Applying a Multiple-Input Single-Output Interleaved High Step-Up Converter with a Current-Sharing Device Having Different Input Currents to Harvest Energy from Multiple Heat Sources

Abstract

In this paper, a thermoelectric conversion system for multiple heat sources is proposed. For design convenience, the overall system employs only a single-stage converter. Such a converter uses coupling inductors and switched capacitors to increase the voltage gain. In order to reduce the high-frequency voltage oscillation of the turn-off of the main switches created from leakage inductors, two active clamp circuits with zero voltage switching (ZVS) turn-on are employed. By doing so, although the current-sharing device with interleave control is embedded in the proposed converter, the input currents can be unequal. Therefore, the inputs of the converter can operate under individual maximum power points and transfer the energy from different thermoelectric generators (TGs) to a single load. Furthermore, the main switches have low voltage stress during the turn-off period. As for the maximum power point tracking (MPPT) method, it utilizes a three-point-weighting method to improve the tracking stability. In addition, the number of inputs of this converter can be extended. The MPPT simulation is presented to verify the feasibility as well as several experimental waveforms to demonstrate the effectiveness. The field programmable gate array (FPGA) is used as a digital control kernel to control the thermoelectric conversion system.

1. Introduction

Green energy includes solar, wind, thermal, hydro, tidal, biomass, thermal, etc. Although green energy is a clean and inexhaustible source, there are still many problems to overcome, such as the low voltage generated by green energy, the susceptibility to unstable voltages or currents due to external environmental influences, and the tendency for voltages or currents to fluctuate with load changes. To solve these problems, a step-up converter is usually connected to the back end of the thermoelectric generator (TG), with maximum power point tracking (MPPT) to extract energy steadily for the back-end equipment, or to a step-up or step-down inverter to convert DC power to AC power in parallel with the mains or for other loads [1,2], as shown in Figure 1.

Concerning multi-input single-output (MISO) converters, the topology proposed by [3] is a switched capacitor (SC) converter, which uses the superposition of capacitor voltages to improve the boost ratio. The circuit presented by [3] is a modification of the circuit [4] with a two-stage interleaved structure, which allows for a higher boost ratio for high currents but increases the number of elements. The structures proposed by [5,6] are simple and are derived from the conventional interleaved boost converter such that they use fewer elements to improve the boost ratio. Consequently, the corresponding boost ratios are limited. The dual-input isolated high-boost structure proposed in [7] incorporates an active clamp circuit to reduce the voltage stress on the switches. The circuit presented by [8] is a dual-input converter derived from the interleaved structure of [9], and therefore is not suitable for systems with multiple MPPTs because this circuit has automatic balance of the input currents. The structure proposed by [10] is a dual-input converter derived from the quasi-Y-source structure. The circuit proposed by [11] is a modification of the conventional buck–boost converter into two inputs. The topology presented by [12] adopts a transformer to enable a full-bridge converter to possess multiple inputs. By doing so, it is not possible to extend more inputs due to the size limitation of the transformer.

In [13], one of the inputs of the multi-input converter is connected to batteries, which have bidirectional operation of charging and discharging circuits. Because of the need to consider the circuit path of the battery, the battery charging and discharging circuitry is more complex than normal. The circuit shown in [14] is composed of two interleaved boost circuits and employs two switches instead of two diodes to reduce conduction losses. In [15], a transformer and an interleaved boost circuit with switched capacitors are utilized to improve the boost ratio. In addition, an active clamping circuit is added to obtain ZVS turn-on of the switch.

The topology presented by [16] adopts an interleaved structure with switched inductors to form a three-port circuit and active clamping circuits to ensure all the switches have ZVS turn-on. In [17], a dual-input boost converter modified from the conventional boost converter possesses a simple structure and a wide input voltage range. However, the second input voltage needs to be of opposite polarity to the output voltage. Consequently, this structure cannot be extended with more inputs. In [18], a converter with a three-port circuit and bidirectional operation is proposed. In [19], a modification of the conventional buck–boost circuit is presented, whose duty cycle can be regulated so that the converter can operate in buck, boost, and buck–boost modes. In [20], a thermal energy harvesting converter with two inputs and an isolated output is proposed. In addition, the number of inputs can be extended.

