https://doi.org/10.6113/JPE.2019.19.6.1366
ISSN(Print): 15982092 / ISSN(Online): 20934718
DualCoupled Inductor High Gain DC/DC Converter with Ripple Absorption Circuit
Jie Yang^{†}, Dongsheng Yu^{*}, Mohammed Alkahtani^{**}, Ligen Yuan^{*}, Zhi Zhou^{***}, Hong Zhu^{****}, and Maxwell Chiemeka^{*}
^{†}State Grid Linyi Power Supply Company, Linyi, China
^{*}School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, China
^{**}Department of Electrical Engineering and Electronics, University of Liverpool, Liverpool, ENG, UK
^{***}State Grid Shanghai Qingpu Electric Power Supply Company, Shanghai, China
^{****}State Grid Anhui Maintenance Company, Hefei, China
Abstract
Highgain DC/DC converters have become one of the key technologies for the gridconnected operation of new energy power generation, and its research provides a significant impetus for the rapid development of new energy power generation. Inspired by the transformer effect and the ripplesuppressed ability of a coupled inductor, a doublecoupled inductor high gain DC/DC converter with a ripple absorption circuit is proposed in this paper. By integrating the diodecapacitor voltage multiplying unit into the quadratic Boost converter and assembling the independent inductor into the magnetic core of structure coupled inductors, the adjustable range of the voltage gain can be effectively extended and the limit on duty ratio can be avoided. In addition, the volume of the magnetic element can be reduced. Very small ripples of input current can be obtained by the ripple absorption circuit, which is composed of an auxiliary inductor and a capacitor. The leakage inductance loss can be recovered to the load in a switching period, and the switchingoff voltage spikes caused by leakage inductance can be suppressed by absorption in the diodecapacitor voltage multiplying unit. On the basis of the theoretical analysis, the feasibility of the proposed converter is verified by test results obtained by simulations and an experimental prototype.
Key words: Dualcoupled inductor, High gain, Quadratic Boost converter, Ripple absorption circuit, Voltage multiplying unit
Manuscript received Feb. 22, 2019; accepted Jun. 21, 2019
Recommended for publication by Associate Editor Wu Chen.
^{†}Corresponding Author: jiey109@sina.com Tel: +8618854902825, State Grid Linyi Power Supply Company
^{*}School Electr. Power Eng., China Univ. of Mining and Tech., China
^{**}Department of Electrical Eng. and Electronics, Univ. of Liverpool, UK
^{***}State Grid Shanghai Qingpu Electric Power Supply Company, China
^{****}State Grid Anhui Maintenance Company, China
Ⅰ. INTRODUCTION
Highgain and highefficiency DC/DC converters, as a key energy conversion technology in photovoltaic power generation, fuel cell power generation and DC systems, have been widely studied since they greatly improve system conversion efficiency [1][3]. Traditional Boost converters and some uncomplicated stepup topologies can obtain a higher efficiency with fewer devices [4]. However, an extremely high duty cycle is unavoidable when it comes to achieving a higher gain for the Boost converter in some high gain requirement applications, and the energy conduction system loss increases due to the enlarged voltage stress of the switch devices [5]. In addition, the input and output current ripples increase for a duty cycle increasing close to the extreme high duty cycle, which results in more aggravated losses of the converter [6]. When compared to the traditional stepup DC/DC converters, highgain DC/DC converters have the following advantages.
(1) A high voltage gain can be obtained by integrating a voltagemultiplying unit, a coupled inductor and a high stepup module without the requirement of an extreme high duty cycle, while reducing the switching loss.
(2) The voltage across switches and diodes can be clamped to the lower voltage of the capacitor voltage.
(3) Very small ripples, close to zero ripples, in the input current can be achieved by the parallel interleaving structure and the design of the coupled inductor in the converter.
(4) The voltage spike of the switch can be effectively reduced by designing a voltage spike absorbing circuit.
(5) Soft switching of the switching devices can be obtained with a freewheeling circuit, which improves the efficiency of the converter.
Transformer based electrical isolated converters have been widely investigated [7][15]. The input and output voltage of isolated highgain DC/DC converters have no common ground [7], [8]. A very high voltage gain can be achieved in isolated highgain DC/DC converters by adjusting the turn ratio of the highfrequency transformer and the duty ratio [9][11]. However, an excessive turns ratio decreases the linearity of the highfrequency transformer, and increase the leakage inductance loss. Furthermore, the leakage inductance that causes weak coupling also triggers voltage spikes of the switch during the turnon and turnoff periods, and increase the voltage stress on the active switch [12]. The isolated high gain DC/DC converter that introduces the structure of a lossless absorption circuit can achieve higher voltage gain and realize the soft switching of the switch during the period of load mutation [13], [14]. However, the increased leakage inductance caused by high turns ratio of the transformer is not be alleviated. It still results in added leakage inductance loss.
