1. Introduction
1.1. General Considerations
Sustainability and climate change concerns have stimulated international interest in proposing policies and strategies to promote zero CO_{2} emissions into the atmosphere. To combat climate change, the European Union and its partner countries have banned the sale of new gasoline and diesel vehicles from 2035, as internal combustion engine (ICE) vehicles are one of the main sources of CO_{2} emissions [1]. Therefore, the transition from ICE vehicles to electric vehicles (EVs) and the prospects for sustainability are expected to significantly increase EV sales in the coming years [2]. In 2023, electric car sales neared 14 million, and sales are expected to grow in 2024. In 2023, electric cars constituted approximately 18% of all car sales, a notable increase from 14% in 2022 and a significant jump from the mere 2% recorded in 2018 [3].
Fast-charging station infrastructure can help overcome barriers to EV adoption by reducing EV charging time, thus making it easier for drivers to travel long distances. Despite its high-power output (>22 kW), the fast-charging infrastructure for EVs grew around the world. In 2023, the public charging infrastructure expanded significantly, with an overall increase of more than 40%. Notably, the growth of fast chargers outpaced that of slow chargers, reaching an impressive 55%. By the end of 2023, fast chargers accounted for more than 35% of the total public charging stock [3].
However, with an increase in fast-charging stations for EVs, a new set of technical challenges is emerging for distribution grid operators. Since fast charging can recharge an EV in less than 30 min, it requires a significant amount of power and, in cases where multiple charging points are available, the aggregate power demand can escalate to several hundred kilowatts. Due to this high-power consumption, fast-charging stations have been connected to the medium voltage (MV) distribution network.
Voltage drops, equipment loading, and power quality are technical issues that can be introduced into MV networks due to EV fast charging [4,5]. Furthermore, due to the voltage quality issue, there can be a substantial increase in the frequency of tap operations carried out by step-voltage regulators (SVRs), leading to a notable reduction in the operational lifespan of this equipment. The excessive rise in the number of tap operations not only escalates the maintenance costs associated with SVRs [6], but could also potentially result in complete equipment failure, leading to unintended feeder outages. The technical issues related to voltage sags and voltage regulation are the main concerns of electricity utilities regarding the future impact of high penetration of fast chargers.
1.2. Literature Review
The impacts of fast charging on distribution systems have become a study concern, considering the increase in work related to this category. In Figure 1, a bibliometric analysis allowed us to identify that only a limited number of studies evaluate the effects of fast recharging on SVRs in distribution networks, and even fewer investigate Volt/Var control as a mitigating strategy. For this purpose, searches using the keywords Volt/Var control, electric vehicles, fast charging, and voltage regulators were made in the Scopus search platform, from which a database of related studies was obtained, filtered by criteria such as year of publication, number of citations, and application of the study. The free software VosViewer version 1.6.20 was used to visualize the results.
The keywords’ thematic map in Figure 1 displays three clusters of keywords, revealing the key areas addressed in this study and their associations with other terms found in the literature. This visualization highlights the correlations among these studies. The analysis indicates that Volt/Var control is closely linked to distribution systems, smart grids, and renewable energies. Furthermore, it is worth noting that there are some studies examining the impacts of SVR tap operations in the context of electric vehicle recharging, which will be explored in this section.
An overview of electric vehicles and the challenges related to charging infrastructure, public policies, fast charging, and its technical impacts on distribution systems, as well as new trends and challenges, can be obtained from the literature reviews presented in [2,4,5,7,8,9]. The main challenges revolve around the grid impact, power quality issues, lack of standards, and the need for appropriate design and mitigation measures.
The key impacts of fast-charging electric vehicles on power distribution systems include increased power demand on the grid transmission side and higher generation requirements. A significant increase in EVs being charged at fast-charging stations can lead to significant grid overload, causing the substation to supply additional power. Electric utilities often use circuit reconductoring, capacitor banks, or SVRs to mitigate voltage drops in MV distribution networks [10,11,12].
In order to improve voltage regulation and reduce the number of tap operations, control strategies applied to the SVR have been proposed [13,14,15,16]. To enhance voltage regulation and reduce tap operations, a decentralized approach that combines SVRs and demand-side management with consumer-controlled loads is presented in [13], which employs innovative techniques to determine dynamic line drop compensation (LDC) parameters for SVRs handling reverse power flow based on measured line current. In [14], the proposed strategy is a centralized, coordinated control that utilizes SVRs and distribution static synchronous compensators (D-STATCOMs) through an intelligent distribution management system (DMS). This strategy aims to reduce distribution losses and tap movements in the presence of distributed photovoltaic (PV) systems, but the investment in additional equipment can increase energy tariffs. The authors of [15] propose a new optimization method to determine the control parameters of an SVR to maximize its voltage control characteristic in DNs with PV systems. In [16], an optimal control method is proposed to calculate the ideal compensation rate for an SVR; the method considers the reverse power flow from a renewable energy source and the output voltage of the under-load tap changer of the main transformer.
In recent years, there has been an increase in studies of distribution grids, including the impact of EVs, and vehicle-to-grid (V2G) analysis [17,18]. In [17], the authors study the impact of different penetration levels of V2G on the substation capacity and the SVR operations considering an unbalanced distribution network. The study shows that increased V2G penetration will improve the distribution system if the capacity is not exceeded. Also, the benefits of optimization techniques are highlighted to determine the maximum V2G capacity for a given substation while minimizing losses and the number of SVR tap operations. In [18], the diagnosis of a power system in terms of voltage profile, voltage stability, SVR operation, and energy losses with V2G is presented. However, neither [17] nor [18] consider the impact of fast charging on distribution systems.