As shown in Figure 2a, the MISO circuit modified from Figure 2b is applied to two heat sources [21]. Staggering the timing for the two maximum power traces solves the problem of two heat sources not being able to carry out individual MPPTs. This is because the capacitor C₂ has a role of automatic current sharing as well as energy transferring [9], as shown in Figure 2b. Speaking lucidly, the gate driving signals for the switches S₁ and S₂ are controlled by interleave, as shown in Figure 2a,b, but the gate driving signals for the switches S₃ and S₄ are controlled by time division, as shown in Figure 2a. By doing so, the capacitor C₂ in Figure 2a has only the role of transferring energy.

As shown in Figure 2c, adding two active clamp circuits forces the two heat sources to realize the respective MPPTs although the proposed circuit is modified from Figure 2b. In more detail, the gate driving signals for the switches S_1a and S_2a are controlled by interleave, but the gate driving signals for the switches S_1b and S_2b are complementary to those for the switches S_1a and S_2a, respectively. By doing this, the capacitor C₂ has only the role of transferring energy. Moreover, the switches S_1b and S_2b have ZVS turn-on and the number of inputs can be extended. To sum up, the proposed converter has ZVS during the turn-on period and low voltages on the switches during the turn-off period, and the thermoelectric modules have individual MPPTs without staggering time.

2. Thermoelectric Module

2.1. P-I-V Curve

As shown in Figure 3, the thermoelectric generator (TG) can be considered as a Thevenin equivalent circuit for analysis convenience. V_oc is the open-circuit voltage at both ends of the TG; R_teg is the equivalent internal resistance; R_L is the load on the TG; V_teg is the output voltage of the TG; I_teg is the output current of the TG; I_sc is the short-circuit current of the TG. Accordingly, maximum power point tracking is required to obtain the maximum power transfer.

As R_L is equal to R_teg, V_teg and I_teg can be shown as follows:

$$V_{teg}=\frac{V_{oc}}{2}$$

(1)

$$I_{teg}=\frac{V_{oc}}{2R_{teg}}=\frac{I_{sc}}{2}$$

(2)

From (1) and (2), the value at the maximum power point can be obtained:

$$P_{mpp}=\frac{V_{oc}}{2}\times \frac{I_{sc}}{2}=\frac{1}{4}{V}_{oc}\times I_{sc}$$

(3)

Therefore, the PVI curve of the TG can be plotted by using the results of (1)–(3), as shown in Figure 4.

2.2. Measured Electrical Parameters of the used TG

Table 1. Measured electrical parameters of the Marlow TG.

Electrical Parameter	Value
Maximum power point voltage (TC = 80 °C/TH = 250 °C)	4.05 V
Maximum power point current (TC = 80 °C/TH = 250 °C)	1.15 A
Maximum power (TC = 80 °C/TH = 250 °C)	3.1 W

is used to describe the electrical parameters of the Marlow TG measured.

3. Proposed MISO Converter

3.1. Converter Description

The circuit of the dual-input step-up converter proposed in Figure 5 consists of two input coupling inductors, four active switches S_1a, S_1b, S_2a and S_2b, two clamping capacitors C₄ and C₅, three energy-transferring capacitors C₁, C₂, and C₃, four diodes D₁, D₂, D₃, and D₄, one output capacitor C_o, and the load represented by the output resistor R_o.

Before proceeding with the analysis of the circuit operation, a brief explanation of the relevant symbols and the assumptions required is given.

(1)

V_d1 and V_d2 are the two input voltages; i_d1 and i_d2 are the two input currents; I_o is the output current; V_o is the output voltage.

(2)

n = N_s1/N_p1 = N_s2/N_p2, where N_p1 and N_s1 are the primary and secondary windings of the first coupling inductor, respectively and N_p2 and N_s2 are the primary and secondary windings of the second coupling inductor, respectively. The currents i_Np1 and i_Ns1 are the currents flowing through the primary and secondary windings of the first coupling inductor, respectively, whereas the currents i_Np2 and i_Ns2 are the currents flowing through the primary and secondary windings of the second coupling inductor, respectively. The leakage inductances L_lkp1, L_lks1, L_lkp2, and L_lks2 are the primary and secondary leakage inductances of the first and second coupling inductors, respectively.

(3)

L_m1 is the magnetizing inductance of the first coupling inductor, and the voltage on and current in it are v_Lm1 and i_Lm1, respectively; L_m2 is the magnetizing inductance of the second coupling inductor, and the voltage on and current in it are v_Lm2 and i_Lm2, respectively.

