Battery Energy Storage Capacity Fading
and Control Strategies for
Deterministic and Stochastic Power Profiles
Stavros Karagiannopoulos∗† , Alexandros Rigas†‡ , Nikos Hatziargyriou‡ , Gabriela Hug∗ , Alexandre Oudalov†
∗
EEH - Power Systems Laboratory, ETH Zurich, Physikstrasse 3, 8092 Zurich, Switzerland
E-mail: {karagiannopoulos, hug}@eeh.ee.ethz.ch
† ABB Corporate Research, Segelhofstrasse 1K, Baden-Dättwil, Switzerland
Email: [email protected]
‡ School of Electrical and Computer Engineering, National Technical University of Athens, 15780, Zografou, Greece
E-mail: {[email protected], [email protected]}
Abstract—As manufacturing costs keep decreasing, battery
energy storage systems (BESS) are expected to play a key role
in modern grids. However, due to their energy constraints and
internal losses, the restoration of the state of charge (SoC) to a
reference range is of vital importance to fulfil their tasks. In this
paper, we propose SoC control schemes based on existing ones,
and then we evaluate their behavior in predictable and stochastic
power system applications. The modifications include parameter
tuning based on the actual BESS state, as well as alternating
the control scheme according to forecasts of the application
signal. Furthermore, we extend a Lithium-Ion battery model in
order to quantify capacity degradation and hence, investigate
the impact of the various SoC restoration strategies. Results
show that potentials to increase the lifetime are applicationdependent, based on the degree of flexibility allowed by a service.
Overall, the calendar aging dominates the cycling aging and
thus, there is limited space for improvement with different SoC
control schemes. On the other hand, by incorporating forecast
information, we can reduce the amount of energy needed for the
SoC restoration and hence, decrease additional energy costs.
Index Terms—battery energy storage system, lithium-ion battery, capacity degradation, state of charge control, peak shaving,
frequency control, ramp rate control
I. I NTRODUCTION
The mix of generation has been changing dramatically
over the last years, with a plethora of distributed energy
resources (DERs) penetrating at different voltage levels. The
high integration of DERs poses several challenges to modern
electrical power systems mainly due to their output variability.
Moreover, DERs, such as wind and photovoltaic generators,
are reducing the available rotational inertia by displacing
conventional generators based on rotating machines.
Battery energy storage system (BESS) technologies are
expected to help overcoming such issues in future grids since
they are able to: support the efficient integration of DERs,
provide ancillary services, emulate grid inertia, allow for offgrid operation, electrify remote areas, enhance power quality
and lead to investment postponements.
However, most of these applications require from a BESS
to respond to non zero-mean signals. In addition to energy
constraints which might get violated, BESS are also faced
with inherent internal losses. Therefore, the restoration of the
state of charge (SoC) close to a reference range is of crucial
importance and different methodologies are proposed in the
literature to achieve this goal [1]–[3]. Each of these SoC
control strategies shows various benefits/drawbacks and yields
different outputs from a BESS, offering the same functionality.
The authors in [1]–[3] demonstrate their methods to maintain
the SoC of a BESS within acceptable levels, offering frequency
regulation. Reference [1] reduces the required BESS dimensions, by recharging/discharging the BESS at a specific power
when the frequency is within an acceptable range, and by using
dissipative resistors when the BESS needs to absorb power but
is fully charged. In [2], the setpoints of the BESS are adjusted
using an average method to make the control signal zeromean. A similar approach is followed in [3], where offsetting
units are activated and contribute also to the required service.
There, the three aforementioned strategies are compared in
terms of energy cycled through the offset, the capability of
slower plants to cancel out the offset and whether the offset
cancels the original application signal or not. However, all the
aforementioned publications consider only one application.
Furthermore, most of them do not study the impact of the
SoC control strategy on capacity fading. Only [3] considers a
degradation model, but in a very simplified way to calculate
financial performance metrics. In order to quantify in more
detail the capacity degradation of a battery, a large range
of fading models are found in the literature [4]–[9]. These
range from analytical ones focusing on theoretical active
material loss mechanisms, to empirical ones based purely on
experimental fading data from real BESS or more common
from testing battery cells or modules. Moreover, combinations
of these offer a good compromise between theoretical formulas
of loss mechanisms and real experimental data series, i.e. semiempirical models.
In [4], a theoretical model for the simulation of battery
cycles is developed, based on the loss of active lithium ions
in the battery. Reference [5] develops a semi-empirical degradation model based on empirical correlations of SoC and film
resistance, whereas the battery’s faded capacity is connected
to SoC. In [6], a purely practical fading model is obtained
by electric vehicles’ batteries operating in real conditions.
