POLITECNICO DI MILANO

Transcription

1 POLITECNICO DI MILANO Facoltà di ingegneria industriale Corso di laurea magistrale in ingegneria elettrica Experimental analysis and modeling of a thermoelectric generator Relatore: Prof. Francesco Castelli Dezza Correlatore: Huilong Yu Tesi di: Daniele Radavelli Anno accademico: 2015/2016

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3 INDEX SYMBOLOGY... 6 ABSTRACT... 9 CHAPTER 1 THE THERMOELECTRIC GENERATOR AND THE MAIN THERMOELECTRIC PHENOMENA Introduction History of thermoelectricity Analysis of thermoelectric phenomena Seebeck effect Peltier effect Thomson effect Joule effect Link between the thermoelectric effects Thermoelectric generator CHAPTER 2 DC-DC CONVERTERS AND MPPT ALGORITHMS TEG application areas DC-DC converter Duty cycle and modulation techniques DC-DC converters DC-DC buck/step down converter DC-DC step up/boost converter Buck-boost converter Cuk converter Comparison between the converters MPPT algorithms P & O Algorithm: perturb and observe IC algorithm: incremental conductance Simple coupling between module and load CHAPTER 3 MODELLING AND SIMULATION OF THE THERMOELECTRIC GENERATOR Thermal model Electric model Calculation of the constitutive parameters of the model Efficiency of a thermoelectric generator Simulation of the thermoelectric generator with Matlab Simulink Thermal Circuit Electric circuit Electric circuit without the DC-DC converter Electric circuit with a DC-DC buck converter Electric circuit with a DC-DC boost converter Electric circuit with a DC-DC buck-boost converter Electric circuit with a DC-DC cuk converter CHAPTER 4 EXPERIMENT TEST design Overall description of the system Simulation of the MPPT algorithm with LabView Description of the main components of the system Thermoelectric generator Heat sink Heat Gun Control Board... 99

4 CHAPTER 5 CONCLUSION BIBLIOGRAPHY

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6 SYMBOLOGY V: voltage; I: current; R: resistance; T: temperature; ΔT: temperature difference; P: power; Q: thermal power; S: entropy; t: time; T1: temperature of the junction 1; T2: temperature of the junction 2; Ta: temperature of the side a; Tb: temperature of the side b; TH: temperature of the heat source; TE: temperature of the environment; THJ: temperature of the hot junction; TCJ: temperature of the cold junction; α: Seebeck coefficient; αa: Seebeck coefficient of the material A; αb: Seebeck coefficient of the material B; αab: Seebeck coefficient of the thermocouple; αpn: Seebeck coefficient of the p-type and n-type materials; N: number of thermocouple inside the TEG; E: electric field; Eel: electric field linked to the diffusion current; Egap: electric field linked to the drift current; EAB: voltage due to the Seebeck effect; π: Peltier coefficient; πa: Peltier coefficient of the material A; πb: Peltier coefficient of the material B; πab: Peltier coefficient of the thermocouple; τ: Thomson coefficient; τa: Thomson coefficient of the material A; τb: Thomson coefficient of the material B; Ts: switching period; fs: switching frequency; ton: close switch period; toff: open switch period; D: duty cycle; VS: source voltage; IS: source current; VO: output voltage; IO: output current; vl: inductor voltage; il: inductor current; il0: initial value of the inductor current; ΔIL_on: current variation during the conducting state; ΔIL_off: current variation during the non-conducting state; IL_min: minimum value of the inductor current;

7 IL_max: maximum value of the inductor current; ΔVO: output voltage variation; ΔVC: capacitor voltage variation; ΔQC: charge stored in the capacitor; L: inductance; Lmin: minimum inductance to have the continuous conductiion mode; C: capacitance; Cmin: minimum capacitance to have the continuous conduction mode; ILB: minimum value of the inductor current to have the continuous conduction mode; IOB: minimum value of the output current to have the continuous conduction mode; Pin: input power of the converter; Pout: output power of the converter; VT: voltage on the switch of the converter; IT: current in the switch of the converter; PT: power in the switch of the converter; QH: thermal power transferred from the heat source to the hot side; QC: thermal power transferred from the cold side to environment; Qin: thermal power exchanged at the hot junction; Qout: thermal power exchanged at the cold junction; Qp: heat transferred due to the Peltier effect; Qj: heat dissipated by Joule effect; Rin: internal resistance of the TEG; Kin: internal conductivity of the TEG; Pprod: electric power produced by the TEG; VOC: open circuit voltage of the TEG; m: ratio between the load resistance and the internal resistance of the TEG; VL: load voltage; IL: load current; ρ: resistivity; k: thermal conductivity; TH_MAX: maximum temperatures at which the hot side of the TEG may be subjected; TC_MAX: maximum temperatures at which the cold side of the TEG may be subjected; PmL: maximum transferable power to the load in coupled load conditions; VmL: voltage on the load in coupled load conditions; ηmax: maximum conversion efficiency; ηml: maximum power transfer conditions efficiency; ηc: efficiency of the ideal Carnot cycle; Z: index of merit.

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9 ABSTRACT Energy harvesting is one of the most important challenges in the current century. Among other technologies, thermoelectric energy conversion, which uses heat to generate electricity, has very strong potential. The aim of this project is to analyze the electrical performance of a thermoelectric generator. In the first chapter, after some short historical mentions, are described the main thermoelectric effects (Seebeck effect, Peltier effect, Thomson effect and Joule effect) and the thermoelectric module, highlighting its principal elements and its operating modes. In chapter 2 are described the DC_DC converters and MPPT algorithms used to optimize the performances of the thermoelectric generators. In chapter 3 are introduced the models that represent the thermal and electrical behavior of the thermoelectric generators. Theese models allow us to develop a simulation of the device object of this thesis in Matlab Simulink environment. Chapter 4 analyzes the test bench's configuration used to evaluate the theoretical model previously analyzed. We will also characterize the components that make up the system. Finally, in chapter 5, the obtained results are discussed.

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11 CHAPTER 1 THE THERMOELECTRIC GENERATOR AND THE MAIN THERMOELECTRIC PHENOMENA 1.1 Introduction Due to an increasing electric energy demand and a greater sensitivity to environmental problems the renewable energy sources gain increasing interest. In Italy the production of electric energy from renewable sources was 37,0% in 2014 (+3,6%). In particular, thanks to the push of incentive systems of renewable sources, geothermal energy production has reached 5916,3 GWh (+4,5%), wind energy production has reached 15178,3 GWh (+1,9%) and PV energy production has reached 22306,4 GWh (+3,3%). Another low cost renewable energy is the heat. It is experiencing a strong interest in the search of saving technologies for the direct conversion of waste heat into electric energy, but so far they have found applications only in a few sectors. The application of thermoelectric generators (TEG) in the field of large power generation represents a new step with regard to the overall efficiency of the production system from fossil sources. The conversion of heat (poor energy) for the production of electric energy (valuable energy) typically employs a combustion process of chemical energy and the use of a generator for the production of electric energy. The efficiency of conversion systems is the main variable to be considered in terms of evaluation and planning of investment. A first evaluation to study the problem can be made in relation to a traditional thermoelectric power plant, where, for every 100 units of chemical energy used (typically natural gas, petroleum or coal) are obtained 40 units of electric energy. The increase of the conversion efficiency can be through the use of combined gas-steam cycles, but this still collides with the limits imposed by the increasing installation costs. A solution to increase the overall efficiency of the plant without the burden of a conversion, may arise from the use of exhaust gases of the combustion process. The production of thermal energy from the exhaust fumes already founds wide application in cogeneration plants with endothermic engines, where the insertion of a fumes/water heat exchanger allows to produce hot water which will then be used for various uses, from district heating to heat generation for industrial purposes. The use of these solutions, however, clashes with the actual convenience in economic terms and then with the sustainability of the investment. The sale of heat for district heating is on one side an interesting perspective in particular as regards the cost containment and the individual utilities losses, but it becomes a difficult investment in urban areas where the competition with the traditional distribution network of

12 natural gas tends to limit its spread. A further consideration is the quality of the energy produced, in fact, as already mentioned, the heat is, from a thermodynamic point of view, a type of degraded energy, and therefore less attractive also for the market. On the contrary, the electric energy is becoming increasingly important and is an irreplaceable source for the countless applications of electric devices. Offering a direct conversion of heat into electric energy is an interesting prospect for a world that is increasingly hungry for power consumption, optimization of the production and investment in new storage systems. [1] 1.2 History of thermoelectricity The thermoelectricity is the branch of physics that gathers and studies the various phenomena of conversion of heat into electric energy and vice versa. Although this phenomena are present in all materials, only in the so called thermoelectric materials they become appreciable and exploitable. The date of birth of thermoelectricity is located at February 10, 1794, when Alessandro Volta discovered the existing link between heat and electric energy by observing how, by heating the ends of a metal arc, is obtained a voltage which will disappear with their cooling. The first thermoelectric phenomenon discovered was the Seebeck effect in 1821, when the estonian physicist noted that in a circuit composed by different metallic conductors or semiconductors connected to each other, a temperature difference generates a voltage difference. In 1834, the reverse phenomenon, the Peltier effect was discovered: in a circuit composed by different metallic conductors or semiconductors connected to each other, a current flowing generates a transfer of heat. In 1851, the english physicist William Thomson (Lord Kelvin) demonstrated the link between the Seebeck and Peltier effects: a material subjected to a thermal gradient and crossed by an electric current exchanges heat with the external environment, and mutually, a material subjected to a thermal gradient and crossed by a heat flow generates an electric current. The fundamental difference between the Seebeck and Peltier effects and the Thomson effect is that the latter is manifested in a single material (homogeneous thermoelectric effect) and therefore does not require junctions. [2] The research and development of thermoelectric applications began in the early 30's. A gradual disengagement starts in the 60's because, despite the discovery of new materials, the efficiency of the thermoelectric generators remained invariably an order of magnitude lower than that wrongly expected at the end of the 50's. In 1970 came the International Thermoelectric Society that brings together all the greatest experts of thermoelectricity and promotes it, presenting all the technological innovations in an international meeting which is held annually since 1970 in the major world capitals.

