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Factoring the Cycle Aging Cost of Batteries

Participating in Electricity Markets

Bolun Xu, Student Member, IEEE, Jinye Zhao, Member, IEEE, Tongxin Zheng, Senior Member, IEEE,

Eugene Litvinov, Fellow, IEEE, Daniel S. Kirschen, Fellow, IEEE

Abstract—When participating in electricity markets, owners of

battery energy storage systems must bid in such a way that their

revenues will at least cover their true cost of operation. Since

cycle aging of battery cells represents a substantial part of this

operating cost, the cost of battery degradation must be factored

in these bids. However, existing models of battery degradation

either do not ﬁt market clearing software or do not reﬂect

the actual battery aging mechanism. In this paper we model

battery cycle aging using a piecewise linear cost function, an

approach that provides a close approximation of the cycle aging

mechanism of electrochemical batteries and can be incorporated

easily into existing market dispatch programs. By deﬁning the

marginal aging cost of each battery cycle, we can assess the actual

operating proﬁtability of batteries. A case study demonstrates the

effectiveness of the proposed model in maximizing the operating

proﬁt of a battery energy storage system taking part in the ISO

New England energy and reserve markets.

Index Terms—Energy storage, battery aging mechanism, arbi-

trage, ancillary services, economic dispatch

I. INT ROD UC TI ON

In 2016, about 200 MW of stationary lithium-ion batteries

were operating in grid-connected installations worldwide [1],

and more deployments have been proposed [2], [3]. To ac-

commodate this rapid growth in installed energy storage ca-

pacity, system operators and regulatory authorities are revising

operating practices and market rules to take advantage of the

value that energy storage can provide to the grid. In particular,

the U.S. Federal Energy Regulatory Commission (FERC) has

required independent system operators (ISO) and regional

transmission organizations (RTO) to propose market rules that

account for the physical and operational characteristics of

storage resources [4]. For example, the California Independent

System Operator (CAISO) has already designed a market

model that supports the participation of energy-limited storage

resources and considers constraints on their state of charge

(SoC) as well as on their maximum charge and discharge

capacity [5].

As electricity markets evolve to facilitate participation by

battery energy storage (BES), owners of these systems must

develop bidding strategies which ensure that they will at

least recover their operating cost. Battery degradation must

be factored in the operating cost of a BES because the life of

electrochemical battery cells is very sensitive to the charge and

discharge cycles that the battery performs and is thus directly

B. Xu and D.S. Kirschen are with the University of Washington, USA

(emails: {xubolun, kirschen}@uw.edu).

J. Zhao, T. Zheng, and E. Litvinov are with ISO New England Inc., USA

(emails: {jzhao, tzheng, elitvinov}@iso-ne.com).

affected by the way it is operated [6], [7]. Existing models

of battery degradation either do not ﬁt dispatch calculations,

or do not reﬂect the actual battery degradation mechanism.

In particular, traditional generator dispatch models based on

heat-rate curves cannot be used to represent the cycle aging

characteristic of electrochemical batteries.

This paper proposes a new and accurate way to model of

the cost of battery cycle aging, which can be integrated easily

in economic dispatch calculations. The main contributions of

this paper can be summarized as follows:

•It proposes a piecewise linear cost function that provides

a close approximation of the cost of cycle aging in

electrochemical batteries.

•System operators can incorporate this model in market

clearing calculations to facilitate the participation of BES

in wholesale markets by allowing them to properly reﬂect

their operating cost.

•Since this approach deﬁnes the marginal cost of battery

cycle aging, it makes it possible for BES owners to design

market offers and bids that recover at least the cost of

battery life lost due to market dispatch.

•The effectiveness of the proposed model is demonstrated

using a full year of price data from the ISO New England

energy markets.

•The accuracy of the proposed model in predicting the

battery cycle aging cost is demonstrated using an ex-post

calculation based on a benchmark model.

•The model accuracy increases with the number of lin-

earization segments, and the error compared to the bench-

mark model approaches zero with sufﬁcient linearization

segments.

Section II reviews the existing literature on battery cycle

aging modeling. Section III describes the proposed predictive

battery cycle aging cost model. Section IV shows how this

model is incorporated in the economic dispatch. Section V

describes and discusses case studies performed using ISO New

England market data. Section VI draws conclusions.

II. LI TE RATU RE RE VI EW

A. Battery Operating Cost

Previous BES economic studies typically assume that bat-

tery cells have a ﬁxed lifetime and do not include the cost

of replacing the battery in the BES variable operating and

maintenance (O&M) cost [8]. The Electricity Storage Hand-

book from Sandia National Laboratories assumes that a BES

performs only one charge/discharge cycle per day, and that

2

the variable O&M cost of a lithium-ion BES is constant and

about 2 $/MWh [9]. Similarly, Zakeri et al. [10] assume that

battery cells in lithium-ion BES are replaced every ﬁve years,

and assume the same 2 $/MWh O&M cost. Other energy

storage planning and operation studies also assume that the

operating cost of BES is negligible and that they have a ﬁxed

lifespan [11]–[13]. These assumptions are not valid if the BES

is cycled multiple times per day because more frequent cycling

increases the rate at which battery cells degrade and hasten the

time at which they need to be replaced. To secure the battery

lifespan, Mohsenian-Rad [14] caps the number of cycles a

battery can operate per day. However, artiﬁcially limiting the

cycling frequency prevents operators from taking advantage

of a BES’s operational ﬂexibility and signiﬁcantly lessens its

proﬁtability. To take full advantage of the ability of a BES to

take part in energy and ancillary markets, its owner must be

able to cycle it multiple times per day and to follow irregular

cycles. Under these conditions, its lifetime can no longer be

considered as being ﬁxed and its replacement cost can no

longer be treated as a capital expense. Instead, the signiﬁcant

part of the battery degradation cost that is driven by cycling

should be treated as an operating expense.

A BES performs temporal arbitrage in an electricity market

by charging with energy purchased at a low price, and dis-

charging this stored energy when it can be sold at a higher

price. The proﬁtability of this form of arbitrage depends not

only on the price difference but also on the cost of the battery

cycle aging caused by these charge/discharge cycles. When

market prices are stable, the expected arbitrage revenue is

small and the BES owner may therefore opt to forgo cycling

to prolong the battery lifetime and reduce its cycle aging cost.

