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Contract No. DE-AC36-08GO28308

Charge Management Optimization 

for Future TOU Rates

Preprint

Jiucai Zhang and Tony Markel

National Renewable Energy Laboratory

Presented at EVS29: Electric Vehicle Symposium and Exhibition

Montreal, Quebec

June 19–22, 2016

Conference Paper

NREL/CP-5400-66121

July 2016
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EVS29 Symposium

Montréal, Québec, Canada, June 19-22, 2016

Charge Management Optimization for Future TOU Rates

Jiucai Zhang and Tony Markel

National Renewable Energy Laboratory, Golden, Co 80007, {Jiucai.Zhang and Tony.Markel}@nrel.gov

Summary

The effectiveness of future time of use (TOU) rates to enable managed charging depends on the vehicle’s

flexibility and the benefits to owners. This paper adopts opportunity, delayed, and smart charging methods 

to quantify these impacts, flexibilities, and benefits. Simulation results show that delayed and smart 

charging methods can shift most charging events to lower TOU rate periods without compromising the 

charged energy and individual driver mobility needs.

Keywords: EV (electric vehicle), smart grid, charging, off-peak, renewable

1 Introduction

The growing penetration of renewable resources in the electricity grid results in higher levels of noncontrollable variable generation resources [1]. The 2020 33% Studies [2] shows that by 2020, in times of 

low load and high renewable generation, as much as 60% of energy production could come from renewable 

generators. The high level of non-controllable variable generation resources will require far more flexibility 

of the green grid. The California Independent System Operator (CAISO) has created the “duck chart” [2, 3] 

to illustrate how net load varies with changing grid conditions. To maintain reliability, the Independent 

System Operator must direct controllable resources to match both variable demand and variable supply. 

The Independent System Operator uses pricing signals to influence these controllable resources to take 

advantage of low-cost electricity during over-generation of renewable energy but also encourages users to 

conserve energy during peak periods. Electric vehicles (EVs) present a demand that is flexible and 

potentially controllable [4, 5]. Managing a controllable EV load may benefit a utility by taking advantage 

of this to smooth the load by shaving peaks, filling valleys, and allowing more efficient use of excess 

energy produced by renewable energy resources. The effectiveness of price signals depends on the 

flexibility, availability, and benefits of EVs providing grid services. Therefore, there is a fundamental need 

to quantify the flexibility and benefits of EVs for providing the grid services and how the public charging 

affect the flexibility of EVs to provide the grid services.

The existing research mainly focuses on the study of the impacts of vehicle charging on the grid side. The 

flexibility and benefits of smart charging to the EV owners are rarely studied. How public charging affects

the flexibility and benefits of EVs has not been thoroughly studied. Wang et al. (2011) used a unit 

commitment model to study the interaction among plug-in hybrid EVs (PHEVs), wind power, and demand 

response [6]. The paper simulated four PHEV charging scenarios, including unconstrained charging, 3-hour 

delayed constrained charging, smart charging, and smart charging with demand response. Their simulation 

results showed that optimally dispatching the PHEV loads could significantly reduce the total system

operating costs. Ahn et al. (2011) proposed a two-level optimal charging algorithm to achieve both load 

shifting and frequency regulation [7]. A decentralized charging algorithm is proposed for load shifting by 

emulating the charging pattern identified through linear programming optimization solutions. The 

simulation results showed that the proposed algorithm minimized electricity generation cost and emissions 

and reduced the usage of the conversional regulation power plants without compromising battery charging 
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performance. Rotering and Ilic (2011) used a dynamic programming method to optimize the charging time 

and energy flows [8]. Their method offers a cost-competitive alternative to fast charging. The daily 

charging cost is reduced from $0.46 to $0.20. Cao et al. (2012) proposed an intelligent method to control 

EV charging load in response to time-of-use (TOU) price in a regulated market [9]. Their simulation results 

showed that the optimized charging pattern has great benefit in reducing cost and flatting the load curve if 

the peak and valley time periods are partitioned appropriately. Weiller (2011) concluded that non-home 

charging increases daily electric energy use of PHEVs from 24% to 29% (1.5–2 kWh/day) [10]. The 

delayed and average charging strategies can have the same fuel reduction as opportunity charging, but have 

different instances electricity consumption impacts [11]. Delayed charging at home-related locations can

move PHEV charging from peak hours to off-peak and decrease the PHEV demand peak load by 50%.