13 Now it has again raised interest in the thermoelectricity. This time, to push the research is a theoretical prediction: the efficiency of the thermoelectric devices can be greatly increased (reaching efficiencies up to 17%) through the use of low-dimensional systems, i.e. making use of nano structured thermoelectric materials. Also, the thermoelectric modules production costs are continuing to fall both for physiological reasons in the market and for academic studies, which lead to the definition of new construction standards at low cost, and make extremely advantageous to use this technology in the direct conversion of heat into electric energy. [3] 1.3 Analysis of thermoelectric phenomena Seebeck effect The Seebeck effect is a thermoelectric phenomenon whereby, in a circuit consisting of two different conductors (or semiconductors) connected together, a temperature difference between the two junctions generates a potential difference. T2 B A T1 Fig 1.1 Seebeck effect The resulting voltage in Fig. 1.1 is given by: T2 V = [α B (T ) α A (T )] dt T1 where: αa and αb are the Seebeck coefficients related to metals A and B; (1.1)

14 T1 and T2 are the temperatures of the two junctions. The Seebeck coefficients are non-linear, depending on the absolute temperature and the molecular structure of the materials, but if they may be regarded constant in the temperature range considered, the above formula can be approximated in this way: [4] V =(α B α A ) (T 2 T 1) (1.2) Cold Hot Temperature Conductor Voltage Hot Cold Fig. 1.2 Increase of free charge carriers as a function of the temperature gradient The number of free charge carriers in a metal at thermodynamic equilibrium increases with the temperature according to the Fermi-Dirac statistic. Therefore, a sample subject to a temperature gradient develops a gradient of concentration of charge carriers, and then, a diffusion current. If the sample is isolated this current give rise to an accumulation of opposite charges at the two ends of it and therefore to an increasing electric field which is opposed to the diffusion of additional charge carriers. The system reaches equilibrium when the electric field induces a drift current of equal intensity and opposite to the diffusion current. These currents are parallel and have opposite signs, the fields they generate tend to cancel: E el + E gap =E= V (1.3) where: Eel is the electric field linked to the diffusion current; Egap is the electric field linked to the drift current; E is the sum of the two electric fields. The Seebeck coefficient α (expressed in μv/k) is equal to: α= E V dv = = T T dt (1.4)

15 A material characterized by a high Seebeck coefficient must possess a density of majority carriers of p-type or n-type, otherwise the fields generated would tend to zero. Materials having a majority of charge carriers of the p-type (gaps flow) have a positive Seebeck coefficient, while materials with a majority of charge carriers of the n-type (electrons flow) have a negative Seebeck coefficient. V HOT V COLD e E T HOT T COLD V HOT V COLD h E T HOT T COLD Fig. 1.3 With reference to the temperature and voltage gradients in the figure, the n-type doped material will have α negative, while the p-type doped materials will have α positive To effectively exploit the Seebeck effect is necessary to solder two wires together. A single conductor would be subject to a local temperature gradient, but the difference in temperature between its extremes would be null, generating a null e.m.f.. [5] Peltier effect The Peltier effect is the thermoelectric phenomenon whereby an electric current flowing between two different conductors (or semiconductors) connected together produces a transfer of heat, it is the opposite of Seebeck effect.

16 T 2 B A I T 1 Fig. 1.4 Peltier effect When a current I flows in a circuit as in Fig. 1.4, a quantity of heat is absorbed by the junction at temperature T1 and emitted by the junction at temperature T2. Reversing the direction of the current reverses the behavior of the two junctions. The amount of heat transferred between the junctions per unit of time is: [6] dq =P=( π B π A) I =π AB I dt (1.5) where: P is the power exchanged with the environment; I is the current flowing in the junction; πa and πb are the Peltier coefficients of the two materials; πab is the Peltier coefficient of the thermocouple. Therefore the Peltier coefficient, which is expressed in volts, represents the amount of heat transported by a single charge (electron or hole). If one reverses the direction of the current the sign of the Peltier coefficient of the thermocouple changes. The semiconductors of p-type usually have a positive Peltier coefficient, those of n-type a negative one. The Peltier effect is due to the discontinuity of the thermal conductivity at the junction between the two conductors. With reference to Fig. 1.5, where the current flows from the semiconductor of p-type to that of n-type, the electrons that pass through the junction move to a lower energy level releasing kinetic energy in the form of thermal energy that is

17 released to the environment. In the same way, the holes that pass through the junction move to a higher energy level absorbing thermal energy and converting it into kinetic energy. [7] Fig Peltier effect in a junction between two different semiconductors [8] Thomson effect The Thomson effect is a thermoelectric phenomenon whereby in a homogeneous conductor (or semiconductor), a temperature gradient and an electric current generate a transfer of heat. The thermal power absorbed or generated per unit length is proportional to the product between the current flowing in the circuit and the temperature gradient and is equal to: [9] dq =P=τ I T dt (1.6) where: P is the power exchanged; τ is the Thomson coefficient; I is the current. The Thomson effect can be interpreted as a contribution to Joule effect. It is expressed in V/K. The sign of the Thomson coefficient is closely related to the sign of the carriers and the type of conductor and assumes positive or negative values depending on whether the semiconductor is of p-type or n-type. In materials characterized by positive coefficients is observed a heat absorption when the current flows in the same direction of the temperature gradient and a heat emission when the current flows in the opposite direction to the gradient. The materials with negative

18 coefficient behave in opposite way. [10] Joule effect The Joule effect is a thermoelectric phenomenon whereby a conductor crossed by a current is heated, releasing the heat in the surrounding environment. The heating of the conductor is due to the transfer of energy that affects the electrons and the ions when the first collide with the seconds. The coupling of these with the external environment is responsible for the diffusion of heat: the ions near the surface, vibrating, collide with the air molecules transferring to them part of the energy they possess. The result is therefore an increase of the thermal energy of the molecules of the external environment. [11] environment surface vibration ion electrons conductor Fig. 1.6 Joule effect [12] The power dissipated by Joule effect in a current carrying conductor, with resistance R, is proportional to the applied voltage and the current that runs through it according to: 2 P=V I =R I = V2 R (1.7) therefore the heat transferred to the environment at a time t is equal to: 2 Q=R I 2 t= V t R (1.8)

19 1.3.5 Link between the thermoelectric effects Consider an isolated circuit, consisting of two different conductors, A and B connected together. The temperatures of the junctions between the two materials are kept constant by two heat reserves with an infinite thermal capacity, the cold side is at temperature Ta = T and the hot one is at temperature Tb = T+ΔT. metal A Ta Tb metal B Fig. 1.7 Thermocouple The voltage, due to the Seebeck effect, generated by the temperature difference is EAB, the Seebeck coefficient of the two conductors can then be expressed as: α AB = de AB dt (1.9) The power generated can be expressed as: E AB I = de AB Δ T I dt (1.10) where: I is the current flowing in the thermocouple: ΔT is the temperature difference between the two junctions. Per unit of current flowing in the thermoelectric circuit the power generated is equal to: E AB= de AB Δ T dt (1.11) The other factors that influence a thermoelectric circuit are: the Peltier and Thomson effects, the heat exchanged between the hot and cold junctions and the losses by Joule effect. Neglect the last two terms. Having considered the circuit as a closed ideal system without irreversibility, we can apply

20 the law of conservation of energy: de AB Δ T =π AB (T + Δ T ) π AB T + τ B Δ T τ A Δ T dt (1.12) where the terms at the right of the equals are, from left to right: the energy absorbed by the hot junction due to the Peltier effect; the energy released from the cold junction due to the Peltier effect; the energy absorbed by the conductor B due to the Thomson effect; the energy released from the conductor A due to the Thomson effect; dividing both sides by ΔT: de AB π AB (T + Δ T ) π AB T = + τ B τ A dt ΔT (1.13) where: πab is the Peltier coefficient of the thermocouple; τa and τb are the Thomson coefficients of material A and B. if ΔT tend to zero, we obtain the relation between the Seebeck coefficient and the Thomson and Peltier coefficients of the thermocouple: α AB d π AB ( τ B τ A )=0 dt (1.14) this equation relates the Seebeck, Peltier and Thomson effects, emphasizing how the Seebeck effect is present in the circuit regardless of the current that flows while the Thomson and Peltier effects, in the absence of external generators, depend on the presence of the Seebeck effect. Applying now the second law of thermodynamics, assuming again that the processes are reversible, we obtain: dq ds = dt =0 (1.15) Tb π AB b π τ τ I AB a I + ( A B dt ) I =0 Tb Ta T Ta (1.16) where: S is the entropy of the system. where the first two terms correspond to the entropy emitted and absorbed by the cold and hot junctions, while the third one is the entropy associated to the heat exchange along the conductor. Dividing by T, and differentiating with respect to T is obtained: d π AB π AB + (τ B τ A )=0 dt T (1.17)

21 We can solve the system consisting of the equations (2.14) and (2.17), adding up both members of the equations we obtain the relation between the Seebeck and Peltier coefficients: α AB = π AB T (1.18) Differentiating (2.18) with respect to T, we get: 1 d π AB π AB d α AB 2= T dt dt T (1.19) substituting (2.19) in (2.17), we obtain the relation between the Seebeck and Thomson coefficients: [13] d α AB τ A τ B = dt T (1.20) 1.4 Thermoelectric generator A thermoelectric module is constituted by N pairs of thermoelectric materials of p-type and n-type electrically connected in series. Generally, the N pairs are made using a single material doped n and p respectively for the two thermoelements, the parameters of electrical and thermal conductivity of the two elements can then be supposed as the same. The p-type materials have a positive Seebeck coefficient, while the n-type materials have a negative Seebeck coefficient, thus the Seebeck coefficient of the thermocouple is positive (αpn = αp αn). It is also assumed that the Seebeck coefficient is equal to the average Seebeck coefficient, thus we can write that: α pn= α pn( T HJ )+ α pn (T CJ ) 2 where: THJ is the temperature of the hot junction of the thermocouple; TCJ is the temperature of the cold junction of the thermocouple; αpn (THJ) is the Seebeck coefficient of the thermocouple at temperature THJ; αpn (TCJ) s the Seebeck coefficient of the thermocouple at temperature TCJ. The N pairs are held together by two plates of insulating material generally consisting of ceramic material that put the thermocouples in parallel from the thermal point of view. The ceramic has a fundamental role because it has a very high thermal conductivity and a very low electrical conductivity. The materials commonly used are the Alumina or Aluminium Oxide (Al2O3), the Aluminium Nitride (AlN) or the Beryllium Oxide (BeO). The thermal energy is transmitted from a heat source at temperature TH to the hot junction at temperature THJ, while the cold junction at temperature TCJ transfers heat to the

22 environment at temperature TE. Fig 1.8 Thermoelectric module [14] Ceramic plate QH TH Hot Junction THJ p n TCJ Cold Junction TE QC Ceramic plate IL RL Fig. 1.9 Scheme of a thermoelectric module connected to a load resistance R L The thermoelectric module can be used to: warm up - Thermoelectric Heater (TEH); refrigerate - Thermoelectric Cooler (TEC); produce energy - Thermoelectric Generator (TEG); these configurations differ in how the bars of thermoelectric material of p-type and n-type are polarized.