On the other hand, if the market exhibits frequent large price

ﬂuctuations, the BES owner could cycle the BES multiple

times a day to maximize its proﬁts. Fig. 1 shows that the

price proﬁle in a given market can change signiﬁcantly from

day to day. Although the average market price is higher in

Fig. 1a, arbitrage is not proﬁtable in this case because the price

ﬂuctuations are small, and the aging cost from cycling is likely

to be higher than the revenue from arbitrage. On the other

hand, a BES owner is likely to perform three arbitrage cycles

if the price proﬁle is similar to the one shown on Fig. 1b,

because the revenue opportunities arising from the large price

ﬂuctuations are likely to be larger than the associated cycle

aging cost. It is thus crucial to accurately incorporate the cost

of cycle aging into the optimal operation of a BES.

B. Electrochemical Battery Degradation Mechanisms

Electrochemical batteries have limited cycle life [15] be-

cause of the fading of active materials caused by the charging

and discharging cycles. This cycle aging is caused by the

growth of cracks in the active materials, a process similar to

fatigue in materials subjected to cyclic mechanical loading [6],

[16]–[19]. Chemists describe this process using partial differ-

ential equations [20]. These models have good accuracy but

cannot be incorporated in dispatch calculations. On the other

hand, heuristic battery lifetime assessment models assume

that degradation is caused by a set of stress factors, each

0 5 10 15 20

-200

-100

0

100

200

LMP[$/MWh]

[hr]

(a) An example of stable market prices (Jan 7, 2015).

0 5 10 15 20

-200

-100

0

100

200

LMP[$/MWh]

[hr]

(b) An example of highly variable market prices (Jan 2, 2015).

Fig. 1. Market price daily variation examples (Source: ISO New England).

of which can be represented by a stress model derived from

experimental data. The effect of these stress factors varies with

the type of battery technology. In this paper, we focus on

lithium-ion batteries because they are widely considered as

having the highest potential for grid-scale applications. For

our purposes, it is convenient to divide these stress factors

into two groups depending on whether or not they are directly

affected by the way a grid-connected battery is operated:

•Non-operational factors: ambient temperature, ambient

humidity, battery state of life, calendar time [21].

•Operational factors: Cycle depth, over charge, over dis-

charge, current rate, and average state of charge (SoC) [6].

1) Cycle depth: Cycle depth is an important factor in a

battery’s degradation, and is the most critical component in

the BES market dispatch model. A 7 Wh Lithium Nickel

Manganese Cobalt Oxide (NMC) battery cell can perform

over 50,000 cycles at 10% cycle depth, yielding a lifetime

energy throughput (i.e. the total amount of energy charged

and discharged from the cell) of 35 kWh. If the same cell is

cycled at 100% cycle depth, it can only perform 500 cycles,

yielding an lifetime energy throughput of only 3.5 kWh [22].

This nonlinear aging property with respect to cycle depth is

observed in most static electrochemical batteries [7], [23]–

[25]. Section III explains in details our modeling of the cycle

depth stress.

2) Current rate: While high charging and discharging cur-

rents accelerate the degradation rate, grid-scale BES normally

have capacities greater than 15 minutes. The effect of current

rate on degradation is therefore small in energy markets

according to results of laboratory tests [25]. We will therefore

not consider the current rate in our model. If necessary, a

piecewise linear cost curve can be used to model the current

rate stress function as a function of the battery’s power output.

3) Over charge and over discharge: In addition to the

cycle depth effect, extreme SoC levels signiﬁcantly reduce

battery life [6]. However, over-charging and over-discharging

are avoided by enforcing upper and lower limits on the SoC

3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0

10

20

30

40

50

60

SoC [%]

[h]

s2

s3

s4

s5

s6

s7

s1

s0 s8

(a) An example of SoC proﬁle.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0

10

20

30

40

50

60

SoC [%]

[h]

δ1 = 10%

δ3 = 10%

remaining

profile...

δ2 = 40%

(b) The cycle counting result.

Fig. 2. Using the rainﬂow algorithm to identify battery cycle depths.

either in the dispatch or by the battery controller.

4) Average state of charge: The average SoC level in each

cycle has a highly non-linear but slight effect on the cycle

aging rate [22], [26]. Therefore we do not consider this stress

factor in the proposed model.

C. The Rainﬂow Counting Algorithm

The rainﬂow counting algorithm is used extensively in

materials stress analysis to count cycles and quantify their

cumulative impact. It has also been applied to battery life

assessment [7], [27]. Given a SoC proﬁle with a series of

local extrema (i.e. points where the current direction changed)

s0,s1,..., etc, the rainﬂow method identiﬁes cycles as [28]:

1) Start from the beginning of the proﬁle (as in Fig. 2a).

2) Calculate ∆s1=|s0−s1|,∆s2=|s1−s2|,∆s3=

|s2−s3|.

3) If ∆s2≤∆s1and ∆s2≤∆s3, then a full cycle of

depth ∆s2associated with s1and s2has been identiﬁed.

Remove s1and s2from the proﬁle, and repeat the

identiﬁcation using points s0,s1,s4,s5...

4) If a cycle has not been identiﬁed, shift the identiﬁcation

forward and repeat the identiﬁcation using points s1,s2,

s3,s4...

5) The identiﬁcation is repeated until no more full cycles

can be identiﬁed throughout the remaining proﬁle.

The remainder of the proﬁle is called the rainﬂow residue and

contains only half cycles [29]. A half cycle links each pair of

adjoining local extrema in the rainﬂow residue proﬁle. A half

cycle with decreasing SoC is a discharging half cycle, while

a half cycle with increasing SoC is a charging half cycle. For

example, the SoC proﬁle shown on Fig. 2b has two full cycles

of depth 10% and one full cycle of depth 40%, as well as a

discharging half cycle of depth 50% and charging half cycle

of depth 50%.

The rainﬂow algorithm does not have an analytical math-

ematical expression [30] and cannot be integrated directly

0 10 20 30 40 50 60 70 80 90 100

Cycle depth [%]

0

0.02

0.04

0.06

Cycle life loss [%]

cycle life curve

1-segment

2-segment

4-segment

Fig. 3. Upper-approximation to the cycle depth aging stress function.

within an optimization problem. Nevertheless, several efforts

have been made to optimize battery operation by simplifying

the rainﬂow algorithm. Abdulla et al. [31] and Tran et al. [32]

simplify the cycle depth as the BES energy output within each

control time interval. Koller et al. [33] deﬁne a cycle as the

period between battery charging and discharging transitions.

These model simpliﬁcations enable the incorporation of cycle

depth in the optimization of BES operation, but introduce

additional errors in the degradation model. He et al. [34]

decompose the battery degradation model and optimize BES

market offers iteratively. This method yields more accurate

dispatch results, but is too complicated to be incorporated in

an economic dispatch calculation.

