energies
Article
Hybridizing Lead–Acid Batteries with Supercapacitors:
A Methodology
Xi Luo 1 , Jorge Varela Barreras 2
1
2
3
4
*
Citation: Luo, X.; Barreras, J.V.;
Chambon, C.L.; Wu, B.; Batzelis, E.
Hybridizing Lead–Acid Batteries
, Clementine L. Chambon 3
, Billy Wu 4
and Efstratios Batzelis 1, *
Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK;
xi.luo19@imperial.ac.uk
Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK;
j.varela-barreras@imperial.ac.uk
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK;
c.chambon13@imperial.ac.uk
Dyson School of Design Engineering, Imperial College London, London SW7 2AZ, UK;
billy.wu@imperial.ac.uk
Correspondence: e.batzelis@imperial.ac.uk
Abstract: Hybridizing a lead–acid battery energy storage system (ESS) with supercapacitors is a promising solution to cope with the increased battery degradation in standalone microgrids that suffer from
irregular electricity profiles. There are many studies in the literature on such hybrid energy storage
systems (HESS), usually examining the various hybridization aspects separately. This paper provides a
holistic look at the design of an HESS. A new control scheme is proposed that applies power filtering to
smooth out the battery profile, while strictly adhering to the supercapacitors’ voltage limits. A new lead–
acid battery model is introduced, which accounts for the combined effects of a microcycle’s depth of
discharge (DoD) and battery temperature, usually considered separately in the literature. Furthermore, a sensitivity analysis on the thermal parameters and an economic analysis were performed
using a 90-day electricity profile from an actual DC microgrid in India to infer the hybridization
benefit. The results show that the hybridization is beneficial mainly at poor thermal conditions and
highlight the need for a battery degradation model that considers both the DoD effect with microcycle
resolution and temperate impact to accurately assess the gain from such a hybridization.
Keywords: hybrid energy storage system; supercapacitor; lead–acid battery; energy management
system; battery degradation; depth of discharge; techno-economic analysis
with Supercapacitors: A
Methodology. Energies 2021, 14, 507.
https://doi.org/10.3390/en14020507
Received: 18 December 2020
Accepted: 13 January 2021
Published: 19 January 2021
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1. Introduction
Among the Sustainable Development Goals (SDGs) established by the United Nations
General Assembly in 2015 [1], SDG 7 aims at affordable, reliable, sustainable and modern
energy access for all. Microgrids are a key technology to this end, and have seen recently
remarkable expansion in isolated rural areas around the world with limited or no access to
the main electric grid. The typical standalone microgrid utilizes renewable or other local
energy sources to provide electricity in places where long-distance power transmission
and substantial grid investments are deemed uneconomical [2]. An irreplaceable component of these miniature power grids is the energy storage system (ESS), whose main
role is to ensure power quality and energy balance between the intermittent supply and
demand [3,4]. Batteries are the most widely used energy storage technology in microgrids,
mainly due to their scalability, modularity and limited maintenance needs. Lead–acid
batteries, in particular, remain to this day the most commonly found battery technology
in operating microgrids, being the most commercially mature. A big challenge in these
ESS, however, is battery degradation due to deep discharge and surge currents often found
in standalone microgrids supplied by intermittent renewables supply, such as solar [5].
For example, lead–acid batteries under high charge/discharge rates suffer from the formation of smaller sulphate crystals that lead to inhomogeneous current distribution and
Energies 2021, 14, 507. https://doi.org/10.3390/en14020507
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Energies 2021, 14, 507
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increased internal resistance, all of which have a negative impact on battery life [6]. To this
day, the longevity and associated replacement costs of batteries remain one of the most
critical factors for the economic viability of an off-grid microgrid investment.
To overcome these challenges, the scientific community has explored in the last decade
how to hybridize a battery ESS with other storage technologies, such as supercapacitors [7–14], fuel cells [15,16] and flywheels [17], to come up with a more reliable hybrid
energy storage system (HESS) that features longer lifespan and higher resistance to degradation. Supercapacitors (or ultracapacitors) are deemed among the most suitable coupling
candidates, as they exhibit high power density (though low energy density) and complementary characteristics to electrochemical batteries [18,19]. They can readily support high
charge/discharge rates as often as required with negligible impact to their life, which typically exceeds a decade [20]. For this reason, they couple nicely with batteries in absorbing
the sudden changes in power demand that allows for a smoother power profile to the
batteries and reduced deterioration. Furthermore, the two energy storage technologies
exhibit relatively similar operating principles as they are both electrochemical devices,
which translates to similar low set-up costs [2]. Furthermore, the long-term operation
and maintenance (O&M) costs of supercapacitors are lower than those of batteries [21].
This paper takes a deep look on how to hybridize an ESS with lead–acid batteries and
supercapacitors, providing recommendations for the topology selection, the design of
the control scheme, the battery degradation modeling and economic viability analysis of
the investment.
The state of the art in HESS topologies involves mainly three different configurations
of batteries and supercapacitors: passive, semi-active and fully active [2,7]. The most
appropriate topology for an application is selected based on factors such as the set-up cost,
efficiency, controllability, system complexity and utilization rate. The passive HESS is the
simplest and cheapest topology, according to which the batteries and supercapacitors are
directly coupled in parallel at the DC link without any power electronics or control [8,9];
this approach is widely applied in high voltage ESS, benefiting from low internal losses
and reduced system complexity. However, this way the supercapacitors voltage varies
little and their capacity is severely underutilized, which entails only limited extension of
the battery life. Furthermore, this approach faces also challenges related to impedance
matching between the batteries and supercapacitors. The semi-active configuration, on the
other hand, employs power electronics in either batteries or supercapacitors—not both—to
expand the operating region of the latter [10,11]. With this approach, one of the two storage
devices is effectively isolated, thus allowing for more flexible power allocation between
the two. Nonetheless, the passive element may suffer from surge currents—if it is the
battery—or cause bus voltage fluctuation and negatively impact the power quality—if it is
the supercapacitors. The third option of fully active configuration tackles all these issues.
Usually a parallel connection is adopted [5,12–14], but cascade implementations are also
reported [22]. The big gain with this topology is effective decoupling of the two components
permitting independent control during operation and separate sizing at the design phase.
Especially for DC standalone microgrids, this is a viable option for getting the energy storage
mix right and extending the HESS lifespan as much as possible. It is worth noting that there
are some recent alternatives that involve distributed hybridization combined with active
balancing, achieved by incorporating supercapacitors into the balancing bus in order to
enable cell-level hybridization [23]. However, this is still a new and more complex solution,
so far targeted only at Li-ion batteries in e-mobility applications. Therefore, this paper
adopts the fully active HESS method as the most appropriate for isolated DC microgrids.
Various philosophies exist in the literature regarding the control strategy of fully active
HESS to allocate the power flows between the batteries and supercapacitors and maintain
the system stability. These control strategies, commonly referred to as energy management
systems (EMS), may involve power filtering [5,14,24–26], deterministic rule-based control [13,27], fuzzy logic [10,28] and optimization-based control [29–31]. In [28], a fuzzy logic
rule-based control is applied to a HESS to ensure that the ESS elements operate in the safe
Energies 2021, 14, 507
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region. Alternatives employing neural networks [29] and model predictive control [30,31]
are based on multi-objective or cost functions that aim to optimize the power allocation.
A combination of the rule-based concept with optimization algorithms is proposed in [27].
However, the aforementioned approaches employ sophisticated algorithms that require
large amounts of input data and complex mathematical calculations, which have acted as
barriers towards wider adoption. By contrast, the power filtering approach has proven
quite popular, as it is both effective and easy to implement. It has been also shown that a
simple filter-based control is effective in off-line sizing applications as well, yielding very
similar results to more complex, non-causal, optimization control approaches as long as
battery model accounts for sufficiently complex dynamics [32]. Given these considerations,
this paper focuses on the power filtering method.