An isolated converter integrated with the switching capacitor unit can achieve a higher gain with a smaller turn ratio and duty ratio [15]. The leakage inductance energy can be recovered to the primary side of the converter by adding an energy recovery circuit consisting of a clamp diode and an energy storage capacitor [16]. However, the energy transfer between the two sides of the high frequency transformer is accompanied by increased ferromagnetic losses for the electromagnetic conversion process, which reduces the efficiency and power density of the converter.
In order to obtain a higher voltage gain and conversion efficiency, nonisolated high gain DC/DC converters have been studied [17][28]. Energy conduction and voltage lifting can be achieved through the dynamic charging and discharging period among energy storage inductors and capacitors. The nonisolated DC/DC converter by means of a coupled inductor can realize a higher voltage gain [17][19]. However, leakage inductance of the coupled inductor is inevitable [20], [21]. A clamping circuit consisting of energy storage capacitors and diodes is designed to suppress the voltage spikes of active switches caused by leakage inductance, and an added energy recovery circuit is integrated to reduce the leakage inductance loss [22][24]. A coupled inductor nonisolated high gain converter integrating the diodecapacitor voltage multiplying unit can effectively widen the adjustable range of the gain, and it naturally forms a passive clamp circuit and a leakage inductance energy recovery circuit [25][27]. The voltage spike in a switch caused by the leakage inductance can be effectively suppressed and the leakage inductance loss can be recovered to the load side, which improves the efficiency of the converter [28].
The Input Current Ripple (ICR) in high frequency switching converters is one of the reasons for the high current peak of a switching device and the low efficiency of converters. There has been a lot of effort to solve the abovementioned problems in power electronics converters [29][36]. One common method of ripplesuppression is to adopt a dual or multiphase converter operated with interleaving control [29]. However, the interleaving control can lead to high cost and control complexities since multiphase converters are necessary and operated in synchronization [30,31]. A Boostbased high gain converter can reduce the ICR by adjusting the value of the input inductor [32]. However, the dynamic response speed decreases when the filter inductor increases. In addition, this method increases the hardware size of converters. The converter proposed in [33] can decrease the ICR by properly configuring the duty cycle. However, the voltage gain and ICR are simultaneously controlled by the duty cycle, which limits the adjustable range of the gain. The method of ripplesuppression in [34] is the design of a resonant ripple absorption circuit. However, an additional absorption circuit is necessary to alleviate voltage spikes in the switch. The BoostSepic converter in [35] can obtain small input current ripples by integrating the input inductor and the intermediate inductor into a magnetic core and properly configuring the coupling coefficient. Nevertheless, the coupling strength of the coupled inductors can be adjusted with high precision [25].
Inspired by the transformer effect and the ripplesuppressed capability of coupled inductors, a doublecoupled inductor high gain DC/DC converter with a ripple absorption circuit is proposed in this paper. The proposed converter has a diode capacitor voltage multiplying unit integrated into a Quadratic Boost Converter (QBC) and independent inductors assembled into one magnetic core to structure the coupled inductors, which can reduce the size of the magnetic components. This converter can effectively expand the adjustable range of the voltage gain without an extreme duty cycle. Very small ripples, close to zero input current ripple, can be obtained by the ripple absorption circuit composed of an auxiliary inductor and a capacitor. In addition, the current of the absorption branch is low, the loss can be negligible, and the volume of the absorption branch is tiny. The leakage inductance loss in one switching period can be recovered to the load through the diodecapacitor voltage multiplying unit, and the voltage spikes of switches due to leakage inductance can be suppressed by an absorption circuit composed of a clamping diode and a storage capacitor. Based on the PSIM simulation platform and a hardware platform, an experimental prototype with an input voltage/output voltage of 18V/400V and a rated power of 200W is constructed to verify feasibility of the proposed converter through simulation and experimental results.
