The photovoltaic (PV) power conditioning system for smallscale applications has gained significant interest in the past few decades. However, the standalone mode of operation has been rarely approached. This paper presents a twostage multilevel microinverter topology that considers the different operation modes. A multioutput flyback converter provides both the DCLink voltage balancing for the multilevel inverter side and maximum power point tracking control in grid connection mode in the PV stage. A modified Hbridge multilevel inverter topology is included for the AC output stage. The multilevel inverter lowers the total harmonic distortion and overall ratings of the power semiconductor switches. The proposed microinverter topology can help to decrease the size and cost of the PV system. Transient analysis and controller design of this microinverter have been proposed for standalone and gridconnected modes. Finally, the system performance was verified using a 120 W hardware prototype.
I. INTRODUCTION
Traditional largescale powergenerating stations connected to a central grid have several shortcomings because of the ever increasing demand for electrical power and its resulting complexity. Distributed Generation (DG) provides a solution for this problem because of its quick installation time unlike largescale power stations and the added flexibility it provides to the system. DG also increases in the generation and transmission efficiency because it is located closer to consumers. Most research efforts in DG systems have mainly focused on sources with the least carbon footprints given that it has become an essential criterion for electrical power generation systems to minimize greenhouse gas emission levels. Photovoltaic (PV) solar power, wind turbine power, and fuelcell power generation systems have become the essential research topics in this area because they have literally zerocarbon footprint
[1]
,
[2]
. PV systems have higher longevity and lower operational costs among these sources because of the lack of mechanical movements and being devoid of fuel costs. Given the rapid growth in the PV system capacity and decrease in the PV panel prices, smallscale PV systems are obtaining a larger share in the market
[3]

[7]
. Although the PV panel costs have been largely decreased, the size and cost of the power conditioning system (PCS) that interfaces with the PV panels with the load/grid remains relatively high
[7]

[10]
. This work attempts to decrease the PCS size and cost used for the PV panels without compromising the IEEE standards.
The PCS for gridconnected PV systems are traditionally classified into three groups: centralized type, string type, and microinverters or moduleintegrated converters (MIC). Although the centralized and string types are suitable for largescale PV systems, operating in optimal operating conditions during partiallyshaded conditions is difficult. MIC systems are connected to each PV module separately, which allow them to achieve better energy conversion efficiency during partiallyshaded conditions. These systems also have inherent advantages of manufacturing and installation costs from modularity unlike other types
[11]
,
[12]
. PV microinverter systems can be divided into groups based on the number of converters used, such as singlestage, twostage, or sometimes threestage systems. A singlestage has only one converter that connects the PV module to the grid as the name suggests. Twostage microinverter systems are generally preferred because of the wide range of PV voltage and reduction in the value of the power decoupling capacitor compared with singlestage systems
[13]
. However, the operation and control of microinverterbased systems in the standalone mode was rarely approached in literature. The PV system is stably connected to the grid under normal operating conditions. However, the standalone mode is sometimes necessary when a fault occurs in the grid and the local load should remain working (
Fig. 1
). In this case, one of the microinverter modules should maintain the AC bus stable in the normal range, whereas the other modules work in the gridconnection mode. This paper presents a smallscale PCS that uses a multilevel inverter with an integrated cellbalancer and analyzes it in both gridconnected and standalone operating modes. The controllers for both modes are then derived.
Configuration of a PV system with parallel MIC modules connected to the grid and residential loads.
The operating principles of the newly suggested PV system architecture of the abovementioned multilevel inverter and flyback converter are explained in Section II. Consequently, the derivation and validation of the statespace averaged linear transfer functions for the converter stages that use smallsignal modeling is shown in Section III. Section IV discusses the design procedure of the digital controller used for the stable operation of the system in standalone and gridconnected modes. The experimental setup and results of the hardware prototype are shown Section V. Section VI concludes this paper.
II. PROPOSED SMALLSCALE PCS
A twostage PCS generally consists of a DC–DC converter to boost the PV and an inverter that converts the boosted DC to an AC output connected to the grid or local loads.
Figure 2
shows the schematic of the proposed smallscale PCS in a grid connection.
Complete circuit diagram of the proposed twostage multilevel PCS.
