1
Size and Topology Optimization for
Supercapacitor-Based Sub-Watt Energy Harvesters
Sehwan Kim
Department of Electrical and Computer Engineering
University of California, Irvine, CA, 92697–2625 USA
Email: shawn.kim@uci.edu
and
Pai H. Chou,
Member, IEEE
Department of Electrical and Computer Engineering
University of California, Irvine, USA,
and Department of Computer Science
National Tsing Hua University, Hsinchu, Taiwan
Email: phchou@uci.edu
Abstract
This paper explores sizing and topology reconfiguration strategies for charging and discharging multiple supercapacitors as
energy storage in subwatt-scale energy harvesters. To maximize energy efficiency for storage (hEstorage ), total leakage power is
kept low by selecting the supercapacitors to charge sequentially, alternatingly, or in series based on their voltages. To maximize
energy efficiency for driving load (hEdriving ), residual energy is minimized by switching to series composition of the supercapacitors
in order to raise the voltage above the minimum input voltage of the load-side dc-dc converter. Due to the nonlinear, stateful,
load-dependent behavior of such harvesters, parameter sweeping is used for system-level optimization. A topology-reconfigurable
structure consisting of two larger, symmetric “reservoir” supercapacitors and one voltage-raising “bootcap” prove to be efficient
and practical for considering combinations of symmetric and asymmetric capacitance values. Experimental results on an actual
implementation show that for charging, series topology is best when input power is high due to lower leakage, individual topology
is best when input power is low due to lower voltage; for discharging, series topology is effective in reducing residual energy
while individual topology with alternating discharging effectively minimizes leakage.
Index Terms
Energy harvesting, supercapacitor subsystem, leakage rate, reconfigurable topology
I. I NTRODUCTION
S
UBWATT-SCALE energy harvesters are fast becoming a compelling feature for embedded systems that are deployed at
remote sites outdoors, where utility power is unavailable and battery replacement is costly [1]–[6]. Several recent features
distinguish subwatt-scale harvesters from their utility-grade [7]–[9], larger counterparts, including emphasis on low overhead
in maximum power point tracking (MPPT), and the use of supercapacitors as a potential type of energy storage elements
(ESE).
2
Energy
Transducers
Power Converters
Embedded
Target Loads
Light
PV Cell
charge, regulate,
etc.
Eco
MPP Tracking
Motion
Control Unit
PZT
iMote2
Temp.
TEG
Supercapcitors
Mica2
Energy Storage
Subsystem
Fig. 1.
The block diagram for EHS
However, anecdotes have often been about how costly and bulky these energy harvesters may be, how they fail to sustain
days of poor weather, and how their batteries still fail after a year or two. The cost, size, and poor-weather sustainability
can be addressed by incorporating energy-harvesting circuitry that can extract the maximum amount of power from an energy
transducer such as a solar panel over a wide range of supply conditions with low overhead. To address the battery aging
problem, researchers started proposing supercapacitors as an increasingly viable form of energy storage element (ESE) for
these harvesters.
Supercapacitors, or electric double-layer capacitors (ELDC), have lower energy density than batteries by an order of magnitude
but much higher power density, which enables their use in applications that require short-term high power draw, such as electric
vehicles and medical equipment [10], [11]. In particular, despite the lower energy density, their very long life cycles make
them suitable for use as ESE for energy harvesting systems [3]–[5]. Such a system usually consists of the following four
components: the energy transducers, (e.g., solar, wind, vibration etc.), energy-harvesting circuitry, energy storage subsystem,
and target load, as shown in Fig. 1.
Although supercapacitors are an excellent form of ESE for sustainable operation of the harvesters, they are far from being
drop-in replacements for batteries due to their very different characteristics. Unlike batteries, the stored energy of a capacitor
is proportional to V 2 , which means two voltage conversions are usually required: once from the energy transducer for charging
the supercapacitor, and once from the supercapacitor for driving the load. For battery charging, chargers based on buck/boost
regulators are commonly used for converting the input voltage to the target voltage; for supercapacitor charging, charge pumps
have been shown to be more efficient by raising the voltage without having to target a specific output voltage. In either case,
such converters may be 80-90% efficient [3]–[5] but they have a minimum operating voltage of around 0.7 V [6], [12], [13].
This means the residual energy below the minimum voltage of the dc-dc converter or the charge pump is normally unusable,
and it grows linearly with the capacitance value and quadratically with the voltage. Another problem is the exponentially
increasing leakage current near the rated voltage, usually 2.5-2.7V.
To address some of these problems, previous work has proposed (1) switching between multiple supercapacitors of different
3
sizes [5] and (2) reconfiguring the topology of an array of supercapacitors and charging them using a programmable charge
pump with perturbation-free MPPT [14]. The former enables faster charging with lower residual energy by prioritizing a smaller
supercapacitor (bootcap) when the ambient power is scarce, and it switches to one of the larger reservoir supercapacitors when
the ambient power is plentiful. However, it does not address the residual energy problem in the reservoir ones. The latter
extracts more residual energy from the reservoir ones by composing them in series and enables charging with a lower input
voltage by configuring them as individuals to be charged sequentially (i.e., one at a time). However, how the sizes of these
supercapacitors should be chosen optimally and how their charging can be scheduled optimally were not addressed. In addition,
the problems of leakage and charge redistribution during composition need to be addressed.
The contribution of this work is a systematic way to maximize storage and driving efficiencies of the proposed subwatt-scale
harvester by (1) statically selecting the relative sizes of the supercapacitor array (2) dynamically reconfiguring the topology
over different solar profiles (3) deciding which supercapacitors to charge and discharge based on the charge state. The efficiency
gain comes from reduced residual energy, reduced leakage, and low switch overhead. Experimental results reveal that series
composition is more effective than individual in terms of lower leakage loss, asymmetric series composition is most effective for
sustainable driving energy, and voltage balancing during charging and discharging is optimal in terms of minimizing leakage.
II. BACKGROUND
This section first defines the symbols and the key concepts. Next, it provides a background on the residual energy and
leakage characteristics of supercapacitors, and the output-stage efficiency of subwatt-scale harvesters.
A. Basics of Supercapacitor-Based Subwatt-Scale Harvesters
A subwatt-scale, supercapacitor-based energy harvester can be characterized in terms of the following variables based on
Fig. 1.
Pcharge : the power supplied by the transducer (at time t), assumed maximized and converted to the appropriate voltage,
whether accepted by the supercapacitor or not. If not accepted, then it is dissipated as heat.
Paccepted : the power actually accepted and stored by the supercapacitor (at time t). Note that charging power below the
supercapacitor’s voltage or beyond the supercapacitor’s full capacity is discarded.
8
>
>
<(Vcharge Vsupercap ) · Icharge if (Vcharge > Vsupercap ) and (Vcap,max > Vsupercap )
Paccepted =
>
>
:0
otherwise
(1)
Poverhead : the overhead of a power switch, consisting of conductive loss and switching loss.
2
Poverhead = Pcond, loss + Psw, loss = RDSon · i2D +Coss ·VDS,off
· fsw
(2)
where Coss is the output capacitance and VDS,off is the drain-source voltage when the switch is off.
Eheld : the energy held by the supercapacitor (at time t), after accounting for leakage and power switch loss. The leakage
model Pleak is given in Eqn. (8) in Section II-C.
