_{o}
, Equation (1) is used in practical applications. Resonant inductors L=L
_{1}
=L
_{2}
=L
_{3}
=L
_{4}
=40μH and resonant capacitors C=C
_{1}
=C
_{2}
=0.15μH are used.
The output capacitor is used to filter out high-order harmonic component of output voltage
u
_{Co}
. The greater the output capacitor, the better the filter. However, if the output voltage is constant, the greater the output capacitor C
_{o}
, the larger the reactive-current flowing in the output capacitor, which increases the size and weight of the inverter and reduces efficiency of the inverter. In general, the current flowing in the output capacitor is less than 50% I
_{o}
. Output power is 160VA. Output voltage is 48V. Output current is given as
The current flowing in the output capacitor is I
_{Co}
≤1.67A.
The current flowing in the output capacitor can be defined as
According to Equation (7), the output capacitor can be calculated as
where C
_{o}
=60μF is used.
IV. MATHEMATICAL MODEL AND SIMULATION RESULTS OF MODIFIED DUAL-BUCK INVERTER
Because the resonant period of the quasi-resonant circuit is equal to or less than the switching period, which does not comply with linear assumption of harmonic components, the traditional state-space method is no longer applicable. Symbolic analysis
[17]
and discrete mapping modeling
[18]
are used, and a mathematical model of the MDBI is proposed.
Seven state variables exist, i.e.,
u
_{C1}
,
i
_{C1}
,
u
_{Co}
,
u
_{C2}
,
i
_{C2}
,
i
_{D1}
, and
i
_{D2}
.Referencesignal
. The effective working status of the MDBI is shown in
Fig.3
.The differential equation of
Fig.3
can be obtained as follows:
Effective working status of MDBI.
Table I
shows the symbolic functions.
SYMBOLIC FUNCTION
Combing the state equation with the symbolic function gives a comprehensive estate function equation, as shown in equation (10).
The state equation of MDBI can be set as
The state variable x(t) is
where
Supposing the input is constant, a discrete iteration equation may be derived:
where H is sample time and
Equation (15) can be solved by iteration, and simulation results are shown in
Fig.4
.As shown in
Fig. 4
(a), output voltage
u
_{o}
can track reference signal
u
_{ref}
.
Fig. 4
(b) shows the voltage across resonant capacitor C
_{1}
u
_{C1}
, which validates that maximum voltage
u
_{C1max}
is close to 2U
_{d}
.
Fig. 4
(c) shows the driving signals of S
_{1}
and S
_{2}
. As shown in
Fig. 4
(c),the working time of the negative soft-switching resonant circuit is longer than the positive soft-switching resonant circuit when
u
_{ref}
<0 and vice versa.
Simulation results of the MDBI.
V. EXPERIMENT RESULTS
To verify the results from the simulation and test the usefulness of the MDBI, a 160-VA prototype is fabricated in the laboratory. The parameter of the MDBI is listed in
Table II
.
THE PARAMETER OF THE MDBI
THE PARAMETER OF THE MDBI
The experiment results are shown in
Fig. 5
.