Ⅱ. WORKING PRINCIPLE OF THE CONVERTER
A diodecapacitor voltage multiplying unit and an input current ripple absorption circuit are integrated into a QBC to obtain the circuit topology of a converter shown in Fig. 1(a). The main working circuit includes a DC input power supply V_{in}, an active power switch tube Q, five diodes D_{1}D_{5}, three storage capacitors C_{1}C_{3}, one output filter capacitor, two pairs of coupled inductors T_{1}T_{2}, and one weak voltage and current ripple absorption circuit. The voltage multiplying unit (composed of diodes D_{3} and D_{4}), the storage capacitor C_{2} and the secondary side of the coupled inductor T_{2} can be used to increase the voltage gain of the converter. The ripple absorption circuit is composed of the auxiliary inductor L_{r}, the auxiliary capacitor C_{r }and the secondary side of the coupled inductor T_{1}. The input inductor L_{1 }and the inductor L_{2} are assembled into one magnetic core to structure a coupled inductor that can reduce the amplitude of the input current ripple to a low level. The peak absorption circuit is composed of the parasitic capacitance of the switch Q, the clamping diode D_{3} and the capacitor C_{3}. The maximum voltage across the switch Q is clamped to the voltage of the capacitor C_{3}. Fig. 1(b) shows a topology equivalent circuit of the converter. The coupled inductor T_{1 }is a fully coupled inductor, where the turns ratio can be expressed as N_{1}(N_{1}=(L_{1}/L_{2})^{½}). The mutual inductance of T_{1 }can be expressed as M. The coupled inductor T_{2} can be equivalent to a highfrequency transformer with a turns ratio of N_{2}(N_{2}=N_{s}/N_{p}). In addition, the magnetizing inductance is L_{m}, and the leakage inductance of the primary and secondary sides are L_{k1 }and L_{k2}, respectively. In order to simplify the circuit analysis and ignore the interference on the converter characteristics caused by the device parameters, the following assumptions should be made.
(a) 
(b) 
1) All of the capacitors in the circuit are large enough so that the voltage ripples across both terminals can be ignored, and the voltage across all of the capacitors is constant in a switching period.
2) Except for containing the antiparallel diode and capacitors, the switch tube and diodes are ideal devices without switching losses.
3) The coupled inductor T_{2} is a highfrequency transformer considering the magnetizing inductance and leakage inductance, and its coupling coefficient is k_{2}=L_{m}/(L_{k1}+L_{m}).
According to the above assumptions and the onoff states of the switch, the diode and the energy storage device, a converter operating in the continuous conduction mode (CCM) of the inductor current can be divided into six operating modes in a switching period. Modal equivalent circuits of the converter are shown in Fig. 3. Fig. 2 shows waveforms of the inductor current, the voltage and the current of the switching devices during a switching period. The modal switching process is as follows.
Fig. 2. Working principle waveforms of the converter in a switching period.
(a) 
(b) 
(c) 
(d) 
(e) 
(f) 
1) Mode 1[t_{0}<t<t_{1}, as shown in Fig. 3(a)]: At time t_{0}, the switch Q and the diodes D_{1} and D_{4} are turned on, and the diodes D_{2}, D_{3} and D_{o} are turned off and supported by the reverse voltages V_{C1}, V_{C3} and V_{o},_{ }respectively. The energy from the DC source V_{in} is delivered to the primary side winding L_{1 }through D_{1} and Q, and the current i_{L1} is linearly enlarged. In this mode, i_{L1} is smaller than the effective value of the input current, and the secondary side of T_{1 }and the auxiliary inductor L_{r }are charged by the auxiliary capacitor. Meanwhile, the secondary side current i_{L2} of T_{1},_{ }which is greater than zero, is opposite to the variation tendency of i_{L1}. As a result, the input current ripple is reduced. The energy storage in the capacitor C_{1} is released to the primary side of T_{2 }through Q, and the current i_{Lk} rises linearly. The energy stored in the secondary side of T_{2} is transferred to the capacitor C_{2} by using the transformer effect, and the current i_{Ls} rises in the opposite direction.
2) Mode 2[t_{1}<t<t_{2}, as shown in Fig. 3(b)]: In this mode, the switch Q and the diodes D_{1} and D_{4} continue to conduct, and the diodes D_{2}, D_{3} and D_{o} are turned off. The energy from the DC source Vin is released to the primary side of T_{1} via D_{1} and Q, C_{1 }is discharged to the primary side of T_{1} through Q, and i_{L1} and i_{Lk} continue to rise. The secondary side of T_{2} and the capacitor C_{3} are discharged to C_{2}, and the current i_{Ls} rises. i_{L1} is greater than the effective value of the input current. In addition, the current i_{L2} is opposite to i_{L1} and its amplitude is less than zero. Therefore, the input current ripple is reduced by the sum of the ripples of the currents i_{L1} and i_{L1}.
3) Mode 3[t_{2}<t<t_{3}, as shown in Fig. 3(c)]: In this mode, the switch Q and the diode D_{1} are turned off, and the diode D_{2} is continuously turned on. At t_{2}, D_{3} with support from the forward voltage is conducted and forms a discharge circuit with the parasitic capacitors of Q and C_{3}. The voltage across Q is clamped to the voltage of C_{3}. The current path of i_{Lk} is rapidly switched from the switch Q to C_{3}. In addition, i_{Lk }declines rapidly. The leakage energy in both sides of T_{2} is stored in C_{2} via D_{4}, and the current i_{Ls} decreases linearly.
