Investigation of novel thermoelectric sensor array conﬁgurations operating under non-uniform temperature distribution conditions for the measurement of maximum output power in an energy harvesting system

This research work proposes a conﬁguration study of thermoelectric module (TEM) sensor array operating under uniform and non-uniform temperature distribution (NUTD) conditions. The four different (10 × 10) TEM array conﬁgurations, which are electrically connected in series-parallel (SP), all-tied (AT), bridge-joint (BJ), and bee-hive (BH), are considered to evaluate its performance under six cases of NUTD conditions. The electrical characteristics of the various sensor array conﬁgurations has been analysed and tested under both temperature distribution conditions using MATLAB-Simulink. A comparison of results of the various conﬁgurations is carried out in terms of maximum output power, voltage and current corresponding to maximum power, utilization factor, losses, relative error, standard deviation, and root mean square error. The maximum output power obtained from various cases of NUTD conditions conﬁrm that the performance of bridge-joint conﬁguration is best than all other conﬁgurations in the ﬁeld of thermoelectric energy harvesting systems.


INTRODUCTION
In the world, the demand for energy is rising every day because of the growth of the human population. Fossil fuels fulfil almost the energy necessity of humans. However, fossil resources are being exhausted [1,2], and their environmental damage [3] is growing day by day. Hence, research is increased dramatically in the production of clean electrical energy. A significant amount of waste heat energy is released directly into the environment from various sources include industries [4], vehicles [5][6][7][8], stoves [9][10][11], and helicopter [12]. Recovery of waste heat is, therefore, remarkable because it can save significant energy and reduce emissions [13]. The thermoelectric generator (TEG) is the most frequently used waste heat recovery technology. It is a solid-state device providing direct conversion of the waste heat energy into electrical energy that uses the Seebeck effect. Also, it has the advantages of quiet operation, no environmental pollution, less maintenance [14], and highly reliable. However, low conversion performance and high cost for manufacturing limit the development of TEGs. Therefore, enormous research works on thermoelectric materials have been effectively carried out to obtain high conversion performance [15]. Until now, bismuth telluride (Bi 2 Ti 3 ) alloy is commonly used thermoelectric materials with relatively high commercial value when compared to other materials, and therefore the conversion efficiency seems to be around 5% [16]. In actual applications, the performance of TEG depends on the boundary conditions of thermal transfer and their configuration [17,18]. By decreasing the thermal resistance between thermoelectric modules (TEMs) helps to enhance the conversion efficiency and the output power [19]. Furthermore, the TEMs can produce a maximum output power with the use of maximum power point tracking (MPPT) controllers [20][21][22]. The concept of maximum power transfer theory says that, when the whole source internal resistance is equal to the load resistance, the TEMs delivers maximum power to the load. When the difference in temperature between the cold and hot sides of the TEM remains constant, the output performance curve of the module follows the theory described above. However, it is a challenging task to sustain a constant ΔT across the TEM in practical applications [23].
The performance of the TEGs also depends on the conditions of temperature distribution. An analysis of the effect of the non-uniformity temperature on TEG is carried-out by using a heat spreader [24]. With the use of simulation and experiments, an analysis is carried out under uniform and non-uniform distribution of temperature conditions on TEG in terms of output power. From the simulation and experimental results, the authors found that the uniform distribution of temperature on the heat spreader has enhanced performance. Moreover, a numerical and experimental study has performed in terms of power under non-uniform heat flux conditions [25] to analyse the performance of TEGs that are associated in series and parallel. The results proved that the output power is mainly affected in a parallel configuration under the above condition. A two TEMs are associated in parallel under various varying temperature conditions [26]. In this work, the authors analysed the energy harvesting system by performing simulation and experimental studies. The effect of electrical and thermal configurations on three TEMs has been investigated [27]. It concentrated mainly on TEMs that are associated with thermally and electrically in different forms. This work stated that TEMs linked thermally and electrically in parallel are optimal for acquiring maximum power. A series and parallel connection of three TEMs in temperature mismatch effect under different temperature conditions were analysed [28]. This work recommended that the series connection of TEMs provide enormous power than that of parallel connection.
To overcome the drawbacks of the NUTD conditions and hardware implementation of MPPT, such as slow speed of convergence, low convergence efficiency, complex coding, a larger number of sensors required in TEG systems and high cost. Hence, a configuration study on TEM array has been proposed for enhancing the output power of the system. Also, this research work proposes analytical modelling and simulation of (10 × 10) TEM array connected in SP, AL, BJ, and BH configurations. It analyses the performance of the configurations, as mentioned above, under uniform temperature distribution (UTD) and six different cases of NUTD conditions. Moreover, it compares the various configurations in terms of output power, voltage and current corresponding to maximum power, utilization factor, losses, relative error, standard deviation, and root mean square error to determine a suitable configuration for the energy harvesting applications. Figure 1 shows the various topologies of TEM array configurations considered in this proposed research work under UTD and NUTD conditions and the performance parameters to evaluate the TEM array configurations.