(4)

The voltages v_gs1a, v_gs1b, v_gs2a and v_gs2b are the gate driving signals for the switches S_1a, S_1b, S_2a, and S_2b, respectively; the voltages v_D1, v_D2, v_D3, and v_D4 and the currents i_D1, i_D2, i_D3, and i_D4 are the voltages on and currents in the diodes D₁, D₂, D₃, and D₄, respectively.

(5)

The voltages V_C1, V_C2, V_C3, V_C4, and V_C5 and the currents i_C1, i_C2, i_C3, i_C4, and i_C5 are the voltages and currents in energy-transferring capacitors C₁, C_2, and C₃ and clamping capacitors C₄ and C₅, respectively.

(6)

T_s is the switching period of switches S_1a and S_2a, and the corresponding duty cycles are D_a and D_b, respectively.

(7)

k₁ and k₂ are the coupling coefficients of the first and second coupling inductors, respectively, equal to k₁ = L_m1/(L_m1 + L_lkp1) and k₂ = L_m2/(L_m2 + L_lkp2).

(8)

L₁₁ and L₁₂ are the primary-side and secondary-side self-inductances of the first coupling inductor, respectively; L₂₁ and L₂₂ are the primary-side and secondary-side self-inductances of the second coupling inductor, respectively.

(9)

The switches, diodes, inductors, and capacitors are considered ideal components.

(10)

The circuit is operated in the continuous current mode (CCM).

(11)

All the circuit operating principles are analyzed in the steady state.

(12)

The voltage conversion ratio is derived by assuming that the voltage drops caused by the leakage inductance are ignored.

Based on the above assumptions, Figure 6 shows the illustrated waveforms associated with the proposed circuit operation.

3.2. Basic Operating Principles

3.2.1. State 1 [$t_0\le t\le t_1$]

As shown in Figure 7, the switches S_1a and S_2a are on, the switches S_1b and S_2b are off, and the diodes D₁, D₂, D_3, and D₄ are off. The input voltages V_d1 and V_d2 excite the magnetizing inductances L_m1 and L_m2 and the leakage inductances L_lkp1 and L_lkp2, whose voltages on them are $k_1{V}_{d1}$, $k_2{V}_{d2}$, $\left(1-k_1\right)V_{d1}$, and $\left(1-k_2\right)V_{d2}$, respectively. The reverse-biased voltage of diode D₁ is $V_{C2}+n\left(k_1{V}_{d1}-k_2{V}_{d2}\right)$; the reverse-biased voltage of diode D₂ is $V_{C1}-V_{C2}-n\left(k_1{V}_{d1}-k_2{V}_{d2}\right)$; the reverse-biased voltage of diode D₃ is $V_{C2}+V_{C3}-V_{C1}+n(k_1{V}_{d1}-k_2{V}_{d2})$; the reverse-biased voltage of diode D₄ is $V_o-V_{C2}-V_{C3}+n{k}_2{V}_{d2}$. In addition, since all the four diodes are cut off, only the output capacitor C_o releases energy to the load in this state. Once the switch S_2a is turned off, state 1 comes to an end.

3.2.2. State 2 [$t_1\le t\le t_2$]

As shown in Figure 8, the switch S_1a is on, the switches S_1b, S_2a, and S_2b are off, the diodes D₂ and D₄ are on, and the diodes D₁ and D₃ are off. During this state, the input voltage V_d1 continues to excite the magnetizing inductance L_m1 and the leakage inductance L_lkp1, whose voltages on them are $k_1{V}_{d1}$ and $(1-k_1)V_{d1}$, respectively. At the same time, the magnetizing inductance L_m2 and the leakage inductance L_lkp2 are demagnetized and the voltages on them are $k_2(V_{d2}-V_{C5})$ and $(1-k_2)(V_{d2}-V_{C5})$, respectively, forcing diodes D₂ and D₄ to conduct. There are three key paths in this state. Path 1 is that the current i_lkp2 flows through the body diode of S_2b and hence the leakage inductance L_lkp2 releases energy to the clamping capacitor C₅; path 2 is that the energy-transferring capacitor C₂ charges the energy-transferring capacitor C₁ and at the same time the leakage inductance L_lks1 is magnetized in the opposite direction with a voltage of $-n{k}_1{V}_{d1}+V_{C1}+V_{C3}-V_o$; path 3 is that the energy-transferring capacitors C₂ and C₃ are connected in series and release energy to the load and at the same time the leakage inductance L_lks2 is magnetized with a voltage of $V_{C5}-n{k}_2(V_{d1}-V_{C5})+V_{C2}+V_{C3}-V_o$. It is worth mentioning that the two coupling inductors have transformer behavior. In addition, the diode D₁ is connected in parallel with the energy-transferring capacitor C₁, which has a reverse-biased voltage of V_C1, and the diode D₃ is connected in parallel with the energy-transferring capacitor C₃ and has a reverse-biased voltage of V_C3, such that both the diodes D₁ and D₃ are cut off in this state. As the switch S_2b is turned on, state 2 ends.

