Design of a high performance AC-DC LED driver based on SEPIC topology

Received Mar 31, 2020 Revised Jan 15, 2021 Accepted Feb 1, 2021 Light emitting diodes (LEDs) are current driven devices. So, it is essential to maintain the stability of LED voltage and current. Variation of temperature may cause of instabilities and bifurcations in the LED driver. Driving LEDs from an offline power source faces design challenges like it have to maintain low harmonics in input current, to achieve high power factor, high efficiency and to maintain constant LED current and to ensure long lifetime. This paper proposes the technique of harmonics reduction by using parametric optimization of Single ended primary inductor converter (SEPIC) based LED driver. Without optimization of SEPIC parameters input energy will not be properly transferred to the load and this un-transferred energy will be transmitted to the source. Consequently, the quality of input current will be hampered i.e. harmonics will contaminate the input current. Focussing this, the paper has presented the design of a non-isolated integrated-stage singleswitch constant current LED driver operating in discontinuous conduction mode (DCM) in SEPIC incorporating the design of control circuit with soft start mechanism. This LED driver has achieved a good efficiency (90.6%) and high-power factor (0.98) with reduced harmonics (3.35%). System stability has been determined and simulation studies are performed to confirm the validity of the LED driver circuit. A laboratory prototype is built to verify the functionality and performance of the proposed LED driver.


SEPIC PFC CONVERTER
For an input voltage , let is the rectifier output voltage and the inductor current 1 and 2 flows through inductor 1 and 2 respectively. The (1)-(4) are taken from Rui [24] to derive some useful relations in DCM mode ( Figure 1).
Input voltage, = , So according to the SEPIC functionality 1 = 2 . The total inductor current.
The relationship between voltage and current in an inductance is as follows, 1 ( ) = 1 ( ) So, the inductance current changes as.
Diode current = 2 + , where is the average output current. Since average of 2 = 0, we get average of = . So, the average output current is as.
If the average output current flows through resistor .
The (14) shows that in SEPIC DCM input current follows input voltage and it is possible to achieve unity power factor. However, as discussed earlier, for bridge rectifier diode input current wave shape becomes distorted and harmonics is contaminated in the input current. So, harmonics reduction is essential to achieve high power factor.

