- Email: [email protected]
A maximum power point tracking control strategy with variable weather parameters for photovoltaic systems with DC bus
Renewable Energy 74 (2015) 478e488
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
A maximum power point tracking control strategy with variable weather parameters for photovoltaic systems with DC bus Shaowu Li a, *, Amine Attou b, Yongchao Yang a, Dongshan Geng a a b
Science and Technology College, and School of Information Engineering, Hubei University for Nationalities, Enshi, China Intelligent Control & Electrical Power Systems Laboratory, Djillali Liabes University of Sidi Bel-Abbes, Sidi Bel-Abbes, Algeria
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 April 2014 Accepted 21 August 2014 Available online
In photovoltaic (PV) system, the most commonly used DC/DC converter is the basic buck or boost circuit to implement the maximum point power tracking (MPPT) due to their simple structure and low cost while there are some MPPT constraint conditions. By contrast, the conventional buck/boost DC/DC converter without MPPT constraint condition is seldom used because of its high cost or poor performance. To keep the advantages of these three DC/DC converters while overcoming their shortcomings, in this paper, the constraint conditions of capturing the maximum power point (MPP) of PV systems with direct-current (DC) bus are found out. Then, on the basis of this work, a MPPT control strategy with variable weather parameters is proposed. In this strategy, a new buck/boost DC/DC converter is proposed, which not only avoids the MPPT constraint conditions of basic buck or boost DC/DC converter but also overcomes the shortcomings of conventional buck/boost DC/DC converter. Finally, lots of simulated experiments verify the accuracy of MPPT constraint conditions, test the feasibility and availability of proposed MPPT control strategy, analyze the MPPT performance of proposed PV system and compare the output transient-state performance with conventional perturb and observe (P&O) method. © 2014 Elsevier Ltd. All rights reserved.
Keywords: PV system MPPT DC bus Constraint condition DC/DC converter
1. Introduction To PV system with DC bus, in order to avoid power losses, different DC/DC converters can be usually used as the connectors between PV cells and DC bus to implement MPPT control. This topology has advantages of simple structure, low cost, convenient installment and maintenance and has been widely used by PV generation microgrid at present [1]. For them, some existing methods such as the constant voltage tracking [2], the P&O method [2e6], the incremental conductance (IncCond) method [2,6,7], the quadratic maximization method [8,9] and so on can be directly used, however other algorithms such as the predictive control technique [10], the fuzzy logic control method [11e14], the neural network method [15], the sliding mode control method [16] and so on need be modified properly to meet the requirements of these special topologies. Nowadays there are some MPPT methods which are specifically used to PV systems with DC bus, such as the variable weather parameters (VWP) method [17], which makes the use of these PV systems wider. In all these MPPT methods, the P&O and IncCond methods are used more widely than others. The
* Corresponding author. Tel.: þ86 13997799701. E-mail addresses: [email protected], [email protected] (S. Li). http://dx.doi.org/10.1016/j.renene.2014.08.056 0960-1481/© 2014 Elsevier Ltd. All rights reserved.
advantages of P&O method mainly include its good operation without solar irradiance and temperature varying quickly with time and its simple analog circuitry or very-low-cost microcontroller. By contrast, its shortcomings are the tracking slowness and the output power oscillation around the MPP. The IncCond method has better performance than P&O, however it requires differentiation, division circuitry and a relatively complex decision making process, and therefore requires a more complex microcontroller with more memory, which makes the implementation of this method difficult. In this paper, to study the output transient-state performance of proposed MPPT strategy, the P&O method is selected as the comparison object. To PV systems with three basic DC/DC converters, the buck/ boost topology is the only one which allows the follow-up of the PV module MPP regardless of temperature, irradiance and connected load [18]. However, either the overall cost of this circuit is still too high or the MPPT performance is poor at present, which makes its integration, application and extension difficult. For example, to the basic buck/boost DC/DC converter, the input and output currents are all discontinuous, which makes MPPT performance poor, meanwhile the Cuk, Sepic and Zeta DC/DC converters all need two inductances and two capacitors and lots of circuit components must withstand higher voltage or higher current, which makes the component cost higher. Therefore, in actual installment and
S. Li et al. / Renewable Energy 74 (2015) 478e488
application. the buck or boost DC/DC converter is still the main circuit selected to implement MPPT control while there are some constraint conditions for their MPPT implementation. It is obvious that the best way to solve these above-mentioned questions is the acquisition of a new circuit which keeps the advantages of buck, boost and buck/boost DC/DC converters as well as overcomes their shortcomings. To achieve this goal, in this paper, what conditions the MPPs of different PV systems with DC bus can be tracked successfully under will be studied firstly. Then a new buck/boost DC/ DC converter which a buck is cascaded by a boost is proposed, which can switch between buck circuit and boost circuit to meet the MPPT demand with changes of external parameters. With regard to the issue how the changing weather has some effects on MPPT control, some works have been done [19e21], and some MPPT methods such as the VWP methods have found out the direct relationships between control signals and variable weather parameters [17,22], which makes the study on the overall performance of PV systems more convenient. In this paper, the VWP method is studied continuously and specially for PV system with DC bus. This paper is divided into the following sections: Section 2 presents the MPPT constraint conditions of PV systems with different topologies and the proposition of MPPT control strategy. How this proposed MPPT strategy is implemented is presented in Section 3. The accuracy of these MPPT constraint conditions is certified and the feasibility, availability and advantages of this proposed MPPT control strategy are analyzed by simulation experiments in Section 4. Some discussions are had in Section 5. Finally, some conclusions are drawn in Section 6.
