NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Application of Distribution 

Transformer Thermal Life 

Models to Electrified Vehicle 

Charging Loads Using 

Monte-Carlo Method 

Preprint

Michael Kuss, Tony Markel, and William Kramer

Presented at the 25th World Battery, Hybrid and Fuel Cell Electric 

Vehicle Symposium & Exhibition

Shenzhen, China

November 5 - 9, 2010

Conference Paper

NREL/CP-5400-48827

January 2011
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1

Application of Distribution Transformer Thermal Life Models to

Electrified Vehicle Charging Loads Using Monte-Carlo Method

Michael Kuss1, Tony Markel1, and William Kramer1

1

National Renewable Energy Laboratory

1617 Cole Blvd, Golden, CO 80401, USA

E-mail: Michael.Kuss@nrel.gov

 Abstract— Concentrated purchasing patterns of plug-in vehicles may result in localized distribution transformer overload 

scenarios. Prolonged periods of transformer overloading causes service life decrements, and in worst-case scenarios, results

in tripped thermal relays and residential service outages. This analysis will review distribution transformer load models 

developed in the IEC 60076 standard, and apply the model to a neighborhood with plug-in hybrids.

 Residential distribution transformers are sized such that night-time cooling provides thermal recovery from heavy load 

conditions during the daytime utility peak. It is expected that PHEVs will primarily be charged at night in a residential 

setting. If not managed properly, some distribution transformers could become overloaded, leading to a reduction in 

transformer life expectancy, thus increasing costs to utilities and consumers.

 A Monte-Carlo scheme simulated each day of the year, evaluating 100 load scenarios as it swept through the following 

variables: number of vehicle per transformer, transformer size, and charging rate. A general method for determining 

expected transformer aging rate will be developed, based on the energy needs of plug-in vehicles loading a residential 

transformer.

Keywords—Distribution transformer, smart grid, Monte-Carlo, plug-in hybrid, PHEV

1. Introduction

 It is expected that plug-in hybrids (PHEVs) will be 

introduced to the public by auto manufacturers in late 2010 

and early 2011 [1]. Based on the adoption pattern of 

standard hybrids in the early 2000s, we anticipate that early

adopters of PHEVs will be similarly clustered in residential 

neighborhoods – that is, as one neighbor purchases a PHEV, 

neighbors on the same street, and same transformer, become 

more likely to purchase a PHEV. The non-homogeneous 

distribution of PHEVs plugging into the power grid means 

that some distribution transformers may see several PHEVs, 

whereas a distribution transformer in another part of the 

neighborhood may see none [2]. An example of the nonuniform distribution of PHEVs, even at a city-wide level, is 

shown on the Southern California Hybrid Vehicle 

registration map in Figure 1. 

 Electric utilities are already looking forward to PHEV 

implementation and are conducting capacity and operations 

studies of their distribution networks. This analysis is an 

overview of distribution transformer life modeling, with a 

focus on the application of existing transformer life models 

to determine the unique characteristic of PHEV loading 

impacts. The transformer life models used in this analysis 

are dependent solely upon thermal loading characteristics, as 

developed in IEC 60076. Non-fundamental harmonic 

currents are excluded from the thermal model.

 The focus of this work is to develop hotspot temperature 

(HST) duration curves that may be integrated to evaluate 

transformer wear. Sensitivity to increasing plug-in fleet 

penetrations and varying geographical climate will be

evaluated based on real-world drive cycle and 

meteorological data. Over one year, 36,500 travel-days were 

simulated for each scenario. A charge-delay algorithm was 

implemented in the simulator to show how grid 

communication may preserve transformer life without 

significantly impacting service to the utility consumer.

2. Distribution Hardware Model

 According to [4, 5, 6, 7, 8], the primary degradation 

mechanism in transformers is elevated HST. Hotspot 

temperature is defined as the hottest temperature of any 

location in the transformer winding. At large electrical 

loads, elevated core-winding temperatures cause chemical 

breakdown of insulating paper and insulating oil [8]. When 

the dielectric properties of the insulation change, the voltage 

isolation within the transformer is compromised, leading to 

failure. 