MATHEMATICAL MODEL OF THE THERMOELECTRIC MODULE
A TEM consists of series-connected thermocouples with P-type and N-type semiconductor thermoelements. When the heat circulates through thermoelements, it excites the free electron to travel from one end to the other end. As a result, an opencircuit voltage V oc is created [29] which is directly proportional to the ΔT exist across the module that can be represented as: where, N signifies the overall quantity of thermocouples; T indicates the Seebeck coefficient, T h and T c are the TEM temperature at its hot and cold sides. The T can be represented as: where, ΔT m denotes the difference in temperature taken from the device datasheet; V match represents the matched voltage of the TEM. The internal resistance R TEM can be indicated for the TEM as: where, i t and s e stand for the intercept and slope of whole internal resistance versus maximum temperature, respectively. The Matlab-Simulink model of TEM (GM250-127-28-10) is shown in Figure 2. Using this model, one can analyse the per- formance characteristics of TEM, such as power-current (P-I) and voltage-current (V-I).
The specifications for the TEM mentioned above are given in Table 1.

TEM ARRAY CONFIGURATIONS
The TEMs can be connected in various configurations such as SP, AT, BJ, and BH to obtain an appropriate output power as needed by applications.

Series-parallel configuration
In this configuration, the TEMs are associated in series to obtain a required voltage and then in parallel to obtain a required current. It is the most frequently used configuration since it is inexpensive, simple structure, and easy to construct. Moreover, in this arrangement, the voltage and current simultaneously increases when increasing the TEMs. The power losses owing to mismatching are more in this configuration as more number of TEMs is connected in series. Figure 4 shows the topology of (10 × 10) array SP configuration. The TEM array in this configuration consists of ten rows and ten strings of TEMs, and each string has ten seriesconnected TEMs. Consequently, the voltage across the output is the sum of each TEM voltage in a string, whereas the output current is equal to the sum of all strings currents.
The output voltage V TEM and output current I TEM of this topology can be signified as: The output power P TEM of array configuration of TEM can be represented as The open-circuit voltage V oc across each TEM can be expressed as

All-tied configuration
The topology of (10 × 10) array AT configuration is shown in Figure 5. In this topology, initially, multiple TEMs are associated in parallel, and then those parallel TEMs are connected in series. This topology has excess power losses because of more number of wiring connections, complex, and high cost due to electrical wiring. In this configuration, the voltage across the output is the addition of each module voltage in a row. The current through the load is computed by adding the currents in all TEMs of a row. The output voltage V TEM and output current I TEM of this topology can be signified as Figure 6 shows the topology of (10 × 10) array BJ configuration. This configuration makes use of bridge architecture. In  All-tied configuration of TEMs this bridge structure, two TEMs are in series, and then the series modules are connected in parallel. The series connection of BJ configuration is more than the AT configuration and less than SP configuration. This topology overcomes the drawback of SP configuration and has fewer power losses due to mismatching. By adding the voltage of the series modules and the currents in the parallel modules, a required amount of output voltage and output current are obtained. The output voltage V TEM and out-put current I TEM of this topology can be signified as:

Bee-hive configuration
The topology of (10 × 10) array BH configuration is shown in Figure 7. In this topology, every six TEMs are group together in a hexagonal shape like a honey bee architecture. The series connection of BH configuration is more than the BJ and AT configuration and less than SP configuration. Therefore, the power losses owing to mismatching are more than AT and BJ config-urations. The voltage of the series modules and the current in the parallel modules are added, to acquire the required output voltage and output current. The output voltage V TEM and output current I TEM of this topology can be signified as:

ANALYSIS OF NUTD CONDITIONS
The different cases of NUTD conditions are shown in Figures 8(a-d) and Figure 9(a,b).      Figure 9(a) shows the case 5. Case 6: The three ΔT values are distributed randomly in the TEM array. Figure 9(b) shows the case 6. Figure 10(a,b) shows the P-I and V-I characteristics of TEM array configurations at UTD conditions. The performance of TEM array configurations is analysed by operating all TEMs with the same ΔT of 200 • C. Table 2 shows the maximum power of the TEM array P TEM(max) in all configurations at the UTD conditions. From Table 2, one can examine that the same maximum power of 2360.92 W is acquired from all configurations. Moreover, the voltage V TEM(max) and current I TEM(max) corresponding to maximum power are given in Table 2.