Eheld (t) = Eheld (0) +
Z t
0
(Paccepted (t)
Pleak (t)
Poverhead (t)) dt
(3)
4
B. Unusable Residual Energy
The unusable energy in the supercapacitor whose voltage is below the minimum dc-dc conversion threshold is called residual
energy.
Eresidual : the unusable remaining energy within the supercapacitor.
8
>
>
<Eheld (t)
Eresidual (t) =
>
>
: 1 C(0.7)2 ⇡ 0.245C
2
if V (t) < Vconv,min
if V (t)
(4)
Vconv,min
where Vconv,min is the minimum conversion voltage of a dc-dc converter or a charge pump, assumed to be 0.7V in
this paper.
Eusable :
the available energy in the supercapacitor for actually driving load.
Eusable (t) = Eheld (t)
Eresidual (t)
(5)
Most commercially available supercapacitors have a voltage range of 0-2.7V. For a supercapacitor to supply regulated power
(typically 3-5V) to the load, most subwatt-scale harvesters use a boost-up dc-dc converter. However, the minimum voltage of
most commercial off-the-shelf dc-dc converters is 0.7V (e.g., MAX 1763), below which the converter may work in pass-through
mode but the voltage is still too low to drive the typical load. All supercapacitors can withhold up to
1
2
·C · (0.7V)2 of residual
energy. For example, the residual energy of a harvester using a 300F supercapacitor is up to 73.5J. Many subwatt-scale harvesters
are designed for wireless sensor nodes that consume 100-150 mW while in active mode: e.g., Mica2 at 3.3V/16mA; iMote
at 2.5V/60mA; Eco node at 3.3V/30.8mA. This 73.5J residual energy can operate Eco node (52.8mW) for 1392 seconds (23
minutes and 12 seconds) in active mode. This is a considerable amount of unusable residual energy and should be minimized.
C. The Leakage Model of Supercapacitors
An empirical leakage model for supercapacitors can be obtained by measuring the leakage current of three types of
supercapacitors (10F, 25F, and 150F). The three supercapacitors are first charged by a voltage source, and then the circuit
is opened to observe the leakage. During self-discharging, the voltage change is measured using a digital multimeter every
one-half hour (Dt). The leakage current and power can be stated by:
V (t + Dt)
Dt
DV 2 (t)
Pleak (t) = Ileak (t) · DV (t) = C ·
Dt
Ileak (t) = C ·
DV (t)
V (t)
=C·
Dt
(6)
(7)
where V (t) is Vsupercap (t) in entire leakage equations. These equations are plotted in Fig. 2(a) to show that the leakage power
of each supercapacitor increases rapidly near its maximum voltage, and that the practical leakage patterns do not match the
simple RC leakage model. The empirical leakage data from a 25F supercapacitor suggest a leakage model by polynomial
approximation as shown in Fig. 2(b). The whole leakage model can be expressed by:
Pleak (V ) = amV m + am 1V m
1
+ · · · + a0
(8)
where a0 , . . . , am are polynomial interpolation coefficients. This equation predicts that the leakage power of supercapacitors
grows rapidly with the physical size (i.e., capacitance) and with the amount of energy residing within a supercapacitor.
5
(a) Measured leakage power loss
(b) Polynominal Fitting Leakage Model
Fig. 2.
Leakage Model of Supercapacitors
Using Eqn. (8), the energy loss due to leakage can be written as:
Eleak (t) =
Z t
0
Pleak (t) dt =
Z V (t)
V (t+Dt)
Pleak (V ) dV
(9)
Pdischarge : the power drawn from the supercapacitor (at time t). Note that if the supercapacitor’s voltage is below the dc-dc
converter’s minimum voltage, then the discharge power is assumed to be 0 rather than pass-through.
8
>
>
<Pload /hdc-dc if Vsupercap Vconv,min
Pdischarge =
>
>
:0
otherwise (assuming no pass-through)
(10)
where hdc-dc is the dc-dc converter’s efficiency and is load-dependent.
Pload : the load being driven by the dc-dc converter powered by the supercapacitor (at time t).
D. Efficiency of dc-dc Converter (hdc-dc )
The efficiency of a dc-dc converter depends on its input voltage, output voltage, and output current. Most dc-dc converters
operate most efficiently when the input and output voltages are similar [15]. Therefore, assuming constant current load is
connected to the energy storage subsystem of a subwatt-scale harvester, boosting the supercapacitor’s output voltage to the
maximum input voltage of a dc-dc converter by series connection will be able to improve the efficiency of a dc-dc converter
so that the efficiency at the output stage of the harvester is also improved. For instance, suppose all output voltages of three
supercapacitors are 0.8V; then, series connection will increase the net efficiency of the dc-dc converter [13] from 80% (at
0.8V) to 92% (at 2.4V) for Eco [16] (at 52.8 mW) while decreasing the total residual energy by 16.7% at the same leakage
level.
6
E. Efficiency Terms
The efficiency terms can be defined for power and for energy as follows.
The charging power efficiency (at time t, supercapacitor energy Eheld ):
Paccepted
Pcharge
hPcharging =
(11)
The charging energy efficiency:
The energy efficiency of storage (up to time t):
hEstorage =
R
(12)
Pleak (t) Poverhead (t)) dt
P
0 accepted (t) dt
(13)
t
Paccepted (t) dt
hEcharging = R0 t
0 Pcharge (t) dt
Rt
0 (Paccepted (t)
Rt
The driving power efficiency (at time t):
hPdriving =
Pload
Pdischarge
(14)
The driving energy efficiency (at time t):
Rt
(15)
hEe2e (t) = hEcharging hEstorage hEdriving (t)
(16)
hEdriving = R t
0 Pload (t) dt
Rt
0 Pdischarge (t) dt + Eresidual (t) + 0 Poverhead (t) dt
The overall end-to-end energy efficiency is conceptually
However, due to the stateful and discrete behavior of the energy storage, the end-to-end energy efficiency cannot be optimized
by taking its derivative but needs to be considered for the different cases based on the state of charge. In this sense, the leakage
and residual energy of supercapacitors, and the efficiency of a dc-dc converter are important figures of merit and are optimized
discretely at the system level to maximize energy efficiency of storage (hEstorage ) and driving energy efficiency (hEdriving ) defined
in Eqns. (13) and (15), respectively.
III. R ELATED W ORK
This section reviews previous work that attempted to address residual energy with reconfigurable supercapacitor topologies
for sustainable operation of the target embedded systems. If a single large supercapacitor is employed as the primary energy
buffer (reservoir) for sustained operation, then larger capacitance can cause the longer charging time as well as more unusable
residual energy. A related problem is cold booting [17], the futile cycles of repeated booting and exhaustion while starting
a system with little or no usable charge (i.e., near the usable threshold) in the supercapacitor, despite the nontrivial residual
charge in it. To address the issues with the size constraint of the harvester, the topology of ESE needs to be considered at the
system level.
7
(RSA)
=
usable
(SS)
usable
C1
(RSA)
+
usable=
usable
C2
C1
+
usable
usable
+
C
C2 bc
+
usable
usable
(DRS)
=
usable
(RSA)
usable
+
(sym.)
usable
+
(aym.)
usable
(SS)
usable
C1
usable
C1
C2
usableusable
(sym.)
C2
usable
(aym.)
Cbc
usable
C
Cbc
usable
C
C1
C1
C2
C2
Cbc
usable
usable
Cbc
usable
Cbc
C1
C2
Cbc
Bootcap.