23 When they work as a TEH or TEC, the thermoelements are polarized by a potential difference, such configuration allows to control the temperature difference between the two plates. When they work as a TEG the thermoelements are polarized by a temperature gradient that produces a potential difference at the ends of the conductors. With reference to Fig the current I is considered positive if it goes from the hot junction to the cold one. The thermal power QH and QC are considered positive respectively for heat fluxes entering in and exiting from the thermoelectric element. The figure schematizes the three operation configurations of a thermoelectric module, the thermal quantities are in gray while the electric quantities are in black. Fig 1.10 TEG versus TEC and TEH [15] We can distinguish the following potential difference: α(th Tc), voltage due to the Seebeck effect; and the following thermal power fluxes: αith and αitc, thermal power fluxes due to the Peltier effect; K(Th - Tc), thermal power flux transmitted by conduction; (1/2)RI2, power losses due to the Joule effect. [16]

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25 CHAPTER 2 DC-DC CONVERTERS AND MPPT ALGORITHMS 2.1 TEG application areas The TEG can be applied in many areas. This overview mainly focuses on its application in three different areas: space, automobiles and buildings. SPACE For numerous planetary exploration missions, solar power is not an enabling option to produce electricity because of the progressively weaker solar brightness. It is said that the brightness is about 45% of that in earth orbit on Mars, less than 4% on Jupiter and for the farther out it is essentially nil. In fact, the radioisotope thermoelectric generator has been used during the last four decades to convert the thermal power generated by a radioisotope heat source to electricity for many planetary exploration missions. The radioisotope thermoelectric generator can be operated continuously and independently of the sun. This characteristic suits well with the long time (7 10 years) missions which use either a radioactive or a nuclear reactor heat source to provide a wide range of electrical power. This technology is also extensively used in terrestrial applications. The US has built the systems nuclear auxiliary power (SNAP) program which is applied for space and military use with a set of RTGs and small reactors [17], and the Russia has built the Beta-M RTGs which was uses in unmanned lighthouses, coastal beacons and remote weather and environment monitoring stations. AUTOMOBILES For the energy consuming of the automobiles, more than two thirds of fuel is dissipated to the surroundings as waste heat. The TEG can be used to convert heat energy to electricity to improve the total efficiency. Hsiao et al. [18] have simulated a thermoelectric module composed of thermoelectric generators and a cooling system which is purposed to enhance the efficiency of an internal combustion engine. The results show that the maximum power of mw/cm 2 is produced from the module for a temperature difference of 290 C and that the TE module presents better performance on the exhaust pipe than on the radiator. Yu et al. [19] have purposed and implemented a TE waste heat energy recovery system, which uses a maximum power point tracking algorithm and a DC DC Cuk converter, for internal combustion engine automobiles including gasoline vehicles and hybrid electric

26 vehicles. The analysis and experimental results reveal that the system can work well under different working conditions and compared with the cases with no MPPT algorithm and even without power conditioning, the resulting power improvements can be up to 14.5% and 22.6%, respectively. BUILDINGS Because of the low conversion efficiency of the thermoelectric module, it is uneconomical to build up a heat source just for thermoelectric power generation because the duration of the cost recovery period is unforeseeable. Thus, Zheng et al. [20,21] have investigated a domestic thermoelectric cogeneration system (TCS) which can use available heat sources in domestic environment to produce preheated water for home use and generate electricity. The system can also be adopted to other sectors or areas where the combustion appliances are used and preheating is needed. With the increase of the temperature difference, the conversion efficiency also monotonously increases. The economic analysis shows that for the giving condition the annual saving is 213 per domestic boiler user and the corresponding cost recovery period is about 5.59 years. Alanne et al. [22] have investigated the domestic thermoelectric cogeneration system (DTCS). In comparison with a standard pellet-fueled boiler, the integrated DTCS can cut the annual non-renewable primary energy by 11% and CO2 emissions by 21%. FLEXIBLE DEVICES One distinct advantage of the TEG is its flexibility, which makes it very effective to use the low-grade waste heat to supply the electricity for small devices such as wearable electronics, wireless communication units and sensors. Nevertheless, this technology is still at the primitive stage. In recent years, as the new potential market for self-powered wearable mobile electronics is booming, researches on flexible TEG have drawn more attentions. The technological advances in the fields of the physical sensing, the integrated circuits and the wireless communication have paved the way for the utilization of the wearable wireless body area networks. Traditionally, those devices powered by the rechargeable batteries have many disadvantages: they need to be renewed and they contain chemical substances that can harm the environment. The lightweight, flexible, miniature and wearable TEG is the promising solution for those problems. Yu et al. [23] have developed a kind of self-renewing photovoltaic and thermoelectric hybrid power source for sensor nodes. The whole system combines solar cells, thermoelectric generators and heat sinks. The solar cell is the heat sources for the TEG. The results show that the photovoltaic and thermoelectric hybrid power source can refill the energy itself. Leonov et al. [24] have investigated the hybrid wearable energy harvesters consisting of a thermoelectric generator and photovoltaics which are used to power two autonomous medical devices: an electroencephalography (EEG) system and an electro-cardiography

27 (ECG) system in a shirt. [25] DC-DC converter To optimize the operation of a thermoelectric generator, it is possible to work the module at the maximum power for any given value of thermal power through various tracking methods similar to those used in photovoltaic systems. The MPPT (Maximum Power Point Tracking) algorithms are recursive and they act on the control logic of the DC-DC converters' switch until the point of maximum power operation is reached. We will now analyze the various types of existing DC-DC converters and evaluate their advantages and disadvantages. The DC-DC converters are widely used in DC power supplies and DC motor drives. Generally, the input of these converters is an unregulated voltage, in this case the voltage is generated by the thermoelectric module and is proportional to its temperature gradient. The converter has the twofold task of maintaining a constant voltage to the load and to vary the input resistance seen from the generator so as to track the maximum power point. [26] Battery TEG DC Filter Load DC Unregulated voltage Unregulated voltage Regulated voltage Voltage control Fig. 2.1 DC-DC conversion system We will study the following DC-DC converters: buck converter (step-down); boost converter (step-up); buck-boost converter (step-down/step-up); cuk converter. The basic circuit diagrams of all the fundamental converters are shown in Fig. 2.2, they consist of the same basic elements: a DC supply, a load, a diode, a power electronics switch, an inductor and a capacitor.

28 Fig. 2.2 Basic converters [27] It is worth noticing that any converter works in two distinct modes with respect to the inductor current: the continuous conduction mode (CCM) and the discontinuous conduction mode (DCM). When the inductor current is always greater than zero the converter is in CCM, when it isn't always greater than zero (due to the high load resistance or to the low switching frequency) the converter is in DCM. The CCM is preferable for high efficiency and efficient use of semiconductor switches and passive components, the DCM requires a special control since the dynamic order of the converter is reduced. Thus, it is required to find out the minimum value of the inductor to maintain the CCM. We can assume that the converters are in steady-state condition, the switches and the inductive and capacitive elements are ideal, the internal resistance of the source is null, the voltage does not have significant ripple and the load is represented as an equivalent resistance. [28] Fig. 2.3 Small-ripple approximation [29] Duty cycle and modulation techniques In a DC-DC converter, the average output voltage must be adjusted so as to equal the desired level, even if the input voltage and the load vary. Analyze the simple circuit in Fig. 2.4, it is constituted by a DC voltage generator, a switch and a resistor.

29 The average value Vo of the output voltage vo(t) of the converter is regulated by acting on the closing and opening timings of the switch (ton and toff). Fig. 2.4 DC chopper and regulated voltage Vo [30] There are various methods to control the output voltage: 1. A widely used method to control the output voltage uses a constant switching 1 frequency f S =, with T S =t on+ t off, and varies the duration of the conduction TS time of the switch ton. This technique is called PWM (Pulse Width Modulation) because the width of the switch control pulse, and therefore the utilization factor of the switching period (duty cycle) are controlled. The power dissipated by commutation on the switch is very low, so this conversion technique allows to obtain very high efficiencies. Generally it prefers the PWM because a fixed switching frequency allows an accurate filtering of the harmonics that produce ripple on the input and output waveforms of the converter. The control signal of the switch, that regulates its state of open or closed, is generated by comparing a control voltage with a repetitive voltage. The frequency of the repetitive voltage determines the switching frequency (varies from a few khz to a few hundreds of khz). When the control voltage is larger than the repetitive voltage, the signal which controls the switch determines the closing, otherwise the switch remains open. The duty cycle is defined as the ratio between the conduction time of the switch ton and the switching period TS or, analyzing Fig 2.5, it can be expressed as a function of the control voltage and of the peak value of the repetitive voltage: D= t on v control = TS V st (2.1)

30 Fig. 2.5 PWM control voltage generator [31] 2. The PFM (Pulse Frequency Modulation) technique of voltage control keeps ton fixed and varies TS. The main limitation of the PFM is that it is not possible to obtain a complete variation of the average value, since to do so would require a null or infinite frequency, also, while in the PWM the frequency is fixed, and therefore we know exactly the harmonic content that can be filtered, with the PFM we don't have a constant harmonic content and therefore the attenuation of the harmonics at the output is less effective. In operation with PFM must also take account of a limit on the maximum switching frequency of the switch, it increases with the increasing of the power dissipated during the switching time that for the real devices is finite and for some converters is very influential, as for the GTO that have high time of switching on and switching off and thus a high power dissipation in switching. [32] DC-DC converters DC-DC buck/step down converter The buck converter is mostly used for DC drives systems like electric vehicles, electric traction and machine tools. It generates an average output voltage Vo lower than the input voltage VS. Conceptually, the basic circuit is the one represented in Fig. 2.6, it consists of a DC supply, two ideal switches: a diode and a switch (they can be semi-controlled or fully-controlled power electronics switches), a two-pole low-pass filter (an inductor and a capacitor) and a purely resistive load.

31 Fig. 2.6 Buck converter [33] CONTINUOUS CONDUCTION MODE The circuit in Fig. 2.6 can be studied in two different states, during the first state the switch is on, while during the second one it is off. The circuit diagrams for these two states are given in Fig. 2.7 and Fig. 2.8 respectively. During the conducting mode the inductor voltage is equal to: di (t ) v L (t)=l L =V S V o dt (2.2) Fig. 2.7 Buck converter circuit: conducting mode [34] While during the non-conducting mode the inductor voltage is equal to: v L (t)= V o (2.3)

32 Fig. 2.8 Buck converter circuit: non-conducting mode [35] The waveforms of the switch current, the diode current, the inductor current and the inductor voltage during the switching period are shown in Fig. 2.9.

