Flyback Converter for Solid-State Lighting Applications with Partial Energy Processing

: The main contribution of this paper is to show a new AC/DC converter based on the rearrangement of the ﬂyback converter. The proposed circuit only manages part of the energy and the rest is delivered directly from the source to the load. Therefore, with the new topology, the efﬁciency is increased, and the stress of the components is reduced. The rearrangement consist of the secondary of the ﬂyback is placed in parallel with the load, and this arrangement is connected in series with the primary side and the rectiﬁed voltage source. The re-arranged ﬂyback is only a reductive topology and with no magnetic isolation. It was studied as a power supply for LEDs. A low frequency averaged analysis (LFAA) was used to determine the behavior of the proposed circuit and an equivalent circuit much easier to analyze was obtained. To validate the theoretical analysis, a design methodology was developed for the re-arranged ﬂyback converter. The designed circuit was implemented in a 10 W prototype. Experimental results showed that the converter has a THDi = 21.7% and a PF = 0.9686.


Introduction
Nowadays, LEDs are considered the future of lighting, since they have an increasing demand caused by the long useful life that they have, around 50,000 h [1] and the lighting efficiency they present, which can reach up to 160 lm/W in the laboratory. Power supplies must meet power quality standards, which contemplate total harmonic content (THDi) at the input current and power factor (PF) [2]. The guidelines for lighting systems connected to the line are specified in the IEC61000-3-2 class C standard [3].
In general, it is common to find LED power supplies with a power factor correction (PFC) stage, after the bridge of the rectifier diode, to ensure regulatory compliance. The single-stage PFC converter has the advantage of having high efficiency since only one converter processes the total energy. However, the power supply also must convert the AC power from the main line to the constant power that the LED needs for good performance [4,5], but to achieve this, it is necessary to have an element that can store a large amount of pulsing energy. A large capacitor could solve this problem; however, large capacitance values are generally handled in electrolytic capacitors, which generate a bottleneck due to their short lifespan, compared to LEDs, so it is recommended to avoid their use [6][7][8]. In order to carry out the analysis of the rearranged flyback converter, a low-frequency average analysis (LFAA) was used; This is used to know in a general way if a topology complies with the corresponding regulations, knowing its efficiency, and evaluating its feasibility of implementation. The LFAA model the behavior of the flyback converter at the frequency line. At this frequency and due to the discontinues conduction mode (DCM) of the flyback converter, the primary side can be represented as a loss-free resistance (RF), this resistance represents the average power delivered to the primary side of the flyback converter (PFi), the energy "consumed" by this resistance is transferred to the secondary side of the flyback converter that is modeled as a direct current voltage source (VF), as shown in Figure 2.
On the LED side, it can be modeled as a series direct DC voltage source with a resistor, as shown in Figure 3. Figure 4 shows the equivalent low-frequency scheme corresponding to the circuit proposed in Figure 1. Where: vr is the rectified Voltage, ir is the rectified Current, VF is the average voltage in the secondary of the flyback converter, RF Loss-free resistance representing the primary of the flyback converter, VD representing the LED threshold voltage of the LED model, RD is the resistance of the LED model.   In order to carry out the analysis of the rearranged flyback converter, a low-frequency average analysis (LFAA) was used; This is used to know in a general way if a topology complies with the corresponding regulations, knowing its efficiency, and evaluating its feasibility of implementation. The LFAA model the behavior of the flyback converter at the frequency line. At this frequency and due to the discontinues conduction mode (DCM) of the flyback converter, the primary side can be represented as a loss-free resistance (R F ), this resistance represents the average power delivered to the primary side of the flyback converter (P Fi ), the energy "consumed" by this resistance is transferred to the secondary side of the flyback converter that is modeled as a direct current voltage source (V F ), as shown in Figure 2. In order to carry out the analysis of the rearranged flyback converter, a low-frequency average analysis (LFAA) was used; This is used to know in a general way if a topology complies with the corresponding regulations, knowing its efficiency, and evaluating its feasibility of implementation. The LFAA model the behavior of the flyback converter at the frequency line. At this frequency and due to the discontinues conduction mode (DCM) of the flyback converter, the primary side can be represented as a loss-free resistance (RF), this resistance represents the average power delivered to the primary side of the flyback converter (PFi), the energy "consumed" by this resistance is transferred to the secondary side of the flyback converter that is modeled as a direct current voltage source (VF), as shown in Figure 2.
On the LED side, it can be modeled as a series direct DC voltage source with a resistor, as shown in Figure 3. Figure 4 shows the equivalent low-frequency scheme corresponding to the circuit proposed in Figure 1. Where: vr is the rectified Voltage, ir is the rectified Current, VF is the average voltage in the secondary of the flyback converter, RF Loss-free resistance representing the primary of the flyback converter, VD representing the LED threshold voltage of the LED model, RD is the resistance of the LED model.  On the LED side, it can be modeled as a series direct DC voltage source with a resistor, as shown in Figure 3. In order to carry out the analysis of the rearranged flyback converter, a low-frequency average analysis (LFAA) was used; This is used to know in a general way if a topology complies with the corresponding regulations, knowing its efficiency, and evaluating its feasibility of implementation. The LFAA model the behavior of the flyback converter at the frequency line. At this frequency and due to the discontinues conduction mode (DCM) of the flyback converter, the primary side can be represented as a loss-free resistance (RF), this resistance represents the average power delivered to the primary side of the flyback converter (PFi), the energy "consumed" by this resistance is transferred to the secondary side of the flyback converter that is modeled as a direct current voltage source (VF), as shown in Figure 2.
On the LED side, it can be modeled as a series direct DC voltage source with a resistor, as shown in Figure 3. Figure 4 shows the equivalent low-frequency scheme corresponding to the circuit proposed in Figure 1. Where: vr is the rectified Voltage, ir is the rectified Current, VF is the average voltage in the secondary of the flyback converter, RF Loss-free resistance representing the primary of the flyback converter, VD representing the LED threshold voltage of the LED model, RD is the resistance of the LED model.    Figure 4 shows the equivalent low-frequency scheme corresponding to the circuit proposed in Figure 1. Where: v r is the rectified Voltage, i r is the rectified Current, V F is the average voltage in the secondary of the flyback converter, R F Loss-free resistance representing the primary of the flyback converter, V D representing the LED threshold voltage of the LED model, R D is the resistance of the LED model. The loss free resistance is evaluated with the following expression: where IRrms is the RMS value of ir.