The goal of this study is to quantify the flexibility and benefits of EVs due to delayed and smart charging 

with intelligent state-of-charge (SOC) management methods, the impact of the charging methods on the 

grid load, as well as needed communication. This paper firstly employs year-long sequences for 317 

vehicles of trip and parking events to analyze the impact of EV charging on the green grid peak demand, 

and then studies the flexibility of EVs for providing grid services. This paper also quantifies the benefits to

EV owners from delayed and smart charging.

2 Methods

2.1 Trip Patterns

This simulation adopts 317 year-long sequences of trip and parking events as shown in Figure 1(a). These 

sequences of trip and park events were selected from 445 individual long-term trip history data from the 

Puget Sound Regional Council’s Traffic Choices Study. Each sequence provides distance, duration, 

destination, and parking for each event.

(a) 317 year-long trip patterns (b) Miles travelled distribution for 317 year-long trip patterns

Figure 1: The 317 year-long trip patterns and their miles travelled distribution, sorted based on annual miles travelled. 

The annual miles travelled range from less than 1,000 miles to more than 25,000 miles.

Figure 1(b) compares the distribution of miles travelled for the travel events and vehicle utility of 317 trip 

patterns. Vehicle utility is defined as the ratio of the miles traveled provided by the battery in the charge 

depleting mode to the total miles traveled per event. The trip pattern is sorted according to the percentage 

of travel events with fewer than 20 miles traveled per event. The percentage of travel events with fewer 

than 20 miles traveled is more than 85% for the last 299 trip patterns. The percentage of travel events with 

fewer than 40 miles traveled for all trip patterns is greater than 85%. If there are enough Level 2 chargers

deployed, the utility of a PHEV with a range of 20 miles (PHEV-20) is very close to the percentage of 

travel events with fewer than 20 miles. The utility of a PHEV-40 is very close to the percentage of travel 

events with fewer than 40 miles. There are some spikes on the vehicle utility plots. These spikes are mainly 

caused by the limited time the vehicle is parked between neighboring travel events or the unavailability of 

charging stations. Charging events during these short parking time periods do not have much flexibility to 

delay charging or reduce the charging rate for providing grid services. If these charging events happen 

during demand hours, they increase the peak load of the utility.
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2.2 Rate Structure

During certain times of the day, energy production can outpace demand. The CAISO duck chart shows that 

increased solar generation paired with conventional base load resources that cannot be turned off could 

cause excess generation in the afternoons during certain months beginning in 2018. Based on data from the 

California Public Utility Commission’s 2024 long-term procurement planning process and 2021 wind and 

solar projections, as well as demand forecasts for 2021 and 2024 produced by the California Energy 

Commission[12, 13], CAISO created projections of future load time blocks of anticipated electricity needs,

as shown in Figure 2. The load time blocks show that supply is expected to be constrained during the peak 

hours of 4 p.m. to 8 p.m. when the sun is setting and solar output is declining throughout the year. 

Increasing solar generation could cause excess generation during super off-peak hours from 10 a.m. to 4 

p.m. from September to June when solar generation is at its highest. The low demand in March and April 

could result in super off-peak hours from 10 a.m. to 4 p.m. The high demand in July and August could also 

cause the peak hours to begin as early as noon and super peak hours to occur from 3 p.m. to 8 p.m. [2, 3, 8].

