Abstract
For gridconnected power system based on photovoltaic (PV) source and fuel cells, high stepup and highefficiency DC–DC converters are needed, due to the bus voltage of the gridconnected inverter is much higher than the output voltage of PV and fuel cells. In this paper, a novel high stepup converter is proposed. An auxiliary capacitor is introduced into the boost converter, which serves as a voltage source. It is in series with the input voltage source with the same voltage polarities. Thus, the input voltage is increased equivalently and the voltage gain is increased accordingly. To reduce the voltage stresses of the switch and the diode, multiple output capacitors are introduced. The voltage of each output capacitor is degraded leading to the reduced voltage stress. To replenish energy for the multiple output capacitors, a coupled inductor is adopted. Based on this, high stepup converter adopting auxiliary capacitor and coupled inductor is derived. The operating principles and voltage gain of the proposed converters are analyzed in this paper. In the end, experiment results are given to verify the theoretical analysis.
1 Introduction
Since it takes centuries for the traditional fossil energy to be replenished, it will be exhausted with the growing demand for energy of human society. Thus the energy crisis is increasingly serious. Meanwhile, the excessive usage of the traditional fossil energy has polluted the environment and resulted in greenhouse effect on a global scale [1]. Therefore, it is becoming more and more important to optimize the energy consumption structure and to utilize clean and renewable energy. Solar energy and hydrogen energy are two promising renewable energy, and have extensive application prospect. As the utilization methods of the two new energy, photovoltaic (PV) and fuel cells power generations have been applied on a large scale [2,3,4,5,6,7], such as photovoltaic power station and electric vehicle.
In recent years, the gridconnected power generation based on PV source for residential application has become globally popular. Usually, an interface unit is necessary, as the output voltage of PV source is relatively too low for the line voltage. If the line voltage is 220 V, the input voltage needed by the gridconnected inverter would approach 380 V. But the output voltage of PV source generally varies from 25 to 45 V. To boost the output voltage of PV source, one possible solution to is to make seriesconnected PV arrays. But the total output power of PV arrays will be degraded due to module mismatch or partial shading [8]. Another promising solution is to utilize a high stepup DC–DC converter to match the low output voltage of PV source and high input voltage of the inverter. Then every PV source can realize the function of maximum power point tracking. For the isolated DC–DC converters, the voltage gain can be increased by adjusting the turns ratio of the transformer. But the energy stored in the leakage inductor is difficult to be transferred to the output. Thus, for the application without galvanic isolation requirement, nonisolated high stepup DC–DC converters is preferred.
The boost converter is wildly used for voltage stepup. However, its duty cycle would be too large when the input voltage is much smaller than the output. And for the actual power switch and diode, a certain delay between turnon and turnoff state will probably result that the power switch is turned on before being cut off completely and the diode is cut off before conducting. Thus, the reliability is degraded. When the duty cycle approaches unity, a large pulse current will conduct through the diode in a short time, which leads to large the current stress of the diode and severe reverse recovery problem. This will greatly affect the efficiency and brings about a serious electromagnetic interference problem [9,10,11,12]. By cascading another boost converter, a high voltage gain can be easily obtained. But the additional switch makes the control scheme more complex. And it may cause instability issue for cascaded systems.
The impedance source networks are widely used in the inverters [13,14,15,16] to increase the voltage boost inversion ability. Likewise, the impedance source networks can also be used in high stepup DC–DC converters to achieve high voltage gain [17,18,19,20]. The converters can operate with a much smaller duty cycle, which improves the reliability. By combining quasiZsource network and transformer, the voltage stress of the switch is reduced. But most of the converters adopt multiple power switches, and have a relatively complex control scheme. In [21], a single power switch was adopted to simplify the control design. However, the voltage stress of the switch is as high as the output voltage, which brings large switching loss.
Another method of increasing the voltage gain is to introduce a coupled inductor [22,23,24,25,26,27,28]. However, the current through the coupled inductor is discontinuous. It goes against the lifetime of PV and fuel cell when the coupled inductor is placed on the input side. Especially for the low input voltage application, the input current is very large. Thus, the continuous input current is preferred.