2. Principle of MPPT control strategy 2.1. Analysis of mathematical model of PV system The configuration of PV generation system with DC bus can be shown in Fig. 1. Where V and I represent the output voltage and current of PV panel, respectively; Vo and Io represent the output voltage and current of DC/DC converter, respectively; RL represents the equivalent load resistance. In PV system shown in Fig. 1, three different topologies can be divided as PV-buck-bus, PV-boost-bus and PV-buck/boost-bus corresponding to the basic buck, boost and buck/boost DC/DC converters, respectively. It is obvious that the theoretical basis studying the constrain conditions of capturing the MPP is the mathematical models of PV cell and three DC/DC converters. Therefore, our work will start from analyzing these models. Firstly, in the practical application, the mathematical model of PV cell can be expressed by Eq. (1) [20,23].
h V i I ¼ Isc 1 C1 eC2 Voc 1
(1)
Where C1¼(1Im/Isc)exp(Vm/C2Voc);C2¼(Vm/Voc1)/ln(1Im/ Isc);ISC, VOC, Im and Vm represent the short circuit current, the open circuit voltage, the maximum power point current and voltage at
Fig. 1. Configuration of PV system with DC bus.
479
standard conditions (1000 W/m2 and 25 C), respectively. All data above are given by the PV array manufacturer. Secondly, with regard to the models of three DC/DC converters, the boost circuit is firstly analyzed as an example, and the buck or buck/boost circuit can be also analyzed by analogy. Here, Fig. 1 can be represented by Fig. 2. To simplify the boost DC/DC converter, assuming that: (1) the switch, diode, inductance and capacitor are all ideal electronic components; (2) the wires have no resistance and the output equivalent load can be represented by pure resistance RL; (3) the values of inductance and capacitor are large enough to ensure the output current continuous. Now the circuit shown in Fig. 2 can be analyzed through laws of circuit and conservation of energy, and Eqs. (2)e(4) can be given.
Vo ¼ V=ð1 DÞ
(2)
VI ¼ Vo Io
(3)
. Po ¼ Vo Io ¼ Vo2 RL
(4)
Where D represents the duty cycle of pulse width modulation (PWM) control signal of the boost DC/DC converter;Po represents the output power. According to Eqs. (1)e(4), Eq. (5) can be given.
Po ¼ RL ð1
2 DÞ2 Isc
pffiffiffiffiffiffi Po RL 1D C Voc
1 C1 e
2
2 1
(5)
Eq. (5) shows the theoretical relationship between D and Po, which is the mathematical model of PV system with PV-boost-bus topology. Likewise, the mathematical models of PV system with PVbuck-bus topology and PV-buck/boost-bus topology can be given as Eq. (6) and Eq. (7), respectively.
Po ¼
pffiffiffiffiffiffi 2 Po RL 2 RL Isc C2 DVoc 1 C e 1 1 D2
2 Po ¼ RL Isc
pffiffiffiffiffiffi 2 Po RL ð1DÞ ð1 DÞ2 C2 Voc D 1 C e 1 1 D2
(6)
(7)
2.2. Analysis of MPPT constraint conditions According to Eq. (5), in order to obtain the duty cycle Dmboost o corresponding to the MPP, we take the equation dP ¼ 0 into acdD count and have.
Dmboost ¼ 1
C Vomax
Fig. 2. Structure of PV system with PV-boost-bus topology.
(8)
480
S. Li et al. / Renewable Energy 74 (2015) 478e488
Where Vomax represents the maximum value of Vo; C represents a variable weather parameter whose value is related with the parameters of solar cell, solar irradiance S and solar cell temperature T. The value of C can be calculated by Eq. (9). Meanwhile, it can be seen from Eq. (9) that C whose unit is “V” is really a voltage and its value is a constant under a certain weather condition.
1 þ C1 1 C ¼ C2 Voc lambertw e C1
(9)
To an ideal boost circuit, Eq. (8) can be described as Eq. (10) when its output terminal is directly connected with a DC bus. Where Vbus represents the voltage of DC bus.