Analysis of the Power Factor (PF) and the Current Total Harmonic Distortion (THDi) Using LAAA
In Figure 4, it is observed that the LED is powered by the voltage source VF, it is interesting to obtain the expression of ir. applying Kirchhoff's voltage law to the scheme we obtain: Additionally, the following observations were made: 1. The topology is reductive, so it is always true that VF < Vr, where Vr is the peak voltage of vr(t), as shown in (4). 2. There will be current flow through RF if vr > VF, when vr < VF the current ir(t) = 0, as Vr approaches VF there will be very long death times. Therefore, the ir waveform will be the same as iac at T/2 as shown in Figure 5.
where tx is a constant that represents the dead time, which is given by: where m= VF/Vr is the gain of the proposed converter, ω is the angular frequency and f is the line frequency. In order to calculate the PF and THDi in the proposed converter, it is necessary to know the harmonics of the input current waveform (iac), shown in (6). For this, tx can be used in the integration limits of the calculation of the Fourier coefficients of iac in (7) and verify if the topology meets the requirements of IEC61000-3-2 class C. The loss free resistance is evaluated with the following expression: where I Rrms is the RMS value of i r .

Analysis of the Power Factor (PF) and the Current Total Harmonic Distortion (THDi) Using LAAA
In Figure 4, it is observed that the LED is powered by the voltage source V F , it is interesting to obtain the expression of i r . applying Kirchhoff's voltage law to the scheme we obtain: Additionally, the following observations were made: 1.
The topology is reductive, so it is always true that V F < V r , where V r is the peak voltage of v r (t), as shown in (4).

