Power Factor Corrector with Bridgeless Flyback Converter for DC Loads Applications

: Since power systems with a DC distribution method has many advantages, such as conversion efﬁciency increase of about 5–10%, cost reducing by about 15–20% and so on, the AC distribution power system will be replaced by a DC distribution one. This paper presents a DC load power system for a DC distribution application. The proposed power system includes two converters: DC/DC converter with battery source and power factor corrector (PFC) with a line source to increase the reliability of the power system when renewable energy or energy storage equipment are adopted. The proposed PFC adopts a bridgeless ﬂyback converter to achieve power factor correction for supplying power to DC loads. When the bridgeless ﬂyback converter is used to achieve PFC, it needs two transformers to process positive and negative half periods, respectively. In order to increase conversion efﬁciency, the ﬂyback one can add two sets of the active clamp circuit to recover energies stored in leakage inductances of transformers in the converter. Therefore, the proposed bridgeless ﬂyback converter can not only integrate two transformers into a single transformer, but also share a clamp capacitor to achieve energy recovery of leakage inductances and to operate switches with zero-voltage switching (ZVS) at the turn-on transition. With this approach, the proposed converter can increase conversion efﬁciency and decrease component counts, where it results in a higher conversion efﬁciency, lower cost, easier design and so on. Finally, a prototype with a universal input voltage source (AC 90–265 V) under output voltage of 48 V and maximum output power of 300 W has been implemented to verify the feasibility of the proposed bridgeless ﬂyback converter. Furthermore, the proposed power system can be operated at different cases among load power P L , output power P DC1 of DC/DC converter and output power P DC2 of the proposed PFC for supplying power to DC loads.