Optimization techniques are an essential enabler for V2G integration and the optimal location of FCSs [19,20,21]. An optimization approach for the intelligent operation of four-quadrant EV slow chargers is proposed in [19]. The reduction of tap changing is presented as a particular effect of this approach, but the simulation times used are insufficient to consider accurate tap changing operations (TCO). In [20], a multi-objective optimization strategy is presented for EV fast-charging. The algorithm evaluates the achievable network controllability to increase the network hosting capacity for domestic load facilities. Reactive power injection or a decrease in recharging power are some techniques used for current violation mitigation. The results indicate that the controllability of recharging stations depends on the location of the recharging station. The study does not have SVRs. On the other hand, the authors of [21] study the impact of fast-charging stations on a power transmission network by integrating renewable energy sources in order to determine the optimal locations and capacities for these stations to minimize voltage violations over 24 h.
Volt/Var strategies to control voltage on the feeder are presented in [22,23,24,25,26]. The paper in [22] introduces a three-stage model predictive control (MPC) scheme for coordinating EV charging and Volt/Var devices for voltage regulation in distribution networks. This control strategy optimizes EV charging schedules and Volt/Var operations, maintaining voltage levels and the EV battery state of charge (SoC) while minimizing control resources and electricity costs. The paper in [23] presents models for optimal power flow and EV charging with reactive power support. The study shows that coordinated charging at non-uniform power factors reduces costs and supports higher EV penetration.
An algorithm to coordinate the operation of EV chargers with other Volt/Var control devices for voltage control purposes in distribution feeders is proposed in [24]. The benefits of the methodology include voltage regulation in the distribution system, which is crucial for maintaining grid stability and reliability. Other benefits include the reduction of grid losses and the integration of renewable energies, but the authors do not evaluate the number of taps during the day.
In [25], an approach is presented for coordinating EV charging that integrates Volt/Var control and the management of on-load tap changers (OLTCs), SVRs, and switchable capacitors. As a solution to the problem of electric vehicle charging coordination, Volt/Var control, storage systems, and distributed generation, as well as load voltage dependency, are proposed and discussed by the authors. However, the authors do not assess their effects on SVR tap operations. Ref. [26] introduces a coordination scheme to determine the optimal tap position of an OLTC, the extent of reactive power to be exchanged by a D-STATCOM and a PV inverter, and the phase connection of EVs. While the results were generated over a 24 h period using a 10 min time step, the findings suggest further reducing the time step to achieve a more accurate assessment of tap operations. Table 1 summarizes the literature review on electric vehicles, classified according to the approaches analyzed in our work.
1.3. Research Contributions
As evidenced by the literature review, one literature gap identified is an extended analysis and evaluation of the impacts of electric vehicle fast-charging stations (EVFCS) on SVR tap operations, with appropriate time-step simulations and considering uncertainties associated with the charging process. This paper attempts to address this gap through the following contributions:
Characterizing and analyzing the issue of excessive SVR tap operations due to undervoltage caused by EV fast charging at different penetration levels: This study thoroughly characterizes the problem using synthetic probabilistic data that considers the stochastic behavior and uncertainties associated with the EV charging process. Synthetic data are combined with measured data for the power load connected to the feeder, and the analysis includes a comparison of the presence or absence of the LDC function in the SVR. Additionally, a sensitivity analysis is performed on undervoltage probabilities and the number of SVR tap operations, focusing on the impact of EV penetration levels and the feeder R/X ratio. Study cases that lead to SVR tap saturation, which can cause voltage regulation issues, are also examined to provide a comprehensive understanding of the problem.
Application of a Simplified Local Volt/Var Control Strategy for Voltage Drop Mitigation: This study proposes the application of a local Volt/Var control strategy at each EV charging point within an FCS to address voltage issues such as dips and excessive tap operation of the SVR due to EV fast charging. This approach involves locally adjusting the Volt/Var curves by modifying the slopes or voltage levels for reactive power injection. Importantly, this strategy does not require communication between EV charging points (EVCP). The literature review does not show the use of Volt/Var control in EV charging considering excessive tap operation of the SVR. The control of the SVR and EVCP without communication has not been explored. This work fills this gap in the literature. This innovative approach provides a practical solution to improve voltage regulation in buses where FCSs are connected, using local control to improve system power quality without the need for complex infrastructure.
This paper is organized as follows: Section 2 presents the tools and methodology used in this research. This section includes the problem characterization caused by an EV FCS in a feeder with the SVR. Section 3 shows the results and discusses the finding issues related to voltage and tap operations, including the sensitivity studies for R/X and penetration level variations. Finally, Section 4 states the conclusions of this article.
2. Methodology and Tools for Problem Characterization
2.1. Problem Characterization
For the problem characterization, a four-bus distribution system is used, as illustrated in Figure 2. The SVR configuration incorporates three single-phase autotransformers interconnected in a closed delta arrangement, providing ±16 available tap positions. The values of the active and reactive power of the loads were obtained from daily measurements. The EV charging profile is generated utilizing synthetic data. For this work, an FCS consists of six charging points, each with a maximum capacity of 100 kVA, connected to the distribution system using a 13.8 kV/0.38 kV transformer.
