Research Article Dynamic Modeling and Simulation of a ...downloads.hindawi.com/journals/mse/2014/376781.pdfDynamic Modeling and Simulation of a Thermoelectric-Solar Hybrid Energy System

Research ArticleDynamic Modeling and Simulation ofa Thermoelectric-Solar Hybrid Energy System Usingan Inverse Dynamic Analysis Input Shaper

A. M. Yusop, R. Mohamed, A. Ayob, and A. Mohamed

Department of Electrical, Electronic and Systems Engineering, Faculty of Engineering and Built Environment,Universiti Kebangsaan Malaysia (UKM), 43600 Bangi, Selangor, Malaysia

Correspondence should be addressed to A. M. Yusop; [email protected]

Received 8 February 2014; Accepted 27 May 2014; Published 24 June 2014

Academic Editor: Mingcong Deng

Copyright © 2014 A. M. Yusop et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This study presents the behavioral model of thermal temperature and power generation of a thermoelectric-solar hybrid energysystem exposed to dynamic transient sources. In the development of thermoelectric-solar hybrid energy system, studies havefocused on the regulation of both systems separately. In practice, a separate control system affects hardware pricing. In this study,an inverse dynamic analysis shaping technique based on exponential function is applied to a solar array (SA) to stabilize outputvoltage before this technique is combined with a thermoelectric module (TEM).Thismethod can be used to estimate themaximumpower point of the hybrid system by initially shaping the input voltage of SA.The behavior of the overall system can be estimated bycontrolling the behavior of SA, such that SA can follow the output voltage of TEM as the time constant of TEM is greater than thatof SA. Moreover, by employing a continuous and differentiable function, the acquired output behavior of the hybrid system can beattained. Data showing the model is obtained from current experiments with predicted values of temperature, internal resistance,and current attributes of TEM.The simulation results show that the proposed input shaper can be used to trigger the output voltageof SA to follow the TEM behavior under transient conditions.

1. Introduction

Issues involving the continuous increase in oil price and envi-ronmental awareness have attracted extensive research inter-ests for renewable energy power generation. Solar energy,hydro energy, nuclear energy, andwind energy are commonlyused to produce electricity, thereby reducing carbon dioxidegas emissions [1]. Solar energy is one of the most frequentlyused types of renewable energy; however, solar energy shouldbe stored for future use because sunlight is the only sourceof this type of energy; as such, the availability of this type ofenergy varies with time.

The conversion of solar energy into electricity can be con-ducted by applying photovoltaic technology.This technologyhas received remarkable progress since 1839 [2]. However,solar array (SA) fails to function at certain times of theday; for this reason, researchers have been prompted toimprove SA efficiency. Although efficiency can be further

enhanced, the improvement of SA performance has beenimpeded because of heat dissipation and development costs[2, 3]. TEM is a preferable device to overcome the currentproblems on photovoltaics, in which this solid state deviceis able to transform waste thermal energy into electricitywhen thermal gradient is present between two junctions [4].This device can be considered as one of the most efficientcandidates used for energy conversion because this energyproduces no waste matter during conversion. However, TEMcannot operate individually as a beneficial energy converter.In several studies, SAs and TEMs have been combined todevelop a hybrid energy system that utilizes the benefits ofboth technologies [1, 5–7].

SA and TEM are nonlinear devices with output char-acteristics depending permanently on external substantialeffects, such as maximum power point that should be trackedefficiently [5]. In a previous study [1], a hybrid energy systemcomprised a dual Ćuk converter to lodge power for multiple

Hindawi Publishing CorporationModelling and Simulation in EngineeringVolume 2014, Article ID 376781, 13 pageshttp://dx.doi.org/10.1155/2014/376781

2 Modelling and Simulation in Engineering

inputs; this hybrid is suitable for a grid connected system.Theproposed method in another study [5] considers an optimalcircuit design to control solar energy power, in which SA andTEM are arranged in a master/slave mode. Using an optimalcircuit, a controller is developed to predict the maximumpower point and can control both systems simultaneously.An extension hybrid TEM-SA system with liquid cooling isassembled to increase the efficiency of current hybrid systems[6, 7].

