Design optimization of hydraulic energystorage and conversion system for waveenergy convertersDong Wang* and Kaiyuan Lu
Abstract
Wave energy collected by the power take-off system of a Wave Energy Converter (WEC) is highly fluctuating due tothe wave characteristics. Therefore, an energy storage system is generally needed to absorb the energy fluctuationto provide a smooth electrical energy generation. This paper focuses on the design optimization of a HydraulicEnergy Storage and Conversion (HESC) system for WECs. The structure of the HESC system and the mathematicalmodels of its key components are presented. A case study and design example of a HESC system with appropriatecontrol strategy is provided. The determination of the ratings of the HESC system is also investigated in order toachieve optimal system energy efficiency.
Keywords: Energy storage, Hydraulic system, Wave energy, System modelling, System optimization
1 IntroductionAs a kind of renewable energy, wave energy and itsutilization have obtained increasing interests in the pastdecade [1–4]. Wave Energy Converter (WEC) is nor-mally used to harvest the wave energy and transform itto electrical energy. Many different WEC systems havebeen studied and reported [1–8], and they can be cate-gorized into two main types as turbine-type and buoy-type [1]. The turbine-type WECs, including OscillatingWater Column (OWC) WEC [4] and overtopping WEC[5, 6], use turbines as the main energy conversion device.While the buoy-type WECs, which are also known asPoint Absorber (PA) WECs, utilize fully submerged(below surface) absorber (e.g. the Archimedes WaveSwing (AWS) based [7]) or floating (on the surface)absorber [8–10] to capture the wave energy. ThePA-WECs are considered to be more environmentalfriendly [1] and have obtained interests from both academicresearches [7–10] and industrial prototypes [11, 12].The Power Take-Off (PTO) systems of the PA-WECs
can be categorized into two main types as electric-typeand hydraulic-type [3]. The electric PTOs, includinglinear generator [7, 10] and rotary generator with
gearbox [9], directly convert the captured wave energyto electricity. While the hydraulic PTOs transfer thewave energy to hydraulic energy, which is used to driveeither a turbine [13] or a hydraulic motor [8] that is con-nected to an electric generator.The situation of waves with large force at low speed
can be well suited by the hydraulic PTOs since they canprovide much larger force density than the electricPTOs, especially at high system pressure [2]. Thus,hydraulic PTOs should be more compact in size andweight, economically competitive, and relatively easy toinstall and maintain [2, 14]. Furthermore, since the waveenergy is highly fluctuating, from both the wave-to-waveand wave states time scales, the required peak powercapacity of the PTOs greatly exceeds the time-averagedpower delivered to the grid. Energy storage system isthus generally required to smoothen the final electricalpower output to avoid the impairment of power qualityfrom the grid point of view [3, 14]. In order to reducethe power ratings of the key components of the PTO forachieving a compact and energy efficient design, theenergy storage device is expected to be located directlyafter the wave energy absorbers. The gas accumulator,which stores the hydraulic energy and fluid by compressingthe gas, is currently the most common choice [2, 3, 14].* Correspondence: [email protected]
Department of Energy Technology, Aalborg University, Pontoppidanstraede111, DK-9220 Aalborg, Denmark
In this paper, the design optimization of the HydraulicEnergy Storage and Conversion (HESC) system used inthe hydraulic PTO system for PA-WECs is presented.The ratings of the HESC system are investigated in orderto optimize the system energy efficiency. This paper isorganized in the following manner. Section 2 illustratesthe structure of the HESC system for PA-WECs and themathematical models of all the key components are pre-sented. In Section 3, the integration of the HESC systemin the WEC is discussed and its performance is illustrated.Design optimization of the HESC system regarding energyefficiency is carried out and system design guidelines areprovided in Section 4. Finally, Section 5 draws conclusion.
2 HESC system modellingFigure 1 illustrates the structure of the HESC system thatcan be adopted in WECs. It consists of high-pressure gasaccumulator, hydraulic motor, low-pressure reservoir, pipe-lines, and electrical generator. The gas accumulator absorbsthe fluctuating flow from the hydraulic input and providesrequired flow to drive the variable displacement swash-platehydraulic motor and the connected electrical generator atcertain power level. A pressure relief valve is used to protectthe system against over-pressure. The energy overflow canbe collected by another energy storage system, which can beshared by several PTOs. The fluid loss caused by the over-flow is compensated by the backflow to maintain the pres-sure in the reservoir. The mathematical models of the keycomponents are given in details in this section.
