THD Improvement of a Bidirectional Flyback [624080]

THD Improvement of a Bidirectional Flyback
Inverter by Using Sliding-Mode Control

Octavian Cornea Gheorghe-Daniel Andreescu Catalin-Cornel Patrascu, Nicolae Muntean
Electrical Engineering Department Automation & Applied Informatics Dept. Electrical Engineering Department
Politehnica University of Timisoara Politehnica University of Timisoara Politehnica University of Timisoara
Timisoara, Romania Timisoara, Romania Timisoara, Romania
[anonimizat] [anonimizat] [anonimizat] ,
[anonimizat]

Abstract —This paper is focused on a control method to
improve the THD factor of a bidirectional flyback inverter. The
inverter structure, presented in a previous paper of the authors,
contains a DC-DC converter tracking a rectified sinusoidal voltage waveform, and a full-bridge to obtain the AC waveform. The flyback inverter has a zero in the right half plane for the
output voltage transfer function in continuous conduction mode
(i.e., non-minimum phase system) that produces instability. A novel control method is proposed using a phase lead type compensator for the output voltage error to stabilize the inverter,
followed by a sliding mode-PI controller to ensure good dynamic
tracking performance and robustness. An average model for stability analysis is developed and used to test the flyback inverter operation with the proposed controller. A detailed
system switching model is implemented in PSIM to confirm the
results obtained by using the average model. The THD factor is reduced more than three times to a value below 1%, compared with the previous work of the authors. Simulation results involving the flyback inverter switching model prove that the
proposed control method provides a good dynamic tracking
performance with robust response to step variations in the output current and in the input power supply voltage.
Keywords—average model; bidirectional power flow; flyback
inverters; sliding mode control; stability analysis; total harmonic distortion (THD)
I. INTRODUCTION
Sinusoidal AC power supplies are required in various
applications, for example in renewable energy systems, uninterruptible power supplies, microgrids, etc. Usually, they have constant amplitude and frequency and in most cases a low harmonic content is a demand. PWM control strategies applied
for power inverters, that employ passive filters for harmonics
reduction, are often used [1-4].
Not all DC-AC inverters require galvanic isolation between
the DC and AC parts, but when it is needed, a DC-DC power converter including a transformer or a coupled inductor working at high frequency is used as a first stage, followed by an inverter [5, 6].
In some applications, which do not require galvanic
isolation, a simple bidirectional buck-boost converter tracking a rectified sinusoidal voltage waveform is used as a first DC-DC conversion stage at high frequency, and then a full bridge inverter working at low frequency is employed to obtain the
AC output voltage. The topology is simple and it was proved to produce good results even with a simple controller [7].
The buck-boost converter is replaced by a bidirectional
flyback DC-DC converter in [8, 9]. The output capacitor is split in two equal parts to replace the full bridge with a half bridge [8], reducing the number of transistors by two. This topology has two main drawbacks: the flyback output voltage is two times bigger, and the THD factor is high caused by the imbalance of the energy stored in the split capacitor. In [9], a single output capacitor is used as in [7] and a full bridge is
employed to obtain the AC output voltage with improved THD
factor. The stability analysis with Bode plots of small signal average model is used, and a simple phase lead type controller is proposed, which shows satisfactory results and proves robustness to step load changes.
THD improvement is a topic of concern for DC-AC
inverters in almost any application, and several solutions were presented in the literature [10, 11].
The voltage transfer function of the flyback converter in
CCM has a zero in the right half plane (non-minimum phase system), which produces some tough limitations in classical control techniques. In this context, sliding mode control (SMC) techniques, with fast switching to do rapid and robust dynamic responses, are a good choice. SMC is recommended for systems with uncertainties, variable parameters, or large disturbances, and also for tracking control [17].
A sliding-mode PI control using the output voltage error
and magnetizing current error is employed to regulate the output voltage of the DC-DC flyback converter in response to line, load and set point variations, with good simulation results [12, 13]. A second order sliding mode controller, i.e., a super-twisting sliding mode control, for flyback converter is developed in [13], [14], with reduced chattering effect and good dynamic response and robustness proved by simulation results [14] and by experimental results [15]. A control structure with two sliding mode controllers is proposed in [16] to obtain a low THD value.
This paper is focused to improve the THD factor of the
bidirectional flyback inverter [9] by using a novel control containing: i) a phase lead type compensator to stabilize the
488 978-1-4763-7239-8/15/$31.00 ' 2015 IEEE

