Performance Evaluation of Fuzzy Logic Controlled Bidirectional DC to DC Converter

Transcription

1 TECHNIA International Journal of Computing Science and Communication Technologies, VOL. 3, NO., Jan.. (ISSN ) Performance Evaluation of Fuzzy Logic Controlled Bidirectional DC to DC Converter B. L. Narasimharaju, Satya Prakash Dubey, 3 S. P. Singh Indian Institute of Technology, Roorkee narasimharaju.bl@gmail.com, simhadee@iitr.ernet.in, 3 spd@gmail.com Abstract This paper presents the systematic design procedure of fuzzy logic controller for the coupled inductor bidirectional DC-DC converter. The converter contains nonlinear elements making the mathematical model more complex which instigate the use of FLC. The design guidelines, and FLC based voltage controller design of the bidirectional converter is discussed in detail. The proposed FLC for bidirectional DC-DC converter is validated through simulation in Matlab/Simulink environment. The closed loop results of the converter is presented and discussed. Simulation results demonstrate that the converter can be regulated with good performance irrespective of source and load disturbance. I. INTRODUCTION THE DC-DC conversion technique has been greatly developed to achieve high-efficiency, cheap topology in simple structure and without extreme duty ratio. The uninterruptible power supply (UPS) systems employed in computer industry typically provide ten to thirty minutes reverse time, which is highly inadequate for telecommunication system. The convergence of computer and telecommunication industries makes the 48V DC battery plant as an innate choice to offer long backup during AC mains outages [-3]. It is more economical for storage batteries to use a few large-capacity cells than many small-capacity cells, and for that reason the number of cells used in small/micro power grid is limited. Usually, inverters used in DC-UPS (DUPS) systems require comparatively high input DC voltages of about 4V; which necessitates voltage step up when discharging batteries, and step down when charging them. Thus, batteries need high voltage diversity ratio in discharging, and charging modes. The above shortcomings can be fulfilled by using bidirectional DC- DC (BDC) converters between the storage devices and grid supply/load. However, conventional based BDC topologies [4-6] are well reported in the literature. Unfortunately, switches of four and beyond in isolated and cascading non-isolated topologies increase production costs. Also, high rated devices are required to develop relatively low voltages which lead to high voltage/current stress on the devices, and reduced efficiency. In addition, the major concerns related to the efficiency of the DC backup converter; large input current, high output voltage and rectifier reverse recovery problem. Thus, circuit trends are requiring voltage/current requirements outside the efficient range of most classical converters; the duty cycle is below. or above.9, and therefore new converter topologies must be developed [7]. In order to overcome the above problems, high performance coupled inductor DC-DC converters are proposed [8-4] which gives high-efficiency, high-voltage diversity without utilizing extreme duty ratio. Therefore, proposed BDC topology could be more attractive for small power grid in renewable energy conversion systems. Power converters provide a highly efficient means to deliver a regulated voltage from a standard power source. In addition, these converters/regulators are susceptible to various disturbances from the attached load or the power source. These disturbances, if not controlled, may damage or shutdown devices attached to the converter. To maintain the output voltage constant, irrespective of load and line disturbances, it is necessary to operate the converter as a closed loop system. In fact, the very familiar classical PI controller is required to be tuned for acceptable dynamic response, where as in the sample based controller only gain is to be adjusted for a given system to regulate overshoot. Also, in recent years, the Fuzzy Logic Control (FLC) has become more popular in many applications. These FLCs provides a method of nonlinear control using piece-wise linear functions to apply varying gains depending on the error signal between the desired output and the actual output. FLCs have already been incorporated in various DC-DC converter systems [6-8] and applications [9-4]. The fuzzy logic controller is advantageous over classical controls where the gains are fixed. An FLC allows the proportional, integral, and derivative gains to be adjusted to work optimally to control the system and therefore make it a suitable for control of DC-DC converters [6-8]. The fuzzy logic [9-4] based controller gives nonlinear control with fast response and virtually no overshoot. In this paper, operation, and FLC based voltage controller design of the proposed BDC topology is discussed and then validated through simulation. The paper organized in four sections. Starting with Section I, the others sections cover the converter and controller designs in Section-II, simulation results and analysis in Section-III, and conclusive observations in Section-IV. II. CONVERTER AND CONTROLLER DESIGNS A. Converter Operation and Design The BDC converter operation can be identified in two modes. One is discharge mode during which the BDC is used to boost the battery voltage to a suitable high level DC bus voltage. Second is the charging mode during which the BDC is used to buck the DC bus voltage to a 598

2 TECHNIA International Journal of Computing Science and Communication Technologies, VOL. 3, NO., Jan.. (ISSN ) suitable low level battery voltage. The converter operation in continuous conduction mode (CCM) is a suitable choice to get a better dynamic response and also a tight regulation of output voltage for the entire load variation. The proposed bidirectional DC-DC converter topology is depicted as in fig. (a). The converter operation is categorized into four modes. In mode- and mode- converter operates in forward boost mode, the power flow is from battery to DC bus. In mode-3 and mode-4 the converter operates in reverse buck mode, the power flow will reverses and is now from the DC bus to battery. The characteristic waveforms of both boost and buck modes are depicted in Fig.. The major symbol representations are summarized as follows. V LV and V HV, respectively, denote the voltages at the low-voltage (LV) and highvoltage (HV), Land L represent individual inductors in the primary and secondary sides of the coupled inductor respectively, where the primary side is connect to a battery module. The symbols S and S are the lowvoltage step-up switch and high-voltage step-down switch respectively. The operation in mode- and mode- is equally valid for mode-4 and mode-3 respectively. Thus, only operation in mode- and mode- is described as follows:. Mode-[fig. (b)] In this mode, the LV side switch (S) is conducting for TON time. Because the inductor is charged by the battery, the magnetizing current increases gradually in an approximately linear way. The secondary current is zero since diode D is reverse biased.. Mode-[Fig. c)] In this mode, the LV side switch (S) is turned off for TOFF time. Thus reverses the polarities of the coupled inductors. The diode D gets forward biased and the mode begins when the primary current equals the secondary current. The battery and the coupled inductor are connecting in series to discharge into the HV DC bus through the diode D by way of a low current type. Because the inductor is supplied to the DC bus, the magnetizing current decreases gradually in an approximately linear way. V Lv V Lv I Lv I Lv C L C L i cl(t) r L V cl(t) i L(t) L (n ) V L D L (n ) (a) Proposed Coupled Inductor Bidirectional DC-DC Converter V L S i L(t) L (n V ) L i (n ) L(t) i L(t) r L V L V L -NVLv i cl(t) V cl(t) S D V ch(t) V ch(t) i ch(t) C H i ch(t) (b) When S ON & D OFF (Discharge mode) or D ON & S OFF (Charge mode) V Lv I Lv C L i cl(t) V cl(t) L (n ) L i (n ) L(t) i L(t) r L V L V L (V HvNV Lv)/(N) i ch(t) V ch(t) (c) When D ON & S OFF (Discharge mode) or S ON & D OFF(Charge mode) Fig.,,3: Proposed BDC Converter and Equivalent Circuits for Operating Modes C H C H I Hv V Hv R I Hv V Hv R I Hv V Hv R Mode-3 and mode-4 are similar to the mode- and mode- respectively. Hence, the converter operation is now considered to be in reverse buck mode during which switch (S) is pulse modulated and the diode D is the freewheeling device. The secondary current (IL) is from the DC bus by way of the two series windings (Land L) of the coupled inductor to charge the battery in the LV side. As the converter operation is chosen for continuous current mode (CCM), the relationship between the VLv and the VHv can be attained with volt-second balance principle. It can be expressed by ( VHV VLV )( ) T VLV T () ( N ) From (), the DC gains of the boost mode (G) and buck mode (G) is developed as ( N) ( ) G G () ( ) ( N) Where δ is the duty ratio of the switch S for boost mode and δ =(-δ ) is the duty ratio of the switch Sfor buck mode, T is the switching period, and n N is the n turn s ratio of the coupled inductors L and L. The coupled inductor in Fig. can be modelled as an ideal transformer including the magnetizing inductors (L m and L m ) and leakage inductors (L k and L k ) those are not shown in the fig. The coupling coefficients (k and k ) of ideal transformer are