Bootcap.
Reservoir
Reservoir
Supercapacitors
Supercapacitors
(a) Single Supercapacitor (b) Reservoir Supercapacitor Array Topology (c) Dynamic Reservoir Supercapacitor Topology
Topology
Fig. 3.
Supercapacitor Topologies for ESE
A. Single Supercapacitor Topology
The single supercapacitor (SS) topology is the simplest static topology as shown in Fig. 3(a). A single small supercapacitor
(SSS, around 1 F) [6], [18] can charge faster but cannot sustain too many days without sunlight. On the other hand, those
with a single large supercapacitor (SLS, 50-100 F) [3], [4] have a larger amount of storage energy for sustainable operation,
but it can not only suffer from cold booting but also take longer charging time. Furthermore, SLS causes a larger amount of
residual energy than SSS does.
B. Reservoir Supercapacitor Array Topology
To address the problems with SS, reservoir supercapacitors arrays (RSA) were proposed [5], [19], as shown in Fig. 3(b).
The purpose of the topology is to shorten the charging time by dividing an SLS into an array of supercapacitors. Since the
leakage rate is dependent on the capacitance of supercapacitors, the RSA topology is also helpful in reducing the leakage rate.
In particular, DuraCap [5] uses a bootstrap supercapacitor, named bootcap (Cbc ), which has relatively smaller capacitance
than the reservoir supercapacitors (C1 ,C2 ), to solve the cold booting problem by reaching a higher voltage faster with more
usable energy for booting. The bootcap has a higher priority to charge, and when it is full, the reservoir ones are charged
sequentially (one at a time). However, by fully charging the reservoir supercapacitors sequentially, DuraCap can suffer from
lower energy efficiency of storage. Because the leakage rate of supercapacitors increases rapidly as they approach their rated
voltage (Section II-C), one fully charged reservoir supercapacitor would experience the rapid leakage rate while the other
reservoir supercapacitor is being charged. One way to address this problem is to keep the supercapacitors voltage-balanced by
either alternating charging or charging them in series, as proposed in this paper.
C. Dynamic Reconfigurable Supercapacitors
According to Fig. 2, the leakage power increases rapidly as the terminal voltage approaches the rated voltage of the
supercapacitor. Particularly, the leakage power near the rated voltage may be as much as 40 times greater than the lowest
leakage power. However, this sharp increase of leakage power near the rated voltage is mitigated along with the lower
capacitance of supercapacitors. The SS topology does not have any leakage replenishment techniques. The RSA topology
8
has better control because it divides an SLS into several supercapacitors, although the leakage sum does not make a great
impact on leakage reduction. To address all issues, the dynamic reconfigurable supercapacitors (DRS) scheme was proposed
[14]. During charging and discharging phases, the DRS can be configured for different topologies to control the energy leakage,
reduce unusable residual energy in supercapacitors, and improve output stage efficiency.
D. Contribution of This Work
This paper proposes improvements with different charging schemes, including series charging, sequential charging, and
alternating charging of the supercapacitors, depending on the charge level and solar power availability. As shown in Fig. 3(c),
during discharging, DRS can continue to extract more energy even after the RSA-equivalent circuit stops when it cannot access
the residual energy. The DRS can change to series composition of symmetric capacitance of the two reservoirs; subsequently,
the two can further compose with the bootcap in series with asymmetric capacitance to further increase the voltage while
reducing residual energy.
In this paper, the harvester platform is assumed to be EscaCap [14] to validate the topology concept of energy storage
subsystem. The problems are to build the energy storage subsystem with an array of supercapacitors that can improve not
only energy efficiency of storage in Eqn. (13) but also driving energy efficiency in Eqn. (15). The maximization of energy
efficiency of storage (hEstorage ) can be maximized by exploring individual vs. series configuration of the supercapacitors and
charging and discharging strategies to minimize leakage at the system level, whereas the driving energy efficiency (hEdriving )
can be enhanced by exploring supercapacitor topologies and sizes for minimizing the residual energy, as well as adapting the
efficiency of a dc-dc converter.
IV. T OPOLOGY- BASED E NERGY S UBSYSTEM M ODELING
This section discusses generalization from a single supercapacitor to multiple supercapacitors and the newly enabled
opportunities for efficiency improvement. In particular, the supecapacitor array of two larger reservoir supercapacitors with one
smaller bootcap is considered for the satisfaction of size constraint for subwatt-scale harvesters. Due to the constraint design
space and practical considerations, we explore the connectivity and symmetry of two supercapacitors. Connectivity refers to
how the supercapacitors are connected to the charger and the load, and they may be in series composition, and individual
configuration (sequential or alternating). Symmetry refers to whether the supercapacitors are of the same or different capacitance
values. We explore the connectivity and symmetry of the supercapacitor array in optimizing the energy efficiency of storage,
driving energy efficiency, and the supercapacitor sizing.
A. Connectivity
In Fig. 1, the Pcharge from power converters is transferred to the Paccepted through a power path switch (Poverhead ) during
charging. Similarly, the Pdischarge drives the target load via a power path switch (Poverhead ) and a dc-dc converter (hdc-dc ), and is
transferred to the Pload at the target load during discharging. For reconfiguring the composition, sequential and alternating can
use the same power path switch between power converters and supercapacitors with on/off control. However, series composition
needs to add one more power switch between two supercapacitors; thus, it would provoke additional switch overhead (Poverhead ).
9
2
Additionally, in the DRS topology, the conduction loss dominates the switching loss (Coss ·VDS,off
· fsw ) in Eqn. (2), which is
trivial.
B. Energy Efficiency of Storage (hEstorage )
According to Eqn. (13), energy efficiency of storage can be maximized by adjusting the connectivity between a charger and
an energy storage subsystem, which can be reconfigured for the supercapacitors topology (i.e., individual or series) depending
on solar power availability and the state of charge of the supercapacitors. Subsequently, the leakage of supercapacitors can be
minimized during charging phase. In addition to minimizing the leakage, the overhead of the power switch should be reduced
at design time. To determine which charging strategies would be better in terms of minimizing the leakage and the overhead of
power switches, in this section, the individual (i.e., sequential and alternating) and the series charging schemes are explored in
terms of energy efficiency of storage. Specifically, after separating the bootcap with the highest charging priority to address the
cold booting problem, the energy efficiency of storage is derived for the model with two symmetric reservoir supercapacitors
in charging phase.
1) Individual vs. Series : Individual charging can be categorized into two schemes: sequential and alternating. The sequential
charging is a good scheme to charge supercapacitors under the low solar irradiation condition in the morning, evening, or
on cloudy days. This is because it can simply charge the supercapacitor array one by one without considering symmetric or
asymmetric capacitance. However, the simple charging control could lead to the abundant leakage loss because the first fully
charged reservoir supercapacitor undergoes the rapid leakage rate while the other supercapacitor is being charged, as mentioned
in Sec. III-B.