(a) Weekdays (b) Weekends and holidays

Figure 2: CAISO high-renewables TOU period [14]

To maximize the use of renewable resources and support greenhouse gas reduction, TOU price signals as 

listed in Table 1 could encourage customers to conserve energy consumption during peak and super-peak 

times [3], which could avoid the need to invest in additional generation and help keep electric costs down. 

Meanwhile, the TOU price could also provide incentives to consumers to take advantage of low-cost 

electricity during periods of excess generation, thereby reducing greenhouse gas.

Table 1: High-renewables TOU rates for Southern California Edison [14]

Weekdays Weekends and Holidays

Month Super Off

Peak ($)

Off Peak 

($)

Peak

($)

Super 

Peak ($)

Super Off

Peak ($)

Off Peak 

($)

Peak

($)

Super 

Peak ($)

1-2 - 0.14 0.17 - 0.075 0.14 0.17 -

3-4 0.075 0.13 0.33 - 0.075 0.13 0.33 -

5-6 - 0.14 0.31 - 0.075 0.14 0.31 -

7-8 - 0.15 0.41 0.6 - 0.15 0.41 -

9-12 - 0.14 0.17 - 0.075 0.14 0.17 -

Fixed Charge: $11.33 per month (in 2021)

2.3 Charging Methods

We adopted three charging methods: opportunity charging, delayed charging, and smart charging with SOC 

management to quantify benefits and impacts of the charging methods to EV owners. Opportunity charging 

charges vehicles immediately. Delayed charging selects the charging schedule based on TOU rates and 

driver’s schedule, but charges the same energy per event as opportunity charging. Smart charging with SOC 

management not only delays vehicle charging based on TOU rates and the driver’s schedule, but also 

manages charged energy per event based on the energy requirement for future trips.
4

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2.3.1 Opportunity Charging

The opportunity charging method assumes that an EV is plugged in as soon as it arrives at a charge station. 

The vehicle is charged immediately after it is plugged in. The vehicle keeps charging until the battery pack 

is fully charged or unplugged. Opportunity charging ignores price signals and charges the vehicle as soon

as possible. All price signals have the same priority when charging the vehicle.

2.3.2 Delayed Charging

The delayed charging method utilizes the relatively long parking period to selectively charge the vehicle at 

as low a TOU rate as much as possible at each charge event. It is known when the vehicle will leave and 

how much energy is required for the future trip. Delayed charging will charge the same energy for each 

event as opportunity charging. Delayed charging does not compromise future driving needs. Therefore, 

delayed charging will not affect the battery life and range anxiety. Delayed charging does not need the 

battery SOC information to control the charging process. This method employs simple energy and schedule 

information from the driver to maximize the benefits for EV owners and reduce grid peak demand.

We define each peak time period as a stage. For each charge event, the vehicle is charged to full or

unplugged after the Nth stage. N is the total number of stages. The goal of delayed charging is to minimize 

charging cost under the constraint of the required charging energy throughput, which is formulated in Eq. 1.

i i i

N

i

delayed C = min r * p *τ =1

∑

Subject to : En (N) = En (N) delayed op

(1)

where pi and ri are the charging power and TOU rate at the i

th stage, respectively. Endelayed(N) and Enop(N)

are charged energy for delayed and opportunity charging at the end of plugged in time, respectively. τi is the 

duration of the i

th stage.

2.3.3 Smart Charging with SOC Management (V1G)

The method of smart charging with SOC management not only charges a vehicle during low TOU rate 

periods as much as possible as in delayed charging, but also skips some charging periods at peak or super 

peak periods when the remaining SOC is high enough for the next trip. Smart charging uses the maximum 

of the predefined range to avoid charging at the peak periods as much as possible. Smart charging can still 

meet the range requirement for driving, but has the potential to increase driver’s range anxiety and may 

impact battery life due to the increased SOC swing. This method represents a global optimized SOC 

management method. Smart charging manages SOC based on all future vehicle travel information, and no 

unexpected trips are taken.