The SoC, depth of discharge (DoD) and temperature effect
on capacity fade are considered. Similarly, [7] also considers
temperature and the effect of SoC on battery degradation while
using a semi-empirical model based on crack propagation
theory. The authors of [8] and [9] adopt the latter approach as
well, considering the effect of all battery characteristics, such
as SoC, DoD, temperature, charge/discharge rate, elapsed time
and number of cycles.
The contribution of this paper is twofold. First, we expand
the semi-empirical model of [8], considering real data from
various vendors. Then, being able to estimate BESS lifetime,
we compare existing and new SoC restoration strategies for
BESS offering deterministic and stochastic ancillary services.
The rest of the paper is organized as follows: Sections II
and III describe the proposed capacity fading model and the
different SoC restoration strategies, respectively. Section IV
introduces the considered case studies and presents the simulation results. Finally, conclusions are drawn in Section V.
II. C APACITY FADING MODEL
A semi-empirical degradation model tunes theoretical stress
models with parameters obtained by real experimental data. In
order to achieve a satisfactory model’s accuracy, the real experimental tests should represent various operational conditions.
This allows us to build models which convert the BESS
cyclic characteristics, such as SoC, DoD, charge rate, temperature, and time, into capacity degradation. In this paper, we
adopt and extend the semi-empirical capacity fading model
introduced in [8] and [9], where the interested reader can find
more modeling details. In the following section, we analyze
the main principles of the considered model and we describe
extensions and modifications.
A. Remaining Capacity
The remaining capacity of a BESS, denoted by L, represents
the available usable BESS capacity and is expressed as a
percentage of the initial energy capacity. According to [9], the
remaining capacity L of a battery is given by the two-term
exponential formula
L = (1 − pSEI ) · e−t·d + pSEI · e−t·rSEI ·d
(1)
where pSEI is the amount of the total battery capacity that
has been spent during the early stages of the battery lifetime
due to solid electrolyte interface (SEI) film formation that
occurs when the new cells start operation, rSEI represents
the SEI film formation ratio, t the total elapsed time of the
battery operation and d the linearized degradation function
with respect to battery cycle or time [9]. A value of L = 0.8
is defined arbitrarily as the end of the battery’s lifetime.
The total linearized -with respect to battery cycles or timedegradation d can be expressed by the sum of the cycling
and calendar aging of the battery, which are assumed to be
independent of each other. Calendar aging refers to the part
of the battery degradation that is caused independent of the
BESS usage, while cycling aging to the part that is affected
by the operational conditions of the battery.
Therefore, the total degradation d is given by,
d = dcal (SoCavg , Tavg , t) + dcyc (SoC, DoD, T, C, n)
(2)
where, SoCavg and Tavg correspond to the averaged values of
SoC and temperature over the considered time t, whereas SoC,
DoD, temperature T , charge rate C and the number of cycles
n represent stress factors of the BESS. Note that due to the
independence assumption, the elapsed time is not considered
in cycling aging.
B. Calendar aging
Calendar aging is a function of SoC, temperature and
the elapsed time. The linearized calendar aging function is
calculated according to
dcal = kt · fSoC (SoC) · fT (T )
(3)
where kt is the time stress coefficient, and fSoC and fT the
degradation models for SoC and temperature, respectively.
These stress models describe the way that SoC and temperature affect battery degradation. The same SoC and temperature
stress models are valid also for the cycling aging, and as a
result, these models are calculated only once.
Several SoC stress models can be found in literature
(e.g. [6], [7]) where a specific pattern is observed, concerning
how SoC affects degradation. That is, as SoC increases, battery
degradation is aggravated. For instance, the SoC stress model
described in [7] is given by
fSoC = ekSoC ·(SoC−SoCref )
(4)
where kSoC is the SoC stress model coefficient and SoCref is
the reference SoC level which is usually selected around 0.5.
However, considering experimental datasets from battery
cells from various vendors, we encountered cells with a different SoC stress model. More specifically, capacity degradation
does not show the worst impact at the maximum SoC level of
100%, but at a lower level. In such cases, the use of empirical
SoC stress models instead of theoretical ones can enhance
accuracy levels. Hence, we propose the stress function
=e
fSoC
−(
SoC−SoCref 2 SoCref
) · SoC
kSoC
(5)
We have to underline that this stress model may not be
applicable to all kind of battery cells since it is an empirical
one derived from a certain family of battery cells.
