Analyzing the influence of electric vehicle charging scheduling on distribution transformer lifespan

Abstract

The ongoing growth in global electricity demand and rapid proliferation of electric vehicles (EVs) are posing challenges to the operation of the low voltage power networks and their components. This study aims to analyze the impacts of peak-load demand on the distribution transformers, considering mild and extreme combinations of electric energy demand and localized charging of plug-in EVs under their different penetration levels, hypothesizing that shifting the demand for charging throughout the day can reduce the aging of distribution transformers. The proposed method employs a fuzzy-logic-based tool, which incorporates the influence of ambient temperature, higher harmonics, reactive power compensation, reverse power flows, and overload. Three different charging/discharging modes have been considered: demand charging, off-peak charging, and synergy of off-peak charging and vehicle-to-house technology. The results indicate that off-peak charging emerges as 2.1 times more effective than demand charging in terms of the transformer's loss of life, particularly for ultimate EV penetration of 100 %. It is demonstrated that the utilization of charging scheduling for EVs should be prioritized to defer costly system upgrades and reinforcements, particularly when EV penetration exceeds 50 %.

List of abbreviations

DSO

Distributed System Operator

EV

Electric Vehicle

LoL

Loss of Life

LV

Low Voltage

MF

Membership Function

PDS

Power Distribution System

PF

Power Factor

PQ

Power Quality

PV

Photovoltaic

PVGIS

Photovoltaic Geographical Information System

SCB

Shunt Capacitor Bank

THD

Total Harmonic Distortion

V2G

Vehicle-to-Grid

V2H

Vehicle-to-House

1. Introduction

1.1. Motivation

Concerns about the preservation of the environment, reduction of greenhouse gas emissions, and depletion of natural gas and oil reserves are among the major stimuli to accelerate and support the growth of electric vehicles in use [1]. In July 2021 the European Commission proposed the “Fit for 55” package, pursuing to reduce net greenhouse gas emissions by at least 55 % by 2030, also by means of diminishing of CO₂ emissions of cars and vans [2]. In this context, EVs are being treated as a sustainable alternative to traditional automobiles with internal combustion engines, which can be integrated into the modern power system. With advancing technologies in batteries, power electronics, microelectronics and control, the share of electric cars in the transportation sector is constantly increasing. According to the latest edition of the “Global Electric Vehicle Outlook” from the International Energy Agency [3], in 2023 the sales of EVs hit a new record of 14 million, and the interest kept rising strongly into 2023, despite disruptions in global supply chains. In the short term, the main limiting factors to the continued proliferation of electric cars are soaring prices for several critical minerals utilized in battery manufacturing, jamming in supply chains caused by russia's military invasion of Ukraine. In the longer horizon, more active deployment of charging infrastructure is required to service the anticipated increment in EV sales [3].

At the same time, there are serious concerns about the safe and reliable operation of the power distribution systems (PDSs) due to the increasing penetration of EVs into the electric grid. Charging of accumulators consumes a greater amount of electricity compared to typical household appliances, particularly due to the widespread adoption of high-power fast chargers ranging from 10 to 22 kW in many contemporary residential houses, as opposed to the traditional charging capacity of 3–6 kW [4]. With random or uncoordinated charging activities, power lines and transformers can become overloaded at high penetration of EVs, deteriorating the performance and reliability of the network asset [1]. Moreover, just several high-power fast charging connectors operating simultaneously can cause a blackout in residential areas supplied by transformers that are not designed for such loads [4]. In this context, development of strategies to preserve the distribution transformers' lifetime is of particular importance.

1.2. Literature survey

In the academic literature the issue of EVs' impact on the PDS and its elements has been addressed from a range of perspectives [[5], [6], [7], [8], [9], [10]]. The review and quantification of the potential impacts of EV charging on the elements of the PDSs was done in Ref. [7]. The authors of [5] evaluated the actual role of battery electric and plug-in hybrid electric vehicles in the reduction of greenhouse gas emissions. A probabilistic method to assess the influence of higher harmonics caused by plug-in EVs on the PDS is proposed in Ref. [6]. A review of the impact of fast charging stations for EVs on the power quality (PQ) in a utility grid is presented in Ref. [7]. The paper [8] introduced a method to estimate and reduce the influence of EV chargers on PQ and the lifetime of transformers. A stochastically formulated method was proposed in Ref. [9] to simulate the influence of battery EVs on the thermal aging of transformers. An approach to quantify the transformers’ aging acceleration as a result of additional loading from plug-in EVs is described in Ref. [10], concluding on the importance of smart charging and load management.

The results of the above-mentioned studies show that the main factors that affect the transformer's lifetime are the ambient temperature, the EV penetration level, and the start time of charging [4,9,10], while the poor PQ can additionally worsen the condition of the distribution transformer [[6], [7], [8]].