The goal of smart charging (V1G) with SOC management is to minimize charging cost under the 

constraints of the SOC limits, as shown in Eq. 2.

i i i

K

i

V G C = min r * p *τ =11 ∑







≤

≥

+

−

i max

i min

SOC SOC

SOC SOC Subject to :

(2)

where K is total number of charge stages for the whole year. SOCi

+ and SOCi-

denote SOC before and after 

the i

th stage, respectively. The first constraint is to ensure that SOC after each driving event is above the 

minimum SOC limit. The second constraint is to avoid overcharging the EV battery.

Table 2 compares the three charging methods. The opportunity charging method is used as a baseline for 

this comparison. Delayed charging only adjusts the charging time according to the TOU rates to minimize 

the charging cost. There is no impact on the charging energy throughput, battery degradation, or range 

anxiety. Delayed charging needs a future trip schedule to select the charging time. No communication is 

needed to get the vehicle battery information. The V1G with SOC management schedules vehicle charging 
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and optimizes the SOC according to the TOU rates and future trip information. The increased SOC swing 

speeds up the battery degradation. The V1G with SOC management also needs communication between 

vehicles and aggregators to get the battery status. The future travel schedule and trip information is also 

needed to manage charging.

Table 2: Impacts of three charging methods (per charge event)

Method Energy Degradation Range Anxiety Schedule Future Trip Communication

Opportunity Base Base Base No No No

Delayed Base Base Base Yes No No

Smart charging Adjusted Increased Increased Yes Yes Yes

2.3.4 Solution

In this section, we present a charge scheduling algorithm to find solutions for the optimization problem 

expressed in Eqs. (1) and (2). The objective of delayed charging and smart charging (V1G) is to selectively 

charge a vehicle at low TOU rates as much as possible to minimize the charge cost and maximize

renewable energy utilization. The delayed charging algorithm selects the charge stages under the following 

three situations: (1) the charging time is equal to the time the vehicle is plugged in; (2) the plugged-in time 

is more than the charging time, and there is only one TOU rate stage while the vehicle is plugged in; (3) the 

plugged-in time is more than the charging time, and there is more than one stage while the vehicle is 

plugged in. For situation 1, there is no choice in terms of scheduling charging. The vehicle will be charged 

as long as it is plugged in. For situation 2, the vehicle has the flexibility to charge, but smart charging does 

not bring any benefits to the EV owners from the TOU rate. However, the vehicle may still be able to earn 

benefits from providing ancillary services, such as frequency regulation and spinning reserves. For situation 

3, EV owners can utilize TOU rates to minimize the charging cost. According to Fig. 1(b), very few 

vehicles and charging events take place in situations 1 and 2. Therefore, the scheduling algorithms only 

focus on situation 3 in this paper.

The follow criteria are adopted to schedule vehicle charging: (1) charging time: the vehicle should be 

charged to the required energy as soon as possible. This criterion maximizes the availability of the vehicle 

for the future driving. (2) Charged energy per charge event: charged energy per charge event should be as 

close to the energy throughput for opportunity charging as possible. This criterion is to make the driver 

comfortable with managed charging. (3) Minimum SOC: the minimum SOC is defined as the minimum 

SOC that is required to cover future unexpected trips before the next charging event. This criterion tries to 

minimize the impact of smart charging on the EV’s unavailability and is mainly used for SOC management 

of smart charging (V1G).

The objective of delayed charging is to charge the vehicle at each charging event at as low TOU rates as 

possible to minimize the charging cost. To achieve this goal, a priority-based scheduling algorithm is 

proposed. The priority of each stage is determined by the TOU rates. The lower the TOU rate, the higher 

the priority for charging, and vice versa. That is, the Super Off Peak period has the highest priority. The

Super Peak period has the lowest priority for charging. The priorities of the different types of loads are

listed in the Table 3, where a lower number represents a higher priority. The vehicle is charged at the 

highest priority stage to minimize charging cost. Equal-priority stages are scheduled in first-come firstserve order to charge vehicle as soon as possible. The vehicle stops charging until the charged energy per 

charge event reaches the energy throughput for opportunity charging.