There are many studies on power filtering in the literature. Somayajula et al. in [33]
demonstrated an active supercapacitor control scheme to achieve smoothing of intermittent
renewables generation; the adopted cascade control comprising an outer voltage loop and
an inner current loop has been also applied to battery-supercapacitor hybrid systems to
ensure power quality. Decoupling the high frequency part of the power control using a firstorder low-pass filter (LPF) is proposed in [5,14,24,25]. However, these studies do not properly
consider the safe operating region of the ESS components. Especially for the supercapacitors,
their low energy density and high charge/discharge rates lead to highly volatile voltage;
if not properly contained within the safety limits, this may result in irreversible damage if
overcharged (e.g., voltage exceeding the structural limits) or power converter malfunction if
left uncharged (e.g., power converter not managing to step-up the low input voltage). To this
end, State of Charge (SoC) controllers are proposed in [26,34], which however aim to maintain
the energy of the supercapacitors around the reference level and do not directly control the
voltage. This may occasionally result in voltage out of limits due to SoC miscalculation
caused by various factors, such as parasitic resistances or capacitance deviation due to aging
and deterioration. To this day, a complete control scheme for hybrid batteries-supercapacitors
systems based on power filtering that strictly adheres to the supercapacitor voltage limits is
missing from the literature.
To evaluate the contribution of the hybridization to the battery lifespan, the battery
degradation needs to be captured and modeled. There are three different degradation
modeling philosophies in the literature: physical-mechanistic models, empirical models
and data-driven models [35–37]. Physical-mechanistic models are generally based on electrochemical aging processes inside the battery and involve physics-inspired differential
equations. For example, Dufo-López et al. in [35] consider the phenomena of internal
corrosion of the battery and aging of the active material to quantify the capacity loss. Although very well-aligned with the physics, these models require many unknown parameters
and laborious computations that limit their applicability only to research purposes. The empirical models, on the other hand, entail simpler mathematical functions and coefficients
extracted from fitting to experimental results. This makes this approach more effective
and practical, except that it requires lots of experimental data to capture a wide range of
operating conditions and degradation factors. Making assumptions for untested conditions,
to make up for missing data, may introduce uncertainty in the results [36]. A popular
extension of this category are the cycle-counting models [38]; by adopting the principle
of fatigue damage, these models measure the degradation for each cycle of use assuming
that the aging factors are independent and cumulative. This allows for a more abstract and
universal model structure that relies on limited empirical information usually available in
the manufacturer datasheet. Examples of such quantitative cycle-counting models may
be found in [6,14,22,39–42]. The third category of data-driven degradation models apply
statistical analysis and machine learning on a large database to predict the battery status
and extract patterns to quantify the lifespan [37,43]. These methods are not yet widely
used due to their dependence on large datasets and sophisticated implementation. This
paper, therefore, adopts the cycle-counting empirical approach due to practicality and wide
acceptance in the field.
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The battery ages and degrades over time mainly due to (i) calendar aging, i.e., capacity
decrease under idle conditions, and (ii) cycle life aging, i.e., degradation during usage [44].
In standalone microgrids, the ESS is in continuous operation and the latter type of aging
prevails; this is why the degradation model of this paper focuses on cycle life aging,
as generally done in HESS studies. This type of deterioration can be manifested as corrosion
of positive grid, hard/irreversible sulfation and shedding [45]. The most prevalent failure
mode for lead–acid batteries in standalone stationary systems is the former, also known
as anodic corrosion [46], which used to be a major problem in early design, thereafter
overcome by the adoption of improved grid alloys. The corrosion rate is accelerated
by high temperatures, extreme voltages and cycling operation (versus constant current
operation) [46]. Primary factors of this degradation are the depth of discharge (DoD)
(i.e., how deeply the battery is discharged), the charge/discharge rates and the battery’s
operating temperature [6]. Most relevant models take into account only the DoD factor and
employ a cycle-counting method, such as the rainflow counting method [6,40], to capture
the number and depth of the cycles [42,47]. However, these models are designed for
moderate and deep discharge cycles (e.g., more than 10%) and may fail to accurately
capture the effect of smaller cycles, i.e., microcycles, often found in off-grid microgrids
with irregular power flows due to intermittent supply and demand [14,22]. The case study
of this paper show that it is imperative to employ a microcycles DoD model when there is
access to high time-resolution electricity data (e.g., second resolution) in order to accurately
capture the DoD degradation. Furthermore, battery temperature is also an important
stress factor to battery degradation, usually studied separately from the DoD effect [48].
The investigation in this paper demonstrates that the two factors are strongly related in the
presence of microcycles and rapidly changing battery currents. Narayan et al. [38] have
proposed a model that combines both DoD and temperature effects, albeit following an
alternative dynamic capacity fading approach that is too complicated for classical cycle
counting and fundamentally differs from the aforementioned mainstream DoD models.
There is still a need in the literature for a lead–acid battery degradation model that accounts
for the combined effect of microcycles DoD and temperature.
In applications of lead–acid battery and supercapacitor hybrid systems, the selection
of energy storage components mainly depends on the availability, system size and cost.
Lead–acid batteries are the industry standard for small-scale standalone photovoltaic (PV)
systems, both in valve-regulated and flooded deep-cycle designs [49]. The batteries are
usually connected in series to meet the system voltage requirements, and then several
strings are added in parallel to meet the required capacity. Twelve-volt batteries are
considered the most cost-effective solution for systems comprising up to 4–6 parallel
strings, and two-volt batteries are usually preferred for larger systems. Suggestions on the
selection of lead–acid battery types in different scenarios are given in [49], where there is a
need to strike a balance between lifespan, cost and energy density. The supercapacitors
are commercially available in modules, consisting of several cells connected in series;
the maximum voltage of a single cell is usually 2.7 V. For the selection of supercapacitors,
the capacity is determined by the maximum energy variation required by the system and its
operating voltage range [26]. As supercapacitors are much more expensive than batteries,
a thorough cost-benefit analysis should take place to come up with the appropriate size of
the two components.
The aim of this paper is to propose a complete methodology to hybridize a lead–acid
battery ESS with supercapacitors for standalone DC microgrids. A new power allocation
control scheme and battery degradation model are proposed to accurately capture and
maximize the battery life extension due to hybridization. A thorough techno-economic
analysis takes place based on a 90-day electricity dataset from a real-life 4.8 kW standalone
microgrid installed in rural India, to determine the viability of the hybridization at six
different scenarios. The main novel points of this study are as follows:
Energies 2021, 14, 507
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•
•
•
A complete ESS hybridization methodology is developed, including the control design,
battery degradation and economic viability analysis, while the results are based on
data from a real-life DC microgrid.
A new power allocation control scheme is proposed, based on power filtering that
strictly abides by the supercapacitors’ voltage operating limits.
A new degradation mechanism model for lead–acid batteries (or simply "battery
degradation model") is introduced that accounts for the combined effect of microcycles
DoD and battery temperature, appropriate for high time-resolution profiles.
The structure of the paper is as follows. Section 2 presents the control scheme and
power filtering method that respects the supercapacitors’ voltage limits, while the new
battery degradation model that accounts for both DoD and temperature impact is given
in Section 3. In Section 4, the real-life case study of this paper is detailed, followed by a
sensitivity analysis on the thermal parameters. Section 5 discusses the economic benefit
from the hybridization at six different scenarios and Section 6 concludes this study.
2. Topology and Control Strategy of the HESS
The HESS under consideration corresponds to the case-study 24 V DC microgrid
described in Section 4. Figure 1 shows a simplified diagram with aggregated PV generation
and load that involves the proposed parallel, fully-active HESS. Both the battery bank and
supercapacitors bank have their own bidirectional DC/DC converter to allow separate
power flows according to the controller. The objective of the controller is multi-fold: to
regulate the DC link voltage and maintain the power balance in the microgrid, whilst
cleverly allocating the power demand between the two storage components to smooth out
the battery power profile but respecting the supercapacitor voltage limits. The details of
the topology and control strategy follow.
Figure 1. Selected system topology: DC microgrid with a parallel, fully-active hybrid energy storage
system (HESS).