PROPOSED LED DRIVER CIRCUIT
The LED driver circuit consists of single-phase ac voltage source, inductor, capacitor, diode, MOS switch and LED module. The schematic diagram of LED driver circuit is shown in Figure 3. Control circuit design, the control circuit consists of two closed loops control units-outer circuit controls output current by regulating the output voltage and inner circuit controls input current to improve power factor. Outermost closed loop realizes the current through the LED module and keeps it constant. This current is sensed with a resistor and the corresponding sensed voltage is compared with a fixed reference dc voltage in a voltage error amplifier. Voltage error amplifier is an integrator and generates an error signal. The current generated from it is passed through the current error amplifier as its reference current. Current error amplifier is shown in Figure 4 (a). The inductor current ( ) is sensed and compared with the reference. Current error amplifier performs proportional and integral function (PI control). It addresses the slow response of voltage error amplifier. It ensures stable operation and makes compensation easier. . If increases rise-time decreases, overshoot increases and overshoot error decreases. If increases rise-time decreases, overshoot increases, settling time increases, eliminates steady state error. First the parameters of the compensator are optimized by the simulation of LED driver (Main circuit +control circuit). By using the circuit parameter, the transfer function has been determined. The following steps are taken to choose gain in order to get the desired response, i) obtaining the open loop response and determine what needs to be improved, ii) adding proportional control to improve rise time, iii) adding integral control to eliminate the steady state error and, iv) adjustment and by changing circuit parameters until obtaining a desired overall response. If stability is bad and gain is needed to change to meet stability criterion the above procedure will be repeated. Finally, the stability has been determined by (i) step response and (ii) root-locus method explained in Section 5.
In DCM though power factor is high, the input current harmonics is high. Bridge rectifier draws distorted current from input AC and causes high THD, very low PF and very low efficiency to the LED module. In order to reduce harmonics in the input current, multiplier is used in the control circuit. It eliminates the distortion in input current wave shape by multiplying the output of current error amplifier with replica of the input ac voltage. The output signal of multiplier is naturally synchronized and symmetric to the input AC voltage, which is the condition to achieve unity power factor with reduced harmonics. Then PWM pulses are generated by comparing a saw-tooth wave with the reference produced by the multiplier. The details control circuit is shown in Figure 4 (b). The function of the soft start circuit is to prevent sudden rise of input current and overshoot of voltage in the starting period to prevent damage. Pulse thinning mechanism is used to remove some pulses from a clock pulse and generates thin pulse. In the soft start circuit, clock pulse is generated by using A stable multivibrator. The output of the multivibrator is clamped to get only positive pulse. Clk2 is obtained from clock pulse generator after removing some pulses' waveform is generated from control circuit. Clk2 and PWM are the inputs of AND gate and thinner pulse is obtained from the output. This thinner pulse is fed directly to the MOSFET through MUX at the onset of starting. The selector of 2-1 MUX determines starting period and normal operation. In normal operation regular PWM pulses are fed to the MOS gate. It is to be noted that all wave forms required in the driver is generated internally and no external source is needed in the drive circuit. In the designed LED driver, the voltage error amplifier uses single Opamp for both comparison and amplification purposes. Similarly, the current error amplifier uses a single Opamp for comparison and PI controlling purposes. The function of sawtooth wave is obtained from square wave generator by using single Op-Amp only. Thus, the number of components in the control circuit is reduced. The overall control circuit is used to improve the step response and increase the stability of the circuit. It also plays the role in reducing THD and improving power factor.

HARMONICS REDUCTION BY SEPIC PARAMETER OPTIMIZATION METHODOLOGY
LEDs are a nonlinear load that generates harmonics. LED driver delivers constant current to LED lamp. In order to get desired DC output from AC input a full bridge rectifier is used before SEPIC. These diode rectifiers cause highly distorted input current and generates harmonicist of the input current is an important factor in LED driver and it should be kept as low as possible. Lower THD in LED driver ensures higher Power Factor, lower peak currents and higher efficiency.
We know that for a sinusoidal source and nonlinear load 1 is the RMS value of input current of fundamental frequency and is the RMS value of total component of input current frequency. According to (14) for the LED driver operating in discontinuous The (16) if the RMS value of input current of fundamental frequency is higher, distortion factor becomes higher and THD becomes lower. Theoretically, if = 0 , distortion factor will be 1 as from (16), and This is possible only when the converter parameters are optimized to make input current distortion to zero and to make the input current in phase with input voltage to impose the circuit behavior as a resistive load. But practically in order to reduce harmonics in the input current the input inductance( 1 ), output inductance ( 2 ) and input capacitance( 1 ) are required to be optimized [25]. Output capacitor ( 2 ) is required to optimize to reduce output voltage and current ripple. This harmonic compensation and power factor improvement can be done by optimizing SEPIC parameters by the following methodology for nonlinear load LEDs along with properly designed feedback circuit.

SEPIC parameter optimization methodology
Harmonics arises in the input current for bridge rectifier diode, switch, and nonlinearity of LEDs. The factors that effect on harmonics in the input current are the value of inductor 1 , capacitor 1 , energy transfer between capacitor 1 and inductor 2 . Output current ripple depends on the filter capacitor 2 .