2.
There will be current flow through R F if v r > V F , when v r < V F the current i r (t) = 0, as V r approaches V F there will be very long death times. Therefore, the i r waveform will be the same as i ac at T/2 as shown in Figure 5. The waveform being analyzed (iac) is an odd function, therefore there are only odd harmonics. The THDi is obtained from (8), where I1 is the fundamental component that is defined in (9), and In is the amplitude of the n-th harmonic that is defined in (10).
Returning to (8) and assuming the main voltage is sinusoidal the PF is obtained by: Figure 6 shows the plot of (8), assuming THDi ≤ 32%., it can be seen that the gain m can vary from 0 to 0.46. If m > 0.46 the THDi will be very high and the power factor PF very low.
Regarding the requirements of the IEC61000-3-2, Figure 7 shows the curves for the odd harmonics from n = 3 to n = 15, it is observed that the topology is limited in a range of 0 < m < 0.41.
From Figure 8, where (11) is plotted, it can be seen that the topology meets the requirements of a PF > 90 without a problem in a range of 0 < m < 0.41.  v r = V r |sin ωt| (4) where t x is a constant that represents the dead time, which is given by: where m = V F /V r is the gain of the proposed converter, ω is the angular frequency and f is the line frequency. In order to calculate the PF and THDi in the proposed converter, it is necessary to know the harmonics of the input current waveform (i ac ), shown in (6). For this, t x can be used in the integration limits of the calculation of the Fourier coefficients of i ac in (7) and verify if the topology meets the requirements of IEC61000-3-2 class C.
(a n cos(nωt) + b n sin(nωt)) ac The waveform being analyzed (i ac ) is an odd function, therefore there are only odd harmonics. The THDi is obtained from (8), where I 1 is the fundamental component that is defined in (9), and I n is the amplitude of the n-th harmonic that is defined in (10).
Returning to (8) and assuming the main voltage is sinusoidal the PF is obtained by: (11) Figure 6 shows the plot of (8), assuming THDi ≤ 32%., it can be seen that the gain m can vary from 0 to 0.46. If m > 0.46 the THDi will be very high and the power factor PF very low.  Regarding the requirements of the IEC61000-3-2, Figure 7 shows the curves for the odd harmonics from n = 3 to n = 15, it is observed that the topology is limited in a range of 0 < m < 0.41.     From this section it is concluded that the proposed topology complies with all applicable standards in the range of 0 < m < 0.41.

Analysis of the Power Flow in the Converter
In order to analyze the power flow in the proposed converter the following concepts are defined in Table 1. Figure 9 shows the power flow diagram of a conventional flyback compared with the proposed rearranged flyback. In this diagram, it is easier to understand the operation of the proposed converter, in which it is observed as part of the input power P i is supplied directly to the load, while the other fraction is processed by the P Fi flyback converter. Therefore, the total efficiency concerning the conventional flyback will be improved.

Symbol
Description Definition P L Average power consumed by the load Average power delivered by the main source

P Fi
Average power delivered to the primary side of the flyback converter (14) P Fo Average power delivered by the secondary side of the flyback converter Q Ratio between the power processed by the flyback converter and the input power of the proposed converter η Efficiency of the proposed converter η = P L P i (17) η F Efficiency of the flyback η F = P Fo P Fi  Figure 9 shows the power flow diagram of a conventional flyback compared with the proposed rearranged flyback. In this diagram, it is easier to understand the operation of the proposed converter, in which it is observed as part of the input power Pi is supplied directly to the load, while the other fraction is processed by the PFi flyback converter. Therefore, the total efficiency concerning the conventional flyback will be improved.
The percentage of power processed by the flyback is called the constant Q. The range of Q must be 0 < Q < 1, if Q is greater than 1 there is no point in implementing the topology since instead of having benefits, low efficiency and greater electrical size would be obtained concerning an isolated basic flyback. According to Figure 9 the total efficiency η of the converter will be: This equation was plotted in Figure 10 assuming an arbitrary value for the flyback efficiency ηF = 0.9. As can be seen in this figure, regardless of the Q value, the efficiency of The percentage of power processed by the flyback is called the constant Q. The range of Q must be 0 < Q < 1, if Q is greater than 1 there is no point in implementing the topology since instead of having benefits, low efficiency and greater electrical size would be obtained concerning an isolated basic flyback.
According to Figure 9 the total efficiency η of the converter will be: This equation was plotted in Figure 10 assuming an arbitrary value for the flyback efficiency η F = 0.9. As can be seen in this figure, regardless of the Q value, the efficiency of the proposed converter will always be greater than the efficiency of a conventional flyback. Total efficiency will increase as the flyback converter processes less energy. the proposed converter will always be greater than the efficiency of a conventional flyback. Total efficiency will increase as the flyback converter processes less energy. Substituting (3) and (4) in the expressions of Table 1 with the definition of m:  Table 1 with the definition of m: In Figure 11, the graph (23) is obtained, in which it is observed that when m increases, Q decreases; this is favorable since the flyback by processing fewer power benefits the total efficiency of the system.

