A Novel Single-Switch Single-Stage LED Driver with Power Factor Correction and Current Balancing Capability

: A novel single-switch single-stage high power factor LED driver is proposed by integrating a ﬂyback converter, a buck–boost converter and a current balance circuit. Only an active switch and a corresponding control circuit are used. The LED power can be adjusted by the control scheme of pulse–width modulation (PWM). The ﬂyback converter performs the function of power factor correction (PFC), which is operated at discontinuous-current mode (DCM) to achieve unity power factor and low total current harmonic distortion (THDi). The buck–boost converter regulates the dc-link voltage to obtain smooth dc voltage for the LED. The current–balance circuit applies the principle of ampere-second balance of capacitors to obtain equal current in each LED string. The steady-state analyses for different operation modes is provided, and the mathematical equations for designing component parameters are conducted. Finally, a 90-W prototype circuit with three LED strings was built and tested. Experimental results show that the current in each LED string is indeed consistent. High power factor and low THDi can be achieved. LED power is regulated from 100% to 25% rated power. Satisfactory performance has proved the feasibility of this circuit.


Introduction
Compared with fluorescent lamps and high-intensity discharge (HID) lamps, LEDs have the advantage of being small size, long-life, easy dimming, have high luminous efficiency, better color rendering and fast response. In addition, unlike fluorescent lamps that need to use mercury metal that is harmful to the environment, LEDs do not contain any mercury and are environmentally friendly. Therefore, LED has gradually replaced fluorescent lamps and HID lamps, and has become the mainstream light source of modern lighting [1][2][3]. LED is a point light source with a small size, so it is difficult to dissipate heat, therefore, the power of a single LED is usually not large. For high-power LED lighting systems, multiple LEDs must be used to meet the power requirements. When many LEDs are used, the connection method is to connect multiple LEDs in series to form a LED string, and then connect the LED strings in parallel [4,5].
For parallel-connected LED strings, due to the inevitable subtle differences between each LED, when the number of LEDs in series increases, the conduction voltage difference of each string will increase, resulting in inconsistent LED currents in each string. Moreover, LEDs have negative temperature coefficient characteristics, which will strengthen the current imbalance between each string, and even result in LED thermal runaway and burn. Therefore, the research on current-balance technology of parallel LEDs is an important topic of LED lighting systems [4]. The current-mirror technology is that each LED string is connected in series with a power transistor of the same model. In theory, when the control voltage of each power transistor is equal, the current will also be equal [6,7]. The advantage of the current-mirror method is that the control circuit is simple, but the disadvantage is that the conducting voltage of the transistors are high, resulting in high conducting losses. Therefore, current-mirror technology is only suitable for low power applications.
For medium and high-power LED drivers, many literatures have proposed LED current-balance methods, which are mainly classed into active current balancing technology [8][9][10][11] and passive current balancing technology [12][13][14][15]. The cost of active technology is higher because each LED string needs to be equipped with an independent current feedback control circuit to control its own active switch, and the current of each string can be adjusted independently, which is conducive to creating a unique lighting situation. Passive technologies do not need to use active switches and the corresponding control circuits. They only use passive components such as diodes, inductors, capacitors or transformers. Some passive approaches connect the primary windings of transformers in series to obtain the same average current in the secondary windings [12,13]. Some approaches connect each LED string in series with a high reactance capacitor. Due to the series connection, the LED current is mainly dominated by the high reactance capacitor. In this way, the impact of current imbalance caused by the difference in LED impedance is reduced [14,15]. Compared with active technologies, passive technologies do not require additional active switches and control circuits. However, these passive methods need to use bulky transformers or capacitors. This hinders the realization of a small and light-weight LED driver.
On the other hand, in order to improve power quality, increase the utilization of power equipment and reduce electromagnetic interference (EMI), advanced countries have formulated strict specifications for power factor and THDi of electrical products. For example, IEC 61000-3-2 Class D and IEEE 519 set the power factor and THDi specifications of lighting products. Therefore, the LED driver needs to add an additional ac/dc converter to perform the function of power factor correction (PFC). This results in two-stage LED drivers. The first stage is a PFC converter, and the second stage is a dc/dc converter which is used to regulate LED power. The additional PFC converter can improve the power factor and reduces THDi. However, these two-stage circuits must use more components and two control circuits. Furthermore, it takes two energy conversion processes, leading to more losses. In order to improve circuit efficiency and reduce the number of components, many researchers have proposed the single-stage solutions by integrating the PFC converter and the dc/dc converter [16][17][18][19]. In a single-stage circuit, the PFC converter and the dc/dc converter share one or more active switches. This not only saves the active switch and its control circuit, but also reduces the energy conversion process, thereby reducing the cost and improving the conversion efficiency.
In this paper, a novel single-stage circuit is proposed to drive multiple LED strings. The circuit architecture mains integrate a flyback converter and a buck-boost converter. This circuit only uses an active switch which is PWM controlled to adjust the LED power. It can achieve high power factor, low THDi and the current-balance capability. Figure 1 shows the proposed single-stage high power factor LED driver. This circuit is suitable for driving odd strings of LEDs. Figure 1a,b show the LED drivers with three LED strings and seven LED strings, respectively. This article will take Figure 1a as an example to illustrate the operation principle of the proposed circuit. The circuit configuration mainly consists of a flyback converter, a buck-boost converter, and some L-C passive components used as the current balancing circuit. Both converters share an active switch S 1 . V in is the mains ac voltage, L f and C f form a low-pass filter to remove the high-frequency current of the flyback converter. The flyback converter serves as a power-factor corrector which is designed to operate at discontinuous-current mode (DCM) to achieve high power factor and low THDi. The buck-boost converter is pulse-width modulated to adjust the power of the LED strings. By using the principle of ampere-second balance of capacitor, the current of each LED string can be equalized. The resistor R sense is used to detect the current of the LED string one, so as long as the current of the LED string one is controlled, the current of each string of LEDs can be controlled. high power factor and low THDi. The buck-boost converter is pulse-width modulated to adjust the power of the LED strings. By using the principle of ampere-second balance of capacitor, the current of each LED string can be equalized. The resistor Rsense is used to detect the current of the LED string one, so as long as the current of the LED string one is controlled, the current of each string of LEDs can be controlled.

