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Optimal bidding strategy of battery storage in power markets considering performance
based regulation and battery cycle life
He, Guannan; Chen, Qixin; Kang, Chongqing; Pinson, Pierre; Xia, Qing
Published in:
IEEE Transactions on Smart Grid
Link to article, DOI:
10.1109/TSG.2015.2424314
Publication date:
2016
Document Version
Peer reviewed version
Link back to DTU Orbit
Citation (APA):
He, G., Chen, Q., Kang, C., Pinson, P., & Xia, Q. (2016). Optimal bidding strategy of battery storage in power
markets considering performance based regulation and battery cycle life. IEEE Transactions on Smart Grid,
7(5), 2359 - 2367. https://doi.org/10.1109/TSG.2015.2424314
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
IEEE TRANSACTIONS ON SMART GRID 1
Optimal Bidding Strategy of Battery Storage in
Power Markets Considering Performance-Based
Regulation and Battery Cycle Life
Guannan He, Qixin Chen, Member, IEEE, Chongqing Kang, Senior Member, IEEE,
Pierre Pinson, Senior Member, IEEE, and Qing Xia, Senior Member, IEEE
Abstract—Large-scale battery storage will become an essential
part of the future smart grid. This paper investigates the optimal
bidding strategy for battery storage in power markets. Battery
storage could increase its profitability by providing fast regulation
service under a performance-based regulation mechanism, which
better exploits a battery’s fast ramping capability. However,
battery life might be decreased by frequent charge–discharge
cycling, especially when providing fast regulation service. It is
profitable for battery storage to extend its service life by limiting
its operational strategy to some degree. Thus, we incorporate
a battery cycle life model into a profit maximization model to
determine the optimal bids in day-ahead energy, spinning reserve,
and regulation markets. Then a decomposed online calculation
method to compute cycle life under different operational strate-
gies is proposed to reduce the complexity of the model. This
novel bidding model would help investor-owned battery stor-
ages better decide their bidding and operational schedules and
investors to estimate the battery storage’s economic viability.
The validity of the proposed model is proven by case study
results.
Index Terms—Battery cycle life, battery storage, optimal
bidding strategy, performance-based regulation (PBR), power
markets.
NOMENCLATURE
Indices and Sets
t Time index.
s Scenario index.
k Half cycle index.
H Set of time.
S Set of scenarios.
C Set of half cycles.
e Superscript for energy market.
res Superscript for spinning reserve market.
reg Superscript for regulation market.
Manuscript received January 4, 2015; revised March 5, 2015 and
April 7, 2015; accepted April 11, 2015. This work was supported by
the National Natural Science Foundation of China under Grant 51107059,
Grant 51325702, and Grant 5136113570402. Paper no. TSG-00004-2015.
G. He, Q. Chen, C. Kang, and Q. Xia are with the State Key Laboratory of
Power Systems, Department of Electrical Engineering, Tsinghua University,
Beijing 100084, China (e-mail: qxchen@mail.tsinghua.edu.cn;
cqkang@tsinghua.edu.cn).
P. Pinson is with the Department of Electrical Engineering, Technical
University of Denmark, Lyngby, Denmark.
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TSG.2015.2424314
cap Superscript for regulation capability.
perf Superscript for regulation performance.
day Superscript for daily variables.
Parameters and Constants
R
mileage
Mileage ratio for regulation resource.
P
max
Rated power capacity of battery storage, MW.
E
max
Rated energy capacity of battery storage, MWh.
c
m
Daily maintenance cost per unit power capacity,
$/MW.
c
op
Operational cost per unit energy, $/MWh.
P
(·)
s,t
Market price at time t in scenario s,$/MWhor
$/MW.
γ
res
Probability of spinning reserve deployment.
α Self-discharge rate of battery storage.
η
0
Charging/discharging efficiency of battery.
T
float
Float life of battery storage, year.
Variables
Cap
(·)
t
Capacity bid in market at time t,MW.
Pay
reg,(·)
(·),(·)
Payment for regulation service, $.
T
service
Service life of battery storage, year.
T
cycle
Cycle life of battery storage, year.
Cost
op
t
Operational cost of battery storage at time t,$.
Cost
m
Daily maintenance cost of battery storage, $.
d Depth of discharge (DOD).
N
fail
d
Maximum number of charge–discharge cycles at
a DOD of d before the battery’s failure.
n
d
Number of cycles at a DOD of d.
E
t
Battery’s energy stored level at time t, MWh.
E
t
Battery’s energy level change at time t, MWh.
g
res
t
Spinning reserve deployment at time t,MW.
I. I
NTRODUCTION
B
ATTERY storage will play a critical role along the
entire value chain of the future smart grid [1]. The
largest obstacle that prevents large-scale battery storage from
commercial operation is the relatively high-investment cost
and revenue risk. Thus, how to explore the best cost-
benefit results and more precisely evaluate the economics
of battery storage in power markets have become significant
issues.