2.1 Gas accumulatorThe connection interface between the accumulator andthe hydraulic system can be described by two variables:the actual flow rate of the fluid entering the accumulatorQa and the fluid pressure at the accumulator inlet pa.Since the accumulator stores the hydraulic fluid by
compressing the gas in it, the actual flow rate of the fluidentering the accumulator Qa is equal to the compressionrate of the gas in the accumulator
Qa ¼ −mgdυdt
; ð1Þ
where t is the time, mg is the gas mass, and υ is the gasspecific volume. The gas specific volume can be calcu-lated by integrating both sides of (1) if the initial gas spe-cific volume υ0 is known.The accumulator inlet pressure pa is determined by
the gas absolute pressure pg and the pressure differencebetween them. The gas absolute pressure pg can be cal-culated according to the Benedict-Webb-Rubin (BWR)equation of state as
pg ¼ RT=υþ B0RT−A0−C0=T2
� �=υ2 þ aα=υ6
þ bRT−að Þ=υ3 þ C 1þ γ=υ2� �
e−γ=υ2
� �=υ3T 2;
ð2Þwhere A0, B0, C0, a, b, c, α, and γ are constants in BWRequation, and T is the gas temperature. In this analysis,nitrogen is considered.Gas temperature T varies during the compression and
expansion process and it will cause irreversible heattransfer, i.e. from gas to accumulator wall and eventuallyto the outside environment. Elastomeric foam with ap-propriate properties is inserted to perform as “heat sink”and the thermal loss can be reduced significantly. Sincethe foam has large contacting surface with gas and verysmall wall thickness, it is appropriate to assume that thefoam and gas are at the same temperature T all the time[15]. Thus, the gas energy equation can be written basedon the energy balance principle as
mgdudt
¼ −pgdVdt
−mf c fdTdt
−hAw T−Twð Þ; ð3Þ
where u is the gas internal energy per unit mass,V is thegas volume, mf is the foam mass, cf is the specific heat offoam, h is the heat transfer coefficient, Aw is theeffective heat convection area of the accumulator, andTw is the accumulator wall temperature. For a real gas, ucan be described as
du ¼ cυdT þ T∂pg∂T
� �υ−pg
� dυ; ð4Þ
where cυ is the constant-volume specific heat of gas. Itshould be noted that cυ is gas temperature T and specificvolume υ dependent
cυ ¼ c0υ þ6
T 3
C0
υ−cγ
� �þ 3c
T 3
2γþ 1υ2
� �e−γ=υ
2; ð5Þ
where C0, c, and γ are constants in BWR equation, andc0υ is the constant-volume specific heat for ideal gas.Generally, c0υ also varies with the gas temperature T.However, for nitrogen used in this analysis, the change isso small during the normal working temperature rangeand constant c0υ can be used.Combining (2), (3), and (4) yields [15].
DCACHydraulic
Motor/pump
Accumulator
Reservoir
M
Flu
shin
gva
lve
cilu ardyH
inpu
t
G
Inverter
Energy overflow
Backflow
Fig. 1 Hydraulic energy storage and conversion system
Wang and Lu Protection and Control of Modern Power Systems (2018) 3:7 Page 2 of 9
1þmf c fmgcυ
� �dTdt
¼ Tw−Tτ
−1cυ
RTυ
1þ bυ2
� ��
þ 1υ2
B0RT þ 2C0
T 2
� �−
2c
υ3T 2 1þ γυ2
� �e−γ=υ
2
dυdt
;
ð6Þ
with a thermal time constant of
τ ¼ mgcυhAw
: ð7Þ
Obtaining υ from (1), the gas temperature can becalculated by (6). Then, gas absolute pressure pg can beobtained by (2).The pressure difference between pa and pg is the pres-
sure loss caused by the friction, e.g. flow entranceeffects, viscous shear, etc. Detailed modelling of frictionloss is possible but its magnitude does not justify thecomplexity it brings into the analysis. To simplify themodel, the pressure loss (as percentage of the fluid pres-sure pa at accumulator inlet) is assumed to be half of thefriction loss (as percentage of input Lf /E), as
pg−papa
¼ sgn dVð Þ k2Lf
E; ð8Þ
where sgnðdV Þ ¼ þ1−1
fluid outflowfluid inflow
;
Lf is the accumulator friction loss in one cycle, E isthe energy input to the accumulator in one cycle, and kis a factor introduced to avoid pressure jump when flowdirection changes. A simple linear variation of k whenflow direction changes is illustrated in Fig. 2.