We will use the rainﬂow algorithm as the basis for an ex-

post benchmark method for assessing battery cycle life. In this

model, the total life lost Lfrom a SoC proﬁle is assumed to be

the sum of the life loss from all Inumber of cycles identiﬁed

by the rainﬂow algorithm. If the life loss from a cycle of depth

δis given by a cycle depth stress function Φ(δ)of polynomial

form, we have:

L=PI

i=1 Φ(δi).(1)

III. MAR GI NAL COST OF BATTERY CYCLIN G

In order to participate fully in electricity markets, owners

of batteries must be able to submit offers and bids that

reﬂect their marginal operating cost. As we argued above,

this marginal cost curve should reﬂect the cost of battery

degradation caused by each cycle. In order to keep the model

simple, and to obtain a cost function similar to those used

in existing market dispatch programs, we assume that battery

cycle aging only occurs during the discharge stage of a cycle,

so that a discharging half cycle causes the same cycle aging

as a full cycle of the same depth, while a charging half cycles

causes no cycle aging. This is a reasonable assumption because

the amounts of energy charged and discharged from a battery

are almost identical when assessed on a daily basis.

During a cycle, if the BES is discharged from a starting

SoC eup to an end SoC edn and later charged back (or vice-

versa), the depth of this cycle is the relative SoC difference

(eup −edn)/Erate, where Erate is the energy capacity of the

BES. Let a battery be discharged from a cycle depth δt−1at

time interval t−1. This battery’s cycle depth at time tcan be

calculated from its output power gtover time (assuming the

time interval duration is one hour):

δt=1

ηdisErate gt+δt−1,(2)

4

where ηdis is the BES discharge efﬁciency, and gthas non-

negative values because we ignore charging for now. The

incremental aging resulting from this cycle is Φ(δt), and the

marginal cycle aging can be calculated by taking the derivative

of Φ(δt)with respect to gtand substituting from (2):

∂Φ(δi)

∂gt

=dΦ(δi)

dδi

∂δi

∂gt

=1

ηdisErate

dΦ(δi)

dδi

,(3)

To deﬁne the marginal cost of cycle aging, we prorate the

battery cell replacement cost R($) to the marginal cycle aging,

and construct a piecewise linear upper-approximation function

c. This function consists of Jsegments that evenly divide the

cycle depth range (from 0 to 100%)

c(δt) =

c1if δt∈[0,1

J)

.

.

.

cjif δt∈[j−1

J,j

J)

.

.

.

cJif δt∈[J−1

J,1]

,(4)

where

cj=R

ηdisErate JΦ( j

J)−Φ(j−1

J),(5)

and δtis the cycle depth of the battery at time t. Fig. 3

illustrates the cycle depth stress function and its piecewise

linearization with different numbers of segments.

IV. OPT IM IZ IN G TH E BE S DI SPATC H

Having established a marginal cost function for a BES, we

are now able to optimize how it should be dispatched assuming

that it acts as a price-taker on the basis of perfect forecasts of

the market prices for energy and reserve. A formal description

of this optimization requires the deﬁnitions of the following

parameters:

•T: Number of time intervals in the optimization horizon,

indexed by t

•J: Number of segments in the cycle aging cost function,

indexed by j

•M: Duration of a market dispatch time interval

•S: Sustainability time requirement for reserve provision

•E0: Initial amount of energy stored in the BES

•Eﬁnal: Amount of energy that must be stored at the end

of the optimization horizon

•Emin and Emax: Minimum and maximum energy stored

in the BES

•D,G: Discharging and charging power ratings

•cj: Marginal aging cost of cycle depth segment j

•ej: Maximum amount of energy that can be stored in

cycle depth segment j

•e0

j: Initial amount of energy of cycle depth segment j

•ηch,ηdis: Charge and discharge efﬁciencies

•λe

t,λq

t: Forecasts of the energy and reserve prices at t

This optimization uses the following decision variables:

•pch

t,j ,pdis

t,j : Charge and discharge power for cycle depth

segment jat time t

•et,j : Energy stored in marginal cost segment jat time t

•dt,gt: Charging and discharging power at time t

•dq

t,gq

t: BES baseline charging and discharging power at

time tfor reserve provision

•qt: Reserve capacity provided by the BES at time t

•vt: Operating mode of the BES: if at time tthe BES is

charging then vt= 0; if it is discharging then vt= 1. If

the BES is idling, this variable can take either value. If

some sufﬁcient conditions are satisﬁed, for example the

market clearing prices should not be negative, the binary

variable vtcan be relaxed [35]

•ut: If at time tthe BES provides reserve then ut= 1,

else ut= 0

The objective of this optimization is to maximize the

operating proﬁt Ωof the BES. This proﬁt is deﬁned as the

difference between the revenues from the energy and reserve

markets and the cycle aging cost C

max

p,g,d,qΩ := PT

t=1 Mhλe

t(gt−dt) + λq

tqti−C . (6)

Depending on the discharge power, the depth of discharge

during each time interval extends over one or more segments.

To model the cycle depth in multi-interval operation, we

assign a charge power component pch

t,j and an energy level

et,j to each cycle depth segment, so that we can track the

energy level of each segment independently and identify the

current cycle depth. For example, assume we divide the cycle

depth of a 1 MWh BES into 10 segments of 0.1 MWh. If

a cycle of 10% depth starts with a discharge, as between s2

and s3in Fig. 2a, the BES must have previously undergone a

charge event which stored more than 0.1 MWh according to

the deﬁnition from the rainﬂow method. Because the marginal

cost curve is convex, the BES always discharges from the

cheapest (shallowest) available cycle depth segment towards

the more expensive (deeper) segments. So that the proposed

model provides a close approximation to the rainﬂow cycle

counting algorithm, detailed proofs and a numerical example

are included in the appendix.

The cycle aging cost Cis the sum of the cycle aging costs

associated with each segment over the horizon:

C=PT

t=1 PJ

j=1 Mcjpdis

t,j .(7)

This optimization is subject to the following constraints

dt=PJ

j=1 pch

t,j (8)

gt=PJ

j=1 pdis

t,j (9)

dt≤D(1 −vt)(10)

gt≤Gvt(11)

et,j −et−1,j =M(pch

t,j ηch −pdis

t,j /ηdis )(12)

et,j ≤ej(13)

Emin ≤PJ

j=1 et,j ≤Emax (14)

e1,j =e0

j(15)

PJ

j=1 eT,j ≥Eﬁnal ,(16)

Eq. (8) states that the BES charging power drawn from

the grid is the sum of the charging powers associated with

each cycle depth segment. Eq. (9) is the equivalent for the

5

discharging power. Eqs. (10)–(11) enforce the BES power

rating, with the binary variable vtpreventing simultaneous

charging and discharging [36]. Eq. (12) tracks the evolution

of the energy stored in each cycle depth segment, factoring

in the charging and discharging efﬁciency. Eq. (13) enforces

the upper limit on each segment while Eq. (14) enforces the

minimum and maximum SoC of the BES. Eq. (15) sets the

initial energy level in each cycle depth segment, and the ﬁnal

storage energy level is enforced by Eq. (16).