A known strategy to mitigate the impacts of the augmented electricity demand from EVs on the PDS includes grid reinforcements and upgrades. The authors of [4] developed a fuzzy-logic-based framework for diagnostics of the transformers' condition and mitigation of their aging, using photovoltaic (PV) generation, capacitor banks, and battery energy storage. In Ref. [11] the Pareto frontiers were employed to find the trade-off between cost-based optimization and emission-based optimization of EVs' charging under different transformer capacity limits. Although a transformer is often a bottleneck of the distribution network, upgrading the transformer to address grid congestion resulting from EV charging is, in most cases, not advantageous: the additional expenses and emissions associated with increasing the transformer capacity limit do not justify the cost and emissions involved in the upgrade [11]. An analytical method to analyze the effectiveness of the infrastructural reinforcements and to enhance the EVs hosting capacity in low-voltage (LV) PDSs was proposed in Ref. [12]. The probabilistic quantification of the EV high-power fast chargers on the distribution transformers' loss of life (LoL) was performed in Ref. [13]. The authors of [14] demonstrated the negative effects the uncontrolled charging of electrified cars on a LV network and proposed a fuzzy energy management system to coordinate the EV charging. Using the fuzzy cognitive maps, a novel EV charging management system for islanded LV grids, was designed in Ref. [15], allowing to reduce peak load and load variances, while satisfying the EV charging demand. A long-short-term memory neural network was utilized to forecast load demand and electricity price, and a framework for decentralized and coordinated EV charging based on the forecasting information was proposed in Ref. [16]. At the same time, rational EV discharging has been recognized as a significant opportunity for supporting the electric network through vehicle-to-grid (V2G) or vehicle-to-house (V2H) bidirectional charging features [17]. Given that, other common strategies to improve the transformer's loading profile imply: (a) strategic shifting of the EV charging periods during the day and (b) exchange of energy accumulated in the vehicle's battery with the grid, which has attracted the interest of many researchers and has been widely presented in the scientific literature [[18], [19], [20], [21], [22], [23], [24], [25], [26]].

In [18] an optimal scheduling method for EV charging to reduce the load fluctuation, keep the voltage within the acceptable deviation range, and delay the grid infrastructure investments was developed. The authors conclude that aggregation of EVs and management of their charging and discharging can play a positive role in delaying investments in the PDS [18]. The authors of [19] developed a particle-swarm-optimization-based method for EV charging at the parking lot, targeting to minimize the total charging cost, while satisfying technical and operational constraints. In Ref. [20] evaluation of the EVs’ charging/discharging modes for the parking lot in terms of their profitability and effect on the voltage profile and losses was done.

A composite methodology to obtain projections of demand and peak-shaving opportunities from plug-in EVs, and the associated spatial and temporal impacts on peak household electrical load was developed and presented in Ref. [21]. A strategy for sizing of renewable energy sources in residential networks, focusing on the EV's adoption and the individual energy needs of each household, was introduced in Ref. [22]. The authors of [23] compared a probabilistic method, based on quadratic programming, and a deterministic method, based on Monte Carlo simulation, to design a charging/discharging schedule for V2G operation. A multi-objective EV charging scheduling model, which aims to minimize the charging cost and the peak-valley load, was presented in Ref. [24]. An energy management and charging scheduling system, which utilizes battery unit control and communication with charging stations, was introduced in Ref. [25]. The work [26] proposes a framework for a day-ahead charging schedule, which is aimed at increasing the profits of EV owners and distribution system operators (DSOs); the service lifespan of EV batteries and network transformers was taken into account.

In such a way, the common strategies to minimize the negative impacts of plug-in EVs charging on the power distribution systems are:

• •reinforcement of the PDS with PV and energy storing technologies,
• •upgrading the elements of the PDS (e.g., transformers and cable lines),
• •compensation of reactive power,
• •shifting the EV charging to off-peak hours,
• •adoption of smart charging, V2G and V2H features.

These strategies have been reviewed in the above-named publications separately and in combinations. However, many of the earlier presented approaches rely on the electricity market conditions, load, and charging patterns aggregated at the national or regional levels, which may result in inaccurate determination of distribution system impacts in other geographical regions. The studies [4,[11], [12], [13]] are aimed at mitigation of the distribution transformers' LoL through system upgrades and reinforcements, while the potential of different charging and discharging strategies of EVs to prolong the transformer's lifespan is not considered. The solutions presented in Refs. [14,15] do not incorporate a transformer's aging model. The framework from Ref. [16] does not incorporate the influence of local PV generation and higher harmonics on the transformer's LoL. Moreover, the charging scheduling techniques for EV developed in Refs. [[18], [19], [20], [21], [22], [23], [24], [25], [26]] are predominantly targeted at profitability (i.e., minimization of charging-associated expenditures), while the state of the equipment is left out of focus.

1.3. Contributions and organization of the paper

Given the existing challenges and the named limitations of the previous related works, this study aims to develop an integrated method to analyze peak-load impacts in the PDS with EVs on the distribution transformers, considering mild and extreme combinations of localized EV charging and electric energy demand. The method employs a fuzzy-logic-based tool, which incorporates the influence of the ambient temperature, higher harmonics, reactive power compensation, reverse power flows and overloads. The study uses the results of our previous work [4]. However, in contrast to Ref. [4], the model and the controller's logic have been improved, more EV penetration scenarios have been modeled and assessed, and the potential of charging scheduling for EVs and peak-shaving technologies, such as V2H, to mitigate the transformer's LoL has been investigated. The applicability of different EV charging strategies has been assessed with respect to the electricity demand and EV penetration level. This holistic approach allows for a comprehensive analysis of peak-load impacts in the power distribution system with electric EVs.

The developed model examines the parameters and factors that impact the regular functioning of the transformer and warns about the situations threatening reliability and power supply continuity. Application of the tool does not require sophisticated computing, and the model can be easily adjusted to the conditions of different LV PDSs. Additionally, the developed model is user-friendly and based on an understandable fuzzy logic, which enhances the practicality and accessibility of the proposed method for real-world implementation. The results of this work could provide several practical benefits: (a) enhancing preventive maintenance of distribution transformers, (b) optimizing EV charging schedules, (c) assisting in distribution upgrade planning (particularly, for transformers), (d) aiding DSO's operational planning.

As illustrated in Fig. 1, the rest of the paper is organized as follows. Input data, the modelling methodology, and the case study scenarios are presented in Section 2. The algorithm and the model development are explained in Section 3. The results of the simulations are summarized and discussed in Section 4. Finally, the conclusions summarize the key findings and highlight the future work directions.

Fig. 1.

The overarching structure of the paper.