Design of the Rearranged Flyback
For the implementation of the rearranged flyback converter circuit, LEDs were purchased from the manufacturer Seoul Semiconductor with part number SAW0LH0A. An array of 8 LEDs was made in parallel, which is shown in Figure 14.
The resulting specifications of the LED array are shown in Table 2, which will be used to simulate at low frequency. In order to calculate the components of the converter, some design parameters must be proposed, which are shown in Table 3, among them it is worth noting that the flyback dead time is defined in DCM for AC-DC converters [16]. With the values of Table 3, and the equations previously developed, the necessary values for the implementation of the converter are shown in Table 4.

Design of the Rearranged Flyback
For the implementation of the rearranged flyback converter circuit, LEDs were purchased from the manufacturer Seoul Semiconductor with part number SAW0LH0A. An array of 8 LEDs was made in parallel, which is shown in Figure 14.
The resulting specifications of the LED array are shown in Table 2, which will be used to simulate at low frequency. In order to calculate the components of the converter, some design parameters must be proposed, which are shown in Table 3, among them it is worth noting that the flyback dead time is defined in DCM for AC-DC converters [16]. With the values of Table 3, and the equations previously developed, the necessary values for the implementation of the converter are shown in Table 4.  Table 4. Design of the proposed converter.

Parameter Equation and Value
Gain In order to evaluate the proposed circuit before the implementation, a simulation of the circuit was made in Spice. In Figure 12, The schematic is shown, and the results of the simulation are shown in Figure 13.  In order to evaluate the proposed circuit before the implementation, a simulation of the circuit was made in Spice. In Figure 12, The schematic is shown, and the results of the simulation are shown in Figure 13.

Experimental Results
A laboratory prototype has been built to carry out experimental tests and evaluate the performance of the proposed converter. an IR2106 driver and a MOSFET IRF840 were used. The prototype for experimental tests is shown in Figure 14. Figure 15 shows the main line current and voltage waveforms. As can be seen in this Figure the current waveform shows the death time tx predicted by the LFAA and this waveform is similar to the theoretical waveform shown in Figure 5.
The THDi of the input waveforms of Figure 15 was measured with the HIOKI model PW3198 power quality analyzer, which is shown in Figure 16, which shows that the THDi is close to 21.7% and the harmonics are within the requirements of the EN 61000-3-2 class C standard. As for the PF obtained in experimental tests with the energy quality meter, it is shown to be 0.9686 in Figure 17. The instantaneous voltage of the LED lamp obtained in experimental tests is shown in Figure 18. The average voltage applied to the LED was VLED = 60.5, the same of the specifications, the voltage ripple obtained was 18.16%. The instantaneous current of the LED lamp obtained in experimental tests is shown in Figure 19. The average current applied to the LED was ILED = 160.3 mA, the current ripple obtained was 212%. Finally, in Figure 20 the instantaneous output power in the LED is shown. which shows an average power of Po = 10.62 W.
Finally, Tables 5 and 6 summarize what was obtained in the implementation of the topology and the percentages of error obtained, and as expected, there are parameters

Experimental Results
A laboratory prototype has been built to carry out experimental tests and evaluate the performance of the proposed converter. an IR2106 driver and a MOSFET IRF840 were used. The prototype for experimental tests is shown in Figure 14. Figure 15 shows the main line current and voltage waveforms. As can be seen in this Figure the current waveform shows the death time t x predicted by the LFAA and this waveform is similar to the theoretical waveform shown in Figure 5.
The THDi of the input waveforms of Figure 15 was measured with the HIOKI model PW3198 power quality analyzer, which is shown in Figure 16, which shows that the THDi is close to 21.7% and the harmonics are within the requirements of the EN 61000-3-2 class C standard. As for the PF obtained in experimental tests with the energy quality meter, it is shown to be 0.9686 in Figure 17.
The instantaneous voltage of the LED lamp obtained in experimental tests is shown in Figure 18. The average voltage applied to the LED was V LED = 60.5, the same of the specifications, the voltage ripple obtained was 18.16%. The instantaneous current of the LED lamp obtained in experimental tests is shown in Figure 19. The average current applied to the LED was I LED = 160.3 mA, the current ripple obtained was 212%. Finally, in Figure 20 the instantaneous output power in the LED is shown. which shows an average power of P o = 10.62 W.