To overcome the respective disadvantages of quasiZsource network and coupled inductor, some isolated high stepup DC–DC converters combining quasiZsource network and coupled inductor are proposed in [29, 30]. However, due to the isolation, the energy stored in the leakage inductor of the primary winding is difficult to be transferred to the output. In this paper, a nonisolated high stepup DC–DC converter with single switch based on quasiZsource network and coupled inductor is proposed. The input current is continuous and the voltage stress of the switch is low. Besides, the energy stored in the leakage inductor can be absorbed by the output capacitor, which is beneficial for the efficiency. And single switch is used to simplify the control scheme. The operating principle and parameter calculation are given in this paper, and an experiment is conducted to verify the theoretical analysis. The experiment results indicate that the proposed converters can achieve a higher efficiency.
2 Derivation of high stepup DC–DC converters adopting auxiliary capacitor and coupled inductor
2.1 High stepup converter adopting auxiliary capacitor
Figure 1 gives the basic boost converter, where V _{g} is the input voltage, L _{1} is the boost inductor, Q is the switch. To increase the voltage gain of boost converter, an auxiliary voltage source V _{a} can be introduced to the input terminal and the voltage polarity is the same as V _{g}, as shown in Fig. 2. When Q is turned on, V _{g} is in series with V _{a} to charge L _{1}. When Q is turned off, V _{g} is in series with V _{a} and L _{1} to supply the load. And the output voltage is the sum of V _{g}, V _{a} and the voltage of L _{1}. Obviously, the auxiliary voltage source increases the input voltage equivalently, and a high voltage gain is obtained.
The auxiliary voltage source V _{a} in Fig. 2 can be implemented with a capacitor C _{a1}, which is defined as the auxiliary capacitor. To replenish energy for the auxiliary capacitor C _{a1}, the inductor L _{2}, and the diode D_{1} is introduced as shown in Fig. 3a. Obviously, the larger the voltage of the auxiliary capacitor is, the higher the derived voltage gain will be. To obtain a higher voltage for C _{a1}, an additional auxiliary voltage source V _{a} can be added in the charging path of L _{2}, as shown in Fig. 3b. When Q_{a} is turned on, V _{a} is in series with the input voltage source to charge L _{2}. When Q_{a} is turned off, L _{2} replenishes energy for C _{a1}. If V _{a} is equal to the electric potential difference between nodes a and b, the electric potentials of the drain electrodes are identical and can be connected directly. In doing so, Q_{a} can be removed to simplify the structure. Likewise, the auxiliary voltage source V _{a} can be implemented by a capacitor C _{a2}, as shown in Fig. 4. As seen, L _{1} can be used to replenish energy for C _{a2}. This topology has been proposed and analyzed in [19], which is called Zsource DC–DC converter.
As the voltages of C _{a1} and V _{g} in Fig. 4 are constant, the voltage between nodes c and d is also constant and equals the voltage sum of C _{a1} and V _{g}. Thus, a capacitor can be added between nodes C and D to serve as a new input source of the boost inductor L _{1}. As the new capacitor charges L _{1} instead of the original one, the original auxiliary capacitor can be removed as shown in Fig. 5. This structure consisting of the capacitor and inductor is called quasiZsource network [13]. Its operating modes when the network is applied for DC–DC converter with single switch has not been analyzed in detail in [13].
Compared with the converter shown in Fig. 4, the voltage stress of C _{a1} in Fig. 5 is larger. But the input current of the converter in Fig. 5 is continuous, which is beneficial for improving the lifetime of PV and fuel cell.
As shown in Fig. 5, the voltage stresses of the switch and the diode are both as high as the output voltage which leads to a large conduction resistor of the switch and severe reverse recovery problem of the diode. Thus, the conduction loss and the switching loss are both large.
2.2 High stepup converter adopting auxiliary capacitor and coupled inductor
To reduce the voltage stress of the switch and the diode, referring to [31], multiple output capacitors can be used to supply the load, as shown in Fig. 6a. In doing so, the voltage of C _{o1} is reduced, and the voltage stress of Q, D_{1} and D_{o1} are reduced as well. To replenish energy for C _{o2}, the inductor L _{1} in Fig. 5 is replaced by the coupled inductor L _{cp}, and the secondary winding of the coupled inductor is used to charge C _{o2}. In [31], the inductor of the boost converter is replaced by the coupled inductor, which leads to a discontinuous input current. On the contrary, the input current of the converter in Fig. 6b remains continuous, which is beneficial for the lifetime of PV and fuel cell.
As shown in Fig. 6b, the voltage doubling rectifier circuit is adopted to further increase the voltage of C _{o2} in order to reduce the voltage stresses of Q, D_{1} and D_{o1}. As a result, a switch with a lower conduction resistor can be selected, and the conduction loss and switching loss can be reduced.