inverter, followed by ii) a sliding-mode PI controller for output
voltage regulation to ensure good dynamic tracking performance and robustness. The main advantages of the proposed control method are: it uses only one voltage sensor (without current sensor), is robust to load and input voltage variations, and assures tracking control with very low output voltage THD.
II. F
LYBACK INVERTER TOPOLOGY
The main goal of the control system for the flyback inverter
presented in Fig. 1 is to track a reference rectified sinusoidal waveform on the output capacitor C in the DC-DC convertor
stage working at high frequency (20 kHz). To obtain the AC waveform, a full-bridge is used in the second stage working at low frequency (100 Hz). For this purpose, the energy flow must be bidirectional, which is possible by using bidirectional power switches (pair of transistor, diode in parallel).
The description of the flyback inverter topology and its four
operating modes are presented in [9]. Here it is pointed out that the two power transistors T
1-T2, switching at high frequency,
are driven by complementary signals, so when one is in on
state, the other is in off state. The transistor state depends on the
command pulse and its current flow direction in primary or secondary part of the flyback transformer.
The bidirectional power flow is highlighted in what
following. When T
1 switches off, the power transfer is from
primary to secondary through D 2 that switches on, while T 2 is
off even if it has positive gate drive voltage. T 2 will switch on,
by carry the reverse current in the secondary, if D 2 switches off
before the end of the switching period. In this case the
secondary current will not be zero (no interrupt current),
because it is reversed by T 2. If T 2 is a MOSFET, it will take
over the D 2 current after the dead-time between T 1 and T 2
driven signals would be elapsed. Same considerations are also valid for T
1.
Therefore, in opposition to the normal DC-DC flyback
converter that in operation can be run in discontinuous conduction mode (DCM), the circuit shown in Fig. 1 goes always in continuous conduction mode (CCM), which is a very important aspect for the operation and stability analysis. This means that the operation of the flyback converter can be investigated using the average model for CCM, which is presented below.

Fig. 1. Flyback inverter schematic. III. AVERAGE MODEL AND STABILITY ANALYSIS
A. Large Signal Average Model
In order to simplify the circuit that will be averaged, it is
possible to take out the low frequency full bridge and thus, the load resistance R appears directly connected in parallel with the
output capacitor C. The full bridge only connects the voltage
on C to R with corresponding sign to obtain AC output voltage.
In the resulting circuit, given in Fig. 2, there are also present the parasitic resistances that influence the frequency response.
The chosen state variables are: x
1 – the current in the
magnetization inductance of the flyback transformer, and x2 –
the output capacitor voltage, thus the state vector is x = [x1 x2]T.
The circuit has two possible states: i) state on, with T 1 or D 1
in conduction, T 2 and D 2 blocked; and ii) state off, with T 1 and
D1 blocked, T 2 or D 2 in conduction. The detailed schematics of
these two states are presented in [9] and are not repeated here. Only the state-space equations and the corresponded matrices in both states are given. For state on they are:
ݔሶൌܣ
ଵݔ൅ܤ ଵܸ௜௡, (1)
ܣଵൌ൥െ௥భ
௅0
0െଵ
ோ஼൩, ܤଵൌቈଵ
௅
0቉. (2)
For state off:
ݔሶൌܣ ଶݔ൅ܤ ଶܸ௜௡, (3)
ܣଶൌ቎െ௥಴ା௥మ
௅௞మ െଵ
௅௞
ଵ
௞஼െଵ
ோ஼቏ , ܤଶൌቂ0
0ቃ, (4)
where L and r1 is the flyback transformer primary inductance
and resistance, respectively, r2 is the flyback transformer
secondary resistance, rc is the filter capacitor ESR, and k is the
transformation ratio.
Combining (1-4) by the state-space averaging method, the
average model of the flyback inverter is obtained, depending
on D – the PWM duty-cycle of the transistor T 1:
ݔሶൌݔܣ ൅ܸܤ ௜௡, (5)
ܣൌ቎ଵ
௅ቀെݎ ଵ൅௥మା௥಴
௞మቁܦെ௥మା௥಴
௅௞మଵ
௞௅ሺܦ െ 1ሻ
െଵ
௞஼ሺܦ െ 1ሻ െଵ
ோ஼቏, ܤ ൌ ቈଵ
௅
0቉ܦ( 6)