This study aims to conduct a dynamic analysis of ahybrid TEM-SA configuration by using MATLAB with extraidentification to increase the efficiency of the existing hybridTEM-SA and to reduce the energy consumption of thesystem. Previous studies have also focused on an MPPT-designed circuit in hybrid energy systems. As such, thisMPPT circuit should be designed separately for both systemsbecause various maximum power points are obtained fordifferent systems. Although an optimal controller circuit isdesigned to control SA behavior [5], this circuit uses passiveelement devices, together with a digital signal processor.One of the drawbacks of this technique is the increasedpower consumption of the power circuit because of digitalcomputation. For this reason, a feedforward controller withregard to input shaping scheme is introduced in this study.Input shaping is commonly used controller technique tocontrol the vibration of moving or flexible systems [8, 9].This technique is also used to control the settling timeof a positioning system from one value to another [10].Studies have also focused on this field since the 1980s.In input shaping, several approaches, including “posicast”control [11, 12], impulse shaping [13], command shaping [14],zero vibration derivative technique (ZVD) [15], and extrainsensitive technique [16], are used. In a previous study [17],a three-step (TS) input shaping technique was applied, inwhich three-impulse shaping is provided with positive andnegative shapers. In this technique, this new shaper extendsthe current zero vibration derivative (ZVD) technique toa generalized TS shaper method; this improved techniquecan function appropriately in any dynamic model. In thesemethods, input function should be computed and outputbehavior mainly depends on the given input. An inversedynamic analysis type of input shaper has been proposed byPiazzi and Visioli [18] via employing polynomial function asthe acquired output function. Although the ideas of Piazziand Visioli are interesting and useful, they need to switchthe polynomial function into another function because ofthe erratic behaviour of this function after attaining the endpoint. This argument is accepted by all critics. For instance,Iravani and Sahinkaya in [19] hold that the switching willbring in the discontinuity in both the first and secondderivatives of the function which leads to the unstable outputbehaviour of the applied system. Particularly, Zhao et al. intheir continuousworks in [20–22] concentrate on the stabilityproblem in arbitrary switching. The addressed problem issolved by introducing multiple copositive types Lyapunov-Krasovskii functional. Additionally, the multiple copositivetypes Lyapunov-Krasovskii functional is reduced to thecommon copositive type Lyapunov-Krasovskii functional. Inhere, they consider applying the suggested method to the

feedback controller. Anothermethod regarding the switchingsignal is the dwell timemethodwhich has received increasingattention since this method is able to stabilize the systemwhen the dwell time is adequately high; see [23–25].

Moreover, the idea from Piazzi and Visioli has beenextended in previous studies [8, 9, 19, 26] using exponentialfunction which has been proven to overcome the limitationof the polynomial function. On the whole, this inversionscheme is based on the feedforward control technique whichdoes not need feedback measurements. As a matter of fact,in SA design, the occurrence of feedback measurement toobtain the maximum power tends to increase the energyconsumption of the overall system.

In this study, an inverse dynamic analysis type of aninput shaper based on exponential function was added tothe SA model to control the input behavior of a photovoltaicarray. The controller part in SA is designed so that the SAis able to collect solar energy throughout the day. Moreimportantly, the voltage and intensity formed by the SAcan be controlled consecutively to function at the highestoperating point. With this method, the energy consumptionof the system is further minimized. Significant efforts havebeen devoted to the development of this input shaper, inwhich the input shaper is designed according to the acquiredoutput behavior of the hybrid energy system. In addition, theinverse dynamic type input shaper can be established by usingbuilt-in control blocks, which can be further combined usingSimPowerSystem tools for the MPPT circuit development.

2. Modeling of the ThermoelectricModule and Solar Array

Themodels of TEM and SA modules are designed separatelyby inserting the corresponding numbers of modules in seriesor parallel before both systems are combined. As the timeconstant of TEM is evidently greater than that of SA, TEMis designed to function as the master and SA is designed asthe slave.

2.1. Modeling of the Thermoelectric Module. In this model,TEM functions under a dynamic condition, in which thetemperature of the cold side is maintained for natural coolingto produce a dynamic response because many studies havefocused on the analysis of a steady state behavior, whichonly involves constant temperature [4]. In practice, thetemperature of TEM input fluctuates with time.

To obtain the heat model of TEM, we considered severaleffects, including thermal conduction, Joule, Peltier, Seebeck,and Thomson. However, Thomson effect is ignored becausesuch effect is very small.