From Figure 2, the injected current to bus B_03 is given by Equations (1) and (2), where P is the active power and Q is the reactive power on the bus. V_{B_03} and V_{B_02} are the voltage on buses B_03 and B_02, respectively. R is the resistance of the feeder and X is its reactance.
$${\mathrm{I}}^{\mathrm{*}}={\displaystyle \frac{\mathrm{P}+\mathrm{j}\mathrm{Q}}{{\mathrm{V}}_{\mathrm{B}\_03}}}\to \mathrm{I}={\displaystyle \frac{\mathrm{P}-\mathrm{j}\mathrm{Q}}{{\mathrm{V}}_{\mathrm{B}\_03}}}$$
$$\mathrm{I}={\displaystyle \frac{\left({\mathrm{V}}_{\mathrm{B}\_02}-{\mathrm{V}}_{\mathrm{B}\_03}\right)}{\mathrm{R}+\mathrm{j}\mathrm{X}}}$$
Combining Equations (1) and (2) will obtain the expression in Equation (3).
$${\mathrm{V}}_{\mathrm{B}\_03}={\mathrm{V}}_{\mathrm{B}\_02}-{\displaystyle \frac{\mathrm{P}\mathrm{R}+\mathrm{Q}\mathrm{X}}{{\mathrm{V}}_{\mathrm{B}\_03}}}+\mathrm{j}{\displaystyle \frac{\mathrm{Q}\mathrm{R}-\mathrm{P}\mathrm{X}}{{\mathrm{V}}_{\mathrm{B}\_03}}}$$
Assuming that the phase angle between V_{B_03} and V_{B_02} is zero, Equation (3) can be written as in (4), where ΔV is the component of the voltage variation in phase with the voltage on bus B_02 and δV is the voltage phase angle variation.
$${\mathrm{V}}_{\mathrm{B}\_03}={\mathrm{V}}_{\mathrm{B}\_02}-\u2206\mathrm{V}+\mathrm{j}\mathsf{\delta}\mathrm{V}\phantom{\rule{0ex}{0ex}}\u2206\mathrm{V}={\displaystyle \frac{\mathrm{P}\mathrm{R}+\mathrm{Q}\mathrm{X}}{{\mathrm{V}}_{\mathrm{B}\_03}}};\hspace{1em}\mathsf{\delta}\mathrm{V}={\displaystyle \frac{\mathrm{Q}\mathrm{R}-\mathrm{P}\mathrm{X}}{{\mathrm{V}}_{\mathrm{B}\_03}}}$$
The consumed power on bus B_03 is given by (5), where P_{L} and Q_{L} are the active and reactive power of the load connected to the bus, P_{FCS} is the consumed charging power of the FCS, and Q_{FCS} is the reactive power of the FCS, which is zero if it is working at unity power factor.
$$\mathrm{P}+\mathrm{j}\mathrm{Q}=\left({\mathrm{P}}_{\mathrm{L}}+{\mathrm{P}}_{\mathrm{F}\mathrm{C}\mathrm{S}}\right)+\mathrm{j}\left({\mathrm{Q}}_{\mathrm{L}}-{\mathrm{Q}}_{\mathrm{F}\mathrm{C}\mathrm{S}}\right)$$
So, the voltage variation between buses B_02 and B_03 is obtained from Equations (4) and (5) and is shown in Equation (6).
$$\u2206\mathrm{V}={\displaystyle \frac{\left({\mathrm{P}}_{\mathrm{L}}+{\mathrm{P}}_{\mathrm{F}\mathrm{C}\mathrm{S}}\right)\mathrm{R}+\left({\mathrm{Q}}_{\mathrm{L}}-{\mathrm{Q}}_{\mathrm{F}\mathrm{C}\mathrm{S}}\right)\mathrm{X}}{{\mathrm{V}}_{{\mathrm{B}}_{03}}}}$$
Thus, to minimize the impact in the bus voltage variation, the numerator in Equation (6) should be zero, and the FCS should inject the reactive power shown in Equation (7)
$${\mathrm{Q}}_{\mathrm{F}\mathrm{C}\mathrm{S}}={\displaystyle \frac{\left({\mathrm{P}}_{\mathrm{L}}+{\mathrm{P}}_{\mathrm{F}\mathrm{C}\mathrm{S}}\right)\mathrm{R}+{\mathrm{Q}}_{\mathrm{L}}\mathrm{X}}{\mathrm{X}}}$$
Table 2 shows the study cases considering different penetration levels (PL) of EV charging and an SVR with and without the LDC function. Each case was simulated four times with a time step of 1 s for one random day in 2019. The results are the average of the simulations for each study case.
The PL depends on the number of charging points (NCP), the nominal power of each charging point (S_{nom}), and the maximum load (P_{max}) on the feeder. In this study case, P_{max} is 6 MW. To calculate the PL, Equation (8) is used.
$$\mathrm{P}\mathrm{L}\left(\%\right)={\displaystyle \frac{\mathrm{N}\mathrm{C}\mathrm{P}\times {\mathrm{S}}_{\mathrm{n}\mathrm{o}\mathrm{m}}}{{\mathrm{P}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}100\%$$
The LDC function is an integral part of the SVR; it utilizes current and voltage measurements obtained through a current transformer and a potential transformer at the load side. When the SVR does not use LDC, it regulates voltage exclusively at the load-side bus. However, when the LDC function is enabled, voltage regulation extends to a different point beyond the load-side bus.
To utilize the LDC function, it is necessary to configure the resistance (R) and reactance (X) values of the feeder line from the SVR load side to the new regulation point, and set up the dead band, which allows voltage variation centered around a desired point.
In the characterization problem discussed in this article, the regulating point is located at the FCS bus, with specific R, X, and distance values, as shown in Figure 2. The regulation voltage is centered at 0.94 p.u., with a dead band of ±0.01 p.u. This ensures that the voltage remains within the range of 0.93 p.u. to 0.95 p.u., aligning with Brazilian accepted regulated values in MV distribution networks.