Operation Mode Analysis
In order to perform the PFC function, the flyback converter is operated at DCM. In addition, the following assumptions are made to simplify circuit analysis.
1. All components are ideal. 2. The capacitors Cdc, C1, Co1, Co2, and Co3 are large enough, and the voltages across these capacitors (Vdc, VC1, Vo1, Vo2, and Vo3) can all be regarded as constant values. 3. The input voltage is an ideal sinewave, vin(t) = Vmsin(ωt), where Vm represents the amplitude of the input voltage, and ω = 2πfL represents the angular frequency. 4. The switching frequency fs of the active switch is much higher than the input voltage frequency fL (fs >> fL).
All the inductors are designed to operate at DCM. At steady-state, the circuit operation can be divided into six operation modes in a high-frequency switching cycle. Figure  2 shows the current paths of each mode where vrec represents the rectified input voltage. Figure 3 shows the conceptual voltage and current waveforms of the key components. The detailed analysis of each mode is described as follows:

Operation Mode Analysis
In order to perform the PFC function, the flyback converter is operated at DCM. In addition, the following assumptions are made to simplify circuit analysis.

1.
All components are ideal.

2.
The capacitors C dc , C 1 , C o1 , C o2 , and C o3 are large enough, and the voltages across these capacitors (V dc , V C1 , V o1 , V o2 , and V o3 ) can all be regarded as constant values.

3.
The input voltage is an ideal sinewave, v in (t) = V m sin(ωt), where V m represents the amplitude of the input voltage, and ω = 2πf L represents the angular frequency.

4.
The switching frequency f s of the active switch is much higher than the input voltage frequency f L (f s >> f L ).
All the inductors are designed to operate at DCM. At steady-state, the circuit operation can be divided into six operation modes in a high-frequency switching cycle. Figure 2 shows the current paths of each mode where v rec represents the rectified input voltage. Figure 3 shows the conceptual voltage and current waveforms of the key components. The detailed analysis of each mode is described as follows: (e) (f) (e) (f) The operation mode I starts at time t 0 when the gate signal v GS1 changes from lowlevel to high-level, and S 1 is turned on. The rectified voltage v rec is across on the primary winding of the transformer T 1 , and the primary current i pri rises linearly from zero.
where L p represents the inductance of the primary winding. At the same time, the voltage across the inductor L m is equal to the dc-link voltage V dc . L m is charged and its current i Lm rises linearly from zero.
The voltage across the inductor L 1 is equal to: Therefore, the current i L1 starts to rise linearly from zero.
As shown in Figure 2a, C 1 is charged and its voltage rises during this mode. On the other hand, because S 1 and D 1 are conducting, the inductor L r and the capacitor C r form a resonant circuit. The voltage across L r is equal to: Its state equations can be expressed as: From Equation (6), the voltage across the capacitor C r and resonant current i Lr can be obtained and expressed as follows: where Z r and ω r represent the equivalent impedance and angular frequency of the resonant circuit, respectively.
The resonant frequency f r is designed to be greater than the switching frequency f s , and the duty ratio of S 1 is designed to be large enough so that i Lr would resonant to zero before S 1 was turned off. When i Lr resonates to zero at time t 1 , the circuit enters the next operation mode.
In this mode, D 1 and D 2 are off due to reverse bias. Currents i Cr and i Lr are both zero, and the voltage across C r remains unchanged. S 1 remains on, so i pri , i Lm and i L1 continue to rise. When the gate signal v GS1 changes from high-level to low-level, S 1 is turned off, and the circuit enters the operation mode III.