 A. MultiOutput Flyback Converter
One of the main purposes of a prestage DC–DC converter is to boost the PV module voltage up to the DClink so that the inverter can provide the AC output with the desired specifications. The DC–DC converter used for boosting the PV voltage can employ either an isolated or nonisolated converter. Given that the voltage should be balanced between the two input capacitors (C1 and C2) of the multilevel inverter, an active voltage balancing circuit becomes mandatory in this study. Active balancing circuits have been extensively used in electric vehicles to balance the voltage of individual batteries. They can be divided into two major groups, namely, magneticcoupling and capacitivecoupling balancing methods. Among these circuits, the multioutput flyback converter has been selected for this twostage converter scheme (
Fig. 2
). Flybackbased converter schemes have received positive reviews because of the fewer components and potential low cost
[14]

[16]
. The multiwinding transformer in the flyback provides not just isolation and energy transfer but also performs accurate voltage balancing.
The voltage balancing strategy becomes simple in the case of a multioutput flyback converter. By the same turnsratio for the secondary and tertiary outputs in the transformer, the rectified voltage should balance each other regardless of the switch duty cycle.
Fig. 2
shows that the secondary and tertiary windings balance the top capacitor (C1) and bottom capacitor (C2), respectively. This inductivecoupling multiplesecondary scheme helps to minimize the required components, which lowers the cost and size of the proposed smallscale PCS. Additionally, the maximum power point tracking (MPPT) for the PV module can be achieved using the multioutput flyback converter in gridconnected systems. The DClink voltage for the inverter can be balanced from the inverter stage in gridconnected systems, which allows the application of the MPPT scheme through the multioutput flyback converter.
 B. MultiLevel Inverter
Multilevel inverters are traditionally used in highpower industrial applications. However, they are increasingly used in renewable energy systems because of their inherent advantages over conventional twolevel inverters
[17
–
20]
. Multilevel inverters produce a staircase output waveform with low distortion, so it aids in decreasing electromagnetic (EM) compatibility problems. It also draws the input current with low distortion and decreases the
dv
/
dt
stresses
[21]
. They can be operated in either fundamental frequency or high switching frequency pulse width modulation (PWM). A clear disadvantage of multilevel inverters is the utilization of a higher number of power switches compared with conventional Hbridge inverters. Although the voltage ratings are lower, the large number of switches increases the complexity of the gate driver circuit. Therefore, current multilevel studies have attempted to tackle this problem by proposing new multilevel inverter topologies. The current work selects a recently proposed multilevel inverter topology, which is a modified Hbridge topology with a 5level output
[22]
. Unlike wellknown multilevel topologies such as cascaded Hbridge and flying capacitor asymmetric Hbridge (FCAH), the selected topology is ideally suited for smallscale PCS. In contrast, previous topologies are designed for highpower applications that share the power transfer between the cascaded Hbridge modules.
Fig. 3
shows a circuit diagram of the selected multilevel inverter with its output waveform. This topology has fewer switching components compared with conventional multilevel inverters with a 5level output. This feature helps to lower the overall system cost and complexity of the gate driver circuit and controllers.
Table I
shows the comparison of the component number in each circuit. However, a drawback of the inverter topology is that because the average and instantaneous currents of SH and D are completely different, a reliable external voltage balancing circuit is necessary to maintain each of the capacitor voltages.
Lowpower multilevel inverter topology and output. (a) Modified Hbridge topology. (b) 5level output voltage waveform.
COMPARISON OF THE NUMBER OF SWITCHING COMPONENTS IN DIFFERENT MULTILEVEL INVERTER TOPOLOGIES
COMPARISON OF THE NUMBER OF SWITCHING COMPONENTS IN DIFFERENT MULTILEVEL INVERTER TOPOLOGIES
Several modulation techniques have been used for the multilevel topologies such as space vector modulation, selective harmonic elimination, and sinusoidal PWM (SPWM). Among these, SPWM is one of the most simple and widely used modulation techniques. Instead of using the rudimentary form of SPWM technique, a technique combined with a modified unipolar switching strategy has been employed in this study
[23]
. An advantage of such a strategy is that one of the legs that contain two switches always operates at the fundamental frequency of the output, whereas the remaining three switches operate under the switching frequency (
f_{sw}
).