2.1. The Fully Active Topology
Among various HESS configurations, the parallel, fully-active topology allows for
maximum flexibility when designing and operating the system. This flexibility, however,
comes at the cost of an additional DC/DC converter for the supercapacitors on top of the
one used for the batteries. Nonetheless, given the low DC bus voltage of 24 V, a simple
bidirectional two-quadrant converter is sufficient to step-up the supercapacitors’ voltage
(8–16 V in this paper), which is an effective and economical solution [5]. It is also worth
noting that the power rating of the supercapacitor converter is lower than the batteries’
one, here sized at about 30% of the ESS rated power for the case study of Section 4. At any
time, the HESS maintains the power balance in the microgrid by supporting any deviation
between PV generation PPV and load PLoad with power PHESS , the latter consisting of the
batteries PB and supercapacitors PSC contribution. The level of these contributions at any
time is determined by the controller detailed in the following section.
Energies 2021, 14, 507
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2.2. Control Strategy
Figure 2 depicts the overall control strategy designed for the HESS. It comprises three
main parts: the outer voltage control loop, the power allocation mechanism and the inner
current control loop. The outer voltage control loop regulates the DC bus voltage Vo to
the reference Vo ∗ by calculating the total reference power Ptot∗ that the HESS needs to
inject (if positive) or consume (if negative) to maintain the power balance in the microgrid.
The power allocation scheme then splits Ptot∗ to the two components fed into the battery
Pb∗ and supercapacitor Psc∗ ; the battery undertakes a low-pass-filtered version of Ptot∗ ,
possibly adjusted by ∆Psc when the supercapacitors operate close to their limits, and the
remaining goes to the supercapacitors. Finally, these reference power values are converted
to reference currents Ib∗ and Isc∗ that drive the inner loop current controllers in adjusting
the duty cycle Db and Dsc of the separate DC/DC converters. The power filtering and
supercapacitor voltage limitation scheme are described in more detail below.
Figure 2. Proposed HESS control scheme.
2.2.1. Power Filtering
Supercapacitors have several features, such as fast dynamics, long cycle life and low
internal resistance, which make them ideal to deal with the high-frequency power components of the load. Although some studies indicate capacitance drop for high frequencies of
operation [50], they remain very useful in absorbing the high charge/discharge rates to
protect the batteries. To this end, a low pass filter (LPF) is employed here to disaggregate
Ptot∗ to the slow-changing Pb∗ and fast-changing Psc∗ . The simplest approach for the LPF
would be a first-order continuous time filter, with a transfer function
H (s) =
1
1+T·s
(1)
where T is the time constant. The higher the time constant, the better the filtering, albeit
requiring larger capacity from the supercapacitors; if it is too high, their capacity may be
quickly outspent, effectively disabling them for large periods of time. A discussion on the
selection of the time constant follows in Section 2.3.
High-order filters generally perform better in cutting high-frequency signals and have
been employed in power filtering of energy storage systems in the literature [24,51]. There
are two broad categories of digital filters: finite impulse response (FIR) filters and infinite
impulse response (IIR) filters, based on the time domain characteristics of their impulse
response functions. Generally, high-order IIR filters are seen to exhibit convergence and
stability issues, which is in contrast to FIR filters that feature low phase distortion and
are always stable without feedback loops [51–53]. Therefore, the second filter alternative
considered in this study is an FIR filter, expressed in the z-domain as
Energies 2021, 14, 507
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N −1
H (z) =
∑
h[ n] z−n
(2)
n =0
and in the discrete time domain as
h[n] = hd [n]ω [n] =
sin(nωc )
ω [n]
nπ
(3)
where ω [n] represents a window function. The window function (e.g., Hamming window [54], Kaiser window [55]) is used in cutting of the low-pass infinite pulse to obtain
the FIR coefficients. The design parameters of an FIR filter are the filter length N and the
cut-off frequency ωc .
A important feature of a high-order FIR filter is the group delay, directly related to
the length of the window N [52]. High-length windows yield better low-pass filtering
performance, albeit with a larger group delay. However, such delays lead to power lags that
need to be accommodated by the supercapacitors, which may lead to power oscillations
and suboptimal performance in some cases, as shown in Section 2.3. Selection of the FIR
filter length and cutoff frequency is a delicate procedure that needs to strike a balance
between the filtering effect and group delay.
2.2.2. Supercapacitor Voltage Limitation
The supercapacitors’ voltage varies substantially during normal operation due to their
strong coupling with the stored energy: to fully charge, the voltage needs to get to the
nominal value; to fully discharge, the voltage should decrease as low as possible. This
variation, however, must abide by certain safety limits VSC,min ≤ VSC ≤ VSC,max to account
for structural characteristics of the supercapacitors and input voltage limitations of the
power converter.
Take the supercapacitor module used in this case study (see Section 4) as an example [56]. The maximum voltage VSC,max is set to the nominal value of 16 V (6 cells in
series—about 2.7 V per cell), while the minimum value VSC,min is selected as 8 V, so that the
DC/DC converter is required to boost the voltage up to three times to reach the target 24 V.
Past experience has shown that the conduction and switching losses of such converters
skyrocket for conversion ratios of higher than three [57], which entails inefficient operation
or even inability of the power converter to step-up the voltage. Within this voltage range,
the usable energy capacity portion of the supercapacitor ESC would be
ESC =
1
1
2
2
2 CVSC,max − 2 CVSC,min
1
2
2 CVSC,max
=
162 − 82
= 75%
162
(4)
Utilizing 75% of the available energy is quite reasonable, especially given the simple
and economical power converter employed.
To enforce adherence of these limits, the supercapacitor limitation scheme of Figure 2
is used. The main idea is to compensate for any voltage violation by adjusting the battery
power Pb∗ by a signal ∆PSC . ∆PSC will be zero while operating within limits, but it will
get positive values when the supercapacitors voltage exceed the upper bound (need to
discharge) or negative values when it goes below the lower bound (need to charge). To this
end, two PI controllers are employed with appropriate saturation limits and anti-windup
mechanisms, each undertaking regulation around one of the two voltage limits. While
voltage is in the safe region, both PI controllers are driven to their zero saturation bound,
thus exporting zero ∆PSC ; when VSC > VSC,max , the upper PI controller gets activated while
the lower controller remains stuck at zero, which brings the voltage back to VSC,max ; when
VSC < VSC,min , the opposite happens and the lower PI controller regulates the voltage back
into the safe region. Notably, the anti-windup mechanism is crucial for this control scheme,
so that the controllers can "unstick" from saturation immediately after the voltage gets
Energies 2021, 14, 507
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out of bounds. Here, the clamping anti-windup method has been employed, but other
anti-windup alternatives will work equally as well.
2.3. Energy Management System Results
This section evaluates the proposed control scheme on a 10,000-s electricity profile
from the study-case system detailed in Section 4. The following results have been produced
through simulations in MATLAB/Simulink. As a benchmark, the conventional batteryalone ESS is considered first, as shown in Figure 3. The entire power demand PESS is
taken care of solely by the batteries PB , resulting in high-frequency power fluctuation that
accelerates the battery degradation. Please note that positive and negative power values
indicate discharging and charging respectively, while small deviations between PESS and
PB are due to power losses.
600
400
Power (W)
200
0
-200
-400
-600
PESS
PB
-800
0
2000
4000
6000
8000
10,000
Time (s)
Figure 3. Power profile in the battery-alone ESS system.
The same power profile is applied to a HESS employing different power filters, as shown
in Figures 4–6. A simple first-order LPF with a small time constant of 50 s yields a smoother
battery power profile PB in Figure 4a, as the supercapacitors absorb the fast-changing component PSC . It is worth noting that the mean value of PSC is not far from zero, which leads to
limited supercapacitor voltage variation in Figure 4b, well within the safe operating region.
600
18
400
16
Voltage (V)
Power (W)
200
0
-200
-400
-600
PHESS
PB
PSC
14
12
10
8
Vsc
Vsc,min
Vsc,max
6
-800
0
2000
4000
6000
Time (s)
(a) Power profile
8000
10,000
0
2000
4000
6000
8000
10,000
Time (s)
(b) Supercapacitor voltage
Figure 4. Power filtering and voltage results for the HESS with a first-order low-pass filter (LPF) (T = 50 s).