33 Fig. 2.9 Switch current, diode current, inductor current and inductor voltage waveforms [36] During the steady-state condition the integral of the inductor voltage in a period is equal to zero, thus: (V S V o ) t on V o t off =0 (2.4) the average output voltage will then be: V o =V S D (2.5) If we now consider an ideal, losses-free DC-DC converter, the input power will be equal to the output power, so we can write that: P in =V S I S =P out =V o I o thus: (2.6)

34 D= IS Vo = Io V S (2.7) IS D (2.8) the average output current will then be: I o= From equation (2.7) we can note that the operation of this converter can be compared to a hypothetical DC transformer with transformation ratio equal to D, which can vary between 0 and 1. RIPPLE ON THE OUTPUT CURRENT AND VOLTAGE We evaluate the ripple on the output current and the output voltage of the converter, in the absence of infinite capacity. Let's consider the conducting interval of the converter, the inductor current is equal to: t (V V o ) 1 i L (t )= v L (t ) dt+ k = S t+ i L0 L 0 L (2.9) the ripple on the current is therefore equal to: (V S V o ) T S 1 D Δ I L_on = (V S V o ) t on = L L (2.10) If we now consider the non-conducting state, we obtain an inductor current equal to: t V 1 i L (t )= v L (t ) dt+ k ' = 0 (t t on ) i L0 L t L (2.11) on in this case the ripple on the current is equal to: V T 1 Δ I L_off = ( V 0 ) (T s t on )= o S (1 D) L L (2.12) Observing equations (2.10) and (2.12) we can note that the sum of the current variation in the inductor during the conducting and the non-conducting state is equal to zero. The ripple on the curren has a maximum for D = 0,5. From the expression of the current ripple we can find the values of the minimum and maximum inductor current: [ [ ] ] I L_min=I o Δ I V o (V S V o ) 1 TS = T S D=V s (1 D) 2 R 2 L R 2 L I L_max= I o+ 1 T Δ I V o (V S V o ) = + T S D=V s + S (1 D) 2 R 2 L R 2 L (2.13) (2.14)

35 We will now evaluate the trend of the voltage on the capacitor as a function of il(t). Suppose that the AC component of il(t) circles only in the capacitor and that the DC component circles only in the load. The voltage variation across the capacitor is given by the ratio between the charge stored in the capacitor and its capacitance: Δ V o=δ V C = ( ) Δ QC 1 1 T S Δ I L V S T 2S = = (1 D) D C C L C (2.15) as the current ripple, the output voltage ripple has a maximum for D = 0,5. Fig Inductor current versus capacitor voltage [37] BOUNDARY BETWEEN CCM AND DCM The discontinuous conduction mode occurs when the inductor current is less than or equal to zero for at least a part of the switching period. The boundary between continuous and discontinuous conduction is given by the average current of the inductor that (with the assumption of infinite capacity) must never fall below a limit current value equal to: I LB=I ob= Δ I L (V S V o) T S = D 2 2 L (2.16)

36 Fig Continuous conduction mode versus discontinuous conduction mode [38] By evaluating the derivative of (2.16) as a function of the duty cycle D, we obtain the maximum current limit. We distinguish two cases: DC-DC converter with constant VS; DC-DC converter with constant Vo. The maximum value of IoB, maintaining VS constant, is obtained for D = 0,5 and is equal to: I ob_max = T S V S 8 L (2.17)

37 Fig Characteristic curve of a DC-DC converter with constant VS [39] The maximum value of IoB, maintaining Vo constant, is obtained for D = 0 and is equal to: I ob_max= T S V o 2 L (2.18)

38 Fig Characteristic curve of a DC-DC converter with constant Vo [40] The discontinuous operation leads to a nonlinear characteristic of the converter, and is a limit on the variations of the input voltage in the case of constant load and is a limitation on the maximum load in the case of nonconstant load. Equating equation (2.13) to zero we can find the minimum inductance to have the continuous conduction mode: L min= R T S (1 D) 2 (2.19) DC-DC step up/boost converter The DC-DC boost converter generates an average output voltage Vo greater than the input voltage VS. The basic circuit is the one represented in Fig

39 Fig Boost converter circuit diagram [41] CONTINUOUS CONDUCTION MODE Like the buck converter this circuit can be studied in two different states: the conducting and the non-conducting mode. The equivalent circuits for the two states are shown in Fig and Fig respectively. During the conducting mode the inductor voltage is equal to: v L (t)=v S Fig Boost converter circuit: conducting mode [42] (2.20)

40 and during the non-conducting mode it is equal to: v L ( t)=v S V o (2.21) Fig Boost converter circuit: non-conducting mode [43] The waveforms of the switch current, the diode current, the inductor current and voltage during the switching period are shown in Fig

41 Fig Switch current, diode current, inductor current and inductor voltage waveforms [44] In steady state conditions the integral of the inductor voltage in a period is equal to zero, thus: V S t on + (V S V o ) t off =0 (2.22) dividing both sides by TS we obtain: Vo 1 = V S 1 D (2.23) If we now consider an ideal, losses-free DC-DC converter, the input power is equal to the output power: V 2S I L_min + I L_max V 2o =P out =V o I o= = P in =V S I S =V S I L_AV =V S 2 R (1 D)2 R (2.24)

42 thus, from equations (2.23) and (2.24) we obtain: Io =(1 D) IS (2.25) From equations (2.23) and (2.25) we can note that the DC-DC boost converter can be 1 seen as an ideal transformer in continuous with transformation ratio equal to. 1 D As we can see in Fig in reality the ratio between Vo and VS decades when the duty cycle approaches unity, because of the losses associated with the inductor, the capacitor, the switch and the diode. Fig Vo/VS characteristic curve in the ideal and real case [45] RIPPLE ON THE OUTPUT CURRENT AND VOLTAGE We evaluate the ripple on the output current and the output voltage of the converter, in the absence of infinite capacity. Let's consider the conducting interval of the converter, the inductor current is equal to: VS 1 i L (t )= v L (t ) dt+ k = t+ i L0 L L (2.26) the ripple on the current is therefore equal to: V T 1 Δ I L_on = V S t on= S S D L L (2.27)

43 If we now consider the non-conducting state, we obtain an inductor current equal to: (V S V 0) 1 ( t t on ) i L0 i L (t )= v L (t ) dt+ k ' = L L (2.28) and the ripple on the current will then be: (V S V o) T S 1 Δ I L_off = (V S V 0) (T s t on)= (1 D) L L (2.29) In the case of the boost converter, we can find from equation (2.27) (or (2.29)) that the ripple on the current has a maximum for D = 1. The minimum and maximum inductor current are then equal to: I L_min = I L_max= VS 2 R (1 D) VS 2 R (1 D) V S T S D 2 L (2.30) V S T S D 2 L (2.31) + The peak-to-peak value of the ripple of the output voltage can be calculated considering the waveforms shown in Fig in continuous conduction mode, by making the same considerations made for the buck converter: Δ V o=δ V C = ( ) Δ QC 1 1 T S Δ I L V S T 2S = = D C C L C (2.32) as the current ripple the output voltage ripple has a maximum for D = 1. BOUNDARY BETWEEN CCM AND DCM To work in the continuous conduction mode the average current of the inductor must never fall below a limit current value equal to: V o T S 1 VS 1 (1 D) D I LB =I ob= Δ I = t on= 2 2 L 2 L (2.33) By evaluating the derivative of (2.33) as a function of the duty cycle D, we obtain the maximum limit current. We distinguish two cases: DC-DC converter with constant VS; DC-DC converter with constant Vo. The maximum value of IoB, maintaining VS constant, is obtained for D = 1 and is equal to: I o_bmax = V S T S 2 L (2.34)

44 The maximum value of IoB, maintaining Vo constant, is obtained for D = 0,5 and is equal to: I o_bmax = V o T S 8 L (2.35) Equating equation (5.30) to zero we can find the minimum inductance to have the continuous conduction mode: L min= R T S D (1 D)2 2 (2.36) Buck-boost converter The buck-boost converter can be used both to increase and to decrease the output voltage. When the switch is on the inductor start earning power, due to the presence of the diode, at this stage the load is powered only by the capacitor. When the switch is off, the inductor will tend to discharge, supplying energy both to the capacitor and to the load. This converter is an inverting DC-DC converter, so the polarity of the output voltage is reversed compared to the input supply, thus it is a negative-output buck-boost converter. Fig Buck-boost converter circuit diagram [46] CONTINUOUS CONDUCTION MODE Consider the capacitor totally charged before the switch turns on. During the conducting mode the inductor voltage is equal to:

45 v L ( t)=v S Fig Buck-boost converter circuit: conducting mode (2.37) [47] During the non-conducting mode it is equal to: v L (t )= V o Fig Buck-boost converter circuit: non-conducting mode (2.38) [48] The waveforms of the switch current, the diode current and the inductor current and voltage for the buck-boost converter are shown in Fig

46 Fig Supply current, diode current, inductor current and inductor voltage waveforms [49] In steady-state conditions the integral of the inductor voltage in a period is equal to zero, thus: V S t on V o t off =0 (2.39) Vo D = V S 1 D (2.40) dividing both sides by TS we obtain: If we consider an ideal, losses-free DC-DC converter, the input power is equal to the output power, so: 2 I V +I P in =V S I S =V S L_min L_max D=P out =V o I o= o 2 R (2.41)

47 thus, from the above two equations: I o (1 D) = IS D (2.42) From equations (2.40) and (2.42) we can note that the DC-DC buck-boost converter can D be seen as an ideal transformer in continuous with transformation ratio equal to. (1 D) RIPPLE ON THE OUTPUT CURRENT AND VOLTAGE We evaluate the ripple on the output current and the output voltage of the converter, in the absence of infinite capacity. Let's consider the conducting interval of the converter, the inductor current is equal to: VS 1 i L (t )= v L (t ) dt+ k = t+ i L0 L L (2.43) the ripple on the current is therefore equal to: V T 1 Δ I L_on = V S t on= S S D L L (2.44) If we now consider the non-conducting state, we obtain an inductor current equal to: Vo 1 i L (t )= v L (t) dt+ k '= (t t on ) i L0 L L (2.45) the ripple on the current is therefore equal to: V T 1 Δ I L_off = V o (T s t on )= o S (1 D) L L (2.46) the ripple on the current, like for the boost converter, has a maximum for D = 1. The minimum and maximum inductor current are then equal to: I L_min = VS VS D D R (1 D)2 2 L I L_max= VS V D + S D 2 R (1 D) 2 L (2.47) (2.48) The peak-to-peak value of the ripple voltage is given by: ( ) Δ QC 1 1 T S Δ I L V S T 2S Δ V o=δ V C = = = D C C L C (2.49)

