Volume 114 No. 10 2017, 457-465 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Design, Analysis and Simulation of Closed loop Synchronous Buck Converter using k-factor method M. Sai Krishna Reddy *, B.Lakshmi Prasanna Kumar, Aayush Misra K L University, Vaddeswaram, Guntur, AP, India saikrishna.mule@gmail.com K L University, Vaddeswaram, Guntur, AP, India chandanakovvuri@gmail.com K L University, Vaddeswaram, Guntur, AP, India lakshmiupparapalli@gmail.com Abstract Closed loop control of Dc-Dc converters is crucial in many applications for the better voltage regulation and performance of the converters. Traditionally many controller structures are there to get the closed loop control of converter, but each and every control structure is having its own disadvantages. Compensators are more suitable compared to controllers with their advantages. In this paper design and analysis of type-2 compensator using k-factor method for synchronous buck dc-dc converter is presented. Simulation analysis done for two cases 110v to 48v conversion and 110v to 24v conversion. The proposed converter primarily suited for Vehicle Control Unit (VCU) of Electric locomotive which needs variable voltages from standard 110v battery. Key Words and Phrases: K-factor method; DC-DC Converter; Compensator;Closed loop; Synchronous Buck Converter, ZCS Introduction DC-DC converters play significant role in many applications [3]. Many times these converters needed as point of load converters in power management systems. Particularly DC-DC Buck converter [7] used POL converter for matching load current requirements. For an Electric Locomotive Vehicle Control Unit (VCU) is very important to control and monitor various systems and panels in Loco pilot space. For continuous operation without any interruption most of the times VCU operated with standard battery of rating 110V Dc with few amps. One need Buck dc-dc converter to get different stepped down voltage levels for different units of VCU. Traditional buck converters are replaced with synchronous rectified converter to have bidirectional power flow capability from source to load and 457
load to source based on the potential levels at two ends source and load. To maintain maximum power density it is necessary to operate converter at very high switching frequencies the order of few khz to tons of khz. But with the high frequency of operation converter compactness can be achieved but losses incurred in converter increases which will greatly degrade the efficiency of overall system process [4, 6]. To improve the converter efficiency, soft switching concept brought into converter which helps in reduction of switching losses. Although conduction losses present they are not much significant when compared with switching losses in switched mode power dc-dc converters. Converter control strategies are very important in the design to operate the converters over wide range of input and output variations making converter more stable system. Traditional controllers can be designed and implemented for closed loop voltage mode and/or current mode control of dc-dc converters. But they suffer with disadvantages like time taking dynamic response and narrow range control over source or load variations. This paper proposes k-factor method approach for compensator design to control synchronous buck DC-DC converter [1, 8]. Converter operated in two cases 110v to 48v and 110v to 24v. Design calculations for compensator structure and resonant inductor and capacitor values for soft switching are presented in section II. To validate the concept proposed, the converter was simulated in PSIM9.0 [2] and results discussed in section III. Design calculations of the compensator and Converter along with steady state analysis of the Proposed Converter The following assumptions made for the analysis of the ZCS soft switched Buck DC-DC converter which is shown in figure 2.1 1. Filter inductance is large enough to maintain current ripple as low as possible. 2. Filter capacitance is large enough to minimize output voltage ripple. 3. The converter was analyzed under steady state. 4. All the components are assumed to be ideal for analysis. Output voltage of buck converter is given as (2.1) Inductance and capacitance values is given as ( ) (2.2) ( ) (2.3) For the 110/24V Buck converter L=416.667, C=1.736 and for 110/48V Buck converter L=666.667, C=0.8681 458