Operation Mode III (t 2 < t < t 3 )
At the end of mode II, i pri , i Lm and i L1 reach peak values, which are represented by i pri,peak , i Lm,peak and i L1,peak , respectively. When S 1 is off, there must be current loops to maintain the flux balance of T 1 , L m and L 1 . Therefore, there is an induced current in the secondary winding of T 1 . The induced current i sec charges the dc-link capacitor C dc , and can be expressed as: where L s represents the inductance of the secondary winding, and n represents the ratio of the number of turns between the primary winding and the secondary winding (n = N 1 /N 2 ). In this mode, C 1 is discharged and its voltage decreases. Meanwhile, the current of inductor As shown in Figure 2c, i L1 charges C r , C o2 , and C o3 . Because the peak value of i sec is proportional to the input voltage, the time required for i sec to decrease to zero is also proportional to the input voltage and is not a fixed value. Figure 3 shows the conceptual voltage and current waveforms when the input voltage is at the peak value. In this case, the time required for i sec to drop to zero is longer than i Lm and i L1 . In other words, i Lm and i L1 fall to zero earlier than i sec . When i L1 drops to zero, the circuit enters the operation mode IV.
In this mode, S 1 , D 1 , and D 3 are off, D 2 is on, the inductors L s and L m continue to release energy, and i sec and i Lm continue to decrease. At time t 4 , i Lm drops to zero and this mode ends.
In this mode, i sec continues to charge the dc-link capacitor. When i sec drops to zero, the circuit enters the next operation mode.
The currents of all inductors are equal to zero, and the LEDs are continuously lit by the energy provided by the parallel capacitors (C o1 , C o2 , and C o3 ). When the gate signal v GS1 becomes high-level, S 1 is turned on again, and the circuit enters the operation mode I of the next high-frequency cycle.

Principle of Current Balance
According to the description of the operating mode, the discharging current of C r flows through D 1 in mode I. Therefore, the average value of this discharge current in a high-frequency cycle is equal to the average current of the LED string one. In mode III and mode IV, C r is charged. As shown in and Figure 2c,d, this charging current flows through D 2 , so its average value is equal to the average current of the LED string two. Based on the principle of the ampere-second balance of the capacitor, that is that the net current of a capacitor will equal zero. In other words, the average value of the capacitor charging current is equal to the average value of its discharge current. Therefore, the average current of LED string one and LED string two would be equal.
In mode I and mode II, C 1 is charged through D 3 . Similarly, the average value of the charging current of C 1 is equal to the average current of the LED string three. In mode III and mode IV, C 1 is charged through D 2 , and the average value of the discharging current of C 1 will be equal to the average current of the LED string two. Applying the ampere-second balance principle to C 1 , it can be concluded that the average currents of the LED string two and the LED string three are equal.
Combining Equations (11) and (12), the current flowing through each LED string is equal.