2. Input data, modelling approach and case study scenarios

To effectively plan for the impact of EVs on electrical networks and potentially leverage opportunities for peak-shaving using vehicles' batteries, it is crucial to comprehend the additional loading effects that arise from EV charging on the distribution transformers. These transformers are integral components of typical radial PDSs, and their reliability plays a pivotal role in ensuring uninterrupted electricity supply. Under normal conditions, well-sized and properly maintained transformers are designed to serve for around 20–30 years at their nameplate load. However, if these transformers are consistently operated above their rated capacity for prolonged periods, their lifespan may be significantly reduced compared to expectations [13]. Overloading causes overheating of the windings and magnetic circuit, resulting in degradation of insulation, and shortening the transformer's operational life. Several factors contribute to the accelerated aging of transformers, including high ambient temperatures, loading above the nominal value, and the presence of higher harmonics in voltage and current. These factors have been incorporated into the model along with the EV charging patterns and consumer energy demand data.

2.1. The power distribution system

A typical radial PDS, which is common for small localities and countryside in Europe, is selected as a research object for the study. A simplified one-line diagram of such a PDS is shown in Fig. 2. A 20/0.4 kV mineral-oil-immersed transformer is installed in the head of the feeder, and several lines feeding 240 residential houses and a local enterprise are connected to its secondary voltage side, 0.4/0.23 kV. A shunt capacitor bank (SCB) and a community-level PV power station are also located at the secondary voltage bus. Residential houses can have EVs and rooftop PV installations to cover their internal demand or send energy to the grid. The SCB has 12 regulation steps, and its output power can be automatically controlled, with respect to the existing reactive power demand.

Fig. 2.

The secondary distribution system.

2.2. Ambient temperature

According to Ref. [27], the average ambient temperature for a transformer should not surpass 30 °C within a 24-h timeframe. For this study, the ambient temperature data was retrieved from the photovoltaic geographical information system (PVGIS) [28] for the geographical location of Kherson city (latitude: 46.446, longitude: 32.834 decimal degrees).

2.3. Photovoltaic generation

The hourly solar irradiation data and the wind speed data were extracted from the PVGIS [28] for the selected geographical location. The photovoltaic power output P_PV is estimated according to the methodology given in Ref. [29].

The electric energy supplied by the PV unit is the product of the power output P_PV and the operating time t:

$$E_{PV}=\sum _{t=1}^n{P}_{PV}·t$$ (1)

The PV inverters are assumed to have a power factor (PF) of unity.

2.4. Higher harmonics

At high levels of harmonic distortion, the temperature of equipment tends to rise. The presence of higher voltage harmonics amplifies hysteresis losses, losses associated with eddy currents in steel, and losses in transformers' windings [30]. Furthermore, harmonics’ impact on transformers leads to the circulation of zero sequence triple current in the delta-connected windings, resulting in additional loading [30].

The prediction of harmonic components’ composition and levels in a power network is challenging due to their inherently time-varying nature. To address this issue, synthetic data was generated for voltage harmonics at the fundamental frequency and higher harmonics of the 3rd, 5th, 7th, and 11th orders. The voltage harmonic signals were simulated using a random distribution within the following magnitude ranges:

• •fundamental harmonic: 0.9–1.1 p.u. (same as per EN 50160-2010 [31]);
• •3rd harmonic: 0–0.075 p.u.;
• •5th harmonic: 0–0.09 p.u.;
• •7th harmonic: 0–0.075 p.u;
• •11th harmonic: 0–0.0525 p.u.

The upper levels of higher harmonics in simulations exceed the permissible threshold levels defined by EN 50160-2010 [29] by 1.5 times.

The cumulative influence of PQ on the distribution transformer is evaluated indirectly, through the total harmonic distortion (THD), V_THD [32]:

$$V_{THD}=\frac{\sqrt{\sum _{h=2}^{\infty }{V}_h^2}}{V_1}\text{,}$$ (2)

where V_h is the voltage harmonic component in root mean square; V₁ is the fundamental voltage in root mean square.

2.5. Charging demand of electric vehicles

Approximately 80 % of plug-in EV recharging takes place at residential premises, with around 15–20 % of charging events occurring at workplaces [33]. Therefore, in this work it is assumed that EV recharging primarily takes place at residential dwellings, using the alternating current dedicated charge point, available in conventional home electrical supply installations. The domestic charging can occur under Mode 2 or Mode 3, according to IEC 61851-1 [34], which are widely used across the world and in Europe. The power rating of these recharging systems can range from 3.7 kW to 22 kW alternating current charging [35], which would allow recharging a vehicle with a range of 100 km in 1–8 h.

To investigate the influence of different charging strategies, three charging modes are considered:

• 1.Demand charging: is done on a daily basis and starts as soon as the car arrives at home and is parked.
• 2.Off-peak charging: is done daily and is delayed until after the evening peak demand time window, but so that it is possible to recharge the accumulator by the next day.
• 3.Off-peak charging plus V2H: is done on a daily basis and is delayed until after midnight. EVs discharge energy to the dwellings between 17:00 and 24:00, subject to the constraints imposed by battery capacity and off-driveway activity constraints.

The EV charging/discharging profiles per vehicle were replicated from Ref. [21] and are shown in Fig. 3. It is assumed that throughout the year, electricity demand from EVs can vary ±10 % from the reference values. The ranges of variation are outlined with the dotted lines near the corresponding curves in Fig. 3.

Fig. 3.

The EV load profiles per vehicle.