Fig. 4
shows each of the reference signals used in the PWM generation for individual switches. Each signal is derived from the fundamental sinusoidal waveform reference. The reference signals for switches S2 and S4 are inherently the complementary signals of S1 and S3, respectively. Notably, the frequency of PWM outputs for switches S3 and S4 is the fundamental frequency of the output. Thus, the leg (S3 and S4) always operates under the fundamental frequency of the output. This modulation effectively helps lower the switching losses that occur in the inverter and highfrequency EM interference (EMI) noises. The frequency modulation ratio (
m_{f}
) was selected as an odd integer to lower the evenorder harmonics in this strategy.
Table II
shows the switch state of all the individual switches that correspond to the output voltage levels.
Reference signals used in the PWM generation of S1, S3, and SH.
SWITCHING STATES OF THE INDIVIDUAL SWITCHES ACCORDING TO THE OUTPUT VOLTAGE LEVELS (1 = ON, 0 = OFF)
SWITCHING STATES OF THE INDIVIDUAL SWITCHES ACCORDING TO THE OUTPUT VOLTAGE LEVELS (1 = ON, 0 = OFF)
III. SYSTEM MODELLING
 A. GridConnected MultiLevel Inverter Modeling
The gridconnected inverter is regulated by a twoloop control, such as an inner loop of the inductor current and outer loop of the DClink voltage. The corresponding transfer functions should be first derived for the controller design. The state equations of the gridconnected modified Hbridge inverter can be obtained by examining the equivalent circuit in each operating mode.
Fig. 5
depicts the current flow path and switching operation under different voltage levels. When the output voltage is zero, switches S2 and S4 are turned ON (mode 1). When the output voltage is
V_{DC/2}
, the diode is forward biased and switches S1 and S4 are turned ON (mode 2). Similarly, when the output voltage is
V_{DC}
, switches SH, S1, and S4 are turned ON (mode 3).
Current flow according to the output voltage levels. (a) Mode 1(Vo = 0). (b) Mode 2 (Vo = V_{DC/2}). (c) Mode 3 (Vo = V_{DC}).
From each of the above diagrams, the state equations of the inductor current under different voltage levels are derived as follows:
When switch S1 is turned ON and the statespace averaging technique is applied, the controltoinductor current transfer function is derived as follows:
where
d_{1}
is the duty applied to switch S1. Similarly, when the top switch SH is turned ON, the controltoinductor current transfer function is derived as follows:
where
d_{2}
is the duty applied to switch SH. Eqs. (2) and (3) show that the input voltage
V_{DC}
has a significant influence on the inductor current, but the inverter has a large capacitor at the input. Thus, we can assume that the voltage is constant.
The controlto
v_{DC}
should be derived for the outer loop controller design. The output power equals the input power in the case of an ideal inverter.
The input quantities
v_{DC}
and
i_{DC}
are the DClink parameters, whereas the output quantities
v_{o}
and
i_{o}
are rms values. The controllers are designed in such a way that the inner loop controller is always much faster than the outer loop controller. We assume that the output current tracks its reference without any error. Therefore, the output current is assumed to be the multiplication of the phaselockloop (PLL) output and control voltage.
where
k
is the scaling factor, and
v_{con }
is the control voltage from the outer loop controller. Eq. (6) is obtained using Eqs. (4) and (5).
The value of the modulation index
M
of the modified Hbridge inverter can be derived as follows:
where
r_{i}
is the smallsignal resistance of the input. Introducing the perturbation to the above Eqs. (5), (6), and (7), we can obtain Eqs. (8) and (9):
The smallsignal model can be obtained from Eqs. (8) and (9) as shown in
Fig. 6
. The output smallsignal resistance (
r_{o}
) is given by the following:
Smallsignal circuit diagram of the inverter.
The smallsignal circuit model shows that the expression for the control controltoDClink voltage (
V_{DC}
) transfer function can be derived as Eq. (11):
 B. MultiLevel Inverter Modelling under Standalone Mode
In the standalone operating condition, the flyback converter starts to regulate the DClink voltage instead of the MPPT control. The following inverter also starts to generate the output AC voltage. The state equations of the modified Hbridge topology at each of the output levels are provided below.
The transfer functions of the controltooutput and controltoinductor current are derived using the statespace averaging technique as shown in Eqs. (13) and (14), respectively.
The derived transfer functions can be validated by comparing them with the exact models in PSIM as shown in
Fig. 7
.