The accepted, leaked, and held energy values in the sequential charging scheme for two supercapacitors are given by:
Z t2
0
(seq)
Paccepted (t) dt =
Z t2
t1
(seq)
Pleak (t) dt =
(seq)
Eheld (t) =
Z t1
C1V1 (t) dt +
0
Z V1 (t1 )
V1 (t2 )
Z t1
0
Z t2
t1
C2V2 (t) dt
(17)
Pleak (V1 ) dV1
C1V1 (t) dt +
Z t2
t1
(18)
Z V1 (t1 )
C2V2 (t) dt
V1 (t2 )
Pleak (V ) dV
Z t2
0
RDSon · i2D (t) dt
(19)
where t1 and t2 are the times to fully charge the respective supercapacitors. Using Eqn. (13), the energy efficiency of storage
for the sequential charging can be written as:
(seq)
hEstorage
=
R t1
0
C1V1 (t) dt +
R t2
t1
C2V2 (t) dt
R t1
0
R V1 (t1 )
V1 (t2 )
C1V1 (t) dt +
Pleak (V ) dV
R t2
t1
C2V2 (t) dt
R t2
0
RDSon · i2D (t) dt
(20)
(seq)
The sequential charging scheme provokes more held energy loss (Eheld (t)) due to leakage compared to other schemes because
there is no way to replenish leakage.
Alternating charging would be better way to address the leakage caused by the sequential charging. This is because it can
replenish the leakage by dividing the large sequential charging time into a certain smaller interleaved charging time (Dt). In
other words, during every Dt, one supercapacitor not only charges but also replenishes except to last time slot Dt. Therefore,
after finishing the charging process, the leakage is dominated by the fully charged one during Dt, which is a much shorter time
10
than t2 of the charging time of the second supercapacitor in sequential charging. One cycle, T , is the total time for charging
all (reservoir) supercapacitor for Dt each, so for two reservoirs, one cycle is T = 2 ⇥ Dt. The total charging time is tc = N · T .
Accordingly, the amount of energy in the alternating charging for two supercapacitors is given by:
Z tc
0
(alt)
Paccepted
(t) dt = N ·
Z tc
0
(alt)
Pleak
(t) dt =
Z
Z T
0
V2 (tc )
(C1V1 (t) +C2V2 (t)) dt
V2 (tc +Dt)
Z T
(alt)
Eheld
(t) = N ·
0
(21)
Pleak (V ) dV
(22)
(C1V1 (t) +C2V2 (t)) dt
Z tc
0
(alt)
(Pleak
(t) + RDSon · i2D (t)) dt
(23)
The energy efficiency of storage for the alternating charging scheme can be written as:
hE(alt)
storage
=
N·
RT
0
(C1V1 (t) +C2V2 (t)) dt
N·
RT
0
R V2 (tc )
P (V ) dV
V2 (tc +Dt) leak
(C1V1 (t) +C2V2 (t)) dt
R tc
0
RDSon · i2D (t) dt
(24)
In the leakage perspective, alternating charging would be helpful in improving energy efficiency of storage, but it can cause
the additional charging time due to replenishing the leakage.
In series composition, the total capacitance (Ceq ) is lower than that of the individual supercapacitor, and therefore the series
charging time up to a given voltage level is shorter than the time of charging each individually. This is useful when the solar
irradiation intensity is sufficiently high. However, one issue with series charging is the cell balancing of the supercapacitors in
series due to the over-voltage problem as a result of charge distribution among the supercapacitors. For brevity, series charging
assumes symmetric capacitance (i.e., same-sized reservoirs), although series discharging may assume asymmetric capacitance
(i.e., reservoirs or bootcap with reservoirs).
Note that the voltage distribution for supercapacitors in series is initially a function of capacitance. The voltage of an
individual supercapacitor can be described by:
Vi (t) = V (ser) (t) ⇥Ceq ·
1
, where 1/Ceq = Â ni=1 1/Ci
Ci
V (ser) (t) = Â ni=1Vi (t)
(25)
(26)
where n is the total number of supercapacitors. Therefore, after discharging two supercapacitors in series to Vconv,min , the
voltage distribution need to be considered by:
C2
·Vconv,min
C1 +C2
C1
V2(ser) (t) =
·Vconv,min
C1 +C2
V1(ser) (t) =
(27)
(28)
Let ts denote the charging time for series composition, while ts+ denotes the later point in time after auxiliary charging for a
voltage-unbalanced cell. In general, a voltage-balancing charging scheme is required to avoid overvoltage. In more detail, the
harvester should prioritize the charging current to the lower-voltage supercapacitor (V (t) at C) while disabling the charging
circuit for the other supercapacitor until the two supercapacitors’ voltages are equalized (i.e., at ts+ ). Therefore, the amount of
11
energy in series composition can be calculated by:
Z t+
s
0
(ser)
Paccepted
(t) dt =
Z t+
s
ts
(ser)
Pleak
(t) dt =
(ser)
Eheld
(t) =
Ceq
2
Z
Z ts
0
V (ts )
V (ts+ )
Ceq
2
Z t+
s
ts
(V (t)) dt
(29)
Pleak (V ) dV
Z ts
0
(V1 (t) +V2 (t)) dt +C
(30)
(V1 (t) +V2 (t)) dt +C
Z t+
s
ts
V (t) dt
 Z
RDSon · 2 ·
For the series charging, the energy efficiency of storage can be written as:
hE(ser)
=
storage
R ts+
Ceq R ts
2 0 (V1 (t) +V2 (t)) dt +C ts (V (t)) dt
R V (ts )
P (V ) dV
V (t + ) leak
s
0
ts
i2D (t) dt +
Z t+
s
ts
i2D (t) dt
h R
i
R t+
RDSon · 2 · 0ts i2D (t) dt + tss i2D (t) dt
R ts+
Ceq R ts
2 0 (V1 (t) +V2 (t)) dt +C ts V (t) dt
(31)
(32)
According to [14], charging series-composed supercapacitors under high solar irradiance can be 40⇠50% faster than charging
a single supercapacitor. Therefore, if the leakage issue in the series charging scheme is addressed, it could be the best charging
scheme in terms of hEstorage .
2) Over-voltage Protection for Series Charging: To minimize the leakage in series charging, apart from symmetric capacitance, the voltage balancing should be taken into account for over-voltage protection. The voltage distribution of seriesconnected supercapacitors is initially a function of capacitance. However, the capacitance itself is not exactly translated into
the state of charge of supercapacitors. According to [20], the supercapacitor capacitance varies with its terminal voltage as
C = C0 [1 + Kv(Vsupercap
1.35)], where Kv = 0.1 and Vsupercap is the terminal voltage of supercapacitors. For instance, if a
2.0V supercapacitor (e.g., C2 = 320F) and a 0.7V supercapacitor (e.g., C1 = 280F) are connected in series to be charged as
shown in Fig. 4(a), V (ser) goes up to 5.4V when fully charged. According to the Eqn. (25), the maximum series voltage of
5.4V is theoretically divided into V1 = 2.52V and V2 = 2.88V, but V2 would be over its maximum voltage of 2.7V. To avoid
the over-voltage, the charging process should end as soon as either supercapacitor reaches its maximum voltage (2.7V). In
this case, the charging process is ended when V2 = 2.7V, leaving V1 = 2.34V. As a result, C1 cannot store the full amount of
energy as constrained by V2 . This combination of capacitance values results in capacitance fragmentation due to the voltage
unbalancing of supercapacitors.
The effect of voltage unbalancing in series connection can be observed by connecting two supercapacitors in series and
turning on the switch as shown in Fig. 4(a). Assuming C1 is fixed at 300F and C2 is swept from 260F (i.e., 0V) to 340F
(i.e., 2.7V). Fig. 4(b) shows the supercapacitor with greater capacitance will be charged to a lower voltage (i.e., fragmented)
while the smaller one to the maximum voltage (2.7V). The dotted line in Fig. 4(b) indicates over-voltage. The blue line in
Fig. 4(c) shows the total stored energy in the series-composed supercapacitors under this over-voltage protection operation.