2.2. Software Tools and Methodology
The DIgSILENT Power Factory 2022 SP1 software is utilized for conducting simulations. Specifically, the quasi-dynamic simulation tool within this software allows for both medium- and long-term simulations. During each simulation step, the tool calculates multiple load flows. The simulations were executed on a Lenovo Ideapad 320 equipped with an Intel^{®} Core™ i7-7500U CPU processor running at 2.70 GHz–2.90 GHz and 12 GB of RAM.
The visual methodology depicted in Figure 3 is followed to assess the impact of EV fast charging on voltage profiles and the number of tap operations in the SVR within a distribution network.
Network Modeling: This begins by modeling the electrical network to be evaluated, collecting parameters such as power branches, lengths, consumer load, SVR power, and topology. These parameters are implemented in the simulation software.
FCS modeling: The FCS is modeled as a set of different charging points (CPs). Each CP can charge a random number of EVs during one day. Thus, each CP is modeled as a daily charging power profile, namely, the sum of each EV charging power on the CP.
EV Charging Power Profile Modeling: The charging power profile of electric vehicles is defined using random variables related to the charging process, considering factors such as battery capacity, initial and final state of charge, time load, and arrival time. This model is incorporated into the DIgSILENT Power Factory.
Simulation and Analysis: The simulation parameters in the software are configured to run the simulation. The results, including the number of tap operations on the SVR and voltage drop, are analyzed.
The simplified flowchart in Figure 4 illustrates the generation of the EV charging profile in MATLAB^{©} of a CP over a year. Step one defines constants such as the maximum and minimum number of EVs arriving at the station, the standard deviation and mean of the EV arrival time, the minimum and maximum charging time, and the number of charging points per FCS.
The second step evaluates whether the current month of the year is less than 12; if not, it means that the annual profile has been generated and proceeds to the end of the algorithm. If the month is less than 12, go to step three, which asks if the current day is less than the last day of the month. If not, it increases the “month” variable and returns to step two. If the day is less than the last day of the month, it goes to step five, where several EVs are randomly generated with a uniform distribution according to the values in step one.
In step six, stochastic variables are generated for each vehicle. The variables are the initial and final state of charge (SoC), generated with Weibull distributions; the battery capacity, generated according to uniform random numbers between 1 and 8; and its corresponding value of the actual vehicle batteries, as shown in Table 3.
In the seventh step, the charging power (${\mathrm{P}}_{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\_\mathrm{i}}$) of the ${\mathrm{i}}_{\mathrm{t}\mathrm{h}}$ vehicle arriving at the charging point is calculated based on Equation (9), where ${\mathrm{S}\mathrm{o}\mathrm{C}}_{\mathrm{f}\mathrm{i}\mathrm{n}\_\mathrm{i}}$ is the final SoC, ${\mathrm{S}\mathrm{o}\mathrm{C}}_{\mathrm{i}\mathrm{n}\mathrm{i}\_\mathrm{i}}$ is the initial SoC, ${\mathrm{C}}_{\mathrm{B}\mathrm{a}\mathrm{t}\_\mathrm{i}}$ is the battery capacity in kWh, and ${\mathrm{t}}_{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\_\mathrm{i}}$ is the charging time.
$${\mathrm{P}}_{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\_\mathrm{i}}={\displaystyle \frac{{\mathrm{S}\mathrm{o}\mathrm{C}}_{\mathrm{f}\mathrm{i}\mathrm{n}\_\mathrm{i}}-{\mathrm{S}\mathrm{o}\mathrm{C}}_{\mathrm{i}\mathrm{n}\mathrm{i}\_\mathrm{i}}}{{\mathrm{t}}_{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\_\mathrm{i}}}}{\xb7\mathrm{C}}_{\mathrm{B}\mathrm{a}\mathrm{t}\_\mathrm{i}}$$
Finally, in step eight, the charging profile of the fast-charging station is calculated as the sum of all EV charging powers per minute of the day. Figure 5 illustrates the charging profile of an FCS with six charging points during a day. Each EV is charged at constant power.
The EV charging profile is loaded into Power Factory. A 1 s simulation time step was chosen as an appropriate value, considering the control time required for each TCO in the SVR. The first tap adjustment occurs within 30 s after detecting an out-of-range voltage. If the voltage remains outside the desired limits, subsequent taps are made every 5 s until the voltage is within the specified range.
To evaluate system performance, various stochastic test cases were simulated over a 24 h period. Each case underwent multiple simulation runs and the results from these different simulations were averaged at each simulation step. The analysis focused on assessing the probability of voltage limit exceedance and the impact on the increase in the TCO of the SVR.
3. Results and Discussion
3.1. Impacts of EV Fast Charging on Voltage Quality
In order to assess the effect of an FCS on the voltage quality, the probability of a voltage limit violation of less than 0.93 p.u. and greater than 1.05 p.u. on buses B_02 and B_03 is calculated for cases 1–10 (Table 2) and presented as a heat map in Figure 6. The results show that fast recharging does not lead to undervoltage violations on bus 2 for any of the 10 scenarios considered; however, overvoltage conditions are observed at this bus for cases 7–10 as the penetration levels increase and with the LDC function.
For bus 3, there are higher probabilities of undervoltage limit violations without LDC. The probability for case 3 (10% of PL) is 5.3%, for case 4 (20% of PL) is 25%, and for case 5 (30% of PL) is 33.7%, i.e., the probability increases as the penetration level increases. Case 10, with probabilities of 18.8% and 1.1%, respectively, causes undervoltage (bus 3) and overvoltage (bus 2) limit violations.