1949-3053
c
2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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2 IEEE TRANSACTIONS ON SMART GRID
One major application for battery storage is to provide reg-
ulation service. Compared with traditional generators, battery
storage could ramp much more rapidly and respond faster with
better performance. However, for most of the existing reg-
ulation markets, regulation resources are only compensated
based on the committed capacity, with no regard for its actual
performance. Therefore, battery storages’ potential to pro-
vide flexibility is not fully exploited, and the revenue from
regulation markets might be underestimated.
Federal Energy Regulatory Commission (FERC)
Order 755 [2], issued on October 20, 2011, started to
address this problem. It requires market operators to develop
pay-for-performance protocols and tariffs, which compensate
regulation providers according to their actual performance
to remedy undue discrimination [3], [4]. This order has
already been implemented in most independent system
operator/regional transmission organization under FERC. For
example, in PJM, a new performance-based regulation (PBR)
mechanism is instituted in which regulation service providers
receive a two-part payment consisting of a capability payment
and a performance payment. A new fast regulation signal
is introduced that brings approximately three times the
performance revenue of a traditional signal for eligible
resources.
A few papers have evaluated the economics of energy stor-
age considering their participation in power markets. Some of
them only consider participation in energy markets, leaving
out the possible revenues from providing ancillary services.
Though the others well formulate energy storage’s participa-
tion in both energy and ancillary service markets, the PBR
mechanism is not considered. The economic viability and
potential of energy storages’ arbitraging in power markets
is researched in [5]. Storages’ self-scheduling in energy and
ancillary service markets is researched in [6]–[10], some of
which also consider joint operation with wind farms.
Another problem missed by the literature above is that
battery storages’ frequent charge–discharge cycling incurs an
extra cost as it accelerates depreciation. This extra cost of
depreciation might be significant when the regulation signal
is extraordinarily fast. Thus, it is essential to introduce for-
mulations accounting for battery life into an optimal bidding
model in joint energy and ancillary service markets.
Some papers have studied the relations between the bat-
tery’s life and its operation including providing regulation
services. However, none of them introduce formulations
accounting for battery life into the battery’s optimal bid-
ding model. Thus, the battery life’s impact on the battery’s
economic viability has not been totally revealed. A few
papers [11]–[21] have provided some data on different bat-
teries’ cycle lives at different DOD. In [11], the data are
used to calculate the cost per cycle of primary frequency
regulation for the purpose of selecting the cheapest bat-
tery technology. Reference [15] presents a short-term battery
storage scheduling model in conjunction with traditional gen-
erators considering battery cycle life. Reference [16] applies
the battery life model to better manage an energy storage sys-
tem in microgrids. In [20], battery lifetime is calculated to
assess the battery and ultracapacitor ratings in electric vehicles.
Reference [22] calculates a battery’s capacity reduction from
its cycles. Some papers derive formulations on the relation
between battery cycle life and DOD using different fitting
techniques. Reference [20] uses a fourth-order polynomial
function, whereas [21] and [22] used an exponential function.
Another widely used function is the power function [14]–[16],
which also fits the data in [12] and [13] very well.
Regardless of the specific cycle life models, a rain-
flow counting algorithm is commonly used to calculate
a battery’s lifetime, as referenced in [13], [14], [22
], and [23].
Most papers above apply this algorithm for static evaluation
with fixed operating strategies. However, because a battery’s
cycle life is affected by its cycling strategy, it is necessary
to incorporate cycle life calculation into dynamic strategy
optimization. Moreover, as the calculation algorithm of cycles
includes some discrete logical judgment and cannot be ana-
lytically expressed with respect to the operation strategies, it
is difficult to embed the calculation algorithm into an analyt-
ical programming model that can be solved by a commercial
optimization solver.
To solve the problems addressed above, this paper proposes
a model that decides the optimal joint bidding strategy of
battery storage in joint day-ahead energy, reserve, and reg-
ulation markets with multi-scenario settings to consider price
uncertainty. The PBR mechanism is included in this model.
A battery cycle life model is embedded into the optimization
scheme to calculate the cycle life under different operational
strategies. Additionally, a decomposition method is introduced
to simplify the battery life calculation with little loss of accu-
racy while largely reducing the complexity of modeling and
computation. By applying the proposed model, investors could
obtain more accurate and realistic economic evaluation results
of battery storage, and storage owners could make better day-
ahead bidding decisions. Case study results prove a significant
impact through considering the PBR mechanism and cycle life
on a battery’s bidding strategy and overall profits.
This paper is organized as follows. Section II introduces the
market mechanisms with PBR settings. Section III presents
the battery life model and calculation method. Section IV for-
mulates the optimal bidding strategy decision-making model.