Due to the over-voltage protection, even if the symmetric capacitors are connected in series, a lower-voltage supercapacitor
need to be charged up to 2.7V by spending additional charging time (i.e., ts+
ts in Eqn. (30)) to equalize the voltage of the
supercapacitors. However, the additional charging time (ts+ ) to balance the voltage would translate into (high) leakage of the
fully charged supercapacitor.
To accomplish over-voltage protection while maximizing energy efficiency of storage, the leakage due to the additional
charging time (ts+ ) should be addressed. Both can be accomplished by using a Zener diode with 2.7V break-down voltage
(VBr ) in parallel with each supercapacitor, so that the Zener diode not only protects overvoltage but also replenishes the leaked
12
IPV
C1
IPV
VC1
C1
V(ser)
SW=On
C2
SW=On
C2
VC2
(a) w/o balancing vs. w/ balancing of series composition
2.9
V
Voltage[V]
2.8
C1,OV
VC2,OV
2.7
VC2
2.6
VC1
2.5
260
270
Total Charged Energy [J]
Total Charged Energy [J]
2400
280
290
300
310
Capacitance of C2 [F]
320
330
340
320
330
340
320
330
340
(b) The voltage distribution in series connection
No Control
Charging Control
2300
2400
No Control
Charging Control
2200
2300
2100
2200
2000
2100
1900
2000
1800
1900
260
1800
260
270
280
270
280
290
300
310
Capacitance of C2 [F]
290
300
310
Capacitance of C2 [F]
(c) The total accepted energy of series connection
Fig. 4.
Supercapacitor Charging Scheme considering voltage balancing
energy until the two supercapacitors’ voltages are equalized. Utilizing this voltage balancing control, the total stored energy
can be increased as shown by the red line in Fig. 4(c). The stored energy is in that case at its maximal possible value, taking
into account the values of C1 (300F) and C2 (260F ⇠ 340F).
Considering the voltage balancing technique, Eqns. (30) and (32) can be rewritten as:
Z t+
s
ts
(ser)
Pleak
(t) dt =
hE(ser)
=
storage
Z V (ts )
Pleak (V ) dV ⇡ 0
V (ts+ )
Rt
Ceq R tsb
2 · 0sb RDSon · i2D (t) dt
2 0 (V1 (t) +V2 (t)) dt
Ceq R tsb
2 0 (V1 (t) +V2 (t)) dt
(33)
(34)
Therefore, the leakage problem in series charging is resolved so that under high solar irradiation intensity, the series charging
can maximize the energy efficiency of storage.
13
C. Driving Energy Efficiency (hEdriving )
To maximize the driving energy efficiency by reducing residual energy, static and dynamic topologies are explored. Fig. 3
shows two static topologies (SS, RSA) and one dynamic (DRS) for energy storage subsystems. Note that SS actually means
SLS to be comparable to RSA and DRS. This section explores ways of optimizing driving energy efficiency by minimizing
residual energy depending on the topologies. First, mathematical models are derived for each topology as mentioned in Sec. III.
Based on the models, the related factors for residual energy are identified, and therefore the way of maximizing the driving
energy efficiency by topology control is described.
Using Eqns. (4) and (10), the amount of driving energy, residual energy, and overhead of the power switch for SS topology
can be given by:
Z tSS
0
Z tSS
0
(SS)
Pdischarge
(t) dt = tSS ·
(SS)
Eresidual
(t) =
(SS)
Poverhead
(t) dt =
Pload
= CSS ·
hdc-dc
Z tSS
0
Vsupercap (t) dt, where Vsupercap (t)
0.7V
1
·CSS · (0.7)2 ⇡ 0.245 ·CSS
2
Z
tSS
0
(35)
(36)
RDSon · i2D (t) dt
(37)
where the tSS is the discharging time for a single large supercapacitor and the CSS is the capacitance of a single supercapacitor
as shown in Fig. 3(a). The driving energy efficiency for SS topology can be expressed using Eqn. (15)
hE(SS)
=
driving
CSS ·
R tSS
0
Pload · tSS
Rt
Vsupercap (t) dt + 0.245 ·CSS + 0SS RDSon · i2D (t) dt
(38)
In RSA topology, for the (two) reservoir supercapacitors and one bootcap as in DuraCap [5], the amount of driving energy
for the RSA topology is
Z tRSA
0
Z tRSA
0
Z
trs
(2 · trs + tbc ) · Pload
(rs)
= 2·
Crs ·Vsupercap (t) dt +
hdc-dc
0
1
(RSA)
Eresidual
(t) = (Crs + ·Cbc ) · (0.7)2 ⇡ 0.49 ·Crs + 0.245 ·Cbc
Z 2
Z
(RSA)
Pdischarge
(t) dt =
(RSA)
Poverhead
(t) dt = 2 ·
trs
0
RDSon · i2D (t) dt +
tbc
0
Z tbc
0
bc)
Cbc ·Vsupercap (t) dt where Vsupercap (t)
0.7V (39)
(40)
RDSon · i2D (t) dt
(41)
Where the trs is the discharging time for a reservoir supercapacitor, tbc is the discharging time for a bootcap, the Crs is the
capacitance of the reservoir supercapacitor, and the Cbc is the capacitance of the bootcap as shown in Fig. 3(b).
Thus, the driving energy efficiency for RSA topology is
hE(RSA)
=
driving
2·
R trs
0
Crs ·Vsupercap (t) dt +
R tbc
0
Pload · tRSA
Cbc ·Vsupercap (t) dt + 0.245 · (0.5 ·Crs +Cbc ) +
R tRSA (RSA)
0
Poverhead (t) dt
(42)
Since the RSA topology divides an SS into an array of supercapacitors (i.e., Css > Crs ), the residual energy of RSA is smaller
than that of SS. Furthermore, due to smaller trs , the conduction loss of the power path switch is also decreased. As a result,
the driving energy efficiency of RSA topology is enhanced compared to that of SS topology. However, the static topologies
discharge the stored energy above 0.7V without addressing the problem of unusable residual energy.
To overcome the limitations with static topology, EscaCap [14] supports dynamic topology. To take a more structured
approach similar to DuraCap, three supercapacitors are considered: one smaller bootcap and two reservoirs. Both symmetric
capacitance for two reservoirs and asymmetric capacitance for a bootcap with combination of the series-connected reservoirs
14
TABLE I
T HE IMPROVEMENT OF ENERGY AND EFFICIENCY BY DRS TOPOLOGY IN SYMMETRIC COMBINATION
After 1st discharging
Individual (Sequential)
C1
C2
V1
V2
Eheld
(seq)
Eusable
300F
300F
0.7V
0.7V
147J
0J
Series Topology
Individual to Series
(seq)
Eresidual
(rec.)