Introduction
Since power systems with a DC distribution method has many advantages, such as conversion efficiency increase of about 5-10%, cost reducing by about 15-20% and so on, the AC distribution power system will be replaced by a DC distribution one [1]. Figure 1 shows a block diagram of a power system for DC load applications. The power sources of the power system can adopt utility line, solar arrays, battery or wind turbine, etc. The power system using a power processor is widely applied to the general electrical or electronic equipment. In order to obtain a lighter weight and a smaller volume, a switching-mode converter is regarded as the power processor of the power system. When a power factor corrector (PFC) is used for the AC/DC power system [2][3][4][5][6][7][8][9][10][11][12] to protect the line source from harmonic current pollution, it has to meet the recommended limits of harmonics in supply current by various international power quality standards, such as the International Electrotechnical Commission (IEC) 61000-3-2 [2]. Therefore, the AC/DC converter adopts PFC techniques to increase converter. Therefore, the topology of two stages is used to achieve a lower output voltage, resulting in a higher cost and a lower conversion efficiency. Single stage topology with buck-boost converter has been an alternative solution in various power conversions. In order to further increase the stepdown ratio, a bridgeless flyback converter is regarded as the power processor because of its topological advantages, such as simple circuit structure, low cost, and galvanic isolation, as depicted in Figure 4. It is adopted in not only low power isolated single-stage single-phase AC/DC converters which is regarded as the front end of the switching-mode power supply, but also uninterrupted power supplies (UPS), induction heating, electronic ballast, telecom power supplies, light emitting diode drivers [13][14][15], etc.  In general, a boost converter, as shown in Figure 2, or buck-boost converter is adopted in the PFC system. In order to reduce the conduction losses of diodes, a bridgeless boost converter is adopted to achieve a higher power factor, as shown in Figure 3. Due to the universal input voltage source (AC 90-265 V), its output voltage is regulated at approximately 400 V. For a power system under a lower level output voltage condition, it needs an extra DC/DC converter as a step-down converter. Therefore, the topology of two stages is used to achieve a lower output voltage, resulting in a higher cost and a lower conversion efficiency. Single stage topology with buck-boost converter has been an alternative solution in various power conversions. In order to further increase the step-down ratio, a bridgeless flyback converter is regarded as the power processor because of its topological advantages, such as simple circuit structure, low cost, and galvanic isolation, as depicted in Figure 4. It is adopted in not only low power isolated single-stage single-phase AC/DC converters which is regarded as the front end of the switching-mode power supply, but also uninterrupted power supplies (UPS), induction heating, electronic ballast, telecom power supplies, light emitting diode drivers [13][14][15], etc.
Appl. Sci. 2017, 7, x FOR PEER REVIEW 2 of 20 techniques to increase power factor (PF), in which input voltage waveform can be made to be completely in phase with the input current one, implying approximately unity power factor. In general, a boost converter, as shown in Figure 2, or buck-boost converter is adopted in the PFC system. In order to reduce the conduction losses of diodes, a bridgeless boost converter is adopted to achieve a higher power factor, as shown in Figure 3. Due to the universal input voltage source (AC 90-265 V), its output voltage is regulated at approximately 400 V. For a power system under a lower level output voltage condition, it needs an extra DC/DC converter as a step-down converter. Therefore, the topology of two stages is used to achieve a lower output voltage, resulting in a higher cost and a lower conversion efficiency. Single stage topology with buck-boost converter has been an alternative solution in various power conversions. In order to further increase the stepdown ratio, a bridgeless flyback converter is regarded as the power processor because of its topological advantages, such as simple circuit structure, low cost, and galvanic isolation, as depicted in Figure 4. It is adopted in not only low power isolated single-stage single-phase AC/DC converters which is regarded as the front end of the switching-mode power supply, but also uninterrupted power supplies (UPS), induction heating, electronic ballast, telecom power supplies, light emitting diode drivers [13][14][15], etc.   Since a flyback converter adopts a transformer to be regarded as a stored inductor and an isolated transformer, a leakage inductance exists in the primary side, resulting in a higher voltage stress across switches of the converter when switches are turned off. In order to limit a high voltage stress across switches, a resistor-capacitor-diode (RCD) clamp circuit is used to reduce switch voltage spike. Although the RCD circuit can smooth out the voltage spike, the energy stored in leakage inductance is released to the clamp resistor. As a result, the conversion efficiency of the flyback converter does not increase. For improving conversion efficiency of the one with the RCD clamp circuit, an active clamp circuit is used to replace the RCD clamp circuit, as shown in Figure 5. With this approach, the energy stored in leakage inductance can be recycled and switches in the converter can be operated with zero-voltage switching (ZVS) at the turn-on transition [16,17]. When the PFC adopts a bridgeless flyback converter, it needs to process power in a positive and negative half periods of the line source, resulting in that its component counts almost need twofold of its counterpart circuit [18,19]. Particularly, using more than one magnetic device in the bridgeless flyback converter impacts the advantage, which is the circuit simplicity. In order to further simplify the circuit structure, two transformers in the bridgeless flyback converter is replaced with a threewinding transformer, as illustrated in Figure 6. Furthermore, two active clamp circuits share a capacitor. It will reduce weight, volume and component counts, significantly.  Since a flyback converter adopts a transformer to be regarded as a stored inductor and an isolated transformer, a leakage inductance exists in the primary side, resulting in a higher voltage stress across switches of the converter when switches are turned off. In order to limit a high voltage stress across switches, a resistor-capacitor-diode (RCD) clamp circuit is used to reduce switch voltage spike. Although the RCD circuit can smooth out the voltage spike, the energy stored in leakage inductance is released to the clamp resistor. As a result, the conversion efficiency of the flyback converter does not increase. For improving conversion efficiency of the one with the RCD clamp circuit, an active clamp circuit is used to replace the RCD clamp circuit, as shown in Figure 5. With this approach, the energy stored in leakage inductance can be recycled and switches in the converter can be operated with zero-voltage switching (ZVS) at the turn-on transition [16,17]. When the PFC adopts a bridgeless flyback converter, it needs to process power in a positive and negative half periods of the line source, resulting in that its component counts almost need twofold of its counterpart circuit [18,19]. Particularly, using more than one magnetic device in the bridgeless flyback converter impacts the advantage, which is the circuit simplicity. In order to further simplify the circuit structure, two transformers in the bridgeless flyback converter is replaced with a threewinding transformer, as illustrated in Figure 6. Furthermore, two active clamp circuits share a capacitor. It will reduce weight, volume and component counts, significantly. Since a flyback converter adopts a transformer to be regarded as a stored inductor and an isolated transformer, a leakage inductance exists in the primary side, resulting in a higher voltage stress across switches of the converter when switches are turned off. In order to limit a high voltage stress across switches, a resistor-capacitor-diode (RCD) clamp circuit is used to reduce switch voltage spike. Although the RCD circuit can smooth out the voltage spike, the energy stored in leakage inductance is released to the clamp resistor. As a result, the conversion efficiency of the flyback converter does not increase. For improving conversion efficiency of the one with the RCD clamp circuit, an active clamp circuit is used to replace the RCD clamp circuit, as shown in Figure 5. With this approach, the energy stored in leakage inductance can be recycled and switches in the converter can be operated with zero-voltage switching (ZVS) at the turn-on transition [16,17].  Figure 3. Schematic diagram of a boost converter using bridgeless topology for PFC applications. Since a flyback converter adopts a transformer to be regarded as a stored inductor and an isolated transformer, a leakage inductance exists in the primary side, resulting in a higher voltage stress across switches of the converter when switches are turned off. In order to limit a high voltage stress across switches, a resistor-capacitor-diode (RCD) clamp circuit is used to reduce switch voltage spike. Although the RCD circuit can smooth out the voltage spike, the energy stored in leakage inductance is released to the clamp resistor. As a result, the conversion efficiency of the flyback converter does not increase. For improving conversion efficiency of the one with the RCD clamp circuit, an active clamp circuit is used to replace the RCD clamp circuit, as shown in Figure 5. With this approach, the energy stored in leakage inductance can be recycled and switches in the converter can be operated with zero-voltage switching (ZVS) at the turn-on transition [16,17]. When the PFC adopts a bridgeless flyback converter, it needs to process power in a positive and negative half periods of the line source, resulting in that its component counts almost need twofold of its counterpart circuit [18,19]. Particularly, using more than one magnetic device in the bridgeless flyback converter impacts the advantage, which is the circuit simplicity. In order to further simplify the circuit structure, two transformers in the bridgeless flyback converter is replaced with a threewinding transformer, as illustrated in Figure 6. Furthermore, two active clamp circuits share a capacitor. It will reduce weight, volume and component counts, significantly. When the PFC adopts a bridgeless flyback converter, it needs to process power in a positive and negative half periods of the line source, resulting in that its component counts almost need twofold of its counterpart circuit [18,19]. Particularly, using more than one magnetic device in the bridgeless flyback converter impacts the advantage, which is the circuit simplicity. In order to further simplify the circuit structure, two transformers in the bridgeless flyback converter is replaced with a three-winding transformer, as illustrated in Figure 6. Furthermore, two active clamp circuits share a capacitor. It will reduce weight, volume and component counts, significantly.  This paper proposes a bridgeless flyback converter, illustrating that the proposed one is without bridge diodes to remove the diode conduction loss and increase conversion efficiency. In addition, the proposed one adopts a three-winding transformer to substitute for two transformers. When the output maximum power of the proposed bridgeless flyback is the same as that of the conventional bridgeless flyback converter, as shown in Figure 5, its maximum input current Ii is also the same as each other, and maximum working flux Bpk of the transformer in the proposed converter is also the same as that in the conventional bridgeless flyback converter. Figure 7 shows a B-H curve of the transformer Tr in the flyback converter. Since the conventional flyback converter uses a bridge rectifier to rectify input current Ii, the rectified input current Ii can be obtained by a positive value during a complete switching cycle. Its B-H curve is illustrated in Figure 7a. As a result, the conventional flyback converter can use a set of transformers to implement PFC function. While, the bridgeless flyback converter, as shown in Figure 5, needs two sets of transformers to process energy under the positive half period and the negative half period. Its B-H curve is illustrated in Figure 7b. Due to the proposed bridgeless flyback converter with a three-winding transformer, its B-H curve is the same as the conventional flyback one, as shown in Figure 7a. Therefore, the proposed bridgeless converter can save a set of transformers. It can simplify the circuit structure, significantly. Therefore, the proposed bridgeless flyback converter for the PFC power system can achieve a higher power factor to avoid the line source from harmonic pollution, possesses soft-switching features in which switches are operated in ZVS at turn-on transition to increase conversion efficiency. It is suitable for a low power level application. This paper focuses on design and analysis of the proposed bridgeless flyback converter and power management for DC loads of power system.  This paper proposes a bridgeless flyback converter, illustrating that the proposed one is without bridge diodes to remove the diode conduction loss and increase conversion efficiency. In addition, the proposed one adopts a three-winding transformer to substitute for two transformers. When the output maximum power of the proposed bridgeless flyback is the same as that of the conventional bridgeless flyback converter, as shown in Figure 5, its maximum input current I i is also the same as each other, and maximum working flux B pk of the transformer in the proposed converter is also the same as that in the conventional bridgeless flyback converter. Figure 7 shows a B-H curve of the transformer T r in the flyback converter. Since the conventional flyback converter uses a bridge rectifier to rectify input current I i , the rectified input current I i can be obtained by a positive value during a complete switching cycle. Its B-H curve is illustrated in Figure 7a. As a result, the conventional flyback converter can use a set of transformers to implement PFC function. While, the bridgeless flyback converter, as shown in Figure 5, needs two sets of transformers to process energy under the positive half period and the negative half period. Its B-H curve is illustrated in Figure 7b. Due to the proposed bridgeless flyback converter with a three-winding transformer, its B-H curve is the same as the conventional flyback one, as shown in Figure 7a. Therefore, the proposed bridgeless converter can save a set of transformers. It can simplify the circuit structure, significantly. Therefore, the proposed bridgeless flyback converter for the PFC power system can achieve a higher power factor to avoid the line source from harmonic pollution, possesses soft-switching features in which switches are operated in ZVS at turn-on transition to increase conversion efficiency. It is suitable for a low power level application. This paper focuses on design and analysis of the proposed bridgeless flyback converter and power management for DC loads of power system.  This paper proposes a bridgeless flyback converter, illustrating that the proposed one is without bridge diodes to remove the diode conduction loss and increase conversion efficiency. In addition, the proposed one adopts a three-winding transformer to substitute for two transformers. When the output maximum power of the proposed bridgeless flyback is the same as that of the conventional bridgeless flyback converter, as shown in Figure 5, its maximum input current Ii is also the same as each other, and maximum working flux Bpk of the transformer in the proposed converter is also the same as that in the conventional bridgeless flyback converter. Figure 7 shows a B-H curve of the transformer Tr in the flyback converter. Since the conventional flyback converter uses a bridge rectifier to rectify input current Ii, the rectified input current Ii can be obtained by a positive value during a complete switching cycle. Its B-H curve is illustrated in Figure 7a. As a result, the conventional flyback converter can use a set of transformers to implement PFC function. While, the bridgeless flyback converter, as shown in Figure 5, needs two sets of transformers to process energy under the positive half period and the negative half period. Its B-H curve is illustrated in Figure 7b. Due to the proposed bridgeless flyback converter with a three-winding transformer, its B-H curve is the same as the conventional flyback one, as shown in Figure 7a. Therefore, the proposed bridgeless converter can save a set of transformers. It can simplify the circuit structure, significantly. Therefore, the proposed bridgeless flyback converter for the PFC power system can achieve a higher power factor to avoid the line source from harmonic pollution, possesses soft-switching features in which switches are operated in ZVS at turn-on transition to increase conversion efficiency. It is suitable for a low power level application. This paper focuses on design and analysis of the proposed bridgeless flyback converter and power management for DC loads of power system.