To ensure that heat is distributed equally at both junc-tions, we should ensure that TEM exhibits high thermalconductivity. Thermal conductivity is expressed according toFourier process with heat transfer, 𝑄tc, as follows:

𝑄tc = −Δ𝑇𝜅tc, (1)

where 𝜅tc is the thermal conductivity and Δ𝑇 is the differencebetween sides of high and low temperatures. Joule effect is

Modelling and Simulation in Engineering 3

produced internally when electrical current, 𝐼, flows acrossa thermoelectric leg. This effect is observed in both sides atdifferent temperatures but with the same amount of energyas follows:

𝑄joule = 𝐼2𝑅, (2)

where 𝑅 is the electrical resistance. Peltier effect is observedwhen electrical current flows through two different junctionsand the total heat transfer is expressed as follows:

𝑄peltier = 𝛼Δ𝑇𝐼, (3)

where 𝛼 is the Seebeck coefficient of the TEG. Seebeck effectshows that the temperature difference between two differentelectrical conductors or semiconductors produces a voltagedifference between two junctions. Seebeck coefficient is alsodefined as follows:

𝛼 =𝑉

Δ𝑇. (4)

In the design of a TEM at specific thermal flow and tem-perature, the maximum power point should be obtained. Ifload resistance is equal to the internal resistance of TEM,output power is equal to the peak value. Equation (5) showsthe energy balance equations used for steady state analysis athot and cold junctions of TEM as follows:

𝑄ℎ= 𝛼𝑇ℎ𝐼 − 𝜅tcΔ𝑇 − 0.5𝐼

2𝑅,

𝑄𝑐= 𝛼𝑇𝑐𝐼 − 𝜅tcΔ𝑇 + 0.5𝐼

2𝑅.

(5)

To develop a good TEM, a high Seebeck coefficient, togetherwith low electrical resistance and low thermal conductivity,should be provided [27]. In the figure of merit, 𝑍 relates thisstatement and is expressed as follows:

𝑍 =𝛼2

𝑅𝜅 tc. (6)

In terms of the electrical properties of TEM, the followingparameters are frequently used to specify TEM characteris-tics: 𝑇

ℎ, temperature in the hot side; 𝑇

𝑐, temperature in the

cold side; 𝑊𝑚, the power at the load resistance, 𝑅

𝐿, internal

resistance,𝑅, where (𝑅𝐿= 𝑅); and𝑉

𝑚, load voltage. Electrical

resistance and Seebeck coefficient are expressed as follows:

𝑅 = 𝑅𝐿=𝑉2

𝑚

𝑊𝑚

,

𝛼 =2𝑉𝑚

Δ𝑇.

(7)

The following relationship shows that load resistance can bevaried in proportion to internal resistance. Consider

𝑅𝐿= 𝑚𝑅, (8)

where 𝑚 is the ratio between load resistance and internalresistance. In (4), 𝐼 is expressed as follows:

𝐼 =𝛼Δ𝑇

(1 + 𝑚)𝑅. (9)

Table 1: Specification of TEM (TEP1-12656-0.6).

Specifications ValuesHot side temperature (∘C) 300Cold side temperature (∘C) 30Open circuit voltage (V) 8.4Matched load resistance (Ω) 1.2Matched load output voltage (V) 4.2Matched load output current (A) 3.4Matched load output power (W) 14.6Heat flow across the module (W) ≈365Heat flow density (W cm−2) ≈11.6AC resistance measured at 27∘C and 1000Hz (Ω) 0.5–0.7

Themaximum output power at matching load, 𝑅𝐿= 𝑅, is

obtained before any controller or MPPT circuit is designed.The maximum current of TEM is the short-circuit current atzero load voltage, 𝑉

𝐿= 0, which is expressed as follows:

𝐼short-ckt = 2𝐼𝑚 =2𝑊𝑚

𝑉𝑚

. (10)

According to Ohm’s Law and the resulting equations (9)and (10), the TEM voltage can then be obtained as follows:

𝑉 = −𝑅 (𝐼 − 𝐼short-ckt) . (11)

The TEM model TEP1-12656-0.6 (Thermonamic) is usedin this model, in which steady-state analysis is initiallyconducted to verify the electrical parameters of the TEMmodel. The specifications of the TEG module (TEP1-12656-0.6) are listed in Table 1 and the parameters for steady statecondition verification are obtained by applying equations (1)to (6). The value of the model parameter under steady stateanalysis can be calculated as follows; 𝛼 = 0.031V/K, 𝑅 =1.2Ω, 𝜅tc = 20.85W/K, and 𝑍 = 3.869 × 10

−5𝐾−1.

The TEM model is implemented using MATLAB/SIM-ULINK as shown in Figure 1. The inputs of the modelinclude the sides with cold and hot temperatures of the TEMconfiguration.

2.2. Modeling of Solar Array. The characteristics of SAdepend on the solar radiation and temperature of the SAsurface. As solar radiation is increased, power produced bySA is increased; by comparison, an increase in temperaturereduces output power. To attain the highest output power, weshould reduce the temperature of SA. The equivalent circuitof the solar cell is shown in Figure 2.