Fig. 2. Simplified circuit of the flyback inverter used to determine the state-
space average model.
489

Eq. (5), with time variant matrices (6) depending on D,
fully characterize the large signal average model of the flyback
inverter and can be used for digital simulation to investigate the
inverter ability to track the reference signal.
B. Small Signal Average Model
An investigation into the flyback inverter operations reveals
that oscillations in the output capacitor voltage can appear at high voltage reference values, and it is found that the steady-
state operating point at X
20 = 200V (close to the mean rectified
sinusoidal waveform) can be used for stability analysis.
The steady state vector X0(X10, X20)T for any operating point
determined by a certain known value is given by:
ܺ଴ൌሺ െ ܣିଵܤሻܸ ௜௡. (7)
The state-space small signal average model [18] is derived
from (5), for small variation d of D with Vin constant:
ݔ෤ሶൌݔܣ ෤൅ܤ ௗ݀ሚ, (8)
where Bd depends on the operating point:
ܤௗൌ቎െ௥భ
௅ଵ
௞௅
െଵ
௞஼0቏·൤ܺଵ଴
ܺଶ଴൨൅ቈଵ
௅
0቉ܸ௜௡. (9)
The output voltage Vout is very close to the state variable x2,
the difference between them is given by the voltage drop on rc.
The resistance rc is estimated to have a very low value of 10
mΩ, and it only has influence at frequencies that are outside of
the frequency range relevant for stability.
C. Stability Analysis and Compensator Design
The stability analysis employs the Bode plot of the open
loop transfer function x෤2 / d෨ obtained from (8), shown in Fig. 3.
It is clear that the system does not have the phase margin
required for stability with unity feedback.
A phase lead type compensator having the transfer function
with one zero and one pole was proposed in [9] to assure the stability. A phase margin of 34 degree at a cutoff frequency of 2.55 kHz was obtained for the compensated flyback inverter. In this paper, to boost more the phase margin, a compensator transfer function with two poles and two zeroes given by (10)
is considered for the compensation.
ܪ௖ሺݏሻൌ0 . 1·ቀ௦ାହ଴଴଴
௦ାଵହ଴଴଴ቁଶ
(10)
The Bode plot of the compensated system, shown in Fig. 4,
exhibit a phase margin of 49 ° at a cutoff frequency of 2.28
kHz. The usage of the compensator Hc(s) in the output voltage
control loop eliminates or highly reduces oscillations that would otherwise appear in the controlled voltage.
Fig. 3. Bode plot of the uncompensated flyback inverter – instable.

Fig. 4. Bode plot of the flyback inverter compensated by (10) – stable.
IV. CONTROL STRUCTURE AND IMPLEMENTATION
The large signal average model described in Section III is
implemented in Matlab/Simulink environment. The block scheme of the flyback inverter model is presented in Fig. 5. Two function blocks,
Fcn1 and Fcn2, are used to calculate the
time derivative of the state variables x1 and x2, according to (5)
and (6).
The structure of the sliding mode-PI (SM-PI) controller is
pointed out in Fig. 6. The compensator Hc(s) acts on the output
voltage error and is serially connected with the controller. Only the sign of the transformed error is used at the PI controller input, giving the character of sliding-mode regulation. The PI controller
kp(1+1/ Tis) has the parameters kp=0.25 and Ti =0.002. -40-20020406080Magnitude (dB)
101
102
103
104
105
10690135180225270315360Phase (deg)
Frequency (Hz)
-60-40-2002040Magnitude (dB)
10110210310410510690135180225270315360405Phase (de g)
Frequency (Hz)
490

Fig. 5. Block scheme of the control system for flyback inverter using large
signal average model and SM-PI controller implemented in Matlab/Simulink.