Because the revenues that a BES collects from providing

reserve capacity are co-optimized with the revenues from the

energy market, it must abide by the requirements that the North

American Electric Reliability Corporation (NERC) imposes on

the provision of reserve by energy storage. In particular, NERC

requires that a BES must have enough energy stored to sustain

its committed reserve capacity and baseline power dispatch

for at least one hour [37]. This requirement is automatically

satisﬁed when market resources are cleared over an hourly

interval, as is the case for the ISO New England day-ahead

market. If the dispatch interval is shorter than one hour (e.g.for

the ﬁve-minute ISO New England real-time market), this one-

hour sustainability requirement has signiﬁcant implications on

the dispatch of a BES because of the interactions between its

power and energy capacities. For example, let us consider a

36 MW BES with 3 MWh of stored energy. If this BES is not

scheduled to provide reserve, it can dispatch up to 36 MW

of generation for the next 5-minute market period. On the

other hand, if it is scheduled to provide 1 MW of reserve,

its generation capacity is also constrained by the one hour

sustainability requirement, therefore it can only provide up

to 2 MW baseline generation for the next 5-minute market

period.

0≤dt−dq

t≤D(1 −ut)(17)

0≤gt−gq

t≤G(1 −ut)(18)

dq

t≤Dut(19)

gq

t≤Gut(20)

gq

t+qt−dq

t≤Gut(21)

qt≥εut(22)

S(gq

t+qt−dq

t)≤PJ

j=1 ej,(23)

Equations (17)–(23), enforce the constraints related to the

provision of reserve by a BES. In particular, Eq. (23) enforces

the one-hour reserve sustainability requirement. Depending on

the requirements of the reserve market, the binary variable ut

and constraints (17)–(23) can be simpliﬁed or relaxed.

The optimization model described above can be used by

the BES owner to design bids and offers or self-schedule

based on price forecasts. The ISO can also incorporate this

model into the market clearing program to better incorporate

the aging characteristic of BES. In this case, the cycle aging

cost function should be included in the welfare maximization

while constraints (8) - (23) should be added to the market

clearing program constraints. A BES owner should include

cycle aging parameters cjand ejin its market offers, and

parameters D,G,Emin,Eﬁnal ,ηch,ηdis for ISO to manage

its SoC and its upper/lower charge limits.

V. CASE STUDY

The proposed model has been tested using data from ISO

New England to demonstrate that it improves the proﬁtability

and longevity of a BES participating in this market. All simu-

lations were carried out in GAMS using CPLEX solver [38],

and the optimization period is 24 hours for all simulations.

A. BES Test Parameters

The BES simulated in this case study has the following

parameters:

•Charging and discharging power rating: 20 MW

•Energy capacity: 12.5 MWh

•Charging and discharging efﬁciency: 95%

•Maximum state of charge: 95%

•Minimum state of charge: 15%

•Battery cycle life: 3000 cycles at at 80% cycle depth

•Battery shelf life: 10 years

•Cell temperature: maintained at 25◦C

•Battery pack replacement cost: 300,000 $/MWh

•Li(NiMnCo)O2-based 18650 lithium-ion battery cells

These cells have a near-quadratic cycle depth stress func-

tion [19]:

Φ(δ) = (5.24E-4)δ2.03 .(24)

Fig. 3 shows this stress function along with several possible

piecewise linearizations. We assume that all battery cells are

identically manufactured, that the battery management system

is ideal, and thus that all battery cells in the BES age at

the same rate. Since the BES dispatch is performed based on

perfectly accurate price forecasts, our results provide an upper

bound of its proﬁtability in this market.

B. Market Data

BES dispatch simulations were performed using zonal price

for Southeast Massachusetts (SE-MASS) region of ISO New

England market price data for 2015 [39] because energy

storage has the highest proﬁt potential in this price zone [40].

Three market scenarios were simulated:

•Day-Ahead Market (DAM): Generations and demands

are settled using hourly day-ahead prices in this energy

market. The DAM does not clear operating reserve ca-

pacities. DAM is a purely ﬁnancial market, and is used in

this study to demonstrate the BES dispatch under stable

energy prices.

•Real-Time Market (RTM) with 1-hour settlement period:

The real-time energy market clears every ﬁve minutes and

generates 5-minute real-time energy and reserve prices.

Generations, demands, and reserves are settled hourly

using an average of these 5-minute prices. The reserve

sustainability requirement is one hour.

•RTM with 5-minute settlement periods: ISO New England

plans to launch the 5-minute subhourly settlement on

March 1, 2017 [41]. The reserve sustainability require-

ment remains one hour.

Fig. 4a compares the energy prices in these different markets

and shows that the 5-minute real-time prices ﬂuctuate the

6

5 10 15 20 25 30 35 40 45

-200

-100

0

100

200

LMP[$/MWh]

[hr]

DA hourly

RT hourly

RT 5-min

(a) Locational marginal price in the day-ahead market (DAM), in an hourly and a 5-minute real-time market (RTM).

0 5 10 15 20 25 30 35 40 45

0

20

40

60

80

100

SoC [%]

[hr]

no cost 1-segment 2-segment 4-segment 16-segment

(b) BES SoC proﬁle in RTM with 5-minute settlement.

0 5 10 15 20 25 30 35 40 45

-1

-0.5

0

0.5

1

Power [normalized]

[hr]

no cost 1-segment 16-segment

(c) BES output power proﬁle in RTM with 5-minute settlement.

Fig. 4. BES dispatch for different cycle aging cost models (ISO New England SE-MASS Zone, Jan 5th & 6th, 2015).

most, while the day-ahead prices are more stable than real-

time prices.

C. Accuracy of the Predictive Aging Model

Fig. 4b and 4c compare the BES dispatches for piecewise-

linear cycle aging cost functions with different numbers of

cycle depth segments. A cost curve with more segments is a

closer approximation of the actual cycle aging function. The

price signal for these examples is the 5-minute RTM price

curve shown in Fig. 4a. Fig. 4b shows the SoC proﬁle while

Fig. 4c shows the corresponding output power proﬁle, where

positive values correspond to discharging periods, and negative

values to charging periods.

