T. Bezina and R. Jabloski (eds.), Mechatronics 2013, 265 DOI: 10.1007/978-3-319-02294-9_34, Springer International Publishing Switzerland 2014

Simulation Modelling of MEMS Thermoelectric Generators for Mechatronic Applications

L. Janak1, Z. Ancik2, and Z. Hadas1

1 Brno University of Technology, Faculty of Mechanical Engineering, Technicka 2, 616 69, Brno, Czech Republic ludek.janak@gmail.com, hadas@fme.vutbr.cz

2 Unis, a.s., Mechatronic & embedded systems, Jundrovska 33, 624 00, Brno, Czech Republic ancikzdenek@seznam.cz

Abstract. This paper deals with an introduction to the simulation modelling of transient behaviour of MEMS thermoelectric generators (TEGs) for mechatronic applications. Special emphasis is put on the simulation of recently commercially achievable modules. At first is given the overview of prospective mechatronic applications of MEMS TEGs and the existing commercially achievable MEMS TEG modules are listed in a short trade review. Afterwards, the main features of thermoelectric energy conversion are described together with the simple govern-ing equations. In the main part of paper is presented the simulation model for investigations of transient behaviour of MEMS TEG module. Derived model is implemented in MATLAB/Simulink Simscape. Results given by dynamic model are compared with results obtained by other modelling approaches and transient behaviour of MEMS TEG is evaluated.

1 Introduction

Thermoelectric generators are one of the promising ways to produce the environ-mentally clean energy. Due to their relatively small efficiency are particularly considered their applications in the field of thermal energy harvesting recovery of the small amounts of waste heat to the useful electric energy [1]. The main advantages for the use of TEGs in mechatronic applications are no movable parts which represent low demands on maintenance.

Promising area is the use of small amounts of locally harvested energy for powering the wireless applications, telemetry units, sensors, etc. This approach is particularly advantageous in the places where is difficult to trace wiring or where the battery replacement is challenging due to disassemble difficulties. Typical cases of this kind of application are the diagnostic systems in aerospace field [2, 3], portable medical devices [4], or autonomous measurement units in process control systems [5].

266 L. Janak, Z. Ancik, and Z. Hadas

Wider commercial use of the MEMS thermoelectric generators is in its in-fancy [6]. There are only a few existing commercial solutions in the field of MEMS TEGs and even fewer amount could be bought as a standalone solution. Standalone MEMS solutions have been developed by Micropelt GmbH [7], Nex-treme Thermal Solutions, Inc. [8], Thermo Life Energy Corp., Inc. [9], Hi-Z Technology, Inc. [10] and Perpetua Power Source Technologies, Inc. [11]. Mod-ules from the first two above-mentioned manufacturers Nextreme and Micropelt which are currently easily achievable through worldwide electronics compo-nents retailers are shown in Fig. 1.

a) b) Fig. 1 a) Micropelt TGP-751 in package [8], b) Nextreme eTEG HV56 [9]

In this paper is presented an approach to the modelling of MEMS TEG based on simulation model implemented in MATLAB/Simulink Simscape. The model is capable to carry out the dynamic simulations which give us the overview of tran-sient behaviour and other time-domain properties of MEMS TEG. The model input data were set according to the specific case of Nextreme eTEG HV56 [12].

2 Basic Principles of Thermoelectricity

Physical nature of thermal energy harvesting - the Seebeck effect is based on the diffusion of electrons through the interface between two different materials con-ductors or semiconductors. This diffusion is achieved by applying a heating at the junction of two materials which make a thermocouple. Heating causes the net changes in the materials and allows electrons to move from material where they have lower energy into material where the energy of electrons is higher. Because the electrical current is exactly a flow of electrons, this effect of passing electrons from one material to another makes an electromotive force (voltage) on the terminals of thermoelectric module [1, 13, 14]. Generated open circuit voltage is linearly dependant on the temperature difference between hot and cold sides of thermoelectric module:

( )CTHTNocU = .. (1) where N is number of thermocouples, is differential Seebeck coefficient (material constant), TH is hot-side temperature and TC is cold-side temperature [13].

Simulation Modelling of MEMS Thermoelectric Generators 267

In practical applications is TEG operated with electric load RL (Fig. 2). TEG is, in fact, the temperature-controlled constant voltage source with internal resistance Ri. Thus the voltage UL on load is:

ocU

iRLRLR

LU .+= (2)

Current IL in the TEG circuit can be easily calculated using Ohms law. The maximum power point (MPP) is achieved when Ri = RL. This mode of operation is called operation with matched load. Operation in the MPP mode with maximum electrical power on load PL is desired in the most of applications [13].