A group of solar cells is then combined in series-parallelconfiguration to structure as an SA. In Figure 2, cell pho-tocurrent, 𝐼PH, functions as current source,𝑅SH is the internalshunt resistance of the cell, and 𝑅

𝑆is the series resistance

of the cell. In a previous study [28], SA can be modeledmathematically using (12) to (15). The 𝐼-𝑉 characteristic ofSA is represented as follows:

𝐼SA = 𝑁𝑃𝐼PH − 𝑁𝑃𝐼SAT [exp{𝑞 (𝑉SA + 𝐼SA𝑅𝑆)

𝑁𝑆𝐴𝑘𝑇

} − 1] , (12)


2Voltage scope

1Current scope

Voltage scope

To workspace3

I

To workspace2

V

To workspace1P

To workspace

115 Current scope

Voltage scope

Subsystem

Scope3

Scope1

Repeatingsequence

interpolated

Product Power scope

Current scope

Th1Th

Tc

Tc

Figure 1: TEM block model as applied in MATLAB.

LoadIPH

ISAT

RSH

RS

ISA

Figure 2: Equivalent circuit of a solar cell.

Table 2: Factor of 𝐴 depends on PV technology [31].

Technology Value of 𝐴Si-mono 1.2Si-poly 1.3a-Si:H 1.8a-Si:H tandem 3.3a-Si:H triple 5CdTe 1.5CIS 1.5AsGa 1.3

where 𝐼SA and 𝑉SA are the output current and the outputvoltage of SA, respectively, 𝐼SAT is the saturation current thatvaries with cell temperature,𝑁

𝑃and𝑁

𝑆are the total number

of cells in parallel and in series, respectively, 𝑞 is the chargeof an electron (1.6 × 10−19 C), 𝑅

𝑆is the series resistance,

𝐴 is the ideality factor of a p-n junction, which dependson the photovoltaic voltage (PV) technology (Table 2), 𝑘 isBoltzmann constant (1.3805×10−23 J/K), and𝑇 is themoduleoperating temperature.

𝐼PH is directly proportional to solar insolation and isdefined as follows:

𝐼PH = [𝐼SC + 𝐾𝑖 (𝑇 − 298)] ×𝜆

1000, (13)

where 𝐼SC is the short circuit current, 𝐾𝑖 is the shortcircuit current coefficient at 𝐼SC, and 𝜆 is the PV moduleillumination.

Table 3: Specification of solar module (SR10-36).

Specifications ValuesMaximum power (W) 10Maximum power voltage (V) 17Maximum power current (A) 0.59Open circuit voltage (V) 21.6Short circuit current (A) 0.64

Themodule saturation current, which keeps changes withcell temperature, is expressed as follows:

𝐼SAT = 𝐼RS(𝑇

𝑇ref)

3

exp [𝑞 × 𝐸𝑔

𝐴𝑘(1

𝑇ref−1

𝑇)] , (14)

where 𝐼RS is the reverse saturation current,𝑇ref is the referencetemperature, and 𝐸

𝑔is the band gap for silicon (1.1 eV). 𝐼RS in

(14) is expressed as follows:

𝐼RS =𝐼SC

[exp (𝑞 × 𝑉OC/𝑁𝑠𝑘𝐴𝑇) − 1], (15)

where 𝑉OC is the open circuit voltage.Solar module SR10-36 from Raloss is used as the SA

model in this design. The details of the electrical character-istics of the module are listed in Table 3 and this specificationis modeled using MATLAB/SIMULINK (Figure 3).

The 𝐼-𝑉 and 𝑃-𝑉 characteristics of SA depend on ter-minal operating voltage, insolation, and surface temperature.These characteristics are obtained by varying insolation atconstant temperature or varying temperature at constantinsolation. The polycrystalline silicon solar cells chosen inthis SA yield low power consumption and entail less pro-duction costs, which likely increase the total performance ofdevelopment [6].

3. Input Shaper for the Hybrid Energy System

The thermoelectric-solar hybrid energy system is imple-mented in the SIMULINK/MATLAB (Figure 4). The input


pv char

iv char

Voltage

Temperature

Temperature

Insol

Temp

Subsystem

Scope SA power

SA current

ProductIrradiation

Insolation

Vin Vout

Ipv

Figure 3: SA block model applied in MATLAB.

shaper used in inverse dynamic analysis is added at the inputof SA to control the output characteristic of SA, such thatthe TEM characteristic is observed. This system comprisessix pieces of TEM, two pieces of SA, and an input shaper.TheTEM is connected in series and thermally in parallel, whereasboth SAs are connected electrically in parallel to increase theoutput power of an individual system before these SAs arecombined to perform a hybrid energy system.

