Efficiency Optimization Method for Cascaded Two-Stage Boost Converter

A method of optimal intermediate voltage tracking (OIVT) is proposed in this paper to improve efficiency for the cascade boost converter. The intermediate voltage can be adjusted by regulating the duty cycle of front stage and rear stage converters. To improve the control speed of the algorithm, the intermediate voltage range is determined by calculating the overall system loss. In addition, with the input-output relationship maintained, the root-mean-square (rms) current of the intermediate capacitor can be reduced by changing the phase difference between front and rear side PWM signals. On this basis, a method of optimal phase-shift angle tracking (OPAT) is proposed to further improve efficiency for the system and extend service life for the capacitor through relatively simple implantation. Besides, the proposed OIVT and OPAT method is applicable to other cascade topologies. A 1-KW prototype is constructed in the laboratory to verify the proposed control method. As confirmed by the experimental results, the maximum efficiency reaches 95.23% when the proposed control method is adopted, which is 2% higher than under the uncontrolled condition. It is demonstrated that the proposed OIVT and OPAT method is effective in improving efficiency for the system without needing any additional components.


I. INTRODUCTION
Photovoltaic (PV) cell is one of the most important energy in the sustainable energy system. However, the voltage level of this source is too low and unpredictable unstable. In addition, the output voltage of the photovoltaic cell is changed with climate conditions. Therefore, converters with high voltage conversion ratio are essential in new energy resources system as shown in Fig.1 [1], [2]. A classical boost converter is widely used in these applications, but high conduction losses on the power devices and serious reverse recovery problems can be occurred under the extremely large duty cycle condition.
Although both transformer-based and transformer-less dc/dc converters can be applied in high voltage gain condition. The requirements in power density, weight, size and cost of the power devices make the transformer-less topologies to become a better choice [3][4][5][6]. In addition, voltage spike generated by the leakage inductance of the coupled inductor can not be neglected for transform-based converters. Cascade converters are adopted in many power systems to manage sources and loads at different voltage levels simultaneously. In terms of cascade boost converter, the voltage conversion ratio is high enough with low conduction loss on the power devices [7][8][9]. In addition, the cascade boost converter represents a good trade-off between efficiency and duty cycle operating range. A robust controller design to obtain output voltage regulation in a quadratic boost converter with high DC-gain is discussed in [10]. However, the implementation of the proposed hybrid control method is difficult to implement. In addition, the output power is only 100-W and it has not been verified at high power rating. A hybrid control method for the voltage regulation of conventional boost converter is presented in [11]. The mathematical model and the control process are simple, but the implementation is difficult because many detect sensors and control elements are applied in the proposed control method.
Buck, boost, buck-boost, and Cúk converters are analyzed and compared as dc-dc converters that can be cascaded in [12], The buck and boost converters are shown to be the most efficient topologies for a given cost, while flexible in voltage ranges, buck-boost, and Cúk converters are always at an efficiency or alternatively cost disadvantage. However, the voltage gain ratio and power ratio of the traditional topologies are relatively low. In addition, maximum power point tracking (MPPT) method is applied to many PV panels which is difficult to realize.
A generalized switching modification method is proposed in [13] to reduce the rms current flowing into a dc-link capacitor in a dc-dc-ac structure consisting of a boost converter and a three-phase inverter, the proposed method has a better capacitor rms current reduction performance in the mid-power factor level (0.95 to 0.1). However, the proposed method is hard to implement and the control accuracy is not guaranteed.
Kolar and Round [14] analyzed the current stress on the dc-link capacitor in a voltage PWM converter system. The paper focuses on a one-stage inverter system and states that the capacitor RMS current is determined by the load current. The bus capacitor ripple current of cascaded two-stage converters for dc systems is analyzed in [15], the capacitor RMS current value can be reduced without affecting the converter normal operation or the need for extra sensing circuits. However, the intermediate voltage is not considered and the proposed method is not verified under high power rating.
Lu et al. [16] propose a carrier modulation method to synchronize the dc/dc converter and sinusoidal PWM (SPWM) inverter in order to reduce the dc-link capacitor ripple current. This modulation method is only designed for an ac inverter to be the rear stage. Focusing on the threephase back-to-back ac/dc/ac conversions, Gonzalez et al. [17] analyzed the dc-link current and proved that synchronizing PWM signals of the rectifier and inverter either in phase or antiphase would provide the lowest RMS current. This paper also only focuses on the ac/dc/ac topology and it is not suit for other topologies and dc-dc conversions.
The current and voltage ripple of a capacitor can be reduced by attaching an additional circuit composed of an energy storage element and a switch element to a dc-link capacitor in series or in parallel [18][19][20][21][22]. This method has the advantage of effective control of the power flow between the converters through the switching device and energy storage element. However, the cost and volume increase due to the additional auxiliary circuit, the complexity increases owing to additional control, and the ripple current generated due to the nonlinear characteristic of the switches cannot be reduced. Some methods have been proposed in [23][24][25][26] in order to increase efficiency of the dc-dc converter, however, additional components are required in terms of these studies which increases the difficulty of design.
According to the literature presented above, the dc-dc converter applied to renewable energy should satisfy the following requirements.
(1) The voltage conversion ratio is high enough in order to matching the dc-bus voltage.
(2) The control method is simple and accurate in order to easy to implement.
(3) The output power and efficiency of the overall system should be high enough.
(4) The proposed control method is effective in improving efficiency without needing any additional components.
In order to solve the problems presented above. This paper focus on analyzing the influence of different intermediate voltage and phase-shift angles of two-stage boost converter. The intermediate voltage can be adjusted by regulating the duty cycle of the front stage and rear stage converters. In addition, the rms current of the intermediate capacitor can be decreased by changing the phase difference between the front and rear side PWM signals. Therefore, OIVT and OPAT control method are proposed to improve the system efficiency quickly and accurately and prolong the capacitor lifetime with relatively simple implantation. A 1-KW prototype was set up in the laboratory in order to verify the proposed control method. The results of the experiment confirmed that the maximum efficiency of the proposed control method is 95.23% which is 2% higher than the uncontrolled condition.