3 Analysis of high stepup DC–DC converters adopting auxiliary capacitor and coupled inductor
3.1 Operating principle of CCM
Considering the parasitic parameters of the coupled inductor, the equivalent circuit is given in Fig. 7. When the currents of L _{1} and the magnetizing inductor L _{m} are both continuous, there exist four operating modes and the key waveforms are shown in Fig. 8, where i _{L1} is the current of L _{1}, i _{Tr_s} is the current of the secondary winding of the coupled inductor, i _{Lm} and i _{Llk} are the currents of the magnetizing inductor and the leakage inductor of the coupled inductor respectively, i _{D1} and i _{Do1} are the currents of D_{1} and D_{o1}. The operating modes are shown in Fig. 9.
Mode 1 [t _{1} ~ t _{2}]: When Q is turned on, V _{g} is in series with C _{a2} to charge L _{1}, and C _{a1} charges the magnetizing inductor L _{m}. In this mode, the secondary winding of the coupled inductor charges C _{o3} through D_{o3}.
Mode 2 [t _{2} ~ t _{3}]: When Q is turned off, L _{1} and L _{m} charge C _{a1} and C _{a2} through D_{1} respectively, and the input voltage source is in series with L _{1} and L _{m} to charge C _{o1}. In this mode, i _{Lm} is smaller than i _{Llk}, where i _{Lm} and i _{Llk} are the currents of the leakage inductor and the magnetizing inductor, respectively. Thus, the current direction of the secondary winding remains and the secondary winding still charges C _{o3} through D_{o3}.
Mode 3 [t _{3} ~ T _{s}]: In this mode, i _{Lm} is larger than i _{Llk}, leading to the current direction of the secondary winding changed. And the secondary winding charges C _{o2} in series with C _{o3} through D_{o2}.
Mode 4 [T _{s} ~ t _{4}]: In this mode, since i _{Lm} is larger than i _{Llk}, the secondary winding still charges C _{o2} in series with C _{o3} through D_{o2}.
3.2 Operating principle of DCM
When the current of L _{1} is discontinuous, the key waveforms and operating modes in DCM are shown as Figs. 10 and 11, respectively. There are five operating modes for DCM, in which Mode 1, Mode 2, and Mode 3 are the same with those in CCM. Here, only Mode 4 and Mode 5 are given in detail.
Mode 4 [t _{4} ~ t _{5}]: When i _{L1} = i _{Do1} − i _{Llk}, the current through D_{1} decreases to zero and is cut off.
Mode 5 [t _{5} ~ T _{s}]: The currents through L _{1} and L _{cp} are zero, and C _{o1} and C _{o2} are in series to supply the load.
3.3 Voltage gain of CCM
As the leakage inductor is much smaller compared with the magnetizing inductor, the duration of Modes 2 and 4 in Fig. 8 are relatively short. Thus, the leakage inductor is neglected here, to simplify the analysis.
For steady state, according to the voltsecond relationship of L _{1}, we have:
where V _{g} is the input voltage; D is the duty cycle of the switch; T _{s} is the switching period; V _{a1} and V _{a2} are the average voltages of C _{a1} and C _{a2}, respectively.
Similarly, the voltsecond relationship can be applied to L _{m}, then we have:
According to (1) and (2), V _{Ca1}, V _{Ca2} can be derived as:
Referring to Fig. 9c, the voltage of C _{o1} equals the voltage sum of C _{a1} and C _{a2}.
The voltage of C _{o3} can be expressed as:
where N _{sp} = N _{s}/N _{p}; N _{s} is the secondary winding turns; N _{p} is the primary winding turns.
The voltage of C _{o2} is:
Combing (5) and (7), the output voltage is:
Referring to Fig. 9a and c, the voltage stresses of Q, D_{1} and D_{o1} equal V _{Co1}, which are much smaller than the output voltage. And it is beneficial for improving the efficiency of the converter.
3.4 Voltage gain of DCM
To simplify the analysis, an assumption is made that the leakage inductor is neglected. Thus, Mode 2 and Mode 4 are neglected as well. Then only Mode 1, Mode 3 and Mode 5 need to be considered.
For steady state, applying the voltsecond balance principle to L _{1} and L _{m}, we have:
where D _{r} T _{s} = t _{4} − t _{1}.
Referring to Fig. 11, we have:
Combining (9), (10) and (11), we can derive:
Thus, the average current of L _{1} can be derived:
If the power loss is neglected, the input average current is:
Combining (14), (18) and (19), we can derive:
3.5 Comparison of high stepup converters
Table 1 gives the comparison of the proposed converter with stateofart high stepup converters adopting coupled inductor [31,32,33,34,35]. Fig. 12 gives the curves of the voltage gains in Table 1, where N _{sp} is selected as 4. As seen, the proposed configuration in Fig. 6b has larger voltage gain than the other high stepup converters with the same duty cycle and reaches a considerable value although the duty cycle has not been close to 0.5. As shown in Fig. 6b, since the coupled inductor replaces L _{1} in Fig. 5 rather than L _{2} on the input side, the input current is continuous, which is beneficial for the lifetime of PV and fuel cell. As a consequence, the voltage stress of Q in the proposed converter is a little larger.
4 Experiment verification
To verify the effectiveness of the proposed configurations in Figs. 5 and 6b, two prototypes are fabricated in the lab for contrast with the following specifications:

1)
Input voltage V _{g}: 25–45 V _{dc};

2)
Output voltage V _{o}: 380 V _{dc};

3)
Switching frequency f _{s}: 100 kHz;

4)
Maximal output power P _{o}: 300 W.
4.1 Parameter design
As the design progress of the converters in Figs. 5 and 6b are similar, the topology as shown in Fig. 6b is taken as an example to design the parameter.
Prior to the design procedure of capacitors and inductors, an assumption is made to simplify the analysis. Since the leakage inductor is relatively small compared with the magnetizing inductor, its influence can be ignored.

1)
Design of coupled inductor L _{cp}
As shown in Table 1, the voltage stress of the switch decreases with the increase of N _{sp.} However, higher N _{sp} would increase the current stress of the switch. Thus, a tradeoff design should be considered between the voltage stress and current stress of the switch. Here, we prefer the voltage stress lower than 100 V, and the resultant N _{sp} is 4.
Referring to Fig. 7, according to Kirchhoff’s circuit laws, we have:
Based on the charge balance principle, the average currents of capacitors, I _{Ca1_avg}, I _{Ca2_avg}, and I _{Co3_avg} are zero. Thus, the average current of L _{1} equals the average current of L _{m,} and we have:
Setting the maximum current ripple of L _{m} is 30% of the maximum average current, then we have:
Substituting (22) into (23), yields:
When V _{g} = 25 V, the right part of (24) reaches the maximum value. Then we have L _{m} = 50 μH.

2)
Design of inductor L _{1}
Likewise, the maximum current ripple of L _{1} can be expressed as:
Substituting (22) into (25), yields:
When V _{g} = 25 V, the right part of (26) reaches the maximum value. Then we have L _{m} = 50 μH.