3.2.3. State 3 [$t_2\le t\le t_3$]

Before the start of state 3, the body diode of S_2b is on, so S_2b has zero voltage switching (ZVS) turn-on as shown in Figure 9. In addition, the energy-transferring capacitor C₅ is charged with a negative slope. The moment the current i_C5 reaches zero, state 3 comes to an end.

3.2.4. State 4 [$t_3\le t\le t_4$]

As shown in Figure 10, the switches S_1a and S_2b are on, the switches S_1b and S_2a are off, the diodes D₂ and D₄ are on, and the diodes D₁ and D₃ are off. All the components except the clamping capacitor C₅ operate in the same state 3. Since the current i_C5 rises in the opposite direction, the clamping capacitor C₅ is discharged. Once the switch S_2b is turned off, state 4 ends.

3.2.5. State 5 [$t_4\le t\le t_5$]

As shown in Figure 11, the switch S_1a is on, the switches S_1b, S_2a, and S_2b are off, the diodes D₂ and D₄ are on, and the diodes D₁ and D₃ are off. During this state, the input voltage V_d1 continues to excite the magnetizing inductance L_m1 and the leakage inductance L_lkp1; the magnetizing inductance L_m2 and the leakage inductance L_lkp2 continue to be demagnetized. As soon as the switch S_2a is turned on, state 5 comes to an end.

3.2.6. State 6 [$t_5\le t\le t_6$]

As shown in Figure 12, the switches S_1a and S_2a are on, the switches S_1b and S_2b are off, the diode D₂ is on, and the diodes D₁, D_3, and D₄ are off. During this state, the input voltages V_d1 and V_d2 excite the magnetizing inductances L_m1 and L_m2, respectively. The leakage inductances L_lks1 and L_lks2 charge the energy-transferring capacitor C₁ to achieve leakage inductance energy recovery.

3.2.7. State 7 [$t_6\le t\le t_7$]

The operation principle of this state is the same as that of state 1.

3.2.8. State 8 [$t_7\le t\le t_8$]

As shown in Figure 13, the switches S_1a, S_1b and S_2b are off, and the diodes D₂ and D₄ are off, and the diodes D₁ and D₃ are on. During this state, the input voltage V_d2 continues to excite the magnetizing inductance L_m2 and the leakage inductance L_lkp2, whose voltages on them are $k_2{V}_{d2}$ and $(1-k_2)V_{d2}$, respectively. At the same time, the magnetizing inductance L_m1 and the leakage inductance L_lkp1 are demagnetized and the voltages on them are $k_1(V_{d1}-V_{C4})$ and $(1-k_1\left)\right(V_{d1}-V_{C4})$, respectively, forcing diodes D₁ and D₃ to conduct. There are three key paths: path 1 is that the current i_lkp1 flows through the body diode of S_1b and hence the leakage inductance L_lkp1 releases energy to the clamping capacitor C₄; path 2 is that the energy-transferring capacitor C₁ charges the energy-transferring capacitor C₃; path 3 is that the output capacitor C_o releases energy to the load. It is worth mentioning that the two coupling inductors have transformer behavior. In addition, the diode D₂ is connected in parallel with the energy-transferring capacitor C₁ and has a reverse-biased voltage of V_C1, and the diode D₄ has a reverse-biased voltage of $V_o-V_C{}_2-V_C{}_3+n{V}_d{}_2$, so that both the diodes D₂ and D₄ are cut off in this state. As the switch S_1b is turned on, state 8 ends.

3.2.9. State 9 [$t_8\le t\le t_9$]

As shown in Figure 14, before the start of state 9, the body diode of S_1b is on, so S_1b has zero voltage switching (ZVS) turn-on.

3.2.10. State 10 [$t_9\le t\le t_{10}$]

As shown in Figure 15, the switches S_2a and S_1b are on, switches S_1a and S_2b are off, diodes D₁ and D₃ are on, and diodes D₂ and D₄ are off. All the components except the clamping capacitor C₄ operate in the same state 9. Since the current i_C4 rises in the opposite direction, the clamping capacitor C₄ is discharged. Once the switch S_1b is turned off, state 10 ends.