The temperature stress model is adopted from [9], where
Arrhenius’ equation is used to derive the following formula
fT = ekT ·(T −Tref )·
Tref
T
(6)
where kT is the temperature stress coefficient and Tref is the
reference temperature, usually chosen at 25 ◦ C.
The cycling aging model is given by
N
fDoD (DoDi ) · fSoC (SoCi ) · fC (Ci ) · fT (Ti ) · ni (7)
dcyc =
i=1
where fSoC , fDoD , fT and fC are the stress functions of SoC,
DoD, temperature and charge rate, respectively; n determines
whether the cycle is full (n = 1) or half (n = 0.5) and N is the
number of battery cycles. We define here as half cycle a single
charge or discharge event and as full cycle, the combination of
two symmetrical half cycles with opposite direction and equal
DoD [9]. The charge rate and DoD stress models are given
in [9], as
(8)
fC = ekC ·(C−Cref )
fDoD =
1
(ka · DoDkb + kc )
(9)
where kC is the charge rate stress coefficient, ka , kb , kc are the
DoD stress model coefficients and Cref is the reference charge
rate value which is usually chosen as 1.
Overall, as can be seen from (2), limited flexibility is provided by the calendar component in order to reduce capacity
degradation. There, one needs to identify the most suitable
level of SoC when the BESS is idle, and to maintain a
certain cell temperature. The cycling component offers more
flexibility, but on the other hand, is linked to a specific service
that the BESS is expected to offer. Respecting this service, a
BESS can e.g. be charged/discharged at various charge rates,
having different influence on capacity fading.
D. Calculation of cycling characteristics
In order to calculate the capacity degradation, the cycling
characteristics of every cycle need to be known. In this
direction, the use of the rainflow cycle-counting algorithm
is proposed in [9], [11], [12]. By modifying [13], which is
designed to perform rainflow cycle-counting for mechanical
stress profiles, we managed to count battery cycles, as well
as calculate correctly the charge rate for charging/discharging.
Reference [13] does not take into account the resting time
periods of the profile, but instead, it considers these as part of
the cycle itself. Finally, further modifications were necessary
to translate characteristics of mechanical cycles into features
of battery cycles, namely cycle amplitude and average cycle
amplitude into DoD and SoC, respectively.
The coefficients used in our model are presented in Table I.
Figure 1 shows a comparison between the derived model and
real data for a BESS stressed with 9.5 cycles of 100% DoD
TABLE I
C OEFFICIENTS OF THE CAPACITY FADING
Equation
L
dcal
fSoC
fT
fC
fDoD
Remaining Capacity L (%)
C. Cycling aging
100
Experimental data
Capacity fading model
95
90
85
80
0
100
300
400
500
Time (days)
Fig. 1.
Comparison between model and experimental data.
at a charge rate of 1 and 25 ◦ C every day. The derived model
is fitted based on experimental data and thus, may not be
applicable to specific families of battery cells.
III. S O C C ONTROL A LGORITHMS
The SoC of a BESS changes due to two mechanisms. The
first is related to a specific application/service which the BESS
is expected to offer, e.g. peak shaving, while the second comes
from the self-discharging as well as the round-trip efficiency
of the BESS (losses). Figure 2 shows the input signals to the
BESS which guarantee: a) that the BESS is responding to a
specific application and b) that a control strategy is applied in
order to restore the SoC to a reference range.
A. Overview over SoC restoration strategies
Several SoC restoration strategies have been proposed in
the literature, e.g. [1]–[3]. The following equation expresses
the general relation between the power requested by a service
PAPP , the power needed to respect the energy constraints of
SoCctrl
OUT
and the total output of the BESS PBESS
:
the BESS PBESS
OUT
SoCctrl
= PAPP + PBESS
PBESS
(10)
As will be described, the different SoC control strategies focus
SoCctrl
on how PBESS
is formulated. Although their final goal is similar, they show differences in terms of mainly two aspects. The
first one refers to the timing when the restoration occurs, i.e.
whether they allow SoC regulation only at specific periods in
time or continuously. The second difference concerns whether
the BESS solely provides the total power requested by the
application, or whether other mechanisms, such as intra-day
markets or secondary control reserves, are required to provide
additional offsets. Some of these strategies are explained below
for the case of frequency regulation with PAPP = − Δf
S , where
Δf is the system frequency deviation from the nominal value
and S is the droop.
6WDWHRIFKDUJH
FRQWURO
6HWSRLQWV
&RQVWUDLQWV
VHWSRLQWV
$SSOLFDWLRQ
FRQWURO
MODEL .