Fig. 5
(a) depicts the output voltage of the DBI and the MDBI, which shows that the harmonic components of the DBI is much higher than that of the MDBI. When the output filter inductor and output capacitor for the DBI and the MDBI are identical,
C
_{o}
=60ìF and L
_{2}
=L
_{4}
=40μH,and the harmonic components of the DBI and the MDBI are 1.93% and 0.56%, respectively. If the harmonic components of the DBI and the MDBI are similar and the output capacitor is identical,
C
_{o}
=60ìF,and the capacity of output filter inductor for the DBI and the MDBI are L
_{2}
=L
_{4}
=450μH and L
_{2}
=L
_{4}
=40μH, respectively. The driving signal of S
_{3}
and S
_{1}
, and output voltage
u
_{o}
are shown from top to bottom in
Fig. 5
(b). The current flowing through inductors L
_{1}
and L
_{3}
, i.e.,
i
_{L1}
and
i
_{L3}
, and output voltage
u
_{o}
are illustrated in
Fig. 5
(c).As shown in
Figs. 5
(b) and
5
(c),output voltage
u
_{o}
is almost identical with sinusoidal. In the positive half cycle of the output voltage, the working time of the positive soft-switching resonant circuit is longer than that of the negative soft-switching resonant circuit. In the negative half cycle of the output voltage, the working time of the negative soft-switching resonant circuit is longer than the positive soft-switching resonant circuit. The waveforms of the voltage across resonant capacitor C
_{1}
,
u
_{C1}
, current flowing through inductor L
_{1}
,
i
_{L1}
, and the driving signal of S
_{1}
during a comparison process are depicted in
Fig. 5
(d). Switch S
_{1}
is turned on and off with ZCS. The voltage across resonant capacitor C
_{1}
,
u
_{C1}
, current flowing through inductor L
_{2}
,
i
_{L2}
, and the driving signal of S
_{2}
during a comparison process are shown from top to bottom in
Fig. 5
(e). Switch S
_{2}
works in ZCS. The voltage across resonant capacitor C
_{2}
,
u
_{C2}
, current flowing through inductor L
_{3}
,
i
_{L3}
, and the driving signal of S
_{3}
during a comparison process are depicted in
Fig. 5
(f). Switch S
_{3}
is turned on and off with ZCS. The waveforms of the voltage across resonant capacitor C
_{2}
,
u
_{C2}
, current flowing through inductor L
_{4}
,
i
_{L4}
, and the driving signal of S
_{4}
during a comparison process are shown in
Fig. 5
(g). Switch S
_{4}
works in ZCS. As illustrated in
Figs. 5
(d)-(g), the MDBI works in PDM mode, and the maximum voltage across the resonant capacitor is close to 2U
_{d}
. A very good agreement is shown between the simulation and the experiment results.
Experiment results of the MDBI.
VI. CONCLUSION
In this paper, an MBDI has been proposed. A detailed analysis of the topology and working principle of MDBI was performed. The three-level hysteresis controller with the PDM was used to obtain constant switching frequency, which reduced the dimensions of the MDBI and decreased the capacity of the filter inductor. Because of the quasi-resonant link, the MDBI can achieve ZCS at turn on and soft turnoff and decrease the harmonic components with low output voltage. The parameter selection principle of the MDBI was introduced, and the parameter used was given. The mathematical model of the MDBI using symbolic analysis and discrete mapping modeling has been presented. The mathematical model was verified by the simulation results. An experiment prototype was set up, and the experiment results were given. The simulation and experiment results validated the feasibility and correctness of the scheme.
Acknowledgements
This work was supported by Science and Technology Development Program of Shandong Province (No.2013 GSF11607) and the Fundamental Research Funds for the Central Universities of China (No.13CX06090A).
BIO
Rong Chen was born in Shandong, China, in 1976. He received his B.S. degree in industrial automation in 1998 and his M.S. degree in control theory and control engineering in 2001 from Shandong University of Science and Technology, Shandong, China. He is currently working toward his Ph.D. degree in control theory and control engineering at China University of Petroleum (Huadong), Qingdao, China. His research interests include electric machine drives, power electronics, high-frequency soft switching converters, and power factor correction.
Jia-Sheng Zhang was born in Shandong, China in 1957. He received his B.S. degree in applied electronic technology from China University of Petroleum, Shandong, China, in 1982 and his M.S. and Ph.D. degrees in electrical and electronic engineering from Beijing Jiaotong University, Beijing, China in 1988 and 1998, respectively. In 1982, he joined the Department of Electrical Engineering, China University of Petroleum, where he is currently employed as a full-time professor. His research interests include power electronics, motor drives, power quality control, renewable distributed power sources, and digital-signal-processor-based control of power converters.
Wei Liu was born in Hebei, China, in 1990. In 2014, he received the M.S. in electrical engineering and automation from China University of Petroleum, Shandong, China, where he is currently working toward his M.S degree in electrical engineering. His research interests include high-frequency DC–AC inverters, soft switching techniques, inverter modeling, and nonlinear control techniques.
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