The gray curve in Fig. 4 shows the dispatch of the BES

assuming zero operating cost. This is the most aggressive

dispatch, and the BES assigns full power to arbitrage as long

as there are price ﬂuctuations, regardless of the magnitude of

the price differences. Fig. 4c shows that the BES frequently

switches between charging and discharging, and Fig. 4b that

it ramps aggressively. This dispatch maximizes the market

revenue for the BES, but not the maximum lifetime proﬁt,

because the arbitrage decisions ignore the cost of cycle aging.

We will show in Section V-D that this dispatch actually results

in negative proﬁts for all market scenarios.

The yellow curve in Fig. 4 illustrates the dispatch of the

BES when the cycle aging cost curve is approximated by a

single cycle depth segment. In this case, the marginal cost of

cycle aging is constant and, as shown in Fig. 3, it overestimates

the marginal cost of aging over a wide range of cycle depths.

Therefore, this dispatch yields the most conservative arbitrage

response, and the BES remains idle unless price deviations are

very large, as demonstrated in Fig. 4c. Consequently, the BES

collects the smallest market revenues, but the BES never loses

money from market dispatch because the actual cycle aging is

always smaller than the value predicted by the model.

As the number of segments increases, the BES dispatch

becomes more sensitive to the magnitude of the price ﬂuc-

tuations, and a tighter correlation can be observed between

the market price in Fig. 4a and the BES SoC in Fig. 4b. The

red curve shows the dispatch of the BES using a 16-segment

linearization of the cycle aging cost curve. When small price

ﬂuctuation occurs, the BES only dispatches at a fraction of

its power rating, even though it has sufﬁcient energy capacity.

This ensures that the marginal cost of cycle aging does not

exceed the marginal market arbitrage income.

Besides considering the impact of the piecewise lineariza-

tion on the BES dispatch, it is also important to compare the

cycle aging cost used by the predictive model incorporated

in the dispatch calculation with an ex-post calculation of this

cost using the benchmark rainﬂow-counting algorithm. Using

the ˆet,j calculated using the optimal dispatch model (6), we

generate a percentage SoC series:

σt=PJ

j=1 ˆet,j /Erate ,(25)

7

TABLE I

DIS PATCH OF A 20MW / 1 2.5MW H BES IN IS O-NE EN ERG Y MAR KET S (FU LL-Y EA R 2015).

Market DAM RTM with hourly settlement RTM with 5-minute settlement

Cycle aging cost model no cost 1-seg. 16-seg. no cost 1-seg. 16-seg. no cost 1-seg. 16-seg.

Annual market revenue [k$] 138.8 0 21.3 382.5 197.5 212.5 789.3 303.8 372.3

Revenue from reserve [%] No price for reserve in DAM 29.6 74.1 73.6 13.8 34.9 29.8

Annual life loss from cycling [%] 24.4 0 0.3 43.6 1.0 1.1 77.0 2.2 2.6

Annual prorated cycle aging cost [k$] 913.8 0 11.3 1626.3 36.3 38.8 2887.5 81.3 96.3

Annual prorated proﬁt [k$] -775.0 0 10 -1243.8 161.3 173.8 -2101.3 222.5 276.3

Proﬁt from reserve [%] No price for reserve in DAM - 90.7 90.0 - 47.7 40.2

Battery life expectancy [year] 2.9 10.0 9.7 1.9 9.1 9.1 1.1 8.2 8.0

0 5 10 15 20 25 30 35 40

0

10

20

30

40

Number of cost blocks

Relative error [%]

Fig. 5. Difference between the cycle aging cost calculated using the predictive

model and an ex-post calculation using the benchmark rainﬂow method for a

full-year 5-minute RTM dispatch simulation.

This SoC series is fed into the rainﬂow method as described

in Section II-C, and the cycle life loss Lis calculated as in

(1) with the cycle stress function (24). The relative error ǫon

the cycle aging cost is calculated as:

ǫ=|ˆ

C−RL|/(RL),(26)

where ˆ

Cis the cycle aging cost from (7). Fig. 5 shows the

difference between the predicted and ex-post calculations for

the simulations based on the RTM with a 5-minute settlement.

As the number of segments increases to 16, the error becomes

negligible.

D. BES Market Proﬁtability Analysis

Table I summarizes the economics of BES operation under

the three markets described in Section V-B and for three

cycle aging cost models: no operating cost;single segment

cycle aging cost; and 16-segment cycle aging cost. The market

revenue, proﬁt, and battery life expectancy calculations are

based on dispatch simulations using market data spanning all

of 2015. On the ﬁfth row, the life loss due to market dispatch

is calculated using the benchmark cycle life loss model of

Eqs. (1), and (24). In the sixth row, we calculate the cycle

aging cost by prorating the battery cell replacement cost to

the dispatch life loss. In the seventh row, the cost of cycle

aging is subtracted from the market revenue to calculate the

operating proﬁt. In the last row, we estimate the battery cell

life expectancy assuming the BES repeats the same operating

pattern in future years. The life estimation Lexp includes shelf

(calendar) aging and cycle aging

Lexp = (100%)/(∆Lcal + ∆Lcycle),(27)

where ∆Lcal is the 10% annual self life loss as listed in

Section V-A, and ∆Lcycle is the annual life loss due to cycle

aging as shown in the sixth row in Table I.

The 16-segment model generates the largest proﬁt in all

market scenarios. Compared to the 16-segment model, the no

cost model results in a more aggressive operation of the BES,

while the 1-segment model is more conservative. Because the

no-cost model encourages arbitrage in response to all price

differences, it results in a very large negative proﬁt and a very

short battery life expectancy in all market scenarios. The 1-

segment model only arbitrages during large price deviations.

In particular, the BES is never dispatched in the day-ahead

because these market prices are very stable.

The BES achieves the largest proﬁts in the 5-minute RTM

because this market has the largest price ﬂuctuations. The

revenue from reserve is lower in the 5-minute RTM than the

hourly RTM. This result shows that the proposed approach

is able to switch the focus of BES operation from reserve to

arbitrage when market price ﬂuctuations become high. In the

RTM, the BES collects a substantial portion of its proﬁts from

the provision of reserve, especially in the hourly RTM. A BES

is more ﬂexible than generators at providing reserves because

it does not have a minimum stable generation, it can start

immediately, and can remain idle until called. Therefore, the

provision of reserve causes no cycle aging. In the hourly RTM,

the provision reserve represents about 74% of the market

revenue and 90% of the prorated proﬁts for this BES.