The demand charging profiles are realistic in light of statistical results from real-world EV trials [36,37]. As was demonstrated in Ref. [36], EVs' charging behavior does not exhibit distinct seasonal patterns, and there is rather negligible variation in the start-charging times between weekdays (from Monday to Friday) and weekends (Saturday and Sunday). However, these might have some variations depending on the demographic category (e.g., age, gender) of an EV's owner [37]. On average, on weekdays the first charge would start around 8:00 (before work) or at 18:00 (afterhours); while a second charge (if any) usually starts after 18:00 [36]. It is projected that electricity consumption for recharging on a working day is about the same as for a weekend, and similar curve patterns of the EV charging were used for weekdays and weekends.

Basing on [21], it is assumed that the average peak charging load in the demand charging scenario is 0.64 kW per EV, with the highest load typically observed around 19:00, and the average daily household energy demand is 1.9 kW. For the off-peak charging the average peak charging load is 0.87 kW per EV, peaking at around 02:15, and the average daily household energy demand is 1.75 kW. For the off-peak charging with V2H exchange, the average peak charging load is 1.42 kW per EV, which is supervised at around 03:45 and is balanced by the potential of peak-shaving of up to 0.45 kW during the discharging hours. The average daily household energy demand for this scenario is 1.59 kW.

To manage the EV charging, techniques for reducing the charging power or shifting the charging load can be employed. During the peak demand periods, charging power can be adjusted in real-time using smart chargers. Shifting of the EV charging loads can be achieved through the introduction of time-of-use electricity rates: the owners receive a motivation to delay the start of EV charging to off-peak hours, when electricity prices are lower [19].

2.6. Shunt capacitor bank

The projected reactive power of the SCB at the moment t, Q_SCB,t, is determined by the difference between the consumed reactive power Q_Load,t and the amount of the reactive power Q_PDS,t set by the power system [38]:

$$Q_{SCB,t}=Q_{Load,t}-Q_{PDS,t}$$ (3)

Therefore, the reactive power of the compensating SCB can be calculated as [38].

$$Q_{SCB,t}=P_{Load,t}\left(tg{\phi }_1-tg{\phi }_2\right)$$ (4)

In (6) the values tgφ₁ and tgφ₂ are determined based on the values of cosφ₁ and cosφ₂, respectively, where cosφ₁ is the PF of the cumulative load before the installation of compensating devices; cosφ₂ is the PF of the cumulative load after the installation of compensating devices (desired or specified by the electric energy supply company). In this work, it is assumed that tgφ₂ = 0.4.

The actual value of the reactive power injected by the SCB at the moment t, Q^act_SCB,t, depends on the number of regulative capacitor units (steps) available, based on the SCB's design:

$$\begin{array}{l}{Q}_{SCB,t}^{act}=\{\begin{array}{l}{n}_{step,t}\cdot Q_{step}\approx \left|\text{Re}\left\{S_{dem,t}^{tot}\right\}\right|\cdot \left(tg{\phi }_1-tg{\phi }_2\right),Q_{SCB,t}\le n_{step}^{\max }\cdot Q_{step}\\ n_{step}^{\max }\cdot Q_{step},Q_{SCB,t}>n_{step}^{\max }\cdot Q_{step}\end{array}\\ Q_{step}=const\end{array}$$ (5)

In (7) n_step,t is the number of capacitor units to be activated at the moment t; n_step^max is the maximum number of steps of the SCB, which corresponds to its rated power; Q_step is the rated reactive power of one capacitor unit; S_dem,t^tot is the aggregated demand at the transformer's secondary side, which is defined as

$$S_{dem,t}^{tot}=\sqrt{{\left(P_{Load,t}+P_{EVs,t}-P_{PV,t}\right)}^2+{Q_{Load,t}}^2}\text{,}$$ (6)

where P_Load,t, Q_Load,t are the t-th real and reactive power demands of the grid consumers, respectively; P_EVs,t is the t-th EV charging demand; P_PV,t is the t-th PV installations' power output.

2.7. Transformer's loading

The aggregated apparent power demand after reactive power compensation, which corresponds to the transformer's loading at each sampling step, can be as assessed with the formula

$$S{\prime }_{dem,t}^{tot}=\sqrt{{\left(P_{Load,t}+P_{EVs,t}-P_{PV,t}\right)}^2+{\left(Q_{Load,t}-Q_{SCB,t}^{act}\right)}^2}\text{,}$$ (7)

where Q^act_SCB,t is the t-th power output of the SCB.

To avoid the transformer's overloading, the total power demand in the PDS, S'_dem,t^tot, should be constrained by the transformer's capacity, S_tr^max, at each timestep t:

$$-S_{tr}^{\mathit{max}}\le {S^{\prime }}_{dem,t}^{tot}\le S_{tr}^{\mathit{max}}\forall t$$ (8)

The residential loads are assumed to be non-controllable. Therefore, the transformer's loading can be controlled by altering of EV charging behavior, PV real power output, and SCB's reactive power output.

In this work, for the values of P_Load,t, Q_Load,t, the annual hourly load profiles of eleven residential dwellings and a small enterprise were utilized [4]. The power demand patterns of residential and manufactural loads are integrated at the transformer's secondary side. While the load profiles employed in this research may be specific to Eastern Europe, the methodology is applicable in a broader sense and can be adapted for different geographical regions.

2.8. Transformer's temperature model

The methodology employed in this study is for mineral-oil-immersed transformers with insulation systems rated for a 65 °C or a 55 °C average winding temperature rise at rated load.

The rate at which insulation deteriorates is primarily influenced by the temperature conditions of the transformer [39], which is a function of temperature, specifically the winding hottest-spot temperature [27]. Furthermore, temperature plays an important role in oil oxidation and significantly affects the processes of moisture penetration into the transformer [27]. In addition, the thermal expansion of conductors, structural components, or insulation materials can lead to permanent deformations, increasing the risk of mechanical or dielectric failures [27].