Parameter Value (-)
pSEI = 0.0296
rSEI = 150.24
kt = 3.4 · 10−10
kSOC = 0.5345
kT = 0.0693
kC = 0.2374
ka = 16215
kb = −1.722
kc = 8650
200
6HWSRLQWV
$FWXDOVWDWH
%(66
Fig. 2.
Application and SoC control.
1) Strategy 1 - [1]: Here, the SoC control actions are
allowed under certain conditions of the application signal.
Offering primary control reserves, this strategy allows charging/discharging at a predetermined power when the frequency
is within its deadband, e.g. ±10 mHz in the European interconnected system. As seen below, the recharging power is fixed
and expressed with the coefficient c ∈ [0, 1], as a percentage
max
of the installed power capacity of the BESS PBESS
:
SoCctrl
max
(11)
PBESS (t) = ±c · PBESS , when PAPP (t) = 0
strategies has an effect on the total BESS response leading to
a shorter/prolonged lifetime compared to the initial targets, on
the frequency of SoC limit violations and on the total energy
needed to be cycled for the SoC restoration.
B. Consideration of Forecast Information
This section discusses modifications of the aforementioned
strategies, focusing on dynamic up/down thresholds according
to forecasts of the application signal as well as on variable
values for the parameters.
It is important that this control action can only be active when
Trying to forecast the application signal PAPP can be a very
PAPP = 0 and the SoC is outside of predetermined thresholds. challenging task for some applications (e.g. forecasting the
A more sophisticated approach is to define the parameter frequency signal in interconnected Europe) due to lack of
c as a function of the actual frequency position within a data/models and various sources of uncertainties. However, for
deadband, i.e. its deviation from upper and lower bounds. This other applications, such as off-grid configurations where RES
would result in better SoC restoration, since the SoC control comprise a large share of the available generating units, it may
signal will drive the BESS more precisely to its reference be meaningful and may lead to improvements regarding the
range.
design (sizing) and operation of the BESS. In such cases, RES
2) Strategy 2 - [2]: A dynamic recharging can be used in forecasts with a satisfactory prediction accuracy could lead to
order to make the application signal zero mean. To achieve preventive BESS control actions (e.g. charge or discharge a
this, the moving average method is used in [2]. The combi- BESS according to an anticipated event).
nation with the application signal drives the SoC back to its
In this section, we analyze the parameters of the aforemenreference value. The moving average method is described by
tioned SoC control strategies which could be altered due to
t
forecast information:
j=t−a (−PAPP (j) + Ploss (j))
SoCctrl
(12)
(t + d) =
PBESS
1) Strategy 1:
a
where parameter α defines the past window considered, while
a) Dynamically adjustable SoC limits instead of fixed ones,
d introduces a delay in the offset implementation. This control
as proposed in [1]: Thus, in addition to the set of rules
action is active continuously forcing the final BESS response
described in the classical strategy, a new one is added
to be zero-mean, while the offset adjustment needs to have
based on the signal forecast. In case the SoC is above the
thres
slower dynamics than the application signal.
) and we anticipate
allowable threshold (SoC > SoCup
3) Strategy 3 - [3]: This method adds a time dependent
a frequency drop in the coming time steps, it would
offset to the application signal that is canceled out by other
make sense to increase the maximum SoC threshold and
plants. As explained in [3], when the SoC exceeds certain
let the frequency signal itself reduce the SoC instead of
thresholds, plants with slower dynamics than the application
imposing an external control signal.
signal modify their operation points, offering offsets with
b) Variable recharging power (parameter c in (11)) based
predetermined ramps. The different sections of this offset
on the anticipated application signal. As an example,
mechanism for the positive case are given by
in case of an isolated system with low grid inertia, we
⎧ Poffset
would prefer the recharging control action to affect the
, i = 1 : tR
⎨ tR · i
SoCctrl
frequency signal as little as possible. Thus, we can use
PBESS (t+i) = Poffset
, i = tR + 1:tO + tR (13)
thres
⎩
a larger value of the parameter c when SoC < SoClow
Poffset
Poffset− tR ·(i−tR−tO ) , i=tO+tR+1:tO+2tR
and a frequency rise is anticipated.