Dmboost ¼
Vbus C Vbus
(10)
Eq. (10) shows the theoretical relationship between Dmboost and Vbus at the MPP of PV system with PV-boost-bus topology. Because Dmboost belongs to the interval [0, 1], Eq. (11) can be given according to Eq. (10).
0
Vbus C 1 Vbus
(11)
That is.
Vbus C
(12)
It is obvious that Eq. (12) is the constraint condition under which the MPP capture will be possible for PV system with PVboost-bus topology. Likewise, according to Eq. (6), the theoretical relationship between Dmbuck and Vbus at the MPP of PV system with PV-buck-bus topology can be given as Eq. (13). Where Dmbuck represents the duty cycle corresponding to the MPP.
Dmbuck ¼
Vbus C
(13)
According to Eq. (13), the constraint condition under which the MPP capture will be possible for PV system with PV-buck-bus topology is obtained:
0 < Vbus C
(14)
Likewise, according to Eq. (7), the theoretical relationship between Dmbuckboost and Vbus at the MPP of PV system with PV-buck/ boost-bus topology can be given as Eq. (15). Where Dmbuckboost represents the duty cycle corresponding to the MPP.
Dmbuckboost ¼
Vbus C þ Vbus
(15)
Eq. (15) shows that there is always an appropriate Dmbuckboost to make this equation work regardless of Vbus. Therefore, a conclusion can be drawn that the MPP of PV system with PV-buck/ boost-bus topology can be always captured. All in all, the constraint conditions of capturing the MPPs of PV systems with three topologies can be shown in Table 1.
Table 1 MPPT constraint conditions for PV systems with three topologies. Different topologies
Constraint conditions
PV-buck-bus PV-boost-bus PV-buck/boost-bus
0 < Vbus C Vbus C none
According to Table 1, we can answer this question: What are the appropriate Vbus ranges in which the MPPs of PV systems with three topologies can be captured successfully? That is to say, in actual installment and application, MPPT control can be implemented successfully by selecting the appropriate Vbus according to the calculated value of C or choosing the right topology of PV system according to the parameters C and Vbus. On the other hand, Table 1 shows that PV system with PV-buck/ boost-bus topology is the only one which allows the follow-up of the PV module MPP regardless of temperature, irradiance and connected load. However, the overall cost of this circuit is still too high at present, which makes its integration and extension difficult. In actual installment and application, the buck or boost DC/DC converter is still the main circuit used to implement MPPT control. Therefore, it is of great significance to find out the control strategy through using buck and boost DC/DC converters to implement MPPT control regardless of temperature, irradiance and connected load. 2.3. Proposition of MPPT control strategy According to these results and analysis in Section 2.2, an MPPT control strategy can be proposed that the MPP can be tracked successfully by selecting PV-buck-bus topology for 0
C ¼ 4:62 106 ðS 638:25Þ2 0:0516 T þ 18:577
(16)
Eq. (16) shows C is determined by S and T. Therefore, in actual application, the values of S andT must be measured by sensors or measuring devices, then the real-time value of C which will be compared with Vbus can be calculated by Eq. (16). 3.2. Proposition of PV system configuration After the value of C has been calculated, PV system may change its topology to match the corresponding MPPT condition according to the comparison between C and Vbus. To simplify the configuration and reduce the cost, a new buck/boost converter which is used as MPPT device in PV system with DC bus is proposed and shown in Fig. 3 and its work status can be switched by the switches S1 and S2. When the duty cycle of PWM2 keeps at 0, the PWM1 signal controls this converter to work at buck status. That is to say, the circuit in
S. Li et al. / Renewable Energy 74 (2015) 478e488
Fig. 3. PV system configuration to implement the proposed MPPT strategy.
dashed frame is just a buck DC/DC converter. On the other hand, when the duty cycle of PWM1 keeps at 1, the PWM2 signal just controls this circuit to work at boost DC/DC converter status. In Fig. 3, the main function of MPPT controller is to use the control signals (PWM1 and PWM2) to make PV system always operating at the MPP. Here, the duty cycles of PWM1 and PWM2 are calculated by Eq. (13) and Eq. (10), respectively, according to the sampling values of parameters S, T and Vbus. The main flow chart of controller can be shown in Fig. 4. Where DPWM1 and DPWM2 represent the duty cycles of PWM1 and PWM2, respectively. It is obvious that, to the proposed new buck/boost converter, DPWM1 is equal to Dmbuck for buck status while DPWM2 is equal to Dmboost for boost status. In addition, to make the MPPT control more convenient, the proposed buck/boost converter is kept at buck status when C¼Vbus. 4. Simulation experiments and results analysis 4.1. Verification experiments of MPPT constraint conditions To verify the accuracy of constraint conditions shown in Table 1, many simulation experiments are conducted by MATLAB. Where PV cell model whose parameters are the same as Section 3.1 is built by Simulink according to Eq. (1); the inductances, capacitors, switches and diodes are all ideal components; the frequency of
Fig. 4. Flow chart of MPPT control.