Bode plots of G_{vd} and G_{id}. (a) Derived transfer function with MATLAB. (b) Numerical simulation PSIM.
 C. MultiOutput Flyback Converter Modeling under Grid Connection
Similar to the modified Hbridge topology, the state equations of the multioutput flyback converter can be obtained by examining the current flow during switch ON and OFF conditions. The state equations when the switch is turned ON are shown in Eq. (15) as follows:
The state equations when the switch is turned OFF are shown in Eq. (16):
where
V_{DC}
is the flyback converter output voltage. Using the statespace averaging technique, the linearized transfer function for the controltoinput voltage is derived as Eq. (17):
The derived linearized transfer function can be verified by comparing it with the bode plot of the exact model in PSIM.
Fig. 8
shows the bode plots of the averaged model and exact model, which matching each other.
Bode plot of G_{vd}. (a) Derived transfer function with MATLAB. (b) Numerical simulation by PSIM.
 D. Flyback Converter Modeling under Standalone Operation
In the case of standalone operation, the function of the DC–DC converter is to provide a fixed DCLink voltage to the multilevel inverter. The characteristics of the controltooutput voltage should be analyzed to develop the controller.
Fig. 9
shows the equivalent circuit of the flyback converter with a single output in the standalone operation. The state equations can be derived from the equivalent circuit diagram as shown in
Table III
. The controltooutput transfer function is derived for the flyback converter shown in Eq. (18). The derived transfer function can be validated by comparing them with the averaged model plot in MATLAB and exact model plot in PSIM as shown in
Fig. 10
.
Equivalent circuit diagram of the flyback converter with a PV source in standalone mode.
STATE EQUATIONS OF THE FLYBACK CONVERTER
STATE EQUATIONS OF THE FLYBACK CONVERTER
Bode plot of G_{vd}. (a) Derived transfer function with MATLAB. (b) Numerical simulation by PSIM.
IV. CONTROLLER DESIGN
This section present the design process of the digital controllers used for the stable operation of the converter in standalone and gridconnected modes. The highfrequency PWM (
f_{sw}
) was set at 20 kHz for both the flyback converter and multilevel inverter switches. The value of the input capacitor of the flyback converter was set as 300 μF to ensure that the PV module ripple voltage was less than 1%. The turnratio of the multioutput transformer was 1:3:3. The magnetizing inductance was twice the boundary value at 600 µH to ensure the CCM mode of operation in the flyback converter. The capacitor used for the DClink voltage should lower the 120 Hz ripple to less than 5% of the DClink voltage. The value of 600 µF was selected for both of the DClink capacitors. Given that the output voltage of the multilevel inverter is a 5level staircase waveform, the low values of 1.3 mH and 2 µF are sufficient for the inverter LC filters. The validated transfer functions derived in the previous sections are utilized to design the feedback controllers. The controller function
H(s)
is presented in continuous domain in Eq. (19). The bilinear transformation is applied to the controller function to obtain the digital form of the controllers shown in Eq. (20).
 A. Standalone Mode
In the case of standalone operation, the flyback converter should provide a constant DClink voltage independent from the operation of the multilevel inverter stage. This condition is achieved using a voltage loop PI controller. The DClink voltage is fed back to the controller, and then the PI controller is used to eliminate the error voltage by varying the dutycycle given to the switch of the flyback converter. The cutoff frequency of the controller was set at 50 Hz. The
K_{p}
and
K_{i}
values of the designed controller are 4396330.77 and 33817.751, respectively.
Fig. 11
shows the closed loop performance of the designed controller. The control dynamics indicate the characteristics of the openloop transfer function and designed controller, respectively. The red line indicates the closed loop performance of the flyback converter in standalone operation. The figure shows that the controller provides a 110° phase margin that guarantees the stability.
Bode plot of the dynamic characteristics of the closed loop flyback converter. G_{vd}: controltooutput, H(s): Controller, T_{v}: Loopgain.
In standalone mode, the multilevel inverter is controlled using a twoloop controller, innerloop that controls the inductor current, and outer loop that controls the output voltage. The cutoff frequency of both the control loops was set at 3 kHz. Given that the digital controllers decrease the phase margin by the sample and hold effect, an excessive phase margin of 70 degrees was selected.
The designed PI control values for the inner and outer loops are K
_{p}
= 480000, K
_{i}
= 96000, and K
_{p}
= 768230, K
_{i}
= 2926242.6, respectively.