VI. CONCLUSION

This paper proposes a method for incorporating the cost

of battery cycle aging in economic dispatch, market clearing

or the development of bids and offers . This approach takes

advantage of the ﬂexibility that a battery can provide to the

power system while ensuring that its operation remains prof-

itable in a market environment. The cycle aging model closely

approximates the actual electrochemical battery cycle aging

mechanism, while being simple enough to be incorporated

into market models such as economic dispatch. Based on

simulations performed using a full year of actual market price

data, we demonstrated the effectiveness and accuracy of the

proposed model. These simulation results show that modeling

battery degradation using the proposed model signiﬁcantly

improves the actual BES proﬁtability and life expectancy.

8

APP EN DI X

In this appendix we prove that the proposed piecewise linear

model of the battery cycle aging cost is a close approxi-

mation of the benchmark rainﬂow-based battery cycle aging

model, and that the accuracy of the model increases with

the number of linearization segments. The proposed model

produces the same aging cost as to the benchmark aging

model for the same battery operation proﬁle with an adequate

number of linearization segments. To prove this, we ﬁrst

explicitly characterize the cycle aging cost result calculated

using the proposed model (Theorem 1). We then show that

this cost approaches the benchmark result when the number

of linearization segments approaches inﬁnity (Theorem 2).

We consider the operation of a battery over the period T=

{1,2,...,T}, the physical battery operation constraints are

(∀t∈ T )

dt≤D(1 −vt)(28)

gt≤Gvt(29)

et−et−1=M(dtηch −gt/ηdis)(30)

We denote d={d1, d2,...,dT}as the set of all battery charge

powers, and g={g1, g2,...,gT}as the set of all discharge

powers. Hence, a set in the form of (d,g)is sufﬁcient to

describe the dispatch of a battery over T. Let P(e0)denote

the set of all feasible battery dispatches that satisfy the physical

battery operation constraints (28)–(30) given an battery initial

energy level e0.

Since we are only interested in characterizing the aging

cost calculated by the proposed model for a certain battery

operation proﬁle, we will regard the battery operation proﬁle

as known variables in this proof. It is easy to see that once

the dispatch proﬁle (d,g)is determined, any battery dispatch

problem that involves the proposed model with a linearization

segment set J={1,2,...,J}, such as the one formulated

in Section IV, can be reduced to the following problem if we

neglect any operation prior to the operation interval T

ˆ

p∈arg min

p∈R+PT

t=1 PJ

j=1 Mcjpdis

t,j ,(31)

s.t.

dt=PJ

j=1 pch

t,j (32)

gt=PJ

j=1 pdis

t,j (33)

et,j −et−1,j =M(pch

t,j ηch −pdis

t,j /ηdis )(34)

0≤et,j ≤ej(35)

PJ

j=1 e0,j =e0(36)

where (d,g)∈ P(e0)is a feasible battery dispatch set,

and p={pch

t,j , pdis

t,j |t∈ T , j ∈ J } denotes a set of the

battery charge and discharge powers for all segments during

all dispatch intervals. Although the objective is still cost

minimization, the problem in (31)–(36) does not optimize

battery dispatch, instead it simulates cycle operations pand

calculates the cycle aging cost with respect to a dispatch proﬁle

(d,g). Hence, the evaluation criteria to this problem is its

accuracy compared to the benchmark aging cost model.

Let c={cj|j∈ J } denote a set of piecewise linear battery

aging cost segments derived as in equation (4), so that cjis

associated with the cycle depth range [(j−1)/J, j/J )and

J=|J | is the number of segments. We say that a battery has

aconvex aging cost curve (i.e., non-decreasing marginal cycle

aging cost) if a shallower cycle depth segment (i.e., indexed

with smaller j) is associated with a cheaper marginal aging

cost such that c1≤c2≤...≤cJ, and let Cdenote the set of

all convex battery aging cost linearizations.

Theorem 1. Let ˆ

p={ˆpch

t,j ,ˆpdis

t,j |t∈ T , j ∈ J } and

ˆpch

t,j = min dt−Pj−1

ζ=1 ˆpch

t,ζ ,(ej−ˆet−1,j )/(ηchM)(37)

ˆpdis

t,j = min gt−Pj−1

ζ=1 ˆpdis

t,ζ , ηdis ˆet−1,j /M(38)

ˆe0,j = min ej,max(0, e0−Pj−1

ζ=1 ˆe0,ζ )(39)

ˆet,j = ˆet−1,j +M(pch

t,j ηch −pdis

t,j /ηdis ).(40)

Then ˆ

pis a minimizer of the problem (31)–(36) as long as

the battery dispatch is feasible and the cycle aging cost curve

is convex, i.e.,

ˆ

p∈arg min

p∈R+(31)–(36) ,

∀(d,g)∈ P(e0),e0∈[Emin, Emax],c∈ C.(41)

Proof. Equations (37)–(40) describe a battery operating policy

over the proposed piecewise linear model. To calculate this

policy, we start from (39) which calculates the initial segment

energy level from the battery initial SoC e0. (39) is evaluated

in the order of j= 0,1,2,3,...,J such as (note that

P0

ζ=1 ˆe0,ζ = 0)

ˆe0,1= min e1,max(0, e0)

ˆe0,2= min e2,max(0, e0−ˆe0,1)

ˆe0,3= min e3,max(0, e0−ˆe0,1−ˆe0,2)

. . . ,

so that energy in e0is ﬁrst assigned to ˆe0,1which corresponds

to the shallowest cycle depth range [0,1/J], the remaining

energy is then assigned to the second shallowest segment ˆe0,2,

and the procedure repeats until all the energy in e0has been

assigned.

We then calculate all battery segment charge power at t= 1

in the order of j= 0,1,2,3,...,J as

ˆpch

1,1= min dt,(e1−ˆe0,1)/(ηchM)

ˆpch

1,2= min dt−ˆpch

1,1,(e2−ˆe0,2)/(ηchM)

ˆpch

1,3= min dt−ˆpch

1,1−ˆpch

1,2,(e3−ˆe0,3)/(ηchM)

. . . ,

and the procedure is similar for segment discharge power

ˆpdis

1,j . We calculate the segment energy level ˆe1,j at the end

of t= 1 using (40), and move the calculation to t= 2. This

procedure repeats until all values in ˆ

phave been calculated.

Therefore in this policy, the battery always prioritizes energy

in shallower segments for charge or discharge dispatch. For

example, if the battery is required to discharge a certain

amount of energy, it will ﬁrst dispatch segment 1, then the

9

remaining discharge requirement (if any) is dispatched from

segment 2, then segment 3, etc.

