Title: Improved maximum power point tracking algorithm with cuk converter for PV systems
Abstract: The Journal of EngineeringVolume 2017, Issue 13 p. 1676-1681 ArticleOpen Access Improved maximum power point tracking algorithm with cuk converter for PV systems Zongchang Sun, Corresponding Author Zongchang Sun [email protected] School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, People's Republic of ChinaSearch for more papers by this authorZhoujun Yang, Zhoujun Yang School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, People's Republic of ChinaSearch for more papers by this author Zongchang Sun, Corresponding Author Zongchang Sun [email protected] School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, People's Republic of ChinaSearch for more papers by this authorZhoujun Yang, Zhoujun Yang School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, People's Republic of ChinaSearch for more papers by this author First published: 19 January 2018 https://doi.org/10.1049/joe.2017.0617Citations: 16AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The maximum power point tracking (MPPT) techniques are essential for the optimisation of the efficiency in the photovoltaic (PV) systems. Here, a practical PV model is discussed and employed, and cuk converter is selected as MPPT's DC–DC converter for PV systems. Then, on the basis of the power–current (P –I) characteristics curve of a PV cell, an improved MPPT algorithm with direct control by using the fuzzy controller is proposed. Compared with some algorithms mentioned here, the proposed algorithm is able to track a more accurate MPP quickly and have a smaller steady-state oscillation. To validate its correctness and good performance under the varying environmental conditions, simulation study on it is carried out in MATLAB/Simulink. Also, simulation results demonstrate the proposed algorithm here is feasible and in contrast, it has a faster dynamic and more robust steady-state performance. 1 Introduction Recently, with the global energy crisis and the environmental pollution problems growing more and more seriously, the development of renewable and clean energy has become one of the most effective approaches to solving both problems. Many renewable energy sources, such as solar energy, wind energy, water energy etc., have been fully utilised in many countries [1, 2]. Nowadays, among these renewable energy sources, solar energy has become more and more popular all over the world. Photovoltaic (PV) energy are mainly applied in several aspects, e.g. battery charging, home energy supply, pumping systems etc. [3]. Compared with other means of harvesting renewable energy sources, PV systems have several basic merits, such as clean, static, and movement-free characteristics, longevity, low-maintenance cost etc. [4]. Although there are many advantages for PV systems, conversion efficiency of PV systems has a significant impact on the wide application of PV generation. The conversion efficiency of PV systems is mainly constrained by three factors, including efficiency of a PV cell, efficiency of power converters, and efficiency of maximum power point tracking (MPPT) techniques [5]. In contrast, improving MPPT techniques, which is much easier, low cost, and can also be easily implemented in the existed PV systems, is the best choice of improving the efficiency of PV systems. However, the maximum power point is easily influenced by solar insolation and temperature, and all the characteristics of a PV panel are non-linear so that tracking MPP becomes a difficult and complicated work in most cases. Presently, many MPPT algorithms have been put forward in the literature. They are generally separated into two main groups, namely the conventional MPPT algorithms and the advanced MPPT algorithms. The former mainly consist of hill-climbing (HC) [6], perturbation and observation (P&O) [7], incremental conductance (IC) [8], which is based upon the simple rule that the derivative of the power with respect to voltage should be positive on the left, zero at the MPP, and negative on the right of the power–voltage characteristic curve of a PV panel. HC method directly introduces a duty cycle perturbation value of converter for PV systems, while P&O and IC methods introduce an output voltage or current perturbation value of a PV panel. The latter are mainly composed of artificial neural network [9], evolutionary algorithm (EA) [10], fuzzy logical controller (FLC) [11, 12] etc. In contrast with the conventional methods, the advanced methods are much cheaper, quicker, and more accurate. In particular, despite that among them FLC method ordinarily has a better performance under the varying environmental conditions, FLC algorithms have great reliance on the designer's knowledge level of PV systems. In this paper, a practical PV model is discussed and employed, and through analysis, cuk converter is selected as an MPPT's DC–DC converter for PV systems. Then, based on the power–current (P –I) characteristics curve of a PV cell, an improved MPPT algorithm with direct control by using FLC is proposed. Besides, in order to validate its correctness and analyse its dynamic and steady-state performance under varying insolation and temperature conditions, simulation study on it is carried out in MATLAB/Simulink. Finally, simulation results are obtained and analysed, which demonstrate the proposed algorithm is feasible and compared with some algorithms mentioned in this paper, it has a better dynamic and steady-state performance. 