A. VOLTAGE REGULATION METHOD OF THE CASCADE BOOST CONVERTER
Circuit diagram of the cascade boost converter is shown in The intermediate voltage can be calculated as The inductor current ripple generates an inductor core loss Pcore, which can be given as core sw where α,β,and γare the coefficient values of the core, B, IL, L and N are represent the flux density, inductor current, inductance and number of wingdings of the inductor. fsw is the switching frequency, and A is the cross-sectional area of the core. The current ripple of the front stage inductor L1 and rear stage inductor L2 can be expressed as in L1 The flow chart of the proposed OIVT method is described in Fig.3. The detailed tracking process is shown as follow: 1) The initial dc input voltage Vin0 and intermediate voltage Vm0 are applied. Vm0 is applied within a reasonable range. The converters on the front side and rear side are automatically adjust duty cycle to generate the designated intermediate voltage and output voltage. In addition, the input power Pin0 is measured and recorded by the controller.
2) The intermediate voltage Vm is then increased (or decreased) slightly to a new value Vm1 =Vm0+ΔVm (Vm1 =Vm0-ΔVm). The duty cycle of boost1 and boost2 are forced to regulate the output voltage to 380V. The input power is measured and record as Pin1 under this condition.
3) Compare Pin1 and Pin0. When Pin0 is smaller than Pin1, then repeat step 2 (Vm1 =Vm0+ΔVm) until the input power stops decreasing. Then, a maximum efficiency point is found. Otherwise, when Pin0 is larger than Pin1, the tracking direction is reversed, then repeat step 2 (Vm1 =Vm0-ΔVm) until the input power stops decreasing and a maximum efficiency point is found. 4) After waiting the time interval td, a new tracking process is presented in case that the load and/or the input voltage Vin have varied.
By applying the proposed control method, it is easy to find the optimal intermediate voltage value. Compared with the simulation methods proposed in [15], the proposed method is more accurate than the simulation method because of the real-time characteristic in terms of the tracking process.
The voltage control loop is shown in Fig.4, in terms of the output voltage Vo, the reference voltage Vo_ref is set to 380V which is taken as a constant value, the reference voltage Vm_ref is calculated from Fig.3 which is obtained from OIVT control method. The output voltage Vo and intermediate voltage Vm can be accurately controlled by adopting the voltage closed loop control.
From the above analysis, the system efficiency can be improved by applying the OIVT control method. However, the data processing speed is slow. From part III, the power loss can be calculated based on the polynomial taken Vm as the variable. Therefore, the variation range of intermediate voltage can be calculated based on the function (16)-(23), VOLUME XX, 2017 9 then the precise intermediate voltage can be obtained through OIVT control method rapidly.