The results reveal that including an FCS in the distribution network alongside SVRs leads to specific voltage issues. When SVRs operate without LDC, undervoltage limit violations occur on the bus where the FCS is connected. The voltage drops below the acceptable range due to the FCS’s power demand, which can adversely affect the performance of connected household appliances.
In cases where the SVR operates with LDC, the observed problems shift to overvoltage limit violations. Here is the underlying cause: The SVR in LDC mode regulates the voltage on the most distant bus where the FCSs are connected. The SVR adjusts its tap position to increase the FCS bus voltage. However, this adjustment also increases the voltage on the load side of the SVR. The SVR’s tap position keeps increasing until it stabilizes the voltage on the FCS bus. However, this can lead to an overvoltage violation on the load side of the SVR.
Both undervoltage and overvoltage can have detrimental effects on household appliances. Poor performance or damage may occur if voltage levels deviate significantly from the desired range.
3.2. Impacts of FCS on SVR’s TCO
The impact on the TCO is assessed based on the increase in the number of tap operations and the percentage increase relative to the base case. Additionally, we analyze scenarios where the SVR tap reaches its maximum position (tap saturation). Figure 7 presents the results.
With LDC, cases C1 to C5 exhibit increasing TCO as the EV penetration level rises. The maximum TCO occurs in case 5, where 27 daily SVR operations lead to tap saturation. This results in a 200% increase in the TCO compared to the base case. Even at a 1% penetration level (PL), 30 operations occur, representing a 233.3% increase without tap saturation.
Without LDC, cases C6 to C10 also show rising TCO with increasing EV penetration. Scenarios 7 to 10 fall within a TCO range of 29 to 32, all causing tap saturation. Case 7 represents the highest percentage increase (250%). Notably, SVRs using LDC may experience tap saturation at a lower penetration level than those without LDC, potentially leading to voltage regulation challenges.
The next sections will demonstrate how different R/X feeder ratios and penetration levels affect the TCO in the SVR and the feeder voltage quality. The test feeder system is the same as in the previous section. Tests were carried out for PLs of 0%, 5%, 10%, 15%, and 20% using commercial aluminum–steel wire feeders. Table 4 shows the wire gauges used and their values of resistance and reactance. The LDC function in the SVR was not used.
3.3. Sensitivity Analysis of Undervoltage Limit Violation
Table 5 illustrates the probabilities of undervoltage violations on bus number three, considering the PL and the R/X ratio. Additionally, it indicates whether tap saturation exists for different combinations of PL and R/X. If tap saturation exists, it is indicated as (Yes). Otherwise, it is indicated as (No).
The violation probability is zero for the first three R/X values (with zero EV penetration). However, at an R/X ratio of 1.38543, there is a 10.2% probability of undervoltage violation. The probability remains zero when the PL is 5% or 10% and the R/X ratio is 0.780941. For the same R/X ratio but PL values of 15% and 20%, the probabilities increase to 4.2% and 13.9%, respectively. Overall, violation probabilities rise as both PL and R/X increase.
The maximum limit violation probability for each penetration level (PL) corresponds to the maximum R/X ratio. Specifically, the highest probability observed is 44.5%, which occurs when the PL is 20% and the R/X ratio is 1.38543. Regarding tap saturation, the SVR tap reaches its upper limit at a PL of 15% with an R/X ratio of 1.38543. Additionally, tap saturation occurs across all tested R/X values when the PL is 20%. Figure 8 depicts a heat map illustrating the relationship between PL, R/X, and undervoltage limit violation probabilities. Notably, as both PL and R/X increase, the violation probabilities also rise.
3.4. Sensitivity Analysis of TCO
Figure 9 provides a heat map graph illustrating the TCO as a function of PL and the R/X ratio. Notably, the TCO in the SVR increases with higher R/X ratios and greater PL values. The minimum TCO occurs when the PL is 5% and the R/X ratio is 0.780941.
Table 6 presents the number of tap operations for the SVR regarding PL and R/X, along with an indication of tap saturation. Increasing PL at a given R/X ratio results in a higher TCO. Similarly, increasing the R/X ratio for any PL value leads to an increase in the TCO. The maximum TCO within the PL range of 0% to 15% occurs when R/X equals 1.38543. However, at a PL of 20%, this same R/X ratio does not yield the maximum TCO due to tap saturation. The overall maximum TCO corresponds to 34 tap operations, where the SVR reaches saturation at a PL of 20% across all R/X ratios.
3.5. Proposed Mitigation Solution
The Volt/Var control (VVC) is proposed as a solution to the voltage problem. This method is recommended in electrical systems where the conductors have X > R to reduce the voltage drop caused by the extensive length of the feeder and its respective impedance. The VVC is characterized by maintaining the measured voltages on the EV charging point bus within regulatory voltage limits in steady-state operation by adjusting the reactive power available (Q_{ava}) in the power converter [31]. According to Equation (10), the Q_{ava} for VVC control depends on the active power consumed by the EV charging point at the current time instant (${\mathrm{P}}_{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}}$) and the nominal power capacity of the charger (${\mathrm{S}}_{\mathrm{n}\mathrm{o}\mathrm{m}}$). The operation of the VVC is presented in Figure 10.
$${\mathrm{Q}}_{\mathrm{a}\mathrm{v}\mathrm{a}}=\sqrt{{{\mathrm{S}}_{\mathrm{n}\mathrm{o}\mathrm{m}}}^{2}-{{\mathrm{P}}_{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}}}^{2}}$$
In Figure 10, the x-axis represents the steady-state voltage values measured on the EV charging point bus and the y-axis represents the value of the reactive power injected by the charging equipment. Equation (11) presents this behavior from a mathematical perspective.