Figs. 12
(a) and
12
(b) show the Bode plots of the inner and outer loop characteristics, respectively.
Bode plot of the designed feedback loop. (a) G_{id}: controltoinductor current, H_{i}(s): Inner loop controller, T_{i}: Inner loopgain. (b) G_{vd}: controltooutput voltage, Outer loop controller, T_{v}: Outer loopgain.
Three PWM signals are generated to control the inverter switches using the modified unipolar strategy in
Table II
.
Fig. 13
shows the complete circuit diagram of the power stages with the digital controller in standalone mode.
Circuit and controller diagram of the proposed twostage multilevel inverter closedloop PCS under standalone mode.
The controller was simulated in PSIM software to test its functionality. A reference of 110
V_{AC}
was selected for the load, whereas the DClink reference was set at 200 V. The results show that the designed controllers successfully track each of the references as shown in
Fig. 14
. The flyback capacitors also have an equivalent voltage level (
V_{DC1}
,
V_{DC2}
), although the multilevel inverter draws the input current in imbalance between the switch (SH) and diode (D).
Simulation result for the standalone control scheme. (a) 110 V_{AC} reference vs. load voltage. (b) 200 V DCLink voltage. (c) Top switch (SH) current. (d) Diode current.
 B. GridConnected Mode
The focal point of the controller moves to the MPPT operation in case of a gridconnected operation. The DClink voltage is fixed by the inverter stage in this mode. The MPPT algorithm is perturbandobserve (P&O). PVvoltage control is used to track the reference provided by the P&O algorithm. The coefficients of the PI controller
K_{p}
and
K_{i}
were calculated as 224545.5 and 102066.12, respectively.
Fig. 15
shows the closedloop characteristics of the designed controller with a sufficient phase margin of 70° that guarantee the system stability.
Fig. 16
shows the circuit diagram of the PCS with its controller scheme under grid connection. The parameters
V_{pv}
and
I_{pv}
are used to calculate the
V_{ref}
in the P&O MPPT algorithm.
Bode plot for the closed loop operation of the voltage loop PI controller for MPPT. G_{vd}: controltoinput voltage, H(s): Voltage controller, T_{v}: Loopgain.
Circuit and controller diagram of the closedloop PCS in gridconnected mode with MPPT operation.
The controller of the inverter part includes a PLL, an outer voltage loop that regulates the DCLink voltage, and an inner current loop for the output current control. Eqs. (3) and (11) show that design of the PI controllers for the voltage and current loops. The bode plots of both loops are shown in
Fig. 17
. The cutoff frequency of the current loop was set at 600 Hz, whereas the cutoff frequency of 5 Hz was selected for the voltage loop. The simulation results that verify the feasibility of the control design is presented in
Fig. 18
. The MPP voltage was located at 38 V, and 110 V is the grid voltage.
Bode plots of the designed feedback loop gain. (a) Voltage loop G_{vd}: controltoDClink voltage, H(s)Outer loop controller,T_{v}: Outer loop gain. (b) Current loop G_{id}: controltoinductor current, H(s) Inner loop controller, T_{i}: Inner loop gain.
Simulation results for the gridconnected control scheme. (a) Grid current, (b) grid voltage, (c) PVsource voltage (V_{pv}), MPP (38 V), and (d) balanced DCLink capacitor voltages.
V. EXPERIMENTAL RESULTS
A 120 W hardware prototype was realized to verify the proposed chargebalancer integrated multilevel PVPCS. The selected specifications for the hardware prototype are provided in
Table IV
. The inductance
L_{o}
is 1.3 mH, which is relatively smaller than that of conventional 2level or 3level inverters. Texas Instruments DSC TMS320F28335 was used to execute the designed controllers in the hardware prototype.
Fig. 19
shows the 5level inverter output voltage waveform. The step of the voltage level is even because of the flyback charge balancer.
Fig. 20
shows a closedloop result of the PCS under standalone operation with a 200 V DCLink voltage and 110 V reference. The experimental data was collected from the oscilloscope and used to accurately calculate the THD value in the MATLAB FFT scope.
Fig. 21
shows the measured THDs of the output voltage at 4.43%.
SPECIFICATIONS AND DESIGN OF THE HARDWARE PROTOTYPE
SPECIFICATIONS AND DESIGN OF THE HARDWARE PROTOTYPE
5level inverter output voltage.