The standards [27,40,41] define real transformer's thermal models, employing the LoL index, which primarily correlates with the winding hottest-spot temperature, Θ_HS. At each given moment in time, t, the temperature of the hottest spot in the winding is defined by summation of three components [27]:

$${\mathrm{\Theta }}_{HS.t}={\mathrm{\Theta }}_{A.t}+\Delta {\theta }_{O.t}+\Delta {\theta }_{HSO.t}\text{,}$$ (9)

where Θ_A is the ambient temperature (cooling medium), °С; Δθ_O is the difference between the transformer's top oil temperature and the ambient temperature, °С; Δθ_HSO is the difference between the transformer's top oil temperature and hot-spot temperature, °С.

It is assumed that the temperature increases Δθ_O.t and Δθ_HSO.t remain unaffected by the ambient temperature within its range of variation from +40 to −20 °C [40,41]. In greater detail, the method to estimate the dynamics of Δθ_O and Δθ_HSO under the transient thermal processes and loading changes is presented in Ref. [4].

The transformer's relative wear is determined by Θ_HS through the aging acceleration factor F_AA [27], that is defined as:

$$F_{AA}=e^{\left(\frac{15000}{{\mathrm{\Theta }}_{HS}^{ref}+273}-\frac{15000}{{\mathrm{\Theta }}_{HS}+273}\right)}\text{,}$$ (10)

where Θ_HS^ref is the reference hottest-spot temperature, which is 110 °C for 65 °C average winding rise and 95 °C for 55 °C average winding rise transformers [27].

The cumulative relative wear over the entire duration of the temperature cycle is assessed using the equivalent aging factor:

$$F_{EqA}=\frac{\sum _{i=1}^T{F}_{AA,i}\cdot \Delta t_i}{\sum _{i=1}^T\Delta t_i},i=1,2...T\text{,}$$ (11)

where F_AA,i is the aging acceleration factor for the temperature existing during the period of time Δt_i; T is the total number of periods.

Having F_EqA, and knowing the total number of periods, the yearly LoL can be determined:

$$Lo{L}_y\%=\frac{F_{EqA}\cdot T}{L_N}\cdot 100\text{,}$$ (12)

where L_N is the normal life of the insulation, which is 1.8·10⁵ h, according to Ref. [27]; T is the number of hours in a not leap year, T = 8760 h.

2.9. What-if scenarios

Three scenarios are considered in this study, and their descriptions are given in Table 1. To cover the wide range of EVs’ charging consequences in the present and the future, six EV penetration levels of 15 %, 33 %, 50 %, 67 %, 85 %, and 100 % have been simulated for each what-if scenario.

Table 1.

Scenarios with varying conditions for the study.

Scenario	Description
Case 1	The feeder includes the residential and manufacturing loads, PV installations, the SCB. Six penetration levels of EVs are moderately considered. Demand charging mode is considered, and the recharging starts once the car arrives at home and is parked.
Case 2	Similar to the previous one, but off-peak charging mode is considered, and the start of the recharging is delayed until after evening peak demand.
Case 3	Similar to the previous one, but off-peak charging mode in combination with V2H is considered. The recharging starts after midnight, and between 17:00 and 24:00 the EVs discharge energy to the houses, if the battery capacity and off-driveway activity allow it.

Given that the hosting capacity of a low-voltage PDS might be constrained, in the first instance, by the distribution transformer [36], this study does not take into account overloads of overhead lines and underground cables. The branches might become overloaded in cases of very long feeders and at penetrations of EVs over 90 % [36].

3. Approach and model explanation

Diagnostic tools for power systems usually must be tuned to specific conditions, which requires taking and comparing several measurements before a reasonable performance can be guaranteed [42]. Given the difficulties associated with the creation of precise numerical models for predicting and analyzing failure modes in distribution transformers, the mathematic tool of fuzzy logic was favored for analyzing the operational limits (e.g., extra high load, temperature overheating). The fuzzy approach allows to deal with the values that are specified unambiguously and with indistinct input data (e.g., constantly changing over time) [43]. On the other hand, it allows a user to qualitatively assess both input data and output results. Therefore, the selected approach is highly appropriate for analyzing the operational limits (such as extra high load and temperature overheating) during the transformer's operation.

The following subsections present the algorithm and the modelling methodology to analyze the projected impacts of EV charging and discharging on peak electrical load under the three developed scenarios.

3.1. Algorithm and model development

The block diagram in Fig. 4 illustrates the algorithm of the elaborated fuzzy-logic-based method to assess the transformer's LoL. Based on the evaluation of the transformers' state, the tool will show a caution message for a user (e.g., a DSO), based on which preventive actions to avoid failures can be taken by automatics or manually. Such actions may include curtailment of loads or PV generation, reconfiguration of the PDS, initiation of the market electricity price changes, etc.

Fig. 4.

The block diagram of the fuzzy-logic-based approach employed in the study.

The algorithm starts with activation of the fuzzy logic control system for diagnostics of the distribution transformer, which comprises a set of input membership functions (MFs), a rule-based controller, and a defuzzification process, as shown in Fig. 5. The MFs are mathematical representations that determine the degree of membership of an input value to a specific fuzzy set, mapping points in the input space to membership values from 0 to 1 [44]. Using the available input data, the aggregated power consumption and the PF at the transformer's secondary bus 0.4/0.23 kV will be calculated and, in case of overloading or poor PF, the SCB will be activated to compensate the reactive power demand.

Fig. 5.

The diagnostics module within the MATLAB-Simulink model.