Figure 1: Hybrid vehicle registrations – number of vehicles per 

13 km2 [3]
2 

 The HST of transformers has been observed in the field and 

modeled in a variety of ways. The transformer heating 

model used in this analysis is based on standard IEC 60076-

7:2005 “Loading guide for oil-immersed power 

transformers” [4]. Difference equations C.6–C.11 (Annex C 

of IEC 60076) were used as the basis to numerically 

calculate the HST. The calculations were performed in 

MATLAB and Microsoft Excel. IEC 60076 develops the 

HST equations in the following way: 

 

 ߠ௛ሺ௡ሻ ൌ ߠ௢ሺ௡ሻ ൅ Δߠ௛ሺ௡ሻ (1) 

where ߠ ௛is the HST in degrees Celsius, ߠ ௢is the top-oil 

temperature at the current load, and Δߠ ௛is the total HST rise 

at the nth timestep, where Δߠ ௛is calculated in (2): 

 Δߠ௛ሺ௡ሻ ൌ Δߠ௛ଵሺ௡ሻ ൅ Δߠ௛ଶሺ௡ሻ (2) 

Δߠ௛ଵሺ௡ሻ and Δߠ௛ଶሺ௡ሻ come from the difference equations for 

HST rise, and can be calculated: 

Δߠ௛ଵሺ௡ሻ ൌ Δߠ௛ଵሺ௡ିଵሻ ൅ ஽௧

௞మమఛೢ

ൈ ൣ݇ଶଵ ൈ Δߠ௥௛ܭ௬ െ Δߠ௛ଵሺ௡ିଵሻ൧

 (3) 

where Dt is the timestep in minutes, k22 and k21 are 

experimentally-derived constant related to the thermal 

recovery of the transformer, ߬௪ is the winding time constant 

in minutes, Δߠ ௥௛is hotspot-to-top-oil gradient at rated 

current in Kelvin, K is the load factor (current load/rated 

load), and y is the exponential power of current versus 

winding temperature rise (winding exponent). Similarly, 

Δߠ௛ଶ can be evaluated: 

Δߠ௛ଶሺ௡ሻ ൌ Δߠ௛ଶሺ௡ିଵሻ ൅ ௞మమ஽௧

ఛ೚

ൈ ൣሺ݇ଶଵ െ 1ሻ ൈ Δߠ௥௛ܭ௬ െ

Δߠ௛ଶሺ௡ିଵሻ൧ (4) 

where ߬௢ is the average oil time constant in minutes. The 

top-oil temperature must be calculated and substituted back 

into (1): 

ߠ௢ሺ௡ሻ ൌ ߠ௢ሺ௡ିଵሻ ൅ ஽௧

௞భభఛ೚

ቈቂሺଵା௄మோሻ

ଵାோ ቃ

௫

ൈ ሺΔߠ௥௢ሻ െ ൣߠ௢ሺ௡ିଵሻ െ ߠ௔൧቉

 (5) 

where ݇ଵଵ is another experimentally derived thermal 

Baseline constant of the transformer, R is the ratio of load 

losses at rated current to no-load losses, Δߠ ௥௢is the top-oil 

temperature rise at rated load, and ߠ ௔is the ambient 

temperature in degrees Celsius. The HST equations were 

validated using the test case given in Annex C – the model 

calculates the HST over a 120-minute period, based on the 

load factor and ambient temperature. The model followed 

the results of the test case within 0.05%. 

2.1 Transformer Aging Characteristics 

 The goal of this analysis is to define the limits of HST 

increase and aging due to PHEV charging loads for a 

specific transformer type. The distribution transformer’s 

properties used in the analysis for this paper are shown in 

Table 1. 

Table 1: Distribution Transformer Properties 

Symbol Property Value Units 

gr

Average winding-to-averageoil temperature gradient 

at rated current 

14.5 Ws/K 

H Hot-spot factor 1.4 

k11 Thermal model constant 1 

k21 Thermal model constant 1 

k22 Thermal model constant 2 

Prated Transformer rated power 25 or 

37.5 kW 

R Ratio of load losses at rated 

current to no-load losses 8 

Dt Simulation timestep 1 minutes 

x 

Exponential power of total 

losses v. top-oil temperature 

rise (oil exponent) 

0.8 

y 

Exponential power of current 

v. winding temperature rise 

(winding exponent) 