B. PHASE DIFFERENCE REGULATION METHOD OF THE CASCADE BOOST CONVERTER
The efficiency of a system can be improved by applying the optimal intermediate voltage tracking method and the loss of power can be reduced by adopting OIVT. However, the intermediate capacitor as a component plays a vitally important role in the smooth operation of the two-stage boost converter. In addition, the service life and operating conditions of electrolytic capacitor can have a significant impact on the overall performance of the converter. According to [27], Thot is represented by the ambient temperature Tamb and the capacitor ripple current denoted as Thot increases in accordance with the increase of root-meansquare (rms) current in the capacitor shown as below where Thot is the capacitor temperature under operstion condition, Rha is the equivalent thermal resistance from hotspot to ambient, ESR(fi) is the equivalent series resistance at frequency fi , and Irms(fi) is the rms value of the ripple current at frequency fi. The equivalent circuits for different opeartion conditions are shown in Fig.5. According to the ON and OFF states of the two power switches S1 and S2, the current of the intermediate capacitor can be expressed as It can be inferred that both temperature and power loss can be reduced for the capacitor by reducing the rms current acting on the equivalent series resistance (ESR) of the capacitor. As for the cascade boost converter, the rms current of the intermediate capacitor is expressed as Power losses on the intermediate capacitor can be given as Depending on the exact combinations of phase-shift between the two power switches, the overall operating principle can be divided into three modes, as shown in Fig.6. DT is the phase-shift time of the two PWM signals and d is expressed as the phase-shift ratio. K1,U t and K1,D t denote the upstream slope and downstream slope of the corresponding inductor currents IL1, respectively. The rms current of the intermediate capacitor is shown in (9)- (11). Based on (9)-(11), the current of capacitor RMS in the three modes is calculated and compared, as shown in Fig. 7.  The calculated system efficiency is shown in Fig.7, from which it can be seen that, the optimal system efficiency based on phase difference is reached at 600W, 120°. The phase shift angle can be calculated and achieved rapidly using the calculated value. Therefore, the overall system efficiency can be calculated and improved by adjusting the phase difference value.  Regarding cascade boost converter, the rms current of the intermediate capacitor can be adjusted by regulating the phase difference of the duty cycle D1 and D2. In addition, the input and output relationship of the converter can be maintained even in the case of significant phase angle changes. Taking advantage of this feature, an optimal phase angle tracking (OPAT) method is proposed in this paper. Fig.8 shows the inductor current IL1 and IL2 and capacitor current Icm under different phase-shift conditions. It can be seen from this figure that as the phase angle changes for the inductor currents IL1 and IL2, the current of the intermediate capacitor varies accordingly. That is to say, the current of the intermediate capacitor can be changed by regulating the phase difference of the duty cycle D1 and D2. The flowchart is presented in Fig.9 and the tracking process is detailed as follows. 1) First, the approximate range of the phase-shift angle is calculated based on (9)-(11) in order to improve the computing speed.
2) The converters on the front and rear sides are used to adjust duty cycle automatically for the generation of specified intermediate voltage and output voltage. In addition, the input power is measured and recorded using the controller.
3) Then, the phase difference θ is increased slightly to a higher level (Δθ=5°). The duty cycle of boost1 and boost2 is forced to regulate the output voltage to 380V. In addition, the input power is measured and recorded again using the controller.
4) A comparison is drawn between Pin(n) and Pin(n+1). When Pin(n+1) is smaller than Pin(n), step 2 is repeated until the decline of input power stops. Then, the optimal phaseangle point is determined.   Fig.10 shows the block diagram of the proposed control method. As for the intermediate voltage range, it can be calculated according to part III for the improvement of control speed. Then, the optimal intermediate voltage is calculated and operated using the OIVT control method, while the intermediate voltage and output voltage are stabilized using the PI control method. In the meantime, the OPAT-enabled signal is started. Afterwards, the OPAT control method is applied. Since OPAT control method has effects only on the current of the intermediate capacitor, there is not conflict between the OPAT and OIVT control methods. The optimal phase-angle θ can be adjusted using the OPAT control method, while the input and output power is calculated using the input output voltage Vin and Vo, as well as the input output current IL1 and Io. With the proposed control method used, the optimal intermediate voltage and phase-angle can be determined in a fast and accurate way. In addition, the proposed tracking method is effective under different input and output conditions.