SA exhibits a nonlinear characteristic because the outputcharacteristics depend on external factors, such as tempera-ture and sunlight irradiation. Considering these factors, weshould accurately track the maximum power point of thisdevice. In this study, the inverse dynamic analysis exponentialtype of input shaper is used to simulate the input voltageof SA before it is connected to the other parts of the SAsubsystem. This input shaper also aims to reverse the controlmethod by initially indicating the system output functionand then deriving the input form. In this way, the formof output characteristics can be selected based on systemlimitations. In the present study, the output function shouldbe usedwith only one parameter to control the characteristicsfrom the final point onwards; as a result, a simple inputfunction is obtained.The particular constraint of output formdetermines output power along with controlling the systemlimitations. Figure 5 shows the 𝐼-𝑉 and𝑃-𝑉 characteristics ofa solar cell. In particular, power curve contains a maximumpower point (MPP). In this study, the MPP voltage, 𝑉MPP,is less than the open circuit voltage, 𝑉OC, and 𝐼MPP is lowerthan 𝐼SC. AtMPP, current and voltage exhibit almost the samerelation to irradiance and temperature changes.

The power behavior of SA is constant from an initialtime point to a specific end point until power decreasesdrastically to a negative value. For the selected SA model,power decreases to a large negative value, which likely resultsin an overall power curve to follow SA behavior. As aresult, TEM automatically follows the SA behavior, whichis impractical to obtain the maximum power of the overallsystem, when an SA diagram and a TEM block diagram arecombined to form a hybrid system.

3.1. Inverse Dynamic. The inverse dynamic is only applied tothe voltage equation of the SA since the current behaviourautomatically changed when the voltage function is changed.

As mentioned earlier, the SA power needs to be set to followthe TEM behaviour. Before designing any input shaper, theform of the target output waveform needs to be confirmedfirst. In the simulation, the SA input voltage is set to be asawtooth signal and based on Weisstein [30] this signal isrepresented as follows:

𝑉SA (𝑥) = 𝐴 frac(𝑥

𝑇+ 𝜙) , (16)

where frac(𝑥) is the fractional part frac(𝑥) ≡ 𝑥− ⌊𝑥⌋,𝐴 is theamplitude, 𝑇 is the period of the wave, and 𝜙 is its phase. Theoutput voltage of the SA is equivalent to the input voltage.From (16), it shows that the SA voltage form is a first ordersystem.

The system transfer function by only concentrating onvoltage form is expressed as follows:

𝑉SA (𝑢) × 𝐹 (𝑢) = 𝑋 (𝑢) , (17)

where 𝐹(𝑢) is the normalized input of the SA and𝑋(𝑢) is thenormalized desired output function. The normalized inputis obtained using inverse dynamic by substituting the SAsawtooth function and the desired output form in (17).

3.2. Desired Output Behavior. The function representing thepoint-to-point output characteristic should be differentiableand continuous at least up to a second order derivative atwhich the first derivative and the second derivatives at initialand final simulation time points, 𝑋

𝐸, are zero and remain

zero. According to [18], asymptotic behavior is desired whenthe final position is reached to remain in the same positionand the use of exponential functions introduced by [8] isone of the most efficient solutions. Here, the third orderexponential function of the output function is evaluated tocontrol the system from time = 0 to 𝑋

𝐸as the target output

waveform is similar to the first derivative of this exponentialfunction (Table 4). This third order exponential function isexpressed as follows:

𝑥 (𝑡) = 𝑋𝐸[1 − 𝑒

−(𝛼𝑡)3

] . (18)

To generalize the analysis, we can define the normalized time𝑢 as follows:

𝑢 = 𝛼𝑡. (19)

From (18) and (19), the normalized equation of the desiredoutput function is derived as follows:

𝑋(𝑢) =𝑥 (𝑡)

𝑋𝐸

= 1 − 𝑒−𝑢3

. (20)

The derivatives are shown in the following equations:

�̇� (𝑢) =1

𝛼𝑋𝐸

�̇� (𝑡) = −𝑒−𝑢3 𝑑

𝑑𝑢(−𝑢3) = 3𝑢

2𝑒−𝑢3

,

�̈� (𝑢) =1

𝛼2𝑋𝐸

�̈� (𝑡) = 3 [𝑢2 𝑑

𝑑𝑢(𝑒−𝑢3

) + 𝑒−𝑢3 𝑑

𝑑𝑢(𝑢2)]

= (6𝑢 − 9𝑢4) 𝑒−𝑢3

.