Table 3: Priority of the different peak loads

Load Type Super Off Peak Off Peak Peak Super Peak

Priority 0 1 2 3

The objective of smart charging (V1G) is to charge the vehicle at lower TOU rates as much as possible to 

minimize the charging cost. Smart charging provides a global optimization method to schedule vehicle 

charging to minimize the total charging cost. To find the solution, we use the Lagrange multiplier method to 

relax two constraints in Eq. (2). The relaxed problem can then be solved using dynamic programming. 

Specifically, we first define the set of admissible decision vectors U=[u1,u2,...,uk], where ui is charged 

energy at the i

th stage. Then, we define a Lagrangian cost function in Eq. 3.
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− +

∑ i i i + i + i

K

i

J U r p 1SOC 2SOC

=1

2 , 1λ λ ( ) = * *τ λ λ (3)

where λ1 and λ2 are the Lagrange multipliers. It can easily be derived from [15] that, if there exists a pair 

λ1

* and λ2* such that α*=arg[minJλ1*,λ2*(U)], which leads to SOCi-

≥ SOCmin and SOCi

+

≤SOCmax, then U is 

also an optimal solution to Eq. (2). Therefore, the task of solving Eq. (2) is converted into an easier one, 

which is to find the optimal solution to the unconstrained problem in Eq. (3). The problems can be easily 

solved by the dynamic programming algorithm.

3 Simulation Results

3.1 Experiment Setup

3.1.1 Charger Power and Availability

Two different power levels are considered for chargers within this study, as listed in Table 4. Each driver 

assigns his or her own home charge station in his or her place of residence. This is assumed to be a 

dedicated charger that is available per the elected charger timing scenario. Implementation of the workplace 

class is performed identically, with the exception that the charger is located at the driver’s place of business. 

The public class assumes chargers are available per the elected charger timing scenario at every location 

that is not the driver’s place of residence or work. Note that we do not discriminate between commercial 

and residential locations nor do we consider the possibility that such chargers are unavailable due to use by 

other drivers. As such, this represents an idealized, best-case scenario with respect to providing drivers 

access to charging infrastructure. Charge timing scenarios are set to maximize the periods that EVs are 

connected to the grid, such that use of the EVs would improve the charging flexibility. The charge timing 

scenarios also enable active thermal management to improve battery life.

Table 4. Charge station parameters

Scenario AC Circuit Efficiency [16] DC Power

Level 1(L1) 120V,16A 86% 1.6kW

Level 2(L2) 240V,32A 86% 6.6kW

3.1.2 Charge Station Selection

Each driver will select the power level of his or her power station at home. We assume that the driver will 

select the same power level as the charge station at his or her workplace. The public charging station 

provides Level 2 power to speed up the charging process. To quantify the impact of the power level on the 

flexibility of EV charging and the impacts on the grid, six groups of charging stations have been selected to 

represent driver preferences. Groups I, II, V, and VI assign charging power levels according to their battery 

sizes, which represents the typical way to select the charge station. Groups III and IV assign Level 2 charge 

stations to charge PHEV-20s at residential and work places. Both groups represent the preferences of 

drivers who prefer to charge their vehicle at a high power rate. Groups I, III, and V denote the EV owners 

who do not like public charging. Groups II, IV, and VI denote the EV owners who like public charging. All 

of these groups are used to study the impact of public stations and charging rates on battery life.