Fig. 2 Principle of operation of TEG into the load resistance RL (current IL, voltage UL)

TEG is, in fact, a type of heat engine operating between two temperatures TH and TC. Thus a theoretical efficiency of the thermoelectric energy conversion is limited by the Carnots Theorem [1]. The efficiency of real TEG is exactly around 2 5 %. This reduction is caused by the materials- or design-related problems. Enhancement of efficiency and higher integration with surrounding systems are the tasks for MEMS and NEMS TEGs. [14]

3 Dynamic Model in MATLAB/Simulink Simscape

The considered dynamic model is an extension of steady-state Simscape model published in [15]. Parts of the model describing the transient behaviour of TEG are built-in according to the scheme of SPICE model described in [16]. Derived model was implemented in Simscape using the objects from Electrical and Ther-mal folders of Foundation Library. Overview of the model is shown in Fig. 3 5.

The whole simulation model consists of the thermal and electrical part and model of interconnections between these parts. The thermal part, shown in Fig. 3, is composed of thermal resistances and masses of wafer and thermocouples (Rwafer,

268 L. Janak, Z. Ancik, and Z. Hadas

Cwafer, Rtcs, Ctcs). Thermal materials properties are not directly offered by manufac-turer and their estimation based on information from [12, 14] is necessary. Tem-perature dependences of the materials were neglected and their fixed values were estimated at the room temperature. Ideal heat flow sources Qjoule, QpelC and QpelH represent phenomena of the Peltier cooling and Joule heating which occur in TEG.

Fig. 3 Thermal Part of Model Implemented in Simscape

Heat fluxes generated by heat flow sources are dependant on the current pass-ing through the electrical part of TEG model. Thus the thermal and electrical parts are interacting together. Equations describing the implementation of multi-domain phenomena of Peltier cooling and Joule heating are shown in Fig. 4.

Fig. 4 Model of interconnections between thermal and electrical parts

Simulation Modelling of MEMS Thermoelectric Generators 269

Finally, the electrical part of TEG is built as the constant voltage source with internal resistance as described in the chapter 2. Output voltage is controlled by the real temperature difference on the thermocouples. Implementation of electrical part is shown in the Fig. 5.

Fig. 5 Electrical Part of Model

Examined time-dependant output values from above-described simulation model include the voltage on load UL, current through the circuit IL and resulting electrical power PL.

3.1 Comprehension of Results Transient behaviour of MEMS TEG module was examined by applying the step function of hot-side temperature TH. Input simulation parameters are set to the temperature difference of 50 C and matched resistive load. Resulting step re-sponse of voltage UL is shown in Fig. 6. As could be seen in Fig. 6, the occurring time constant is in the millisecond range. This rapidity is caused by the very small thermal masses appearing in the MEMS TEG module.

Fig. 6 Step response of dynamic Simscape model (MEMS eTEG HV56, conditions: Tout = 50 C, TC = 25 C, TH = 75 C, TH applied at t = 0)

270 L. Janak, Z. Ancik, and Z. Hadas

The steady-state value reached by the dynamic model was compared with re-sults of other simulation modelling approaches. Steady-state values are listed and compared below in the Table 1. In the comparison are included results given by the simple modelling approach using (2) and Ohms law, Analytic Model with Constant Resistances [14, 17] and FEM analyses [15]. Obtained output values are also compared with the datasheet values provided by manufacturer in [12].

Table 1 Comprehension of results (conditions: T = 50 C, TC = 25 C, TH = 75 C, matched load)

Type of Model Voltage on the matched load UL [V]

Passing current IL [mA]

Produced electric power PL [mW]

Simscape dynamic 0,651 63,784 41,552 Voltage source with Ri 0,688 67,412 46,379 Analytic with contact res. 0,566 62,393 39,318 FEM (ANSYS) 0,688 - - Datasheet value 0,6 60 36

4 Conclusions

The above-described dynamic model of MEMS TEG was successfully imple-mented in Simscape and verified by application of the trivial input conditions constant temperature difference and matched load. Very small time constant in the millisecond range was observed. The maximal observed difference between data-sheet value and simulation was 15,4 % (PL). In the comprehension with other simulation modelling approaches was observed the maximum difference of 15 % in the case of voltage UL and analytic model with contact resistances. These inac-curacies could be reduced by identification of input parameters based on meas-urement. Better identification of input parameters and verification of models based on MEMS TEG module measurements are the tasks for future development.

The biggest challenges for the further work in energy harvesting area are the co-simulations with surrounding systems [18]. The Simscape model will be chiefly used for the co-simulations of MEMS TEG with surrounding power condi-tioning electronics.

Acknowledgments. This work has been funded by the European Commission within the FP7 project "Efficient Systems and Propulsion for Small Aircraft | ESPOSA", grant agree-ment No. ACP1-GA-2011-284859-ESPOSA. And this work has been additionally sup-ported by the project "Complex Affordable Aircraft Engine Electronic Control (CAAEEC)" TA02010259 under The Technology Agency of the Czech Republic.

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Simulation Modelling of MEMS Thermoelectric Generators for Mechatronic Applications1 Introduction2 Basic Principles of Thermoelectricity3 Dynamic Model in MATLAB/Simulink Simscape3.1 Comprehension of Results

4 ConclusionsReferences