Control Algorithm of the Proposed System for DC Load Applications
The proposed bridgeless PFC is applied to a DC load power system. In order to implement a DC load power system, the proposed one and a DC/DC converter with a battery source connected in parallel to supply power for DC loads. Its block diagram is shown in Figure 8. The control algorithm of the proposed power system for DC load applications is described in the following sections.

Circuit Topology of the Proposed Power System
The proposed DC load power system consists of a DC/DC converter with a battery source and a bridgeless PFC and single-chip control circuit. The output voltage VDC2 of the bridgeless PFC is close to and is greater than the output voltage VDC1 of the DC/DC converter. Therefore, the diode DB is used to block the voltage difference between voltages VDC2 and VDC1. The DC load RL is supplied power from the proposed PFC and the DC/DC converter. When the load power PL is less than or equal to PDC2(max) which is the maximum output power of the proposed PFC, the proposed PFC supplies power to load. If PL is greater than PDC2(max), the proposed PFC and the DC/DC converter supply power to load for achieving a DC load power system.

Control Algorithm of Each Unit
The DC/DC converter adopts a boost converter with a single-capacitor snubber [20]. It can transfer power from the battery to load. Since its output voltage VDC1 is less than the voltage VDC2, a diode DB is used to protect the DC/DC converter. Therefore, the protection diode with the output diode of boost converter is replaced by the extra diode DB. If the operational state is in the 0 < PL ≤ PDC2(max) state, the battery with the DC/DC converter can be operated in the charging mode. It needs an extra charger to charge the battery. When the proposed power system is operated in an abnormal state, the single-chip control circuit sends a shutdown signal SD1 under a high level to the pulse width modulation (PWM) control circuit of the DC/DC converter. The DC/DC converter can be operated in the shutdown state to protect the DC/DC one.

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The Proposed PFC The proposed PFC uses a bridgeless flyback converter which is regarded as a power factor corrector for increasing power factor between input voltage and input current of a line source. Its control circuit adopts a PWM IC for PFC control. Figure 9 illustrates conceptual waveforms of voltage VC1 and current ID1. Variation of current ID1 follows the sine waveform of input voltage VC1.

Control Algorithm of the Proposed System for DC Load Applications
The proposed bridgeless PFC is applied to a DC load power system. In order to implement a DC load power system, the proposed one and a DC/DC converter with a battery source connected in parallel to supply power for DC loads. Its block diagram is shown in Figure 8. The control algorithm of the proposed power system for DC load applications is described in the following sections.
Appl. Sci. 2017, 7, x FOR PEER REVIEW 6 of 20 a positive half period. When the proposed one is operated in the A and C areas, inductor current ILK is in the DCM state due to a lower voltage level of input voltage VC1. If input voltage VC1 is during the B area interval, the proposed converter is operated in CCM. According to the operational method of the proposed one as mentioned above, input voltage Vin and current Ii are in phase. Therefore, the proposed flyback converter can increase PF and reduce total harmonic distortion (THD). In Figure 8, when output current IDC2 of the proposed PFC is less than or is equal to the maximum output current IDC2(max), the output feedback voltage VF is equal VDC2 (diode DP1 is forward biased). The proposed PFC is operated as the voltage regulator. If IDC2 is greater than IDC2(max), the output current IDC2 is regulated at IDC2(max). That is, the proposed one is operated as the current regulator. The voltage VF is equal to IDC2(max) and the diode DP2 is in the forwardly bias state. In addition, when the proposed power system has an abnormal operational condition, the shutdown signal voltage SD2 is changed from a low level to a high level. The proposed PFC is shut down to protect the proposed one.  Figure 8. Block diagram of the proposed power system applications. Figure 8. Block diagram of the proposed power system applications.