Eheld
(ser)
Eusable
(ser)
Eresidual
(seq!ser)
Egain
147J
147J
110J
37J
110J "
(seq!ser)
hEdriving
61%"
can be used to reduce the residual energy. After discharging two fully charged reservoirs individually (sequentially) as done for
RSA, the DRS initiates the adjustment to the supercapacitor topology as follows: first, two reservoirs with 0.7V are connected
in series (i.e., 1.4V) to drive the target loads until the voltage drops to 0.7V. Next, the fully charged bootcap (i.e., 2.7V) is
connected in series to the two series-connected reservoirs (at 0.7V) so that the voltage can be increased to 3.4V. These three
stacked supercapacitors start to supply the power to the loads through dc-dc converter until the total voltage goes down to
0.7V as shown in Fig. 3(c).
Based on the DRS discharging strategy, the driving energy of the DRS topology can be expressed as:
Z tDRS
0
(DRS)
Pdischarge
(t) dt =
=
Z tRSA
0
Z tRSA
0
0
where Ceq =
Crs ·Cbc
Crs +2·Cbc
+
(RSA)
Pdischarge
(t) dt
(DRS)
Eresidual
(t) =
Z tDRS
(sym)
(RSA)
Pdischarge
(t) dt
(DRS)
Poverhead
(t) dt =
+
tdr
(asy)
· Pload
+
hdc-dc
Z t (sym)
dr
Crs
N
0
·Vsupercap (t) dt
1
·Ceq · (0.7)2 ⇡ 0.245 ·Ceq
2
Z tRSA
0
(RSA)
Poverhead
(t) dt + 2 ·
Z t (sym)
dr
0
+
tdr
· Pload
hdc-dc
Z t (asy)
dr
0
RDSon · i2D (t) dt + 3 ·
0
(sym)
(asy)
(43)
(44)
Z t (asy)
dr
is the equivalent capacitance, Cbc is the capacitance of a bootcap, tdr
symmetric reservoirs in series, and tdr
Ceq ·Vsupercap (t) dt
RDSon · i2D (t) dt
(45)
is the discharging time of two
is the discharging time of three stacked supercapacitors as shown in Fig. 3(c).
Using Eqn. (15), the driving energy efficiency for multiple supercapacitors in the DRS topology can be express as:
hE(DRS)
driving
(sym)
Pload · (tRSA + tdr
= Rt
DRS
(DRS)
Pdischarge
(t) dt + 0.245 ·Ceq +
(sym)
(asy)
0
(asy)
+ tdr )
R tDRS (DRS)
0
Poverhead (t) dt
(46)
Compared to Eqn. (42) for the driving energy efficiency of RSA, the driving energy of DRS topology can extend the
discharging time from tRSA to tRSA + tdr
+ tdr
with the minimization of the residual energy. Consequently, the dynamic
topology can maximize the driving energy efficiency.
D. Supercapacitor Sizing
It is difficult to provide a single formula that determines the optimal sizes of the supercapacitors in the class of harvesters
considered in this paper. Instead, a designer with the system-level view should be able to sweep the sizes and other parameters to
determine the combination that meets their requirements while maximizing the efficiency. This section illustrates size selection
by considering primarily the discharging phase while comparing individual vs. series compositions, using a pair of 300F
reservoir supercapacitors as a starting point.
15
TABLE II
T HE IMPROVEMENT OF ENERGY AND EFFICIENCY BY DRS TOPOLOGY IN ASYMMETRIC COMBINATION
Reservoir vs. Bootcap
Ceq
Cbc
Veq
150F
150F
100F
50F
0.7V
5F
Individual (Sequential)
Series composition
Vbc
Eheld
(seq)
Eusable
2.7V
584J
510J
74J
434J
415J
18J
2.7V
401J
340J
61J
346J
332J
17J
2.7V
219J
170J
49J
217J
208J
21J
2.7V
55J
17J
38J
28J
27J
34J
Individual to Series
(seq)
Eresidual
(rec.)
Eheld
(ser)
Eusable
(ser)
Eresidual
(seq!ser)
Egain
245J #
63J #
36J "
17J #
(seq!ser)
hEdriving
16%"
21.8%"
23.3% "
16.4%"
1) Symmetric Combination for Reservoir ESE: Two 300F reservoir supercapacitors both at 0.7V as individuals have Eheld =
(seq)
Eresidual
(seq)
= 147J, (therefore, usable energy Eusable = 0J) because it is at or below the minimum dc-dc converter voltage (Section
V-C). However, by reconfiguring the topology to series as shown in Fig. 4(a), the total voltage goes up to 1.4V, yielding
(ser)
Eusable
= 12 · 150F·(1.42
(ser)
0.72 ) = 110J due to reduction of residual energy Eresidual
by 37J.
To present the benefits of topology changing from individual (sequential access) to series, the energy gain from sequential
(seq!ser)
to series (Egain
) is introduced. This can be simply determined by adding the decrement of Eheld to the increase of Eusable
(seq!ser)
through topology change. In this symmetric combination, the Egain
Eheld
(rec.)
(ser)
Eheld
) to 110 J (Eusable
is 110 J, which is calculated by adding 0 J (i.e.,
(seq)
Eusable ). Using Eqn. (15), the driving energy efficiency for sequential discharging is 0%
R
because the transferred energy to the load ( 0t Pload (t) dt) is 0J, whereas that of the series composition is 61%. Therefore, the
(seq!ser)
DRS topology can improve the driving energy efficiency (hEdriving
) by changing the topology from individual (sequential) to
series to 61%. Table I summarizes the improvement for a symmetric combination in terms of energy gain and driving efficiency
2) Asymmetric Combination for Bootcap: To illustrate how to select the size of the secondary energy buffer (i.e., bootcap) at
design time, consider two 300F supercapacitors at 0.7V in series (i.e., Ceq = 150F, Veq = 0.7V) with a bootcap (i.e., Vbc = 2.7V)
while sweeping its size as shown in Table II. In the asymmetric combination, since the equivalent capacitance (Ceq ) of series
composition is lower than the capacitance of smaller supercapacitor, despite of the increase of supercapacitor voltage, the
(rec.)
recoverable held energy (Eheld
) in series composition is to be decreased. Therefore, if the decrease in held energy (Eheld ) is
higher than the increase of usable energy due to topology change, the DRS control cannot bring any benefits. In this sense, the
loss of held energy (Eheld ) dominates the gain of usable energy in the asymmetric combination. As a result, when the topology
(seq!ser)
is changed from sequential to series, the energy gain (Egain
) is decreased except for the 150F/0.7V+50F/2.7V pair.
(seq!ser)
In addition, even considering the driving energy efficiency (hEdriving
) to select the optimal size of the secondary buffer,
the 150F/0.7V+50F/2.7V combination still has the highest driving energy efficiency, the highest additional usable energy over
sequential, and the lowest residual energy after two full discharge cycles. Table II delineates the way to select the size of the
bootcap by examining energy gain, as well as driving energy efficiency in asymmetric capacitance combination while changing
the topology from sequential to series.
16
(a) Miniature PV Cell
(b) I(P)-V curve at 1000 W/m2
(c) Eco powered by the EscaCap
Fig. 5.
Experimental Setup for DRS topology evaluation
V. E VALUATIONS
A. Experimental Setup
To validate the concept of DRS topology selection, its control strategies, and topology-based models for supercapacitorbased solar harvesters, experiments were conducted using a halogen lamp in an indoor environment. Under the
1000 W/m2
irradiation condition, a monocrystalline 3 VDC/40 mA miniature photovoltaic (PV) cell (Fig. 5(a)) was measured using a
commercial solar module analyzer (PROVA-200) to plot the V(P)-I characteristic curve (Fig. 5(b)). A miniature version of
EscaCap [14] was used as the subwatt-solar harvester platform to power the ultra-compact wireless sensor platform called Eco
[16] as its load (Fig. 5(c)). During the experiment, EscaCap boosted up the Vpv from 2.924 V to 5.4 V, and the output current
was 16.7 mA at 105 kHz pumping frequency, while Eco consumed 52.8 mW (16 mA at 3.3 V).