When increasing the time constant to 300 s, the power profile of the battery becomes
clearly smoother in Figure 5a, albeit at the cost of risking voltage going out of limits in
Figure 5b. As explained by Equation (4), there is strong relation between the energy stored in
the supercapacitors and their terminal voltage. For the selected supercapacitor module [56],
the absolute maximum voltage is 17 V, which creates a safety margin of 1 V above the 16 V
nominal voltage. In addition, the lower voltage bound of 8 V set is not really a strict limit; the
power converter can readily operate slightly lower, e.g., at 7 V, for a short time, temporarily
resulting in more losses that will not however risk the system integrity for a few seconds.
Energies 2021, 14, 507
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This safety margin of 1 V from the upper and lower voltage limits provide the space for the
proposed supercapacitor voltage limitation scheme to detect any deviation and act upon in
by nullifying PSC whenever VSC is exceeding the limits. In fact, the designed control is very
fast in responding to these events, recording an imperceptible voltage overshoot of less than
0.01 V in the example of Figure 5b, well below the 1 V margin.
18
Voltage (V)
16
14
12
10
8
Vsc
Vsc,min
Vsc,max
6
0
2000
4000
6000
8000
10,000
Time (s)
(b) Supercapacitor voltage
(a) Power profile
Figure 5. Power filtering and voltage results for the HESS with a first-order LPF (T = 300 s).
A similar smoothing effect is achieved by the high-order FIR filter except for a noticeable group delay, as shown in Figure 6 (N = 420, ωc = 0.0005π rad/sample). This
results in a phase delay between PB and PHESS , seen more clearly by comparing the zoom
boxes in Figures 5a and 6a. This group delay may trigger power oscillations and pose
control and stability challenges, and use the supercapacitors’ capacity in a suboptimal
manner. The conclusion from this investigation is that "too much" filtering may lead to the
opposite result, with power spikes and oscillations that do not resemble a smooth profile
for the battery. There is no golden rule on the selection of the filter parameters, as they
strongly depend on the electricity profile and the supercapacitors’ capacity. The parameters
selection for the case study of this paper is discussed in Section 4.
18
Voltage (V)
16
14
12
10
8
Vsc
Vsc,min
Vsc,max
6
0
(a) Power profile
2000
4000
6000
8000
10,000
Time (s)
(b) Supercapacitor voltage
Figure 6. Power filtering and voltage results for the HESS with a finite impulse response (FIR) filter (N = 420 and
ωc = 0.0005π rad/sample).
3. Battery Degradation Model
This section presents a new degradation model for lead–acid batteries used to evaluate
the contribution of the hybridization to the battery life. This is a cycle-counting model
that accounts for the cumulative fatigue from the most prevalent stress factors: the DoD
and battery temperature. Most conventional models explore these effects separately and
focus on medium and deep discharge cycles, i.e., DoD higher than 10%, thus neglecting
smaller changes in the SoC, i.e., microcycles. However, the ESS in small-scale PV microgrids
often experiences irregular charging/discharging patterns that involve lots of microcycles
Energies 2021, 14, 507
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and rapidly changing currents that have increased DoD-related and temperature-related
impact on the battery life. This paper shows that it is important in these cases to use highresolution time series that allow for accurate approximation of both effects and thus the
battery degradation. The objective of the following paragraphs is to describe a methodology
for such a degradation model, which can be easily adapted to any lead–acid battery given
the appropriate coefficients and inputs.
3.1. Depth of Discharge (DoD) Model
To evaluate the DoD degradation, one needs first to extract the number of cycles and
their depth of discharge as explained in Section 3.1.1, to be used afterwards in a cycle life
model to quantify their impact on the battery life in Section 3.1.2.
3.1.1. Rainflow Counting Method
The most widely adopted method to capture the DoD profile is the rainflow counting
method. Using the SoC variation as an input, this method extracts the number of cycles,
their depth and length. An example is given in Figure 7: the plot of SoC over time is
rotated 90◦ clockwise and treated as a roof upon which raindrops fall. Starting from a
local maximum point “a”, the rainflow reaches the next local minimum point “b” and then
drops. The portion of the profile (b-c-b’) forms a whole cycle, denoted as “whole-cycle
1”. Then, the flow continues dropping till point “d” when it meets the minimum SoC
value. The transition (a-b-d) is counted as a half-cycle. Thereafter, “d” is set as the new
initial point for the next raindrop and these steps are repeated to identify the remaining
whole and half cycles, as illustrated in Figure 7. More details on the implementation of the
Rainflow counting method may be found in [6,40].
Figure 7. Example application of the rainflow counting algorithm based on a SoC profile.
3.1.2. Cycle Life Model—CL(DoD)
Given the extracted cycles pattern, the next step is to evaluate their effect on the battery
life. This is done by calculating the cycle life CL(d), i.e., the number of cycles that the battery
will last if the DoD of all cycles is d. Usually, CL(d) is a mathematical expression that is unique
for every battery and is derived based on information from the manufacturer datasheet.
An example of such datasheet information is given with the purple star markers in
Figure 8a for Trojan’s deep-cycle gel lead–acid battery [58]: the cycle life heavily depends
on the DoD, with higher DoD resulting in shorter cycle life. Since only a few such data
points are typically provided in the datasheet, there is a need for a mathematical model to
capture the cycle life for all possible DoDs. One commonly used such model, thereafter
referred to as the conventional model, is given by [40–42]
CL(d) = a5 d5 + a4 d4 + a3 d3 + a2 d2 + a1 d + a0
(5)
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where ai are coefficients extracted by fitting Equation (5) on the given data points. For the
study-case battery, the fitted model is shown with a blue line in Figure 8a in regular scale
and in Figure 8b in logarithmic scale, while the ai coefficients are given in Table 1.
However, a major limitation of this method is that it does not accurately capture
the effect of microcycles with DoD less than 10%. Since the datasheet rarely includes
information for so low DoD, the Conventional model may overestimate the impact of the
microcycles, projecting low cycle life even for near-zero DoD (see how to blue line meets the
y-axis in Figure 8a). This proves to be problematic when there is access to high resolution
time series that permits visibility on the numerous existing microcycles. For these cases,
a microcycles model is required, such as [14,22]
CL(d) = b4 d−4 + b3 d−3 + b2 d−2 + b1 d−1 + b0
(6)
where bi are again coefficients extracted from the datasheet. Accurate identification of
these coefficients would normally require data points for smaller DoD; in absence of this
information, this paper assumes additional extrapolated points using a linear relationship
in the logarithmic scale, as shown with green markers in Figure 8b (coefficients in Table 1).
This way, the cycle life is very high for small DoD, providing a more realistic approximation
of the limited microcycles effect.
In fact, without sufficient input data at low DoD, both models are approximations of
the microcycles impact: a pessimistic one with the Conventional model and an optimistic
one with the microcycle model. However, the case study of Section 4 shows that the former
is clearly unsuitable in presence of microcycles, while the latter yields reasonable results.
In addition, with the microcycle model the supercapacitor’s contribution to the battery life
extension is more limited, which makes it a conservative benchmark when evaluating the
economic viability of the hybridization. Therefore, this paper recommends adoption of the
microcycle model as the safest approach in the design of a HESS.
Table 1. Coefficients of conventional and microcycle models.
Model
Conventional model
a5 = −46,573
a2 = 212,925
a4 = 187,495
a1 = −76,291
a3 = −288,854
a0 = 11,761
Microcycle model
b4 = −1.345 × 10−12
b1 = 601.5
b3 = 1.495 × 10−7
b0 = −122.5
b2 = −1.507 × 10−3
104
2
108
Datasheet Data
Conventional model
Microcycles model
1.5
Cycle life (cycles)
Cycle life (cycles)
Coefficients
1
0.5
0
0
0.2
0.4
0.6
Depth of Discharge
(a) in regular scale
0.8
1
Datasheet Data
Extrapolated Data
Conventional model
Microcycles model
106
104
102
10-4
10-3
10-2
Depth of Discharge
(b) in log-log scale
Figure 8. Battery cycle life vs. depth of discharge (DoD) curve.
10-1
100
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3.2. Temperature Model
The battery’s operating temperature is also an important factor to the battery life.
In the following, Section 3.2.1 explains how to calculate the battery temperature and
Section 3.2.3 how to evaluate its effect on the cycle life.