481
PWM control signal is 20 kHz. On the one hand, at standard conditions, the PoD curves of PV-buck-bus, PV-boost-bus and PVbuck/boost-bus modules with various Vbus are shown in Figs. 5e7, respectively. Here, the value of C is calculated as 17.91 by Eq. (9) and the ideal MPPs of all modules are about 150.6 W. It can be seen from Fig. 5 that, at standard conditions, to PV system with PV-buck-bus topology, Po has an available MPP which can be tracked by an appropriate MPPT method when Vbus such as 17 V is less than C; Po does just reach its MPP when D and Vbus (17.91 V in Fig. 5) is just equal to 1 and C, respectively; Po has not an available MPP when Vbus such as 19 V is more than C, therefore no method can make PV system implement MPPT control. Fig. 6 shows that, at standard conditions, to PV system with PV-boost-bus topology, Po has not an available MPP when Vbus such as 17 V is less than C, therefore MPPT control can not be implemented; Po does just reach its MPP when D and Vbus (17.91 V in Fig. 6) is just equal to 0 and C, respectively; Po has an available MPP which can be tracked by an appropriate MPPT method when Vbus such as 19 V is more than C. Fig. 7 shows, to PV system with PV-buck/boost-bus topology, MPPT control can always be implemented at standard conditions. Therefore, to PV system with three topologies, the constraint conditions shown in Table 1 are all accurate at standard conditions. By the way, it can be seen from Figs. 5 and 6 that there is a critical value of Vbus which is represented by Vbusth. It is the voltage of DC bus for ideal PV-buck-bus module with D¼1 or ideal PV-boost-bus module with D¼0. According to the above-mentioned analysis, the ideal value of Vbusth is just equal to C. On the other hand, at non-standard conditions, some experiments are done by MATLAB simulation and results can be shown in Figs. 8e11. Figs. 8 and 9 show the DmbuckS and DmbuckT curves of PV-buck-bus module, respectively, and 17.287 and 17.13 represent the minimum values of C in these two experiments, respectively. Figs. 10 and 11 show the DmboostS and DmboostT curves of PV-boost-bus module, respectively, and 19.15 and 19.2 represent the maximum values of C in these two experiments, respectively. To simplify the analysis of these experiments, the ranges of T andS are set as 0e40 C0 and 0e1276.5 W/m2, respectively. It can be seen from Fig. 8 that, to PV system with PV-buck-bus topology, the DmbuckS curves are eventually cut their tops with the increment of Vbus, which illustrates the MPPT control can not be implemented in these corresponding S range (such asS2½249; 1027 when Vbus¼18 V); these curves are just cut their
Fig. 5. PoD curves of PV-buck-bus module at various Vbus.
482
S. Li et al. / Renewable Energy 74 (2015) 478e488
Fig. 6. PoD curves of PV-boost-bus module at various Vbus.
Fig. 9. S ¼ 1000 W/m2,DmbuckT curves at various Vbus.
Fig. 7. PoD curves of PV-buck/boost-bus module at various Vbus.
Fig. 10. T¼25 C, DmboostS curves at various Vbus.
Fig. 8. T¼25 C,DmbuckS curves at various Vbus.
Fig. 11. S¼1000 W/m2, DmboostT curves at various Vbus.
S. Li et al. / Renewable Energy 74 (2015) 478e488
tops when Vbus is equal to 17.287 V which is the critical value of implementing the MPPT. Under these conditions which the MPP can be captured (such as Vbus17.287 V), the maximum value of Dmbuck is reached when S ¼ 638.25W/m2, which means the easiest appearance of “cut top” phenomenon here. Fig. 9 shows that the DmbuckT curves are eventually cut their tops with the increment of Vbus, which illustrates the MPPT control can not be implemented in these corresponding T range; these curves are just cut their tops when Vbus is equal to 17.13 V which is the critical value of implementing the MPPT. Therefore, to PV system with PV-buck-bus topology, the constraint condition shown in Table 1 is accurate at non-standard conditions. It can be seen from Fig. 10 that, to PV system with PV-boost-bus topology, the DmboostS curves are eventually cut their bottoms with the decrement of Vbus, which illustrates the MPPT control can not be implemented in these corresponding S range (such asS2½0; 249∪½1027; 1276:5 when Vbus¼18 V); these curves are just cut their bottoms when Vbus is equal to 19.15 V which is the critical value of implementing the MPPT. Under these conditions which the MPP can be captured (such as Vbus19.15 V), the minimum value of Dmboost is reached when S¼0 or 1276.5W/m2, which means the easiest appearance of “cut bottom” phenomenon here. Fig. 11 shows that theDmboostT curves are eventually cut their bottoms with the decrement of Vbus, which illustrates the MPPT control can not be implemented in these corresponding T range; these curves are just cut their tops when Vbus is equal to 19.2 V which is the critical value of implementing the MPPT. Therefore, to PV system with PV-boost-bus topology, the constraint condition shown in Table 1 is accurate at non-standard conditions. 4.2. Feasibility and availability experiments of proposed control strategy To test the feasibility and availability of the proposed MPPT control strategy, lots of experiments for PV system shown in Fig. 3 are conducted by MATLAB simulation. Where PV cell model whose parameters are the same as Section 3.1 is built by Simulink according to Eq. (1); the inductance (L) and capacitor (C) whose values are 1 mH and 1 mF, respectively, are the ideal components;