First, the offsetting unit increases its power gradually with
c) Reduction of the reference SoC when the BESS is
a ramp of fixed slope, the total duration of which is tR . For
expected to remain idle for a long time period. In
the next tO timesteps the unit stays constant offering Poffset
this way, we can assess the trade-off between reduced
power and then, a negative ramp absolves the unit. The inverse
calendar aging due to smaller average SoC and increased
offsetting behavior is straightforward. This control action is
cycling aging due to changing the reference SoC.
active when the SoC exceeds predefined thresholds, namely
2)
Strategy
2:
thres
thres
SoClow
and SoCup
.
a) Variable targeted SoC based on the anticipated applica4) Strategy 3 : A direct modification of the third method is
tion signal. In the classical strategy, the main focus is
to define multiple SoC thresholds and hence, multiple offset
to make zero-mean signal and hence lead the SoC to its
initiations. Thus, each time one of the upper/lower thresholds
reference value. In presence of forecasts, small biases
is hit, a new offset block of energy will be triggered.
may be allowed expecting that the future application
The most suitable control strategy depends on many paramsignal will lead the SoC towards the reference value.
eters, such as the nature of the BESS service, the availability
3) Strategy 3 and 3 :
of other units for the offsetting part, the access to power
a) Dynamically adjustable SoC limits similar to 1a.
markets or not, etc. The selection among the appropriate
IV. C ASE S TUDIES
A BESS can offer a very wide range of power system
functionalities such as frequency regulation, reactive power
control or RES smoothing. Some of these show a deterministic
behavior with respect to the response and the cyclic profile
of the BESS, while others depend on a random process and
hence, the cyclic profiles do not follow a certain pattern.
A. Deterministic Profiles
1) Peak Shaving: A BESS can be used in order to reduce
the capacity-based charge since it can provide the appropriate
amount of power over a short time interval and bridge the peak
consumption. Several industrial customers rely on processes
which require large amounts of power (e.g. to start bulk machines). Using a BESS, the dimensions of which are selected
for a continuous discharge of the required peak reduction, they
can optimize their electricity procurement.
Strategies 2 and 3 do not seem suitable for this service,
since during the time when the BESS is to be utilized, i.e.
PAPP = 0, an offsetting unit would provide also part of the
service. Therefore, we focus on strategy 1 and we investigate
cases for various charging powers (parameter c in (11)). Please
note that large values of this parameter restore faster the SoC
and indicate that smaller BESS dimensions might be adequate.
However, for the sake of a fair comparison, we keep the
dimensions fixed, changing only the recharging powers.
Reference [10] provides a yearly aggregated industrial profile in 15-min resolution for the area of Bavaria, Germany.
By scaling it down and deciding on the maximum acceptable
power, we can derive the yearly power profile demanded from
the BESS. Figure 3a shows such a (negative) power profile
over one week, for a 1 MW/580 kWh Li-ion BESS (solid
SoCctrl
is shown for c = 1% (dashed)
line). The control profile PBESS
and c = 1.5% (dash-dotted), and corresponds to the (positive)
power needed to recharge the BESS. Finally, the total response
of the BESS is equal to the sum of the application power
SoCctrl
or just Pcontrol . The different
PAPP and the respective PBESS
SoC trajectories are shown in Fig. 3b. As expected, the higher
the parameter c, the faster the BESS reaches the nominal
SoC of 0.9. Concerning forecast information, we show in the
same figure the case with c = 1.5%, where the reference
SoC is kept lower at weekends and non-working hours when
no peak shaving is needed (dashed-dotted line). For the SoC
restoration at 06:00, the additional charging is performed at
power (cf = 10%) so as the BESS is ready to fulfill its task.
Table II summarizes the remaining capacity measured according to Section II, after one and 10 years of operation,
assuming that the same profile is repeated every year at a
constant BESS temperature of 20◦ C. We observe that having a
0
-20
PAPP (Peak shaving)
P
-40
-60
control
(for c=1%)
Pcontrol (for c=1.5%)
24
48
1
BESS SoC (-)
b) Variable offset values (Poffset ) based on the anticipated
application signal. According to the expected signal
evolution, different offset values may lead to less energy
cycled through the offsetting units and avoid phenomena
where the min/max thresholds are hit repeatedly due to
large amount of energy offered by the offsetting unit.
Power (kW)
20
72
96
Time (hours)
120
144
168
72
96
Time (hours)
120
144
168
0.5
0
SoC (for c=1%)
SoC (for c=1.5%)
SoC-f (for c=1.5%)
24
48
Fig. 3. BESS response offering peak shaving service.
a) Application, SoC control and total BESS power profiles.
b) SOC trajectories for different control powers using strategy 1.
higher parameter c helps restoring the SoC faster, but results in
marginally increased degradation. For the specific application
and BESS dimensions, values above c = 1% do not lead
to SoC violations. A large value of parameter c, e.g. 20%,
restores the SoC to its reference value fast, ensuring that the
energy constraints of the BESS will hold, and indicating that
smaller BESS dimensions might be adequate for the specific
application. However, this comes with the cost of higher
degradation. Reducing the SoC when being idle, results in
0.57% more remaining capacity after 10 years of operation
(c=1.5%, cf =10% case). The benefits of the reduced average
SoC exceed the cycling fading from the later charging process.