2 PV model A PV array consists of many PV cells, Fig. 1 depicts the PV cell equivalent circuit, which is composed of a PV current generator in parallel with a diode and a shunt resistor, R sh, for the surface roughness along the cell periphery and with a serial resistor, R s, for the interface metal semiconductor and the intrinsic silicon resistances [13]. Fig. 1Open in figure viewerPowerPoint Equivalent circuit of a PV cell According to Fig. 1, the output current characteristic for a PV cell can be expressed by (1) (2) where I pc is the photo current, I o the reverse saturation current of the diode, q the electron charge, n the ideality factor of the diode, k the Boltzmann's constant, and T the junction temperature in Kelvin. The above-mentioned mathematical model is convenient for theoretical analysis, However, because of the uncertain parameters value (I pc, I o, R s, and R sh), it is not convenient for direct application in the engineering. In the next section, a practical engineering model is derived and built. On the one hand, in view of a very large R sh value, last item of formula (2) is ignored. On the other hand, since R s value is much less than the forward conduction resistance of the diode, the photo current I pc is thought to be equal to the short-circuit current I sc [14]. In a result, formula (1) is simplified as (3) When the output voltage V is at the MPP (4) According to (3) and (4), C 1 and C 2 can be solved (5) (6) where V oc, V m, and I m are the open-circuit voltage of a PV cell, the voltage and current of a PV cell at the MPP, respectively. When solar irradiance and temperature are considered, we have (7) where (8) (9) (10) (11) where S and S ref are the actual irradiance and reference irradiance, T and T ref the actual temperature and reference temperature of a PV cell, T e is the environmental temperature, and a, b, and c are the current temperature coefficient, voltage temperature coefficient, and the PV cell temperature coefficient, respectively. According to this PV cell model, the current–voltage (I –V), power–voltage (P –V), and power–current (P –I) characteristics curves of STP060P PV module are shown in Fig. 2. Table 1 presents the electrical parameters of STP060P PV module. Fig. 2Open in figure viewerPowerPoint PV characteristics curves under the varying conditionsa Under the varying insolation and temperature conditions b Under the varying insolation and temperature conditions c Under the varying insolation and temperature conditions Table 1. STP060P PV module specifications Electrical parameters Value maximum power (P m) 60 W maximum voltage (V m) 17.2 V maximum current (I m) 3. 49 A open-circuit voltage (V oc) 21.6 V short-circuit current (I sc) 3.97 A current temperature coefficient (a) 0.003 A/K voltage temperature coefficient (b) −0.13 V/K 3 DC–DC converter To improve the operating efficiency of a PV model, apart from selecting an optimal MPPT method, a highly efficient DC–DC converter plays an important role in the highly efficient MPPT design. Therefore, a proper DC–DC converter for PV systems is also supposed to be taken into serious consideration. Many converters' topologies have been discussed in the previous papers. Compared with other converter topologies, buck-boost converter and cuk converter are able to have a better performance regardless of the load value [15]. However, buck-boost converter has some drawbacks such as poor transient response, discontinuous input current, and higher peak current, which contribute to a low efficiency. In contrast, cuk converter has a continuous input and output current characteristics, and because of two inductors, the output current ripples are approximately zero, which makes it have a low power loss. Hence, cuk converter is an optimal power supply configuration to be applied in the MPPT design. Cuk converter is composed of two inductors, two capacitors, a switch, and a diode. Fig. 3 depicts cuk converter's two operating modes in the MPPT design. When cuk converter operates in the first mode, the switch is on, and the diode is in the reverse-biased state. In this mode, because of Vc 1 > V o, the capacitor C 1 supplies power energy for the load. In the second mode, the switch is off, and the diode is in the forward-biased state. In this mode, C 1 is charged by V s through the diode, and the load harvests energy from inductor L 2. Fig. 3Open in figure viewerPowerPoint Cuk converter's operating modes a Switch is on b Switch is off That the average values of the periodic inductor voltage and capacitor current waveforms are zero in the operating steady state is the rule of the cuk converter working condition [16]. The relations between the output and the input are expressed by (12) In this study, the main parameter values of the cuk converter employed for the MPPT design are: L 1 = L 2 = 8 mH, C 1 = 100 