(21)


Table4:Ch

aracteris

ticso

fthe

prop

osed

output

functio

n.

Type

ofou

tput

functio

nEq

uatio

nof

theo

utpu

tfun

ction

Outpu

tfun

ctionbehavior

Actualou

tput

functio

n𝑋(𝑢)=𝑥(𝑡)

𝑋𝐸

=1−𝑒−𝑢3

00.05

0.1

0.15

0.2

0.25

0.3

Nor

mal

ized

tim

e, u=𝛼t

1

0.8

0.6

0.4

0.2 0

Actual output function

Firstd

erivativeo

factualoutpu

tfun

ction

𝑋(𝑢)=

1

𝛼𝑋𝐸

𝑥(𝑡)=−𝑒−𝑢3𝑑 𝑑𝑢( −𝑢3)=3𝑢2𝑒−𝑢3

1.4

1.2 1

0.8

0.6

0.4

0.2 00

0.05

0.1

0.15

0.2

0.25

0.3

Nor

mal

ized

tim

e, u=𝛼t

First derivative of actual output function


Table4:Con

tinued.

Type

ofou

tput

functio

nEq

uatio

nof

theo

utpu

tfun

ction

Outpu

tfun

ctionbehavior

Second

deriv

ativeo

factualoutpu

tfunctio

n𝑋(𝑢)=

1

𝛼2𝑋𝐸

𝑥(𝑡)=3[𝑢2𝑑 𝑑𝑢(𝑒−𝑢3

)+𝑒−𝑢3𝑑 𝑑𝑢( 𝑢2)]=(6𝑢−9𝑢4)𝑒−𝑢3

00.05

0.1

0.15

0.2

0.25

0.3

Nor

mal

ized

tim

e, u=𝛼t

Second derivative of actual output function

2.5 2

1.5 1

0.5 0

−0.5

−1

−1.5

−2

−2.5


2Out2

1Out1

i-v char

To workspace3

To workspace2

To workspace1

To workspace

-C-

TemperatureTemperature

Insol

Temp

Subsystem6

Current scope

Voltage scope

Subsystem

Scope5

Scope4

Scope3

Scope

SA power2

SA power1

SA power

SA current

Repeatingsequence2

Repeatingsequence Product1

Product

IrradiationInsolation

Add2

Vin Vout

IpvIpv

Vpv

Ppv

Tc

Tc

ThTh1

f(u)fcn1

Figure 4: Thermoelectric-solar hybrid energy system block model applied in MATLAB.

ISC

IMPP

Cell

curr

ent (

A)

PMPP

Cel

l pow

er (W

)

Cell voltage (V)VOCVMPP

MPP

00

Figure 5: 𝐼-𝑉 and 𝑃-𝑉 characteristics of a solar cell [29].

Stop

Start

Does the power behavior of the hybrid system follow TEM?

Recalculate theinput function

NO

Determine input function by inverse dynamic analysis

Integrate inputfunction in the

hybrid energy system

YES

Generate the desired motion

Obtain outputresponse

Figure 6: Design process of the inverse dynamic analysis.

0 100 200 300 400 500 600 7002030405060708090

Time (s)

Col

d sid

e tem

pera

ture

(∘C)

Figure 7: Temperature variation in the cold side of TEM.

Table 4 shows the characteristics of the proposed outputfunction defined by the actual output function as well as thefirst and second derivatives of the actual output functions. Asthe desired output voltage function of the SA is the same asthe first derivative of the third order exponential function,𝑋(𝑢) is set to be

𝑋(𝑢) = �̇� (𝑢) = 3𝑢2𝑒−𝑢3

. (22)

3.3. Exponential Input Shaping Design. The input functioncorresponds to the input voltage, which initially increasesproportionally with time to the exponential behavior. Assuch, the input function is calculated to be

𝐹 (𝑢) =(3𝑢2) 𝑒−𝑢3

𝑉SA (𝑢),

𝐹 (𝑢) =(3𝑢2) 𝑒−𝑢3

𝐴 frac (𝑢/𝑇 + 𝜙),

(23)

where 𝐴 = 30V, 𝑇 = 10 s, and 𝜙 = 0∘.