1.6 

Δθhr

Hot-spot-to-top-oil gradient 

at rated current 20.3 K 

Δθor

Top-oil temperature rise at 

rated load 38.3 K 

τ0 Average oil time constant 180 minutes 

τW Winding time constant 10 minutes 

Figure 2: Simulated hotspot and transformer load factor as a 

function of time. From IEC60076 Annex C example, used for 

validating the numerical model implementation. 
3 

Table 2: Net Aging Rate Summary: Based on 1-Hour Daily 

Peak Load 

Insulation Type Peak HST (°C) 

(1 hour duration) Net Aging Rate 

Standard 127 2x 

Standard 137 5x 

Upgraded 144 2x 

 Using the validated model implementation, the increase in 

HST from PHEV loading was calculated. Battery charging 

profiles for each PHEV are assumed to be a square wave 

from 0 kW to 3.3 kW. Figure 3 shows the relationship 

between load and temperature increase, which is nearly 

linear below rated load – once above the rated load, the 

elevated HST results in a rapid increase in aging rate, as 

shown in Figure 4. The labels above the horizontal lines 

indicate the daily-averaged aging rate, assuming a one-hour 

peak HST. The average aging rate is calculated: 

 ܸௗ௔௜௟௬ ൌ ௏೛೐ೌೖାଶଷ

ଶସ (6) 

 Upgraded insulation is a figure of merit defined by 

IEEE/ANSI, which states that thermal insulation paper is 

considered upgraded if it exhibits “50% retention in tensile 

strength after 65,000 hours in a sealed tube at 100°C” [9]. 

Replacing older distribution transformers with upgradedinsulation models on known PHEV-loaded transformers 

appears to be one immediate solution for preventing 

accelerated transformer replacement. However, grid 

communication networks may provide additional 

opportunity for utilities to sufficiently offset PHEV charging 

loads, in addition to other valuable services provided by an 

intelligently operated power grid [10, 11, 12, 13, 14, 15, 16]. 

3. Analysis 

 Two analyses were conducted to demonstrate the 

capabilities of the model: a baseline analysis and a MonteCarlo analysis. The baseline analysis demonstrates a worstcase scenario, assuming a 3.3-kW charging rate, where all 

PHEVs plug in at the same time during peak load. The 

Monte-Carlo analysis utilizes data that reflect actual driver 

behavior, load characteristics, and weather data to determine 

how actual operating conditions affect a transformer from 

the base scenario. 

3.1 Baseline Analysis 

 The goal of the base scenario analysis is to define the 

maximum limits of transformer aging rate due to additional 

PHEV charging loads. The base scenario analysis makes the 

following assumptions: 

1. Ten houses are served by a 25-kVA or 37.5-kVA 

transformer. 

2. Vehicle charging loads are summed with an existing 

customer peak representing 80% of the transformer 

rating. 

3. Ambient air temperature is 30°C. 

4. Vehicles charge at a rate of 3.3 kW. 

 Figure 5 shows the effect that simultaneous battery 

charging will have on aging rate for a transformer already 

Figure 5: Base Scenario: relative aging rate vs. number of 

PHEVs on a distribution transformer, assuming an initial peak 

load of 80% of the transformer rating, ambient temperature of 

30°C, and 3.3 kW level-2 charging. 

Figure 4: Relative aging rate as a function of hotspot 

temperature. Upgraded and non-upgraded insulation curves 

are included, as defined in IEC 60076 [8]. The horizontal 

dashed lines correspond to the daily max loading for one hour 

per day. Text above the line indicates the averaged aging rate.

Figure 3: Hotspot temperature increase as a function of load. 

Square and diamond markers indicate each additional PHEV 

loading the transformer at 3.3 kW. 
4

operating at 80% of the rated load during its peak hour. The 

dashed horizontal lines indicate the peak aging rate for 1 

hour of the day, while the number above the line indicates 

the daily averaged aging rate, based on the peak load. 

Assuming four PHEVs are served by a 25-kVA transformer, 

this scenario suggests a service life decrement of 10–50%. 

However, the 37.5-kVA distribution transformer saw a 

negligible decrease in expected service life. Real-world

PHEV loading is less than this base scenario due to the 

diversity of vehicle arrivals.