3.2.11. State 11 [$t_{10}\le t\le t_{11}$]

As shown in Figure 16, the switch S_2a is on, the switches S_1a, S_1b, and S_2b are off, the diodes D₁ and D₃ are on, and the diodes D₂ and D₄ are off. At the same time, the input voltage V_d2 continues to excite the magnetizing inductance L_m2 and the leakage inductance L_lkp2; the magnetizing inductance L_m1 and the leakage inductance L_lkp1 continue to be demagnetized. As soon as S_1a is turned on, state 11 comes to an end.

3.2.12. State 12 [$t_{11}\le t\le t_{12}$]

As shown in Figure 17, the switches S_1a and S_2a are on, the switches S_1b and S_2b are off, the diode D₁ is on, and the diodes D₂, D_3, and D₄ are off. At the same time, the input voltages V_d1 and V_d2 excite the magnetizing inductances L_m1 and L_m2, respectively. The leakage inductances L_lks1 and L_lks2 charge the energy-transferring capacitor C₂ to achieve leakage inductance energy recovery.

3.3. Voltage Conversion Ratio

To facilitate the derivation of the voltage conversion ratio and voltages across the energy-transferring capacitors C₁, C_2, and C₃, only states 1, 4, and 8 are considered. In addition, the blanking times of the switches, the primary-side leakage inductances L_lkp1 and L_lkp2, and the secondary-side leakage inductance L_lks1 and L_lks2 are ignored.

$$n=\frac{N_{s1}}{N_{p1}}=\frac{N_{s2}}{N_{p2}}$$

(4)

From state 1 shown in Figure 7, the expressions for the voltages on L_m1 and L_m2 are as follows:

$$v_{Lm1}=V_{d1}$$

(5)

$$v_{Lm2}=V_{d2}$$

(6)

From state 4 shown in Figure 10, the expression for the voltage on L_m1 is the same as that state 1 but the voltage on L_m2 is as follows:

$$v_{Lm2}=V_{d2}-V_{C5}$$

(7)

Additionally, the expressions for the voltages V_C1, V_C5, and V_o can be expressed as

$$V_{C1}=V_{C5}-n(V_{d2}-V_{C5})+V_{C2}+n{V}_{d1}$$

(8)

$$V_o=V_{C5}-n(V_{d2}-V_{C5})+V_{C2}+V_{C3}$$

(9)

$$V_{C5}=\frac{V_{d2}}{1-D_b}$$

(10)

On the other hand, from state 9 shown in Figure 14, the expression for the voltage on L_m2 is the same as that for state 1 but the voltage on L_m1 is as below:

$$v_{Lm1}=V_{d1}-V_{C4}$$

(11)

At the same time, the voltages on C₂, C_1, and C₄ are given by

$$V_{C2}=V_{C4}-n(V_{d1}-V_{C4})+n{V}_{d2}$$

(12)

$$V_{C1}=V_{C3}$$

(13)

$$V_{C4}=\frac{V_{d1}}{1-D_a}$$

(14)

By substituting (14) into (12), the expression for V_C2 is given by

$$V_{C2}=\frac{(n+1)V_{d1}}{1-D_a}+n(V_{d2}-V_{d1})$$

(15)

By substituting (10) and (12) into (8), the expression for V_C1 can be obtained as

$$V_{C1}=\frac{(n+1)}{1-D_a}{V}_{d1}+\frac{(n+1)}{1-D_b}{V}_{d2}$$

(16)

By substituting Equations (10), (12)–(14), and (16) into Equation (9), the output voltage V_o is given by

$$V_o=\frac{2+n(1+D_a)}{1-D_a}{V}_{d1}+\frac{2(1+n)}{1-D_b}{V}_{d2}$$

(17)

3.4. Unequal Currents between the Two Inputs

This subsection will show that the proposed structure has an automatic current sharing element embedded but does not have an automatic current sharing feature. To simplify the analysis, it is assumed that there is no loss in power conversion in this circuit, i.e., the input power is equal to the output power. According to (17), the power of the two inputs can be split and their DC output currents can be assumed to be the same, equal to I_o.