RESULTS AND DISCUSSION
Moreover, the performance of TEM array configurations has examined under the NUTD conditions by simulating the six different cases of it. Table 3 shows the comparison of the simu-   the AT configuration gives the least maximum output power (1157.35 W). Figures 11(a-d) and 12(a,b) show a comparison of P-I characteristics for the cases (1)-(4) and cases (5) and (6), respectively under NUTD conditions. Table 4 shows a sum of maximum power from individual TEMs in various cases of NUTD conditions. For each case, the maximum power P TEM(max),i is the same for all TEM array configurations.  The maximum power and its corresponding voltage and current for various cases under NUTD and UTD conditions are compared. Consequently, the maximum power from SP, AT, BJ, and BH configuration is the same for UTD conditions and Case 1. For all other cases, the BJ configuration has provided the highest maximum output power. Moreover, the results obtained from the UTD and various cases of NUTD conditions are compared in terms of utilization factor, losses, relative error, standard deviation, and root mean square error. The above parameters can be computed by using the expressions that are given below: The utilization factor is investigated and compared among all configurations under both conditions. The obtained results are shown in Table 5.
From Table 5, it is seen that the array utilization is the same for all configurations under case 1 and UTD conditions. The BJ configuration provides a higher array utilization in all other cases of NUTD conditions. Moreover, it is observed that the array utilization is less in cases 1 and 6, whereas it is almost above 90% in all other cases. However, the array utilization is higher in case 4 among the different cases of NUTD conditions. The comparison of the utilization factor under UTD and various cases of NUTD conditions is shown in Figure 13.
Root mean square error = √ ( The mismatch power losses of all configurations are compared, and the values are given in Table 6. From Table 6, it is noticed that the losses in an array are more in cases 1 and 6. The losses taking place in the BJ array configuration is less than that of other configurations. As a result, the efficiency is higher. Moreover, the losses are less in all configurations of case 4, among the other cases. Figure 14 shows the comparison of mismatch power losses among the various configurations under UTD and various cases of NUTD conditions.
The error analysis, such as relative error, standard deviation, and root mean square error, are investigated for all configurations under both conditions. The results are computed and reported in Tables 7-9. From Tables 7-9, it is observed that the relative error, standard deviation, and root mean square error are highest in AT configuration. Moreover, it is found that all the above errors are lowest in BJ configuration when compared with all other configurations. Hence, we recommend that the BJ configuration is suitable to generate higher power in the field of thermoelectric energy harvesting systems. The comparison of relative error, standard deviation, and root mean square error are shown in Figures 15-17, respectively.

CONCLUSION
This research work analysed the performance of electrical connections of (10 × 10) TEM sensor array configurations such as SP, AT, BJ, and BH configurations that influences the maximum output power under UTD and different cases of NUTD conditions. The P-I performance characteristic of all the above configurations is investigated under both conditions. The performance of the TEM array configurations is examined in terms of maximum output power, voltage and current related to max-

FIGURE 15
The relative error for four different configurations

FIGURE 16
The standard deviation for four different configurations imum power, utilization factor, mismatch power losses, relative error, standard deviation, and root mean square error. From the simulation results, it is seen that the maximum power is the same in all configurations under UTD and the first case of NUTD conditions. However, under NUTD conditions, it is different for all configurations and depends mainly on various cases of NUTD conditions. It is observed that the bridgejoint TEM configuration has provided the highest maximum output power when compared to other configurations for the cases (2-6) under NUTD conditions is due to the minimal mismatch power loss. The minimal mismatch power loss is due to the advantage of fewer series connections than that of series-parallel and Bee-hive configuration. Also, it has a higher open-circuit voltage than that of the All-tied configuration. Therefore, it is recommended to prefer a bridge-joint configuration for the applications of thermoelectric energy harvesting systems.