0 5 10 15 20 25 30 35 40 45 500

102030405060708090

TEM voltage

TEM

pow

er

(a)

0

1

2

3

4

5

6

7

TEM

curr

ent

0 5 10 15 20 25 30 35 40 45 50TEM voltage

(b)

Figure 8: TEM characteristics at a temperature variation from 25∘C to 85∘C: (a) 𝑃-𝑉 characteristic and (b) 𝐼-𝑉 characteristic.

0 5 10 15 20 2505

101520

Voltage (V)

Pow

er (W

)

1000W/m2

800W/m2500W/m2

300W/m2

(a)

00.20.40.60.8

11.2

Curr

ent (

A)

0 5 10 15 20 25Voltage (V)

1000W/m2

800W/m2500W/m2

300W/m2

(b)

Figure 9: SA characteristics at different insolation: (a) 𝑃-𝑉 characteristic and (b) 𝐼-𝑉 characteristic.

The new output power is determined to be the samebehavior as the input voltage. As a result, the total hybridpower tracks the TEM behavior because the SA powerbehavior is changed by the new input signal. Figure 6 showsthe design process of inverse dynamic analysis.

4. Simulation Results

Two simulation models are designed using MATLAB: onemodel is the hybrid systemwith an input shaper and the othermodel does not have an input shaper. From the standpoint ofthe TEM application, the maximum output power is desired,in which load resistance is set at the same value as internalresistance. The behavior of the individual system is plottedto configure mathematical modeling and the characteristicof output performance. For TEM, the low temperature datafrom a previous study [4] is used in the dynamic analysis ofthe TEM block at a constant high temperature of 115∘C. Thevariation in the low temperature is shown in Figure 7. Thelow temperature is gradually increased from 25∘C to 75∘C andmaintained at that value until the end of simulation time.

The characteristic of TEM, in which six thermoelectricgenerators are connected in series, is shown in Figure 8. AsTEGs are cascaded, single TEG voltages are combined andexpressed as follows:

𝑉𝑖= 𝑖 × 𝑉, (24)

where 𝑖 is the number of cascaded thermoelectric generators.Considering that power is directly proportional to voltage, wecan express total power as themaximumpower of single TEGmultiplied by the factor of 𝑖. In Figure 8, the total power is87.6W at the matched load current of 3.4 A and the matchedload voltage of 25.2 V.

For the SA block, the surface temperature is maintainedat 40∘C and simulation is conducted by varying insolation at300, 500, 800, and 1000W/m2. The 𝑃-𝑉 and 𝐼-𝑉 characteris-tics of SA are shown in Figure 9.

We compared the characteristics to verify the design byadding the input shaper to the input of SA and to the otherone without the input shaper. After the input shaper wasadded, the input voltage of SA changed to the first derivativeof exponential behavior (Figure 10).

For the next analysis, the SA voltage curve is changedto different curvature to see the effect after adding thesame input shaper as the previous analysis. It is notable bycomparing Figures 10 and 11 that the characteristic of the SAvoltage with input shaper is the same regardless of the givencurve of the initial SA voltage.The curve shows its peak valueis 1.18 V at time 0.88 s for both cases. This is the beauty ofthis exponential input shaper in view of the fact that it is ableto maintain and stabilize any form of curve according to itsexponential characteristic.

The performance of the hybrid energy system with theinput shaper is observed by varying the input of TEM asthe SA branch is fixed at 1000W/m2. The temperature of the


0 5 10 15 20 25 300

5

10

15

20

25

30

Time (s)

SA v

olta

ge w

ithou

t in

put s

hape

r (V

)

(a)

00.20.40.60.8

11.21.4

0 5 10 15 20 25 30Time (s)

SA v

olta

ge w

ithin

put s

hape

r (V

)

(b)

Figure 10: Case 1: SA voltage (a) without and (b) with input shaper.

0

5

10

15

20

25

SA v

olta

ge w

ithou

t in

put s

hape

r (V

)

0 5 10 15 20 25 30

Time (s)

(a)

00.20.40.60.8

11.21.4

0 5 10 15 20 25 30

Time (s)

SA v

olta

ge w

ithin

put s

hape

r (V

)

(b)

Figure 11: Case 2: SA voltage (a) without and (b) with input shaper.

20 30 40 50 60 70 80 900

102030405060708090

Hyb

rid p

ower

(W)

Cold side temperature (∘C)

Figure 12: Total hybrid power.

cold side of TEM is varied from 25∘C to 85∘C as observedin the power curve in Figure 12. The result shows that theoverall output power corresponds to the TEM behavior byonly controlling the SA part.

To summarize this method, we present the comparisonresults of the performance of the individual system and thehybrid systemwith and without the input shaper in Figure 13.