3.2 Monte-Carlo Analysis

 GPS travel survey data from the Southern California 

Association of Governments (SCAG) shows all of the arrival 

times for 1,150 drivers to their homes, superimposed on top 

of a single-phase distribution transformer load, shown in the 

green curve of Figure 6 [17, 18]. The behavior of PHEV 

owners will be a primary factor faced by distribution

networks. For consumers wishing to charge their 18-kWh 

battery pack (PHEV40) within 2 hours of arriving home, 

SAE J1772 level-2 charging will provide the 6.6-kW

charging power necessary to meet this need. However, 

overnight vehicle charging may not need the full power 

capabilities of the circuit, and so a 3.3-kW charging scenario 

is compared to the 6.6-kW maximum.

 All of the vehicles have 11.6 kWh of useable energy 

storage and have a charging efficiency of 81%. The 

simulated vehicles’ electric motor provides 100% of the 

traction power when in charge-depleting (CD) mode. The 

vehicles drive in CD mode until the battery reaches a 35% 

state-of-charge (SOC), at which time an auxiliary gasoline 

engine runs a generator that maintains the battery’s SOC for 

the duration of the trip. The ambient temperature data come 

from the typical meteorological year data set for Los 

Angeles [19].

 Figure 7 shows the MATLAB simulation inputs and 

outputs – standard residential load profiles, meteorological 

data, and GPS travel data are combined to calculate the HST 

rise and corresponding transformer wear acceleration. The 

year-long baseline increase in aging rate due to PHEVs was 

calculated by running the data through a one-year simulation 

period. Each day was simulated 100 times, using unique 

sets of driving profiles for each simulated day. The 

simulation assumes that PHEV owners immediately plugged 

in upon arrival home.

Figure 9: Hotspot temperature as a function of time, 

corresponding to the example in Figure 8.

Figure 8: Transformer load as a function of time, before and 

after PHEV charging load contribution. Transformer serves 4 

PHEVs charging at 3.3 kW. The baseline assumes each 

vehicle travels 40 miles per day; a random monte-carlo 

simulation was plotted, illustrating the temporal diversity in 

charging events.

Figure 7: MATLAB model data inputs and outputs for

Monte-Carlo analysis.

Figure 6: Expected transformer load and number of arrivals as 

a function of time. Driving data come from SCAG GPS travel 

survey data and represents 1,150 drivers in the Los Angeles

area. The green curve is an averaged residential transformer 

load and does not include PHEV charging.
5

Table 3: Summary of PHEV charging events from the daily 

example in Figure 8

Vehicle Charging 

Start Time

SOC 

(%)

Energy 

Needed 

(kWh)

Duration 

(minutes)

2 16:00 83 3.0 55

3 16:50 63 6.6 120

4 17:50 90 1.8 36

2 18:20 87 2.3 42

 A daily load and HST profile are shown in Figure 8 and 

Figure 9. Under this scenario, there are four separate 

PHEVs charging at various times. The plug-in loads are 

obvious spikes in load for two-hour periods, and contribute a 

significant additional load onto the transformer. The 

transformer thermal response can be seen in Figure 9, and a 

summary of PHEV charging events can be found in Table 3. 

In this example, the PHEVs typically arrive on an empty 

battery, except for one early-evening trip by vehicle 4, which 

promptly went back out until later in the evening. The other

vehicles arrivals were distributed between 5 p.m. and 8 p.m., 

giving the transformer sufficient time to thermally recover 

from the previous charging events. 

Table 4: Monte-Carlo simulation case definition

Test Case Transformer 

Rating (kVA) Number of PHEVs

Base 25 0

Base 37.5 0

1 25 1

2 25 3

3 25 6

4 37.5 1

5 37.5 3

6 37.5 6

 The year-long maximum increase in aging rate due to 

PHEVs was calculated by running the simulation over a oneyear period, taking the maximum aging per day based on 

100 daily simulations. The maximum case was chosen 

because the averaged load data do not reflect periods of 

elevated load that would accelerate the aging process. 

Additionally, the typical meteorological year data do not 

reflect prolonged heat waves during the summer time, which 

would also contribute to accelerated transformer aging. The 

natural diversity of vehicle arrivals still provided sufficient 

time for the transformers to cool down in nearly all cases. 

 The resulting HST-duration curves from the six test cases

described in Table 4 are shown in Figure 10 and Figure 11. 

In the most extreme Monte-Carlo scenario, where six 

PHEVs were loading a 25-kVA transformer at 6.6-kW each.

The addition of PHEV charging loads reduced the 

transformer nominal lifetime by 12%; all other simulations 

yielded life reductions less than 1%. 