mF, C 2 = 50 μF. 4 Proposed MPPT algorithms As is depicted in Fig. 4, power–current (P –I) characteristic curve of a PV cell is also a single-peak curve. Therefore, we can know from the figure that the slope of the P –I characteristics curve of a PV cell must be zero at the maximum power point. Since P = V ·I, then (13) Fig. 4Open in figure viewerPowerPoint Power–current characteristics curve Owing to I > 0, (13) is further readjusted for (14) where V, I, and P are the voltage, current, and power of a PV cell. V /I and dV /dI are defined as the instantaneous resistance and incremental resistance, respectively. Also, e IR is an error value between them. Ideally, e IR is equal to zero at the maximum power point. However, just as the error of IC algorithm [16], in most cases, it is not always zero at the actual maximum operating point but a small marginal error. The proposed algorithm makes direct use of this small marginal error signal by a small given error range, instead of PI controllers. The basic idea of the proposed MPPT algorithm can be expressed by (15) As is identical with the aforementioned MPPT algorithms, a given error signal is too small to track the MPP at a rapid convergence speed, so that the efficiency of the PV system is greatly reduced. On account of some advantages of FLC, it is selected as the basic controller of this algorithm. Therefore, the proposed algorithm is defined as incremental resistance algorithm with direct control by using the fuzzy controller. The absolute of the marginal error e IR at the K th sampling time is one of the input variables of the basic controller. The other input variable is the change of duty cycle at the (K −1)th sampling time. The output variable of the basic-controller is the change of duty cycle at the K th sampling time. The flowchart of the proposed algorithm is presented in Fig. 5. Fig. 5Open in figure viewerPowerPoint Flowchart of the proposed algorithm Since the absolute of the marginal error signal between the instantaneous resistance and the incremental resistance e IR is always not less than zero. So the input and output variables of the basic controller are fuzzified for three basic fuzzy subsets, including PS (positive small), PM (positive middle), and PB (positive big). Fig. 6 presents the basic fuzzy subsets and the membership functions of the variables of the basic controller. Fig. 6Open in figure viewerPowerPoint Basic fuzzy subsets and the membership functions of input and output variables The basic idea of the rules of the basic controller is that the change of duty cycle should follow the change of the marginal error signal e IR. For the marginal error signal e IR, the basic fuzzy subsets represent the distance between the operating point of the PV system and the MPP. Thus, this means that if the operating point is almost at the MPP (e IR is almost equal to zero), the duty cycle should have a small change. If the distance between the operating point and the MPP is moderate, the duty cycle should have a moderate change. Also, if the operating point is distant from the MPP, the change of duty cycle should be big. So the rules of the basic controller are shown in Table 2. Table 2. Rules of the basic controller ΔD (k)| EC (ΔD (k −1)) PS PM PB E (| e IR |) PS PS PS PS PM PM PM PM PB PB PB PB The output variable of the basic controller is a fuzzy value, so defuzzification is an inevitable process. Owing to the high precision of centre of area (COA) method, it is used in the process of defuzzification. In the COA method, (16) is employed to computer the change of duty cycle at the K th sampling time ΔD (k) (16) Then, the duty cycle of the cuk converter D (k) can be expressed as the following: (17) 5 Simulation results Fig. 7 shows the model of the PV system with cuk converter established in MATLAB, which is composed of a PV model, a cuk converter, a resistance load, and an MPPT controller. Fig. 7Open in figure viewerPowerPoint Model of the PV system with cuk converter 5.1 Simulation results of the proposed algorithm Simulation results of the proposed algorithm under different atmospheric condition are presented in Fig. 8. From results, it is found that the proposed algorithm has a rapid response at the beginning and a small steady-state oscillation under the normal irradiance and temperature condition. Also, when irradiance and temperature have a step change, the proposed algorithm can still make a rapid response to find MPP. Fig. 8Open in figure viewerPowerPoint Results under different atmospheric condition a Under the normal atmospheric condition (1000 W/m2, 25°C) b Under a step change irradiance condition (1000–600–1000 W/m2) c Under a step change temperature condition (25–40–25°C) 5.2 Comparison between proposed algorithm and other algorithms Fig. 9 shows comparison results between different algorithms. When irradiance and temperature are normal (1000 W/m2, 25°C), the convergence speed of the proposed algorithm is faster than other algorithms, and the proposed algorithm has a smallest steady-state oscillation in five algorithms. When irradiance has a step change (1000–600–1000 W/m2), it is observed that the proposed algorithm is still able to track the