Fig. 6. Controller structure: phase lead type compensator Hc(s) and sliding
mode-PI (SM-PI) controller. The SM-PI controller generates the control signal Vd ∈[-1,
1] which is translated to the duty cycle D ∈ [0, 1] by a simple
model of the PWM modulator: D = (Vd +1)/2.
The parameter values of the average model used in Fig. 5
are presented in Table I being for a flyback inverter prototype that is under construction at the moment. The simulation with the average model is used to check that the average output capacitor voltage tracks the reference voltage waveform.
A detailed switching model is implemented in PSIM for the
bidirectional flyback inverter with SM-PI controller. It is presented in Fig. 7, some details are removed from the model for the sake of clarity. The switching model contains also the low frequency full bridge to obtain AC voltage across the load.
TABLE I. INVERTER PROTOTYPE DATA
Name Value Unit Specification
Vin 50 V Input voltage
L 20 µH Flyback transformer primary winding inductance
L1 1.6 µH Flyback transformer primary winding leakage
inductance
r1 4.5 mΩ Flyback transformer primary winding resistance
L2 20 µH Flyback transformer secondary winding leakage
inductance
r2 50 mΩ Flyback transformer secondary winding resistance
C 100 µF Filter capacitor
rc 10 mΩ Filter capacitor ESR
R 50 Ω Load resistance
k 5 Transformation ratio of the flyback transformer
finv 20 kHz Inverter switching frequency

Fig. 7. Control system of the flyback inverter using a detailed switching model and SM-PI controller with Hc(s) compensator implemented in PSIM. T1T2
100u
COMP0.95
-0.9532520u
Vc
10.01
IC1
Vin
VoutS2
S3RAIout
V20
S2S3
Vc
Ti=0.002
Sign
Iin
Kkp=0.25
H(s)500.01
Vref
325
S2
S31
Vdzeros(s)
poles(s)
Hc(s)
(Eq. 10) Sign Saturation
PI(s)
PI Controlle r 2
uc 1
uc*
SM-PI Controller x1
VinD
dx2/dtdx1/dt
x2- Capacitor Voltage x1- Flyback Inductor
Magnetization Current
Vinuc*
uc
Voltage
Controlle r Generato r D
PWM
Modulato r
Model
1
s f(u)Fcn2f(u)Fcn1
|u|
Abs 1
s
Flyback Inverto rx
2 Vd
491

Fig. 8. Flyback inverter normal operation waveforms. Top: simulation results
from the average model implemented in Matlab/Simulink. Other waveforms: simulation results from the detailed switching model implemented in PSIM.
V. SIMULATION RESULTS
Fig. 8 highlights that the simulations using the average
model (5) and the detailed switching model give similar results and prove the ability of the proposed controller to follow the rectifier sine wave reference with very low voltage THD. The output power is light higher than 100% rated power of 1kW.
The SM-PI controller brings a reduction of the THD factor
at a value of 1%, which is an important improvement over the controller presented in [9] where THD = 3.75%. The better result is explained especially by the better tracking of the reference voltage close to the zero crossover. This is clear if the output voltage is compared with the waveform shown in [9].
However, the peak value of the primary current is
approximately 10% higher comparing with [9], which is a little disadvantage.
To check the specific robustness of the SM-PI controller, a
load step change from 55 Ω (P
out≈1050W) to 550 Ω (Pout≈100W)
and vice versa are simulated. The system responses are shown in Fig. 9, where the transient distortion of the output waveform at the moment of load changing is almost imperceptible. The flyback inverter operates at high loads (10% rated power) with
an output voltage THD factor even lower than 1%.
Fig. 9. Flyback inverter responses to step output load variations: R load
changes from 55 Ω (Pout≈1050W) to 550 Ω (Pout≈100W) and vice-versa.