THD reduction a. Fixing the value of input Inductor 1
The relationship between input inductor 1 and input ripple current △ 1 .
; where switching frequency (18) Input inductor current ripple △ 1 can be reduced by using greater value of 1 , otherwise harmonics will be high.

b. Fixing of output inductor
The voltage conversion ratio M can be obtained by applying the Power-balance principle [26]: where conduction parameter = 2 ; here is the equivalent inductance of 1 and 2 in parallel and is the dynamic resistance of LED load, For DCM operation, 1 < 1 − Thus, the value of − can be evaluated [28] by: For DCM operation should be = 0.85 − . Thus, by evaluating an equivalent inductance is obtained as (20).
The value of 2 can be expressed as (21).
c. Fixing Input capacitor 1 has a significant influence in the input current wave shaping. The value of 1 [27] will be such that < < , where , line current and resonance frequency respectively.  1 , 2 and 1 should be optimized for THD reduction. Without optimization harmonics in the input current becomes high. The simulated plot in Figure 5 (a). is obtained without optimization of 1 but 1 and 2 optimized. Here 1 = 0.05 , 1 = 10 2 = 36.24 . It shows . . =0.76, = 64.89% and hence P.F. and THD are not satisfactory. It is found that the effect of 1 is dominating in the input current THD.
Capacitor 1 is fundamental in obtaining a high-quality input current. 2 has comparatively less effect on THD. Without optimization of 2 and 1 , the energy of 2 will not be properly transferred to the load and this un-transferred energy will be transmitted to the source, as a result harmonic will be contaminated in the input current. Again, current ripple of input inductor( 1 ) also effect the THD and it can be reduced by increasing 1 as discussed before. By using the (18)

Reduction of output voltage and current ripple
Fixing output capacitor C 2 , according to the (23) relationship, 2 can be obtained for the desired ripple value of output voltage ( ).

≥ 2
If capacitor current is and capacitor voltage ripple is∆ then ) is low, so the AC part will flow through the output capacitor. A ripple voltage is produced at the output. This ripple of output voltage needs to be sufficiently low so as output current does not flicker. From the (23) and (24), the large the capacitor, the better it reduces the ripple. The simulation of output voltage and current before and after optimization of 2 are shown in Figure 6. After optimization LED voltage and current becomes smoother. Thus, a high-performance LED driver can be designed by optimization of SEPIC parameters along with a well-designed feedback control circuit.
Table1 shows the simulated data of optimization of SEPIC parameters ( 2 , 1 ), for harmonic reduction. From the data in Table 1 and simulation result, it is found that the input capacitor 1 plays the main role of transferring energy from input port to output port and via output inductor 2 . 1 must be a low valued capacitance. The energy of 2 and 1 must be reimbursement to each other. Input current ripple mainly depends on Inductor 1 so it also plays a vital role in harmonics reduction. 2 is filter capacitor and it smooths the output.
The total power loss shown in simulation is 6.2%, Efficiency is 93.78%, THD 3.7% at 220V. The Simulated Power losses are shown component wise in Figure 7. Here Divider is the resistance used to take replica of input voltage to the Multiplier and R-diode and S-diode denote rectifier diode and SEPIC diode respectively. It is seen that the largest power loss occurs in MOS Switch(2%), slightly above 1% is in divider resistance, below 1% in rectifier diode and then in SEPIC diode and least power loss occurs for biasing.

TRANSFERFUNCTION AND FEEDBACK CONTROL
The power stage (SEPIC) of closed loop system is nonlinear system. Nonlinear system is usually difficult to model and it is also difficult to predict the system behavior. So, it is better to approximate nonlinear system to linear system. For this state space averaging technique is used to describe SEPIC using a system of linear differential equations. Differential equations of SEPIC and average matrices are given in section 5.1. in the paper. Details Operating point is not discussed here as it is a well-known phenomenon.

State space equations
The state space equations for SEPIC during three switching states in DCM as shown in Figure 8. for state A: < < where the rectified input voltage is ( ) and ̇= and the state vector is defined as (28). The output vector Y = 0 . The averaged matrices for the steady-state and linear small-signal statespace equations can be written as = 1 + 2 1 + 3 2 and = 1 + 2 1 + 3 2 . From the equivalent circuit the matrices 1 , 2 , 3 , 1 , 2 , 3 and more are as (29) to (33).