48 as the current ripple it has a maximum for D = 1. BOUNDARY BETWEEN CCM AND DCM The boundary between continuous and discontinuous conduction mode is given by the average current of the inductor that must never fall below a limit current value equal to: V o T S 1 VS 1 (1 D) I LB =I ob= Δ I = t on= 2 2 L 2 L (2.50) By evaluating the derivative of (2.50) as a function of the duty cycle D, we obtain the maximum limit current. We distinguish two cases: DC-DC converter with constant VS; DC-DC converter with constant Vo. The maximum value of IoB, maintaining VS constant, is obtained for D = 1 and is equal to: I ob_max= V S T S 2 L (2.51) The maximum value of IoB, maintaining Vo constant, is obtained for D = 0,5 and is equal to: I ob_max= V o T S 2 L (2.52) Equating equation (2.47) to zero we can find the minimum inductance to have the continuous conduction mode: L min= T S R 2 (1 D) 2 (2.53) It is worth noting that: when D < 0,5, the buck-boost converter acts as a step-down/buck converter; when D > 0,5, the buck-boost converter acts as a step-up/boost converter; when D = 0,5, the input and output voltages are equal. The converter discussed above is a negative-output buck-boost converter, but in some applications, reversal of polarity is not allowed, in such cases, we require a positiveoutput converter whose configuration diagram is given below:

49 Fig Positive-output buck-boost converter circuit diagram [50] Cuk converter A cuk converter can be obtained by cascading the boost converter followed by the buck converter. As in the case of the simple buck-boost converter, it has a negative output polarity, but we have assumed here that the polarity of the output is positive. Fig Cuk converter circuit diagram [51]

50 CONTINUOUS CONDUCTION MODE During the conducting mode the voltage on the inductor L is equal to: v L (t)=v S (2.54) and on the inductor Lo: v Lo (t )= (V C + V o) (2.55) Fig Cuk converter circuit: conducting mode [52] During the non-conducting mode the voltage on the inductor L is equal to: v L (t)=v S V C (2.56) v Lo (t )= V o (2.57) and on the inductor Lo:

51 Fig Cuk converter circuit: non-conducting mode [53] The waveforms of the voltages and currents during the switching period are shown in Fig

52 Fig Switch voltage, capacitor C voltage, inductor L current, inductor LO current, capacitor CO current, capacitor CO voltage, capacitor C current and load current waveforms [54] In steady state conditions the integral of the inductor voltage in a period is equal to zero, thus, for the inductor L:

53 V S t on+ (V S V C ) t off =0 (2.58) dividing both sides by TS we obtain: VS =1 D VC (2.59) (V C V o ) t on V o (T S t on)=0 (2.60) and for the inductor Lo: dividing both sides by TS we obtain: V o =V C D (2.61) Vo D = V S 1 D (2.62) thus, from equations (2.59) and (2.61): If we consider an ideal, losses-free DC-DC converter, the input power is equal to the output power: P in =V S I S =P out =V o I o (2.63) thus, from the above two equations we obtain: I o (1 D) = IS D (2.64) Looking at equations (2.62) and (2.64) we can note that the DC-DC cuk converter can be D seen as an ideal transformer in continuous with transformation ratio equal to. 1 D RIPPLE ON THE INDUCTORS CURRENTS AND CAPACITORS VOLTAGES We evaluate the ripple on the inductors currents and the capacitors voltages of the converter, in the absence of infinite capacity. Let's consider the conduction interval of the switch, the inductor L current is equal to: t V 1 i L (t )= v L (t ) dt+ k = S t+ i L0 L 0 L (2.65) the ripple on the inductor L current is therefore equal to: V S T S 1 D Δ I L = V S t on= L L and it has a maximum for D = 1. (2.66)

54 If we now consider the switch in the non-conducting state, the inductor Lo current is equal to: t V 1 i Lo (t)= v Lo (t) dt+ k ' = o (t t on) i Lo0 Lo t Lo (2.67) on the ripple on the inductor Lo current is therefore equal to: Δ I Lo= V T 1 V o (T s t on )= o S (1 D) Lo Lo (2.68) and it has a maximum for D = 1. The ripple voltage across the capacitor C is equal to: Ts I S T S ΔQ 1 Δ V C= = i C (t ) dt= (1 D) C C t C (2.69) on and the ripple voltage across the capacitor Co is equal to: T 2 T 2 Δ I Lo Δ I Lo V S T 2S 1 1 dt = Δ V Co= i Co ( t) dt= T = D Co 0 Co C o S 8 C o L Lo (2.70) BOUNDARY BETWEEN CCM AND DCM For the CCM, we have: Δ I L= ( ) V S T S 2 V S D D=2 I L_AV =2 I S = L R 1 D 2 (2.71) thus, from the previously equation we can obtain the minimum inductance L to have the CCM: R T S (1 D)2 L min= 2 D (2.72) Similarly, from equation (2.73) we can obtain the minimum inductance Lo to have the

55 CCM: Δ I Lo= V S T S Vo D=2 I Lo_AV =2 I o =2 L Lo R (2.73) R T S (1 D) 2 (2.74) thus: Lo_min = The minimum capacitance C to have the CCM is obtained from the next equation: Δ V C= I S T S (1 D)=2 V o=2 I o R C (2.75) thus: C min = TS D 2 R (2.76) and the minimum capacitance Co to have the CCM is obtained in this way: ( ) 2 V T D Δ V Co= S S D=2 V o=2 V S 8 C o Lo 1 D (2.77) thus: C o_min = TS 8 R (2.78) The main benefit of the Cuk converter is that you can control the continuous current at both the input and output of the converter as it is based on the capacitor energy transfer. It has a low-switching loss making it more highly efficient. The downside of this converter is that it includes a high number of reactive components (L and C) and heavy current

56 stresses on the components. And since the capacitor C provides a transfer of energy, the ripples in the capacitor C current are high Comparison between the converters The step-up, step-down, buck-boost and cuk converters can transfer energy only in a single direction. To assess how well the switch is used in the circuits of the converters, are formulated the following hypotheses: the average current is at its nominal value Io. The ripple current inside the inductor is negligible, then il(t) = IL. This condition implies a continuous conduction mode for all converters; the output voltage vo(t) is at its nominal value Vo. It is assumed that the ripple of vo(t) is negligible, then vo(t) = Vo; It is permitted the variation of the input voltage VS. The duty cycle should be controlled to maintain Vo constant. With these operating conditions are calculated the maximum value of the voltage VT of the switch and the maximum value of the current IT. The nominal value of the power of the switch is calculated as: P T =V T I T (2.79) The exploitation of the switch is expressed as Po/PT, where Po = VoIo is the rated output power.

57 Fig Exploitation of the switch for the considered converters [55] Fig shows the graph of the exploitation factor of the switch for the considered converters. It can be noted that, if the input and output voltages are of the same order of magnitude, in the step-up and step-down converters the exploitation factor of the switch is very good. The switch in the buck-boost converter is largely untapped. 2.3 MPPT algorithms We will now analyze different MPPT algorithms in the literature. The MPPT algorithms are used to extract the highest possible power from the thermoelectric generator and transfer it to the load. The algorithm acts on the control logic of the DC-DC converter, by changing the duty cycle, thus the impedance seen by the generator, so as to operate the thermoelectric generator in the condition of maximum power during the variation of the thermal power transiting in the module. The MPPT techniques analyzed are the following: P & O: perturb and observe; IC: incremental conductance; Simple coupling between modules and load P & O Algorithm: perturb and observe This family of algorithms works by perturbing the system through an increase or a decrease in the operating voltage/current of the TEG (depending on whether the check is

58 performed in voltage or current), via a DC-DC converter, and observing the effect on the output power of the system. We can have three types of P & O algorithms: direct control on duty cycle; current control; voltage control. DIRECT CONTROL ON DUTY CYCLE The algorithm is implemented with a DSP that controls the DC-DC converter which is connected to the generator. The purpose is to sample the current and the voltage of the module, to calculate the power and check if this is greater than the power of the previous step. Start Set Duty out Read V,I P_new = V*I No P_new > P_old Duty = Duty - C Yes P_old = P_new Duty = Duty + C Fig MPPT algorithm with direct control on duty cycle If this occurred the duty-cycle is varied with a positive increase, conversely with a decrease. The algorithm is shown in Fig. 2.29, once reached the MPP it will continue to oscillate close to this point and the oscillation will depend in a proportional way to the amplitude of the perturbation (C), which is applied to the duty cycle. So the smaller the

59 perturbation, the lower the oscillation at regime of the output power of the module, and the greater will be the time needed to reach the MPP. The oscillation also causes a power loss proportional to the amplitude of each individual disturbance. The ideal value of the disturbance pass is determined experimentally for each system. The disadvantage of this type of algorithm is due to the lack of control of the input current and the input voltage which can lead to limitations on the operation of the algorithm as a function of the dimensioning of the DC-DC converter. [56] DIRECT CONTROL ON CURRENT In this case, the MPPT algorithm provides the reference current (IREF), which is compared with the one present at the input of the DC-DC converter. Begin P & O Measure: V(k), I(k) DVref(k) = Vref(k) - Vref(k-1) P(k) = V(k)*I(k) DP(k) = P(k) - P(k-1) Yes No DP(k)>= 0 DVref(k) > 0 DVref(k) > 0 Yes Iref(k) = Iref(k-1) - C No Iref(k) = Iref(k-1) + C No Yes Iref(k) = Iref(k-1) + C Iref(k) = Iref(k-1) - C Fig P & O algorithm with direct control on the current The algorithm, shown in Fig. 2.30, is based on the sampling of the output voltage and output current, it multiplies them to obtain the power output at step k, and compares it with

60 the power sampled at step k-1. If the value at step k is higher than that at step k-1 and the voltage at step k is greater than that in the previous step, it decrements the reference current. Conversely, it increases the current reference. The same thing, in the opposite way, takes place if the power at step k is smaller than that at the step k-1. Here too, once reached the MPP, there will be an oscillation proportional to C. The smaller the variation C of the reference current the lower the oscillation. [57] DIRECT CONTROL ON VOLTAGE Begin P & O Measure: V(k), I(k) DVref(k) = Vref(k) - Vref(k-1) P(k) = V(k)*I(k) DP(k) = P(k) - P(k-1) Yes No DP(k)>= 0 DVref(k) > 0 DVref(k) > 0 Yes Vref(k) = Vref(k-1) + C No Vref(k) = Vref(k-1) - C No Yes Vref(k) = Vref(k-1) - C Vref(k) = Vref(k-1) + C Fig P & O algorithm with direct control on the voltage This type of control is similar to that of the preceding paragraph, but in this case the MPPT algorithm provides the reference of the input voltage instead of that of the current. The circuit diagram is similar to that of Fig. 2.30, replacing the current comparison with that of voltage. The flowchart of the algorithm is shown in Fig. 2.31, also in this case, once you