3.2 Simulation Results

3.2.1 The Effectiveness of the Delayed and Smart Charging Methods on the Peak Shaving

Figure 3 compares the time percentages of the six groups of charging stations with the three charging 

methods. The opportunity charging method mostly charges vehicles at Off Peak and Peak time blocks and 

uses 5% and 10% of charging time to charge vehicle at Super Off Peak and Super Peak, respectively. The 

opportunity charging method does not fully utilize the renewable energy and TOU rates. The delayed 

charging method significantly shifts the charging time from high TOU rates to low TOU rates, which 

improves the renewable energy utilization and reduces the charging cost. Compared with the delayed 
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charging method, the smart charging method only shifts the charging time from high TOU rates to low 

TOU rates with public charge stations. The high power levels of charging stations, large battery sizes, and 

public charging improve the effectiveness and flexibility of the delayed and smart charging methods on 

peak shaving.

Figure 3: The charging time percentages of six groups of charging stations with three charging methods, where OC, 

DC, and SC denote opportunity, delayed, and smart charging methods, respectively.

5.2.2 Charged Energy Throughput and Benefits Analysis

Figure 4 compares the annual electricity cost of the six groups of charging stations in Table 5 with the three 

charging methods. Delayed charging reduces the annual electricity cost to 70% of the annual cost of 

opportunity charging. The cost reduction mainly comes from shifting the charging time to lower TOU rates, 

especially from Peak and Super Peak times to Off Peak times. The smart charging method further reduces 

the annual electricity cost. Considering battery degradation, range anxiety, and additional overhead for the

communication devices and components for SOC management, the reduced electricity cost may not cover 

the additional overhead to enable SOC management and battery degradation. Public and/or Level 2 charge 

stations provide more opportunities and energy to charge vehicles, which increases charging flexibility and 

reduces the electricity price for delayed and smart charging. A large battery provides more flexibility for 

shifting the charging time from peak and super peak periods to Off Peak and Super Off Peak periods. An 

increased battery size provides more energy for driving, but it also needs to charge at peak periods to 

provide enough energy. Because a larger battery provides more charge-depleting miles for driving, an 

increased battery size does not help to reduce the annual electricity cost.

Figure 4: Annual electricity costs of six groups of charging stations with three charging methods,where OC, 

DC, and SC denote opportunity, delayed, and smart charging methods, respectively.
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Table 5: Charge station selection 

Group I II III IV V VI

EV Model PHEV-20 PHEV-20 PHEV-20 PHEV-20 PHEV-40 PHEV-40

Public - L2 - L2 - L2

Work L1 L1 L2 L2 L2 L2

Home L1 L1 L2 L2 L2 L2

Table 6 lists the annual cost, annual charged energy, average electricity prices, and relative prices for the six 

groups of charging station options with three charging methods. A relative price is defined as the ratio of an 

actual electricity price to an average electricity price. According to the future TOU rates in Table 1, the 

annual average electricity price is $0.167/kWh. Using a public charging station, a higher power EVSE, and 

a large battery in the vehicle provide more opportunities and flexibility to charge vehicles but at an 

increased annual cost and charged energy throughput. The lowest electricity price for opportunity charging 

is $0.186/kWh, which is 11% higher than the annual average electricity price. Opportunity charging 

discourages EV owners from participating in the future TOU rate plan. The prices of both delayed charging 

and smart charging are lower than the annual average electricity prices. Because public charge stations 

often charge vehicles at peak or super peak periods with limited plugged-in time, delayed charging has little 

flexibility to optimize TOU rates for public charging. The lowest electricity price for delayed charging 

using public charging is $0.156/kWh, for which the relative price is 93%. Due to charging flexibility at a 

workplace and at home, delayed charging reduces the relative price to around 85%. Smart charging 

enhances charge flexibility by scheduling both the charged energy and time and can avoid most of the 

charge events at peak and super peak periods, especially for charge station optiions with public charging. 

The lowest electricity price for smart charging is $0.125/kWh, and its relative price is 74%. Smart charging 

provides the lowest electricity cost for charging.