$${\mathrm{Q}}_{\mathrm{s}\mathrm{u}\mathrm{p}}=\left\{\begin{array}{cc}{\mathrm{Q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}& \mathrm{i}\mathrm{f}\mathrm{V}<\mathrm{V}1\\ {\mathrm{Q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\left(1-{\displaystyle \frac{\mathrm{V}-\mathrm{V}1}{\mathrm{V}2-\mathrm{V}1}}\right)& \mathrm{i}\mathrm{f}\mathrm{V}1<\mathrm{V}>\mathrm{V}2\\ 0& \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{e}\end{array}\right.$$
The values V1 and V2 represent the lower limit of the allowed voltage and the desired voltage value, respectively, for the operation of the electrical network, defined according to the design and operational needs of the electrical system. When the voltage value is greater than V2, VVC operation is not required; that is, no Q_{sup} is injected, and the power factor of the charger operation is unity. For voltage values measured greater than V1 and less than V2, the Q_{sup} is modified linearly so that the voltage measured at the EV charging point bus returns to values above V2. This linear variation is used to supply the reactive power proportionally to the voltage variation on the bus.
The maximum operational limit of reactive power injection (Q_{max}) is given by Equation (12), where PF_{max} is the maximum power factor which the charging point can work given by the specifications of each power converter used in the charger. For this article, a target power factor (PF) of 0.8 is maintained to ensure the charger operates within specified limits (similar to a photovoltaic inverter). This solution is implemented directly at each charging point, eliminating the need for communication between the charger and the SVR. Doing so prevents direct intervention in the voltage regulator, streamlining the operation of the system.
$${\mathrm{Q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}={\mathrm{S}}_{\mathrm{n}\mathrm{o}\mathrm{m}}\times \mathrm{sin}\left({\mathrm{cos}}^{-1}\left({\mathrm{P}\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\right)\right)$$
So, with the 100 kVA of nominal power of the charging point, the Q_{max} of each charging point is 60 kvar (Equation (13)). If the Q_{ava} of the charging point is greater than Q_{max}, and if were necessary to supply reactive power, the power converter of the charging point will supply Q_{max} to maintain the 0.8 PF.
$${\mathrm{Q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}=100\mathrm{k}\mathrm{V}\mathrm{A}\times \mathrm{sin}\left({\mathrm{cos}}^{-1}\left(0.8\right)\right)=60\mathrm{k}\mathrm{v}\mathrm{a}\mathrm{r}$$
For example, if there is an EV with a constant charging power of 60 KW, the Q_{ava} calculated from Equation (10) is 80 kvar, as shown in Equation (14), but the converter of the charging point only supplies the Q_{max} of 60 kvar.
$${\mathrm{Q}}_{\mathrm{a}\mathrm{v}\mathrm{a}}=\sqrt{{100\mathrm{k}\mathrm{V}\mathrm{A}}^{2}-{60\mathrm{k}\mathrm{W}}^{2}}=80\mathrm{k}\mathrm{v}\mathrm{a}\mathrm{r}$$
3.6. Simulation of the Proposed Solution
Various tests were simulated and analyzed on an actual medium voltage distribution feeder (Figure 11) located near a highway in northern Brazil to evaluate the proposed solution. The objective was to investigate three different configuration scenarios to mitigate the TCO and undervoltage issues within a distribution network (DN) equipped with FCSs.
The MV network operates at 13.8 kV and spans a feeder length of 12.54 km. Notably, the network features three 2.75 MVA single-phase step-voltage regulators interconnected in a closed delta configuration, along with two 600 kvar fixed capacitor banks (refer to Figure 11). The feeder’s annual load demand profiles were derived from measurements at the substation. The FCSs were strategically placed at the feeder’s end, specifically on bus number B_389, to create a worst-case scenario.
3.6.1. Simulations Overview
Four distinct cases, each representing different configuration parameters for the proposed strategy, were simulated on a randomly selected day in 2019 (specifically, 5 September). In case 0 (Baseline Scenario), no mitigation strategy was applied to the charging points at the FCS. Consequently, the charging points do not inject reactive power into the grid. In subsequent cases (cases 1 to 3), the configurations were modified by adjusting the voltage limits V1 and V2 (Figure 12), thus:
Case 1: V1 = 0.93 p.u. and V2 = 0.98 p.u.;
Case 2: V1 = 0.90 p.u. and V2 = 0.95 p.u.;
Case 3: V1 = 0.80 p.u. and V2 = 0.95 p.u.
Figure 12. Configuration of mitigation strategies for the tested cases.
Figure 12. Configuration of mitigation strategies for the tested cases.
3.6.2. Assessment of Undervoltage Violations
Figure 13 presents a box plot illustrating the voltage measurements at bus B_389 across the different cases. If there is no FCS on the bus, the minimum voltage is 0.942 p.u., which does not cause a limit violation. In case 0, the voltage levels dip below the undervoltage limit, reaching a minimum value of 0.905 p.u. Compared to the base case, cases 1 and 3 improve the minimum voltage by 0.011 p.u. and 0.007 p.u., respectively. Case 2 contains outliers with a minimum voltage of 0.893 p.u.
In the base case, 25% of the data points fall below 0.933 p.u. Conversely, for cases 1 through 3, 25% of the data surpass this threshold, indicating an enhancement in the bus voltage profile when employing the mitigation strategy across all configurations. The most substantial improvement occurs in the configuration of case 2. Specifically, 25% of the data points register below 0.948 per unit (p.u.), representing a significant enhancement of 0.015 p.u. compared to the base case.