Finally, the total energy needed for the SoC restoration over
the time period examined is identical for all cases.
B. Stochastic Profiles
1) RES smoothing: Due to weather-related phenomena, e.g.
cloud movements or sudden wind speed changes, the stochastic RES infeed may ramp up or down very fast, leading to
stability and voltage issues in distribution grids. Such problems
are more apparent in isolated systems, where RES comprise a
large share of the total generation portfolio. Thus, controlling
the ramp rate of the RES infeed is a critical requirement of
many regulators, described in grid codes. A BESS can offer
such a functionality, absorbing RES fluctuations with the goal
to feed a smoothed profile into the grid.
Here all different SoC strategies are applicable. The investigation of various SoC control schemes for the same application
provides insights that could lead to an optimal strategy selection based on the available components for the SoC restoration.
Table III summarizes the selected parameters for each of the
TABLE II
BESS
CAPACITY DEGRADATION FOR PEAK SHAVING AT
Strategy 1
Parameter
c = 1%
c = 1.5%
c = 2%
c = 2.5%
c = 20%
c = 1.5% (cf = 10%)
T = 20 ◦ C.
Remaining Capacity (%)
1-year operation 10-year operation
97.25
86.14
96.92
84.59
96.88
84.42
96.86
84.32
96.76
83.84
97.02
85.07
TABLE III
PARAMETERS FOR THE RES SMOOTHING APPLICATION .
SOCref = 0.75
Strategy 1
Strategy 2
Strategy 3, 3
a=1h
Poffset = 10% · PBESS
BESS SoC (-)
BESS
0.9
0.8
0.7
0.6
BESS SoC (-)
thres1 = 0.7
thres1 = 0.8
SOCup
SOClow
thres2 = 0.65
thres2 = 0.85
SOCup
SOClow
c = 10%
d = 0 sec
tR = 5 min
tO = 10 min
456
480
504
528
Time (hours)
552
600
0.8
0.7
0.6
514
515
Time (hours)
100
Power (kW)
576
516
P
APP
517
(PV smoothing)
0
-100
514
515
Time (hour)
516
517
514
515
Time (hour)
516
517
Power (kW)
20
10
0
-10
Strategy 1
Strategy 2
Strategy 3
Strategy 3'
Fig. 4.
BESS response offering PV smoothing with different control
strategies.
a) Weekly SOC trajectories.
b) 7-hour SOC trajectories.
c) Application and total BESS power profiles.
d) SoC restoration control signals.
strategies, while Fig. 4a shows weekly SoC trajectories of a
50 kWh/100 kW BESS providing PV smoothing under the
rules of the Australian grid code [14]. Real measurements
from a PV installation of 100 kW in Australia over one
year are used. As can be seen, all strategies offer the PV
smoothing functionality over the considered week without
energy violations for the selected parameters. Strategies 3 and
3 are identical until the second threshold is hit for the first
time (at around t = 514 h). Note that bad selection of the
parameters (high offset value, or narrow SoC thresholds) could
lead to oscillations between the upper and lower thresholds.
Table IV summarizes the capacity degradation, after 10
years of operation, assuming that the same PV profile is
repeated every year. The metric Q introduced in [3] calculates
the ratio between the energy cycled through the offset and
the energy required from the ancillary service. It accounts for
the different nature of the SoC strategies, while the BESS
temperature is kept at 20 ◦ C.
Overall, we observe that all examined strategies result
in roughly the same capacity degradation after 10 years of
operation. This is explained by the fact that the calendar
aging mechanism is dominant, compared to the cyclic one,
which is different for each strategy as seen in Fig. 4c. It is
remarkable that strategy 1 requires the least energy through
the offset (1.08%), as seen also in Fig. 4d. On the contrary,
strategy 3 requires 18 times more energy to be cycled due to
the constraints imposed by the offsetting unit. This strategy
would be preferable in presence of SoC limit violations.
As shown in Table IV, reducing the reference SoC to 0.5
when the BESS is idle, has a negative impact on capacity
degradation irrespective of the charging/discharging power
(10% in this case). This happens because the BESS does not
remain long enough at a reduced SoC (maximum 12 hours)
over a daily cycle. The additional cycling events of moving
the SoC prevail, and thus, it is not worthy to reduce the SoC.