defined as k k (3) ( Lk ) L ( Lk ) L The coupling coefficients is simply set at one to obtain L m =L and L m =L via (3). The series windings (L and L ) and their mutual inductance (M) can be taken as a single inductor, and the equivalent magnetizing inductor (L m ) can be represented as L m ( N) L ( ) L ( L L M ) (4) N Mutual inductance M K L L =NL for % coupling (i.e. K=) the equivalent inductor (L) is larger than the value of (L or L ) to limit the ripple and ascendant rates of the charge current. Assuming boundary between CCM and discontinuous current mode (DCM) (i.e. i in ); the peak values of the inductor currents I LPk and I LPk can be expressed as VLV T VLVT IL pk IL pk (5) in ( N) in From (5), the average current through L is developed as VLV ( ) T ILav I (6) HV ( N ) in Since the output current (I HV ) in boost mode is equal to the inductor (L ) average current, therefore, minimum value of inductance (L min ) can be obtained as VLV ( ) T in (7) IHVVHV ( N ) For continuous current conduction the selected value of L and vice versa for discontinuous current L min conduction. Finally equivalent inductance (L m ) and secondary coupled inductor (L ) can be calculated from 599

3 Degree of membership TECHNIA International Journal of Computing Science and Communication Technologies, VOL. 3, NO., Jan.. (ISSN ) (4). In Fig. the filter capacitors C L and C H are used on the LV battery side and HV DC-bus side respectively to achieve ripple free voltages. B. Fuzzy Logic Controller Design The dynamics of DC-DC converters is non-linear with uncertain parameters owing to uncertain output voltage during the operation. The practical converter operation deviates from theoretical prediction because of problems associated with parasitic resistances, stray capacitances and leakage inductances of the components. In order to obtain the desired operating voltage irrespective of the source and the load disturbances, the converter must be operated in closed loop. All these problems are efficiently dealt with in FLC. Fuzzy control method does not need accurate mathematical model of a plant, and therefore, it suits well to a process where the model is unknown or ill-defined [, ]. Even when the plant model is known, there may be parameter variation problem. In general, fuzzy expert system is applicable wherever the knowledge base of expert system contains fuzziness. The converter control regulates nominal operating point of the converter. Fig.3 depicts the block diagram of the fuzzy control scheme for BDC converter. The output voltage amplitude is determined and compared with reference voltage, which is taken as proportional to the rated terminal voltage of the BDC converter. The voltage error (E) and change in voltage error (CE) is determined and processed through FLC. The resulting output is processed through a PWM generator where it is compared with symmetrical triangular wave to obtain suitable pulse. The fuzzy controller [7,8] is divided into five sections: fuzzifier, knowledge base, rule base, decision making and defuzzifier as shown in fig.3. The fuzzifier converts crisp data into linguistic format. The inference system decides in linguistic format with the help of logical linguistic rules supplied by the rule base and the relevant data supplied by the data base. The output of the inference system passes through the defuzzifier wherein the linguistic format signal is converted back into the numeric form or crisp form. The inference system block uses the rules in the format of if-then-else. The inputs of the fuzzy controller are the error and change in error is defined as follows; E( n) V ( n) V ( n) (8) ref o CE ( n) E( n) E( n )) (9) Where, Vref and Vo are terminal voltage and reference voltages at n Th sampling time. The input variables are converted into labels of fuzzy sets in terms of suitable linguistic values, this is called fuzzification process. The scaled inputs are crisp values limited to the universe of discourse of input variables. The Membership Function (MF) is used to convert each of input variables into membership value between and. The overall performance of the system is affected by the shapes and number of the MFs that are chosen according to the experience of expert people about the process. The MFs may take any arbitrary shape or form, such as triangular functions, sigmoidal curves, Gaussian distribution curves, trapezoidal functions and exponential shapes. The several procedures are reported [8-4] that can be used to build MFs. The triangular MFs are chosen to evaluate the degree of membership of the input crisp values. The output of the fuzzy controller is the control signal u which is used to produce modulating pulses which drives the switches of