3)
Design of auxiliary capacitor C _{a1} and C _{a2}
The capacitor C _{a1} and C _{a2} can be derived according to the voltage ripple ΔV _{Ca1} and ΔV _{Ca2}:
Referring to Fig. 9a, during the turn on interval, we have:
Since the average currents of C _{o2} and C _{o3} are zero, the average current through D_{o3} equals to I _{o}. Then we have:
Substituting (29), (30) and (31) into (27) and (28), yields:
Setting the voltage ripple is lower than 5% of the maximum average voltage, we have C _{a1} = 24 μF, C _{a2} = 32 μF.

4)
Design of output capacitor C _{o1}, C _{o2} and C _{o3}
Likewise, the output capacitors can be derived as:
Referring to Fig. 9a, during the turn on interval, we have:
Substituting (31), (37) and (38) into (34), (35) and (36), yields:
Since C _{o1}, C _{o2} is placed on the output side, the voltage ripples of C _{o1} and C _{o2} are limited to a smaller scale. If the voltage ripples of C _{o1} and C _{o2} are limited to 1% of the respective maximum average voltage, and the voltage ripple of C _{o3} is limited to 5% of the maximum average voltage, we have C _{o1} = 4 μF, C _{o2} = 3 μF, C _{o3} = 3 μF.

5)
Switch Q
The voltage stress of the switch is V _{o}/(N _{sp} + 1). When Q is turned on, the current of the switch i _{Q} can be expressed as:
When V _{g} = 25 V, the RMS current of Q reaches its maximum value 19.8 A.

6)
Diode D_{1}, D_{o1}, D_{o2} and D_{o3}
The voltage stresses of D_{1} and D_{o1} are V _{o}/(N _{sp} + 1), and the voltage stresses of D_{o2} and D_{o3} are N _{sp} V _{o}/(N _{sp} + 1).
The currents through D_{o2} and D_{o3} can be expressed as:
According to Fig. 9c, we have:
where v _{Ca1}, v _{Ca2} and v _{Co1} are the instantaneous voltages of C _{a1}, C _{a2} and C _{o1}, respectively.
Combining (46) and (47), the currents through D_{1} and D_{o1} can be expressed as:
According to (43), (44), (48) and (49), the current stresses of D_{1}, D_{o1}, D_{o2} and D_{o3} can be calculated.
4.2 Experiment results
The main components used in the prototypes are listed in the following.
High stepup converter adopting auxiliary capacitor:

1)
Q: IPW65R045C7;

2)
D_{1}: IDW20G65C5, D_{o}: C3D10060A;

3)
L _{1}: 263 μH, L _{2}: 263 μH;

4)
C _{a1}: 5.6 μF, C _{a2}: 6.8 μF, C _{f}: 220 μF.
High stepup converter adopting auxiliary capacitor and coupled inductor:

1)
Q: IPP110N20N3G;

2)
D_{1}: STPS20120C, D_{o1}: STPS10120C;

3)
D_{o2}: C3D10060A, D_{o3}: C3D10060A;

4)
L _{1}: 50 μH, L _{m}: 50 μH, N _{sp}: 4;

5)
C _{a1}: 24 μF, C _{a2}: 32 μF, C _{f}: 220 μF;

