Direct Duty Ratio Controlled MPPT Algorithm for Boost Converter in Continuous and Discontinuous Modes of Operation

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1 Direct Duty Ratio Controlled MPPT Algorithm for Boost Converter in Continuous and Discontinuous Modes of Operation Pallavi Bharadwaj, Vinod John Department Electrical Engineering, Indian Institute of Science Bangalore Abstract Demand of increased lifetime, compact size and reduced cost of PV systems has led to the incorporation of LCL filters in the boost converter of a grid connected PV system. Additional filtering offered at the input by LCL filter reduces the inductance of boost converter. This calls for an algorithm which can track the maximum power in both discontinuous (DCM) and continuous conduction modes (CCM) of boost converter operation accurately. Direct duty ratio based perturb and observe algorithm for MPPT has been implemented in real time using VHDL based FPGA. The sensitivity of the algorithm to DCM and CCM operation of converter is analysed. It is shown that the duty ratio increment used in the MPPT algorithm needs to evaluate. The direct duty ratio based approach is found to work well with both modes of operation, even with mode transitions. Index Terms Solar, photovoltaic, maximum power point tracking (MPPT), boost DC-DC converter, continuous/discontinuous conduction mode, perturb and observe (P & O). I. INTRODUCTION Power converters are normally connected at the output of PV panels as an interface between panel and load. Use of DC- DC converters such as buck, boost and cuk converter have been reported in literature. Buck converter as used in [], may not be suitable for low voltage PV systems, specially when grid connection is involved. Cuk converter as used in [], requires an additional set of LC filter as compared to buck and boost converters. In this work boost converter has been used as the PV system has an MPP voltage of 5V and DC bus voltage needs to be higher for grid connection through an inverter. An LCL filter has been included at the input of the boost converter which reduces the inductance of boost, which can further lead to design of an optimised converter having low cost, low size and high efficiency. But low inductance also leads to DCM operation, therefore need arises for a robust MPPT algorithm which has tracking ability with mode transitions involved. Maximum power point tracking (MPPT) is a method of obtaining the maximum possible power out of static solar panels for given irradiation and temperature conditions. Some of the commonly used MPPT techniques include perturb and observe (P & O) algorithm, incremental conductance algorithm, open circuit voltage and short circuit current based methods [7]. P & O is widely used in PV MPPT applications This work is supported by Department of Information Technology, Govt of India under NaMPET Phase 2 under Project on Mini Full Spectrum Simulator. PV module Ls R s C f R eq Fig.. L Sw D C dc R Inverter Circuit diagram of grid connected PV system. because it is relatively simple and has real time tracking ability of MPP [7]. P & O algorithm has several variations based on control parameter involved. First is the voltage based P & O which is the most common [8], [] [2]. Second one involves current perturbation instead of voltage [9]. In both these methods duty ratio is commonly used as an indirect variable to actually change the voltage or current []. Third kind of P & O is called as direct duty ratio control [8], [3], wherein duty ratio is the direct control variable and it undergoes step changes in order to achieve MPPT. Current perturbation method is not commonly used as it involves short circuit current measurement, which poses difficulty in practical implementation. Out of voltage based and direct duty ratio based P & O methods latter one is preferred for this work as direct duty ratio control offers better energy utilisation and improved system stability than reference voltage control [8]. The main focus of this work is the detailed study of direct duty ratio based algorithm, to study its behaviour for different modes of converter operation namely - continuous conduction mode (CCM) and discontinuous conduction mode (DCM). It has been shown that duty ratio based algorithm is effective for both modes of operation for boost converter. II. DUTY RATIO BASED MPPT ALGORITHM A. Theoretical background Fig. shows a grid connected PV system wherein a PV panel feeds a boost converter with input LCL filter, which further feeds the grid via inverter. The input LCL filter consists of stray inductance L s and resistance R s of cables connecting panel on roof, to the converter located in laboratory. Additional capacitor C f and boost inductor L together form LCL grid