Flyback PFC Circuit
The flyback converter is designed to operate at DCM during the entire input voltage cycle. The primary current i pri of T 1 rises linearly from zero during mode I and mode II (t 0 -t 2 ), and rises to a peak value, which can be expressed as: where D represents the duty ratio of the active switch. High-power factor and low THDi can be achieved by operating the flyback converter at DCM [20]. The high-frequency components of i pri can be filtered out by using the low-pass filter (L f , C f ), so that the input current i in will be equal to the average value of i pri in each high-frequency cycle. The input power is equal to the average value of the instantaneous power, which can be expressed as: Assuming that the conversion efficiency of the circuit is η, the output power is equal to:

Design Equations of the Flyback Converter
From Equation (16), the primary inductance L p of T 1 can be obtained, which is expressed by the following equation: The transformer primary current i pri rapidly drops to zero at the moment when the active switch is turned off. In order to maintain the magnetic flux balance of T 1 , it will induce a current in the secondary winding. The secondary current i sec can be obtained by substituting Equation (14) into Equation (9). At t 2 , i sec starts to decrease linearly from a peak value, and reaches zero at t 5 . The fall time of i sec is denoted as T off .
The primary inductance and secondary inductance of T 1 is proportional to the square of the number of turns, that is: Combining Equations (9), (14), (18) and (19) gets: At DCM operation, T off is less than (1-D)T s .
The longest fall time T off,max occurs when the input voltage is at its maximum and is equal to: In order to operate the flyback converter at DCM during the entire line cycle, the following inequality must exist: The higher the amplitude of the input voltage, the higher the dc-link voltage required to satisfy the inequality (23). However, since the active switch is not operated at zerovoltage switching on (ZVS), high dc-link voltage will cause more switching losses. It means that the proposed circuit is not valid for a universal input voltage range (110-220 Vrms). When the input voltage is different, the turn ratio of the coupled inductor of the flyback converter should also be different. In this way, an adequate dc-link voltage can be chosen to satisfy the inequality (23).

Design Equations of the Current Balancing Circuit
As shown in Figure 3, both inductors L m and L 1 are operated at DCM. At steady-state operation, the average value of the inductor currents is zero. Therefore, the increase in i L1 when S 1 is on is the same as the decrease when S 1 is off.
where D off,L1 is defined as the ratio of the falling time of i L1 to T s . Generally, the voltage and current of each LED string are approximately equal, that is V O1 = V O2 = V O3 = V O, and I LED1 = I LED2 = I LED3 = I LED from Equation (24), which gets: The net change of i Lm when S 1 is turned on and off is also equal to zero.
where D off,Lm is defined as the ratio of the falling time of i Lm to T s , and is equal to: As shown in Figure 1, I LED3 will be equal to the average current of L 1 since the net current of C 1 is zero.
Substituting Equation (25) into Equation (28), the inductance L 1 can be obtained, which is expressed as follows: During mode III and mode IV, i LM and i L1 flow through D 2 , therefore, I LED2 can be expressed as: Substituting Equations (25), (27) and (29) into Equation (30), the inductance L m can be obtained, which is expressed as follows: As stated in mode I, i Lr resonances to zero before S 1 being turned off. Therefore, the following inequality must exist: The inductance L r can be obtained from Equation (32), which is expressed as follows:

Experimental Results
A 90-W prototype circuit was built and tested to demonstrate the functions of power factor correction and current balancing capability. Table 1 shows the specification of the proposed LED driver. The load is three LED strings. Each string consists of 30 1-W LEDs connected in series. The rated voltage and current of each LED is 3.05 V and 0.328 A, respectively. Table 2 shows the circuit parameters. Some of the circuit parameters are designed as follows: The turns ratio n of T 1 is chosen as one. Assuming that the overall efficiency of the circuit is 90% and using Equation (17), the primary inductance and the secondary inductance can be calculated.

Inductance and Capacitance of the Resonant Circuit
The capacitance of the resonant circuit can be obtained as follows: In order to meet Equation (33), inductance of the resonant circuit must satisfy the following inequality: Here, L r is chosen to be 170 µH.

Inductances of L 1 and L m
Using Equation (23), the minimum value of the dc-link capacitance can be obtained.
Here V dc is chosen to be 110 V. The average voltage of the resonant capacitor is approximately equal to half of its maximum voltage. Therefore, the average voltage of the resonant capacitor is equal to: 2 × 0.328 2 × 279 35.8 × 10 −9 × 50 × 10 3 = 91.56 V The inductance L 1 can be calculated by using Equation (29).
The inductance L m can be calculated by using Equation (31).