6)
C _{o1}: 4 μF, C _{o2}: 3 μF, C _{o3}: 3 μF.
where C _{f} is used to realize the power decoupling if high stepup converter is cascaded with an inverter. And it is parallel with C _{o1} and C _{o2} in the high stepup converter adopting auxiliary capacitor and coupled inductor.
The experimental waveforms of high stepup converter based on quasiZsource network under different input voltages at full load are shown in Figs. 13 and 14, where v _{ds} is the drainsource voltage of the switch. As seen in Fig. 14, D_{1} and D_{o} conducts simultaneously. It can be explained as follows. Due to the forward recovery phenomenon of D_{1}, the voltage sum of C _{a1}, C _{a2} and the voltage drop of D_{1} is larger than the output filter capacitor when the switch is turned off. The voltage difference will drop on ESR of the output filter capacitor and cause a large current through D_{o}. As shown in Fig. 14, at the instant of turning off the switch, v _{ds} is slightly large, and there is a large current through D_{o}. Thus, the current supplied by L _{1} to replenish energy for C _{a2} is small, and i _{D1} is small. With the voltage drop of D_{1} reducing gradually, the difference between v _{ds} and the voltage of C _{f} decreases, resulting that i _{Do} decreases and i _{D1} increases. As C _{a1} and C _{a2} are much smaller than C _{f}, the voltage ripples of C _{a1} and C _{a2} are larger. Thus, with the voltages of the auxiliary capacitors increasing, the difference between v _{ds} and the voltage of C _{f} increases, leading to i _{Do} increasing and i _{D1} decreasing.
The experimental waveforms of high stepup converter adopting auxiliary capacitor and coupled inductor under different input voltages at full load are shown in Figs. 15 and 16 where i _{cp_p} is the current of the primary winding, i _{Do3} is the current of D_{o3}, v _{D1} and v _{Do1} are the voltages of D_{1} and D_{o1}. According to the theoretical analysis, i _{Do3} should rise up from zero when the switch is turned on. However, in the real case, there exist reverse recovery problem for D_{o2} at the instant of turning on the switch. During the time interval of the reverse recovery, the voltage of the secondary winding is clamped by C _{o2} and C _{o3}. The voltage is reflected to the primary side by electromagnetic induction and in series with C _{a1} to charge the leakage inductor which leads to the current of the leakage inductor rising up rapidly. After the reverse recovery of D_{o2} is over, the current of the leakage inductor is larger than that of the magnetizing inductor. Thus, i _{Do3} rises up from a positive value. The voltage stresses of the switch, D_{1} and D_{o1} shown in Fig. 16 are much smaller than the output voltage which will reduce the power loss and improve the efficiency.
The dynamic response of high stepup converter adopting auxiliary capacitor and coupled inductor is shown in Fig. 17. The output voltage is regulated in closed loop with single voltage compensator. The experimental result shows that the dynamic performance of the proposed converter is good. The startup waveform (V _{g} = 36 V, P _{o} = 300 W) is shown in Fig. 18, where v _{o} is the output voltage, and i _{L1} is the current of L _{1}. As seen, the overshoot of the output voltage is less than 30 V, which is 7.9% of the steadystate value.
The comparison experiments of the basic boost converter and the cascaded boost converter are also performed. To avoid the instability issue in the cascaded boost converter, the first stage is under open loop control with constant voltage gain of 4. The second stage of the cascaded boost converter regulate the output voltage. The efficiency curves of high stepup converter adopting auxiliary capacitor, high stepup converter adopting auxiliary capacitor and coupled inductor, the basic boost converter, and the cascaded boost converter are shown in Fig. 19. As the conducting period of D_{o} in the basic boost converter is extremely short, the current stress is large and the reverse recovery problem is severe which leads to a large switching loss of the switch. Thus, the efficiency of the basic boost converter is lower than that of high stepup converter adopting auxiliary capacitor at heavy load as shown in Fig. 19. When the coupled inductor is adopted, the efficiency is further improved. Due to the voltage stresses of the switch, D_{1} and D_{o1} decreasing, the switching loss can be reduced effectively and the efficiency is superior to that of the cascaded boost converter over a wide load range.
According to the calculation of the power loss in Appendix A, the estimated efficiency is shown as Fig. 20, which matches the measured efficiency. And the power loss ratios are given in Fig. 21, where r _{Q_sw} = (P _{Q_on} + P _{Q_off})/P _{in}, r _{Q_con} = P _{Q_con}/P _{in}, r _{fe} = (P _{L1_fe} + P _{Lcp_fe})/P _{in}, r _{cu} = (P _{L1_cu} + P _{Lcp_cu})/P _{in}, r _{D} = (P _{D1} + P _{Do1} + P _{Do2} + P _{Do3})/P _{in}. As seen, r _{Q_sw} and r _{fe} decrease with the increase of the output power, while r _{Q_con} and r _{cu} increase with the increase of the output power. Thus, the efficiency increases at light load and decreases at heavy load. And the present of the maximum efficiency depends on the parasitic parameter of the components.
The experiment results indicate that the proposed converters can achieve a higher efficiency and good dynamic performance as well.
5 Conclusion
A novel high stepup DC–DC converter adopting auxiliary capacitor and coupled inductor is proposed in this paper. The input current is continuous, and the voltage stress of the power switch is low, which reduces the switching loss. Thus, the efficiency of the converter is improved. The operating mode of the proposed topology is analyzed and an experiment is conducted. The results indicate that the converters proposed in this paper can operate steadily and the performance is good.
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Appendix A
Appendix A
The main power losses include the power loss of the switch, the diodes, the inductor and the coupled inductor. According to the parameter design in Section 4, the current stresses of the switch, the diodes, the inductor and the coupled inductor are given, and then the power loss of each component can be calculated as follows.