3.2.1. Battery Temperature Calculation
The battery temperature T depends mainly on the ambient temperature Ta and the
power losses Ploss . Taking into account the thermal inertia of the system, their combined
effect can be expressed in the Laplace domain by the transfer function of a first-order low
pass filter
P · R + Ta
(7)
T (s) = loss th
1 + tc · s
where Rth is the thermal resistance and tc is the thermal time constant. Equation (7) reflects
the fact that any change in Ta or Ploss will not be transferred to the battery temperature
immediately. Ta is an input to the model, while Ploss is the aggregate power losses on the
battery Ploss_battery and on the power converter Ploss_converter (assuming they are both placed
in the same cabinet):
Ploss = Ploss_battery + Ploss_converter
(8)
The converter power losses are found directly from the DC/DC converter efficiency.
Typical efficiencies vary around 95% [59], thus Ploss_converter is assumed here to be 5% of the
actual power output at any time. The internal losses of the battery is described in detail in
Section 3.2.2 below.
3.2.2. Battery Electrical Equivalent Circuit Model
The battery internal losses Ploss_battery are calculated using the equivalent circuit of
the battery shown in Figure 9. This circuit involves the following parasitic elements [60]:
(i) an internal series resistance Rserial that reflects losses due to ohmic polarization of
instantaneous nature; (ii) a pair of resistance/capacitance Rt_ f ast , Ct_ f ast that accounts for
activation polarization (or charge-transfer) phenomena with fast dynamics; and (iii) another
pair Rt_slow , Ct_slow that models slower concentration polarization effects. The parameter
values used in this paper are listed in Table 2, taken from [61]. The power losses were
found by solving the algebraic and differential equations of this circuit for the given input
battery current Ibat :
Ploss_battery =
2
Ibat
Rserial
+
Vt_2 f ast
Rt_ f ast
+
2
Vt_slow
Rt_slow
(9)
Ibat = Ct_ f ast
dVt_ f ast
Vt_ f ast
+
dt
Rt_ f ast
(10)
Ibat = Ct_slow
V
dVt_slow
+ t_slow
dt
Rt_slow
(11)
Table 2. Parameters of lead–acid battery equivalent circuit [61].
Parameter
Value
Rserial
Rt_ f ast
Rt_slow
Ct_ f ast
Ct_slow
0.0401 × e0.0908×SoC + 0.0366 Ω
3.041 × 10−10 × e0.1874×SoC + 0.0344 Ω
0.101 × e0.0203·SoC + 0.0219 Ω
1200 F
5000 F
It is worth noting that the relation between Ploss_battery and Ibat is non-linear; there
is a quadratic dependence of the I 2 R losses on the current, which means that the charg-
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ing/discharging pattern matters for the losses. For example, charging the battery with a
constant current yields lower power losses than with a fluctuating current with the same
mean value. However, the equivalent model of Figure 9 does not consider any dependence
of the parasitic elements on the operating frequency, which some experimental studies
have shown to be apparent.
Figure 9. Equivalent electrical model of the lead–acid battery [61,62].
3.2.3. Temperature’s Effect on Cycle Life
The temperature mainly affects the corrosion of the lead–acid battery’s positive electrode [6]: the higher the temperature, the faster the corrosion process. An investigation
in [38] has shown that there is a linear relationship between the battery temperature and
the cycle life for the same DoD, as shown in Figure 10. This means that the cycle life of the
battery CL(d) calculated in Section 3.1 is only valid at 20 ◦ C and needs to be translated to
the actual operating temperature T by multiplying with a coefficient nCL( T ) given here by
nCL( T ) = −0.0225 · T + 1.45
(12)
Normalized cycle life
1
0.9
0.8
0.7
0.6
0.5
0.4
20
25
30
35
40
45
Temperature (°C)
Figure 10. Normalized cycle life with temperature in a lead–acid battery [38].
This equation taken from [38] refers to a flooded lead–acid battery, but it is assumed
here that it applies more or less to deep-cycle gel-type lead–acid batteries as well. The typical gel battery datasheet does not provide any information on the cycle life-temperature
relationship, but it includes data on the dependence of the battery capacity loss on the temperature, which is also linear [58,63]. Therefore, in absence of datasheet information or other
relevant knowledge on the battery, this paper deems it better to use Equation (12) to model
the temperature effect rather than to ignore it completely, as often done in the literature.
3.3. The Complete Battery Degradation Model
Given the cycles profile and operating temperature calculated in the previous paragraphs, the battery fatigue damage D is given by the Palmgren-Miner rule [64]:
d=100%
D=
∑
d=0%
count(d)
CL(d) · nCL( T )
(13)
where count(d) is the number of cycles with a DoD equal to d, and CL(d) · nCL( T ) the
respective battery cycle life at battery temperature T. Equation (13) reflects that D comes
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essentially from the weighted average of the various cycles depending on their frequency
in the profile. It is worth noting that during a particular cycle, the temperature T is not
constant and may vary; here the maximum temperature recorded during each cycle is
selected for T.
The fatigue damage D gives by how much the battery has degraded for the particular
charging/discharging profile, e.g., 5%. To get an estimate of the life expectancy Lbat assuming
that the battery will operate under that profile, one needs to simply divide the duration of
the study-case profile Ndays by D:
Ndays
(14)
Lbat =
D
For example, if a 90-day profile is used that yields 5% aging, the estimated lifespan of
the battery will be 1800 days or equivalently 4.9 years. The full picture of the proposed
battery degradation model is given in Figure 11.
•
•
•
•
•
First, the input SoC profile is analyzed using the rainflow counting method to identify
the various cycles, which are then grouped together based on their DoD.
Then, the microcycle model (Equation (6)) is applied to every DoD captured to determine the respective cycle life CL(d).
Next, the battery temperature variation is calculated from Equations (7)–(11) for the
entire profile.
For every cycle, the temperature coefficient nCL( T ) is determined based on the respective temperature through Equation (12).
Finally, applying Equations (13) and (14) yields the fatigue damage D and lifespan of
the battery Lbat .
Figure 11. Flowchart of the proposed battery life estimation method.
4. Case Study and Analysis
This section outlines the case study adopted in this paper to evaluate the proposed
hybridization methodology. The electricity profile from a real-life standalone DC microgrid
is used, followed by a sensitivity analysis on the impact of various thermal factors. It
is worth noting that many parameters related to the ESS are assumed or taken from the
literature and do not necessarily correspond to the case-study microgrid. The purpose of
this section is to extract general conclusions on how different factors influence the battery
life and hybridization benefit, rather than to be contained to a specific system.
4.1. The Case Study
The system under consideration is a DC microgrid installed in rural India (Bahraich
district, Uttar Pradesh) that supplies electricity to 43 households. The microgrid comprises
a total of 4.6 kWp of solar PV generation, 24 lead–acid batteries of 12 V/100 Ah each, and a
24 V distribution network over 1 km distance. The household loads are LED bulbs (1 W or
4 W), fans (15 W) and mobile phone chargers (max 5 W). Two profiles were provided over
a period of 2 days and 90 days that include information on generation, load and ambient
temperature at 1 s time resolution. It is worth noting that the acquired profiles refer to a
subset only of the entire system.
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Figure 12a depicts the PV generation and load profiles for two days in April 2019,
extracted from the 90-day dataset. Solar generation expectedly varies slowly during the day,
although it occasionally features high-frequency oscillations due to intermittent clouding.
The domestic load profile exhibits its peak in the evening hours, when the people finish
their agricultural activities and return back to their home. This deviation between supply
and demand is the net power profile seen by the ESS. Figure 12b shows the ambient
temperature profile during that period.
40
1000
Temperature (°C)
800
Power (W)
600
400
200
0
-200
PV Power
Load Profile
5
30
25
Net Power
-400
0
35
10
20
15
Time (s)
0
5
104
(a) PV generation, load and net power profiles
10
15
Time (s)
104
(b) Ambient Temperature
Figure 12. Two-day electricity and temperature profiles.