4) Mode 4[t_{3}<t<t_{4},_{ }as shown in Fig. 3(d)]: In this mode, the switch Q and the diode D_{1} remain turned off, and the diode D_{2} is conducted. At t_{3}, the leakage inductance energy in both sides of T_{2} is completely discharged. In addition, the diode D_{4} is turned off, and output diode D_{o} is conducted. The energy from the primary side of T_{1 }and V_{in} is transferred to C_{1} via D_{2}. In addition, i_{L1} decreases linearly. The energy stored in the primary side of T_{2 }is released to C_{3} through D_{3}, and discharged to the output side through D_{o} with the secondary side of T_{2} and C_{2}. In addition, i_{Lk} decreases linearly, and the current i_{Ls} rises linearly. The current i_{L1 }is greater than the effective value of the input current, and C_{r} is charged by the secondary side of T_{1 }and the auxiliary inductor L_{r}. In addition, i_{L2} rises linearly and its amplitude is less than zero.
5) Mode 5[t_{4}<t<t_{5}, as shown in Fig. 3(e)]: At t_{4}, the storage capacitor C_{3 }is completely charged and the diode D_{3} is turned off. In this period, Q and D_{1} are turned off, and D_{2} and D_{o} are conducted. The energy in the primary side of T_{1} is discharged to C_{1} through D_{2}, and i_{L1} maintains a downward trend. C_{r} is charged by the secondary side of T_{1 }and L_{r}, and the current i_{L2} continues to decrease. The energy stored in the secondary side winding of T_{2} and C_{2 }is released to the output load via D_{o}. In addition, the current i_{Lk} starts to rise, and the current i_{Ls} begins to decline.
6) Mode 6[t_{5}<t<t_{0}′, as shown in Fig. 3(f)]: At t_{5}, the current i_{L1} is equal to the effective value of the input current and i_{L2} drops to zero. In this mode, the primary side of T_{1 }continues to discharge, and i_{L1} declines lower than i_{in}. Meanwhile, the capacitance energy stored in C_{r} is discharged to the secondary side of T_{1 }and L_{r}, and i_{L2} begins to increase. The energy stored in the secondary side winding of T_{2} and C_{2 }is sequentially released to the output load via D_{o}, and the current i_{Lk }continues to increase. Until time t_{0}′, when switch is turned back on, the converter starts the next switching period.
Ⅲ. STEADY STATE ANALYSIS
A. Voltage Gain
In order to reduce the volume of the magnetic component, the coupling inductor T_{1}, the auxiliary inductor L_{r} and the auxiliary capacitor C_{r} are combined to form a ripple absorption circuit, which can reduce the ICR with the ripple suppression capability of the coupled inductor. T_{1 }can be configured as a fully coupled inductor, and its coupling coefficient can be expressed as:
During the two periods of the switch turnon and turnoff, the voltage across the inductor can be approximately constant. In order to simplify the analysis process with the above mode analysis, the inductor voltage in modes 1 and 4 are used to represent the inductor voltage during the two periods of the switch turnon and turnoff, respectively.
In a switching period T_{s}, by using the voltsecond balance law in two sides of T_{1 }and the magnetizing inductance L_{m} of T_{2}, the voltage of C_{1,} C_{2,} C_{3} and C_{r} can be obtained by arranging equations (2)  (5) and (8)  (11):
Based on (10)  (11), the output voltage of the proposed converter can be expressed by:
Therefore, the steadystate voltage gain of the converter can be obtained when the converter operates in the CCM:
Fig. 4 shows gain contrast curves of the converter under different coupling coefficients. It is shown that the leakage inductance and the coupling inductance T_{1 }have no effect on the voltage gain of the converter. However, the gain loss of the converter due to the leakage inductance of T_{2} cannot be ignored. Therefore, the design of coupling inductor T_{2} should ensure that the winding is compact and minimize the air gap between magnetic cores for to reduce the gain loss caused by the leakage inductance. When the gain loss caused by the leakage inductance in T_{2 }is ignored (k_{2 }=1), the voltage gain of the converter can be expressed as:
It can be obtained from equation (19) that the voltage gain of the converter is simultaneously controlled by the duty ratio D and the turns ratio N_{2} of T_{2} without considering the influence of the leakage inductance T_{2} on the gain. In other words, increases of the duty cycle D and the turns ratio N_{2 }can enlarge the voltage gain of the converter. In high gain requirement applications, the gain of the converter can be further improved by increasing the turn ratio N_{2} without an extremely high duty cycle.
Fig. 4. Gain comparison curve under different coupling coefficients k_{2}.