Given this policy, this theorem stands if the battery cycle

aging cost curve cis convex, i.e., c∈ C, which means a

shallower segment is associated with a cheaper marginal oper-

ating cost. Since the objective function (31) is to minimize the

battery aging cost and the problem involves no market price,

then a minimizer for the problem (31)–(36) will give a cheaper

segment a higher operation priority, which is equivalent to the

policy described in (37)–(40).

Following Theorem 1, the cycle aging cost calculated by the

proposed piecewise linear model Cpwl for a battery dispatch

proﬁle (d,g)can be written as a function of this proﬁle and

the linearization cost set as

Cpwl(c,d,g) = PT

t=1 PJ

j=1 Mcjˆpdis

t,j ,(42)

where ˆ

pis calculated as in (37)–(40).

Let Φ(δ)be a convex battery cycle aging stress function, and

c(Φ) be a set of piecewise linearizations of Φ(δ)determined

using the method described in equation (4). Let |c(Φ)|denote

the cardinality of c(Φ), i.e. the number of segments in this

piecewise linearization.

For a feasible battery dispatch proﬁle (d,g)∈ P(e0), let

∆be the set of all full cycles identiﬁed from this operation

proﬁle using the rainﬂow method, ∆dis for all discharge half

cycles, and ∆ch for all charge half cycles. The benchmark

cycle aging cost Cben resulting from (d,g)can be written

as a function of the proﬁle and the cycle aging function Φ

(recall that a full cycle has symmetric depths for charge and

discharge)

Cben(Φ,d,g) = RP|∆|

i=1 Φ(δi) + RP|∆dis|

i=1 Φ(δdis

i).(43)

Theorem 2. When the number of linearization segments

approaches inﬁnity, the proposed piecewise linear cost model

yields the same result as the benchmark rainﬂow-based cost

model:

lim

|c(Φ)|→∞ Cpwlc(Φ),d,g=Cben Φ,d,g.(44)

Proof. First we rewrite equation (42) as

PJ

j=1 cjPT

t=1 Mˆpdis

t,j =PJ

j=1 cjΘj,(45)

where Θj=PT

t=1 Mˆpdis

t,j is the total amount of energy

discharged at a cycle depth range between (j−1)/J and j/J.

Once the number of segments |c(Φ)|=Japproaches inﬁnity,

we can rewrite Θjinto a function Θ(δ)indicating the energy

discharged at a speciﬁc cycle depth δ, where δ∈[0 1]. With an

inﬁnite number of segments, we substitute (3) in and rewrite

the cycle aging function in (42) in a continuous form

Cpwl(Φ,d,g) = Z1

0

R

ηdisErate Θ(δ)dΦ(δ)

dδ dδ . (46)

We deﬁne a new function Ndis

T(δ)the number of discharge

cycles of depths equal or greater than δduring the operation

period from t= 0 to t=T, accounting all discharge half

cycles and the discharge stage of all full cycles. Ndis

T(δ)can be

calculated by normalizing Θ(δ)with the discharge efﬁciency

and the energy rating of the battery

Ndis

T(δ) = 1

ηdisErate Θ(δ),(47)

recall that Θ(δ)is the amount of energy discharged from the

cycle depth δ. This relationship is proved in Lemma 1 after

this theorem.

Now the proposed cost function becomes

Cpwl(Φ,d,g) = RZ1

0

dΦ(δ)

dδ Ndis

T(δ)dδ , (48)

which is a standard formulation for calculating rainﬂow fatigue

damage [42], and the function Ndis

T(δ)is an alternative way

of representing a rainﬂow cycle counting result. We substitute

(51) from Lemma 1 into (48)

Cpwl(Φ,d,g)

=RZ1

0

dΦ(δ)

dδ |∆|

X

i=1

1[δ≤δi]+

|∆dis|

X

i=1

1[δ≤δdis

i]!dδ

=R

|∆|

X

i=1 Z1

0

dΦ(δ)

dδ 1[δ≤δi]dδ +R

|∆dis|

X

i=1 Z1

0

dΦ(δ)

dδ 1[δ≤δdis

i]dδ

=R

|∆|

X

i=1

Φ(δi) + R

|∆dis|

X

i=1

Φ(δdis

i)

=Cben(Φ,d,g),(49)

then it is trivial to see that this theorem stands if the proposed

model yields the same counting result Ndis

T(δ)as the rainﬂow

algorithm. This relationship is proved in Lemma 1.

Lemma 1. We assume that the proposed model has an inﬁnite

number of segments, then Ndis

T(δ), as deﬁned in Theorem 2,

is the number of discharge cycles of depths equal or greater

than δduring the operation period from t= 0 to t=T,

accounting all discharge half cycles and the discharge stage

of all full cycles, hence

Ndis

T(δ) = Θ(δ)/(ηdisErate )(50)

=P|∆|

i=1 1[δ≤δi]+P|∆dis|

i=1 1[δ≤δdis

i],(51)

where 1[x]has a value of one if xis true, and zero otherwise.

Proof. (50) deﬁnes Ndis

T(δ)as the number fo times that energy

is discharged from the cycle depth δ, while (51) means the

number of cycles with depths at least δ. Therefore in this

lemma we prove that these two deﬁnitions are equivalent,

hence the proposed model has the same cycle counting result

as the rainﬂow method.

Let Ndis

t(δ)be the number of times energy is discharged

from the depth δduring the operation period [0, t], accounting

all discharge half cycles and the discharge stage of all full cy-

cles. Similarly, deﬁne Nch

t(δ)accounting all charge half cycles

and the charge stage of all full cycles. Because we assume

charge dispatches cause no aging cost, we can alternatively

model battery initial energy level e0as an empty battery being

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0

10

20

30

40

50

60

SoC [%]

[h]

δ1 = 10%

δ3 = 10%

remaining

profile...

δ2 = 40%

initial SoC

δdis = 50%

Fig. 6. Cycle counting example.

charged to e0at the beginning of operation (such as in Fig. 6),

hence at t= 0 we have

Nch

0(δ) = (1δ≤e0

0δ > e0

, Ndis

0(δ) = 0 .(52)

Now assume at time t1the battery is switched from charging

to discharging, and eventually resulted in a cycle of depth x

that ends at t2, regardless whether it is a half cycle or a full

cycle. We also assume that there is no other cycles occuring

from t1tp t2, since in the rainﬂow method The battery must

have been previously charged at least δdepth worth of energy

since we now assume the battery starts from empty. Therefore

according to Theorem 1, segments in the range [0, x]must be

full at t1, hence

Nch

t1(δ)−Ndis

t1(δ) = 1 ∀δ≤x , (53)

which is a sufﬁcient condition for all discharge energy in this

cycle being dispatched from segments in the depth range [0, x],

according to Theorem 1. After performing this cycle, all and

only segments within the range [0, x]are discharged one more

time, in other words, all and only cycle depths in the range

[0, x]have one more count at end of this cycle t2compared

to t1when the discharge begins, hence

Ndis

t2(δ)−Ndis

t1(δ) = 1[δ≤x].(54)

Therefore the proposed model has the same counting result

as to the rainﬂow method for any cycles, which proves this

lemma.