Fig. 10. Flyback inverter responses to step changes in the input voltage.
Good results for the transient responses are also obtained in
the case of input voltage step variation, pointed out in Fig. 10.
Even in the case less favorable than in reality ( േ10V step input
voltage changes), the transient distortion in the output
waveform is acceptable. 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.060100200300Reference and Actual Capacitor Voltage – MatlabVc , Vref (V)
0.02 0.03 0.04 0.05 0.060100200300Reference and Actual Capacitor Voltage – PS IMVc , Vref (V)
0.02 0.03 0.04 0.05 0.06-300-1500150300Output Voltage – PSIMVout (V)
0.02 0.03 0.04 0.05 0.06-1000100200Primary and S econdary Currents – PS IMIpri , Isec (A)
0.02 0.03 0.04 0.05 0.06-1000100200Magnetization Current – PS IM
Time (s )Imag (A) 0.02 0.03 0.04 0.05 0.06 0.07 0.080100200300Reference and Actual Capacitor Voltage – PSIMVc , Vref (V)
0.02 0.03 0.04 0.05 0.06 0.07 0.08-300-1500150300Output Voltage – PSIMVout (V)
0.02 0.03 0.04 0.05 0.06 0.07 0.08-5-2.502.55Load Current – PSIM
Time (s)Iload (A)
0.02 0.03 0.04 0.05 0.06405060Input Voltage – PSIMVin (V)
0.02 0.03 0.04 0.05 0.060100200300Vc , Vref (V)Reference and Actual Capacitor Voltage – PSIM
0.02 0.03 0.04 0.05 0.06-300-1500150300Output Voltage – PSIMVout (V)
Time (s)
492