2.2 Hydraulic motor/pumpHydraulic motor/pump is an energy conversion device.It converts hydraulic energy to mechanical energy whenoperating in motor mode, and mechanical energy tohydraulic energy while operating in pump mode. Thus,it has two interfaces: (a) from the hydraulic side whereactual flow rate entering the hydraulic motor/pump Qm
and pressure difference between the inlet and outlet Δpare required; (b) from the mechanical side where actualtorque Tm and angular velocity ω are needed.
The ideal flow rate of the fluid entering the hydraulicmotor/pump can be calculated by
Qmi ¼ xωD; ð9Þwhere D is the maximum motor/pump displacement perradian, ω is the angular velocity, and x is the fraction ofmaximum unit capacity. It is known that x is related tothe swivel angle α0 of the hydraulic motor/pump as[http://www.insanehydraulics.com/library/files/Hydraulic-Trainings-for-Axial-Piston-Units.pdf].
x ¼ sinα0sinα0; max
: ð10Þ
Swivel angle α0 can be either positive or negative asthe hydraulic motor/pump has two operation modes. Itis defined in this analysis that the flow rate is positive inmotor mode, which corresponds to positive swivel angle.
2.2.1 The volumetric efficiencyIn reality, the ideal flow rate is always lower than the ac-tual flow rate Qm in motor mode, due to leakage, cavita-tion, and fluid compressibility. By neglecting thecavitation loss, which is small for modern hydraulic motor,the volumetric efficiency can be calculated as [15].
ηυ ¼Qmi
Qm¼ 1
1þ Cs
x Sþ Δp
βþ Cst
x σ
; ð11Þ
where Cs and Cst are the laminar and turbulent leakagecoefficients respectively, and β is the fluid bulk modulusof elasticity (1660 MPa for most hydraulic fluid). S and σare given as.
S ≡μωΔp
; andσ ≡ωD1=3
2Δp=ρð Þ1=2; ð12Þ
where μ is the fluid viscosity, and ρ is the fluid density.
2.2.2 The torque efficiencyThe torque provided by an ideal hydraulic motor is
Tmi ¼ x Δp D: ð13ÞThe motor torque efficiency may be calculated as [15].
ηt ¼Tm
Tmi¼ 1−
CυSx
−C f
x−Chx
2σ2; ð14Þ
where Cυ, Cf and Ch are the viscous, frictional, andhydrodynamic loss coefficients, respectively. Then, theactual torque Tm provided by the hydraulic motor canbe found, which is used to drive the electric generator.Similarly, the equivalent equations for pump mode are
ηυ ¼Qm
Qmi¼ 1−
Cs
xj jS −Δpβ
−Cst
xj jσ ; ð15ÞFig. 2 Illustration of pressure drop coefficient
Wang and Lu Protection and Control of Modern Power Systems (2018) 3:7 Page 3 of 9
2.3 ReservoirThe reservoir normally has a slightly higher pressurethan the minimum intake pressure of the hydraulicmotor/pump to ensure proper operation. A low-pressureaccumulator with a relatively large volume is consideredto serve this purpose in the analysis. Thus, the changingspeed of the gas volume is relatively low during theoperation, which means that the thermodynamic processcan be assumed to be quasi-static and the gas can betreated as ideal. The gas thermodynamic process in thereservoir can be described by the Polytropic relationship
prVnr ¼ Constant; ð17Þ
where pr and Vr are the gas pressure and volume in thereservoir respectively, and n is heat capacity ratio. For adiatomic gas, such as nitrogen, n = 1.4 [16].