B. Energy Efficiency of Storage (Sec. IV-B).
The DRS is helpful in reducing the leakage rate of the supercapacitors by the reconfigurable switch control at run time.
Therefore, the overhead of power switches should be minimized especially at design time for subwatt-scale harvesters. This
section first provides the experimental result of the power switch overhead, and then concentrates on verifying the topology
modeling for energy efficiency of storage in Sec. IV-B depending on sequential, alternating, and series charging strategies.
1) Overhead of Power Switches: Since the RDS(on) is a key parameter to reduce the additional power loss (i.e., overhead),
commercial off-the-shelf (COTS) components with the lowest RDS(on) are adopted to implement the DRS topology (e.g.,
17
Supercapacitor Voltage (V)
6
5
Series Charging (Ceq = 12.5F)
4
Sequential Charging (two 25F Scaps.)
Alternating Charging (two 25F Scaps.)
3
2
1
0
0
250
(a)
Fig. 6.
500
750
1000
1250
1500
Charging Time (sec)
1750
2000
2250
(b)
Measurement results: (a) The conduction loss of the power switch, (b) The charging time comparison between series and sequential topologies.
Si7135DP (RDS(on) = 6.2 mW) for PMOS). Fig. 6(a) compares the charging time of series connection using PMOS with a pullup resistor (2108 seconds to full) and direct series connection (2065 seconds). In this sense, since the accepted power (Paccepted )
of EscaCap is around 90 mW, the overhead of the power switch between two 25F supercapacitors is 3.87 J (90 mW⇥(2108
2065) sec).
2) Charging Strategies: Fig. 6(b) shows the measured charging time of two 25F supercapacitors [21] in three different
charging strategies: series, sequential, and alternating charging. The charging time of the pair in series, sequentially, and
alternatingly take 2107 seconds (up to 5.4V), 2164 seconds, and 2195 seconds, respectively. Therefore, the accepted energy
(Eaccepted ) for two 25F supercapacitors is 182.25 J (= 91.125 J ⇥2) for series charging, 175.47 J (= 84.346 J +91.125 J) for
sequential charging, and 179.79 J (= 88.67 J + 91.125 J). Since the total energy of two fully charged 25F supercapacitors is
182.25 J, the leakage energy (Eleak ) can be 0 J of series charging at 2107 seconds, 6.78 J of sequential charging at 2164 seconds,
and 2.46 J of alternating charging at 2195 seconds. In this experiment, the Paccepted of EscaCap is 90mW. Theoretically, the
fully charging time of a 25F supercapacitor at the Paccepted of 90mW is 1012 seconds, while that of two 25F supercapacitors in
series at the same power supply condition is 2024 seconds. Thus, the
charging, and alternating charging are 7.47 J (90mW ⇥(2107
(90mW ⇥(2195
Rt
0 (Pleak (t) + Poverhead (t)) dt
of series charging, sequential
2024) sec), 12.63 J (90mW ⇥(2164
2024) sec), and 15.4 J
2024) sec), respectively.
Our primary interest is the energy efficiency of storage (hEstorage ) depending on different charging schemes. According to the
Eqn. (13), the energy efficiency of efficiency can be obtained using the accepted energy, the leakage energy, and the overhead
of switches. Therefore, hEstorage during charging phase is 95.88%, 89.34%, and 90.18% for series, sequential, and alternating,
respectively. Note that these are the peak efficiency levels for these charging schemes; leakage will cause the hEstorage to drop
over time.
In summary, charging supercapacitors in series composition has benefits in terms of higher energy efficiency of storage
under strong solar irradiance of
1000 W/m2 . However, the solar irradiation has a wide dynamic range over an entire day or
different weather conditions. Thus, the solar harvester may be able to charge only a single supercapacitor individually under
low solar radiance. In this case, the sequential or alternating charging scheme can be selected based on the power demand of
target embedded systems.
18
3.5
50F, Vout of DC/DC
25F, Vout of DC/DC
SS topology (50F)
RSA topology (2ea-25F)
DRS topology (2ea-25F)
3
2.5
Supercapacitor Voltage (V)
Supercapacitor Voltage (V)
3.5
2
1.5
1
0
2.5
2
1.5
1
500
1000
1500
2000
Discharging Time (sec)
2500
3000
0
(a) The discharging time comparison
Fig. 7.
Vout of DC/DC
25F(0.7V)/10F(2.7V) in series
50F(0.7V)/10F(2.7V) in series
25F(0.7V)/25F(0.7V) in series
3
100
200
300
400
500
Discharging Time (sec)
600
700
800
(b) The impact of boost-up using 2.7V, 10F supercap.
The evaluation of energy transfer efficiencies depending on different topologies
C. Driving Energy Efficiency (Sec. IV-C).
This section evaluates driving energy efficiency (Sec. IV-C) of the DRS topology modeling using two metrics: (1) the impact
of SS, RSA, and DRS topologies on discharging time, and (2) impact of symmetric or asymmetric capacitance on driving
energy efficiency (Sec. IV-C). As mentioned in Sec. III-C, the DRS topology discharging can be divided into (1) “symmetric
phase”: discharging two symmetric reservoir supercapacitors in series down to 0.7V and (2) “asymmetric phase”: discharging
the series composition between the bootcap and the two reservoir supercapacitors down to 0.7V.
1) Symmetric Phase: Fig. 7(a) shows the experimental results under different topologies: SS discharges a single 50F
supercapacitor (blue dashed line), RSA discharges two 25F supercapacitors sequentially (blue solid line), and DRS discharges
two 25F supercapacitors sequentially, and then the topology is reconfigured to series composition. By the topology change, the
total voltage of the supercapacitors in series goes up to 1.4V, so that the remaining energy can be supplied to Eco (blue dash-dot
line). Since the leakage rate of a single 50F supercapacitor is higher than that of 25F, the discharging time of RSA (two 25F
supercapacitors) is longer than SS (one 50F supercapacitor). The DRS topology is more beneficial in terms of minimizing
residual energy, as well as enhancing the driving energy efficiency. Due to the minimum input voltage of the dc-dc converter,
SS (50F) and RSA (two 25Fs) have the unusable residual energy (Eresidual ) of 12.25 J respectively, while DRS has 3.063 J.
Since the power consumption (Pload ) of Eco is 52.8mW, the
Rt
0 Pload (t) dt
for SS, RSA, and DRS are 133 J (Pload ⇥2515 sec),
141 J (Pload ⇥2670 sec), and 149 J (Pload ⇥2820 sec), respectively, as in Fig. 7(a). According to Eqn. (15), the driving energy
efficiency (hEdriving ) is 72.9%, 77.3%, and 81.8%, respectively, at the first discharging.