DClink voltage (V_{DC}) and load voltage (V_{o}) during the standalone operation.
Calculation of the inverter hardware output voltage THD (4.43%) using MATLAB FFT scope.
A dual PVarray simulator (TerraSAS ELGAR) was used to emulate a real PV module (100W SM10024). The module and array parameters, as well as the external conditions such as the solar radiation and temperatures, are all represented in the simulator. The simulator is remotely controlled by a desktop computer, whereas data acquisition is provided by the simulation software.
The PV system is tested under a changeable weather condition of constantly varying temperature and irradiance profiles to evaluate the MPPT and chargebalancing performance.
Fig. 22
shows the variation of a cloudy dayprofile, including a time period from points (a) to (b), applied to test the hardware prototype. The time and voltage steps of the P&O algorithm were set as 0.1 sec and 2 V, respectively. The results in
Fig. 23
(a) show that the controller unit tracks the varying maximum power point rapidly and accurately, even under the fastchanging conditions of solar radiation and temperature over a period of 2 hours.
Fig. 23
(b) shows the shorttime (250 seconds) variation of the PV voltage and current to check the MPPT performance of the controller that responds to the varying atmospheric conditions. The MPPT efficiency is almost 100% and at least 90%. Finally,
Fig. 24
shows that the capacitor voltages share the partial DClink voltage evenly.
Temperature and irradiance parameters in the cloudy day profile.
Experimental results of the MPPT controller during the cloudy day profile test. (a) Entire 2hour period from (a) to (b) in Fig. 22. (b) Zoomin waveforms in Fig. 23(a).
Experimental results of the PV voltage and DCLink voltage during the MPPT operation. The voltages V_{DC1} (200 V) and V_{DC2} (100 V) are well balanced during every step operation change in the PV voltage.
VI. CONCLUSION
This paper presents a twostage microinverter system using an active voltage balancing circuit and recently proposed 5level inverter topologies. The multioutput flyback converter lowers the cost and performs the MPPT control by confirming the voltage balancing operation of the DClink capacitor voltages for the following multilevel inverter. The modified Hbridge topology uses fewer components compared with conventional topologies, which decreases the size and cost of the PCS. The staircase waveform from the multilevel inverter output helps in decreasing the values of the output filter components and mitigates highfrequency EMI.
The analysis and controller design for the proposed PCS scheme has been presented. The proposed scheme and derived controllers were verified using a 120 W hardware prototype. The MPPT operation for the gridconnected systems was verified by testing the prototype under a cloudyday profile using a TerraSAS PV simulator. The MPPT efficiency remained above 95% in most of the testing times during the varying irradiance conditions. The designed controllers for standalone mode were also tested for the 120 W output. The DClink capacitor voltages for the inverter stage were well balanced, and the AC output voltage waveform with 4.43% THD was achieved.
Acknowledgements
This work was supported by the Human Resources Development Program (No. 20144030200600) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea Government Ministry of Trade, Industry, and Energy.
BIO
Mohana Sundar Manoharan received his B.S. degree from the Department of Electrical Engineering of Kalasalingam University, India, in 2011. He received his M.S degree in 2013 and is currently working toward his Ph.D. degree at Soongsil University, Seoul, Korea. His current research interests include the PCS analysis and design.
Ashraf Ahmed received his B.Sc. and M.Sc. in Electrical Engineering from Assiut UniversityEgypt, Cairo UniversityEgypt in 1999 and 2005, respectively. He received his Ph.D. in Renewable Energy Control and Power Electronics from the University of Durham, UK in 2011. He is currently an Assistant Professor at Soongsil University, Seoul, Korea, and a researcher in the desert research center, CairoEgypt. His research interests include the analysis and design of switching power converters for renewable energy applications.
JungWon Seo received his B.S. and M.S. degrees from the Department of Electrical Engineering of Soongsil University, Seoul, Korea. His current research interests include the analysis and design of highfrequency switching converters and renewable energy applications.
JoungHu Park received his B.S., M.S., and Ph.D. degrees from Seoul National University, Seoul, Korea, in 1999, 2001, and 2006, respectively. He is currently an Assistant Professor at Soongsil University, Seoul, Korea. His current research interests include the analysis of highfrequency switching converters and renewable energy applications.
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