2.4 PipelineThe main hydraulic components are connected by pipe-lines, including pipes, hoses, unions, fitting, bends,valves, etc. All these connecting elements have similarcharacteristics regarding the pressure loss, i.e. the loss isproportional to the square of the actual flow ratethrough the element. Thus, the total pressure loss in thepipelines Δpp can be estimated by summing the “equiva-lent pipe length” of all elements
Δpp ¼ fLpDp
ρ2
Q2p
A2p
; ð18Þ
where f is the friction coefficient, Lp is the total effectivepipe length, Dp and Ap are the equivalent pipe internaldiameter and cross-sectional area respectively, and Qp isthe flow through the pipelines.The friction coefficient f is related to the fluid velocity
through the pipelines. When the fluid velocity is highenough, the flow in the pipelines becomes turbulent flowinstead of laminar flow. Reynolds number is used tojudge the flow type
Re ¼ 4 Qp
�� ��π Dp v
; ð19Þ
where v is the fluid kinematic viscosity. For laminar flow
f ¼ 64= Re; Re≤2000: ð20Þ
While for turbulent flow
f ¼ 0:332 Re−1=4; 2000 < Re≤105: ð21Þ
2.5 Electrical generatorThe generator converts the mechanical energy from thehydraulic motor to electrical energy. A Surface-MountedPermanent Magnet Synchronous Generator (SM-PMSG)is chosen to simplify the analysis as well as achievinghigh energy efficiency. The machine torque equation is
Te ¼ nph2
pλpmIs cosφi; ð22Þ
where Te is the machine electromagnetic torque, nph is thenumber of phases, p is the number of pole-pairs, λpm is theflux linkage from the permanent magnets, Is is the machinecurrent amplitude, and φi is the internal power factor angle(angle between current and internal voltage).To use the machine current effectively, the machine
current vector angle is controlled to achieve unit internalpower factor, i.e. cosφi = 1. Thus, Is can be obtainedaccording to (22) for certain Te. Then, the machine copperloss can be calculated as
pCu ¼ 0:5nphI2s Rs; ð23Þ
where Rs is the machine phase resistance.At certain machine rotary speed nr, the corresponding
machine electrical frequency fs can be calculated as
f s ¼ p � nr=60: ð24ÞThe machine iron loss includes the hysteresis loss and
eddy current loss, which are proportional to fs and f 2s ,respectively. Then, the generator energy efficiency canbe calculated as
ηg ¼Pout
Pin¼ Teωr−pCu−Chys f s−Cedy f
2s
Te þ Bmωrð Þωr; ð25Þ
where Bm is the machine viscous friction coefficient, Chys
and Cedy are the hysteresis and eddy current loss coeffi-cients, respectively.
2.6 System integrationTo integrate the above main components and form thehydraulic system illustrated in Fig. 1, the following rulesshould be complied with.
2.6.1 The continuity equationThe effective flow rate Qe is equal to the sum of theactual flow rates entering the accumulator Qa and thehydraulic motor Qm
Qe ¼ Qa þ Qm: ð26ÞThe effective flow rate Qe is equal to the system input
flow rate Qin when relief valve is not activating
Wang and Lu Protection and Control of Modern Power Systems (2018) 3:7 Page 4 of 9
Qe ¼ Qin
Qm
;when pa < pa; max;when pa≥pa; max
ð27Þ
2.6.2 Pressure balanceThe pressure difference between the accumulator andreservoir is equal to the pressure drop on the hydraulicmotor and pipelines
Δp ¼ pa−pr− sgn α0ð Þ Δpp: ð28Þ
where
sgn α0ð Þ ¼ þ1−1
motor modepump mode
: ð29Þ
2.6.3 The equation of motionThe connection between the hydraulic motor and elec-trical generator should follow the motion equation as
Tm ¼ Jdωr
dtþ Bmωr þ Te: ð30Þ
where J is the total moment of inertia of the rotary partsof the hydraulic motor and electrical generator.
3 System implementationThe HESC system can either be integrated into the PTOsystem or be included as a subsystem of the WEC. Fig. 3aillustrates a typical PTO system (e.g. a float module of aPA-WEC) integrated with a HESC system. The bi-
directional flow obtained from the symmetric cylinder isconverted to unidirectional flow by e.g. a hydraulic “H-bridgerectifier” consisted of four non-return valves. Then the uni-directional flow serves as the input of the HESC system. Inaddition, the HESC system could be integrated as a subsys-tem of the WEC as shown in Fig. 3b, so that the hydraulicmotor and generator used in the PTOs are not oversized [8].A PTO system integrated with HESC system is studied
in this paper. Fig. 4 shows the extracted power profile,which is optimized by certain Wave Power ExtractionAlgorithm (WPEA) [8]. It corresponds to the power pro-file that the PTO system of Wavestar WEC [11] canextract from sea state 3, which has large waves. Whilesea state 1 and 2 correspond to small and medium waveconditions, respectively.When knowing the extracted power from the cylinder
Pin, the system input flow rate can be calculated as
Qin ¼ Pin=pa; ð31Þ
where pa is the accumulator inlet pressure.