Control Circuit and Experimental Results
The closed-loop control circuit of the driving circuit adopts the PWM controller (TL494), as shown in Figure 4. The output of TL494 is used to turn the active switch on and off, and its frequency can be determined by capacitor C T and resistor R T . The voltage across R sense in the main circuit is sensed via R 1 and R 2 and compared with the internal sawtooth-wave voltage of TL494 to adjust the duty ratio of the active switch. In this way, the LED current can be regulated.
Electronics 2021, 10, x FOR PEER REVIEW  12 of 16 are 33, 30, and 27, respectively. Figure 10 shows measured currents of the three LED strings. It was demonstrated that the current of each string still remains the same when the load power changes by plus or minus 10%. When the input voltage changes within a range of +/−20%, the duty cycle needs to be adjusted to maintain rated power operation. Figure 11 shows the measured efficiency at different input voltages. The circuit efficiency only slightly changes under different voltages. The LED power can be regulated by the control scheme of PWM. Figure 12 shows the currents of each string at 75%, 50% and 25% rated power. Similarly, when operating at different powers, the current of each string of LEDs is still the same. Figure 13 shows the measured efficiency at different output power. As shown, the circuit efficiency drops to 73.5% at 25% rated power. Figure 14 shows the prototype LED driver.    Figure 5. It is demonstrated that the input current is an approximate sinusoidal wave and in phase with the input voltage. It ensures high power factor and low THDi. The measured power factor and THDi are 0.99 and 2.91%, respectively. The measured output power and total losses are 90.3 W and 10.8 W, respectively. The circuit efficiency is calculated to be 89.3%. Figure 6 shows the harmonic spectrum of the input line current. The THDi is 2.91% and all harmonics are in compliance with the IEC 61000-3-2 Class C. Figure 7 shows the waveforms of the primary and secondary currents of T 1 . Both currents are operated at DCM, which is consistent with the design goal. Figure 8 shows the current waveforms of the inductors L m , L 1 , and L r , showing that i Lr has resonated to zero before the active switch is turned off; i L1 drops to zero before i Lm , and they all operate at DCM. Figure 9 shows the current waveforms of three LED strings with the same number of LEDs, showing that the current of each string is equal. This proves the current balancing capability of the circuit.
In order to further verify the current balancing function, the circuit driving three LED strings of different numbers of LEDs was tested. The number of LEDs in the three strings are 33, 30, and 27, respectively. Figure 10 shows measured currents of the three LED strings. It was demonstrated that the current of each string still remains the same when the load power changes by plus or minus 10%.     When the input voltage changes within a range of +/−20%, the duty cycle needs to be adjusted to maintain rated power operation. Figure 11 shows the measured efficiency at different input voltages. The circuit efficiency only slightly changes under different voltages. The LED power can be regulated by the control scheme of PWM. Figure 12 shows the currents of each string at 75%, 50% and 25% rated power. Similarly, when operating at different powers, the current of each string of LEDs is still the same. Figure 13 shows the measured efficiency at different output power. As shown, the circuit efficiency drops to 73.5% at 25% rated power. Figure 14 shows the prototype LED driver.  (c) 25% rated power (ILED1: 100 mA/div, ILED2: 100 mA/div, ILED3: 100 mA/div, time: 5 ms/div)

Conclusions
A single-stage LED drive circuit with power factor correction and current balancing capability is proposed. The circuit configuration mainly integrated a flyback converter, a buck-boost converter and a current balancing circuit. The flyback converter was used as a PFC converter, and the winding current was designed to operate at DCM to effectively reduce the THDi and improve the power factor; while the current balancing circuit applied the principle of capacitor ampere-second balance to achieve the same current for each LED string. Only one active switch was used and controlled by the method of PWM. A 90-W prototype circuit was built and tested. At rated power operation, the measured power factor was 0.99, the THDi was 2.91%, and the conversion efficiency was 89.3%. In addition, even where the number of LEDs in each string was different, the current balancing capability could still be achieved. Finally, the LED power was regulated from 100% to 25% rated power. The satisfactory experimental results have proved the feasibility of the proposed LED driver.

Conclusions
A single-stage LED drive circuit with power factor correction and current balancing capability is proposed. The circuit configuration mainly integrated a flyback converter, a buck-boost converter and a current balancing circuit. The flyback converter was used as a PFC converter, and the winding current was designed to operate at DCM to effectively reduce the THDi and improve the power factor; while the current balancing circuit applied the principle of capacitor ampere-second balance to achieve the same current for each LED string. Only one active switch was used and controlled by the method of PWM. A 90-W prototype circuit was built and tested. At rated power operation, the measured power factor was 0.99, the THDi was 2.91%, and the conversion efficiency was 89.3%. In addition, even where the number of LEDs in each string was different, the current balancing capability could still be achieved. Finally, the LED power was regulated from 100% to 25% rated power. The satisfactory experimental results have proved the feasibility of the proposed LED driver.