483
the internal and snubber resistance of switches (S1 and S2) are 1 mU and 100 kU, respectively; the internal resistance, snubber resistance and forward voltage of diodes (D1 and D2) are 1 mU, 0.5 kU and 0.8 V, respectively; the internal resistance of DC bus is 1 mU; the frequency of control signals (PWM1 and PWM2) is 20 kHz. The experimental results under various (S,T) and various Vbus conditions are shown in Table 2 and Table 3, respectively. Where C and Cc represent the calculated values according to Eq. (9) and Eq. (16), respectively; Dpwm1c and Dpwm1p represent the duty cycles of PWM1 while the proposed PV system is operating at its MPP through the proposed MPPT control strategy and P&O method, respectively; Dpwm2c and Dpwm2p represent the duty cycles of PWM2 at MPP corresponding to the proposed MPPT control strategy and P&O method, respectively; Pmax represents the maximum output power of PV cell; Pomax and Pomp represent the maximum output powers of proposed buck/boost converter with proposed MPPT control strategy and P&O method, respectively; Pbuck and Pboost represent the maximum output powers of PV systems with PV-buck-bus and PV-boost-bus topologies through using the P&O method, respectively; “/” in Tables 2 and 3 represents the failure of capturing the MPP. It can be seen from Table 2 that, on the one hand, the values of Pomax are approximately equal to those of Pomp under a given (S,T) conditions when Vbus keeps at 18 V, which illustrates the proposed MPPT strategy is controlling PV system to operate around its MPP. On the other hand, the errors between Dpwm1c and Dpwm1p or between Dpwm2c and Dpwm2p are small and have little influence on accuracy of Pomax. Meanwhile, Table 2 also shows that, because of the internal and snubber resistance of switches and diodes in Fig. 3, there are some errors between Pomax and Pbuck or Pboost, which are all less than 7 W. It is obvious that these errors owing to circuit component parameters can be ignored in verifying MPPT theoretical analysis. Therefore, a conclusion can be drawn that the MPP can be tracked well by proposed MPPT control strategy. That is to say, the proposed MPPT control strategy is feasible and available under various S,T and invariable Vbus conditions. It can be seen from Table 3 that, under various Vbus and standard S,T conditions, the errors between Pomax and corresponding Pomp are all less than 5 W, which illustrates that the values of Pomax are
Table 2 Experimental results under various (S,T) and Vbus ¼ 18 V conditions. (S,T)
C
Cc
Dpwm1c
Dpwm1p
Dpwm2c
Dpwm2p
Pmax(W)
Pomax(W)
Pomp(W)
Pbuck(W)
Pboost(W)
(500,0) (500,10) (800,10) (500,20) (800,20) (1000,20) (500,30) (800,30) (1000,30) (1200,30) (1000,40) (1200,40)
18.630 18.129 18.165 17.629 17.663 18.164 17.128 17.162 17.648 18.475 17.133 17.935
18.665 18.149 18.182 17.633 17.666 18.150 17.117 17.150 17.634 18.487 17.118 17.971
0.964 0.992 0.990 1 1 0.992 1 1 1 0.974 1 1
0.971 0.996 0.993 1 1 0.993 1 1 1 0.973 1 1
0 0 0 0.0203 0.0186 0 0.0490 0.0472 0.0204 0 0.0490 0.0016
0 0 0 0.024 0.0187 0 0.0498 0.0481 0.0250 0 0.054 0.0036
73.7 73.3 117.9 72.8 117.4 150.9 72.4 117.0 150.5 188.7 150.1 188.3
68.8 68.8 110.4 69.0 110.8 141.8 68.76 110.4 141.9 176.7 141.2 177.1
69.3 69.1 110.9 69.0 110.8 142.8 68.78 110.5 142.3 177.7 141.6 177.3
72.4 72.3 115.8 / / 148.4 / / / 184.7 / /
/ / / 69.3 111.4 / 69.2 111.2 143.4 / 142.8 179.4
Table 3 Experimental results under various Vbus and standard S,T conditions. Vbus(V)
C
Cc
Dpwm1c
Dpwm1p
Dpwm2c
Dpwm2p
Pmax(W)
Pomax(W)
Pomp(W)
Pbuck(W)
Pboost(W)
12 15 17 18 20 24
17.91 17.91 17.91 17.91 17.91 17.91
17.89 17.89 17.89 17.89 17.89 17.89
0.671 0.838 0.950 1 1 1
0.710 0.868 0.962 1 1 1
0 0 0 0.006 0.105 0.255
0 0 0 0.012 0.128 0.275
150.7 150.7 150.7 150.7 150.7 150.7
132.9 136.3 140.2 141.6 142.4 143.6
137.7 140.6 141.7 142.6 144.2 145.0
143.9 147.5 148.4 / / /
/ / / 143.5 144.4 145.2
484
S. Li et al. / Renewable Energy 74 (2015) 478e488
Table 4 Values of experimental parameters under standard conditions. Range of time (s)
From 0 to 0.1
From 0.1 to 0.25
From 0.25 to 0.5
Experiment Experiment Experiment Experiment
