scenario #2: Worst-Case Scenario

This research aimed to identify the maximum number of BEVs that could be charged simultaneously in a critical grid condition without causing a voltage violation, line overloading, and transformer overloading. In order to create the worst-case scenario for the grid’s load, we assumed that the peak hour for the residential area and the BEVs charging processes must coincide when modeling the BEV profiles (Section 2.2). Therefore, if the BEV charging process was finished before the peak hour, this BEV charging profile would not be approved, and the Qt-application should be run again until our assumption was verified.

In this scenario, the number of BEVs was gradually increased along the feeder. To generate the worst-case scenario for the voltage drop, we assumed that the BEVs were connected sequentially to the residential units, starting at the end of the feeder and moving toward the local grid substation; there was only one BEV per residential unit. Following each BEV’s connection to the feeder, the QDS was executed to record the grid’s parameters; when the voltage at the feeder’s last connection point exceeded the minimum limit of 0.95 p.u. and the first segment of the line reached its maximum loading limit of 100%, the feeder’s calculation was completed. It should be noted that identical BEV profiles were used in each feeder to provide the same condition so that the impact of BEVs on the voltage magnitude and the loading of cables with cross sections of 150 mm² and 240 mm² could be more effectively compared. In addition, the transformer-related calculation was finished when its loading limit reached 120%.

3.2. Simulation Results

This subsection presents the study’s results and looks into how the aforementioned scenarios might affect the LV grid’s bottlenecks (Section 2.3).

The transformer loading for scenario #1 over the simulation time is shown in Figure 2 using the QDS tool. As can be observed, the loading value reached its maximum of 34.79% at 20:00; thus, this time was chosen as the peak load hour for household loads in our study.

Figure 3a depicts a comparison of the line loadings for scenario #1 over the time. The maximum loadings for the first segment of cables with cross sections of 150 mm² (in Feeder 1) and 240 mm² (in Feeder 2) were 8.83% and 11.68%, respectively. Similarly, Figure 3b compares the voltage at the feeders’ last connection points. At 20:00, the voltage magnitude in Feeder 1 (150 mm² cable) and Feeder 2 (240 mm² cable) dropped to 0.987 p.u. and 0.988 p.u., respectively.

The Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9 illustrate the simulation outcomes for scenario #2 with BEV penetration.

Figure 4 displays the voltage magnitude at the feeders’ final connection points as a consequence of progressively increasing the number of BEV charging operations that take place simultaneously at 20:00. In Feeder 1 (150 mm² cable) and Feeder 2 (240 mm² cable), the minimum voltage fell to 0.948 p.u. and 0.949 p.u., respectively, thus exceeding the acceptable 0.95 p.u. limit.; it resulted from 7 and 14 simultaneous BEV charging processes, respectively.

Furthermore, the impact of BEV charging on cables with different cross-sections and similar lengths can also be evaluated from the line loading perspective. A total of 14 simultaneous BEV charging events led to 100.2% loading in the first section of NAYY 4 × 150 mm² cable, as seen in Figure 5; however, for the same circumstance, the loading of NAYY 4 × 240 mm² cable was 74.06%. The 240 mm² cable was overloaded by 102.6% due to 20 simultaneous BEVs charging events, whereas the 150 mm² cable was subject to an additional 39.2% overloading that could cause the cable to overheat.

Figure 6 demonstrates that the maximum loading of the transformer surpassed the limit of 120% by reaching 121.58% when 47 BEVs in the LV grid were charged simultaneously during peak hour.

In summary, as seen in Figure 4, Figure 5 and Figure 6, the critical numbers of simultaneous charging processes during the peak hour at which the grid’s bottlenecks violated their standard restrictions were 7, 14, 20, and 47; consequently, Figure 7 shows the total power demand for these critical numbers of BEVs over time. Of course, Figure 7’s depiction of the course is incomplete, since it only displays the loading processes that were active at 8:00 p.m. The BEVs were plugged into the wallboxes between 16:00 and 18:00. Assuming that each wallbox provides 11 kW, the power demands for 7, 14, 20, and 47 simultaneous BEV charging events at 20:00 would be 0.077 MW, 0.154 MW, 0.22 MW, and 0.517 MW, respectively.

Additionally, Figure 8 and Figure 9 provide a helpful visual insight for determining how much load demand in each feeder causes voltage and line loading deviations. In scenario #1, the baseload for all of the feeders was identical.

It should be emphasized that, since we modeled the worst-case scenarios for the LV grid in this paper, we did not include any generation from renewable energy sources (RESs) in our simulations. Furthermore, the peak load hour for the residential area in our study was at 20:00; therefore, it is not particularly useful to take into account RES generation at this time for charging the BEVs.