2 d inc - - load line --- panel characteristic 5 5 d dec Fig. 2. Determination of operating point of a solar PV panel depends on irradiation, temperature and terminal load resistance. The projection of operating point is taken on panel s Power-Voltage curve, shown for three loading conditions obtained by operating at 3 different duty cycles. filter. This combined LCL filter acts as an attenuator to high frequency boost inductor current ripple and effectively only DC current flows from the PV source thereby enhancing its efficiency. Due to the incorporation of LCL filter in the circuit boost inductor value can be reduced for same ripple current. This gives reduced cost and size benefits. However reduction in L value may cause discontinuous mode of operation of boost converter. So the MPPT algorithm needs to have MPP tracking ability in both DCM/CCM. For this the working of direct duty ratio MPPT algorithm is analysed in continuous and discontinuous modes of operations of boost converter. The basic principle behind any MPPT algorithm is digital control of converter in such a manner that the load seen by PV panel corresponds to the maximum possible power output for any given load. Consider the current-voltage and corresponding power-voltage characteristic of a PV panel, as shown in Fig. 2. The operating point is obtained by the intersection of solar panel s current-voltage (I-V) curve and load line which is dependent on load connected. The solar panel terminal equation [] is written as I = I L I s (e V +IRs mnsv t ) V + IR s R sh () And the equation of load line for a load resistance R can be written as I = V/R (2) The intersection of the two above mentioned equations is shown in Fig. 2 for three different cases of load resistance. The current gain, voltage gain and equivalent resistance reflected at the source terminals depends on the mode of operation of the boost converter, as given in Table I. Symbols shown in Table I are:- k = 2L R ot s, R o =output resistance, T s =switching period, L = boost inductance, d = duty ratio of switch S w = T on T off +T on. To visualise the effect of duty ratio on equivalent resistance (R eq ) it is plotted in Fig. 3 for CCM mode and DCM mode. In DCM the equivalent resistance is dependent on k, therefore it is shown for two different values of k. TABLE I COMPARISON OF GAINS AND EQUIVALENT RESISTANCE FOR CCM AND DCM OPERATION FOR A BOOST CONVERTER. Equivalent Resistance CCM DCM ( ) k + k 2 + 4kd 2 Current Gain ( d) Voltage Gain ( d) (d+ k + ) k 2 + 4kd 2 (d+ k + ) k 2 + 4kd 2 ( ) k + k 2 + 4kd 2 ( k + k 2 + 4kd 2 Equivalent Resistance R o( d) 2 R o (d+ k + k 2 + 4kd 2 TABLE II CIRCUIT PARAMETERS FOR THREE DIFFERENT BOOST CONVERTER CONFIGURATIONS R eq /R o Case k R o L T s A.24 6Ω µh 5µs B.4 2Ω 7µH 5µs C.6 3Ω 2µH 5µs CCM DCM, k =.24 DCM, k = Duty Ratio (d) Fig. 3. Variation of equivalent resistance with duty ratio in CCM mode and DCM mode. For values of k higher than.5 converter operates in CCM always and equivalent resistance in CCM mode is independent of k. In this paper analysis is done for 3 cases of boost converter configurations corresponding to the three different combinations of R o, L and T s values. These are listed in Table II. As discussed before, operating point of a PV panel depends on the panel s current-voltage characteristic (for given temperature and irradiation condition) and the load line. The slope of the load line is inverse of equivalent resistance as seen by the PV panel. From Table I it can be observed that R eq is a function of duty ratio. By changing the duty ratio of the boost converter, operating point for the PV panel can be controlled. For a particular set of load resistance, inductance and switching frequency of the boost converter, there will be a range of duty ratio for which converter will operate in ) 2 ) 2