Figure 14 shows the series diagram of the undervoltage limit violation probabilities and the reduced percentage compared to the base case. For case 0, the probability of undervoltage limit violation is 22.26%. For cases 1 through 3, the violation probabilities decrease, demonstrating that the mitigation strategy helps to increase the voltage on the bus, thereby decreasing the undervoltage limit violations. Case 1 has a probability of 11.02%, which represents a 50.5% decrease in violation probability from the base case. Cases 2 and 3 have violation probabilities of 16.67% and 18.4%, meaning decreases of 25.11% and 18.4%, respectively. Thus, case 1 has the best result in reducing the probability of violating the undervoltage limit.
3.6.3. Assessment of TCO
The graph of the TCO and the TCO percentage reduction compared to the base case is shown in Figure 15. For case 0, the number of tap operations is 27. With the implementation of the mitigation strategy, the TCO decreased to 23.33 average operations for case 1, 21 for case 2, and 24.33 for case 3. The TCO reductions imply that case 1 reduces the TCO by 13.58%, case 2 by 25.71%, and case 3 by 12.7%. All the strategies of the configurations reduce the TCO; the case 2 configuration is the best in reducing the SVR tap operations.
Figure 16 shows the box plot of the tap position during the simulated day. In case 0, the maximum average tap position is 11.35. However, with the implemented strategy, the top tap position decreases for each analyzed case; thus, the maximum tap position in case 1 is 9, in case 2 is 8.7, and in case 3 is 9.35. This reduction in the maximum tap position is crucial in allowing the SVR to operate further away from saturation.
4. Conclusions
The growth of electric mobility is creating new technical challenges for energy distribution companies. In this work, the problem of installing fast-charging stations in medium voltage distribution network feeders with step-voltage regulators has been characterized. In the problem formulation, it became clear that with an increase in the number of fast-charging stations, the number of tap changes in the step-voltage regulator increases, and so does the probability of violating the low-voltage limits allowed in the network.
The problem was characterized by considering the penetration level of the fast-charging stations of the network and by activating or deactivating the low drop compensation function of the step-voltage regulator. It has been shown that there is a more significant effect in the increase of tap operations and a greater probability of undervoltage violation when the regulator operates with the LDC function; likewise, when operating with this function, the probability of overvoltage appears in the load-side terminal of the step-voltage regulator.
As a proposed solution, a local control strategy based on the Volt/Var curve was presented to mitigate the characterized problems, and it was simulated on an actual medium voltage distribution network in northern Brazil. Based on the quantitative data presented, it can be concluded that implementing mitigation strategies, such as using a simplified local Volt/Var control strategy, significantly improves voltage quality and reduces undervoltage violations in distribution networks affected by electric vehicle fast charging.
The analysis of undervoltage limit violation probabilities showed a clear trend of decreasing violation probabilities with implementing mitigation strategies, exemplified by a 50.5% decrease in violation probability in case 1 compared to the base case. Additionally, the implementation of these strategies led to a reduction in tap positions, allowing the SVR to operate further from saturation. Specifically, the maximum tap position decreased in each analyzed case, with case 2 showing the lowest maximum tap position of 8.7. Furthermore, the tap changing operations (TCO) also decreased with these strategies, with case 2 reducing the TCO by 25.71% compared to the base case.
These findings underscore the effectiveness of mitigation strategies, such as local Volt/Var control, in addressing voltage regulation issues caused by EV penetration in distribution systems. With increasing EV penetration, these strategies can help distribution grids improve voltage quality, mitigate undervoltage violations, and improve overall system performance.
Future work will involve comparing experimental results with simulation outcomes.
Author Contributions
Conceptualization, O.M.H.-G. and J.P.A.V.; methodology, O.M.H.-G.; software, O.M.H.-G.; validation, O.M.H.-G. and J.P.A.V.; formal analysis, O.M.H.-G.; investigation, O.M.H.-G.; resources, O.M.H.-G. and J.P.A.V.; data curation, J.P.A.V.; writing—original draft preparation, O.M.H.-G.; writing—review and editing, O.M.H.-G., J.P.A.V., J.M.T. and L.E.S.e.S.; visualization, O.M.H.-G. and J.M.T.; supervision, J.P.A.V.; project administration, J.P.A.V.; funding acquisition, J.P.A.V. All authors have read and agreed to the published version of the manuscript.
Funding
This article was published with the support of the Directorate of Scientific, Humanistic and Technological Research (DICIHT) of the National Autonomous University of Honduras within the research project Innovation in Energy Systems: Addressing Efficiency and Sustainability Challenges to Achieve Sustainable Development Goals 7 and 11.
Data Availability Statement
The research data can be obtained by written request to the correspondence author.
Acknowledgments
The authors gratefully acknowledge PROPESP/UFPA (PAPQ) for financial support for this article’s publication, Equatorial Energia Pará for providing the feeder’s power consumption data, and DIgSILENT for the thesis version of the software Power Factory©.
Conflicts of Interest
The authors declare no conflicts of interest.
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Figure 1. Thematic map of keywords on electric vehicle charging in distribution systems.
Figure 1. Thematic map of keywords on electric vehicle charging in distribution systems.
Figure 2. Four-bus test system for the problem characterization.
Figure 2. Four-bus test system for the problem characterization.
Figure 3. Diagram of the followed methodology.
Figure 3. Diagram of the followed methodology.
Figure 4. Flowchart to generate the EV FCS charging profile.
Figure 4. Flowchart to generate the EV FCS charging profile.