Fig. 5. Gain comparison curves with different turns ratios N2 and duty cycles.
B. Voltage Stress Analysis
According to the above analysis of the operation mode and steadystate gain, the voltage stress of the switching devices including the switch Q and the diodes D_{1}D_{o} can be derived from (13)(16). Ignoring the influence of the voltage ripple on the capacitor C_{3 }and the leakage inductance of the coupled inductors, the voltage stress of the switch Q can be obtained from modes 3 and 4. The parameter measurement for the armature inductance L_{1} is also executed in a wide frequency range from 40Hz to 100Hz under various V/f ratios. The armature inductance is calculated by using the center of the PQ circle diagram depicted for each driving frequency.
According to mode 1 and mode 3, the voltage stresses of diodes D_{1}, D_{2} and D_{3} are (V_{C3}V_{C1}), V_{C1 }and V_{C3}, respectively. From mode 2 and mode 4, the voltage stresses of the diode D_{4} and the output diode D_{o} are equal to (V_{o}V_{C3}). Therefore, the voltage stress expressions of D_{1} and D_{o }can be expressed as:
Fig. 6 shows variation curves of the ratio of the voltage on the diode and the output under different turn ratios and duty cycles. It is noticeable that the voltage stress of the diode D_{1} is proportional to the duty cycle D and inversely proportional to the turn ratio N_{2}. The voltage across the diode D_{2} is inversely proportional to D and N_{2}. When the voltage spikes of the switching tube are ignored, the voltage stress of the diode D_{3} is equal to the voltage across the switching tube, and the ratio V_{D3}/V_{o} is independent of D and proportional to N_{2}. The voltages across the diodes D_{4} and D_{o} are equal, and the ratio V_{D4}/V_{o} is independent from D and rises with an increase of N_{2}. Therefore, when the input voltage and output voltage are constant, the duty cycle and the turn ratio N_{2} should be reasonably allocated to effectively reduce the voltage stress of the switching devices and to improve the efficiency of the converter.
Fig. 6. Ratio of the diode voltage to the output voltage under different turns ratios and duty cycles.
Fig. 7. Device current stress simplified diagram.
C. Current Stress Analysis
In order to simplify the current stress analysis of switching devices, the simplified current stress diagram shown in Fig. 7 can be obtained by neglecting the leakage inductance influence. According to equations (2) and (3), the current ripple of the inductors L_{1 }and L_{2 }can be expressed as:
According to operating modes 1 and 2, the input current is equal to the sum of the current flowing through L_{1 }and L_{2}. In order to make the ICR as small as possible, it is necessary to properly configure the current ripple of L_{2}. When the absolute value of the current ripple ∆i_{L2} is equal to the_{ }current ripple ∆i_{L1} in same time and the variation tendency is opposite, very small input current ripples that are close to zero can be achieved. Therefore, the current stress of L_{1 }and L_{2} are obtained as:
By using the amperesecond balance law in the capacitor C_{1}, the average current flowing through the primary winding of T_{2} is zero in a switching period. The current i_{Lk} is equal to the superposition of the current flowing through the secondary winding and the magnetizing inductor current of T_{2}. Thus, the following can be obtained:
From the current flowing path of the diodes and the current stress of all the inductors, the current stress of D_{1} and D_{2} can be expressed as follows:
According to mode 2 and mode 4, the current flowing through the diodes D_{3}, D_{4} and D_{o} varies with the change of the current flowing through the secondary winding of T_{2}. Therefore, the current stresses of D_{3}, D_{4} and D_{o} are obtained as follows:
As shown in Fig. 7, the current stress of the switch is equal to the current of the switch at time t_{2}. At this time, the charging process of L_{1 }and the magnetizing inductance of T_{2} is completed. Therefore, the current stress of the switch can be written as follows:
D. Realization Conditions for Zero Ripple of the Input Current
Very small ripples of the input current can be achieved due to the ripplesuppressed capabilities of the coupled inductor. According to the above current stress analysis of L_{1 }and L_{2}, very small input current ripples that are close to zero can be obtained when the absolute value of the current ripple Δi_{L2} is equal to the_{ }current ripple Δi_{L1} in same time and the variation tendency is opposite. Hence, the detailed derivation process of the realization condition for zero ripple of the input current is expressed as follows.
As can be seen from Fig. 7 and from equations (25)(26), the following can be obtained:
Without considering the influence of capacitor voltage ripples, substituting equations (13)  (14) into equation (37) yields:
Assume the coupling coefficient k_{1 }of the coupled inductor T_{1} is 1, that is M=(L_{1}L_{2})^{½}, the condition can be obtained by equation (38) as follows:
Therefore, by using a ripple absorption circuit composed of a coupled inductor T_{1}, an auxiliary inductor L_{r} and an auxiliary capacitor C_{r}, very small ripples of the input current can be achieved by reasonably configuring the turn ratio of the primary and secondary inductors T_{1} and the value of auxiliary inductor L_{r }to satisfy equations (37)(38).