The PV generation output can be controlled in the range from 0.85 to 1 p.u. of the available solar power via the fuzzy logic control system for tuning. For this purpose, a supplementary module for fuzzy logic control is integrated into the MATLAB-Simulink model (see Fig. 6); the “PV_cont” block links the diagnostic and the tuning parts of the tool. In case of the transformer's overloading with the reverse power flows, the PV output can be curtailed according to the logic implemented in the MATLAB S-function. Also, minor PV curtailments are possible in case of the PDS operation focused on the maintaining of a desired PF. A complementary Else-If logic scheme was incorporated for checking purposes.

Fig. 6.

The tuning module within the MATLAB-Simulink model.

The designed tuning part of this model has a minor influence on the transformer's lifespan, since in the studied case the reverse power flows never exceed the transformer's nominal rating. However, it allows mitigation of the daily oscillations of the PF, if its range of change is restricted. The tuning part of the algorithm is optional and can be activated or deactivated, depending on the user's choice.

3.2. Setting up the fuzzy logic control

The fuzzy-logic-based model examines the parameters influencing the normal functioning of the transformer, aiding in the prediction of emergencies. The fuzzy logic input determines the fuzzy value of the input through the MFs [44]. The MATLAB Fuzzy Logic Toolbox provides various MF topologies, including triangular, trapezoidal, sigmoidal, polynomial, and Gaussian functions.

The diagnostics part uses three input variables: the THD, the ambient temperature, and the aggregated demand at the secondary bus of the distribution transformer (see Fig. 7). Each of the named inputs comprises three to four MFs, and the attributes of these MFs can be manipulated to prioritize one input over the others using weighting coefficients. It is assumed that the “harmonic_voltage” is weighted with a coefficient of 1, the “temperature” is weighted with a coefficient of 2, and the “loading” has a weight of 3. This means, for instance, that the “loading” input is 1.5 times more important than the “temperature” and 3 times more important compared to the “harmonic_voltage” in terms of its influence on the transformer's state. The weights are user-defined and can be adjusted. The Mamdani fuzzy system with the centroid method was employed for the defuzzification [45].

Fig. 7.

The fuzzy logic system for diagnostics.

There are three MFs related to the power quality are the Gaussian functions, which always remain flowing and nonzero. They lie in the range from 0 % to 12 % and define the voltage harmonic distortion as low, medium or high, as shown in Fig. 8a. The THD evaluates the reduction in the service life of the transformer, assuming that higher THD values pose greater harm to the windings, while lower THD values have a minimal effect. For the ambient temperature four MFs covering the range from −25 °C to +50 °C were built (Fig. 8b). The “below normal” and “very hot” MFs are two-sided composite Gaussians, while the “normal” and “hot” MFs are triangular. The loading input is scaled between 15 % and 180 % of the transformer's nameplate rating and has three MFs (Fig. 8c). The normal values of the load demand are represented with a simple Gaussian MF, while the two-sided composite Gaussian MFs are selected for below-normal and above-normal loadings, so that these values can spread beyond the scaled range.

Fig. 8.

Membership function plots for the diagnostics fuzzy logic controller: (a) voltage harmonic distortion; (b) ambient temperature; (c) cumulative load; (d) output.

The output also needs MFs to define possible responses of the system under study [42]. In the developed tool, four triangular MFs are assigned to the output: the “No problem” with a peak at 0.12, the “Caution” peaking at 0.38, the “Possible problem” with a peak at 0.64, and the “Imminent problem” peaking at 0.88 (Fig. 8d).

For the fuzzy logic controller of the diagnostic part, twenty-five membership rules have been defined, as listed in Table 2. The corresponding fuzzy control rule surfaces are provided in Fig. 9a-c. It should be noted that the membership rules in this study are user-defined and can be modified, depending on the applications.

Table 2.

Membership rules for the diagnostic fuzzy controller.

Fig. 9.

Fuzzy control rule surfaces for the diagnostic system, showing the dependences of: (a) the output from the ambient temperature and the voltage THD; (b) the output from the ambient temperature and the loading; (c) the output from the loading and the voltage THD.

Further, all the output MFs are integrated into a unified fuzzy set, and a Mamdani defuzzification process is applied to obtain a crisp value that represents the uncertain data from the specified aggregated topology.

After the defuzzification, the output is decoded and divided into four ranges with an integer value ranging from 0 to 3. These integers represent the state of the transformer and can be further translated into a specific message with a degree of caution for a DSO. The decoded information is then conveyed to the scopes and stored in workspace variables. Depending on the integer, the messages are as follows: “No problem” for the crisp value 0, “Caution” for the crisp value 1, “Possible problem” for the crisp value 2, and “Imminent problem” for the crisp value 3.

In such a way, the diagnostic module of the Simulink model keeps track of the state of the distribution transformer and creates a notification with a degree of caution. Such information can assist in anticipating the transformer's potential failure and, subsequently, avoid outages.

During the following steps of the algorithm, the LoL index is calculated to get the numerical assessment of the transformer's aging.

The tuning fuzzy logic module (see Fig. 10) is implemented to additionally improve the PF by controlling the PV output in the range from 0.85 to 1 p.u. of the available solar power. In case of high reverse power flows, the control range can be extended, but this is not the case in this study. As explained earlier, this part of the algorithm can be activated or deactivated by the user.

Fig. 10.

The fuzzy logic system for tuning.

The tuning fuzzy logic controller comprises two inputs: information about the available PV generation output generation, and PF at the secondary side of the transformer. Both inputs have their internal MFs.

The “PV_power” has trapezoidal MFs (Fig. 11a), laying in the range from 0 to 1.4 p.u. of the PV installed power. The extended upper limit considers the possibility of new PV injections to the PDS. The photovoltaic output can be considered as low (up to 0.55 p.u.), high (over 0.95 p.u.) or medium (between the other two bands). The MFs representing “cos_fi” are also trapezoidal and delineate the transition between low and high PF values (Fig. 11b). The output MFs, on the other hand, are triangular and leverage the potential system responses. Values ranging from 0 to 0.5 necessitate a “subtle” tuning, values from 0.25 to 0.75 call for an “active” tuning, and values from 0.75 to 1 require an “intense” tuning (Fig. 11c).