19 17.5 18.5 17
18.5 17 17 19
18.75 17.25 19 17.5
1 2 3 4
Vbus(V) Vbus(V) Vbus(V) Vbus(V)
approximately equal to those of Pomp. Meanwhile, the errors between Dpwm1c and Dpwm1p or between Dpwm2c and Dpwm2p are also small. According to these analysis, we know that PV system can operate around MPP through using proposed MPPT control strategy. Therefore, a conclusion can be drawn that the proposed MPPT control strategy is feasible and available under various Vbus and invariable S,T conditions. By the way, because the built PV system according to Fig. 3 is not ideal, there are some errors between Pmax and Pomax,Pomp,Pbuck,Pboost. Meanwhile, according to Table 3, these errors will become bigger with the decrement of Vbus. However, the verification of feasibility and availability of proposed MPPT strategy is not influenced by them. 4.3. MPPT performance analysis To analyze the MPPT performance of proposed control strategy, some experiments are also done by MATLAB. Here, the parameters of PV system are all same as Section 4.2. Meanwhile, in these experiments, PV system is assumed to operate under invariable S,T conditions, invariable S,Vbus conditions and invariable S,Vbus conditions, respectively. Here, to make a MPPT performance comparison between proposed MPPT strategy and conventional P&O method, their corresponding maximum powers Pomax and Pomp are shown together in all following figures. Note that Pomp shown in these figures only represent the steady-state values at MPP for P&O method. 4.3.1. Experiments under invariable S,T conditions When S and S are selected as 1000 W/m2 and 25 C0, respectively, four experiments are conducted. In these experiments, the changing values of Vbus and its corresponding ranges of time are shown in Table 4 and the MPPT performance is analyzed under Vbus>Cc, 0
Fig. 12. Output power curves under experiment 1 condition.
Fig. 13. Output power curves under experiment 2 condition.
the value of Cc is 17.89. Therefore, according to Table 4, experiment 1, experiment 2 and experiment 3 or 4 correspond respectively with Vbus>Cc, 0
4.3.2. Experiments under invariable T and Vbus conditions When the proposed PV system is operating under T ¼ 25 C and Vbus ¼ 18 V conditions, four experiments are still conducted. In these experiments, the changing ranges of S and corresponding Cc (represented byS(W/m2)/Cc) are shown in Table 5 and the MPPT performance is still analyzed under 0Vbus and uncertain Cc conditions. According to Table 5, experiment 1, experiment 2 and experiment 3 or 4 correspond respectively with
Fig. 14. Output power curves under experiment 3 condition.
S. Li et al. / Renewable Energy 74 (2015) 478e488
Fig. 15. Output power curves under experiment 4 condition.
Fig. 16. Output power curves under experiment 1 condition.
0Vbus and uncertain Cc conditions and their output power curves are shown in Figs. 16e19, respectively. Figs. 16e19 show the output power curves under T ¼ 25 C and Vbus ¼ 18 V conditions. According to these figures, it can be seen that the values of Pomax are all approximately equal to corresponding values of Pomp and the errors between them are always less than 2 W. Therefore, a conclusion can be made that, through using proposed MPPT strategy, the MPP of proposed PV system can be always tracked well under various S and invariable S,Vbus conditions. 4.3.3. Experiments under invariable S and Vbus conditions When the proposed PV system is operating under S ¼ 1000 W/ m2 and Vbus ¼ 18 V conditions, four experiments are still conducted. In these experiments, the changing ranges of T and corresponding Cc (represented byT( C)/Cc) are shown in Table 6 and the MPPT performance is still analyzed under 0Vbus and uncertain Cc conditions. According to Table 6, experiment 1, experiment 2 and experiment 3 or 4 correspond respectively with 0Vbus and uncertain Cc conditions and their output power curves are shown in Figs. 20e23, respectively. Figs. 20e23 show the output power curves under S ¼ 1000 W/ m2 and Vbus ¼ 18 V conditions. According to these figures, it can be seen that the values of Pomax are all approximately equal to corresponding values of Pomp and the errors between them are always less than 2 W. Therefore, a conclusion can be made that, through using proposed MPPT strategy, PV system can always operate around its MPP well under various T and invariable S,Vbus conditions. According to above-mentioned experimental results and analysis, there is always a small error (about 2 W) between Pomax and Pomp (regarded as the true maximum output power), and the percentage of this error to total output power is only about 1.43%. Therefore, the conclusion can be drawn that the proposed MPPT
Fig. 17. Output power curves under experiment 2 condition.