4. Discussion

The calculations in Section 3.2 investigated how many charging operations might occur at full power simultaneously (i.e., an SF value of 1) before the LV grid’s bottlenecks exceeded their acceptable thresholds. Although the SF of 1 assures that the specified number of charging processes can be carried out, even during peak hour, it imposes a substantial cost for grid construction. Therefore, the realistic values of SF must be considered when designing and optimizing LV networks in order to estimate the maximum simultaneous power of charging devices, as well as minimize grid expenses. For this purpose, we made use of the SF values from the VDE FNN study, which were calculated using the natural charging behaviors of BEV owners at 11 kW-private charging points in a residential metropolitan area. According to the VDE FNN study, as the number of charging points in the grid rose, the probability that the BEVs were charged simultaneously decreased, and, at one point, the SF value remained constant.

The values of Figure 7 for scenario #2 are presented in

Table 1. Charging points in a residential metropolitan grid: comparing scenario #2 with the VDE FNN study.

		Scenario #2		VDE FNN Study
The Critical Grid’s Bottlenecks	Total Charging Power (kW)	Number of BEVs	BEV Penetration Level	Number of Wallboxes [23]	SF [23]	BEV Penetration Level
Voltage (in 150 mm2 cable)	77	7	0.26 (7/27)	22	0.32	0.81 (22/27)
Voltage (in 240 mm2 cable) and Line overloading (in 150 mm2 cable)	154	14	0.51 (14/27)	82	0.17	3.03 (82/27)
Line overloading (in 240 mm2 cable)	220	20	0.74 (20/27)	143	0.14	5.3 (143/27)
Transformer overloading	517	47	0.17 (47/270)	376	0.125	1.39 (376/270)

along with a comparison to the VDE FNN study. For instance, in scenario #2, the 77 kW total charging power corresponds to the simultaneous charging of 7 BEVs (SF = 1) at 11 kW each; however, the VDE FNN research indicates that the existence of 22 charging points with an SF of 0.32 results in the same amount of power. With 27 residential units in each feeder, a 26% BEV penetration level resulted in an unacceptable voltage drop in Feeder 1 (150 mm² cable) when considering the SF of 1; nevertheless, by taking into account the realistic value of the SF, the identical outcome would occur at a BEV penetration level of 81%. Since we assumed that each residential unit only had one BEV, the overloading of the transformer and lines, as well as the under-voltage in Feeder 2 (240 mm² cable), did not occur when calculating the BEV penetration levels using the data from the VDE FNN study. By supporting the most BEV charging events in a feeder, line overloading was the least problematic parameter among the bottlenecks in the urban LV grid. On the contrary, the weakest bottleneck differed between the two scenarios; in scenario #2 and the VDE FNN study, the most challenging parameters were, the transformer overloading (at 17% penetration) and the under-voltage at Feeder 1’s (150 mm² cable) final house connection (at 81% penetration).

In summary, scenario #2 enabled us to calculate the total charging power for worst-case voltage, line loading, and transformer loading; afterwards, the VDE FNN study could be used to represent reality by determining the actual number of charge points that corresponded to these total charging powers.

Due to the fact that summer and winter are generally the seasons with the highest electricity consumption, this paper only included the findings for a typical summer day. In the expansion of this work, the studies for a typical winter day will be covered.

5. Conclusions

In this paper, we determined the maximum BEV penetration levels into a typical German metropolitan grid while maintaining the voltage drop and line/transformer loadings within the acceptable limits. The results demonstrated that the LV grid with 270 residential units was capable of supporting 46 ((46 × 100%)/270 = 17% BEV penetration level) simultaneous full power charging events during the peak hour for a residential area (at 20:00) without overloading the transformer. With cable cross sections of 240 mm² and 150 mm², respectively, the feeders—each of which contained 27 residential units—could handle the penetration of 19 (70%) and 13 (48%) BEVs without lines overloading; the voltage at the last house connections of these cables allowed for the penetration of 13 (48%) and 6 (22%) BEVs along the feeders, respectively.

In the short term, worst-case scenarios are sufficient for grid calculations as part of connection testing and grid expansion plans; however, they need to be realistically improved to accommodate the future adoption of EVs. The use of controllable transformers in homogeneous grids or individual feeder regulators to ensure voltage stability, load monitoring for the operation of transformers and lines, dynamic load management for charging stations, smartening of the networks, and attractive tariff models are a few examples of new techniques that will eventually need to be incorporated into planning and operating principles. At a certain point, it would be inevitable to take actions to strengthen the grid by eliminating cables with low cross sections by using parallel cables and employing transformers with higher rated power.