C. CONTROL METHOD OF THE CASCADE BOOST CONVERTER
In addition, the proposed algorithm can be applied to other cascade topologies, such as cascade buck converter and cascade buck-boost converter, of which the former is applied at high current and low voltage while the latter is applied given a wide range of input and output voltage. Table I shows the comparison performed between the proposed control method and other control methods. From the perspective of overall performance, the proposed method is clearly advantageous in efficiency, power rating and complexity. The stability criterion is the adjustment time and accuracy of the control method with the load variation. The complexity criteria are the number of devices and complexity of the control method. VOLUME XX, 2017 9

III. POWER LOSS ANALYSIS OF CASCADE CONVERTER
It is assumed that RS1 and RS2 are the resistance of the power switches S1 and S2, VF1 and VF2 are the threshold voltage of the power diodes D1 and D2. In addition, RL1, RL2 and RC1, Rcm, Rco are the ESRs of the L1, L2 and Cin, CM, Co, respectively. The power loss model of the cascade boost converter is shown in Fig.11.
The power losses of the cascade boost dc-dc converter are mainly consisted by four parts: inductor loss, power switch loss, diode loss, and capacitor loss.
The copper losses of the inductors are given as The rms current of inductor L1 and L2 are expressed as The ripple current of inductor L1 and L2 can be rewritten as The inductor losses are calculated as L LC core P P P =+ (15) The core losses of the inductors are derived in (3) and defined as Pcore. The conduction losses and switching losses of the switches S1 and S2 can be calculated as The capacitor losses are expressed as SC SW S P P P =+ (18) where tru, tfu, tri, and tfi are the voltage rise time, voltage fall time, current rise time, and current fall time, respectively.
The power losses in the diodes include the conduction losses and reverse recovery losses. The reverse recovery loss is neglected because the reverse recovery time in Schottky diode is very short.
According to the efficiency definite above, the efficiency can be derived as The power losses under OIVT control method can be expressed as (19). From (19),Vm and Po are treated as variables.

LOSS
L S D C P P P P P = + + + According to the loss calculation results, the overall loss formula is expressed in (19), which is a function of intermediate capacitor voltage and output power, it is easy to analyze the overall efficiency under different Vm and constant output power.
The efficiency of the overall system is calculated as shown in Fig12. From Fig.12, the optimal efficiency of the system is appeared at 600W, 130V. According to the calculated value, the intermediate voltage range can be achieved rapidly, the optimal intermediate voltage can be accurately obtained by OIVT control method.
The OIVT control method obtains the optimal intermediate voltage by calculating and voltage tracking process. OPAT control method contains the optimal phase difference by calculating and phase-shift angle tracking process with the input-output relationship maintained. The control time is shortened by calculation, the two control methods do not interfere with each other, and the optimal efficiency is obtained by adjusting the current and voltage stress of each component.