Fig. 11.

Membership function plots of the tuning fuzzy logic controller: (a) PV generation; (b) PF; (c) control action.

The fuzzy logic controller of the tuning part has three membership rules, which are listed in Table 3. The corresponding rule surface is shown in Fig. 12.

Table 3.

Membership rules for the tuning fuzzy controller.

Fig. 12.

Fuzzy control rule surface of the tuning system.

The process of tuning is deemed successful when there is a notable enhancement in the PF, and the transformer is not overloaded by the existing reverse power flows. In this study, the control actions are designed to be slight (unnecessary PV curtailment is not desired). Therefore, the tuning part has a minor impact on the transformer's operation.

4. Findings and analysis

This section evaluates and discusses the simulation results depicting the impact of operating transformers under different ambient temperatures and load conditions on their aging. A case study is presented to demonstrate the simulation, specifically examining the effects of peak-load impacts in the PDS Fig. 2 under different operating scenarios, as per Table 1, comprising three charging/discharging modes described in Section 2.

Cumulative charts for different charging strategies have been obtained during simulations. As an example, the cumulative charts for a spring weekday at the considered location, for the 85 % EV penetration level, are demonstrated in Fig. 13a-c. The values on the vertical axis were converted to p. u., using the transformer's rated power as the reference base, and are presented in percent. It can be seen that the load power profiles have a morning and an evening maximum. The curve of the aggregated demand at the secondary bus of the PDS, S_dem,t^tot, is higher than the demand curve after the activation of the SCB, S'_dem,t^tot. Also, the SCB is set to sustain the PF close to the desirable level, cosφ₂, if possible.

Fig. 13.

Load profiles of the low-voltage distribution system at EV penetration 85 %: (a) for demand charging mode; (b) for off-peak charging mode; (c) for off-peak + V2H charging mode.

From Fig. 13c, it can be seen that off-peak charging mode combined with V2H electric energy exchange imposes the highest overloading to the transformer at 85 % EV penetration. This may mean that at high EV penetration levels, other charging modes should be preferred.

It should be noted that Fig. 13a-c serves as a reference by showcasing the load profiles of a particular day, while acknowledging that these profiles undergo variations throughout the year based on load demand and PV output (see Section 2). Given the spatial and temporal variability of household energy demand, EVs can exert a varying (either smaller or greater) relative impact on different types of demand profiles.

The decoded charts of the fuzzy controller output for the demand, off-peak, and off-peak + V2H charging modes for a spring workday are shown in Fig. 14. For the depicted example, at 50 % EV penetration the “Possible problem” status (i.e., the crisp value 2) does not occur for demand and off-peak charging strategies (Fig. 14a and b), but appears just two times and lasts for several minutes for the off-peak + V2H charging mode (Fig. 14c. The subfigures 14d-l clearly show that with the increasing penetration of EVs, the duration of the dangerous statuses “Possible problem” and “Imminent problem” rises. For example, for the off-peak + V2H charging mode at 100 % EV penetration (Fig. 14l) the “Imminent problem” status (i.e., the crisp value 3) appears at around 2:00 and proceeds till 5:15, changing by the less severe “Possible problem” status and, further, by the “Caution” status at around 6:30. To compare, for the demand charging mode at 100 % EV penetration (Fig. 14j) the “Imminent problem” status only occurs between 18:00 and 19:20, and for the off-peak charging (Fig. 14k) it persists from 24:00 till 2:45. This confirms that at higher penetration of EVs the harder operational regimes of the transformer (i.e., those corresponding to the statuses “Possible problem” and “Imminent problem”) occur more frequently and last for longer.

Fig. 14.

The fuzzy logic output for demand, off-peak, and off-peak + V2H charging modes: (a)–(c) at 50 % EV penetration; (d)–(f) at 67 % EV penetration; (g)–(i) at 85 % EV penetration; (i)–(l) at 100 % EV penetration.

To get a better understanding of the impacts of EV charging loads on local LV networks, the simulations for a year period for different what-if scenarios have been performed. Table 4 provides a summary of the transformer's operation modes duration, the aggregated relative wear based on the fuzzy logic output, and the LoL calculation scores. As can be seen, if the penetration level of electric cars is up to 50 %, the extra load associated with the EV charging has a small impact on the transformer's aging, irrespective of the charging/discharging mode. The highest LoL_y of 0.2324 % is supervised for the off-peak + V2H charging mode (case 3), which is a low value.

Table 4.

The transformer's operation modes duration and LoL for the whole year.

Not all charging strategies are equally good and feasible for higher EV penetration levels. At 67 % EV penetration the off-peak charging combined with the vehicle-to-house technique (case 3) results in the transformer's LoL_y of 14.6193 %, which is an unacceptably high value. This charging mode would cause the distribution transformer to work up to 455.96 h with the “Imminent problem” status, which indicates significant overloading. To compare, for the demand charging (case 1) this time is 2.36 h, and the LoL is 0.3394 %. For the simple off-peak charging (case 2) there are 0 h with the “Imminent problem” status and 398.28 h with the “Possible problem”, while the LoL index is 0.0455 % only.

At 85 % EV penetration, sticking to the demand charging mode (case 1) results in the LoL_y of 1.9743 %. Switching to the off-peak charging (case 2) allows to reduce this value 3.8 times, mitigating the LoL_y to 0.5239 %; the duration of the “Imminent problem” status is 2.43 h. The hybrid off-peak + V2H charging mode (case 3) is not suitable for the considered PDS at this EV penetration: the transformer would have to operate 1146.92 h during the year with the “Imminent problem” status, which would inevitably cause a failure.