MPP rapidly and accurately and occurs no mistaken judgement phenomena. When temperature has a step change (25–40–25°C), it can be obtained from the results that compared with other algorithms, the proposed algorithm has a faster response during the dynamic and oscillation in the steady state is smaller, and there are no mistaken judgement phenomena in the whole process of change. Fig. 9Open in figure viewerPowerPoint Results under the step change of insolation condition a Under the normal atmospheric condition (1000 W/m2, 25°C) b Under a step change irradiance condition (1000–600–1000 W/m2) c Under a step change temperature condition (25–40–25°C) 6 Conclusions In this paper, a practical PV model is employed, and because of cuk converter's some advantage, it is selected as MPPT's DC–DC converter. Based on power–current (P –I) characteristics of PV cell, an improved algorithm with direct control by FLC controller is proposed. Compared with some algorithms, including P&O, IC, FLCa (power change is selected as input variable of fuzzy controller), and FLCb (dP /dV change is selected input variable of fuzzy controller), the proposed algorithm in this paper has a better dynamic and steady-state performance. Simulation results in MATLAB demonstrate that the proposed algorithm can track MPP rapidly and accurately in the dynamic and has a small steady-state oscillation under the normal and varying atmospheric conditions, and whether irradiance or temperature have a step change, the proposed algorithm always makes no mistaken judgement phenomena. 7 References 1Sharma P., Agarwal V.: 'Exact maximum power point tracking of grid-connected partially shaded PV source using current compensation concept', IEEE Trans. Power Electron., 2014, 29, (9), pp. 4684 – 4692 (doi: https://doi.org/10.1109/TPEL.2013.2285075) 2Shi J., Zhang W., Zhang Y. et al.: 'MPPT for PV systems based on a dormant PSO algorithm', Electr. Power Syst. Res., 2015, 123, pp. 100 – 107 (doi: https://doi.org/10.1016/j.epsr.2015.02.001) 3Chikh A., Chandra A.: 'An optimal maximum power point tracking algorithm for PV systems with climatic parameters estimation', IEEE Trans. Sustain. Energy, 2015, 6, (2), pp. 644 – 652 (doi: https://doi.org/10.1109/TSTE.2015.2403845) 4Seyedmahmoudian M. et al.: 'Simulation and hardware implementation of new maximum power point tracking technique for partially shaded PV system using hybrid DEPSO method', IEEE Trans. Sustain. Energy, 2015, 6, (3), pp. 850 – 862 (doi: https://doi.org/10.1109/TSTE.2015.2413359) 5Ishaque K., Salam Z., Lauss G.: 'The performance of perturb and observe and incremental conductance maximum power point tracking method under dynamic weather conditions', Appl. Energy, 2014, 119, pp. 228 – 236 (doi: https://doi.org/10.1016/j.apenergy.2013.12.054) 6Teulings W.J.A., Marpinard J.C., Capel A. et al.: 'A new maximum power point tracking system'. Proc. IEEE Power Electronics Specialists Conf. – PESC '93, 1993, pp. 1 – 6 7Femia N., Petrone G., Spagnuolo G. et al.: 'Optimization of perturb and observe maximum power point tracking method', IEEE Trans. Power Electron., 2005, 20, (4), pp. 963 – 973 (doi: https://doi.org/10.1109/TPEL.2005.850975) 8Sera D., Mathe L., Kerekes T. et al.: 'On the perturb-and-observe and incremental conductance MPPT methods for PV systems', IEEE J. Photovolt., 2013, 3, (3), pp. 1070 – 1078 (doi: https://doi.org/10.1109/JPHOTOV.2013.2261118) 9Lin W.M., Hong C.M., Chen C.H.: 'Neural-network-based MPPT control of a stand-alone hybrid power generation system', IEEE Trans. Power Electron., 2011, 26, (12), pp. 3571 – 3581 (doi: https://doi.org/10.1109/TPEL.2011.2161775) 10Kornelakis A., Marinakis Y.: 'Contribution for optimal sizing of grid-connected PV-systems using PSO', Renew. Energy, 2010, 35, (6), pp. 1333 – 1341 (doi: https://doi.org/10.1016/j.renene.2009.10.014) 11Wilamowski B.M.: 'Fuzzy system based maximum power point tracking for PV system'. 2002 28th Annual Conf. of IEEE Industrial Electronics Society IECON 02, 2002, no. 1, pp. 3280 – 3284 12Won C.-Y., Kim D.-H., Kim S.-C. et al.: 'A new maximum power point tracker of photovoltaic arrays using fuzzy controller'. Proc. 1994 Power Electronics Specialists Conf. – PESC'94, 1994, pp. 396 – 403 13Gow J.A., Manning C.D.: 'Development of a photovoltaic array model for use in power-electronics simulation studies', IEE Proc. Electr. Power Appl., 1999, 146, (2), pp. 193 – 200 (doi: https://doi.org/10.1049/ip-epa:19990116) 14Mao M.-Q., Yu S.-J, Su J.-H.: 'Versatile Matlab simulation model for photovoltaic array with MPPT function', J. Syst. Simul., 2005, 17, (5), pp. 1248 – 1251 15Taghvaee M.H., Radzi M.A.M., Moosavain S.M. et al.: 'A current and future study on non-isolated DC-DC converters for photovoltaic applications', Renew. Sustain. Energy Rev., 2013, 17, pp. 216 – 227 (doi: https://doi.org/10.1016/j.rser.2012.09.023) 16Safari A., Mekhilef S.: 'Simulation and hardware implementation of incremental conductance MPPT with direct control method using cuk converter', IEEE Trans. Ind. Electron., 2011, 58, (4), pp. 1154 – 1161 (doi: https://doi.org/10.1109/TIE.2010.2048834) Citing Literature Volume2017, Issue132017Pages 1676-1681 FiguresReferencesRelatedInformation