61 reached the MPP it will continue to have an oscillation close to this point. It will choose, therefore, the constant C looking for a compromise between the speed to reach the MPP and the oscillation in the scheme. [58] IC algorithm: incremental conductance Inputs: V(k), I(k) DI = I(k) - I(k-1) DV = V(k) - V(k-1) No Yes Yes DV = 0 DI/DV = - I/V DI = 0 No Yes DI/DV = - I/V Vref increase Yes No No Vref decrease No DI > 0 Vref decrease Yes Vref increase I(k-1) = I(k) V(k-1) = V(k) Return Fig IC algorithms The incremental conductance algorithm exploits the parabolic characteristic of the PV curve to search for the MPP, this point will feature a derivative of the power with respect to the voltage equal to zero: dp =0 dv when the operating point is to the left of the MPP then a positive variation of the voltage leads to a positive variation of the power, conversely, if it is to the right of the MPP, to a positive variation of the voltage corresponds a negative variation of power. In summary:

62 dp > 0 to the left of the MPP; dv dp =0 dv MPP; dp <0 dv to the right of the MPP. At this point we can define the relative position of the operation point with respect to the MPP as a function of the following equation: di ΔI dp d (V I ) = =I + V I + V dv dv dv ΔV ΔI I > ΔV V to the left of the MPP; I ΔI = ΔV V MPP; ΔI I < ΔV V to the right of the MPP. Therefore, the maximum power point is detected by comparing at each cycle the instantaneous conductance with the incremental conductance, according to the flow chart of the MPPT algorithm shown in Fig First we must sample, through two sensors, the output current and voltage of the module, are then calculated the current (ΔI) and voltage variations (ΔV). If ΔV = 0: if ΔI = 0, MPP; if ΔI > 0, the reference voltage increases (it is to the left of the MPP), otherwise it decreases. If ΔV 0: if the incremental conductance is equal to the instant conductance it is in the MPP; if the incremental conductance is smaller than the instant conductance the reference is increased, otherwise it is decreased. Using the IC algorithm, once the MPP is reached, the reference voltage remains constant not bringing, in theory, to an oscillation of the reference (in the real life the oscillation remains because of the discretization of the system). This method is much faster than the P & O but has the disadvantage of being more complex to implement. [59]

63 2.3.3 Simple coupling between module and load In this method, the optimal operating point of the generator is evaluated at the design stage. Once the MPP is evalueted, and therefore the Vmp and Imp values, the more suitable load is determined. The array of modules is connected with a bank of accumulators which acts as a buffer between the array and the same downstream circuit which is usually a DC-DC or DC-AC converter. The advantage of this configuration is its simplicity, since no additional circuit is used, so the entire system is very reliable and power losses between the panel and batteries are reduced to the losses in the connection conductors. The drawback of this system is that it does not respond to temperature changes on the hot and cold sides which correspond to Vmp variations. For this reason, a difference between the Vmp voltage and the nominal voltage of the bank of accumulators occurs which can produce a significant reduction of the power removable from the array. Consequently, this method is only used for applications of very low power. [60]

64

65 CHAPTER 3 MODELLING AND SIMULATION OF THE THERMOELECTRIC GENERATOR The purpose of the following chapter is to provide a thermal and electric circuit model for the thermoelectric generator. We will then simulate with Matlab Simulink the behavior of the thermoelectric generetor with and without the studied DC-DC converters. 3.1 Thermal model Suppose the thermoelectric generator realized in such a way as to exchange thermal power only through the hot and cold plates. The thermal power QH, transferred from the heat source to the hot junction through the upper ceramic plate, and the thermal power QC transferred from the cold junction to the environment through the lower ceramic plate, are given respectively by: Q H =(T H T HJ ) K (3.1a) QC =(T CJ T E ) K (3.1b) where: TH is the heat source temperature; THJ is the hot junction temperature; TCJ is the cold junction temperature; TE is the environment temperature. The thermal power exchanged at the hot/cold junction is given by the sum of the thermal power produced by the Peltier effect, transferred by conduction, dissipated by the Joule effect and produced by the Thomson effect. Assuming to ignore this last effect, the thermal power exchanged equations become: 2 I R Qin = α pn T HJ I L + K in (T HJ T CJ ) L in 2 (3.2a) I 2L Rin 2 (3.2b) Q out = α pn T CJ I L + K in (T HJ T CJ )+ where: THJ is the hot junction temperature; TCJ is the cold junction temperature; IL is the current that flows in the thermoelectric generator; αpn is the Seebeck coefficient of the thermoelectric generator; Rin is the internal resistance of the thermoelectric generator, given by:

66 ρ h Rin =2 N S (3.3) where: N is the number of thermocouples; ρ is the electric resistivity of the thermoelectric material; h is the height of a thermoelement; S is the surface of a thermoelement. Kin is the internal conductivity of the thermoelectric generator, given by: k S K in=2 N h (3.4) where: N is the number of thermocouples; k is the thermal conductivity of the thermoelectric material; h is the height of a thermoelement; S is the surface of a thermoelement. it is emphasized that Qin and Qout have opposite signs, the current is considered positive when it goes from the hot junction to the cold one, the Peltier effect therefore will subtract thermal power from the hot side and transfer it to the cold side of the thermoelectric generator. It is also supposed that a part of the power dissipated by Joule effect is dissipated on the hot and cold sides of the device. [61] Derive now a simple equivalent thermal circuit recalling the similarity that exists between thermal and electrical parameters. Thermal Quantities Heat Temperature Thermal Resistance Heat Capacity Absolute Zero Temperature Units W K K/W J/K 0K Analogous Electrical Quantities Current Voltage Resistance Capacity Ground Units A V Ω F 0V Tab. 3.1 Comparative table between thermal and electrical parameters Starting from equations (3.2a) and (3.2b) we obtain the equivalent circuit representation of the thermal quantities:

67 H R h C h Q h_in Q k Q C_out HS R c C c HJ (T h - T e ) Q j +Q p C R CJ R c C c CS R sink C sink E Fig. 3.1 Equivalent thermal circuit where: Th, is the temperature of the heat source; Te, is the temperature of the environment; Rh and Ch are, respectively, the thermal resistance and the thermal capacity of the contact surface between the heat source and the hot side of the ceramic plate; Rc and Cc are respectively the thermal resistance and the thermal capacity of the ceramic plate; Rsink and Csink are, respectively, the thermal resistance and the thermal capacity of the heat sink; R and C are respectively the thermal resistance and the thermal capacity of the junction; Qp is the heat transferred due to the Peltier effect: Q p=α pn (T CJ T HJ ) I L (3.5) Qj is the heat dissipated by the Joule effect by the module: Q J =Rin I 2L (3.6)

68 3.2 Electric model The equivalent electric circuit of the thermoelectric generator is constituted by a controlled voltage generator and two resistances in series: the internal resistance of the thermoelectric generator and a load. [62] R in IL RL VL Fig. 3.2 Equivalent electric circuit The electric power produced is given by: P prod =Qin Q out =α pn ( T HJ T CJ ) I L Rin I 2L (3.7) using the Seebeck relationship, the open circuit voltage of the thermoelectric generator is given by: V OC =α pn (T HJ T CJ ) (3.8) thus, the current IL circulating in the circuit is: I L= V OC α (T T CJ ) = pn HJ Rin + R L Rin + R L (3.9) We define the coefficient m as the ratio between the load resistance and the internal resistance of the thermoelectric generator:

69 m= RL Rin (3.10) let's write now the voltage, the current and the electric power produced expressions as a function of the parameter m: V L =V OC I L= RL m =V OC Rin + R L m+ 1 V OC V OC = Rin+ R L (m+ 1) Rin V 2OC Δ T 2 α2 ATE m m P prod = = 2 2 Rin ( m+ 1) ρ l (m+ 1) (3.11) (3.12) (3.13) Starting from equation (3.13), supposing to keep constant both the geometry of the generator and the temperature difference, we can define the thermoelectric power factor as: 2 P.F.= αρ =α 2 σ (3.14) 3.3 Calculation of the constitutive parameters of the model The thermoelectric generator manufacturers generally provide the following parameters to define the technical specifications of its products: [63] TH_MAX, TC_MAX, maximum temperatures at which the hot and cold sides of the thermoelectric generator may be subjected, generally the cold side has a maximum temperature limited by the melting temperature of the solder (significantly lower than the hot side temperature) used to connect the p-n junctions to the power cables. Typical values are: TC_MAX, from 50 C to 190 C, TH_MAX, from 100 C to 800 C; PmL, maximum transferable power to the load in coupled load conditions; VmL, voltage on the load in coupled load conditions; Voc, open circuit voltage of the thermoelectric generator; ηmax, maximum conversion efficiency (m = mη); ηml, maximum power transfer conditions efficiency (m = 1). From these data it is possible to obtain all the parameters necessary to the circuit model so far presented. Calculate the internal resistance of the thermoelectric module, remembering that the condition for maximum power transfer occurs when the internal resistance of the generator and the load resistance are perfectly equal: Rin = RL (3.15)

70 the internal resistance of the module can then be calculated from the maximum power and the module voltage at coupled load conditions: 2 V Rin = ml P ml (3.16) Also the average Seebeck coefficient of the thermoelectric generator can be estimated from the circuit at couple load conditions: V OC =2 V ml (3.17) substituting it into equation (3.7) we obtain: α pn= 2 V ml T HJ T CJ (3.18) R in V OC R L = R in V ml Fig. 3.3 thermoelectric generator electric circuit at couple load conditions To calculate the thermal resistance Θin of the thermoelectric generator we must first obtain the expression of the figure of merit as a function of the conversion efficiency. The conversion efficiency of the thermoelectric generator can be expressed by the ratio between the electric power generated and the thermal power entering the junction at higher temperature: η= [ P prod T HJ T CJ = Q in T HJ m (m+ 1) 2 1 T HJ T CJ m+ 1+ Z T HJ 2 T HJ ] (3.19) where the figure of merit Z is equal to: 2 2 α pn α pn Θin Z= = K in Rin Rin The figure of merit can be calculated in two different way: (3.20)