As shown in Figure 5, the input currents I_d1 and I_d2 can be expressed as

$$I_{d1}=I_{Lm1}-I_{Np1}$$

(18)

$$I_{d2}=I_{Lm2}-I_{Np2}$$

(19)

Next, the DC component of the coupling inductor is analyzed. According to the ampere-second balance, the average current in the capacitor is zero, so the following equations can be obtained as follows:

$$I_{Np1}=\frac{N_{s1}}{N_{p1}}\times I_{Ns1}=\frac{N_{s1}}{N_{p1}}\times I_o=n{I}_o$$

(20)

$$I_{Ns2}=I_{Np2}=0$$

(21)

By substituting (18) into (20), the expression for the current I_d1 can be obtained as

$$I_{d1}=I_{Lm1}-n{I}_o$$

(22)

Additionally, substituting (19) into (21) yields the expression for current I_d2 as

$$I_{d2}=I_{Lm2}$$

(23)

Because there is no loss of power conversion in the circuit, the following equation can be obtained as

$$V_o{I}_o=V_{d1}{I}_{d1}+V_{d2}{I}_{d2}$$

(24)

and also, multiplying (17) by I_o yields

$$V_o{I}_o=\frac{2+n(1+D_a)}{1-D_a}{V}_{d1}{I}_o+\frac{2(1+n)}{1-D_b}{V}_{d2}{I}_o$$

(25)

By comparing (24) and (25) to find the relationship between the input currents I_d1 and I_d2 and the output current I_o, the following Equations (22) and (23) can be obtained as

$$I_{d1}=\frac{2+n(1+D_a)}{1-D_a}{I}_o=I_{Lm1}-n{I}_o$$

(26)

$$I_{d2}=\frac{2(1+n)}{1-D_b}{I}_o=I_{Lm2}$$

(27)

From (26), I_Lm1 can be obtained as

$$I_{Lm1}=\frac{2(1+n)}{1-D_a}{I}_o$$

(28)

By substituting (23) and (26) into (18) and (19), the DC components of the input currents can be found as

$$I_{d1}=\frac{2(1+n)}{1-D_a}{I}_o-n{I}_o$$

(29)

$$I_{d2}=\frac{2(1+n)}{1-D_b}{I}_o$$

(30)

The two input currents will not be identical even if D_a is equal to D_b, according to (29) and (30).

3.5. Extension of Number of Phases

The number of phases can be extended by 2N, where N is a positive integer. Figure 18 shows the four-phase interleaved converter.

4. Hardware Circuit Design

4.1. Thermoelectric Module Specifications

The thermoelectric generator (TG), namedTG12-8, is manufactured by Marlow Industries, Inc. Since this converter has two inputs, the first input is composed of four pieces of TGs connected in series, and the second input is composed of two pieces of TGs connected in series.

Table 2. Specifications of the first thermoelectric module.

First thermoelectric Module Specification	Name or Value
TG product name	TG12-8
TG size	$40\times 40\times 3.2$ mm
Number of TGs	4 in series
Max. Power @ MPP (Pmpp1)	18.52 W
Voltage @ MPP (Vmpp1)	16.22 V
Current @ MPP (Impp1)	1.145 A
Open-circuit voltage (Voc1)	30.26 V
Short-circuit current (Isc1)	2.43 A
Cold-side temperature	80 °C
Hot-side temperature	250 °C

shows the associated information on the first thermoelectric module and

Table 3. Specifications of the second thermoelectric module.

Second Thermoelectric Module Specification	Name or Value
TG product name	TG12-8
TG size	$40\times 40\times 3.2$ mm
Number of TGs	2 in series
Max. Power @ MPP (Pmpp2)	9 W
Voltage @ MPP (Vmpp2)	7.67 V
Current @ MPP (Impp2)	1.177 A
Open-circuit voltage (Voc2)	14.07 V
Short-circuit current (Isc2)	2.46 A
Cold-side temperature	80 °C
Hot-side temperature	250 °C

shows the associated information on the second thermoelectric module. Figure 19 and Figure 20 show the measured curves for the first and second thermoelectric modules, respectively. These measured curves for the two thermoelectric modules are based on the Prodigit 9842-MPPT function under constant voltage mode, sweeping so as to obtain the data relevant to power vs. voltage (PV) and voltage vs. voltage (IV), and then plotting these data by using Microsoft Excel.

As can be seen from Figure 19, the maximum power point of the first TG has 18.52 W at half of the open-circuit voltage and short-circuit current of the first thermoelectric module, with values of V_mpp1 = 16.22 V and I_mpp1 = 1.145 A. As can be seen from Figure 20, the maximum power point of the second thermoelectric module has 9W at half of the open-circuit voltage and short-circuit current of the second thermoelectric module, with values of V_mpp2 = 7.67 V and I_mpp2 = 1.177 A.