Figure 5. Daily charging profiles of the EVs for six charging points.
Figure 5. Daily charging profiles of the EVs for six charging points.
Figure 6. Heat map for undervoltage and overvoltage limit violation probabilities.
Figure 6. Heat map for undervoltage and overvoltage limit violation probabilities.
Figure 7. TCO on 5 September 2019.
Figure 7. TCO on 5 September 2019.
Figure 8. Heat map for undervoltage limit violation probabilities regarding PL and R/X relation.
Figure 8. Heat map for undervoltage limit violation probabilities regarding PL and R/X relation.
Figure 9. Heat map for the number of TCO regarding PL and R/X relation.
Figure 9. Heat map for the number of TCO regarding PL and R/X relation.
Figure 10. Proposed reactive power injection to mitigate the characterized problem.
Figure 10. Proposed reactive power injection to mitigate the characterized problem.
Figure 11. Distribution feeder to validate the proposed problem mitigation strategy.
Figure 11. Distribution feeder to validate the proposed problem mitigation strategy.
Figure 13. Box plot of voltage on bus B_389.
Figure 13. Box plot of voltage on bus B_389.
Figure 14. Diagram of undervoltage limit violation probabilities and percentage decrease.
Figure 14. Diagram of undervoltage limit violation probabilities and percentage decrease.
Figure 15. TCO and percentage decrease for each tested case.
Figure 15. TCO and percentage decrease for each tested case.
Figure 16. Box plot of mean SVR tap position.
Figure 16. Box plot of mean SVR tap position.
Table 1. Relevant literature about electric vehicles’ fast-charging impacts on distribution systems.
Table 1. Relevant literature about electric vehicles’ fast-charging impacts on distribution systems.
Paper Main Subject | Relevant Literature | Type of Papers |
---|---|---|
Fast Charging | [4,5,8,9,21,27,28] | Research Paper/Literature Review |
SVRs | [6,10,16,17] | Research Paper |
Volt/Var control | [22,23,24,26] | Research Paper |
Power Quality due to EVs | [4,5,6,13,25,29,30] | Research Paper/Literature Review |
Table 2. Study cases for the voltage quality and TCO problem characterization.
Table 2. Study cases for the voltage quality and TCO problem characterization.
Case | Description | Case | Description |
---|---|---|---|
C0 | Base case 0% of PL without LDC | - | - |
C1 | 1.6% of PL ^{1} without LDC. | C6 | 1.6% of PL with LDC |
C2 | 3.3% of PL ^{2} without LDC. | C7 | 3.3% of PL with LDC. |
C3 | 10% of PL ^{3} without LDC. | C8 | 10% of PL with LDC. |
C4 | 20% of PL ^{4} without LDC. | C9 | 20% of PL with LDC. |
C5 | 30% of PL ^{5} without LDC. | C10 | 30% of PL with LDC. |
^{1} One charging point (CP); ^{2} Two CPs; ^{3} Six CPs (One FCS); ^{4} Twelve CPs (Two FCSs); ^{5} Eighteen CPs (Three FCSs).
Table 3. Random values for battery capacity.
Table 3. Random values for battery capacity.
Random Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
Battery Capacity (kWh) | 30 | 33 | 38 | 40 | 42 | 50 | 52 | 67 |
Table 4. Resistance (R), Reactance (X), and R/X relation of the used wires for sensibility test.
Table 4. Resistance (R), Reactance (X), and R/X relation of the used wires for sensibility test.
Wire Gauge | R (Ω/km) | X (Ω/km) | R/X |
---|---|---|---|
4/0 | 0.2667 | 0.34151 | 0.780941 |
3/0 | 0.3359 | 0.35965 | 0.933962 |
2/0 | 0.4247 | 0.37279 | 1.139224 |
1/0 | 0.5343 | 0.38565 | 1.38543 |
Table 5. Undervoltage limit violation probabilities and tap saturation as a function of PL and R/X.
Table 5. Undervoltage limit violation probabilities and tap saturation as a function of PL and R/X.
PL | 0% | 5% | 10% | 15% | 20% | |
---|---|---|---|---|---|---|
R/X | ||||||
0.780941 | 0 (No) ^{1} | 0 (No) | 0 (No) | 4.2 (No) | 13.9 (Yes) | |
0.933962 | 0 (No) | 0.4 (No) | 9.4 (No) | 21.6 (No) | 3.2 (Yes) | |
1.139224 | 0 (No) | 11.5 (No) | 25.7 (No) | 33.1 (No) | 21.6 (Yes) | |
1.38543 | 10.2 (No) | 23.7 (No) | 36.2 (No) | 41.7 (Yes) ^{2} | 44.5 (Yes) |
^{1} (No) No Tap Saturation. ^{2} (Yes) Tap Saturation.
Table 6. TCO and tap saturation regarding PL and R/X.
Table 6. TCO and tap saturation regarding PL and R/X.
PL | 0% | 5% | 10% | 15% | 20% | |
---|---|---|---|---|---|---|
R/X | ||||||
0.780941 | 6 (No) ^{1} | 8 (No) | 10 (No) | 14 (No) | 16 (Yes) ^{2} | |
0.933962 | 7 (No) | 11 (No) | 13 (No) | 16 (No) | 30 (Yes) | |
1.139224 | 14 (No) | 16 (No) | 17 (No) | 20 (No) | 34 (Yes) | |
1.38543 | 17 (No) | 21 (No) | 25 (No) | 29 (Yes) | 29 (Yes) |
^{1} (No) No Tap Saturation. ^{2} (Yes) Tap Saturation.
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