3 3 MPP d (-d) CCM CCM kc=c.6 CCM DCM CCM kc=c.24 kc=c.4 d(-d) 2 vscd LC=C µ H,CRC o=c6ω LC=C7µ H,CRC o=c2ω LC=C2µH,CRC o=c3ω DCM DCM DCM CCM DutyCRatio(d) Fig. 4. DCM-CCM boundary is given by the intersection of d( d) 2 = k = 2L for boost converter. Here duty ratio range for CCM/DCM operation R ot s are shown for three different sets of R o, L values, with T s fixed at 5µs. CCM and in DCM for remaining range. CCM-DCM boundary can be observed in Fig. 4, wherein three cases are shown corresponding to the ones listed in Table II. The parameter k is directly proportional to inductance and switching frequency. The value of k falls for small inductance value as well as lower switching frequency. Lower inductance value leads to lower size as well as lower cost of converter. Also, the filtering objective can be met with a smaller inductor L, and this can also lead to higher efficiency. However if k value is small then range of DCM operation is large. If MPP can be tracked effectively in DCM then the converter cost and size can be minimised and higher efficiency can be achieved. From Fig. 4 it is clear that for a given duty ratio, the operation of converter in CCM or DCM mode is determined by R o, L, T s values. Whether MPP falls within the range spanned by d variation in CCM region or DCM region, solely depends on R o, L, T s values. Also it can be observed from Table I and Fig. 3 that duty ratio affects the equivalent resistance differently in DCM and CCM. In other words, the effect of duty ratio variation on the slope of load line differs from CCM to DCM. This effect is discussed in detail in Fig. 5 corresponding to three different converter configurations namely case A, B and C as specified in Table II and for two different conditions for solar panel irradiation. Solar panel was irradiated with Sun and a 5W hallogen lamp separately to get different characteristics of W polycrystalline solar panel [4]. Consider case A of boost converter operation as specified in Table II. Owing to low value of k DCM operation is observed for a wide range of duty ratio from.5 to.85 as shown in Fig. 5(a). This is as expected from Fig. 4. For case B k value is higher, this gives narrow range of DCM operation as shown in Fig. 5(b). However for case C as k value is large enough, it doesnot intersect CCM-DCM boundary as shown in Fig. 4. Thus Fig. 5(c) shows complete CCM operation as duty ratio varies from to. It can be observed that for both CCM and DCM operation as d increases the slope of load line increases, therefore even if there is a transition from CCM to DCM still complete I-V curve can be traced. However P increases W X V increases V increases P decreases Fig. 6. Power voltage characteristics for an array of PV panels, marked with MPP and a boundary which divides two sides of hill. W, X, Y, Z mark four possible operating points on the power - voltage curve. accuracy of tracking MPP will differ. This calls for defination of a term called as sensitivity of MPP tracking. This is defined as change in power compared to change in duty ratio around MPP. Sensitivity can be physically interpreted by how densely load lines cover MPP region. Higher density corresponds to higher sensitivity. Fig. 5(a) shows better sensitivity compared to Fig. 5(b). Fig. 5(a) also corresponds case A with lower inductance value compared to case B with higher inductance. Therefore for a system, selection of L can be done considering effective range of R o which for this case is R o 6Ω, as smaller L can give both cost and MPPT benefits. Sensitivity can also be improved by going for a smaller step size d, but this increases tracking time. As step size is reduced from.5 in Fig. 5(c) to. in Fig. 5(d) sensitivity improves from.5w for.5 to.2w for.. Last two cases shown in Fig. 5 correspond to laboratory setup wherein better control over irradiation conditions is achieved by using a hallogen lamp. Results for step size of.5 are shown in Fig. 5(e) and for. in Fig. 5(f) showing better sensitivity. B. The MPPT algorithm Consider power-voltage curve of a PV panel as shown in Fig. 6. On left side of MPP, power (P) and voltage (V) are in phase, on right side power and voltage are out of phase [3]. By making a small perturbation in the duty ratio, a new operating point is obtained. If P and V increase with this perturbation the operating point is in the left side of MPP, and further movement in the direction of perturbation will lead it to top of the hill. If P reduces with perturbation, V either increases or decreases. In both cases the direction of d perturbation needs to be changed. From Section II-A it is known that as d increases load line moves up in anti-clockwise direction. These facts can be combined in a flowchart as given in Fig. 7. Fig. 7 shows that for a d there are 4 possibilities for power and voltage to increase or decrease. Based on changes in V and P one can judge the way the operating point has moved on the sides of hill, and then increase or decrease d further to reach the top of the hill which corresponds to the MPP. Here W, X, Y, Z correspond to operating points shown in Fig. 6. Y Z