Table 6: Comparison of six groups of charging station options

EVSE Parameters Average

Price I II III IV V VI

Annual Charged Energy (MWh) - 490,258 680,475 605,385 742,019 756,489 834,203

Relative Charged Energy (%) - 100 139 123 151 154 170

Opportunity

Annual Cost ($) - 99,968 135,430 115,951 138,575 144,461 155,494

Price ($/kwh) 0.167 0.204 0.199 0.192 0.187 0.191 0.186

Relative Price (%) 100 122 119 115 112 114 111

Delayed

Annual Cost ($) - 69,475 112,088 86,272 116,359 107,617 130,328

Price ($/kwh) 0.167 0.142 0.164 0.143 0.157 0.142 0.156

Relative Price (%) 100 85 98 86 94 85 93

Smart

Charging

Annual Cost ($) - 64,532 88,181 78,615 99,214 99,042 103,998

Price ($/kwh) 0.167 0.132 0.130 0.130 0.124 0.131 0.125

Relative Price (%) 100 79 78 78 74 78 75

4 Conclusion

This paper has analyzed the flexibility and benefits of EV charging for six groups of charging stations, two 

types of PHEVs, and three charging methods. Delayed and smart charging methods can shift most charging 

events to lower TOU rate periods without compromising the charged energy and individual driver mobility 

needs. Using a public charging station, a higher power EVSE, and a large battery provide more 

opportunities and flexibility to charge the vehicle, but at an increased annual charged energy and cost. The 

electricity price for opportunity charging is at least 11% higher than the annual average electricity price. 

Opportunity charging discourages EV owners from participating in the TOU rate plan. Delayed charging 

effectively reduces the relative electricity price to 93% of the annual average electricty price with public 

charging and 85% without public charging. Smart charging enhances charging flexibility by scheduling 

both charged energy and time and can avoid most of the charge events at peak and super peak periods. 

Smart charging reduces the electricity price to 75% of the annual average electricity price. Compared with 

delayed charging, smart charging significantly reduces the electricity prices for scenarios using a public 

charging station, but slightly reduces the electricity price for the scenarios without public charging. Smart 

charging provides the lowest electricity cost for charging.
9

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Acknowledgments

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08GO28308 

with the National Renewable Energy Laboratory. Funding was provided by the U.S. DOE Office of Energy 

Efficiency and Renewable Energy Vehicle Technologies Office. The U.S. Government retains and the 

publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a 

nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this 

work, or allow others to do so, for U.S. Government purposes.

References

[1]. J. Kim and J. Lee, A model of stability, IEEE Power and Energy Magazine, 9(2011), 75-81.

[2]. CAISO, What the duck curve tells us about managing a green grid, California Independent System Operator

(CAISO), Folsom, CA, Tech. Rep. 1-4, 2013. [Online]. Available: https://www.caiso.com/Documents/ 

FlexibleResourcesHelpRenewables FastFacts.pdf.

[3]. CAISO, Dealing with the duck: how utilities are using pricing to address projected solar impacts, California 

Independent System Operator, Folsom, CA, Tech. Rep. 1-15, 2013. [Online]. Available: http://www.cleancoalition.org/site/wp-content/uploads/2013/06/Renewables-Integration Power-08 ssw-17-May-2013.pdf.

[4]. Z. Fan, A distributed demand response algorithm and its application to PHEV charging in smart grids, IEEE 

Transactions on Smart Grid, 3(2012), 1280-1290.

[5]. M. Alam, K. Muttaqi, and D. Sutanto, A controllable local peak-shaving strategy for effective utilization of 

PEV battery capacity for distribution network support, IEEE Transactions on Industry Applications, 

51(2015), 2030-2037.

[6]. J. Wang, C. Liu, D. Ton, Y. Zhou, J. Kim, and A. Vyas, Impact of plug-in hybrid electric vehicles on power 

systems with demand response and wind power, Energy Policy, 39(2011), 4016-4021, Special Section: 

Renewable energy policy and development. [Online]. Available: http://www. sciencedirect.com/

science/article/pii/S0301421511000528. 