2) Asymmetric Phase: The RSA topology introduced the bootstrap supercapacitor to address the cold booting problem
as mentioned in Section III-B. The capacitance of this bootstrap supercapacitor is smaller than the reservoir ones for faster
charging time. The DRS topology can enhance the advantage of the bootstrap supercapacitor by the combination with the two
series-connected reservoirs at 0.7V after first discharging. This asymmetric combination can not only minimize the unusable
residual energy but also improve the dc-dc converter efficiency by boosting up the voltage, thereby maximizing the driving
energy efficiency. Fig. 7(b) shows the discharging time of the pair of 50F(0.7 V) /10F(2.7 V), 25F(0.7 V)/10F (2.7 V), and
R
25F(0.7 V)/25F (0.7 V), which is 727 seconds, 673 seconds, and 115 seconds. The driving energy ( 0t Pload (t) dt) is 35.5 J,
38.4 J, and 6.1 J respectively.
19
Assuming the energy storage subsystem composed of 25F/25F/10F, after discharging of each 25F, by connecting two
symmetric reservoirs at the minimum voltage (i.e., 0.7V) in series, the driving energy is increased from 170 J to 180 J.
Also, the 10F bootcap is connected again to the 25F supercapacitors in series at 0.7V so that the additional driving energy
is produced by 35.5 J with reducing unusable residual energy to 1.75 J. Therefore, the total driving energy of 25F/25F/10F energy storage subsystem is 215.5 J. In the DRS, the driving energy efficiency (hEdriving ) is improved to 84.9% after finishing
two discharging steps.
VI. C ONCLUSIONS
This paper explores size selection of supercapacitors and their dynamic topology selection for maximizing energy efficiency
for storage (hEstorage ) and for driving (hEdriving ) in a subwatt-scale energy-harvesting system. This paper shows that keeping
the supercapacitors voltage balanced when charging maximizes hEstorage by minimizing leakage power. This paper also shows
that series composition improves hEdriving by raising the voltage above the minimum dc-dc converter’s input voltage, thereby
reducing residual energy. Furthermore, asymmetric configuration using two larger reservoirs and one small bootcap has been
shown to be a practical structure that encompasses the advantages of symmetric capacitance and asymmetric capacitance,
resulting in both high hEstorage and hEdriving . Empirical measurements validated the results. This work represents an important
step towards making supercapacitors a competitive form of energy storage in subwatt-scale energy harvesters.
R EFERENCES
[1] X. Jiang, J. Polastre, and D. Culler, “Perpetual environmentally powered sensor networks,” in Proceedings of Fourth International Symposium on
Information Processing in Sensor Networks (ISPN), April,15 2005, pp. 463–468.
[2] P. Corke, P. Valencia, P. Sikka, T. Wark, and L. Overs, “Long-duration solar-powered wireless sensor networks,” in The Fourth IEEE Workshop on
Embedded Networked Sensors (EmNets ‘07), June,25–26 2007, pp. 33–37.
[3] F. Simjee and P. H. Chou, “Efficient charging of supercapacitors for extended lifetime of wireless sensor nodes,” IEEE Transactions on Power Electronics,
vol. 23, pp. 1526–1536, May 2008.
[4] D. Brunelli, C. Moser, L. Thiele, and L. Benini, “Design of a solar-harvesting circuit for batteryless embedded systems,” IEEE Transactions on Circuits
and Systems, vol. 56, pp. 2519–2528, November 2009.
[5] C.-Y. Chen and P. H.Chou, “DuraCap: a supercapacitor-based, power-bootstrapping, maximum power point tracking energy-harvesting system,” in
Proceedings of the International Symposium on Low Power Electronics and Design (ISLPED).
Austin, TX, USA: ACM, August 2010, pp. 313–318.
[6] T. Zhu, Z. Zhong, Y. Gu, T. He, and Z.-L. Zhang, “Leakage-aware energy synchronization for wireless sensor networks,” in The 8th Annual International
Conference on Mobile Systems, Applications, and Services (MobiSys), June, 15–18 2010.
[7] B. Yang, W. Li, Y. Zhao, and X. He, “Design and analysis of a grid-connected photovoltaic power system,” IEEE Transactions on Power Electronics,
vol. 25, pp. 992–1000, April 2010.
[8] T. Suntio, J. Leppäaho, J. Huusari, and L. Nousiainen, “Issues on solar-generator interfacing with current-fed MPP-tracking converters,” IEEE Transactions
on Power Electronics, vol. 25, pp. 2409–2419, September 2010.
[9] A. Abdelsalam, A. Massoud, S. Ahmed, and P. Enjeti, “High-performance adaptive perturb and observe MPPT technique for photovoltaic-based
microgrids,” IEEE Transactions on Power Electronics, vol. 26, pp. 1010–1021, April 2011.
[10] A. Burke, “Ultracapacitors: why, how, and where is the technology,” Journal of Power Sources, vol. 91, pp. 37–50, November 2000.
[11] C. Park, K. No, and P. H. Chou, “TurboCap: Batteryless, supercapacitor-based power supply for Mini-FDPM,” in Proceedings of 3rd European Symposium
on Supercapacitors and Applications (ESSCAP), Rome, Italy, November 2008.
[12] L. Mateu, C. Codrea, and N. Lucas, “Human body energy harvesting thermogenerator for sensing applications,” in International Conference on Sensor
Technologies and Applications, October, 14–20 2007, pp. 366–372.
20
[13] MAXIM-IC, “MAX1763 datasheet,” http://datasheets.maxim-ic.com/en/ds/MAX1763.pdf.
[14] S. Kim and P. H. Chou, “Energy harvesting by sweeping voltage-escalated charging of a reconfigurable supercapacitor array,” in Proceedings of the 17th
ACM/IEEE International Symposium on Low Power Electronics and Design ISLPED.
New York, NY, USA: ACM, August, 1–3 2011, pp. 235–240.
[15] Y. Kim, N. Chang, Y. Wang, and M. Pedram, “Maximum power transfer tracking for a photovoltaic-supercapacitor energy system,” in Proceeding of the
16th ACM/IEEE International Symposium on Low Power Electronics and Design ISLPED.
New York, NY, USA: ACM, August 2010, pp. 307–312.
[16] S. Yoo, C. Chen, and P. H. Chou, “Low-complexity, high-throughput multiple-access wireless protocol for body area networks,” in Proceedings of Body
Sensor Networks (BSN), June 2009.
[17] P. H. Chou and S. Kim, “Techniques for maximizing efficiency of solar energy harvesting systems,” in Proceedings of the Fifth Conference on Mobile
Computing and Ubiquitous Networking (ICMU 2010), Seattle, WA, USA, April, 26–28 2010.
[18] M. Minami, T. Morito, H. Morikawa, and T. Aoyama, “Solar Biscuit: A battery-less wireless sensor network system for environmental monitoring
applications,” in The 2nd International Workshop on Networked Sensing Systems, June, 27–28 2005.
[19] C. Park and P. H. Chou, “AmbiMax: Efficient, autonomous energy harvesting system for multiple-supply wireless sensor nodes,” in Proceeding of the
3rd Annual IEEE Communications Society Conference on Sensor, Mesh, and Ad Hoc Communications and Networks (SECON), September 25–28 2006,
pp. 168–177.
[20] F. Rafik, H. Gualous, R. Gallay, A. Crausaz, and A. Berthon, “Frequency, thermal and voltage supercapacitor characterization and modeling,” Power
Sources, vol. 165, pp. 928–934, 2007.
[21] maxwell.com, “BCAP0025 datasheet,” http://www.maxwell.com/products/ultracapacitors/docs/DATASHEET HC SERIES 1013793.PDF.