4 DCM (a) (c) (b) (d) DCM (e) 5 5 Fig. 5. Measured Current-Voltage (I-V) characteristics of W solar panel superimposed with family of load lines for varying duty ratio for a boost converter. Duty ratio increases from to in fixed step d. (a) Case A : R o = 6Ω, L = µh, T s = 5µs. d =.5. Projection on P-V curve shows DCM operation for d =.5 to.85. (b) Case B : R o = 2Ω, L = 7µH, T s = 5µs. d =.5. Projection on P-V curve shows DCM operation for d =.25 to.4. (c) Case C : R o = 3Ω, L = 2µH, T s = 5µs. d =.5. For complete d variation only CCM operation observed. Projection on P-V curve shows MPP region (d =.6-.65). (d) Same as (c) with d =.. Projection on P-V curve shows MPP region covered more densely (d = ). MPP occurs at d =.63. (e) Case C, d =.5, MPP region projected on P-V curve. (f) Boost converter case C. d =.. MPP tracked with higher accuracy at d =.25. Panel s I-V and P-V curve shown in (a), (b), (c) and (d) measured on 5//3, 2:3pm, Bangalore, panel temperature 4 o C. Panel s I-V and P-V curve in (e) and (f) measured with panel irradiated with 5W hallogen lamp placed at.3m height from panel. (f)

5 HalogenFLamp ACFVariac.2mHFInductor OUT dn yes IN Vn, In Pn = Vn In IS Pn>Pn- no WFPVF Panel yes no yes no IS Vn>Vn- IS Vn>Vn- W to X Z to Y Y to Z X to W dn = dn-δd dn = dn+δd dn = dn+δd dn = dn-δd FPGA Fig. 7. Flowchart for duty ratio based P & O MPPT algorithm. InverterF+FBoostFConverter ResistiveFLoad TABLE III BOOST CONVERTER PARAMETERS Output Load Resistance (R o) 3Ω Boost Inductance (L).2 mh Switching Frequency (f sw) 2 khz Input Filter capacitance (C f ) 5 µf Output Filter capacitance (C dc ) 44 µf Input Stray Resistance (R s) mω Input Stray Inductance (L s) 7.8 µh Fig. 9. Hardware setup for MPPT. TABLE IV RESULTS WITH MPP TRACKED Input Voltage 6.6V Input Current.2A Duty Ratio.24 Output Voltage theoretical(ideal) 2.8 V Output Voltage theoretical(practical) 2 V Output Voltage measured 2.4 V C. Implementation and results ) Implementation: This algorithm was coded in VHDL and implemented on a FPGA platform, which further controlled the boost converter fed by a W PV panel via a LCL filter. The LCL filter ensures that boost inductor current ripple is not carried over to the PV panel and hence leads to panel s long life. To emulate sun, a 5W halogen lamp is arranged, which irradiates the panel at a distance of.3m. The intensity of light is controlled by an autotransformer which feeds the halogen lamp. Converter parameters are chosen so as to ensure CCM operation throughout duty ratio variation, they are given in Table III, circuit diagram along with MPPT block is shown in Fig. 8. Hardware setup is shown in Fig. 9. 2) Results: Table IV shows the results with the experimentally tracked maximum power point for laboratory setup. This includes a W polycrystalline PV panel irradiated with a 5W halogen lamp. Boost converter specifications are given in Table III. Table IV quantifies the tracked maximum power point for the given setup. Fig. shows maximum power point tracked in steady state for duty ratio perturbation step size of.. It shows panel voltage, current and duty ratio. Results were also obtained for d =.5 and that gives P =.2W, which matches theoretically expected value as mentioned in Section IIA. Fig. shows filtering by LCL filter, it shows panel current, which is.2a dc and boost current which has.2a peak-peak ripple. MPP tracking is shown on power-voltage plane in Fig. 2. Fig. 3 shows effect of varying intensity of light on tracking of maximum power point again on power-voltage plane. It shows as the light intensity reduces to zero, locus of MPP shifts from 6V, 2W to V, W. CH CH2 Ipv Ls Rs L D CH4 PV module Vpv C f Sw C dc R V V d MPPT I Fig. 8. Circuit showing implementation of MPPT. Fig.. Panel voltage (CH), panel current (CH2) and duty ratio (CH4) using the boost switch gating pulse showing the tracking of MPP and steady state operation. Scale :: CH - 2V/div, sensor gain -.3V/V, V mpp = 6.6V; CH2 -.5V/div, sensor gain V/A, I mpp =.2A; CH4-5V/div, time scale - µs/div, duty ratio =.24.