4.2. System Configuration and Its Specifications

Figure 21 shows the system configuration of the proposed circuit applied to a thermoelectric conversion system with two thermoelectric modules at individual inputs. The main power stage is a dual-input high-boost circuit with a digital control kernel based on FPGA to control the system. The FPGA calculates and then sends the duty cycles to the gate drivers to achieve the maximum power tracking. For the voltages and currents to be sampled, analog-to-digital converters (ADCs) are used. The sensed signals are sent to MPPT modules after ADCs via FPGA-embedded series peripheral interfaces (SPIs). Furthermore, the voltage-sensing resistors are used as voltage dividers, the current-sensing resistors are used as current sensors, and the FPGA, named CycloneEP1C3T100, is used as a control kernel, which needs a 20 MHz oscillator and has 2910 logic gates, 104 I/O ports, 59,904 RAM bits, and a phase-lock loop. In addition, the design software is based on the very high-speed hardware description language (VHDL) and

Table 4. System specifications.

System Specification	Name or Value
System operation mode	Continuous conduction mode (CCM)
First input voltage (Vd1)	16.22 V
Second input voltage (Vd2)	7.67 V
Rated output voltage (Vo)	400 V
Rated output current (Io,rated)/power (Po,rated)	68.8 mA/27.52 W
Minimum output current (Io,min)/power (Po,min)	17.2 mA/6.88 W
First duty cycle (Da)	0.575
Second duty cycle (Db)	0.572
First duty frequency (fs)/period (Ts)	100 kHz/10 μs

shows the system specifications.

4.3. Voltage Stresses of Switches and Diodes

The voltage across the switches S_1a and S_1b during the turn-off period can be found from states 9 and 1, respectively, as follows:

$$V_{ds1a}=V_{ds1b}=V_{C4}=\frac{V_{d1}}{1-D_a}=\frac{16.22}{1-0.575}=38.17\mathrm{V}$$

(31)

The voltages across the switches S_2a and S_1b during the turn-off period are given by states 3 and 1, respectively, as follows:

$$V_{ds2a}=V_{ds2b}=V_{C5}=\frac{V_{d2}}{1-D_b}=\frac{7.67}{1-0.572}=18\mathrm{V}$$

(32)

In state 2, the voltage across diodes D₁ and D₃ are as follows:

$$V_{D1}=V_{C1}$$

(33)

$$V_{D3}=V_{C3}$$

(34)

Substituting the results of (13) and (16) into (33) and (34) yields

$$V_{C1}=V_{\mathrm{C}3}=\frac{(n+1)}{1-D_a}{V}_{d1}+\frac{(n+1)}{1-D_b}{V}_{d2}=224.34\mathrm{V}$$

(35)

The voltages across the diodes D₂ and D₄ in state 8 are as follows:

$$V_{D2}=V_{C1}=224.34\mathrm{V}$$

(36)

$$V_{D4}=V_o-V_{C2}-V_{C3}+n{V}_{d2}=71.4\mathrm{V}$$

(37)

4.4. Component Specifications

Table 5. Component specifications.

Component	Specification
MOSFET switches S1a, S1b, S2a, S2b	IRF3205Z
Diodes D1, D2, D3	SFF1008G
Diodes D4	STPS20H100CT
Energy-transferring capacitors C1, C3	100 μF Electrolytic Capacitor
Energy-transferring capacitor C2	68 μF Electrolytic Capacitor
Clamping capacitors C4, C5	10 μF Electrolytic Capacitor
Output capacitor Co	22 μF Electrolytic Capacitor
Coupling inductor 1/Coupling inductor 2	Lm1 = 365.6 μH, n = 3/Lm2 = 87.3 μH, n = 3
Isolated gate driver	FOD3182

is used to describe the specifications of the used components.

5. Maximum Power Point Tracking

5.1. MPPT Algorithm

If a thermoelectric module is to provide maximum power output in different temperature ranges and temperature differences, maximum power tracking is required to operate the thermoelectric module at the maximum power point. In addition, the PV characteristic curve of a thermoelectric module is similar to that of a solar cell. However, the difference between them is that the PV characteristic curve of a thermoelectric module is more symmetrical. Consequently, according to this feature, a maximum power tracking method based on three-point-weighting MPPT is relatively suitable for thermoelectric modules in practice.