3.3 Communication-Enabled Analysis

 Based on the analysis above, a simulation using a PHEV 

demand-control scheme was performed. In this scenario, the 

communication system may delay an individual PHEV 

charger in order to prevent coincident charging during peak 

load. The charge-delay scheme requires that vehicles wait 

for 10-minutes intervals until the transformer HST drops 

below 98°C

Figure 11: HST duration curves for 6 test cases using a 25-

or 37.5-kVA transformer, and 1-6 PHEVs for the maximum 

1% of the time, or 88 hours per year. Assumes 6.6 kW 

charging.

Figure 10: HST duration curves for 6 test cases using a 25 or 

37.5 kVA transformer, and 1-6 PHEVs for the maximum 1% 

of the time, or 88 hours per year. Assumes 3.3 kW charging.
6

 This particular scenario demonstrates how often vehicle 

charging might need to be controlled in the most extreme 

case, when six vehicles are sited on a single transformer. A 

total of 1,200 charge delay periods were requested by the 

utility for the 25-kVA transformer – in other words, a PHEV 

owner might expect to have their vehicle’s charging delayed 

by about 33 hours per year. For the 37.5-kVA transformer, 

240 charge delay periods were requested, totaling 7 hours 

per year per car. The change in HST duration before and 

after grid communication is shown in Figure 12. Even with 

the charge-delay scheme, peak loads on hot summer days 

may still occasionally push the HST above 98°C. 

 The HST curves were integrated and the annual aging rate 

was calculated to determine expected transformer lifetime. 

A summary of expected lifetimes for a 30-year rated 

transformer is shown in Figure 13. The baseline scenario,

where all vehicle coincidentally charge at 3.3 kW on a 25-

kVA transformer, shows what may happen if four PHEVs 

simultaneously charge on a daily basis – the transformer’s 

life would be reduced by 37%. Using the same rating 

transformer with upgraded insulation would produce an 

expected lifetime loss of only 8%. However, arrival 

distribution of drivers show that stacked PHEV loads would 

be infrequent enough to impact transformer life by more

than 3%, given the simulated Monte-Carlo scenarios.

5. Conclusion and Future Work

 This paper developed a method for determining lifetime 

wear on a residential distribution transformer due to plug-in 

vehicles. Driver behavior data shows that the natural

distribution of vehicle arrivals is sufficient to eliminate a 

majority of stacked PHEV charging. For the occasional 

situation where stacked charging does occur, one-way grid 

communication could provide valuable charging-offset 

services. Because increasing the diversity of times when 

people physically arrive at home is not possible, additional 

grid communication capabilities at the distribution level 

could be used to increase the diversity of charging between 

PHEVs connected to the same distribution transformer. 

Further upstream in the power system, this same 

communication network would allow the PHEVs to provide 

ancillary services to the utility [20, 21, 22]. Basic one-way 

communication could ensure that transformer overheating 

does not occur and utility service continues uninterrupted 

during extreme HST excursions. A preliminary example 

showed that PHEV charging would need to be managed for 

fewer than 33 hours per year in the most extreme case, to 

mitigate PHEV-induced degradation.

 These results are specific to parts of the Southern 

California system. Differences in load shape, weather, and 

number of houses per transformer vary substantially 

depending on region, as well as within the same region. 

Future work will include:

• Validating the model’s hotspot temperature 

predictions with actual data collected in the field

• Run the model using non-averaged transformer data 

that includes extreme load excursions seen on 

transformers in the field

• More detailed transformer thermal modeling, 

including harmonic currents [23, 24]

• Collecting large sets of field data to evaluate 

sensitivity of different types of regional 

characteristics, including transformer load shape, 

climate, and transformer sizing 

• Using this model, in collaboration with higher-level 

models, to develop control schemes that enable

PHEV ancillary services and greater integration of 

renewable energy generation

In summary, a simulation process was developed to predict 

the impact of PHEV charging on a particular residential 

transformer. This simulation:

Figure 13: Expected Transformer Lifetime as a Function of 

the Number of Vehicles on the Transformer, and the Scenario 

Type.