Circuit Topology of the Proposed Power System
The proposed DC load power system consists of a DC/DC converter with a battery source and a bridgeless PFC and single-chip control circuit. The output voltage V DC2 of the bridgeless PFC is close to and is greater than the output voltage V DC1 of the DC/DC converter. Therefore, the diode D B is used to block the voltage difference between voltages V DC2 and V DC1 . The DC load R L is supplied power from the proposed PFC and the DC/DC converter. When the load power P L is less than or equal to P DC2(max) which is the maximum output power of the proposed PFC, the proposed PFC supplies power to load. If P L is greater than P DC2(max) , the proposed PFC and the DC/DC converter supply power to load for achieving a DC load power system. The DC/DC converter adopts a boost converter with a single-capacitor snubber [20]. It can transfer power from the battery to load. Since its output voltage V DC1 is less than the voltage V DC2 , a diode D B is used to protect the DC/DC converter. Therefore, the protection diode with the output diode of boost converter is replaced by the extra diode D B . If the operational state is in the 0 < P L ≤ P DC2(max) state, the battery with the DC/DC converter can be operated in the charging mode. It needs an extra charger to charge the battery. When the proposed power system is operated in an abnormal state, the single-chip control circuit sends a shutdown signal S D1 under a high level to the pulse width modulation (PWM) control circuit of the DC/DC converter. The DC/DC converter can be operated in the shutdown state to protect the DC/DC one.

The Proposed PFC
The proposed PFC uses a bridgeless flyback converter which is regarded as a power factor corrector for increasing power factor between input voltage and input current of a line source. Its control circuit adopts a PWM IC for PFC control. Figure 9 illustrates conceptual waveforms of voltage V C1 and current I D1 . Variation of current I D1 follows the sine waveform of input voltage V C1 . Figure 9a shows concept waveforms under a complete line period, while Figure 9b depicts those waveforms under a positive half period. From Figure 9b, it can be seen that the proposed flyback converter can be operated in discontinuous conduction mode (DCM) or continuous conduction mode (CCM) under a positive half period. When the proposed one is operated in the A and C areas, inductor current I LK is in the DCM state due to a lower voltage level of input voltage V C1 . If input voltage V C1 is during the B area interval, the proposed converter is operated in CCM. According to the operational method of the proposed one as mentioned above, input voltage V in and current I i are in phase. Therefore, the proposed flyback converter can increase PF and reduce total harmonic distortion (THD).
Appl. Sci. 2017, 7, x FOR PEER REVIEW 6 of 20 a positive half period. When the proposed one is operated in the A and C areas, inductor current ILK is in the DCM state due to a lower voltage level of input voltage VC1. If input voltage VC1 is during the B area interval, the proposed converter is operated in CCM. According to the operational method of the proposed one as mentioned above, input voltage Vin and current Ii are in phase. Therefore, the proposed flyback converter can increase PF and reduce total harmonic distortion (THD). In Figure 8, when output current IDC2 of the proposed PFC is less than or is equal to the maximum output current IDC2(max), the output feedback voltage VF is equal VDC2 (diode DP1 is forward biased). The proposed PFC is operated as the voltage regulator. If IDC2 is greater than IDC2(max), the output current IDC2 is regulated at IDC2(max). That is, the proposed one is operated as the current regulator. The voltage VF is equal to IDC2(max) and the diode DP2 is in the forwardly bias state. In addition, when the proposed power system has an abnormal operational condition, the shutdown signal voltage SD2 is changed from a low level to a high level. The proposed PFC is shut down to protect the proposed one.  In Figure 8, when output current I DC2 of the proposed PFC is less than or is equal to the maximum output current I DC2(max) , the output feedback voltage V F is equal V DC2 (diode D P1 is forward biased). The proposed PFC is operated as the voltage regulator. If I DC2 is greater than I DC2(max) , the output current I DC2 is regulated at I DC2(max) . That is, the proposed one is operated as the current regulator. The voltage V F is equal to I DC2(max) and the diode D P2 is in the forwardly bias state. In addition, when the proposed power system has an abnormal operational condition, the shutdown signal voltage S D2 is changed from a low level to a high level. The proposed PFC is shut down to protect the proposed one.

Single-Chip Control Circuit
The single-chip control circuit includes three units: The battery protection unit, line source protection unit and output protection unit. According to the operational relationships between DC/DC converter and the proposed PFC, the operational cases are divided into four cases, as listed in Table 1. Symbol definition of the proposed power system is listed in Table 2. Their operational conditions are described in the following section.
Case I: P L = 0 W When P L = 0 W, the DC/DC converter with battery source and the proposed PFC are operated in the shutdown mode.
Case II: 0 < P L ≤ P DC2(max) When 0 < P L ≤ P DC2(max) , P B = 0 W and P DC2 = P L . The DC/DC converter with battery source and the proposed PFC with line source are operated in the working state.
When P DC2(max) < P L ≤ P DC2(max) + P B(max) , P DC2 = P DC2(max) and P B = P L − P DC2(max) . The DC/DC converter and the proposed PFC are in the working state.
Case IV: P L > P DC2(max) + P B(max) When P L > P DC2(max) + P B(max) , the proposed power system is operated in the over-load state. Therefore, the DC/DC converter and the proposed PFC are in the shutdown state.
There are three protection units in the proposed power system: Battery protection, line source protection and output protection units. In order to increase protections of the proposed power system, hardware and software methods are adopted to protect the proposed one. Due to the same protection functions between hardware and software methods, the operation of hardware protection circuit is introduced in this paper. Figure 10 shows a block diagram of the single chip control circuit for the hardware protection circuit. In the battery protection unit, when I B > I B(max) , the discharging current I B is in the over-current state. Voltage V B1 is changed from a low level to a high level. Voltage S D1 is equal to V S1 (=V B1 ). The DC/DC converter is shut down to protect the battery. If V B < V B(min) , the battery is in the under-voltage state. Voltage single V B2 is changed from a low level to a high level, and signal S D1 is the same as V S1 (=V B2 ). Therefore, the DC/DC converter is also shut down.
In the line source protection unit, when V i < V i(min) (=AC 90 V), the proposed PFC is shut down by S D2 . In this case, the line source is in the under-voltage state, and voltage signal V i1 varies from a low level to a high level. Since V i1 = V S3 = S D2 , the proposed PFC is shut down by signal S D2 , which is in a high level state. If I i > I i(max) , the signal V i2 is equal to V S3 (=S D2 ), and V i2 is in a high level state. The proposed PFC is operated in the over-current state and it is shut down by S D2 . In the output protection unit, there are two cases to protect the proposed power system. One is that output voltage is in the under-voltage state. The other one is that output current is in the over-current state. When two protection cases occur, the proposed power system is shut down. In the under voltage state, V DC < V DC(min) , voltage V D1 = V S2 = S D1 = V S4 = S D2 is changed from a low level to a high level to shut down the proposed one. When I DC > I DC(set) , voltage V D2 = V S2 = S D1 = V S4 = S D2 is varied from a low level to a high level. The proposed one is shut down. Therefore, the proposed power system can use the battery protection unit, line source protection unit and output protection unit to avoid the abnormal operational condition in the proposed power system.  Table 2. Symbol definition of the proposed power system for DC load applications.