6 CH CH2 P CH4 V Fig.. Panel voltage (CH), panel current (CH2) and boost inductor current (CH4) showing filtering by LCL filter at the input. Scale :: CH - 2V/div, sensor gain -.3V/V, V mpp = 6.6V; CH2 -.5V/div, sensor gain V/A, I mpp =.2A; CH4 - mv/div, sensor gain -.V/A, I Lmean =.2A, =.2A. I Lpk pk Fig. 3. Tracking of MPP with varying intensity of light, shown on power-voltage plane. MPP moves towards origin as light intensity reduces. Scale :: X axis : CH - 2V/div, sensor gain -.3V/V, voltage varies from 6.6V to V; Y axis : CH2 -.5V/div, scaling -.4V/W, power varies from 2W to W. average power output but higher tracking speeds. P Fig. 2. PV panel power voltage plane (power-y axis, voltage-x axis), showing traking of maximum power point with steady state operation. Scale :: X axis : CH - 2V/div, sensor gain -.3V/V, V mpp = 6.6V Y axis : CH2 -.5V/div, scaling -.4V/W, P mpp = 2W. V III. CONCLUSION The incorporation of LCL filter between PV panel and boost converter results in lower boost inductance value which leads to reduced cost and size benefits. But reduction in inductance leads to higher probability of DCM operation of boost converter. The direct duty ratio based MPPT algorithm is found capable of tracking MPP despite of mode changes, as in both modes duty ratio increase traverses I-V curve of PV panel in same direction. However it has been found that sensitivity of MPP tracking depends on the mode of operation. This issue is resolved by changing the perturbation step size of duty ratio for desired sensitivity. Experimental results show the filtering action of LCL filter and maximum power point tracking for CCM operation with a duty ratio perturbation step size of.. It has been observed that a higher step size perturbs the power in a wider range thereby giving lower tracking accuracy, lower REFERENCES [] Chatterjee, A.; Keyhani, A.; Kapoor, D., Identification of Photovoltaic Source Models, IEEE Transactions on Energy Conversion, vol.26, no.3, pp.883,889, Sept. 2. [2] V. Ramnarayanan, Course Material on Switched Mode Power Conversion, Department of Electrical Engg., IISc. Available online : [3] L. Umanand, Lecture notes on Design of Photovoltaic Converters, DESE, IISc. Available online : [4] Multicomp, MC-SP-GCS-Solar Polycrystalline Panel, W, Available online : 24 [5] Soren Baekhoj Kjaer, Evaluation of the Hill Climbing and the Incremental Conductance Maximum Power Point Trackers for Photovoltaic Power Systems, IEEE Transactions on Energy Conversion, vol. 27, no. 4, December 22 [6] N. Femia, G. Petrone, and M. Vitelli, Optimization of perturb and observe maximum power point tracking method, IEEE Trans. Power Electron., vol. 2, no. 4, pp , Jul. 25. [7] Y. Jiang, J.A. Abu Qahoug, Single Sensor Multi-channel maximum power point tracking controller for photovoltaic solar systems, IET Power Electronics, 22. [8] M.A. Elgendy, B. Zahawi and D. J. Atkinson, Evaluation of P & O MPPT Algorithm Implementation Techniques, Sixth IET International Conference on Power Electronics, Machines and Drives, March 22. [9] S. K. Kollimalla, M. K. Mishra, Variable Perturbation Size Adaptive P & O MPPT Algorithm for sudden changes in Irradiation, Power and Energy Conference at Illinois, Feb. 23. [] T. P. Sahu, T. V. Dixit, Modelling and Analysis of P & O and IC MPPT Algorithm for PV Array using Cuk Converter, IEEE Student s Conference on Electrical, Electronics and Computer Sciences, 24. [] Ahmad Bin-Halabi, Hussain Meshely, Experimental Implementation of Microcontroller Based MPPT for Solar PV system, International Conference on Microelectronics, Communication, and Renewable Energy, 23. [2] Francisco Paz, Martin Ordanez, Zero Oscillation and Irradiance Slope Tracking for Photovoltaic MPPT, IEEE Transactions on Industrial electronics, Nov. 24. [3] M. A. A. Mohd. Zeinum, M. A. Mohd. Relzi, Azure Che Soh, N. A. Rahim, Development of Adaptive Perturb and Observe Fuzzy Control Maximum Power Point Tracking for Photovoltaic Boost DC-DC Converter, IET Renewable Power Generation, 23.