Table 5 Values of experimental parameters under T¼25 C and Vbus¼18 V conditions. Range of time (s) Experiment Experiment Experiment Experiment
1 2 3 4
S(W/m2)/Cc S(W/m2)/Cc S(W/m2)/Cc S(W/m2)/Cc
From 0 to 0.1
From 0.1 to 0.25
From 0.25 to 0.5
800/17.41 1200/18.74 800/17.41 1200/18.74
1000/17.89 1150/18.5 1200/18.74 800/17.41
900/17.6 1300/19.31 1000/17.89 1150/18.5
Fig. 18. Output power curves under experiment 3 condition.
485
486
S. Li et al. / Renewable Energy 74 (2015) 478e488
Fig. 19. Output power curves under experiment 4 condition.
Fig. 20. Output power curves under experiment 1 condition.
strategy can always control the proposed PV system to operate around its MPP regardless of irradiance, temperature and DC bus voltage. 4.4. Performance comparison The MPPT performance has been analyzed and compared in Section 4.3, however, the transient performance of P&O method is not considered. Here, an experiment is done to make the transient performance comparison between proposed MPPT strategy and conventional P&O method and its result can be shown in Fig. 24. Where the parameters of PV system are all same as Section 4.2 and S, T, Vbus and step-size increment of duty cycle D in P&O method are selected as 1000 W/m2, 25 C 17.5 V and 0.005, respectively. The settling time of the output power is about 22 ms when the proposed MPPT control strategy is used in PV system, just as the solid line has been showing in Fig. 24. By contrast, the settling time is about 215 ms when the conventional P&O method is used, just as the dotted line has been showing in Fig. 24. When the step-size increments of P&O method are various, some experiments are done to make a further comparison of the settling time. Experiments results show that, when the step-size increments of P&O method are selected 0.003, 0.006, 0.007, 0.008 and 0.01, the settling times are about 350 ms, 184 ms, 165 ms, 142 ms and 118 ms, respectively, and that, with regard to output power curve, the oscillation around MPP will become bigger with the increment of step size. Therefore, it is obvious that the proposed MPPT strategy has better transient-state performance than the conventional P&O method.
Fig. 21. Output power curves under experiment 2 condition.
5. Discussions Whether the MPP of PV system with DC bus can be captured or not is constrained by conditions shown in Table 1 when the output
Table 6 Values of experimental parameters under S¼1000 W/m2 and Vbus¼18 V conditions. Range of time (s) Experiment Experiment Experiment Experiment
1 2 3 4
T( C)/Cc T( C)/Cc T( C)/Cc T( C)/Cc
From 0 to 0.15
From 0.15 to 0.3
From 0.3 to 0.5
25/17.89 10/18.67 25/17.89 10/18.67
40/17.12 20/18.15 10/18.67 25/17.89
30/17.64 0/19.18 30/17.64 0/19.18
Fig. 22. Output power curves under experiment 3 condition.
S. Li et al. / Renewable Energy 74 (2015) 478e488
487
system can be proposed and designed as follows: Firstly, according to the paper [17], the ideal output power at MPP (represented by Pomax) can be calculated by the measured values of S and T. Secondly, in Fig. 3, Io must be sampled by MPPT controller, then the real-time output power (represented by Po) and difference (represented by Ep) between Pomax and steady-state value of Po can be calculated out. Lastly, a threshold value can be set and represented by ε. Meanwhile, in Fig. 4, a judgment must be added in flow chart. If Ep>ε, which means that PV system fails to operate around MPP, a reserve MPPT method such as P&O method will be switched and operated. 6. Conclusions
Fig. 23. Output power curves under experiment 4 condition.
In this paper, to different PV systems with DC bus, on the basis of finding out the constraint conditions of capturing their MPPs, a MPPT control strategy with variable weather parameters has been proposed. Meanwhile, to implement this MPPT method, a new buck/boost DC/DC converter has been proposed, which has avoided the high-cost and difficult-application problems of basic buck/ boost DC/DC converter. Finally, through lots of simulation experiments, the accuracy of these constraint conditions has been verified, the feasibility and availability of proposed MPPT control strategy have been tested, the MPPT performance has been analyzed and the output transient-state performance has been compared. Acknowledgment This work was supported by guidance project of Hubei Department of Education (No. B2014244 and B2013076). References
Fig. 24. Performance comparison between proposed strategy and P&O method.