P B
Output power of the DC/DC converter with battery source The minimum work voltage of battery - The maximum discharge current of battery - The maximum output power of battery The minimum input voltage of the line source V i(min) < AC 90 V I i Input current of the line source The maximum work current of the line source -V DC Output voltage of the proposed power system -I DC Output current of the proposed power system I DC ≤ I DC(max) I DC(max) Output maximum current of the proposed power system -P DC2(max) The maximum output power of the proposed PFC P DC2(max) = V DC2 I DC2(max) P DC2 Output power of the proposed PFC P DC2 = V DC2 I DC2   The maximum discharge current of battery -PB(max) The maximum output power of battery Input voltage of the line source -

Vi(min)
The minimum input voltage of the line source The maximum work current of the line source -VDC Output voltage of the proposed power system -IDC Output current of the proposed power system IDC ≤ IDC(max) IDC(max) Output maximum current of the proposed power system -PDC2(max) The maximum output power of the proposed PFC PDC2(max) = VDC2IDC2(max) PDC2 Output power of the proposed PFC PDC2 = VDC2IDC2 Battery protection unit D S1 Line source protection unit

Operational Principle of the Proposed PFC
The proposed bridgeless flyback converter uses a three-winding transformer to achieve operations of the positive and negative half periods of the line source, as depicted in Figure 6. Its

Operational Principle of the Proposed PFC
The proposed bridgeless flyback converter uses a three-winding transformer to achieve operations of the positive and negative half periods of the line source, as depicted in Figure 6. Its equivalent circuit is illustrated in Figure 11a equivalent circuit is illustrated in Figure 11a,b, respectively. When the line source enters the positive half period, switches M1 and M2 are operated in complementary. During this time interval, switches M3 and M4 are always turned off, as shown in Figure 11a. The input energy supplied by the line source is transferred to load through windings N1 and N3 of the transformer. Furthermore, when the proposed converter is operated in the negative half period, switches M1 and M2 are turned off and switches M3 and M4, in turn, are operated in complementary, as depicted in Figure 11b. The operational principle of the proposed flyback converter is divided into two different half periods: Positive and negative half periods. According to operational principle of equivalent circuit shown in Figure 11a,b, operational modes of the proposed one operated in the positive period are similar to those modes in the negative period, except that switches M1 and M2 are changed to switches M3 and M4. Furthermore, since the period Tl of the line source is much greater than Ts of switching converter, the input voltage is regarded as a constant value during each switching period Ts. Therefore, the operational principle of the proposed bridgeless flyback converter can adopt, that input voltage is a constant DC voltage and the proposed one is operated in the positive half period of the line source, to explain its operational principle. According to the operational principle of the proposed converter, operational modes of the proposed one are divided into seven modes. Each operational mode is shown in Figure 12 over one switching cycle, and its key waveforms are illustrated in Figure 13. Its operational principle is described in the following.


Mode 1 [ Figure 12a; t0 ≤ t < t1]: Before t0, switch M1 is kept in the turn-on state, while M2 is in the turn-off state. When t = t0, current IDS1 of switch M1 reaches to the initial current which is the minimum inductor current IL(0) of the proposed converter operated in continuous conduction mode (CCM). Within this time interval, the inductor current ILK linearly increases and current IDS1 is equal to ILK. Since the diode D2 is reverse biased, the capacitor Co supplies the load with energy. In this interval, inductance Lm1 is in the stored energy state.  Mode 2 [ Figure 12b; t1 ≤ t < t2]: At t = t1, switch M1 is turned off and M2 is operated in the off state.  Figure 12e; t4 ≤ t < t5]: When t = t4, switch M2 is turned off. A new resonant network is formed between inductance Lk and capacitors CM1 and CM2. Capacitor CM1 is discharged and CM2 is charged through inductance Lk. As a sequence, switch voltage VDS2 changes from 0 V to (Vin + The operational principle of the proposed flyback converter is divided into two different half periods: Positive and negative half periods. According to operational principle of equivalent circuit shown in Figure 11a,b, operational modes of the proposed one operated in the positive period are similar to those modes in the negative period, except that switches M 1 and M 2 are changed to switches M 3 and M 4 . Furthermore, since the period T l of the line source is much greater than T s of switching converter, the input voltage is regarded as a constant value during each switching period T s . Therefore, the operational principle of the proposed bridgeless flyback converter can adopt, that input voltage is a constant DC voltage and the proposed one is operated in the positive half period of the line source, to explain its operational principle. According to the operational principle of the proposed converter, operational modes of the proposed one are divided into seven modes. Each operational mode is shown in Figure 12 over one switching cycle, and its key waveforms are illustrated in Figure 13. Its operational principle is described in the following.