the BDC converter. The proposed fuzzy system consists of seven MFs for error (E), change in error (CE), and seven MFs for output control signal (u). A number of fuzzy reasoning methods are reported in the literature [9-] such as; mamdani s, larsen s, sugeno s and tsukamoto s methods. Herein this work, mamdani fuzzy reasoning method is used to obtain the inference result from a system. The fuzzy reasoning strategy of this method is based-on the MAX-MIN composition. Fig.3 illustrates the fuzzy input MFs plots of the variables E (voltage error), and CE (change in error) respectively. Fig.5 illustrates fuzzy output control variable. The each input and output MFs are divided into seven linguistic variables namely NB(negative big), NM (negative medium), NS (negative small), Z (zero), PS (positive small), PM (positive medium) and PB (positive big). The output MFs are asymmetrical because near the origin the signal requires more precision. The knowledge base is defined in the form of linguistic rules. By naming the numbered symbols ( zero, positive small, positive medium..., - negative small, - negative medium...), we recognize the classical antidiagonal rule base [4] proposed by Macvicar-Whelan. The Table-I shows the corresponding rule table for the controller. The top row and left column of the matrix indicate the fuzzy sets of the variable E and CE respectively, and the MFs of the output variable (du) are shown in the elements of the matrix. NB NS Z PS PB.8 V Ref E(n) CE(n) E(n-) Z - E(n) Fuzzifier Knowledge Base Rule Base Decision Making Fuzzy Logic Controller Defuzzification Input (Vi) BDC Converter PWM Generator with Comparator u(n)=u(n-)du(n) Fig. 3: Fuzzy Logic Control Scheme for BDC Converter System V O E / CE Fig. 4: Membership Functions of Error Input (E) and Change in Error Input (CE) 6

4 Degree of membership TECHNIA International Journal of Computing Science and Communication Technologies, VOL. 3, NO., Jan.. (ISSN ) NB NM NS ZE PS PM du Fig. 5: Membership Functions of Control Output (u) To maintain the voltage at desired level the triangular membership of error and control output are cramped near to zero for the given operating condition. For improving the controller performance, membership functions are further adjusted based on trial and error procedure. The sensitivity of a variable determines the number of fuzzy subsets, respectively. Before fuzzification, the input variables are normalized with respect to reference voltage (V ref ). This gives the system an adaptive characteristic and enables the optimal operating point to be found effectively. The per unit (PU) values of the MF boundaries have been chosen by considering the characteristics of the converter. For example, the boundaries of the small fuzzy set are and., which covers all the errors and derivative errors with value less than percent of the reference value. The fuzzy inference includes the process of fuzzy logic operation, fuzzy rule implication and aggregation. In the fuzzy inference system, the fuzzified input variables are processed with fuzzy operators, and the IF-THEN rule implementation. The proposed system has 5 (7x7) possible rules as described in Table-I that can build by crossing the fuzzy sets considered for each input. Where a rule read as: if E NB and CE Z then du NM () PB III. SIMULATION RESULTS AND ANALYSIS For justification of the proposed BDC converter operation, and closed loop FLC performance; specifications, and design values are obtained as described in table-ii. The Simulink model of the BDC converter with voltage mode control has been developed as depicted in fig.6. Thus, the performance analysis in open loop and closed loop has been evaluated extensively. TABLE-II DATA FOR THE PROPOSED COUPLED BDC CONVERTER Parameter Boost Mode Buck Mode Input voltage VLV=4V VHV=V Output voltage VHV= V VLV=4V Vo (Ripple).5%.5% Output Power 4 Watt 384 Watt Output Current A 6A Switching Frequency 5 khz Turns Ratio Duty Cycles δ=.7, δ=(- δ) Inductors L=5µH, L=µH, M=98µH Resistors RHV= Ω, RLV=.5 Ω, rl=.