Ⅳ. CONVERTER CHARACTERISTICS COMPARISON
In this paper, a number of DC/DC converters with high gains and low switching voltage stresses are selected for a comparative analysis with the proposed converter. Table I gives a comparative analysis of the main performances and experimental results among the converters, including the number of devices, voltage gain, voltage stress of switch, maximum voltage stress of diode, leakage loss, input current ripple and maximum efficiency. Fig. 8 shows a gain comparison among some homothetic converters. Fig. 9 shows a voltage stress comparison of the switching tube when the turns ratios are equal. In addition to a high voltage gain and a low voltage stress, the converter proposed in this paper can achieve zero ripple of the input current.
Converters 
Proposed converter 

Number of switch 
1 
2 
2 
1 
2 
1 
Number of diode 
5 
4 
4 
6 
4 
5 
Number of capacitor 
4 
5 
5 
5 
3 
5 
Voltage gain in CCM 






Voltage stress on switch 






Maximum voltage stress on diodes 






Leakage inductance loss 
Small 
Small 
Small 
Small 
Medium 
Small 
Input current ripples 
Large 
Large 
Large 
Medium 
Small 
Very small 
Maximum efficiency 
95.38% 
96.46% 
96.15% 
93.14% 
97.32% 
94.83% 
Fig. 8. Voltage gain comparison with N_{2}=2.
Fig. 9. Ratios between the diode voltage and the output voltage.
Ⅴ. PARAMETER DESIGN
In order to verify the steadystate characteristics of the converter and the feasibility of the theoretical analysis, an experimental prototype is designed in this paper. The parameters of the experimental prototype are designed as follows.
1) Input voltage range V_{in}= 18V36V.
2) Output voltage V_{o}= 400V.
3) Rated output power P_{o}= 200W.
4) Switching frequency f_{s}= 40kHz.
A. Selection of the Duty Cycle and Turn Ratio N_{2}
According to equation (18) and considering the gain loss due to the leakage inductance of the coupled inductor, the voltage gain can step up in order meet the requirement of the experimental prototype when the input voltage is 18V, the value of N_{2} is 3, and the duty ratio is 0.54.
B. Selection of the Inductors L_{1}, L_{2}, L_{r} and Turn Ratio N_{2}
According to the above analysis of the input current ripples, the inductor L_{1} should be large enough to ensure that its minimum current is greater than zero. The primary side equivalent inductance of the coupled inductor T_{1} is larger than the value of L_{1 }when an independent inductance is used. In order to obtain a continuous inductor current, L_{1} should be selected as follows:
Therefore, the primary inductance value of T_{1} is 240μH. According to equation (39), it is necessary to satisfy N_{1}>1 to achieve zero ripple of the input current. Therefore, N_{1} can be set to 2. Assuming the coupled inductor is a fully coupled inductor, the value of the secondary side L_{2} of T_{1} can be obtained as follows:
Since the leakage inductance of the coupled inductor cannot be ignored, it can be obtained according to equation (38) as follows:
Therefore, the auxiliary inductance L_{r} is selected to be 58μH.
C. Selection of the Magnetizing Inductance L_{m}
To operate the converter in the CCM mode of the inductor current, the minimum value of the magnetizing inductor current i_{Lm} needs to be greater than zero. According to formula (30), L_{m} needs to satisfy the following relational expression:
Therefore, L_{m} can selected to be 200μH, which can ensure that the inductance current operates in the CCM without increasing the number of turns of T_{2 }and reducing the volume of the magnetic components.
D. Selection of the Switch and the Diode
The rated voltage of the switching devices can be obtained based on (20)(24) and (31)(36). In practice, voltage spikes can be triggered during the switching transition process. Hence, FQP34N20 (200V, 31A, 0.075Ω) can be used for the switch, Schottky diodes MBR20200 (200V, 20A) can be used for the diodes D_{1} and D_{2}, and fast recovery diodes SFF1606G (400V) can be used for the diodes D_{3}, D_{4} and D_{o}.