•
Mode 1 [ Figure 12a; t 0 ≤ t < t 1 ]: Before t 0 , switch M 1 is kept in the turn-on state, while M 2 is in the turn-off state. When t = t 0 , current I DS1 of switch M 1 reaches to the initial current which is the minimum inductor current I L (0) of the proposed converter operated in continuous conduction mode (CCM). Within this time interval, the inductor current I LK linearly increases and current I DS1 is equal to I LK . Since the diode D 2 is reverse biased, the capacitor C o supplies the load with energy. In this interval, inductance L m1 is in the stored energy state. • Mode 2 [ Figure 12b; t 1 ≤ t < t 2 ]: At t = t 1 , switch M 1 is turned off and M 2 is operated in the off state. The energies stored in leakage inductor L k and magnetizing inductor L m1 are transferred to capacitors C M1 and C M2 . Voltage V DS1 across switch M 1 is charged from 0V to (V in + V o /N) and voltage V DS2 across switch M 2 is charged from (V in + V o /N) to 0 V. Since the charge time is very small, capacitor C M1 is in an approximately linear charging state and C M2 is in an approximately linear discharging state. The output capacitor C o maintains output voltage V o at a desired value. • Mode 3 [ Figure 12c; t 2 ≤ t < t 3 ]: When t = t 2 , switch voltage V DS1 is equal to (V in + V o /N) and V DS2 equals to 0 V. Diode D 2 and D M2 starts to forwardly bias. Voltage of secondary winding in transformer T r is clamped to output voltage V o . Within this time interval, inductance L k and capacitor C c are in a resonant manner. Furthermore, magnetizing inductor L m1 releases the energy through transformer T r to load. • Mode 4 [ Figure 12d; t 3 ≤ t < t 4 ]: At t 3 , switch M 2 is turned on and switch M 1 is kept in the off state. Since the body diode D M2 is forward biased before switch M 2 is turned on, switch M 2 is operated with ZVS at turn-on transition. Inductance L k and capacitor C c are kept in the resonant state. The energy stored in L m1 is transferred to load by means of transformer T r . • Mode 5 [ Figure 12e; t 4 ≤ t < t 5 ]: When t = t 4 , switch M 2 is turned off. A new resonant network is formed between inductance L k and capacitors C M1 and C M2 . Capacitor C M1 is discharged and C M2 is charged through inductance L k . As a sequence, switch voltage V DS2 changes from 0 V to  Figure 12f; t 5 ≤ t < t 6 ]: At t 5 , switch voltage V DS1 is equal to 0 V. Inductance current I Lk equals a negative value. Voltage across inductance L k is equal to (V in + V o /N). The operational states of magnetizing inductance L m1 and diode D 2 are the same as those states of mode 5. • Mode 7 [ Figure 12g; t 6 ≤ t < t 7 ]: When t = t 6 , switch M 1 is turned on. Since body diode D M1 is forward biased before t = t 6 , switch M 1 is operated with ZVS at turn-on transition. Inductance current I Lk varies from a negative value to the initial current which is the minimum current value of inductance L m1 when the proposed converter is operated in CCM. When t = t 7 , current of magnetizing inductance L m1 reaches its minimum value again, a new switching cycle will start.  (12) where LK is equal to 1~5% of magnetizing inductance Lm1 or Lm2.

 Output Capacitor Co
The output capacitor Co is used to reduce output voltage ripple. Since the input voltage Vin of the proposed converter is a half-wave rectification waveform, output voltage Vo contains a voltage ripple with 120 Hz. When the maximum peak output voltage Vo is specified, output capacitor Co can be given by

Measured Results
In order to verify performances of the proposed power system, as shown in Figure 8, a prototype with following specifications was implemented. The proposed power system includes two converters: The DC/DC converter with battery source and the proposed PFC with line source. Their specifications are respectively shown in the following:

Design of the Proposed PFC
Due to the input voltage with a sine wave, the input current I in is time dependent. A function of peak current of switch M 1 or M 2 is, in turn, a function of duty cycle of the converter. Therefore, peak switch current I DS1 needs to be determined as a function of which the instantaneous operating point is on the input line period. Neglecting ripple current in the switch, switch current I DS1 (φ) can be determined by where I av (φ) is the average input line current and D(φ) is an instantaneous duty cycle. In (1), one half of the line cycle period is considered to be normalized to the interval [0, π], and φ is an arbitrary point on that interval. I av (φ) is given by where P o is the output power of the converter, η indicates the conversion efficiency and V rms is the input voltage of line source. The instantaneous duty cycle is where V o is the output voltage and N is the turns ratio of transformer T r . As mentioned above, D(φ) can vary from D min to 1. In order to achieve systematic design of the proposed bridgeless flyback converter, its design is listed as follows: The turns ratio N of transformer is selected to accommodate a low voltage ratio device for minimum duty cycle of switch to realize reasonable values, when the active clamp circuit in the proposed converter can provide a perfect suppression of the spike voltage across the main switch M 1 or M 3 due to leakage inductance of transformer, the maximum off-state voltage V DS1(max) can be determined by where V HL rms is the high line voltage of input source which is equal to AC 265 V and V o indicates the output voltage. The ranges of the minimum duty cycle can be given by And where V LL rms is the low line voltage of the input source which is equal to AC 90 V. In general, the minimum duty cycle ranges are determined between 0.2 and 0.5 under the input source at high line or low line voltage.
The maximum switch average current I max DS1(av) occurs at the maximum load and the minimum line voltage, when power factor is approximately unity, the maximum switch average current I max

DS1(av)
is written by where P FL O is output power of the proposed converter operated in the full load condition. Its worst case maximum peak current also occurs under the same operating conditions as above. The peak current I max DS1(peak) can be calculated from where L m is the magnetizing inductance of transformer T r and T S is the switching period of switch M 1 or M 3 . For this particular design, since voltage stress and peak current of active clamp switch M 2 or M 4 are the same as that of switch M 1 or M 3 , device selection of switch M 2 or M 4 is the same as M 1 or M 3.

Transformer T r
Since input voltage changes from a low line voltage V LL rms to a high line voltage V HL rms , it will affect the minimum duty cycle D LL min and D HL min . In order to obtain a reasonable value of D LL min or D HL min for active clamp flyback converter, D LL min or D HL min is designed at between 0.3 and 0.5. According to the reasonable ranges of D LL min or D HL min , turns ratio N is determined by Energies 2018, 11, 3096 13 of 20 Or The input voltage V in adopts a sine wave. During the positive half period or the negative half period, input voltage V in can vary from 0 V to the maximum value, and then from the maximum value to 0 V. In order to determine magnetizing inductance L m1 (=L m ) or L m2 (=L m ), current variation value I Lm of magnetizing inductance L m1 or L m2 is determined with the worst case maximum peak switch current as a reference value. Therefore, I Lm can be written by For this particular design, K is determined at approximately 0.1.

Clamp Capacitor C C
Since switches M 1 -M 4 are operated with ZVS at turn-on transition and the energy stored in leakage inductance L K can be recycled, it is by means of leakage inductance L K and clamp capacitor C C operated in the resonant manner. A better design of the proposed converter is to select the clamp capacitor C C value so that one half of the resonant period formed by the clamp capacitor C C and leakage inductance L K exceeds the maximum off time of switch M 1 or M 3 . Therefore, clamp capacitor C C can be determined by where L K is equal to 1~5% of magnetizing inductance L m1 or L m2 .