currents of DC/DC converters are continuous. Therefore, in practical application, the inductor and capacitor selected as filter of DC/DC converter should be large enough to make the output current continuous. In Sections 4.2e4.4, there are some errors between Pomax and Pomp. However, in practical application, these small errors whose values are all less than 2 W can be ignored. If we need to make the MPPT control more accurate for considering the influence on change of circuit element parameters and inaccuracy measurement, the correction terms E1 and E2 can be added to Eq. (13) and Eq. (10), respectively. Where the average difference between Dpwm1p and Dpwm1c can be selected as E1 and the average difference between Dpwm2p and Dpwm2c can be selected asE2. In Tables 2 and 3, the errors between Pomax and Pbuck are always bigger than these between Pomax and Pboost, because, to the circuit shown in Fig. 3, the influence of the switch S2 and diode D2 at buck status is larger than that of S1 and D1 at boost status. It is obvious that the switch or diode with bigger snubber resistance and smaller internal resistance can be used to reduce these errors. In practical application, the parameter uncertainties of PV system maybe make MPPT control failed. To settle this issue, a reserve
[1] Sun Kai, Zhang Li, Xing Yan, Guerrero Josep M. A distributed control strategy based on DC bus signaling for modular photovoltaic generation systems with battery energy storage. IEEE Trans Power Electron 2011;26(10):3032e45. [2] Salas V, Barrado A. Review of the maximum power point tracking algorithms for stand-alone photovoltaic systems. Sol Energy Mater Sol Cells 2006;90(10): 1555e78. [3] Femia N, Petrone G, Spagnuolo G, Vitelli M. Optimization of perturb and observe maximum power point tracking method. IEEE Trans Power Electron 2005;20(4):963e73. [4] Abdelsalam Ahmed K, Massoud Ahmed M, Ahmed Shehab, Enjeti Prasad N. High-performance adaptive perturb and observe MPPT technique for photovoltaic-based microgrids. IEEE Trans Power Electron 2011;26(4): 1010e21. [5] Femia N, Petrone G, Spagnuolo G, Vitelli M. A technique for improving P&O MPPT performances of double stage grid-connected photovoltaic systems. IEEE Trans Indus Electron 2009;56(11):4473e82. [6] Zegaoui A, Aillerie M, Petit P, Sawicki JP, Jaafar A, Salame C, et al. Comparison of two common maximum power point trackers by simulating of PV generators. Energy Procedia 2011;6:678e87. [7] Liu F. A variable step size INC MPPT method for PV systems. IEEE Trans Indus Electron 2008;55(7):2622e8. [8] Ko Shih- Hung, Chao Ru-Min. Photovoltaic dynamic MPPT on a moving vehicle. Sol Energy 2012;86:1750e60. [9] Moradi Mohammad H, Reisi Ali Reza. A hybrid maximum power point tracking method for photovoltaic systems. Sol Energy 2011;85:2965e76. [10] Kakosimos Panagiotis E, Kladas Antonios G. Implementation of photovoltaic array MPPT through fixed step predictive control technique. Renew Energy 2011;36:2508e14. [11] Messai A, Mellit A, Guessoum A, Kalogirou SA. Maximum power point tracking using a GA optimized fuzzy logic controller and its FPGA implementation. Sol Energy 2011;85:265e77. [12] Larbes C, A€It Cheikh SM, Obeidi T, Zerguerras A. Genetic algorithms optimized fuzzy logic control for the maximum power point tracking in photovoltaic system. Renew Energy 2009;34:2093e100. [13] Gounden N Ammasai, Ann Peter Sabitha, Nallandula Himaja, Krithiga S. Fuzzy logic controller with MPPT using line-commutated inverter for three-phase grid-connected photovoltaic systems. Renew Energy 2005;30:909e15. [14] Patcharaprakiti Nopporn, Premrudeepreechacharn Suttichai, Sriuthaisiriwong Yosanai. Maximum power point tracking using adaptive
488
[15]
[16]
[17]
[18]
S. Li et al. / Renewable Energy 74 (2015) 478e488 fuzzy logic control for grid-connected photovoltaic system. Renew Energy 2009;34:1771e88. Lin Whei-Min, Hong Chih-Ming, Chen Chiung-Hsing. Neural-network-based MPPT control of a stand-alone hybrid power generation system. IEEE Trans Power Electron 2011;26(12):3571e81. Chiu Chian-Song, Ouyang Ya-Lun, Ku Chan-Yu. Terminal sliding mode control for maximum power point tracking of photovoltaic power generation systems. Sol Energy 2012;86:2986e95. Gao Xianwen, Li Shaowu, Gong Rongfen. Maximum power point tracking control strategies with variable weather parameters for photovoltaic generation systems. Sol Energy 2013;93:357e67. Enrique JM, Duran E, Sidrach-de-Cardona M, Andujar JM. Theoretical assessment of the maximum power point tracking efficiency of photovoltaic facilities with different converter topologies. Sol Energy 2007;81(8):31e8.
[19] Hussion KH, