**2.1 Thermoelectric Generator (TEG)**

The conversion of sunlight into electrical energy in a solar cell involves three major processes; 1) absorption of the sunlight by solar cell (heat source) at a temperature TH; 2) heating up of the thermocouple junction thus obtaining temperature difference between the ends of metal wires and thermoelectric potentials developed along the wire; and 3) the transfer of these separate thermoelectric potentials, in the form of electric current, to an external system.

A thermoelectric generator is a device that converts heat energy directly into electrical energy using Seebeck effect. This requires a heat source, a thermocouple and reference material. Thermoelectric generator is composed of at least two dissimilar materials, one junction of which is in contact with a heat source and the other junction of which is in contact with a heat sink. The power converted from heat to electricity is dependent upon the materials used, the temperatures of the heat source and sink, the electrical and thermal design of the thermocouple, and the load of the thermocouple (Angrist, 1982). Although TEGs have very low efficiencies (5 to 10 % in the above mentioned applications), their usage makes sense where the heat source is freely available and would otherwise be lost to the environment (Richner *et al*, 2011).

### **2.2 The principles of thermoelectricity**

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higher energy density (more capacity for a given volume/weight) than ultracapacitors, but ultracapacitors have a higher power density than batteries and have traditionally been used

Recently, such capacitors have been explored for energy storage, since they are more efficient than batteries and offer higher lifetime in terms of charge-discharge cycles. However, they involve leakage (intrinsic and due to parasitic paths in the external circuitry), which precludes their use for long-term energy storage. While it is also possible to implement energy storage mechanism using an ultracapacitor and a battery, it is a tradeoff to a decrease in harvesting circuit efficiency due to the increased overhead cost of

Two components are required to have a functional solar energy generator; they are the collector and a storage unit. The collector simply collects the radiation that falls on it and converts a fraction of it to other forms of energy; either electricity and heat or heat alone. Methods of collecting and storing solar energy vary depending on the uses planned for the solar generator. The storage unit is required because of the non-constant nature of solar energy; at certain times only a very small amount of radiation will be

At night or during heavy cloud cover, for example, the amount of energy produced by the collector will be quite small. The storage unit can hold the excess energy produced during the periods of maximum availability, and release it when the productivity drops. In practice, a backup power supply is usually added, too, for the situations when the amount of energy required is greater than both what is being produced and what is stored in the

The conversion of sunlight into electrical energy in a solar cell involves three major processes; 1) absorption of the sunlight by solar cell (heat source) at a temperature TH; 2) heating up of the thermocouple junction thus obtaining temperature difference between the ends of metal wires and thermoelectric potentials developed along the wire; and 3) the transfer of these separate thermoelectric potentials, in the form of electric current, to an

A thermoelectric generator is a device that converts heat energy directly into electrical energy using Seebeck effect. This requires a heat source, a thermocouple and reference material. Thermoelectric generator is composed of at least two dissimilar materials, one junction of which is in contact with a heat source and the other junction of which is in contact with a heat sink. The power converted from heat to electricity is dependent upon the materials used, the temperatures of the heat source and sink, the electrical and thermal design of the thermocouple, and the load of the thermocouple (Angrist, 1982). Although TEGs have very low efficiencies (5 to 10 % in the above mentioned applications), their usage makes sense where the heat source is freely available and would otherwise be lost to the

to handle short duration power surges.

energy storage management.

**2.1 Thermoelectric Generator (TEG)** 

environment (Richner *et al*, 2011).

**2. Solar generator** 

received.

container.

external system.

When two dissimilar metals are connected (i.e. welded or soldered together) to form two junctions, the voltage generated by the loop is a function of difference in temperatures between the two junctions. Such loop is called a thermocouple and the emf generated is called a thermoelectric emf. This thermoelectric phenomenon known as 'Seebeck Effect' was discovered in 1821 by Thomas J. Seebeck (Maycock et al., 1981). If this circuit is broken at the center, the net open voltage (the Seebeck voltage) is a function of the junction temperature and the composition of the two metals.

Fig. 1. A thermocouple made out of two different materials

### **Thermoelectric effects (Seebeck, Peltier, and Thomson)**

There are three main thermoelectric effects experienced in thermo generation: the Seebeck, Peltier, and Thomson effects (Goldsmid, 1995; Nolas *et al.,* 2001). Thermoelectric effects are described in terms of three coefficients: absolute thermoelectric power (S), the Peltier coefficient () and the Thomson coefficient (), each of which is defined for a homogenous conductor at constant temperature. Thermoelectric effects have significant applications in both science and technology and show promise of more importance in the future. Practical applications of thermoelectric effects include temperature measurement, power generation, cooling and heating (Steven, 2010).

**Seebeck Effect:** The Seebeck effect is responsible for the operation of a thermocouple. If a temperature gradient is applied across a junction between two materials, a voltage will develop across the junction, with the voltage related to the temperature gradient by the Seebeck coefficient.

For instance, the Seebeck coefficient of the thermocouple shown in Figure 1 as given by Steven, (2010) is:

$$\approx\_{\rm AB} = \frac{\rm dV}{\rm dT} \tag{1}$$

Where V is the voltage between points x and y, in the case of the thermocouple shown in Figure 1, T = T2 - T1 Then,

$$\mathbf{v\_{xy}} = \mathfrak{a\_{AB}} \text{ (T\_2 - T\_1 \ )}\tag{2}$$

If T2 is fixed and AB is known, then by measuring Vxy, one can determine T1. If this circuit is broken at the center, the net open voltage (the Seebeck voltage) is a function of the junction temperature and the composition of the two metals.

**Peltier Effect:** The Peltier effect is the opposite of the Seebeck effect in which electrical energy is converted into thermal energy. It is observed in applications such as thermoelectric coolers. The Peltier effect is an effect whereby heat is liberated or absorbed at the junction between two materials in which a current I is flowing through. The heat liberated (or absorbed) at the junction is given by

$$\mathbf{Q} = \ \Pi\_{\mathbf{AB}} \mathbf{I} \tag{3}$$

Where ΠAB is the Peltier coefficient (Nolas *et al.,* 2001),**I** is current)

**Thomson Effect:** If there is a temperature gradient across a material and a current is flowing through the material, then heat will be liberated or absorbed. This is Thomson effect, and it is described by the following equation:

$$Q = \text{tr}I\frac{d\mathbf{r}}{dx} \tag{4}$$

Where is the Thomson coefficient (Nolas *et al.,* 2001). The following relationships hold for two materials A and B (Nolas *et al.,* 2001):

$$
\tau\_\mathrm{A} - \tau\_\mathrm{B} = \mathrm{T} \frac{\mathrm{d}a\_\mathrm{AB}}{\mathrm{d}\mathrm{T}} \tag{5}
$$

$$
\Pi\_{AB} = \mathcal{a}\_{AB} T \tag{6}
$$

The coefficients AB and ΠAB defined above are for a system consisting of two different materials with a junction between them. However, it is often useful to define absolute thermoelectric coefficients which describe a single material. All of the above equations are generalized when a single material is being discussed (Nolas *et al.,* 2001). If a material is subjected to a temperature gradient T, then V = T, where is the Seebeck coefficient and V is the volumetric change of the material respectively. Relations (5) and (6) also apply to absolute thermoelectric coefficients, i.e.

$$
\pi\_{\parallel} = T \frac{da}{dT} \tag{7}
$$

and

$$
\Pi = \ aT \tag{8}
$$

#### **2.3 Measuring Seebeck voltage**

The Seebeck voltage cannot be measured directly because a voltmeter must first be connected to the thermocouple, and the voltmeter leads create a new thermoelectric circuit. Connecting a voltmeter across a copper-constantan (Type T) thermocouple and observing the voltage output: the voltmeter should read only V1, but by connecting the voltmeter in an attempt to measure the output of Junction J1, two more metallic junctions have been created: J2 and J3 (Figure 2a).

Fig. 2. Measuring Seebeck voltage

If T2 is fixed and AB is known, then by measuring Vxy, one can determine T1. If this circuit is broken at the center, the net open voltage (the Seebeck voltage) is a function of the junction

**Peltier Effect:** The Peltier effect is the opposite of the Seebeck effect in which electrical energy is converted into thermal energy. It is observed in applications such as thermoelectric coolers. The Peltier effect is an effect whereby heat is liberated or absorbed at the junction between two materials in which a current I is flowing through. The heat

**Thomson Effect:** If there is a temperature gradient across a material and a current is flowing through the material, then heat will be liberated or absorbed. This is Thomson effect, and it

� = �� ��

Where is the Thomson coefficient (Nolas *et al.,* 2001). The following relationships hold for

τ� − τ� = T ����

The coefficients AB and ΠAB defined above are for a system consisting of two different materials with a junction between them. However, it is often useful to define absolute thermoelectric coefficients which describe a single material. All of the above equations are generalized when a single material is being discussed (Nolas *et al.,* 2001). If a material is subjected to a temperature gradient T, then V = T, where is the Seebeck coefficient and V is the volumetric change of the material respectively. Relations (5) and (6) also apply

� =� ��

The Seebeck voltage cannot be measured directly because a voltmeter must first be connected to the thermocouple, and the voltmeter leads create a new thermoelectric circuit. Connecting a voltmeter across a copper-constantan (Type T) thermocouple and observing the voltage output: the voltmeter should read only V1, but by connecting the voltmeter in an attempt to measure the output of Junction J1, two more metallic junctions have been created:

Q = ��I (3)

�� (4)

�� (5)

�� (7)

Р= �� (8)

 �� = ���� (6)

temperature and the composition of the two metals.

liberated (or absorbed) at the junction is given by

is described by the following equation:

two materials A and B (Nolas *et al.,* 2001):

to absolute thermoelectric coefficients, i.e.

**2.3 Measuring Seebeck voltage** 

J2 and J3 (Figure 2a).

and

Where ΠAB is the Peltier coefficient (Nolas *et al.,* 2001),**I** is current)

Since J3 is a copper-to-copper junction, it creates no thermal EMF (V3 = 0), but J2 is a copperto-constantan junction which will add an EMF (V2) in opposition to V1 (Figure 2b). The resultant voltmeter reading V will be proportional to the temperature difference between J1 and J2. This says that we cannot find the temperature at J1 unless we first find the temperature of J2.

In a closed circuit composed of two linear conductors of different metals, a magnetic needle would be deflected if, and only if, the two junctions were at different temperatures giving rise to an emf being generated. The magnitude of the emf generated by a thermocouple is measured on standard by an arrangement shown in figure below.

Fig. 3. Voltage measurement arrangement between two junctions

Points A and B are called junctions. Each junction is maintained at a well-controlled temperature (To or T1) by immersion in a bath (cold junction) or connected to a heat source (hot junction). From each junction, a conductor (metal 2) is connected to a measuring device (potentiometer or an amplifier of low input impedance), which measures the thermal emf.

The Seebeck emf is approximately related to the absolute junction temperatures T0 and T1 by

$$\mathbf{V} = \propto \left(\mathbf{T}\_1 - \mathbf{T}\_o\right) + \chi \left(\mathbf{T}\_1^2 - \mathbf{T}\_o^2\right) \tag{9}$$

Where and are constants for the thermocouple pair.

The differential coefficient of equation above is the sensitivity, or thermoelectric power S, of the thermocouple

$$\mathbf{S} = \frac{d\mathbf{V}}{d\mathbf{T}\_1} = \mathbf{\mathcal{K}} + 2\mathbf{\mathcal{V}}\_1 \text{ (\mu V/ 0 c)}\tag{10}$$

$$\mathbf{E\_{A}(T\_{o}, T\_{1}) = \int\_{T\_{o}}^{T\_{1}} \mathbf{S\_{A}(T)dt}} \mathbf{S\_{A}(T)dt} \tag{11}$$

$$\mathcal{S}\_{\mathbf{A}}(\mathbf{T}) = \lim\_{\Delta \mathbf{T} \to \mathbf{0}} \mathbf{E}\_{\mathbf{A}} \frac{(\mathbf{T}\_{\mathbf{1}}, \mathbf{T} + \Delta \mathbf{T})}{\Delta \mathbf{T}} \tag{12}$$

$$\mathbb{E}\_{\rm AB} \{ \mathbf{T}\_{\rm o}, \mathbf{T}\_{\rm I} \} = \int\_{\mathbf{T}\_{\rm o}}^{\mathbf{T}\_{\rm I}} \mathbb{S}\_{\rm A} \{ \mathbf{T} \} \mathrm{dt} + \int\_{\mathbf{T}\_{\rm o}}^{\mathbf{T}\_{\rm I}} \mathbb{S}\_{\rm B} \{ \mathbf{T} \} \mathrm{dt} \tag{13}$$

$$\mathbf{E\_{BA}(T\_o, T\_1) = \int\_{T\_o}^{T\_1} \mathbf{S\_A(T)dt} - \int\_{T\_o}^{T\_1} \mathbf{S\_B(T)dt} \tag{14}$$

$$\text{E}\_{\text{AB}}\{\mathbf{T}\_{\text{o}}, \mathbf{T}\_{\text{1}}\} = \text{E}\_{\text{A}}\{\mathbf{T}\_{\text{o}}, \mathbf{T}\_{\text{1}}\} - \text{E}\_{\text{B}}\{\mathbf{T}\_{\text{o}}, \mathbf{T}\_{\text{1}}\} \tag{15}$$

$$\mathrm{E\_{AB}\{T\_{\mathrm{o}}, T\_{\mathrm{1}}\}} = \int\_{T\_{\mathrm{o}}}^{T\_{\mathrm{1}}} [\mathrm{S\_{A}}\,\mathrm{(T)}\,\mathrm{dt} - \,\mathrm{S\_{B}}\,\mathrm{(T)}\,\mathrm{I}\,\mathrm{dt}]\,\mathrm{dt} \tag{16}$$

$$\mathbf{E\_{AB}(T\_{\rm o}, T\_1) = \int\_{T\_{\rm o}}^{T\_1} \mathbf{S\_{AB}} \quad \text{(T)}\,\text{dT} \tag{17}$$

$$\rm{\bf \Rightarrow S\_{AB}(T) = S\_A \text{ (T)} - S\_B (T)}\tag{18}$$

These equations lead directly to experimentally and theoretically verified results that in a circuit kept at a uniform temperature (dt = 0) throughout, E= 0 even though the circuit may consist of a number of different conductors (equation 18). If E did not equal 0, the circuit could drive an electric motor and make it perform work. The only source of energy would be heat from the surrounding. A circuit composed of single, homogenous conductor cannot produce thermoelectric emf (equations 6) when SB (T) is equal to SA (T). Finally, equation 6 makes it clear that the source of the thermoelectric emf in a thermocouple lies in the bodies of the two materials of which it is composed rather than the junctions.

#### **The reference junction**

466 Solar Radiation

According to the experimentally established law of Magnus, the thermoelectric emf for homogenous conductors depends only on the temperatures of the junctions and not on the shapes of the samples. This emf can thus be described by the symbol EAB (To, T1) and is determined solely by conductor A and can be written as EA (To, T1). This emf is more conveniently expressed in terms of a property, which depends upon only a single temperature. Such property

> �� ��

> > (��,����)

(T)dt + � S� �� ��

(T)dt − � S� �� ��

E��(T�, T�) = E��T�,T��− E��T�,T�� (15)

S��(T) = S� (T) − S�(T) (18)

If EA (T1, T+T) is known, for example, from measurements involving a super conductor,

If equation 11 is for any homogenous conductor, then it ought to apply to both sides of the thermocouple. Indeed, it has been verified experimentally that the emf EAB (To, T1) produced by a thermocouple is just the difference between the emfs calculated using equation (17),

Employing the usual sign correction, to calculate EAB(To, T1), begin at the cooler bath, integrate SA(T)dT along conductor (metal 2) at junction A up to the warmer bath and then return to cooler bath along conductor (metal 1) through junction B by integrating SB(T)dT.

is the absolute thermoelectric power (thermo power Sa (T)) defined as in equation (11).

S�(T) = lim���� E�

This circular loop produces EAB (To, T1) given by equation 13 and 14.

E��(T�, T�) = � S�

E��(T�, T�) = � S�

E��(T�, T�) = � [S�

Alternatively, combining the two integrals in equation 14

Defining SAB according to equation 16 then yields equation 17

�� ��

> �� ��

> > �� ��

E��(T�, T�) = � S��

According to equation 16, EAB(To,T1) can be calculated for a given thermocouple whenever the thermo powers SA(T) and SB(T) are known for the two constituents over the temperature

> �� ��

= ∝ +2γT� (V/ 0 c) (10)

(T)dt (11)

�� (12)

(T)dt (13)

(T)dt (14)

(T)dt − S�(T)] dt (16)

(T)dT (17)

S = �� ���

**2.4 Measuring thermoelectric power, S** 

 E�(T�, T�) = � S�

then SA (T) can be determined from equation 12

produced by its two arms as follows.

range To to T1.

One way to determine the temperature of reference junction J2 is to physically put the junction into an ice bath, forcing its temperature to be 0oC. Since the voltmeter terminal junctions are now copper-copper, they create no thermal emf and the reading V on the voltmeter is proportional to the temperature difference between J1 and J2.

Fig. 4. External reference junction

Now the voltmeter reading is (see Figure 4):

$$\mathbf{V} = \mathbf{V\_1} - \mathbf{V\_2} \equiv \lnot \left(\mathbf{t\_{\parallel 1}} - \mathbf{t\_{\parallel 2}}\right) \tag{19}$$

If we specify TJ1 in degrees Celsius:

$$\text{T}\_{\|1\|}\text{(°C)} + 273.15 = \text{ t}\_{\|1\rangle} \tag{20}$$

Then V becomes:

$$\mathbf{V} = \mathbf{V}\_1 - \mathbf{V}\_2 = \mathbf{c} \left[ (\mathbf{T}\_{\parallel 1} + 273.15) - \mathbf{T}\_{\parallel 2} + 273.15 \right] \tag{21}$$

$$\mathbf{V} = \lnot \left( \mathbf{T}\_{\mathbf{j}1} - \mathbf{0} \right) = \lnot \mathbf{T}\_{\mathbf{j}1} \tag{22}$$

This derivation is used to emphasize that the ice bath junction output, V2, is not zero volts. It is a function of absolute temperature. By adding the voltage of the ice point, reference junction, we have now referenced the reading V to 0oC. This method is very accurate because the ice point temperature can be precisely controlled. The ice point is used by the National Bureau of Standards (NBS) as the fundamental reference point for their thermocouple tables, so we can now look at the NBS tables and directly convert from voltage V to Temperature TJ1.

Using an iron-constantan (Type J) thermocouple instead of the copper-constantan, the iron wire (Figure 5) increases the number of dissimilar metal junctions in the circuit, as both voltmeter terminals become Cu-Fe thermocouple junctions.

Fig. 5. An Iron- constantan couple

If both front panel terminals are not at the same temperature, there will be an error. For a more precise measurement, the copper voltmeter leads should be extended so that the copper-to- iron junctions (J3 and J4) are made on an isothermal (same temperature) block.

The isothermal block is an electrical insulator but a good heat conductor, and it serves to hold junctions J3 and J4 at the same temperature. The absolute block temperature is unimportant because the two Cu-Fe junctions act in opposition.

#### **Reference circuit**

Replacing the ice bath with another isothermal block (Fig. 7) at JREF, the new block is at reference temperature TREF, and because J3 and J4 are still at the same temperature, we can again show that

$$\mathbf{V} = \mathfrak{x} \text{ (T}\_1 - \text{T}\_{\text{REF}}\text{)}\tag{23}$$

A thermistor, whose resistance RT is a function of temperature, provides us with a way to measure the absolute temperature of the reference junction. Due to the design of the isothermal block, junctions J3 and J4 and the thermistor are all assumed to be at the same temperature.

Fig. 7. Eliminating the ice bath

468 Solar Radiation

Using an iron-constantan (Type J) thermocouple instead of the copper-constantan, the iron wire (Figure 5) increases the number of dissimilar metal junctions in the circuit, as both

If both front panel terminals are not at the same temperature, there will be an error. For a more precise measurement, the copper voltmeter leads should be extended so that the copper-to- iron junctions (J3 and J4) are made on an isothermal (same temperature) block.

The isothermal block is an electrical insulator but a good heat conductor, and it serves to hold junctions J3 and J4 at the same temperature. The absolute block temperature is

Replacing the ice bath with another isothermal block (Fig. 7) at JREF, the new block is at reference temperature TREF, and because J3 and J4 are still at the same temperature, we can

V = ∝ (T� − T���) (23)

voltmeter terminals become Cu-Fe thermocouple junctions.

Fig. 5. An Iron- constantan couple

Fig. 6. Removing junctions from DVM terminals

**Reference circuit** 

again show that

unimportant because the two Cu-Fe junctions act in opposition.

However, the use of thermocouples other than thermistor is more preferable in that thermocouple can be used over a range of temperatures, and optimized for various atmospheres. Thermocouples are much more rugged than thermistors, as evidenced by the fact that thermocouples are often welded to a metal part or clamped under a screw. They can be manufactured on the spot, either by soldering or welding. In short, thermocouples are the most versatile temperature transducers available and, since the measurement system performs the entire task of reference compensation and software voltage to-temperature conversion, using a thermocouple becomes as easy as connecting a pair of wires.