E. Selection of the Capacitor
The rated voltage of the capacitors can be obtained from (13)(16). The selected capacitor capacity needs to be greater than 1.5 times the theoretical value to reduce voltage ripples. In addition, the values of the capacitors are supposed to satisfy the following condition:
Therefore:
The capacitor C_{1}, as the equivalent excitation power of T_{1} should maintain stability. Therefore, its parameters can be selected as 100μF and 100V. In order to reduce the output voltage ripple, the output capacitor C_{o }is selected to be an electrolytic capacitor with parameters of 470μF/450V, the auxiliary capacitor is selected with parameters of 22μF/ 50V, and C_{2} and C_{3} are selected with parameters of 47μF/ 250V.
Ⅵ. SIMULATION RESULTS
Fig. 10 shows waveforms of simulation results under the same parameters as the experimental prototype, including the voltage and current waveforms of the switch, and the current waveform of the diodes and inductors. It can be observed from the results that the input current ripple is approximately zero. When the input voltage and output voltage are 18V/400V, the turns ratio N_{2} is 3 and the duty ratio is 0.54, the switching tube voltage stress is about 80V. The simulation results are basically consistent with the principle analysis.
(a) 
(b) 
(c) 
(d) 
Ⅶ. EXPERIMENTAL RESULTS
An experimental prototype has been constructed to verify the feasibilities of the proposed converter by using the design parameters in this paper. Sampled waveforms are presented in Fig. 11(a) including waveforms of the driving pulse, and current waveforms of the input and the two sides of T_{1}. The ripple absorption circuit, composed of a coupled inductor T_{1}, an auxiliary inductor L_{r} and an auxiliary capacitor, can reduce the input current ripple. This can be seen from the fact that the current variation tendency of the two sides of T_{1} is opposite. By adjusting the auxiliary inductance, the peakto peak value of the input current ripples can be reduced to lower than 5%.
Fig. 11(b) illustrates the gate signal of Q and the current waveform of T_{2}. Figs. 11(c) and 11(d) show current waveforms of all the diodes and the switch tube. Obviously, when the switch is turned off, the primary current of T_{2} decreases, and the diodes D_{3} and D_{4} are conducted. In addition, the energy stored in the primary and secondary side leakage inductances of T_{2} is recovered into the capacitors C_{3} and C_{2} and eventually to the load. The diodes D_{1 }and D_{2} are conducted in the complementary mode. Hence, they can provide loops for the charge and discharge processes of the coupled inductor T_{1}, which can improve the voltage gain of the converter.
(a) 
(b) 
(c) 
(d) 
(e) 
(f) 
As can be seen from Fig. 11(d), the output voltage can be step up to 400V when the input voltage is 18V, and the current stress of the switch is about 10A, which is consistent with the theoretical analysis and simulation test results.
Fig. 11(e) gives the gate signal of Q and voltage waveform of the diodes D_{1}, D_{2} and D_{o}. It is easy to observe that the output diode can achieve approximately zero voltage switching (ZVS). When the diode D_{3} is turned off, the voltage across the diode D_{3} is clamped at a low voltage (V_{Ns}+V_{C2}V_{D4}). In addition, the voltage across the diode D_{1} has a voltage drop at the same time.
Fig. 11(f) illustrates waveforms of the output voltage, the switching voltage and the voltage across the auxiliary capacitor C_{r} when the input voltage is 18V. The voltage stress of the switch is about 80V and the voltage across the auxiliary capacitor is only about 20V. Voltage spikes of the switch can be suppressed by a passive lossless absorption circuit composed of a diode D_{3} and a capacitor C_{3} at the moment of switching turn off. The current flowing through the ripple absorption circuit current is very small. Therefore, this auxiliary branch can be constructed by a capacitor and litz wire with a low tolerance parameter to reduce the place of the converter.
Fig. 12 shows an efficiency comparison of the proposed converter and a converter without a ripple absorption circuit under different loads. As can be seen from Fig. 13, the proposed converter with a ripple absorption circuit contains additional conduction loss due to the auxiliary capacitance and inductance. In addition, the switching device loss and the energy storage device loss of the proposed converter are lower than the converter without a ripple absorption circuit. Therefore, the conversion efficiency of the converter proposed in this paper is slightly lower than the high gain converter without a ripple absorption circuit. The maximum efficiency of the high gain converter without a ripple absorption circuit is 95.82%, and proposed high gain converter proposed achieves a maximum efficiency of 94.83% when the power is P_{o}=60W. Nevertheless, a very small input ripple that is close to zero can be obtained from the high gain converter proposed in this paper, which can provide a good alternative option with attractive performance for some occasions such as PV generation systems.
Fig. 12. Converter efficiency comparison.
Fig. 13. Loss distribution of devices.