Case study results are discussed in Section V. Section VI draws
the conclusion.
II. M
ARKET FRAMEWORK
A. Basic Market Mechanism
Without loss of generality, common settings of power
market mechanisms are implemented in this paper, which
include day-ahead energy, spinning reserve, and regulation
markets [7], [9].
We assume that battery storage simultaneously bids in the
three day-ahead markets, treated as a normal market par-
ticipant like traditional generators. Considering its relatively
small capacity, battery storage is reasonably assumed to be
price-taker. Multi-scenario settings are established to consider
price uncertainty. As a price-taker, the storage has to make an
optimal allocation of its resources in the three markets based
on price prediction to maximize the expected total profit while
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HE et al.: OPTIMAL BIDDING STRATEGY OF BATTERY STORAGE IN POWER MARKETS 3
Fig. 1. 3-h sample profiles of RegA and RegD.
ensuring all operational constraints are satisfied. The bidding
strategy has to be decided every day before the closure of the
day-ahead market for the next day.
B. Performance-Based Regulation
The PBR mechanism is included in this model, typically ref-
erenced from the PJM [24]. This mechanism provides incen-
tives for high-performing regulation resources and reduces the
overall regulation capacity requirement in PJM [3].
Under PBR, a dynamic regulation signal (RegD) is added
as a supplement to the traditional regulation signal (RegA).
Derived from the area control error with a low-pass filter,
RegA is used for resources with a limited ramp rate, whereas
RegD, derived with a high-pass filter, results in much faster
movement, as shown in Fig. 1. Regulation resources receive
a two-part payment that consists of capability payment and
performance payment. The system operator calculates the two
payments based on the regulation market capability clearing
price P
reg,cap
and the regulation market performance clearing
price P
reg,perf
, respectively, as in the following [25]:
Pay
reg,cap
= P
reg,cap
Cap
reg
Score
perf
(1)
Pay
reg,perf
= P
reg,perf
Cap
reg
R
mileage
Score
perf
. (2)
Cap
reg
is the hourly committed regulation capacity. The
performance score Score
perf
reflects the accuracy of a reg-
ulation resource’s response to PJM’s regulation signal [26].
The mileage ratio R
mileage
is the ratio between the requested
mileage (absolute summation of movement) of one signal to
that of RegA. Because RegD’s mileage is approximately three
times that of RegA, the mileage ratio of RegD is approximately
three times larger as well. Thus, qualified resources following
RegD would earn three times the performance revenue.
Most battery storages are capable of ramping from zero
power output to full capacity within seconds or even millisec-
onds, such as the vanadium redox flow battery, and thus could
provide fast regulation service following RegD. RegD’s other
favorable characteristic for battery storage is that it requires
net zero energy over a 15-min time period [4], which reduces
the amount of obligated reserved energy.
III. B
ATTERY LIFE MODEL AND CALCULATION METHOD
In this section, a battery life model is introduced and a rea-
sonably simplified online calculation method is proposed to
compute a battery’s service life based on its cycling strategy.
Fig. 2. Curves of cycle life versus DOD with different k
P
values.
A. Life Model
A battery’s service life (calendar life) T
service
is deter-
mined by its cycle life T
cycle
or float life T
float
, whichever
is shorter [19].
The battery’s cycle life is related to the cycling aging and
dependent on its cycling behavior. Frequent and deep cycles
accelerate cyclic aging and reduce the cycle life. It can be
derived as
T
cycle
=
N
fail
d
W · n
day
d
(3)
where N
fail
d
is the maximum number of charge–discharge
cycles at a specific DOD before the battery’s failure, n
day
d
is the
number of daily cycles at the DOD, and W denotes the aver-
age number of operating days in one year for battery storage,
considering 20% time allotted for necessary maintenance.
The battery’s float life corresponds to the normal corrosion
processes. It is independent of its cycling behavior, and thus
regarded as a constant. Temperature’s impact on battery life
is assumed to be under consideration and beyond the scope of
this paper.
For any type of battery, N
fail
d
is a function of DOD (%), as
N
fail
d
= f (d). (4)
f (d) can be obtained by a fitting technique using detailed
experimental data provided by manufacturers. The cycle life
loss Loss
cycle
for n
d
cycles at d DOD is calculated as
Loss
cycle
(%) =
n
d
f (d)
× 100%. (5)
In this paper, f (d) is adopted to be a power function for its
good applicability in different kinds of batteries, as
f (d) = N
fail
100
· d
−k
P
(6)
where k
P
is a constant ranging from 0.8 to 2.1 [12]–[16] and
N
fail
100
is the number of cycles to failure at 100% DOD.
Fig. 2 shows the curves of cycle life versus DOD with dif-
ferent k
P
, assuming the N
fail
100
to be 10 000. In practice, k
P
can
be obtained by a fitting technique using detailed experimental
data provided by battery manufacturers.