2) Primary frequency control scheme: Primary control is
the fastest frequency spinning reserve, referring to governor
automatic response. It is offered by various generation units
whose main purpose is to restore instantaneously the balance
between generation and consumption. A BESS is suitable to
offer this ancillary service since it can track the frequency
signal much faster than most conventional generators.
All different SoC strategies are applicable as can be seen in
Fig. 5a which shows the response of a 1 MW/580 kWh BESS
to a frequency deviation signal ( [15]). The strategy parameters
are identical to Table III, apart from SoCref = 0.5.
The comparison among the strategies is conducted in terms
of energy cycled through the SoC control mechanism, annual
total time of SoC limit violations and capacity degradation, as
summarized in Table V. Strategy 1 requires the least energy to
be cycled for the SoC restoration, half compared to Strategy 2,
whereas Strategies 3 and 3 require a Q ≈ 33%. The benefit of
strategy 3 in this case is limited to the fact that the BESS is
always available, resulting in no unavailability penalizations.
Using a 5-minute-ahead frequency forecast (strategy 3 f) based
on grey system theory as in [8], results in 638 kWh less
energy to be cycled through the offset per year compared to the
case without forecasts. Results for a perfect 5-minute forecast
(strategy 3 f0) can be regarded as a benchmark, showing that
the maximum potentials are rather limited.
Interestingly, much more SoC violations are observed using
strategy 1 (see t=2 h of Fig. 5a), where 32 hours per year
(0.37% of the time) the BESS cannot provide the requested
power. Strategy 3 fails around 2 hours per year, whereas all the
other strategies do not show any violations. This behavior may
result in large financial penalizations according to the market
rules, when the BESS is not providing frequency control.
Concerning capacity degradation, overall, the dominant
calendar aging results in similar fading for all strategies.
Strategy 1 shows the highest, but the fact that it does not
cancel out the application signal makes it suitable for off-grid
BESS
TABLE IV
RES
CAPACITY DEGRADATION FOR THE
SMOOTHING APPLICATION .
10-year operation
Remaining
Capacity (%)
Q(%)
Strategy 1
Strategy 2
Strategy 3
Strategy 3
83.35
83.33
83.13
83.12
1.08
14.20
17.02
19.31
Remaining
Capacity (%)
reducing SoCref
81.79
81.92
81.72
81.62
0.5
0.1
0
0
1
2
3
4
5
6
7
Time (hours)
8
9
10
11
12
Frequency Deviation (Hz)
BESS SoC (-)
TABLE V
400
Power (kW)
P
APP
(PV smoothing)
200
0
-200
1
Time (hours)
2
Power (kW)
0
Time (hour)
-100
-200
1
Time (hour)
Strategy 1
Strategy 2
2
Strategy 3
Strategy 3
Fig. 5. BESS offering frequency regulation with different control strategies.
(a) Twelve-hour SOC trajectories and application control signal in frequency.
(b) Application and total BESS power profiles.
(c) SoC restoration control signals.
configurations, where the response of the BESS is crucial for
the stability of the system. On the contrary, there are instances
in all other strategies, where the application signal requires
from the BESS a certain behavior, but the BESS responses in
the opposite way due to active offsetting units (e.g. in Fig. 5b
right after t=1 h). A continuous movement of the SoC is
observed in strategy 2, since the goal is to restore the SoC
exactly to its reference value. This leads to slightly higher
degradation compared to strategy 3 where the offsetting is
inactive, as long as the SoC is within thresholds.
Finally, Fig. 5c shows the SoC control signals for all
strategies, where Strategy 3 and 3 are identical until the
second upper SoC threshold is hit. It is important to note
that the selection of the parameters has a great impact on the
evaluation of the results.
V. C ONCLUDING R EMARKS
In this paper, we extended a Lithium-Ion battery fading
model, and we presented control strategies to restore the state
of charge (SoC) of a battery energy storage system (BESS)
back to reference bounds. The proposed degradation model
allows us to quantify the remaining lifetime of the BESS,
with the aim of evaluating the impact of different SoC control
strategies. The modifications to existing SoC control schemes
include the use of variable parameters as a function of the
actual SoC and dynamic thresholds based on forecasts of the
application signal.
We apply the proposed SoC control strategies in various
case studies, where a BESS offers different kind of ser-
BESS
CAPACITY DEGRADATION FOR FREQUENCY REGULATION .