Transfer function of SEPIC with feedback control
The power stage output transfer function of the SEPIC converter is obtained by solving the state space (38) and output to input transfer function is obtained as (39). The open loop transfer function of the whole system can be defined.
is the transfer function of without parameters of the compensator have been optimized for stable operation of the designed LED driver. The transfer function of the compensator of the designed LED driver is obtained.
The overall open loop transfer function for the system with compensator is found from (40). From step response Figure 9 (a) it is found that for compensated model the system reaches to steady state within only 0.2 seconds. From Figure 9 (b) the root locus of the SEPIC converter indicates stable operation of the compensated system.

RESULTS AND DISCUSSION ON PROTOTYPE
A prototype of the proposed LED driver is built to obtain the best execution of the driver circuit. Major objective is to reduce harmonics in the input current with the constant output current and to maintain good power quality. The LED Driver is designed for fifteen LEDs connected in series. Each LED is of 0.5W power rating. Voltage drop of 15 LEDs are about 45 volts for optimum operation as voltage drop of each LED is about 3 volts. This is another salient feature of our designed LED driver that it works at constant LED load by keeping output voltage and current constant with the variation of input voltage from 90V to 270V. So, Load disturbance rejection is not applicable. When input voltage changes, inductor current also changes. The amplitude of inductor current controls two loops of control circuit. This change of Inductor current makes change in output voltage. By realizing the change of output voltage, voltage feedback control signal changes. The inductor current and the feedback control signal altogether act to regulate the output dc voltage to the preselected value. Thus, the control circuit functions in such a way that it completely absorbs input disturbance, no input disturbance rejection is needed.
To enhance power quality i.e., to reduce harmonics in the input current optimization of inductor 2 and capacitor 1 are to perform according to (21) and (22). Output capacitor 2 is also optimized according to (24) to reduce the output current ripple. 1 is optimized according to (18) to get desired input current ripple. No extra component is used in the LED driver power circuit. From the measured value it is clear that after optimization THD has been reduced significantly. Multiplier is used in the control circuit to get a low harmonic with high power factor. After rectifier no filter capacitor is used. Table 2 shows the parameter values of SEPIC and basic specification of the converter. Figure 10  respectively as shown in Figure 10 (b). The result is also satisfactory.  The measured data shows that the designed LED driver consumes 7.745 watt including dc bias at an input voltage of 220 rms and produces an output of 7.0224 Watts. Hence it has measured an efficiency of 90.67% and power loss is 9.33% at power factor= 0.98, = 3.35%. As we have seen from simulated result in Figure 6 the highest power is consumed in the MOS switch. Figure 11 (a) and Figure 11 (b) shows the power factor and efficiency remains almost constant with increase of input voltage and duty cycle. However, THD decreases with increasing input voltage but increases with increase of duty cycle.  Table 3 shows the performance parameters of the proposed LED Driver as obtained in experiment. We know that it is hard to obtain high PF and high efficiency simultaneously and there is a trade-off between the two. The proposed LED driver shows high PF and relatively high efficiency with constant LED driving current achieved by optimization of SEPIC parameters and well-designed feedback control circuit.  Table 4 shows comparisons with LED driver presented in [28], [29] and the proposed one. The proposed LED Driver shows the feature of better input current THD compared to [29] and it offers a smaller number of components with same efficiency compared to ref. [28]. The prototype of LED driver is shown in Figure 12.  Figure 12. Prototype of LED driver

CONCLUSION
In this paper, a high performance SEPIC based LED driver has been designed and a prototype has been built and evaluated. Parametric optimization of SEPIC inductors and capacitors are performed with the design of a double loop feedback control circuit of LED driver. The LED driver maintains around 150mA LED current in universal voltage range 90-270 Volts with 90.6% efficiency, 0.98 power factor and 3.35% harmonics in the input current with a simple control circuit and reduced number of components. These advantages are desirable in residential as well as commercial lighting.