3.1 Control strategyIt is seen from Fig. 4 that the harvested wave energy hasa period around 3 s, which is much longer than the elec-trical time constant of a generator. Therefore, it is justi-fiable to state that the hydraulic motor and the electricalgenerator can be controlled to operate at a constantspeed, e.g. the synchronous speed of the generator.Due to the facts that the system input flow rate varies as
the input wave energy fluctuates (31) and the storagecapability of the accumulator is limited, the flow rate usedto drive the hydraulic motor should be well adjusted toensure smooth power output. Variable-displacement con-trol of the hydraulic motor, which is achieved by varyingthe fraction of maximum unit capacity x defined in (10),can be adopted for constant speed drive.From the storage capacity point of view, a feasible and
direct indication signal can be the fluid level in the accu-mulator, which can be transformed to the gas volume V.The control strategy of x could be:
Floatmodule
...Floatmodule
Floatmodule
Floatmodule
...Floatmodule
Floatmodule
Overflow
DC...
...
...MG
3~grid
HESC system
a
b
HESCsystem
Energy overflow
Backflow
DC
Fig. 3 PTO system with HESC system integrated. a Floatmodule with HESC system. b HESC subsystem handling theoverflow energy of PTOs Fig. 4 Power profile at sea state 3, for the WaveStar [11]
Wang and Lu Protection and Control of Modern Power Systems (2018) 3:7 Page 5 of 9
(a)when V reaches its maximum allowable volumeVmax, no more fluid is allowed to flow out of theaccumulator and x is set to zero;
(b)when V is below a pre-set value Vpre (e.g. 80% ofVmax), x is set to one to enable maximum output;
(c)when V is between Vpre and Vmax, x is given by
x ¼ Vmax−VVmax−Vpre
: ð32Þ
However, the above control strategy of x may result inoverloading of the generator. Therefore, power controlshould be taken into account as well. A simpleproportional-integral (PI) regulator is used to adjust themaximum allowable x, where the rated torque of thegenerator (or the rated phase current amplitude) is setas the reference. The minimum value of x obtained fromstorage capacity control and torque/current control ischosen when driving the hydraulic motor.
3.2 System configurationThe parameters of the gas accumulator, hydraulic motor,and generator used in the analysis are given in Tables 1, 2and 3, respectively.Eight gas accumulators are connected in the HESC
system to provide enough storage capability. The massof gas in the reservoir is 2 kg with a pressure of0.394 MPa. The total effective pipe length and theequivalent pipe internal diameter are estimated to be12 m and 0.015 m, respectively. The fluid in the system isoil with the density and kinematic viscosity of 869 kg/m3
and 60×10−6 m2/s, respectively.
3.3 System operation performanceFigure 5 shows the HESC system operation performanceat sea state 3. It can be seen that the system pressure iscontrolled and limited to the maximum allowable valueof the accumulator inlet absolute pressure (i.e. 21 MPaas listed in Table 1). When the input wave energyexceeds the system’s capability (e.g. during time range of24 s to 28 s), the relief valve activates and the flow enteringthe accumulator is zero. Moreover, it can be observed fromthe time interval 29~ 33 s that the generator output poweris well controlled and limited to its rated power (i.e.35 kW). When the system pressure is about 18 MPa at29 s, the fraction of maximum unit capacity x of the
hydraulic motor is one to maximize its output. Due to thesurge input, the output power of the hydraulic motor in-creases as the system pressure increases. Thus, x is adjustedby the controller to limit the hydraulic motor shaft output,so that the generator will not exceed its rated value. It canbe seen that the energy efficiency of the HESC system itselfis around 61.7%. While for the whole system, where theoverflow is considered as loss, the energy efficiency is about53.2%.