1)
Power loss of the switch Q
The power loss of the switch mainly includes the switching loss and the conduction loss. The switching loss can be derived as:
where f _{s} is the switching frequency; R _{g} is the driving resistor; V _{ds} is the voltage stress of the switch; i _{Q_on} is the current through the switch when Q is turned on; V _{gate} is the driving voltage; C _{iss}, C _{rss}, V _{miller}, V _{th} are the parasitic parameters of the switch, referring to the datasheet of the switch.
The conduction loss can be derived as:
where I _{Q_rms} is RMS current through the switch; R _{dson} is the onstate resistor of the switch.

2)
Power loss of the diodes D_{1}, D_{o1}, D_{o2}, D_{o3}
The voltage drop of the diode can be viewed as a constant value. Then the power loss of D_{1}, D_{o1}, D_{o2}, D_{o3} can be derived as:
where V _{f_D1}, V _{f_Do1}, V _{f_Do2}, V _{f_Do3} are the voltage drops of D_{1}, D_{o1}, D_{o2}, D_{o3}, which are listed in the datasheet; I _{D1_avg}, I _{Do1_avg}, I _{Do2_avg}, I _{Do3_avg} are the average currents through D_{1}, D_{o1}, D_{o2}, D_{o3}, respectively.

3)
Power loss of the inductor L _{1}, and coupled inductor L _{cp}
The power losses of L _{1} and L _{cp} include the copper loss and the core loss. The copper loss of L _{1}, L _{cp} can be derived as:
where I _{L1_dc} and I _{L1_ac} are the dc current and ac RMS current of L _{1}, respectively; I _{Lcp_p_dc} and I _{Lcp_p_ac} are the dc current and ac RMS current of the primary winding, respectively; I _{Lcp_s_dc} and I _{Lcp_s_ac} are the dc current and ac RMS current of the secondary winding, respectively; R _{L1_dc}, R _{L1_ac}, R _{Lcp_p_dc}, R _{Lcp_s_dc}, R _{Lcp_p_ac} and R _{Lcp_s_ac} can be measured by the impedance analyzer.
The core loss of L _{1}, L _{cp} can be derived as:
where V _{e} is the core volume; A _{e} is the effective area of the core; k, m, n can refer to the datasheet of the core; N _{L1} is the turns of L _{1}; N _{Lcp_p} is the turns of the primary winding.
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WU, G., RUAN, X. & YE, Z. Nonisolated high stepup DC–DC converter adopting auxiliary capacitor and coupled inductor. J. Mod. Power Syst. Clean Energy 6, 384–398 (2018). https://doi.org/10.1007/s4056501703428
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DOI: https://doi.org/10.1007/s4056501703428
Keywords
 High voltage gain
 High efficiency
 Nonisolated
 Photovoltaic (PV)
 Fuel cell