Output Capacitor C o
The output capacitor C o is used to reduce output voltage ripple. Since the input voltage V in of the proposed converter is a half-wave rectification waveform, output voltage V o contains a voltage ripple with 120 Hz. When the maximum peak output voltage V o is specified, output capacitor C o can be given by where P max o (=P FL o ) is the maximum output power. Furthermore, the required ripple current rating I max CO(rms) for output capacitor is determined by

Measured Results
In order to verify performances of the proposed power system, as shown in Figure 8, a prototype with following specifications was implemented. The proposed power system includes two converters: The DC/DC converter with battery source and the proposed PFC with line source. Their specifications are respectively shown in the following: According to the previous specifications, the design values of the key components of the proposed power system can be determined. The DC/DC converter with battery source is shown in Figure 14 and the proposed PFC with line source is shown in Figure 6. According to design of the proposed flyback converter, parameter values in the proposed one is listed in Table 3. Semiconductor selection of the proposed one is illustrated in Table 4. Their devices are determined as follows: According to the previous specifications, the design values of the key components of the proposed power system can be determined. The DC/DC converter with battery source is shown in Figure 14 and the proposed PFC with line source is shown in Figure 6. According to design of the proposed flyback converter, parameter values in the proposed one is listed in Table 3. Semiconductor selection of the proposed one is illustrated in Table 4. Their devices are determined as follows:


The DC/DC converter with battery source  Figure 14. Schematic diagram of the DC/DC converter with battery source. Figure 14. Schematic diagram of the DC/DC converter with battery source. Table 3. Parameter values of the proposed flyback converter.

Design Value by Equation Conditions
I  Since this paper focuses on design and implementation of the bridgeless flyback converter, measured results of the DC/DC converter with battery source have only shown that output voltage V DC1 and current I DC1 under step-load changes and under supplying power to load in parallel connection. Measured output voltage V DC1 and current I DC1 waveforms under step-load changes between 10% and 100% of full load condition with duty ratio of 50% and repetitive period of 1s is shown in Figure 15. From Figure 15, it can be seen that the voltage regulation of output voltage V DC1 has been limited within ±1%.

Design Value by Equation Conditions
Iav (  Since this paper focuses on design and implementation of the bridgeless flyback converter, measured results of the DC/DC converter with battery source have only shown that output voltage VDC1 and current IDC1 under step-load changes and under supplying power to load in parallel connection. Measured output voltage VDC1 and current IDC1 waveforms under step-load changes between 10% and 100% of full load condition with duty ratio of 50% and repetitive period of 1s is shown in Figure 15. From Figure 15, it can be seen that the voltage regulation of output voltage VDC1 has been limited within ±1%.