Ⅷ. CONCLUSION
In this paper, a doublecoupled inductor high gain DC/DC converter with a ripple absorption circuit is proposed. When compared with a traditional quadratic high gain converter and a coupled inductor high gain converter, the proposed converter has the following advantages. 1) A voltage multiplier module composed of a diodecapacitor unit and a coupled inductor is integrated into a conventional converter, and a higher voltage gain can be obtained by configuring the turns ratio of the coupled inductor and the duty ratio, which can effectively avoid an extremely high duty cycle and reduce the leakage inductance loss caused by the weak coupling of a high frequency transformer. 2) Very small input current ripples can be achieved by using a ripple absorption circuit composed of an auxiliary inductor and a capacitor, which effectively reduces the switching devices loss. Additionally, the current through the ripple absorption circuit is small and the volume of the absorption branch is tiny. 3) The voltage stress of the switch tube can be clamped at a value much lower than the output voltage since the voltage across the switch and the output voltage are isolated by the voltage multiplying unit. 4) The leakage inductance loss of the coupled inductor can be recovered and fed back to the load in a switching period, which can improve the efficiency of the converter.
APPENDIX
This appendix provides the approximate derivation used to estimate the loss breakdown in the proposed converter [14]. The loss in the active switch is mainly conduction losses [32]. The conduction losses are estimated using the RMS current through the switch and its onstate resistance. Thus, the losses in the active switch Q are given by:
where I_{rms} is the RMS current through the switch Q, and R_{dson} is its onstate resistance.
The diode losses can be obtained by:
where I_{rmsd} is the RMS current through the diode, R_{T} is its onstate resistance, I_{avgd} is its average current, and V_{T }is its onstate voltage drop.
The capacitor losses are estimated by using the following equation:
where I_{rmsc} is the RMS current through the capacitor and R_{ESR} is its equivalent series resistance.
The losses in the magnetic components are comprised of the core losses and the winding losses [10]. The core losses are estimated as:
where k is the eddy current loss coefficient, B_{ac} is the magnetic flux variation, and W_{tfe} is the core weight in grams.
The winding losses in T_{1}, T_{2} and L_{r} are estimated by using the following equation:
where I_{rmscu} is the RMS current through the wire, and R_{cu }is the resistance of the wire.
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Jie Yang received his B.S. degree from the School of Electronic and Information Engineering, Changchun University, Changchun, China, in 2014; and his M.S. degree from the School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, China, in 2017. He is presently working as a Senior Engineer in the State Grid Linyi Power Supply Company, Linyi, China. His current research interests include power electronics, power system and electric drives.
Dongsheng Yu (M'14) received his B.S. and Ph.D. degrees from the School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou, China, in 2005 and 2011, respectively. From 2009 to 2010, he was a Visiting Student with the University of Western Australia, Perth, WA, Australia, where he was an Endeavour Research Fellow, in 2014. He is presently working as an Associate Professor in the School of Electrical and Power Engineering, China University of Mining and Technology. His current research interests include power electronics, renewable energy, electric drives, nonlinear dynamics and memristive systems. He has published two books and over 30 papers in these areas.
Mohammed Alkahtani was born in Arrayn, Saudi Arabia. He received his B.S. (Hons) degrees in Electrical and Electronics Engineering and his M.S. degree in Electrical Power and Control Engineering from the Liverpool John Moores University, Liverpool, ENG, UK, in 2014 and 2016, respectively. He is presently working towards his Ph.D. degree at the University of Liverpool, Liverpool, ENG, UK. His current research interests include soiling management of photovoltaics and PV array efficiency improvements.
Ligen Yuan was born in Taian, China. He received his B.S. degree from the School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, China, in 2018, where he is presently working towards his M.S. degree in the School of Electrical and Power Engineering. His current research interests include power electronic converters.
Zhi Zhou was born in China, in 1991. She received her B.S. degree from the School of Electrical and Mechanical Engineering, Jinling Institute of Technology, Nanjing, China, in 2015; and her M.S. degree from the School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, China, in 2018. She is presently working as a Senior Engineer in the State Grid Shanghai Qingpu Electric Power Supply Company, Shanghai, China. Her current research interests include memory components and microgrid systems.
Hong Zhu was born in Xuzhou, China. She received the B.S. degree from the School of Electronic Engineering, Nantong University, Nantong, China, in 2014; and her M.S. degree from the School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, China, in 2017. She is presently working for the State Grid Anhui Maintenance Company, Hefei, China. Her current research interests include DCmicrogrids, AC/DC bidirectional converters and energy coordination control.
Maxwell Chiemeka was born in Uyo, Akwa Ibom State, Nigeria. He received his Higher National Diploma degree in Electrical and Electronics Engineering from the Federal Polytechnic Nekede, Owerri, Imo State, Nigeria, in 2016. He is presently working towards his M.S. degree in Electrical Engineering at the China University of Mining and Technology, Xuzhou, China. His current research interests include memristor based filters in power line communications and power electronics.