ω, Capacitors CL=CH=µF E(pu) TABLE I: FUZZY RULE BASE MATRIX NB NS Z PS PB CE(pu) NB NB NB NM NS Z NS NB NM NS Z PS Z NM NS Z PS PM PS NS Z PS PM PB PB Z PS PM PB PB The value of output signal is determined in accordance with the linguistic rules. The required rules and data are supplied by the rule base. The linguistic output data is converted back into crisp output data by defuzzification. The membership of the corresponding output is taken as minimum membership value for the two respective inputs. Mathematically, min ( input) ( input ) () Crisp p(m) Output () Where, µ refers to membership value, the output membership is stored in α and p(m) refer to location of peak of membership function. The defuzzified (crisp) value multiplied by a scale factor and integrated to obtain the output (u). Fig. 6: Simulink Schematic of the FLC Based BDC Converter Fig.7 illustrates the open loop steady-state performances of proposed BDC converter. These critical analyses and observations confirm improvements of the proposed topology in providing high voltage diversity. Also, justifies the improved utilization factor of switches. Fig.8 to fig. illustrates the closed loop performances of the converter for various load conditions. The voltage controller increases the immunity of the converter output voltage to changes in the input voltage and load current. The load regulations under wide range of load conditions have been made extensively. As shown in fig. 9 and fig., the effect of step load change are observed at.75sec for boost mode, and at.5 sec for buck mode respectively. The closed loop result analysis clearly shows that at any instants of load changes, output voltage get stabilizes at faster rate to the desired value (V) in boost with small overshoot. Similarly, in buck mode output voltage get stabilizes at very faster rate to the desired to value (4V) in buck mode with smaller overshoot particularly at light load conditions. Thus, it 6

5 ---->ILv ---->VLv ---->IHv ---->VHv ---->V(S) ---->V(S) ---->i(s), i(s ---->i(l), i(l) ---->Vg, Vg ---->VLv ---->I(L), I(L) ---->I(L), I(L) ---->ILv ---->I(S) ---->I(S) ---->VLv ---->VDS, VD ---->VD, VDS ---->IHv ---->VHv TECHNIA International Journal of Computing Science and Communication Technologies, VOL. 3, NO., Jan.. (ISSN ) justifies the excellent load regulation in both modes of operation and also the dynamic performances Boost Mode Coupled BDC >VHv... Time (t) VDS VD I(L) I(L) Buck Mode Coupled BDC I(L) -3 I(L)..... VD VDS..... Time (t) Fig. 7: Current and Voltage Waveforms of Proposed BDC Converter.5 Gate Pulse Voltage's Inductor Current's 5 Boost Mode Buck Mode Switch Current's Switch Voltage Switch Voltage > Time (t) Fig. 8: Closed Loop Performances with Load Changes Closed Loop FLC Performances Boost Mode Buck Mode > Time (t) Fig. 9: Closed loop Performances for Full Load and Over Load 3 Closed Loop FLC Performances Boost Mode Buck Mode > Time (t) Fig. : Closed loop Performances for Full Load and Light Load IV. CONCLUSION The design analysis of the proposed converter has been discussed. The proposed converter circuit offers wide range of voltage diversity, and effective switch utilization factor. Also, it requires only two switches to achieve the bidirectional power flow as compared to the isolated bidirectional bridge converters. The model of the BDC converter with FLC based voltage mode control has been developed in Simulink environment. Thus, the steady-state, and transient performance analysis in open loop and closed loop has been evaluated extensively. The closed loop regulation is evaluated for wide range of load conditions which show the excellent performances of fuzzy logic controller. REFERENCES [] J. Akerlund 48V DC computer equipment topology An emerging technology, Proc. of IEEE-INTELEC, pp. 5, 998. [] T.M. Fruzs and J. Hall AC-DC or hybrid power solutions for today s telecommunications facilities, Proc. of IEEE-INTELEC, pp [3] L. Huber and M.M. Jovanovic, A design approach for server power supplies for networking, Proc. of IEEE-APEC, pp ,. [4] S. Lee, and G.T. Cheng, Quasi-Resonant Zero-Current-Switching Bidirectional Converter for Battery equalization Applications, IEEE Trans. on Power Electronics, Vol., No.5, Sept 6, pp [5] S. Waffler and I.W. Kolar, A Novel Low-Loss Modulation Strategy for High-Power Bi-directional Buck Boost Converters, Record of 7Th International Conf. on Power Electronics, pp , Oct 7. [6] L.R. Chen, N.Y. Chu, C.S. Wang, and R.H. Liang, Design of a Reflex-Based Bidirectional Converter with the Energy Recovery Function, IEEE Trans. on Industrial Electronics, Vol.55, No.8, August 8, pp [7] B. Axelrod, Y. Berkovichm and A. Ioinovici, Switched- Capacitor/Switched-Inductor Structures for Getting Transformer less Hybrid DC-DC PWM Converters," IEEE Trans. on Circuits and Systems, Vol. 55, No., March 8, pp [8] Q. Zhao and F.C. Lee, High performance coupled-inductor DC- DC converter, Proc. of IEEE APEC Conf., pp. 9 3, 3. [9] Q. Zhao and F.C. Lee, High-efficiency, high step-up DC-DC converters, IEEE Trans. Power Electronics, Vol.8, 3, pp [] R.J. Wai and R.Y. Duan, High-efficiency bidirectional converter for power sources with great voltage diversity, IEEE Trans. Power Electron., Vol., No.5, September 7, pp [] R.J. Wai and R.Y. Duan, High Step-Up Converter with Coupled- Inductor, IEEE Trans. on Power Electronics, Vol., No.5, Sept 6

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