A. Numerical example

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0

10

20

30

40

50

60

SoC [%]

[h]

s2

s3

s4

s5

s6

s7

s1

s0 s8

Fig. 7. An example of SoC proﬁle.

We include a step-by-step example to illustrate how the

proposed model is a close approximation of the benchmark

rainﬂow cost model using the battery operation proﬁle shown

in Fig. 7. To simplify this example, we assume a perfect

TABLE II

BATTE RY OPER ATIO N EXAM PL E.

t SoC energy segments discharge power cost

[et] [pdis

t]Ct

- - →deeper depth → → deeper depth →-

0 60 1,1,1,1,1,1,0,0,0,0 0,0,0,0,0,0,0,0,0,0 0

1 10 0,0,0,0,0,1,0,0,0,0 1,1,1,1,1,0,0,0,0,0 25

2 20 1,0,0,0,0,1,0,0,0,0 1,1,1,1,1,0,0,0,0,0 0

3 30 1,1,0,0,0,1,0,0,0,0 0,0,0,0,0,0,0,0,0,0 0

4 20 0,1,0,0,0,1,0,0,0,0 1,0,0,0,0,0,0,0,0,0 1

5 30 1,1,0,0,0,1,0,0,0,0 0,0,0,0,0,0,0,0,0,0 0

6 40 1,1,1,0,0,1,0,0,0,0 0,0,0,0,0,0,0,0,0,0 0

7 50 1,1,1,1,0,1,0,0,0,0 0,0,0,0,0,0,0,0,0,0 0

8 40 0,1,1,1,0,1,0,0,0,0 1,0,0,0,0,0,0,0,0,0 1

9 30 0,0,1,1,0,1,0,0,0,0 0,1,0,0,0,0,0,0,0,0 3

10 40 1,0,1,1,0,1,0,0,0,0 0,0,0,0,0,0,0,0,0,0 0

11 30 0,0,1,1,0,1,0,0,0,0 1,0,0,0,0,0,0,0,0,0 1

12 20 0,0,0,1,0,1,0,0,0,0 0,0,1,0,0,0,0,0,0,0 5

13 10 0,0,0,0,0,1,0,0,0,0 0,0,0,1,0,0,0,0,0,0 7

14 60 1,1,1,1,1,1,0,0,0,0 0,0,0,0,0,0,0,0,0,0 0

all - - - 43

efﬁciency of 1and that the cycle aging cost function is 100δ2.

We consider 10 linearization segments, with each segment

representing a 10% cycle depth range. The proposed model

therefore has the following cycle aging cost curve

c={1,3,5,7,9,11,13,15,17,19}.(55)

According to the rainﬂow method demostrated in Fig. 2 , this

example proﬁle has the following cycle counting results

•Two full cycles of depth 10%, each costs 1

•One full cycle of depth 40% that costs 16

•One discharge half cycle of depth 50% that costs 25

•One charge half cycle that costs zero,

hence the total aging cost identiﬁed by the benchmark

rainﬂow-based model is 43.

We implement this operation proﬁle using the policy in The-

orem 1 and record the marginal cost during each time interval.

The results are shown in Table II. In this table, the ﬁrst two

columns are the time step and SoC. The third column shows

the energy level of each linearization segment represented in

a vector from et.etis a 10 ×1vector, and its energy level

segments are sorted from shallower to deeper depths. Segment

energy levels are normalized so that one means the segment is

full, and zero means the segment is empty. The fourth column

shows how much energy is discharged from each segment

during a time interval, represented by a discharge power vector

pdis

tand is calculated as (the discharge efﬁciency is 1)

pdis

t= [et−1−et]+.(56)

The last column shows the operating cost that arises from each

time interval, which is calculated as

Ct=cpdis

t.(57)

11

This example proﬁle results in the same cost of 43 in both

the proposed model and the benchmark model, as proved in

Theorem 2.

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12

Bolun Xu (S’14) received B.S. degrees in Electrical and Computer Engineer-

ing from Shanghai Jiaotong University, Shanghai, China in 2011, and the M.Sc

degree in Electrical Engineering from Swiss Federal Institute of Technology,

Zurich, Switzerland in 2014.

He is currently pursuing the Ph.D. degree in Electrical Engineering at the

University of Washington, Seattle, WA, USA. His research interests include

energy storage, power system operations, and power system economics.

Jinye Zhao (M’11) received the B.S. degree from East China Normal

University, Shanghai, China, in 2002 and the M.S. degree in mathematics

from National University of Singapore in 2004. She received the M.E. degree

in operations research and statistics and the Ph.D. degree in mathematics from

Rensselaer Polytechnic Institute, Troy, NY, in 2007.

She is a lead analyst at ISO New England, Holyoke, MA. Her main

interests are game theory, mathematical programming, and electricity market

modeling.

Tongxin Zheng (SM’08) received the B.S. degree in electrical engineering

from North China University of Electric Power, Baoding, China, in 1993,

the M.S. degree in electrical engineering from Tsinghua University, Beijing,

China, in 1996, and the Ph.D. degree in electrical engineering from Clemson

University, Clemson, SC, USA, in 1999.

Currently, he is a Technical Manager with the ISO New England, Holyoke,

MA, USA. His main interests are power system optimization and electricity

market design.

Eugene Litvinov (SM’06-F’13) received the B.S. and M.S. degrees from

the Technical University, Kiev, Ukraine, and the Ph.D. degree from Urals

Polytechnic Institute, Sverdlovsk, Russia.

Currently, he is the Chief Technologist at the ISO New England, Holyoke,

MA. His main interests include power system market-clearing models, system

security, computer applications in power systems, and information technology.

Daniel S. Kirschen (M’86-SM’91-F’07) received his electrical and mechan-

ical engineering degree from the Universite Libre de Bruxelles, Brussels,

Belgium, in 1979 and his M.S. and Ph.D. degrees from the University of

Wisconsin, Madison, WI, USA, in 1980, and 1985, respectively.

He is currently the Donald W. and Ruth Mary Close Professor of Electrical

Engineering at the University of Washington, Seattle, WA, USA. His research

interests include smart grids, the integration of renewable energy sources in

the grid, power system economics, and power system security.