Figure 13 shows that the inverse dynamic analysis cancontrol the output behavior of SA to follow the TEMbehaviorunder a transient operating condition. It is worth stressingthat the following remarks can be concluded from Figures 7–13.

(1) This finding is one of the most important factorsthat should be considered before any MPPT circuitis designed for this hybrid system. This observationis considered because the time constant of SA is less

than that of TEM. SA is also established to imitate theTEM behavior. Hence, an appropriate behavior of theoutput power curve is initially developed to falsify theacquired overall output behavior of the hybrid system.

(2) The extra recognition of the inverse dynamic analysisinvolves a user that selects the optimum overallsystem behavior; this behavior is chosen to inducethe designed input function to respond to the selectedoutput function. This procedure can be conducted toreduce hardware pricing by not designing the separatecontroller for both systems before a hybrid system isformed. For this reason, this hybrid system can beused to estimate the MMP of the overall system byusing a single controller to regulate both systems.

(3) In contrast to the method presented in a previousstudy [5], the proposedmethod can reduce the powerconsumption of this hybrid system without usingany digital controller and achieve the desired outputpower curve.

(4) This system also reduces the bare bones of designingthe MPPT for different systems before such bones arecombined to form a hybrid system.

(5) By comparing with the existing works, it can beseen from Figure 10(b) that the SA voltage with theproposed input shaper follows the same character-istics of the similar input shaper applied to flexiblesystem in [8]. This proposed method is able tostabilize the hybrid system to certain condition which


0 5 10 15 20 25 30Time (s)

0

10

20

30

40

50

60

70

80

90TE

M p

ower

(W)

Without input shaper

(a)

0

10

20

30

40

50

60

70

80

90

TEM

pow

er (W

)

0 5 10 15 20 25 30Time (s)

With input shaper

(b)

SA p

ower

(W)

0 5 10 15 20 25 30Time (s)

1

0

−1

−2

−3

−4

−5

−6

×104

(c)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 5 10 15 20 25 30Time (s)

SA p

ower

(W)

(d)

0 5 10 15 20 25 30Time (s)

1

0

−1

−2

−3

−4

−5

−6

×104

Hyb

rid p

ower

(W)

(e)

Hyb

rid p

ower

(W)

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20 25 30

Time (s)

(f)

Figure 13: Power curve comparison.

is to follow the characteristic of the TEM. From thisobservation, the exponential function input shaper iscapable of obtaining the same characteristic in theapplication of energy systems although the system

is different since previously it was solitude to theapplication of flexible systems.

(6) Again, from Figure 10(b), the peak value of the SAvoltage is close to 1.18 V at the normalized time of


0.88 s. The same characteristic is drawn from [8]where the different systems are looking on.

The effectiveness of the exponential function input shaperwhen applied to the hybrid energy system of TEM-SA isconvincible to work very well since the output power curveneeds to be stabilized to certain value before MPPT circuit isdesigned. The stability factor is one of the main parametersthat will be stressed out after the MPPT is designed for thishybrid energy system.

5. Conclusion

A formulation of the TEM-SA behavior, which includesthermal behavior and electrical properties, has been devel-oped using MATLAB/SIMULINK. This model is used todetermine the output power characteristics of TEM, SA,and hybrid energy system for transient analysis. Simulationresults show that an inverse dynamic analysis based onexponential function can be applied to control the outputbehavior of the SA. The satisfactory curve of the hybridoutput power is achieved using this method. In addition,this method simplifies the control of the overall system,in which the controller is only designed to control the SAoutput behavior, such that SA behavior follows the TEMcharacteristic. The controlled input behavior is applied tofurther minimize the energy consumption of the system.Significant efforts have been devoted to the development ofthis input shaper. In this system, the input shaper is designedaccording to the acquired output behavior of the hybridenergy system. In addition, the inverse dynamic type inputshaper can be built by using built-in control blocks, whichcan be combined further using SimPowerSystem tools todevelop the MPPT circuit. The MPPT circuit can then beapplied in the hybrid system to obtain the MPP and generateelectricity for electronic device applications. Considering thatthe overall output behavior follows the TEM behavior, werecommend that only one MPPT circuit should be designedfor this hybrid system.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

Theauthors would like to thank theDepartment of Electrical,Electronic and Systems Engineering, Faculty of Engineeringand Built Environment, Universiti Kebangsaan Malaysia(UKM), the Universiti Teknikal Malaysia Melaka (UTeM),and theMinistry of Higher Education for moral, operational,and financial support for this project.

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