VI. CONCLUSION
This paper is focused on a control method to improve the
THD factor for a single phase bidirectional flyback inverter.
The output voltage transfer function of the flyback inverter
in continuous conduction mode (CCM) has a zero in the right half plane (i.e., non-minimum phase system) that produces instability. A novel control method for the output voltage regulation is proposed having a phase lead type compensator to stabilize the inverter, followed by a sliding mode-PI controller to ensure good dynamic tracking performance and robustness.
To guarantee the system stability, a phase lead compensator
with a transfer function with two poles and two zeros is introduced in the output voltage loop, acting on the error signal, and then it is serial connected with a robust sliding mode-PI controller.
Two simulation models, i.e., a large signal average model
and a detailed switching model, with parameter data from a flyback inverter prototype under construction, are used in tests. They prove the inverter tracking capability with the proposed
controller to follow the rectifier sine wave reference with very
low voltage THD, showing similar results. The reference voltage is tracked better comparing to the controller employed before, especially at low voltage levels, close to the zero crossover. Therefore, the output voltage THD factor is reduced from 3.75% to 1%.
The system robustness is tested to step variations in the
output current (load) and in the input source voltage. In both cases, the SM-PI controller is able to track the voltage reference waveform without oscillations. Only a small voltage transient deviation is seen in the output waveform at the moment of step change.
A
CKNOWLEDGMENT
This work was developed through the Romanian
Partnerships in priority areas program – PN II, with the support of ANCS, CNDI – UEFISCDI, project no. 36/2012.
R
EFERENCES
[1] S.B. Kjaer, J.K. Pedersen, and F. Blaabjerg, “A review of single phase
grid-connected inverter for photovoltaic modules,” IEEE Trans. on
Industry Applications , vol. 41, no. 5, pp. 1292-1306, Sep./Oct. 2005.
[2] R. Majdoul, E. Abdelmounim, M. Aboulfatah, and A. Abouloifa, “The
performance comparative of backstepping, sliding mode and PID controllers designed for a single-phase inverter UPS,” in Proc.
International Conf. on Multimedia Computing and Systems (ICMCS
2014) , pp. 1584-1589, Apr. 2014. [3] P. Sanchis, A. Ursaea , E. Gubia , and L. Marroyo, “Boost DC-AC
Inverter: A new control strategy,” IEEE Trans. on Power Electronics ,
vol. 20, no. 2, pp. 343-353, Mar. 2005.
[4] F.S.F. e Silva, L.A. de S. Ribeiro, and J.G. de Matos, “Bidirectional DC-
AC converter for isolated microgrids with voltage unbalance reduction
capabilities,” in Proc. Energy Conversion Congress and Exposition
(ECCE 2014) , pp. 4985-4991, Sep. 2014.
[5] Quan Li and P. Wolfs, “A review of the single phase photovoltaic
module integrated converter topologies with three different DC link configurations,” IEEE Trans. on Power Electronics , vol. 23, no. 3, pp.
1320-1333, May 2008.
[6] K.J. Lallu Mol and K. Muhammedali Shafeeque, “PV fed flyback DC-
AC inverter with MPPT control,” in Proc. Annual International Conf. on
Emerging Research Areas: Magnetics, Machines and Drives
(AICERA/iCMMD 2014), pp. 1-6, July 2014.
[7] A.M. Salamah, S.J. Finney, and B.W. Williams, “Single-phase voltage
source inverter with a bidirectional buck–boost stage for harmonic injection and distributed generation,” IEEE Trans. on Power
Electronics , vol. 24, no. 2, pp. 376-387, Feb. 2009.
[8] E. Guran, O. Cornea, and N. Muntean, “Novel topology flyback inverter
for a microgrid system,” in Proc. 6th IEEE International Workshop on
Soft Computing Applications (IEEE-SOFA 2014) , July 2014.
[9] G.-D. Andreescu, O. Cornea, N. Muntean, and E. Guran, “Bidirectional
flyback inverter with low output voltage THD,” in Proc. 10th Jubilee
IEEE International Symposium on Applied Computational Intelligence
and Informatics (SACI 2015) , pp. 95-99, May 2015.
[10] M.S. Zadeh and S. Farhangi, “Dynamics and THD improvement in AC
programmable power supplies,” in Proc. IEEE International Symposium
on Industrial Electronics (ISIE 2006), vol. 2, pp. 1149-1154, July 2006.
[11] R.G. Wandhare and V. Agarwa, “A novel technique for THD control in
grid connected photovoltaic systems using step variable inductor approach,” in Proc. 35th IEEE Photovoltaic Specialists Conf. (PVSC
2010), pp. 2844-2848, June 2010.
[12] H.K. Iqbal and G. Abbas, “Design and analysis of SMC for second order
DC-DC flyback converter,” in Proc. IEEE 17th International Multi-
Topic Conf. (INMIC 2014), pp. 533-538, Dec. 2014.
[13] M. Salimi and V. Hajbani, “Sliding-mode control of the DC-DC flyback
converter in discontinuous conduction mode,” in Proc. 6th Power
Electronics, Drives Systems & Technologies Conf. (PEDSTC 2015) , pp.
13-18, Feb. 2015.
[14] Ming-Tsan Lin, “A second order sliding mode controller for the flyback
converter,” in Proc. IEEE International Conf. on Systems, Man and
Cybernetics (SMC 2014) , pp. 2289-2292, Oct. 2014.
[15] Huangfu Yigeng and Wu Yu, “A robust flyback converter based on high
order sliding mode control for fuel cell,” in Proc. 40th Annual Conf. of
the IEEE Industrial Electronics Society (IECON 2014) , pp. 3936-3940,
Oct. 2014.
[16] J. Le Claire and M.F. Benkhoris, “Low THD voltage source involving
two sliding mode controllers,” in Proc. 38th Annual Conf. on IEEE
Industrial Electronics Society (IECON 2012), pp. 525-530, Oct. 2012.
[17] V. Utkin, J. Guldner, and J. Shi, Sliding Mode Control in Electro-
Mechanical Systems , 2nd Ed., Boca Raton, USA: CRC Press, Taylor &
Fracis, 2009.
[18]
N. Mohan, T.M. Undeland, and W.P. Robbins, Power Electronics :
Converters, Applications, and Design, 3rd Ed., USA: John Wiley &
Sons, 2003.

493