For 100 % EV penetration, the demand charging mode (case 1) results in the transformer's LoL_y of 8.9709 %, which is a high value. The “Imminent problem” lasts for 286.52 h, and the “Possible problem” status lasts for 1447.21 h. Under such operational conditions, the transformer's lifetime would be notably deprived, and the possibility of premature failure increases. The synergy of the off-peak charging and V2H (case 3) is not acceptable for handling such a proportion of the EVs: the transformer would have to operate 1381.92 h during the year with the “Imminent problem” status, which would surely cause a failure. Therefore, the off-peak charging mode (case 2) would be preferable to this scenario. Adhering to this charging strategy results in the LoL_y of 4.2978 %, which is 2.1 times better compared to the demand charging. While the duration of the “Possible problem” status is quite long – 1368.82 h, the most adverse “Imminent problem” status lasts only for 127.56 h, which means that this charging mode poses lower risks for the transformer's operation.

The charts in Fig. 15 demonstrate how the duration of the transformer's operation with alarming statuses changes depending on the EV penetration. These durations correspond to the combined operation time with the cautionary messages “Possible problem” and “Imminent problem”. As can be seen, the off-peak charging mode has the lowest duration of those alarming statuses, while the off-peak charging + V2H demonstrates higher risks of overloading, especially at higher EV penetration levels. Therefore, the off-peak charging mode combined with V2H should only be selected for up to 50 % EV penetration. Otherwise, the schedule for EV charging and releasing energy to the house for this mode should be modified.

Fig. 15.

The changes in the combined duration of the transformer's operation under the “Possible problem” and “Imminent problem” statuses depending on the EV penetration.

To foster the widespread adoption of EVs, consideration of the distribution transformers' LoL and wise selection of the charging strategy are essential. For the studied model, any charging mode can be selected for the EV penetration levels up to 50 %. Normally, this selection would be based on the economic and/or operational criteria in the PDS. For example, the electrical energy accumulated in the EVs' batteries can potentially be harnessed and sold at the local energy market or, otherwise, can be used to supply the house loads, supporting the needs of the PDS by reducing peak demand. And the recharging can be shifted to the off-peak hours when lower electricity tariffs are in force. At higher EV penetration levels (i.e., 67 % and above), the transformer's rating can become a limiting factor from the PDS's side. The simple off-peak charging mode is superior to the traditional demand charging in terms of the impacts on the distribution transformers' ageing. Therefore, it can be recommended for use in the considered LV networks when the EV penetration is 85 % or higher.

To shift the load associated with EV charging to off-peak hours, some known motivators can be used, including the introduction of time-of-use electricity rates for charging and using behavioral science techniques and personalization to educate customers on the impact of charging their EVs at different times of the day.

5. Conclusions

Abnormal operating conditions, such as constant overloading, overheating, deviations from the cooling regime, and poor power quality, expedite the aging of consumables within transformers. This leads to a reduction in their service life and poses risks to the reliability of the PDS.

This study underscores the critical role of transformers in the energy supply chain and emphasizes the importance of their reliable operation for ensuring uninterrupted power supply to consumers. Through a comprehensive analysis, the potential impact of plug-in electric vehicle loads on distribution transformers' aging have been quantified. By examining various EV charging scheduling strategies, including demand charging, off-peak charging, and synergy of off-peak charging and vehicle-to-house technology, the study aims to understand and plan for their effects on transformer performance.

A fuzzy-logic-based tool has been developed to reflect the transformer's state based on the penetration level of plug-in EVs and the selected recharging strategy. The proposed algorithm comprises two fuzzy logic controllers. The first controller is responsible for diagnostics, providing cautionary messages: “No problem”, “Caution”, “Possible problem”, “Imminent problem”. A degree of caution can be used by a DSO to anticipate the transformer's overheating and to take preclusive actions to avoid failure. The second controller is projected to improve the power factor using PV output control and to evade the transformer's overloading with reverse power flows.

The effectiveness of the tool was evaluated on a radial power distribution system featuring a mineral-oil-immersed transformer serving residential consumers and a local enterprise. Simulation results highlight the significant impact of EV charging strategies on transformer LoL. The findings underscore the importance of proactive management of EV charging strategies to ensure the reliability and longevity of distribution transformers, thus optimizing the overall performance of the power system.

• •For EV penetration levels up to 50 %, charging/discharging modes can be selected based on economic benefits and operational conditions, with support from vehicle-to-grid (V2G) or vehicle-to-home (V2H) features.
• •Beyond 50 % penetration, the loss of life (LoL) index accelerates significantly. The off-peak charging + V2H mode becomes infeasible at 67 % EV penetration and inevitably leads to transformer failure with further increases, jeopardizing the reliability of the whole power system.
• •The traditional demand charging does not lead to the transformer's failure, but significantly deteriorates its condition. Therefore, for scenarios with a greater share of EVs it is recommended to prioritize the utilization of simple off-peak charging modes to defer costly system upgrades and reinforcements.
• •At 100 % penetration level, the estimated LoL index is 2.1 times better compared to the demand charging approach.

Therefore, different charging/discharging strategies should be utilized to avoid or postpone expensive system upgrades and reinforcements. The potential practical benefits of the proposed approach include: (a) enhancing preventive maintenance of distribution transformers, (b) optimizing EV charging schedules, (c) assisting in distribution systems' upgrade planning, (d) aiding DSO's operational planning.

The future work will incorporate the variations in electricity prices and will consider the charging patterns of different commercial models of EVs, which will allow a better representation of the processes occurring in real power networks.

Data availability statement

Data will be made available on request.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.