71 if we substitute in (3.19) the maximum power transfer to the load condition (m = 1), we obtain: η( m=1)=ηml = 2 Z (T HJ T CJ ) 8+ Z (3 T HJ + T CJ ) (3.21) expressing (3.21) as a function of ηml: Z= 8 ηml T HJ (2 3 ηml ) T CJ (2+ ηml ) (3.22) η =0 we can find the maximum conversion efficiency ηmax of the m thermoelectric generator: from mη 1 ηmax=η( m=mη)=ηc T CJ m η+ T HJ (3.23) where ηc is the efficiency of the ideal Carnot cycle: ηc = T HJ T CJ T HJ (3.24) and: (T + T CJ ) mη= 1+ Z HJ 2 (3.25) we derive now the expression of the figure of merit Z as a function of the maximum efficiency: [( ) ] 2 ηc T HJ + ηmax T CJ 2 Z= 1 T HJ + T CJ (ηc ηmax ) T HJ (3.26) Once calculated the figure of merit Z, the thermal resistance is calculated from its expression (3.20): R Θin = 2in Z α pn (3.27) The last parameters to obtain in order to use the thermoelectric generator model presented in section 3.1 and 3.2 are the thermal capacities of the components of the generator. The general expression of the heat capacity is equal to: C=c ρ v where: (3.28)

72 c [kj/kg K] is the specific heat of the material; ρ [kg/m3] is the material density; v [m3] is the volume. 3.4 Efficiency of a thermoelectric generator Consider equation (3.19), the efficiency η is the product of an ideal efficiency of the Carnot cycle (limit efficiency) for a term that takes into account the irreversibility. To maximize the efficiency is therefore necessary to make this coefficient as close as possible to 1, by adjusting the parameters Z, THJ and m. Figure of merit Z (equation (3.20)), is a characteristic parameter of the thermoelectric material (not dependent on the geometry). To optimize the performance may be used materials with high figure of merit, so the thermoelectric generator must be formed by thermoelements which have high Seebeck coefficient, low thermal conductivity and low electrical resistivity. In most of the metals and non-metals the electrical and thermal conductivity are closely related, to achieve efficient conversion (8-10%), the TEGs on the market use doped semiconductors, belonging to the family of tellurides (e.g. Bismuth Telluride), but they are very expensive and rare (rarer than platinum). Other materials commonly used are the PbTe and SiGe. The figure of merit of these materials, however, is still lower than 1, constraining the maximum conversion efficiency of the thermoelectric generator. Nanotechnology have helped create new thermoelectric materials with low dimensionality (superlattices) that promise to obtain a zt> 3, increasing dramatically the conversion efficiency of the cells. The nanostructured thermoelectric materials use widely available, low cost materials, and greatly reduce the cost per watt of the technology. Fig. 3.4 Figure of merit Z of some common thermoelectric materials [64]

73 m, is the ratio between the load resistance and the internal resistance, we can identify a value of m which maximizes the performance, it is shown in equation (3.25). Vary the ratio m, assuming that the internal resistance can not change (Rin constant), means vary the resistance RL of the circuit seen by the thermoelectric generator. This resistance is given by the ratio between Vout and IL, using a DC/DC converter and an MPPT algorithm we can vary the voltage and current changing the resistance seen by the thermoelectric generator, making work the thermoelectric generator with RL at the optimal value, to which corresponds the maximum efficiency. Working temperature of the cold and hot junctions, the greater the temperature difference, and in particular the greater the temperature of the hot junction, and the greater the efficiency of the device. Consider the derivative with respect to m of (3.13), and equal it to zero. The value of m that maximizes the power is: m p=1 (3.30) from which it follows by substituting (3.9) in (3.13), a maximum power supplied by the generator: V 2OC [ α pn (T HJ T CJ )] P max = = 4 R in 4 Rin 2 (3.31) As can be easily understood, the maximum power extractable from the thermoelectric generator depends on the square of the temperature difference between the two plates, the greater the temperature difference (and therefore the thermal power exchanged between the hot and cold plates), and the greater the electrical power extracted from the module. Increasing the thermal power input, increase the problems relating to heat dissipation on the cold side to maintain the temperature gradient constant, for this reason, the thermoelectric generators are designed to satisfy the condition (3.25), with the maximum electric power extracted at constant thermal power input. [65] 3.5 Simulation of the thermoelectric generator with Matlab Simulink Using what we studied so far, it has developed a Simulink model for the thermoelectric generator that simulates its behavior. All the simulations are referred to the data sheet of a thermoelectric module produced by Adaptive, model GM The data provided by the manufacturer are in Tab. 3.2.

74 Matched load output power Matched load resistance Open circuit voltage Matched load output current Matched load output voltage Heat flow through module Maximum compress (non-destructive) Maximum operation temperature, hot side Maximum operation temperature, cold side 3,27 W 9,7 Ω 11,25 V 0,58 A 5,6 V 65 W 1 Mpa 250 C 175 C Tab. 3.2 GM parameters, they are calculated with the hot side at 250 C and the cold side at 30 C From the above table we can calculate some interesting parameters. The nominal conversion efficiency at maximum power conditions is equal to: ηml= P ml =5% Q T the Seebeck coefficient of the cell can be calculated as: α pn= V OC V =0,051 T H T C K the index of merit Z, is therefore: Z= 8 ηml 4 1 =10,04 10 T HJ ( 2 3 η ml ) T CJ (2+ ηml ) K Thermal Circuit The equivalent thermal circuit of the thermoelectric generator is represented in Fig and Fig. 3.6.

75 Fig 3.5 Equivalent thermal circuit of the thermoelectric generator

76 Fig. 3.6 (Qp + Qj) block It has as input the difference between the temperatures of the heat source (250 C) and the environment (30 C) and as output the temperature difference between the hot and cold junctions, as we can see in Fig. 3.7 this temperature difference is equal, after a short transient, to 213 C. Fig. 3.7 Temperature difference between the hot and cold junction The main elements of this block are the following: Rh and Ch are, respectively, the thermal resistance and the thermal capacity of the contact surface between the heat source and the hot side of the ceramic plate:

77 Rh=10 5 K W C h=10 5 J K Rc1 (and Rc2) and Cc1 (and Cc2) are respectively the thermal resistance and the thermal capacity of the ceramic plate: Rc = h 2 K =6,25 10 k Al2O3 S W where: h=1,5 mm, is the height of the ceramic plate; S =(40 x 40) mm, is the surface of the ceramic plate; k Al2O3=15 W, is the thermal conductivity of the Alumina. m K C c =c Al2O3 ρal2o3 V =6, 93 J K where: J, is the specific heat of the Alumina; kg K c Al2O3=0, ρal2o3 =3,75 10 V =( 40 x 40 x 1,5)mm, is the volume of the ceramic plate. 3 kg m3 is the density of the Alumina; Rsink and Csink are, respectively, the thermal resistance and the thermal capacity of the heat sink: R sink = h 3 K =5,72 10 k Cu S W where: h=12,7 mm, is the height of the heat sink; S =(89 x 64) mm, is the surface of the heat sink; k Cu =390 W, is the thermal conductivity of the copper. m K

78 C sink =c Cu ρcu V =252,78 J K where: J, is the specific heat of the copper; kg K c Cu =390 ρcu=8, V =(89 x 64 x 12,7) mm, is the volume of the heat sink. kg 3 m is the density of the copper; R and C are respectively the thermal resistance and the thermal capacity of the junction; R= Rin K Z =3,73 2 W α pn where: Rin is the internal resistance of the thermoelectric generator; αpn is the Seebeck coefficient of the thermoelectric generator; Z is the index of merit of the thermoelectric generator. C=2 N c Bi2O3 ρbi2o3 V =2,75 J K where: N is the number of thermocouples, J, is the specific heat of the bismuth telluride; kg K c Bi2O3 =544 ρbi2o3 =7, V =(2 x 1 x 1)mm, is the volume of a single thermoelement. kg 3 m is the density of the bismuth telluride; Q p=α pn (T CJ T HJ ) I L, is the heat transferred due to the Peltier effect; Q J =Rin I L, is the heat dissipated by the Joule effect by the module; 2 where: THJ is the hot junction temperature; TCJ is the cold junction temperature;

79 IL is the current of the thermoelectric generator; αpn is the Seebeck coefficient of the thermoelectric generator; Rin is the internal resistance of the thermoelectric generator Electric circuit Electric circuit without the DC-DC converter Fig. 3.8 shows the equivalent electric circuit without the DC-DC converter and the MPPT algorithm. The difference between the heat source temperature (250 C) and the environment temperature (30 C) is the input for the thermal circuit, the output of this block is the temperature difference of the hot and cold junction of the thermoelectric generator, that multiplied by the Seebeck coefficient gives the value of the open circuit voltage that goes into the controlled voltage source of the circuit. As we can see in Fig. 3.9 the value of the open circuit voltage is 10,89 V. The internal resistance of the thermoelectric generator depends on the temperature of the hot side and as we can see in Tab. 3.1 when the hot side is at 250 C and the cold side at 30 C it is equal to 9.7 Ω, the load resistance is choose equal to 20 Ω. Fig. 3.8 Electric circuit without the MPPT algorithm and the DC-DC converter

80 Fig. 3.9 Open circuit voltage In the case the load is equal to 20 Ω the voltage on the internal resistance is equal to 3,55 V, the one on the load is 7,33 V, the current inside the circuit is 0,36 A, t he thermal power transmitted is equal to 57,14 W and as we can see in Fig the output power is equal to 2,68 W, the efficiency will then be equal to 4,69 %. In the case of matched load the voltage on the internal resistance and on the load are both equal to 5,44 V, the current is equal to 0,56 A, the thermal power transmitted is the same of the previous case, Fig 3.11 shows that the output power is equal to 3,05 W, thus the efficiency is equal to 5,34 %. Fig No converter output power

81 Fig No converter - matched load output power Electric circuit with a DC-DC buck converter Fig shows the thermal and electric circuit with the MPPT algorithm and the DC-DC converter. Thanks to the voltage and current sensors the values of the voltage and the current of the electric circuit are sent to the MPPT Controller block, here, a P and O MPPT algorithm with direct control on duty cycle determines the value of the duty cycle. The duty cycle is then used in the PWM block to obtain the PWM signal that is sent to the DC-DC Converter block. This voltage signal is needed to control the opening and closing of the switch of the DC-DC converter. Fig Electric circuit with the MPPT algorithm and the DC-DC converter In Fig. 3.13, Fig and Fig we can see, more in details, the MPPT Controller block. The P and O algorithm, which inputs are the voltage and current values given by two sensors, once calculated, send the duty cycle to the PWM block, here it is compared

82 with a sawtooth wave with a frequency of 30 khz. The result is a voltage signal that will be send to the DC-DC converter block to determine the opening (and closing) time of the switch. Fig MPPT Control block and PWM block Fig PWM block

83 Fig Sawtooth wave block As we can see in Fig the IGBT of the DC-DC converter receives the PWM signal from the MPPT controller block, in this way the converter can control the output voltage of the thermoelectric generator in order to have always the maximum possible output power. The inductor has a value of 150 μh, the two capacitors a value of 4,7 mf. Fig Buck converter In this case the thermal power transmitted is equal to 57,14 W, the open circuit voltage is equal to 10,89 V, the one on the internal resistance is 3,25 V. The input voltage, current and power of the converter are equal to 7,63 V, 0,33 A and 2,56 W. The duty cycle increases linearly from the initial value of 50 % until it reaches the value of 99 %, then it

84 remain constant for all the simulation. The output voltage, current and power of the converter are equal to 6,75 V, 0,34 A and 2,28 W. The efficiency is equal to 3,99 %. In Fig we can see the output power in the case of no converter (blue line) and in the case of matched load (red line), the power that enters in the buck converter (green line) and the one that exits from it (yellow line). Fig Buck converter comparison of powers Electric circuit with a DC-DC boost converter Fig shows the model of the boost converter. The inductor has a value of 150 μh, the capacitors are both equal to 4,7 mf.