[7]. C. Ahn, C. Li, and H. Peng, Optimal decentralized charging control algorithm for electrified vehicles 

connected to smart grid, Journal of Power Sources, 196(2011), 10 369-10 379.

[8]. N. Rotering and M. Ilic, Optimal charge control of plug-in hybrid electric vehicles in deregulated electricity 

markets, IEEE Transactions on Power Systems, 26(2011), 1021-1029.

[9]. Y. Cao, S. Tang, C. Li, P. Zhang, Y. Tan, Z. Zhang, and J. Li, An optimized EV charging model considering 

TOU price and SOC curve, IEEE Transactions on Smart Grid, 3(2012), 388-393.

[10]. C. Weiller, Plug-in hybrid electric vehicle impacts on hourly electricity demand in the United States, Energy 

Policy, 39(2011), 3766-3778.

[11]. L. Zhang, T. Brown, and G. Samuelsen, Fuel reduction and electricity consumption impact of different 

charging scenarios for plug-in hybrid electric vehicles, Journal of Power Sources, 196(2011), 6559-6566.

[12]. California Public Utilities Commission, Long Term Procurement Planning: 2014 - 2024, [Online]. 

Available: http://www.ora.ca.gov/ltpp.aspx

[13]. B. Alcorn, M. Ciminelli, N. Fugate, A. Gautam, C. Kavalec, K. Sullivan, and M. Weng-Gutierrez, California

energy demand 2014–2024 final forecast, California Energy Commission, Tech. Rep. CEC‐200‐2013‐004‐

V1‐CMF, 2013, [Online]. Available:

http://www.energy.ca.gov/2013publications/CEC-200-2013-004/CEC-200-2013-004-V1-CMF.pdf 

[14]. CAISO, Matching time-of-use rate periods with grid conditions maximizes use of renewable resources, 

California Independent System Operator, Folsom, CA, Tech. Rep. 1-2, 2015.

[15]. H. Everett, Generalized LaGrange multiplier method for solving problems of optimum allocation of 

resources, Operations Research, 11(1963), 399-417.

[16]. E. Forward, K. Glitman, and D. Roberts, An assessment of level 1 and level 2 electric vehicle charging 

efficiency, Vermont Energy Investment Corporation, Tech. Rep., 2013. [Online]. Available: https://www.

veic.org/docs/Transportation/20130320-EVT-NRA-Final-Report.pdf.

Authors

Jiucai Zhang is a research engineer at National Renewable Energy Laboratory in 

Golden, Colorado. He got his Ph.D. in computer engineering from the University of 

Nebraska-Lincoln in 2011. His research focuses on electric vehicle grid integration and 

battery life analysis. Prior to joining NREL, he designed and developed algorithms and 

software for battery management systems as well as control systems for utility-scale 

grid energy storage systems, telecommunications cell tower backup power systems, and 

electric vehicles at General Electric and A123 Systems, Inc.
10

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Tony Markel is a Senior Engineer and has worked on systems analysis of advanced 

vehicles for the past 19 years at the National Renewable Energy Laboratory in Golden, 

Colorado. Tony is currently focused on electric vehicle grid integration technology 

development. He earned a B.S. in Mechanical Engineering from Oakland University in 

1995 and an M.S. in Mechanical Engineering from the University of Colorado. Tony’s 

expertise spans advanced vehicle technologies, including hybrid electric, fuel cell, 

plug-in hybrid, and electric vehicles and was instrumental in the development of the 

ADVISOR software tool for vehicle systems simulation. He leads a team researching 

grid integration challenges facing plug-in vehicles with a mission to highlight 

opportunities for electrified transportation to reduce our nation’s petroleum 

consumption and enable a smart, renewable, future electricity grid.