Figure 12: HST duration curves for 6 test cases using a 25-

or 37.5-kVA transformer, and 1-6 PHEVs for the maximum 

1% of the time, or 88 hours per year. Assumes 6.6-kW 

charging and a charge-delaying scheme where charging is 

stopped if the HST rises above 98° C.
7

• Utilized the IEC 60076 standard to develop a 

transformer aging model that can be applied to 

PHEV loads on a distribution transformer

• Combined transformer load profile data, GPS travel 

survey data, and meteorological data

• Provides graphical outputs to predict transformer 

life based on different PHEV control scenarios.

• Shows that the natural distribution of vehicle 

arrivals sufficiently prevents most stacked charging 

events, reducing periods excessive hotspot 

temperature that degrade transformer life

 In conjunction with the higher-level power system benefits 

of grid communication and renewables integration, lowbandwidth one-way communication with PHEVs appears to 

be a simple solution for ensuring reliable operation of the 

distribution system throughout PHEV deployment.

6. Acknowledgements

 The work presented here has been completed as part of 

NREL’s laboratory-directed research and development 

program. Thanks to Dick Cromie of Southern California 

Edison for technical advice. 

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[21] T. Markel, K. Bennion, W. Kramer, J. Bryan, J. 

Giedd, Field Testing Plug-in Hybrid Electric 

Vehicles with Charge Control Technology in the Xcel 

Energy Network, National Renewable Energy 

Laboratory, 2009.

[22] P. Denholm and W. Short, An Evaluation of Utility 

System Impacts and Benefits of Optimally Dispatched 

Plug-In Hybrid Electric Vehicles, National 

Renewable Energy Laboratory, 2006.

[23] M. T. Bishop, J. Baranowski, D. Heath, S. Benna, 

Evaluating Harmonic-Induced Transformer Heating,

IEEE, 1995.

[24] A. Elmoudi, M. Lehtonen, H. Nordman, Effect of 

Harmonics on Transformers Loss of life, IEEE, 2006.

8. Authors

Engineer. Michael Kuss

National Renewable Energy Laboratory

1617 Cole Blvd. MS 1634

Golden, CO 80401 USA

Tel: (303) 275-4458

Email: Michael.Kuss@nrel.gov

Senior Engineer. Tony Markel

National Renewable Energy Laboratory

1617 Cole Blvd. MS 1634

Golden, CO 80401 USA

Tel: (303) 275-4478

Email: Tony.Markel@nrel.gov

Senior Engineer. William Kramer

National Renewable Energy Laboratory

1617 Cole Blvd. MS 5202

Golden, CO 80401 USA

Tel: (303) 275-3844

Email: William.Kramer@nrel.gov
F1147-E(10/2008)

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1. REPORT DATE (DD-MM-YYYY)

January 2011

2. REPORT TYPE

Conference Paper

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Application of Distribution Transformer Thermal Life Models to 

Electrified Vehicle Charging Loads Using Monte-Carlo Method: 

Preprint

5a. CONTRACT NUMBER

DE-AC36-08GO28308

5b. GRANT NUMBER

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6. AUTHOR(S)

M. Kuss, T. Markel, and W. Kramer

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NREL/CP-5400-48827

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FC10.2400

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7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Renewable Energy Laboratory

1617 Cole Blvd.

Golden, CO 80401-3393

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NREL/CP-5400-48827

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13. SUPPLEMENTARY NOTES

14. ABSTRACT (Maximum 200 Words)

Concentrated purchasing patterns of plug-in vehicles may result in localized distribution transformer overload 

scenarios. Prolonged periods of transformer overloading causes service life decrements, and in worst-case 

scenarios, results in tripped thermal relays and residential service outages. This analysis will review distribution 

transformer load models developed in the IEC 60076 standard, and apply the model to a neighborhood with plug-in 

hybrids. Residential distribution transformers are sized such that night-time cooling provides thermal recovery from 

heavy load conditions during the daytime utility peak. It is expected that PHEVs will primarily be charged at night in a 

residential setting. If not managed properly, some distribution transformers could become overloaded, leading to a 

reduction in transformer life expectancy, thus increasing costs to utilities and consumers. A Monte-Carlo scheme 

simulated each day of the year, evaluating 100 load scenarios as it swept through the following variables: number of 

vehicle per transformer, transformer size, and charging rate. A general method for determining expected transformer 

aging rate will be developed, based on the energy needs of plug-in vehicles loading a residential transformer.

15. SUBJECT TERMS

Distribution transformer; smart grid; Monte-Carlo method; plug-in hybrid; PHEV

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