Experimental Results
A laboratory prototype has been built to carry out experimental tests and evaluate the performance of the proposed converter. an IR2106 driver and a MOSFET IRF840 were used. The prototype for experimental tests is shown in Figure 14. Figure 15 shows the main line current and voltage waveforms. As can be seen in this Figure the current waveform shows the death time tx predicted by the LFAA and this waveform is similar to the theoretical waveform shown in Figure 5.
The THDi of the input waveforms of Figure 15 was measured with the HIOKI model PW3198 power quality analyzer, which is shown in Figure 16, which shows that the THDi is close to 21.7% and the harmonics are within the requirements of the EN 61000-3-2 class C standard. As for the PF obtained in experimental tests with the energy quality meter, it is shown to be 0.9686 in Figure 17. The instantaneous voltage of the LED lamp obtained in experimental tests is shown in Figure 18. The average voltage applied to the LED was VLED = 60.5, the same of the specifications, the voltage ripple obtained was 18.16%. The instantaneous current of the LED lamp obtained in experimental tests is shown in Figure 19. The average current applied to the LED was ILED = 160.3 mA, the current ripple obtained was 212%. Finally, in Figure 20 the instantaneous output power in the LED is shown. which shows an average power of such as in the case of THDi with a higher percentage of error, this is since losses of the elements used were not considered, in addition to this the construction of the prototype, to mention the manual manufacture of the transformer, which can considerably affect the performance of the entire system.
It should be noted that the flyback only processes 63% of the input power.   such as in the case of THDi with a higher percentage of error, this is since losses of the elements used were not considered, in addition to this the construction of the prototype, to mention the manual manufacture of the transformer, which can considerably affect the performance of the entire system. It should be noted that the flyback only processes 63% of the input power.         Finally, Tables 5 and 6 summarize what was obtained in the implementation of the topology and the percentages of error obtained, and as expected, there are parameters such as in the case of THDi with a higher percentage of error, this is since losses of the elements used were not considered, in addition to this the construction of the prototype, to mention the manual manufacture of the transformer, which can considerably affect the performance of the entire system.
It should be noted that the flyback only processes 63% of the input power. Finally, Table 7 shows a small comparison with a couple of similar power topologies. It can be seen that the topology has a good efficiency and power factor compared to the other two topologies, and even less energy stored in the capacitor is reported, which translates into a physically smaller capacitor. However, it has a greater current ripple.

Conclusions
Through this document, a new converter has been evaluated which is based on a variant of the flyback converter and is used as a power supply in solid-state lighting systems.
The proposed converter consists of a rearrangement of the components of the conventional flyback, the secondary is placed in parallel with the LED load and this set is in turn placed in series with the primary and the voltage source.
The primary advantage of this converter is the partial processing of energy, which goes beyond the principle of reduced redundant energy processing (R 2 P 2 ) [16], one part of the energy is directly delivered to the load and the other part is processed by the converter. Since in this rearrangement the flyback converter processed less energy, the stress in the components is lower than in a conventional flyback. As well, this operation allows the efficiency of the proposed converter to always will be greater than the conventional flyback converter. The main disadvantages are the converter have not magnetic isolation, it is a reductive topology and the power factor depends on the gain m of the converter.
The mathematical analysis of the topology of the retrofitted flyback converter was performed and it was shown that it complies with the requirements established by the IEC61000-3-2 class C standard and the FIDE directives in an interval of 0 < m < 0.41, with a THDi = 21.7% and a PF = 0.9686.
In order to validate the mathematical calculations, a 10 W prototype was built. Experimental results show the rearranged flyback processed only 63% of the input power and the other 37% flows directly to the load.

Conflicts of Interest:
The authors declare no conflict of interest.