Figure 22 shows the MPPT flow chart used in this paper. The principle of this control method is to calculate the power value by continuously detecting the output power value at three points and comparing their power magnitudes. First of all, set a duty cycle of D_b at the reference point b, and detect the output voltage and current of the thermoelectric module to calculate the power value P_b; sequentially, increase the duty cycle by one unit of disturbance, i.e., $D_b+\Delta D$, to obtain the second duty cycle of D_c at the point c, and detect and calculate the power value of P_c; then reduce the duty cycle by one unit of disturbance, i.e., $D_b-\Delta D$, to obtain the third duty cycle of D_a at the point a, and detect and calculate the power value of P_a. By doing so, the power sampling procedure is completed. Afterwards, if the power P_a is greater than or equal to the power P_b, the weight value of W₁ will be increased by one, and if not, the weight value of W₁ will be decreased by one; if the power P_b is greater than or equal to the power P_a, the weight value of W₂ will be increased by one, and if not, the weight value of W₂ will be decreased by one. Eventually, calculate the weight value to determine the direction of movement of the reference point. If the sum of W₁ and W₂ is $+2$, then the point c is used as the new reference point with the duty cycle of D_c; if the sum of W₁ and W₂ is $-2$, the point a is used as the new reference point with the duty cycle of D_a; if the sum of W₁ and W₂ is 0, then the reference point b remains unchanged with the duty cycle of D_b. After completing the above actions, the weight value is returned to zero and the above actions are repeated to achieve maximum power point tracking.

5.2. MPPT Simulation

In this subsection, the simulation of the proposed MISO circuit applied to a thermoelectric conversion system is used to verify its feasibility based on the power simulation (PSIM) software. Therefore, the simulation environment is constructed by analog devices as shown in Figure 23. From this figure, it can be seen that both thermoelectric modules can be traced to individual maximum power points without need of staggered switching; the first thermoelectric module outputs 18.56 W shown in a green circle, almost corresponding to18.52 W, shown in Table 2; the second thermoelectric module outputs 9.03 W, shown in the purple circle, almost corresponding to 9 W shown in Table 3; both the two thermoelectric modules output 27.23 W shown in the red circle, almost corresponding to 27.51 W, shown in Table 4; the output voltage can be increased to 399.85 V, shown in a blue circle, almost corresponding to 400 V, shown in Table 4.

6. Experimental Results

In this subsection, the experimental results are used to demonstrate the effectiveness of the proposed MISO circuit. The digital control kernel based on the FPGA is adopted herein. From Figure 24, it can be seen that the gate driving signals v_gs1a and v_gs2a are interleaved and v_gs1b and v_gs2b are complementary to v_gs1a and v_gs2a, respectively. From Figure 25 and Figure 26, it can be seen that when the switches S_1a, S_1b, S_2a, and S_2b are turned off, the leakage inductance of the coupling inductor, the parasitic inductance on the line, and the parasitic capacitance of the switch resonate together, so the voltage spike and ring on v_ds1a, v_ds1b, v_ds2a, and v_ds2b will be generated. As shown in Figure 27, the resonance of the leakage inductance with the diode capacitance from state 6 to state 7 and from state 12 to state 1 causes the current spike and oscillation in the input currents i_d1 and i_d2 due to the reverse recover current of the diode D₁. As can be seen from Figure 28, the energy-transferring capacitors C₁, C₂, and C₃ can be stabilized at a certain value for any load. Figure 29 and Figure 30 show that the switches S_1b and S_2b have ZVS turn-on but are turned on with the resonance between the diode capacitance and the leakage inductance, thereby yielding the voltage spike and oscillation on v_ds1b and v_ds2b. From Figure 31, it can be seen that the diodes D₁ and D₃ have the same operating behavior and the oscillation is caused by the magnetizing inductance resonating with the diode capacitance. From Figure 32, it can be seen that the output voltage V_o of the proposed circuit can reach 400 V. From Figure 33, it can be seen that the efficiency can be up to 89.27% at 100% load. Figure 34 shows a photo of the experimental setup.

7. Conclusions

In this paper, the interleaved MISO circuit was applied to a thermoelectric system, where the ultrahigh voltage gain was obtained by using coupling inductors and switched capacitors. The two thermoelectric modules have individual MPPTs even although the passive current-sharing device is embedded in this circuit, and this was verified by Section 3.4. Furthermore, the active voltage clamp circuits ensure that the high-frequency oscillation is reduced, the switches are turned on with ZVS, and that the voltage stresses on the switches are low. Therefore, the rated-load efficiency is 89.27%. In addition, the number of inputs can be extended.