I DC1 V DC1
(VDC1: 25 V/div; IDC1: 1 A/div; time: 500 ms/div) Figure 15. Measured output voltage VDC1 and current IDC1 waveforms of step-load changes between 10% and 100% of full load condition with duty ratio of 50% and repetitive period of 1 s.
For the proposed PFC, since the input voltage Vin of AC 90 V is the worst case for operational states of the proposed one, the experimental results are shown with the input voltage of AC 90 V. Measured waveforms of input voltage Vin and current Ii is shown in Figure 16 under the line source of AC 90 V. Figure 16a shows those waveforms under 10% of full load condition and Figure 16b illustrates those waveforms under 100% of full load condition. From Figure 16, it can be found that For the proposed PFC, since the input voltage V in of AC 90 V is the worst case for operational states of the proposed one, the experimental results are shown with the input voltage of AC 90 V. Measured waveforms of input voltage V in and current I i is shown in Figure 16 under the line source of AC 90 V. Figure 16a shows those waveforms under 10% of full load condition and Figure 16b illustrates those waveforms under 100% of full load condition. From Figure 16, it can be found that input voltage V in and current I i are approximately in phase. Figure 17a illustrates measured waveforms of voltages V C1 , V C2 and currents I D1 , I D3 under 50% of full load condition and the input voltage of 90 V, while Figure 17b shows measured waveforms of voltage V C1 and current I D1 . From Figure 17, it can be seen that waveforms of currents I D1 and I D3 follow ones of voltages V C1 and V C2 variation, respectively. Since duty ratio D varies from 0.204 to 1, and the proposed flyback converter is operated in DCM or CCM. Figures 18 and 19 show measured waveforms of switch voltage V DS and current I DS under input voltage of 90 V. Figure 18 illustrates measured waveforms of switch voltage V DS1 and current I DS1 , and switch voltage V DS2 and current I DS2 and current I DS2 under 10% of full load condition and the input voltage of 90 V. From Figure 18, it can be found that the proposed flyback converter is operated in DCM. The active clamp capacitor can reduce the voltage spike and recover energy stored in leakage inductor of the transformer. Figure 19 depicts those waveforms under 30% of full load condition and the input voltage of 90 V, from which it can be seen that switches M 1 and M 2 are operated in ZVS at turn-on transition. In Figures 18 and 19, voltage V DS1 across switch M 1 has a ring voltage. The ring voltage is generated by leakage inductor of secondary winding of transformer and parasitic capacitor of diode D 2 when switch M 1 is turned on. It can be eliminated by snubber circuit applied to diode D 2 .
Measured output voltage V DC2 and current I DC2 waveforms under step-load changes between 10% and 100% of full load condition with duty ratio of 50% and repetitive period of 1s as shown in Figure 20, from which it can be observed that the voltage regulation of output voltage V DC2 has been limited within ±1%. Figure 21 depicts the measured efficiency of the proposed PFC from light load to heavy load under AC 90 V. When load is greater than 40% of full load condition, each efficiency is greater than 86%. For further increase in conversion efficiency of the proposed converter, switches M 1 -M 4 can adopt a lower conduction resistance to reduce conduction loss. It also decreases the switching frequency of the switch to reduce switching loss. In order to verify a high PF, the plot of power factor of the proposed one from light load to heavy load illustrated in Figure 22, from which it can be found that power factor of the proposed one can be greater than 0.8 under different input voltages. In particular, when input voltage is at a high line level and load is in the light load, PF has a lower value. Due to a lower output current I DC2 , PFC control IC is difficult to control input current I i , resulting in a lower PF. Figure 23 shows the harmonic current from light load to heavy load under different input voltage levels, illustrating that their harmonic current can meet requirements of IEC6100-3-2 class A.
According to operational cases of the proposed power system, there are four operational cases for DC load power variations. Figure 24 shows measured waveforms of voltages V DC1 and V DC2 , and currents I DC1 and I DC2 from P L = 0 W to P L = 125 W. Due to P DC2(max) = 300 W, operational case changes of the proposed one can be varied from case I to case II. When load power P L is from 0 W to 325 W, operational case changes are from case I to case III. Those waveforms are shown in Figure 25. If P L variations are from 0 W to 450 W, operational case charges are from case I to case IV. Those waveforms are shown in Figure 26. As mentioned above, the proposed power system can change operational case by the control algorithm of the proposed power system. input voltage Vin and current Ii are approximately in phase. Figure 17a illustrates measured waveforms of voltages VC1, VC2 and currents ID1, ID3 under 50% of full load condition and the input voltage of 90 V, while Figure 17b shows measured waveforms of voltage VC1 and current ID1. From Figure 17, it can be seen that waveforms of currents ID1 and ID3 follow ones of voltages VC1 and VC2 variation, respectively. Since duty ratio D varies from 0.204 to 1, and the proposed flyback converter is operated in DCM or CCM. Figures 18 and 19 show measured waveforms of switch voltage VDS and current IDS under input voltage of 90 V. Figure 18 illustrates measured waveforms of switch voltage VDS1 and current IDS1, and switch voltage VDS2 and current IDS2 and current IDS2 under 10% of full load condition and the input voltage of 90 V. From Figure 18, it can be found that the proposed flyback converter is operated in DCM. The active clamp capacitor can reduce the voltage spike and recover energy stored in leakage inductor of the transformer. Figure 19 depicts those waveforms under 30% of full load condition and the input voltage of 90 V, from which it can be seen that switches M1 and M2 are operated in ZVS at turn-on transition. In Figures 18 and 19, voltage VDS1 across switch M1 has a ring voltage. The ring voltage is generated by leakage inductor of secondary winding of transformer and parasitic capacitor of diode D2 when switch M1 is turned on. It can be eliminated by snubber circuit applied to diode D2. Measured output voltage VDC2 and current IDC2 waveforms under step-load changes between 10% and 100% of full load condition with duty ratio of 50% and repetitive period of 1s as shown in Figure  20, from which it can be observed that the voltage regulation of output voltage VDC2 has been limited within ±1%. Figure 21 depicts the measured efficiency of the proposed PFC from light load to heavy load under AC 90 V. When load is greater than 40% of full load condition, each efficiency is greater than 86%. For further increase in conversion efficiency of the proposed converter, switches M1-M4 can adopt a lower conduction resistance to reduce conduction loss. It also decreases the switching frequency of the switch to reduce switching loss. In order to verify a high PF, the plot of power factor of the proposed one from light load to heavy load illustrated in Figure 22, from which it can be found that power factor of the proposed one can be greater than 0.8 under different input voltages. In particular, when input voltage is at a high line level and load is in the light load, PF has a lower value. Due to a lower output current IDC2, PFC control IC is difficult to control input current Ii, resulting in a lower PF. Figure 23 shows the harmonic current from light load to heavy load under different input voltage levels, illustrating that their harmonic current can meet requirements of IEC6100-3-2 class A.
According to operational cases of the proposed power system, there are four operational cases for DC load power variations. Figure 24 shows measured waveforms of voltages VDC1 and VDC2, and currents IDC1 and IDC2 from PL = 0 W to PL = 125 W. Due to PDC2(max) = 300 W, operational case changes of the proposed one can be varied from case I to case II. When load power PL is from 0 W to 325 W, operational case changes are from case I to case III. Those waveforms are shown in Figure 25. If PL variations are from 0 W to 450 W, operational case charges are from case I to case IV. Those waveforms are shown in Figure 26. As mentioned above, the proposed power system can change operational case by the control algorithm of the proposed power system.

Conclusions
This paper proposes a power system for DC load applications. The proposed power system adopts the DC/DC converter with battery source and the proposed PFC to supply power for DC loads of 48 V power system. The proposed PFC uses a bridgeless flyback converter to achieve a high PF. In this paper, operational principle and design of the proposed one have been described in detail. According to the experimental results, switches M1 and M2 of the proposed PFC can be operated with ZVS at turn-on transition. Furthermore, the proposed one can also achieve a lower harmonic current, a higher conversion efficiency and a higher PF. Its harmonic current from light load to heavy load under different input voltage levels can meet the requirements of IEC6100-3-2 class A. Therefore, the proposed bridgeless flyback converter has been implemented to apply to the utility line system as a power factor corrector. In addition, the proposed power system for DC loads of 48 V power system also has been implemented to verify its feasibility. It is suitable for a DC distribution of 48 V power system application.

Conclusions
This paper proposes a power system for DC load applications. The proposed power system adopts the DC/DC converter with battery source and the proposed PFC to supply power for DC loads of 48 V power system. The proposed PFC uses a bridgeless flyback converter to achieve a high PF. In this paper, operational principle and design of the proposed one have been described in detail. According to the experimental results, switches M1 and M2 of the proposed PFC can be operated with ZVS at turn-on transition. Furthermore, the proposed one can also achieve a lower harmonic current, a higher conversion efficiency and a higher PF. Its harmonic current from light load to heavy load under different input voltage levels can meet the requirements of IEC6100-3-2 class A. Therefore, the proposed bridgeless flyback converter has been implemented to apply to the utility line system as a power factor corrector. In addition, the proposed power system for DC loads of 48 V power system also has been implemented to verify its feasibility. It is suitable for a DC distribution of 48 V power system application.

Conclusions
This paper proposes a power system for DC load applications. The proposed power system adopts the DC/DC converter with battery source and the proposed PFC to supply power for DC loads of 48 V power system. The proposed PFC uses a bridgeless flyback converter to achieve a high PF. In this paper, operational principle and design of the proposed one have been described in detail. According to the experimental results, switches M 1 and M 2 of the proposed PFC can be operated with ZVS at turn-on transition. Furthermore, the proposed one can also achieve a lower harmonic current, a higher conversion efficiency and a higher PF. Its harmonic current from light load to heavy load under different input voltage levels can meet the requirements of IEC6100-3-2 class A. Therefore, the proposed bridgeless flyback converter has been implemented to apply to the utility line system as a power factor corrector. In addition, the proposed power system for DC loads of 48 V power system also has been implemented to verify its feasibility. It is suitable for a DC distribution of 48 V power system application.