Voltage conversion ratio, (2.4) Characteristic impedance, (2.5) 0resonant frequency, (2.6) By substituting the parameter to the above equations values of the resonant inductance and capacitance. For 110/48V converter obtained are 20 and 0.02 and similarly for 110/24V converter values are 7 and 0.015 respectively. K-factor method approach design: To calculate the cross over frequency the feedback signals bandwidth should be at least 1/10th of the switching frequency. To obtain the necessary cross over frequency we should adjust the gain constant. After obtaining the cross over frequency and phase margin, plant phase is calculated, at the cross over frequency which can be obtained directly using PLECS software or by keeping the cross over frequency in the plant transfer function. Phase lead compensation is determined by Calculate the constant K, Wp, Wz. (2.7) ( ) (2.8) (2.9) (2.10) At the cross over frequency and Kc=0, calculate the magnitude of the loop gain. The designed controller at cross over frequency we get Kc is inversely proportional to magnitude of the loop gain. The proposed converter configuration shown in figure 2.1 and the converter operates in four modes. In Mode-I S1 and S2 both are conducting and the equivalent circuit diagram shown in figure 2.2, prior to this mode S2 is already ON which carries Io through body diode of S2, S1 gated at starting of this interval. Mode-II equivalent circuit shown in figure 2.3 when ILr reaches Io S2 gate pulse removed which ensures ZCS turnoff of the device. Mode-III equivalent circuit shown in figure 2.4, where in this mode ILr reaches to zero, negative current will be flowed through diode which ensures ZCS turn off S1 device. Mode-IV equivalent circuit is shown in figure 2.5 where Icr is negative Io. Figure 2.6 shows the type-ii compensator implemented using Op-Amp Integrator and Comparator circuits for PWM generation for the switches S1 and S2. S-R Flip-Flop is used to hold the state of PWM signal. All the design values for Op-Amps and voltage divider circuit are designed using smart control of PSIM9.0. 459
S1 Lr L Vdc Cr S2 Co RL + Vo - Resonant Circuit Filter Circuit Figure 2.1 Zero Current Switching Synchronous Buck Converter Circuit S1 Lr L Vdc Cr S2 Co RL + Vo - Figure 2.2 Mode-I equivalent circuit diagram S1 Lr L Vdc Cr S2 Co RL + Vo - Figure 2.3 Mode-II equivalent circuit diagram S1 Lr L Vdc Cr S2 Co RL + Vo - Figure 2.4 Mode-III equivalent circuit diagram 460
S1 Lr L Vdc Cr S2 Co RL + Vo - Figure 2.5 Mode-IV equivalent circuit diagram Voltage Divider Op-Amp Comparator Sensed output voltage Op-Amp Integrator S-R Flip flop Figure 2.6 Type-II compensator structure implemented with op-amp Simulation result analysis of the proposed approach The Figure 3.1 shows the results for the 110/48VBuck converter which indicates the input voltage, output voltage and inductor current. Figure 3.2 indicates the input voltage, output voltage and induction current of 110/24V Buck converter. Figure 3.3 indicates the ZCS soft switching for 110/48V buck converter. Figure 3.4 indicates the step change in input voltage and its corresponding closed loop output voltage response for the 110/48V converter. Figure 3.5 and Figure 3.6 indicates the step change in input voltage and its corresponding closed loop output voltage response of 110/24V buck converter. Figure 3.7 and Figure 3.8 shows the pulse width modulation (PWM) of closed loop schemes for the 110/48V and the 110/24V converters respectively. 461
Figure 3.1 Input voltage, output voltage and inductor current for 110/48V Buck Converter. Figure 3.2 Input voltage, output voltage and inductor current for 110/24V Buck Converter. Figure 3.3 Zero Current Switching of 110V/48 Buck Converter. 462
Figure 3.4 Step change in input voltage and closed loop output voltage response for the 110/48V converter. Figure 3.5 Step change in input voltage Figure 3.6 Closed loop output voltage response of 110/24V converter 463
Figure 3.7 PWM pulses for the closed loop 110/48V Buck Converter Figure 3.8 PWM pulses for the closed loop 110/48V Buck Converter Conclusion A new closed loop design approach presented here for making the converter stable for wide range line and /or load variations. Zero current switching achieved by resonant Soft switching converter which reduces switching losses and improved efficiency of the converter. The converter is designed and simulated with 120 khz switching frequency in both 110/48V and 110/24V converter cases, which makes the converter size and weight reduction. References [1] Venable hd the k-factor. A new mathematical tool for stability analysis and synthesis. In: Proceedings of Powercon 10.www.venable.biz [2] PLECS (Piecewise Linear Electrical Circuit Simulation).www.plexim.com/ [3] RASHID MH (2001) Power Electronis Handbook, 6 th edition. [4] Tang w.lee FC, Rid4ey RB (1993) small-signal modeling of average current- mode control. IEEE Trans Power Electronics 8(@):112-119 [5] Lee SW Demystifying Type II and Type III compensators Using Op-Amp and OTA for DC/DC Converters--(Texas Instruments Application Report July 2014) [6] Czarkowski D, Kazimierc zuk MK (1992) Static and dyanamic circuit models of PWM buck-derived DC-DC converters. IEEE Proc Part G. Circuit Devices Syst 139(6):669-679 [7] Renewable energy From Wikipedia, the free encyclopedia. [8] K.M Ravi Eswar and D. Elangovan Design of Closed loop controller for DC-DC converter by using K-factor method for Renewable Energy Applications Springer Lecture notes in Electrical Engineering, 394, 2016. 464
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