SoC restoration
scheme
Strategy 1
Strategy 2
Strategy 3
Strategy 3
Strategy 3 -f
Strategy 3 -f0
Q(%)
26.8
52.2
32.87
32.97
32.77
31.61
Total time
of hitting
SoC limits (h/a)
32.25
0
2.17
0
0
0
Yearly BESS
unavailability
(%)
0.37
0
0.025
0
0
0
Remaining
capacity (%)
(10-year values)
77.35
78.77
78.89
78.91
78.93
79.00
vices. Applications with relatively predictable behavior, such
as peak shaving, show small potentials for increasing the
BESS lifetime. Here, the duration that the BESS remains idle
is of interest, since a reduction of the reference SoC can
lower the dominant calendar aging. In cases where a BESS
follows a stochastic/unpredictable signal, such as participation
in primary frequency control scheme or renewables’ output
smoothing, benefits may arise from using forecasts of the
service signal. By anticipating a certain evolution in this
application signal, less energy could be cycled to restore the
SoC, resulting in cost savings and less stress on the BESS.
R EFERENCES
[1] A. Oudalov, D. Chartouni, and C. Ohler, “Optimizing a battery energy
storage system for primary frequency control,” IEEE Transactions on
Power Systems, vol. 22, no. 3, pp. 1259–1266, 2007.
[2] T. Borsche, A. Ulbig, M. Koller, and G. Andersson, “Power and energy
capacity requirements of storages providing frequency control reserves,”
in Power and Energy Society General Meeting (PES), IEEE, 2013.
[3] O. Megel, J. L. Mathieu, and G. Andersson, “Maximizing the potential
of energy storage to provide fast frequency control,” in 4th Innovative
Smart Grid Technologies Europe (ISGT EUROPE), IEEE/PES, 2013.
[4] G. Ning, R. E. White, and B. N. Popov, “A generalized cycle life model
of rechargeable li-ion batteries,” Electrochimica acta, vol. 51, no. 10, pp.
2012–2022, 2006.
[5] P. Ramadass, B. Haran, R. White, and B. N. Popov, “Mathematical
modeling of the capacity fade of li-ion cells,” Journal of Power Sources,
vol. 123, no. 2, pp. 230–240, 2003.
[6] L. Lam and P. Bauer, “Practical capacity fading model for li-ion battery
cells in electric vehicles,” IEEE Transactions on Power Electronics,
vol. 28, no. 12, pp. 5910–5918, 2013.
[7] A. Millner, “Modeling lithium ion battery degradation in electric vehicles,” in Innovative Technologies for an Efficient and Reliable Electricity
Supply (CITRES), IEEE, 2010.
[8] B. Xu, A. Oudalov, J. Poland, A. Ulbig,, and G. Andersson, “BESS
Control Strategies for Participating in Grid Frequency Regulation,” in
IFAC World Congress, Capetown, South Africa, August 2014.
[9] B.
Xu,
“Degradation-limiting
optimization
of
battery
energy
storage
systems
operation,”
Master’s
thesis,
ETH
Zurich,
Zurich,
Switzerland,
9
2013,
Available:
http://www.eeh.ee.ethz.ch/uploads/tx ethpublications/Xu MA 2013.pdf
[10] Bayernwerk AG, Standardized demand profiles Available:
https://www.bayernwerk.de
[11] M. Swierczynski, R. Teodorescu, P. Rodrı́guez Cortés et al., “Lifetime
investigations of a lithium iron phosphate (lfp) battery system connected
to a wind turbine for forecast improvement and output power gradient reduction,” in Proceedings of the 15th Battcon Stationary Battery
Conference and Trade Show, 2011. Available: http://www.battcon.com/
papersfinal2011/swierczynskipaperdone2011bu 20.pdf
[12] R. Dufo-López and J. L. Bernal-Agustı́n, “Multi-objective design of
pv–wind–diesel–hydrogen–battery systems,” Renewable energy, vol. 33,
no. 12, pp. 2559–2572, 2008.
[13] A. Nieslony, “Rainflow counting algorithm,” 2003. [Online]. Available:
http://www.mathworks.com/matlabcentral/fileexchange/3026-rainflowcounting-algorithm
[14] Technical Requirements for Renewable Energy Systems Connected to
the Low Voltage (LV) Network via Inverters, Specification Number: HPC9FJ-12-0001-2012. [Online]. Available: http://horizonpower.com.au/
[15] The swiss transmission system operator, Swissgrid. [Online]. Available:
http://www.swissgrid.ch/