4 Design optimizationThe efficiency of the example system shown in Fig. 5 isnot very satisfactory. Thus, investigation into the designof the system ratings is carried out in this section tooptimize the system energy efficiency.Figure 6 shows the system energy efficiency with
different system rating configurations at 21 MPa systempressure with generator power rating varying from30 kW to 40 kW. It can be seen from Fig. 6a that theHESC system efficiency increases as the maximumhydraulic motor/pump displacement D decreases in awide range (40 to 120 cm3/rev). However, the maximumaccumulator gas volume Vmax (storage capacity) haslimited influence on the HESC system efficiency. This isbecause that the energy overflow is not considered aslosses of the HESC system, since it could be handled byanother HESC system as shown in Fig. 3b. However,such assumption will result in unreasonable smallsystem capacity, since small D means small torque (13).Thus, the whole system efficiency should be taken intoaccount when performing design optimization. It can beseen in Fig. 6b that there is an optimal D value (around100 cm3/rev), which can provide higher whole systemefficiency.Figure 6c shows the whole system efficiency at sea
state 2, where medium wave condition presents and less
Table 1 Gas accumulator parameters [17]
Mass of Gas 1.213 kg Max. Gas Volume 15.271×10−3 m3
Mass of Foam 1.496 kg Foam Specific Heat 2300 J/kg·K
Wang and Lu Protection and Control of Modern Power Systems (2018) 3:7 Page 6 of 9
energy can be extracted. It can be seen that the optimalD value to achieve best whole system efficiency is re-duced to around 60 cm3/rev. This is reasonable sincethe average wave power is reduced, and a system withpower ratings close to the wave power level could pro-vide higher energy efficiency.Moreover, rather than the HESC system efficiency
shown in Fig. 6a, the whole system energy efficiency isdependent on the accumulator storage capacity Vmax.Large Vmax will certainly help to increase the systemefficiency as shown in Fig. 6b and c. Furthermore, thegenerator power rating, which can be considered as thesystem power rating, will also influence the systemefficiency. However, the influence is small as can be seenin Fig. 6a though higher power rating is likely to giveslightly higher system efficiency when the system isproperly designed.
4.1 Influence of system pressureIt has been observed from Fig. 6a that small D can helpto increase the HESC system efficiency. However, small
D will reduce the system power rating (13), and thewhole system efficiency is decreased due to largeamount of energy overflow. A straightforward way is toincrease the system pressure. According to (13), D can
Fig. 5 HESC system operation performance at sea state 3
Fig. 6 System energy efficiency at 21 MPa system pressure withdifferent generator power ratings. a HESC system efficiency atsea state 3. b Whole system efficiency at sea state 3. c Wholesystem efficiency at sea state 2
Wang and Lu Protection and Control of Modern Power Systems (2018) 3:7 Page 7 of 9
be halved when Δp is doubled. Fig. 7 shows the wholesystem energy efficiency when the system pressure is42 MPa. It can be seen that the whole system efficiencyfor both sea state 2 and 3 can be balanced when D isaround 50 cm3/rev, which is about half of the original Din Table 2.Compared with the system efficiency at 21 MPa, the
energy efficiency increases from 59.8% to 74.0% for seastate 3, from 71.1% to 82.3% for sea state 2. Furthermore, itcan be observed that the system storage capacity has itssaturation value of around 300 l at sea state 2; while thesystem efficiency can still be improved by increasing thestorage capacity at sea state 2 when 21 MPa systempressure is applied. Thus, increasing the system pressurewill help to increase the system efficiency and reduce thesystem storage capacity required.Further increase to the system pressure could be con-
sidered to achieve slightly higher energy efficiency, e.g.76.9% and 83.2% for sea state 2 and 3 respectively at63 MPa. However, the cost of high-pressure devices in-creases as the pressure rises. Detailed evaluation is
needed to find the optimal system pressure, so that themost economical system solution can be obtained.
5 ConclusionIn this paper, a HESC system for WECs is introducedand modelled in details. Control strategy is proposed toensure that all the components are operating properlywithin their maximum limits. A case study of the HESCsystem is provided to evaluate the proposed controlstrategy and the system efficiency by taking the powerprofile of the WaveStar project as an example. Designinvestigation of the HESC system is then carried out tooptimize the system energy efficiency. It is found that i-ncreasing the system pressure will help to increase thesystem efficiency and reduce the required optimalsystem storage capacity although the cost of high-pressurecomponents will also increase. The balance between thesystem cost and payback of extra energy harvest should becarefully evaluated. The analysis carried out in this papercan be used to achieve the optimal system design of theHESC system.
Authors’ contributionsDW carried out the design of the study, developed the system model,performed the system design investigation and optimization, analyzed thedata, and drafted the manuscript. KL initialized the problem, coordinated theresources, participated in the design and data analysis, and helped to draftthe manuscript. All authors read and approved the final manuscript.
Competing interestsThe authors declare that they have no competing interests.
Received: 28 September 2017 Accepted: 31 January 2018
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