IV. EXPERIMENTAL RESULTS
In order to verify the performance of the proposed control method, a 1-KW prototype is constructed in the laboratory. The component parameters of the cascade boost converter are listed in Table II.
Silicon carbide power MOSFETs IRFP4137PBF and IPW60R280P6 are applied as S1 and S2. In addition, fast recovery diode HER3004C and IDW30G65C5 are used as D1 and D2. The dc electronic load serves as a resistance load. The efficiency is measured as the dc load power divided by the supplied dc power. The (Equivalent series resistances) ESRs of the capacitors are denoted as Rcm and Rco, as measured using the ESR meter at the operating frequency. The parameters of the semiconductors are obtained from datasheets.
The experimental waveforms of IL1, Vm, and Vo at different dc input voltages are shown in Fig.13. According to the measurement performed at the minimum dc input voltage, the output voltage Vo stabilizes at 380V when the proposed control method is used. In addition, Fig.13 Fig.13(b), it can be found out that the intermediate voltage Vm =120V and D1=0.5 at the maximum dc input voltage when the OIVT method is applied. Fig.14 shows the experiment results of IL1, IL2, VM, and Vo at different phase-shift angles. The phase-shift angle is adjusted to 150° using the proposed OPAT control method at the minimum input voltage, as shown in Fig.14(a). Differently, the phase-shift angle is adjusted to 120° using the proposed OPAT control method at the maximum input voltage, as shown in Fig.14(b).   Fig.15 shows the transient waveforms of the proposed tracking algorithm from 500-W to 1-kW at different dc input voltages. According to Fig.15, given the maximum and minimum input voltages, as well as load variation, the output voltage maintains stability after transient adjustment made to the proposed OIVT and OPVT control method, which evidences the effectiveness of the proposed control method. Fig.16 shows the capacitor temperature as measured under the controlled and uncontrolled conditions. As show in Fig.16(b), the temperature of the intermediate capacitor is 47° when the proposed control method is not used. From Fig.16(a), it can be seen that the measured temperature is 42° which means it is 5°lower under the controlled condition. These results demonstrate that using the proposed OPAT control method is effective in reducing the RMS current value of the intermediate capacitor without affecting the normal operation or needing additional sensing circuits for the converter. VOLUME XX, 2017 9

(b) FIGURE 18. Calculated power losses distributions with Po=1-KW (a) Vin
The efficiency of the proposed control method is shown in Fig.17. According to Fig.17(a), when the OIVT control method is adopted and the intermediate voltage varies, the maximum efficiency of the overall system reaches 93.33% at Vm =130V and Vin=48V. In addition, the maximum efficiency of the overall system reaches 94.87% at 120V when Vin=60V.The calculated efficiency is close to the measured efficiency. As shown in Fig.17 (b), with the OPAT control method used and the phase-angle changing, the maximum efficiency of the overall system reaches 93.47% at 150° when Vin=48V. In addition, the maximum efficiency reaches 95.23% at 120° when Vin=60V. Therefore, it can be concluded that with the proposed control method applied, the maximum efficiency is 2% higher than under the uncontrolled condition (Vm=90V, θ=30°). As for the uncontrolled voltage, it is set to 90V because the optimal range of duty cycle is 0.35-0.7 for the traditional boost converter. Upon a comparison with the proposed OIVT and OPAT control method, it can be discovered that the OIVT control method can improveefficiency to a more significant extent. To be specific, it is is 5 times higher than the OPAT control method.
Efficiency comparison of the two control methods is shown in Tab.III. The maximum efficiency improvement of OIVT and OPAT are 1.35% and 0.4% respectively. The average efficiency improvement of OIVT and OPAT are 1.25% and 0.35% respectively.
The power loss analysis is conducted under the experimental conditions when Po=1-KW. According to the analytical results of power losses breakdown as shown in Fig.18 (a), the power loss is determined as 65.3W when Vin=48V. Thus, it can be concluded that the major contributor to power loss is conduction loss, including the loss of switching devices and inductors. It accounts for 33% of the total losses. When the input voltage Vin =60V as shown in Fig.18 (b), the power loss is calculated to be 47.7W. In this case, the major contributor to power losses is conduction loss, accounting for 30% of the total losses.

IV. CONCLUSION
In this paper, an analysis is conducted as to the effect of intermediate voltage and phase-shift between the duty cycle of cascade two-stage boost converter. A method of optimal intermediate voltage tracking (OIVT) is proposed in this paper to improve efficiency for cascade boost converter. The intermediate voltage can be adjusted by regulating the duty cycle of front stage and rear stage converters in a fast and accurate way. In addition, a method of optimal phaseshift angle tracking (OPAT) is proposed to further improve efficiency for the system and extend service life for the capacitor through relatively simple implantation.
A 1-KW prototype is built in the laboratory to verify the proposed control method. According to the experimental results, the maximum efficiency reaches 95.23% when the proposed control method is used, which is 2% higher than under the uncontrolled condition. Therefore, the proposed control method is effective in significantly improving the overall efficiency for the system. The model and analysis presented are of generic nature and thus applicable to most of the existing cascaded two-stage converters.
In the future work, in terms of the control method, the current and voltage acquisition process need to be simplified, and the angle calculation needs to be more accurate. Moreover, the control method proposed in this paper needs to be extended to the inverter in the future.