85 Fig Boost converter In this case the thermal power transmitted is equal to 57,14 W, the open circuit voltage is equal to 10,89 V, the one on the internal resistance is 5,45 V. The input voltage, current and power of the converter are equal to 5,45 V, 0,56 A and 3,06 W. The duty cycle decreases linearly from the initial value of 50 % until it reaches the value of 31 %, then it remain constant for all the simulation. The output voltage, current and power of the converter are equal to 6,80 V, 0,34 A and 2,31 W. The efficiency is equal to 4,04 %. In Fig we can see the output power in the case of no converter (blue line) and in the case of matched load (red line), the power that enters in the boost converter (green line) and the one that exits from it (yellow line). Fig Boost converter comparison of powers

86 Electric circuit with a DC-DC buck-boost converter Fig shows the model of the buck-boost converter. The inductor has a value of 150 μh, the capacitors are both equal to 4,7 mf. Fig Buck-boost converter In this case the thermal power transmitted is equal to 57,14 W, the open circuit voltage is equal to 10,89 V, the one on the internal resistance is 5,45 V. The input voltage, current and power of the converter are equal to 5,45 V, 0,56 A and 3,06 W. The duty cycle increases linearly from the initial value of 50 % until it reaches the value of 59 %, then it remain constant for all the simulation. The output voltage, current and power of the converter are equal to - 5,80 V, - 0,29 A and 1,70 W. The efficiency is equal to 2,97 %. In Fig we can see the output power in the case of no converter (blue line) and in the case of matched load (red line), the power that enters in the buck-boost converter (green line) and the one that exits from it (yellow line).

87 Fig Buck-boost converter comparison of powers Electric circuit with a DC-DC cuk converter Fig shows the model of the cuk converter. The two inductors have both a value of 150 μh, the two capacitors have both a value of 4,7 mf. Fig Cuk converter In this case the thermal power transmitted is equal to 57,14 W, the open circuit voltage is equal to 10,89 V, the one on the internal resistance is 5,45 V. The input voltage, current and power of the converter are equal to 5,45 V, 0,56 A and 3,06 W. The duty cycle increases linearly from the initial value of 50 % until it reaches the value of 58 %, then it remain constant for all the simulation. The output voltage, current and power of the

88 converter are equal to - 5,50 V, - 0,27 A and 1,61 W. The efficiency is equal to 2,82 %. In Fig we can see the output power in the case of no converter (blue line) and in the case of matched load (red line), the power that enters in the cuk converter (green line) and the one that exits from it (yellow line). Fig Cuk converter comparison of powers

89

90 CHAPTER 4 EXPERIMENT TEST DESIGN In this chapter we will analyze the test bench's configuration used to evaluate the theoretical model previously analyzed. We will also characterize the components that make up the system. 4.1 Overall description of the system DC Heat gun Temperature sensors TEG Aluminium sheet PWM Data acquisition board Control Board Heat sink Water source Computer Fig. 4.1 Scheme of the system As we can see in Fig. 4.1 the system consist of a thermoelectric generator connected to a load resistance by means of a DC-DC converter. On the external side of both the ceramic plate of the thermoelectric generator there is a thermal sensor in order to detect the hot side and cold side temperature of the device. The temperature values are then send to a computer through a data acquisition board. Fig. 4.2 Thermal sensor PT1000 with platinum resistance The caramic plates are also covered with a thermal interface sheet in order to improve the

91 thermal conductivity of the generator. Fig. 4.3 Thermal interface sheet The hot side is also covered with a Aluminium sheet, it can be considered the heat source, in fact during the experiment a heat gun blow on it continuously a mass of hot air at a certain temperature. Fig. 4.4 Aluminium sheet The cold side is positioned on a liquid heat sink, connected to a faucet. The positive and negative cables of the thermoelectric generator are connected to the DCDC converter, that is connected to the load resistance. The switch of this converter is controlled through the control board that receives the output voltage and the output current

92 values of the converter by means of a voltage and a current sensor. The output voltage and the output current values are also send, with the DC-DC converter voltage input, to the data acquisition board, and then to the computer. 4.2 Simulation of the MPPT algorithm with LabView In this paragraph is performed a HIL (hardware in the loop) simulation, the MPPT algorithm is tested in a virtual environment, in this case LabView, in order to verify the correct functioning of the algorithm. The input of this simulation is a signal produced by the control board sbrio-9636 controlled by a knob. The first block transposes the values assumed by the signal from a range (0 4,22) to another (30-250). The new range of values represent the temperature values that the hot side of the thermoelectric generator can assume. As we can see in Fig. 4.5 the equation used to switch from a range to another is: ( ,22 0 ) T H =30+ x where x represent the original signal values and TH represent the hot side temperature values. Fig. 4.5 Scaling of the original signal The temperature signal then enters a second block, from which we can find the values of the internal resistance of the thermoelectric generator, in fact, this resistance is variable and depends on the values of the hot side temperature of the thermoelectric generator. The equation used is: Rin= R0 [1+ λ (T H T C )] where: Rin is the internal resistance at temperature TH;

93 R0 = 6,4 Ω is the internal resistance at temperature 30 C; λ = 0,0167, the internal resistance varies with this thermal coefficient; TC = 30 C, is the cold side temperature. Fig 4.6 Dependency of the internal resistance of the thermoelectric generator on the hot side temperature The hot side temperature and the internal resistance are used in a third block to find the values of the load voltage. The equation used is: V L= where: α = 0,051 V/K, is the Seebeck coefficient; RL = 20 Ω, is the load resistance. α (T H T C ) Rin+ R L

94 Fig. 4.7 Load voltage Knowing the load voltage, the load current and the load power can be calculated. Fig. 4.8 Load current and load power The last block represent the P and O MPPT algorithm with direct control on the duty cycle. The inputs are the load power calculated at step k an step k-1 and the load voltage calculated at step k and step k-1. As we can see in Fig. 4.9 if both the power difference and the temperature difference are positive (or negative) the duty cycle, whose initial value is 0,5, decrease of a quantity equal to 0,02, otherwise it increase of the same quantity. The output of this block is the duty cycle.

95 Fig. 4.9 MPPT algorithm block 4.3 Description of the main components of the system Thermoelectric generator The thermoelectric generator used for the test is produced by Adaptive, model GM The data provided by the manufacturer are the following: Matched load output power Matched load resistance Open circuit voltage Matched load output current Matched load output voltage Heat flow through module Maximum compress (non-destructive) Maximum operation temperature, hot side Maximum operation temperature, cold side 3,27 W 9,7 Ω 11,25 V 0,58 A 5,6 V 65 W 1 Mpa 250 C 175 C Tab. 4.1 GM parameters, they are calculated with the hot side at 250 C and the cold side at 30 C

96 Fig GM open circuit voltage [66] Fig GM matched load power output [67]

97 Fig GM matched load current [68] Fig GM matched load voltage [69]

98 Fig GM matched load resistance [70]

99 Fig GM geometric parameters [71] The thermocouples of this thermoelectric generator are made by Bi 2Te3 (bismuth telluride), a material which is commonly used in the thermoelectric generators on the market. The solder used to connect in series the thermocouples and to connect them with the power cables, is composed of 95% Sn (Tin) and of 5% Sb (Antimony). This solder has a melting point of 232 C, and since all the welds are made on the cold side of the cell, this is also the maximum temperature that this side can reach. The thermocouples are put in thermal parallel by two plates of Alumina (Al 2O3) treated with molten graphite to improve the thermal contact conductivity. The two cables are coated with Teflon, a good electrical and thermal insulator whose characteristics remain stable up to 250 C.

100 Fig Thermoelectric generator GM Heat sink This MELCOR's liquid heat exchanger (model LI-301) is effective for cooling thermoelectric devices. It is made entirely of copper, it has a machined finish and a solderable surface. The external portion of the tubes are 25,4 mm long, with a outer diameter 6,4 mm long. The internal waterways have a inner diameter 6,4 mm long. It has a sensor hole for temperature monitoring deep 19 mm, with a diameter 1,58 mm long. [72] The dimensons are: width: 64 mm; length: 89 mm; height: 12,7 mm.

101 Fig LI-301 [73] Heat Gun The heat gun (Hot air tool HL 1620 S) is produced by Steinel. It has a two stage airflow rate settings (240/450 L/min), a two stage temperature settings (300/500 C), a weight of 670 g and a power of 1600 W. Fig Heat gun model HL 1620 S by Steinel [74]

102 4.3.4 Control Board The sbrio-9636 embedded control and acquisition device integrates a real-time processor, a user-reconfigurable FPGA, and I/O on a single PCB. It features a 400 MHz industrial processor, a Xilinx Spartan-6 LX45 FPGA, 16 single-ended/8 differential 16-bit analog input channels at 200 ks/s, four 16-bit analog output channels, and 28 digital I/O (DIO) lines. The sbrio-9636 offers a -40 C to 85 C local ambient operating temperature range along with a 9 VDC to 30 VDC power supply input range. It provides 256 MB of DRAM for embedded operation and 512 MB of nonvolatile memory for storing programs and data logging. It features a built-in 10/100 Mb/s Ethernet port you can use to conduct programmatic communication over the network and host built-in web (HTTP) and file (FTP) servers. It also offers integrated USB, CAN, SDHC, RS232 serial, and RS485 serial ports for controlling peripheral devices. It is designed to be easily embedded in high-volume applications that require flexibility, reliability, and high performance. CompactRIO systems are ideal for low- to mediumvolume applications and rapid prototyping. [75] Fig sbrio-9636