Figure 13 depicts the 90-day profile referring to 20 February to 20 May in 2019. The electricity and ambient temperature variation is given in Figure 13a,b, both featuring the anticipated daily fluctuation; the temperature also exhibits an interseasonal variation, increasing
from about 20 ◦ C to 35 ◦ C on average. The power distribution is further studied in the
histogram of Figure 13c: the load varies usually from 0 to 200 W, while solar generation is
often zero or very low during the the night-time and low-light hours. The mismatch between
the two is the net power accommodated by the ESS, varying here from −311 W to 993 W.
To investigate how quickly the net power changes, the distribution of the rate of change of
net power (RoCoP) is given in Figure 13d. It is apparent that rates of ±50–200 W/s are not
rare at all; such high power rates for the scale of the system have a negative impact on the
battery life both in terms of DoD and battery temperature.
The following sections explore how the supercapacitors can mitigate these power
fluctuations, and how this improvement relates to the thermal parameters. The default
parameters of the system used as a benchmark below are given in Table 3. The batteryalone ESS is assumed to comprise 6 batteries, while the HESS has also 1 supercapacitor
module. The rest of the parameters are based on reasonable assumptions taken from the
literature [61,65,66] and do not necessarily reflect the case study system. For the remainder
of the analysis, the 90-day profile is used.
Table 3. Default HESS parameters.
Parameter
Value
Number of lead–acid batteries
Number of supercapacitor modules
HESS LPF time constant
Cycle life model of DoD
Thermal resistance Rth
Thermal time constant tc
Internal series resistance Rserial
Converter power losses Ploss_converter
6 (2 × 3 strings; 100 Ah; 12 V)
1 (BMOD0500 P016: 500 F; 16 V)
45 s (1st order LPF)
Microcycle model
0.6 ◦ C/W
18,000 s (5 h)
0.0401 × e0.0908×SoC + 0.0366 Ω
5%
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50
Temperature (°C)
Power (W)
1000
500
0
Net
-500
0
1
PV Power
2
3
40
30
20
10
Load Profile
4
5
6
0
7
Time (s)
0
10
1
2
1.5
1
0.5
993W
-311W
0
200
400
600
800
1000
Power (W)
(c) Histogram of the power distribution
Frequency (log scale)
2.5
Frequency
5
6
7
106
108
PV Power
Load Profile
Net Power
-200
4
(b) Ambient Temperature
106
3
0
3
Time (s)
(a) Power profiles
3.5
2
6
106
104
102
100
-100
0
100
200
300
Rate of change of power (W/s)
(d) Histogram of the rate of change of net power distribution
Figure 13. Ninety-day electricity and temperature profiles.
4.2. Power Filtering Results and Analysis
Based on the given 90-day profile and design specifications of Table 3, the optimal
parameters for the two power filter alternatives are extracted through exhaustive search
(testing wide ranges for each of the parameters, and select the ones that deliver the most
favorable performance) and are appended in Table 4. Apparently, both filters increase
the expected battery lifespan by almost the same amount. The first-order filter effectively
smooths out the power profile resulting in much lower standard deviation in battery RoCoP
and number of microcycles compared to the battery-alone system. The FIR filter yields
approximately the same life extension but by squeezing more the number of microcycles
while allowing for more deep cycles with higher DoD compared to the first-order LPF.
Given that the FIR filter comes also with some stability and control issues related to the
group delay, the first-order LPF is selected as more preferable and used in the remainder of
the paper.
Table 4. Hybridization benefit with the two power filters.
Parameter
Battery-Alone
1st Order LPF
FIR Filter
LPF parameters
Expected battery life
Standard deviation of the PB RoCoP
Number of microcycles (<10% DoD)
Number of deep cycles (≥10% DoD)
N/A
1858 days
1.7 W/s
1675
89
T = 45 s
2009 days
0.3 W/s
499
89
N = 350; ωc = 0.007π rad/sample
2003 days
1.3 W/s
212
91
For a closer look at the filtering effect on the battery life, Figure 14 compares the
battery RoCoP and DoD distribution between the battery-alone and HESS cases. Clearly,
the hybridized batteries are exposed to a much more narrow RoCoP spectrum with substantially smaller power rates in Figure 14a, which translates to much fewer microcycles in
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Figure 14b (logarithmic scale). Please note also the large proportion of microcycles over the
total number of cycles in each case in Table 4. This analysis consolidates the importance
of an accurate battery degradation model with microcycles DoD resolution in order to
properly assess the hybridization benefit.
104
Battery-alone
HESS
106
104
102
10
Counted cycles (log scale)
Frequency (log scale)
108
Battery-alone
HESS
102
100
0
-100
0
100
200
300
Rate of Change of Power (W/s)
(a) Histogram of the rate of change of battery power
0
0.1
0.2
0.3
0.4
Depth of Discharge (%)
(b) Histogram of the microcycles distribution
Figure 14. Hybridization effect on the battery operation.
4.3. Sensitivity Analysis of Thermal Parameters
Although the importance of the battery temperature on the battery life is a well-known
fact, it is still somewhat unclear how the supercapacitors can influence this phenomenon
and therefore the hybridization benefit. For this reason, the following paragraphs present a
sensitivity analysis, in which some of the most prevalent thermal parameters, i.e., thermal
resistance Rth , thermal time constant tc and converter power losses Ploss_converter , are varied
over a wide range to capture their effect on the temperature and battery life with and
without the hybridization. The default parameters of Table 3 are used as a benchmark.
4.3.1. The Effect of Thermal Resistance
The thermal resistance Rth reflects how the power losses from the battery and power
converter translate to battery temperature. Figure 15a shows the resulting HESS battery
temperature for Rth varying from 0 to 1 ◦ C/W in the form of sorted curves (i.e., the
temperature values of the entire profile are sorted from high to low). Clearly, Rth is a crucial
factor, which may lead to very high temperatures for large values.
Figure 15b illustrates how this relates to the battery life with and without the hybridization. The Rth impact is indeed negative, but the HESS seems to be much more
resilient compared to the battery-alone ESS. This is because the hybridization effectively
reduces the battery internal power losses Ploss_battery due to a smoother battery current Ibat ,
as explained in Section 3.2.2; this entails lower battery temperature, and fewer number of
cycles in total. As a result, the life extension from hybridization in Figure 15c increases
in an exponential manner with Rth . The conclusion from this investigation is that the
supercapacitors not only alleviate some of the DoD degradation, but they also bring a
thermal benefit which proves to be substantial when the thermal resistance is high.
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Cell Temperature (°C)
80
Rth = 1°C/W
60
40
Rth = 0°C/W
20
0
0
2
4
6
8
106
(a) Sorted values of battery temperature for different Rth
Number of values
7
Life (years)
6
5
4
3
2
Lifetime extension (%)
60
Battery alone
HESS
50
40
30
20
10
0
-10
0
0.2
0.4
0.6
0.8
0
0.2
Thermal resistance (°C/W)
0.4
0.6
0.8
Thermal resistance (°C/W)
(c) Life extension from hybridization
(b) Battery life
Figure 15. Thermal resistance’s effect on battery life.
4.3.2. The Effect of the Thermal Time Constant
The thermal time constant tc plays essentially the role of inertia for the battery temperature (see Equation (7)), typically few hours [66,67]. Small values entail steep temperature
rise during short-term power peaks, whereas large values effectively flatten out the temperature distribution. This is why a tc = 1 h in Figure 16a results in occasional very high
temperatures, but most of the time the temperature is slightly lower than the tc = 10 h case.
This effect is reflected to the battery life and hybridization benefit as Figure 16b,c show; the
trend is somewhat similar to the Rth effect but with a reversed x-axis. Again, the supercapacitors may prove of little or major importance depending on the time constant value.
4.3.3. The Effect of Converter Power Losses
The converter power losses Ploss_converter have a rather limited impact on the battery
temperature as shown in Figure 17a: higher losses lead to higher temperatures, but the
difference is not as significant as with the previous factors. This translates to a more limited
effect on the battery life in Figure 17b and to a linear life extension from the hybridization
in Figure 17c. The general conclusion from this sensitivity analysis is: the more severe
the thermal conditions of the ESS, the more useful the supercapacitors are. This gives
an additional perspective on the hybridization benefits, apart from the most commonly
considered DoD impact.
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Cell Temperature (°C)
120
100
tc = 3600s (1h)
80
60
40
tc = 36000s (10h)
20
0
0
2
4
6
8
106
(a) Sorted values of battery temperature for different tc
Number of values
30
Lifetime extension (%)
6
Life (years)
5.5
5
4.5
4
Battery alone
HESS
3.5
1.5
2
2.5
3
20
15
10
5
0
3.5
104
Thermal constant (s)
25
1.5
2
2.5
3
3.5
104
Thermal constant (s)
(b) Battery life
(c) Life extension from hybridization
Figure 16. The thermal time constant’s effect on battery life.
Cell Temperature (°C)
70
60
Ploss = 10%
50
40
30
Ploss = 0%
20
10
0
2
4
6
8
106
Number of values
(a) Sorted values of battery temperature for different Ploss_converter
16
Life (years)
5.5
Lifetime extension (%)
Battery alone
HESS
5
4.5
0
2
4
6
Power loss (%)
(b) Battery life
8
10
14
12
10
8
6
4
2
0
2
4
6
8
Power loss (%)
(c) Life extension from hybridization
Figure 17. Converter power losses’ effect on battery life.
10
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5. Economic Analysis and Discussion
Although the previous section shows that hybridization is more or less beneficial to
the battery’s life, it is not clear when it makes sense in terms of economic viability. Here,
the benefit of more long-lived batteries is weighted against the additional investment
burden of the supercapacitors and their power converter to evaluate the overall economic
benefit of the hybridization. The case study of the previous section is used as an example,
assessed in six different scenarios to understand when the investment is viable and when it
is not.
The net present cost (NPC) metric is adopted in this paper to evaluate the total
investment required for the two alternative ESS over the entire project life. NPC involves
the initial one-time investment I0 , any replacement costs R and operation and maintenance
(O&M) costs OM during the lifetime of the project [22,68]:
NPC = I0 + R + OM
(15)
In the battery-alone system, I0 comprises the costs for the batteries Cbat Ebat and
bat , while the HESS involves additionally the supercapacitors costs
their converter Cconv Econv
sup
Csup Esup and their own converter costs Cconv Econv . Equation (16) shows the full picture for
the HESS case.
sup
bat
I0 = Cbat Ebat + Csup Esup + Cconv ( Econv
+ Econv )
(16)
The parameters used in this paper are given in Table 5. The capital cost accounts for
the main investment. According to [21], the capital cost of lead–acid batteries in 2018 was
approximately 260 $/kWh and it was predicted to drop to 220 $/kWh by 2025. Assuming
that this project starts in 2020, a battery capital cost of 250 $/kWh is considered, with a
discount rate of 2.4%. The capital cost of supercapacitors is typically 10,000 $/kWh [69],
as adopted for example in the case study of [70]. The O&M costs of supercapacitors are
generally lower than that of batteries, selecting here 0.1% and 0.45% of the investment,
respectively, based on [21]. The cost of the power converters is taken from [21,68].
Assuming a project lifetime of 15 years, the replacement costs R in both batteryalone ESS and HESS refer only to the batteries, since the supercapacitors and converters
lifespan typically reaches or exceeds 15 years [21,68]. Given the battery lifespan Lbat
calculated in years by the proposed degradation model in Section 3, the batteries need to
be replaced r = 15/Lbat − 1 times during the project lifetime; every replacement will cost
Cbat Ebat adjusted by the annual market discount rate dr that reflects the fact that technology
becomes cheaper over time. As r may not be an integer, the equation below involves the
cost of full replacements ⌊r ⌋ (rounded down) plus the cost of the final replacement that
accounts only for the remaining years and is adjusted by r − ⌊r ⌋. The latter intervention is
a simple way to account for capital recovery after the project life.
⌊r ⌋
R=
∑
n =1
Cbat Ebat
(1 + dr )
nLbat
+ (r − ⌊r ⌋)
Cbat Ebat
(1 + dr )⌈r⌉ Lbat
(17)
Finally, the O&M costs increase every year due to aging of the equipment, reflected in
the actual discount rate d. During the first battery lifetime, the annual maintenance costs
will be an adjusted version of OM0bat based on d, where OM0bat is a percentage of the initial
investment (see Table 5). When the batteries are replaced, the maintenance costs will be a
discounted value of OM1bat , which is again a percentage but of the respective replacement
cost (see Equation (17)). The final O&M expression is given below for the HESS.
15/Lbat Lbat
OM =
OMnbat
−1
∑ ∑ (1 + d ) t
n =1 t =1
15
+
sup
OM0
∑ (1 + d ) t
t =1
15
+
OM0conv
∑ (1 + d ) t
t =1
(18)
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Table 5. Economic parameters [21,68,69].
Parameter
Lead Acid Battery
Supercapacitor
Power Converters
Capital cost Cbat , Csup , Cconv
bat /Esup
Capacity Ebat , Esup , Econv
conv
sup
Initial O&M costs OM0bat , OM0 , OM0conv
250 $/kWh
7200 Wh
0.45% of invest.
10,000 $/kWh
18 Wh
0.11% of invest.
0.25 $/W
1000 W/ 300 W
1 $/kW
Other Economic Parameters
Market discount rate dr
O&M actual discount rate d
2.4%
−5%
It is worth noting that the O&M costs of the hybridized system will not fundamentally
differ from the battery-alone ESS. Being both electrochemical storage devices, the battery and supercapacitor require simple and straightforward maintenance, i.e., keeping
the surface clean and the connectors sealed etc. [71]. The skillset required by the local
technicians for installation, operation and maintenance is practically the same in the two
systems, which does not create any additional barriers in adopting the HESS in isolated
rural communities. However, it should be noted that supercapacitors consumables are not
as readily available as lead–acid batteries in local markets in rural India, although currently
the market size of Indian supercapacitor manufacturing industry grows steadily every
year [72].
5.1. Base Scenario
The base scenario refers to the default HESS parameters of Table 3 and the economic
considerations of Table 5. This includes a set of reasonable assumptions corresponding to a
realistic system, used thereafter as a benchmark for the remaining scenarios. The results of
the techno-economic analysis are given in Table 6. The battery life in the basic scenario is
estimated to be 5–5.5 years, which is well-aligned with industry’s expectations for real-life
microgrids [71]. The supercapacitors’ contribution reduces the total number of cycles by
2/3, mainly the microcycles, which translates to about 8% longer lifespan for the batteries. However, given the additional investment costs in the HESS, the economic benefit is
much more limited at 1.9%. This makes the hybridization economically viable, albeit very
marginally. The following scenarios explore how these numbers change for different thermal
and economic considerations.
Table 6. Results of the base scenario.
Parameters
Battery-Alone
HESS
Total number of cycles
Life estimation
Life estimation
Number of battery replacements
Invest. on Supercapacitor
Invest. on Battery
Invest. on Converters
O&M
Total invest.
1754
1858 days
5.09 years
1.95
0
4734 $
250 $
140 $
5124 $
579
2009 days
5.50 years
1.73
184 $
4386 $
325 $
132 $
5027 $
Life extension
Economic benefit
8.1%
1.9%
5.2. Scenario 2: Conventional Cycle Life DoD Model
The discussion in Section 3.1.2 outlines two cycle life models that evaluate the DoD
degradation effect: the conventional model designed for cycles with substantial DoD,
and the microcycle model that accounts also for the cycles with very little DoD. Given that
Energies 2021, 14, 507
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the case-study electricity profile is of high time-resolution and the numerous microcycles
are visible, it is of paramount importance to use the latter model in all analyses, as has been
done throughout this paper. To support this claim, scenario 2 employs the conventional
model instead, with the results given in Table 7. Clearly, the battery degradation is severely
overestimated, yielding about 1 year lifespan for the battery-alone and 3 years for the
HESS. Although, hybridization seems very beneficial indeed in this case, the results of
1-3 years are not realistic [71], highlighting that this type of model can not reflect reality
and should not be used to inform an investment. In fact, the main conclusion from this
scenario is how important is to use a microcycles life model when the SoC profile is of high
time-resolution and the microcycles are visible. In cases that a microcycle model is not
available, it is preferable to completely disregard the microcycles from the profile when
evaluating the DoD degradation.
Table 7. Results of scenario 2.
Parameters
Battery-Alone
HESS
Life estimation
Number of battery replacements
Total invest.
1.05 years
13.33
22,346 $
3.04 years
3.93
8382 $
Life extension
Economic benefit
190.6%
62.5%
5.3. Scenario 3: Poor Thermal Characteristics
The thermal parameters of Table 3 are indicative and strongly depend on the specific
system and environment. Their influence on the battery life is discussed in Section 4.3; here,
the respective economic impact is assessed in a scenario with worse thermal characteristics
(e.g., poor ventilation and thermal management system): thermal resistance 0.8 ◦ C/W,
thermal time constant 14,400 s (4 h) and converter losses 8%. For example, [66] shows that
the thermal resistance can be in some cases as high as 1.1 ◦ C/W and the thermal constant
around 3–4 h. The results of Table 8 show a lifespan reduction of more than a year in
both systems compared to the base scenario due to the higher battery temperature. These
severe thermal conditions result in a battery life falling short of the industrial targets [71],
but hybridization manages to mitigate this impact to a large extent. The contribution of the
hybridization is considerable indeed, extending the battery longevity by more than 20%,
which translates to about 12% economic benefit. Clearly, hybridization is highly beneficial
in this case, which indicates that a HESS is a good solution under poor thermal conditions.
Table 8. Results of different scenarios of thermal characteristics.
Scenario 3 (Poor Thermal Char.)
Parameters
Life estimation
Number of battery replacements
Total invest.
Life extension
Economic benefit
Scenario 4 (Good Thermal Char.)
Battery-Alone
HESS
Battery-Alone
HESS
3.80 years
2.95
6627 $
4.59 years
2.27
5840 $
5.72 years
1.62
4605 $
5.93 years
1.53
4716 $
20.7%
11.9%
3.7%
−2.4%
5.4. Scenario 4: Good Thermal Characteristics
On the other hand, improved thermal characteristics should affect the results in the
opposite way. Here, the thermal parameters are: thermal resistance 0.4 ◦ C/W; thermal
time constant 21,600 s (6 h); [67,73] and converter losses remain at 5%. For example, [73]
shows that with a properly designed cooling system, the thermal resistance will almost
Energies 2021, 14, 507
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be lower than 0.4 ◦ C/W, or even be reduced to 0.2 ◦ C/W. Table 8 shows that the battery
life of the only-battery system meets and exceeds the industry expectations, which entails
marginal only life improvement from hybridization and a negative economic benefit indeed.
In other words, the hybridization contribution is too little to overcome the relevant financial
overhead. This highlights once again the importance to consider both temperature and
DoD factors in a battery degradation model to yield reliable conclusions.
5.5. Scenario 5: Economic Parameters in Favor of Hybridization
In order to assess the influence of the economic parameters on the viability of the
hybridization, this section repeats the analysis assuming conditions more favorable to
the supercapacitors. Specifically, the supercapacitors’ capital cost is reduced by 20% to
8000 $/kWh, the batteries are priced 12% higher at 280 $/kWh, the market discount rate
dr drops to 0.4% and the O&M discount rate d is assumed to be −1% (see Table 5 for
comparison). The resulting Table 9 differs from the base case Table 6 only in the financial
figures, now increasing the economic benefit of the hybridization to 3.6%. Apparently,
this is not fundamentally different from the 1.9% in the base case, which entails that
the hybridization viability is more sensitive on the thermal parameters, rather than the
economic ones.
Table 9. Results of different scenarios of economic parameters.
Scenario 5 (In Favor of Hybr.)
Parameters
Life estimation
Number of battery replacements
Invest. on Supercapacitor
Invest. on Battery
O&M
Total invest.
Scenario 6 (Against Hybr.)
Battery-Alone
HESS
Battery-Alone
HESS
5.09 years
1.95
0
5824 $
150 $
6224 $
5.50 years
1.73
147 $
5388 $
140 $
5999 $
5.09 years
1.95
0
3732 $
139 $
4122 $
5.50 years
1.73
224 $
3467 $
132 $
4148 $
Life extension
Economic benefit
8.1%
3.6%
8.1%
−0.6%
5.6. Scenario 6: Economic Parameters against Hybridization
By contrast, this scenario explores economic parameters that stand against the hybridization: supercapacitors cost $12,000/kWh, battery costs $220/kWh, 5% battery market
discount rate and −10% O&M discount rate. Table 9 shows a slightly negative economic
benefit which renders the hybridization marginally inviable. Still, a drop from 1.9% in
the base case to −0.6% here is very limited considering the substantial variations in the
capital costs, which essentially confirms the relative insensitivity of the hybridization to
the economic parameters.
In fact, the main conclusion from this investigation is that the main factors to assess
whether a lead–acid battery ESS should be hybridized with supercapacitors are the thermal
parameters, rather than the economic ones. The poorest the thermal conditions, the more
likely the hybridization to be beneficial.
6. Conclusions
This paper describes a methodology to hybridize a battery-based energy storage system using supercapacitors for a smoother power profile, presenting a new control scheme,
a new battery degradation mechanism model and an economic viability analysis. Compared to a system with only lead–acid batteries, the hybrid system features longer battery
life. The results showed that a simple first-order low-pass filter is an effective and reliable
solution for the power filtering, performing more favorably than higher order FIR filters
given the limited supercapacitors capacity and strict voltage limits. Apparently, the supercapacitors result in fewer microcycles, but also in lower average battery temperature
Energies 2021, 14, 507
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due to the smoother current profile that yields less power losses compared to a fluctuating
current in the battery-alone case. This also highlights the importance in capturing both
DoD and temperature effects in a battery degradation model, such as in the one proposed.
Especially when there is access to second-resolution time series that allows visibility
to numerous microcycles, an appropriate microcycles cycle life DoD model should be
used; if not available, the microcycles should instead be completely disregarded from the
profile to avoid erroneous battery life estimation. A sensitivity analysis showed that the
thermal parameters of the system not only affect the battery life, but play a major role in the
hybridization benefit: poorer or better thermal conditions render the hybridization more or
less useful respectively. This is confirmed by the economic analysis, which concludes that
the financial benefit of the hybridization depends more on the thermal conditions rather
than the economic parameters of the investment.
The methodology and findings of this study may be useful when exploring hybridization options for battery ESS in standalone microgrids. In addition, this type of hybrid ESS
has great grid-connected potential as well, mainly in facilitating high levels of renewables
integration. It is nowadays seen as a credible way to absorb generation and load intermittency and provide ancillary services to the power system, such as frequency response and
inertia emulation, functions that again result in irregular charge/discharge battery profiles
that hint towards a hybrid ESS.
Furthermore, it is worth noting that the core of the proposed methodology applies to
Li-ion battery systems as well, which is increasingly gaining popularity due to longer life,
smaller size and less weight. Most steps of this paper’s methodology will be common in
this case, but with substantially different characteristics and parameters that do not allow
for straightforward extrapolation of this study findings to Li-ion battery systems.
Author Contributions: Conceptualization, X.L. and E.B.; methodology, X.L., J.V.B. and E.B.; investigation, X.L.; writing—original draft preparation, X.L.; writing—review and editing, J.V.B., B.W.,
C.L.C. and E.B.; supervision, E.B. All authors have read and agreed to the published version of
the manuscript.
Funding: This research has been supported by the Royal Academy of Engineering under the Engineering for Development Research Fellowship scheme (number RF\201819\18\86) and EPSRC
Faraday Institution’s Multi-Scale Modelling Project (EP/S003053/1, grant number FIRG003).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: No new data were created or analyzed in this study. Data sharing is
not applicable to this article.
Acknowledgments: The authors would like to thank Oorja Development Solutions Limited and
BBOXX for their kind provision of the electricity profile of the case study, and Mr Hamish Beath and
Mr Philip Sandwell for assisting with acquiring the data.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
DoD
ESS
FIR
HESS
LPF
NPC
O&M
PV
SoC
Depth of Discharge
Energy Storage System
Finite Impulse Response (filter)
Hybrid Energy Storage System
Low-Pass Filter
Net Present Cost
Operation and Maintenance (costs)
Photovoltaic
State of Charge
Energies 2021, 14, 507
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