By keeping the loss of cycle life a constant, the equiva-
lent 100%-DOD cycle number n
eq
100
of n
d
cycles at d DOD is
derived as
n
eq
100
= n
d
· d
k
P
. (7)
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4 IEEE TRANSACTIONS ON SMART GRID
A larger k
P
means fewer equivalent 100%-DOD cycles for
n
d
cycles at d DOD, as d is always no more than 100%.
Taking a vanadium redox flow battery as an example, the
cell stack’s float life T
float
can be expected to last more than
ten years [27], and its number of 100%-DOD cycles to failure
N
fail
100
usually exceeds 10 000 [1]. After replacing some com-
ponents such as the cell stack and pumps, the vanadium redox
flow battery storage station can operate another T
service
years,
totaling 2T
service
years.
B. Battery Cycle Life Calculation Method
For a given bidding strategy and regulation signal, there
exists a corresponding energy changing curve of battery
storage. The first step of cycle life calculation is to iden-
tify each half cycle by picking out every local extreme point
on the curve with corresponding energy level E
m
k
,asin
Fig. 3.
The battery storage completes a half cycle between every
two adjacent local extreme points. E
m
k
is just the energy level
at the end of the kth half cycle. Then, the DOD of every half
cycle d
half
k
is calculated as
d
half
k
=
E
m
k
− E
m
k−1
E
max
. (8)
According to (3) and (7), a battery’s daily equiva-
lent 100%-DOD cycle number and cycle life are derived,
respectively
n
eq,day
100
=
k∈C
0.5 ·
d
half
k
k
P
(9)
T
cycle
=
N
fail
100
W · n
eq,day
100
. (10)
This DOD calculating approach is similar to the rainflow
counting algorithm [23]. However, as the decision variables
would affect the local extreme points on the energy curve and
then the identification of the half cycle, extreme point pick-
ing should be conducted for each feasible bidding strategy
to calculate the battery cycle life. The relation between the
decision variables and the local extreme points can be only
analytically expressed in a very complicated form, so it is dif-
ficult to embed the identification of the half cycle into a model
that can be solved by a commercial optimization solver. Thus,
a decomposition calculation method is proposed to separate
the decision variables from the identification of the half cycle,
while precisely approximating the cycle life.
For a battery storage participating in joint energy, spinning
reserve, and regulation markets, its total energy changing pro-
cess, as shown in Fig. 3, can be decomposed into two parts,
as shown in Fig. 4(a) and (b). The time range in Fig. 4(a) is
24 h, whereas it is 1 h in Fig. 4(b).
The first part is related to the bids in markets in each time
period, typically 1 h, denoted by E
t
, as shown in Fig. 4(a).
The causes of this part of the energy change include charging
and discharging in the energy market, reserve deployment, and
energy loss in providing regulation service.
The other part of energy changing is caused by regula-
tion up and down, according to the RegD with 4-s resolution.
Fig. 3. Energy curve of battery storage’s operation.
Fig. 4. Decomposition of the energy changing process. (a) Energy change
between hours. (b) Intra-hour energy change.
It is reasonable to simulate the real up-coming day’s regu-
lation signal based on the historical regulation signal when
making day-ahead decisions. The simulated signal serves as
a parameter in optimization, and its local extreme points could
be picked out in advance, as shown in Fig. 4(b). RegD
min
k
and
RegD
max
k
denote the energy levels of the kth local minimum
and maximum points on the energy curve of RegD signal,
respectively. t
min
k
and t
max
k
denote the corresponding time of
RegD
min
k
and RegD
max
k
.
When the capacity bid in the regulation market is much
larger than that in the energy and spinning reserve markets, the
second part of the energy change is usually larger than the first
part, as is the corresponding impact on cycle life calculation.
Then, for most adjacent local extreme points in the same hour
that satisfy t−1 < t
min
k
< t
max
k
< t, the DOD of corresponding
half cycles can be simplified as
d
up
k
=
E
t
t
max
k
− t
min
k
h + Cap
reg
t
RegD
max
k
− RegD
min
k
E
max
(11)
d
down
k
=
−E
t
t
max
k
− t
min
k
h + Cap
reg
t
RegD
max
k
− RegD
min
k+1
E
max
(12)
where d
up
k
denotes the DOD of the kth regulation-up move-
ment; d
down
k
denotes the DOD of the kth regulation-down
movement; Cap
reg
t
denotes the capacity bid in the regula-
tion market at time t; h denotes the time interval, which is
equal to1hinthispaper. In (11) and (12), the two parts
of the energy change are arrayed in order. For the remain-
ing adjacent local extreme points at different hours, Cap
reg
t
and E
t
should be adjusted to be hourly weighted aver-
ages. Then, the battery’s daily equivalent 100%-DOD cycle
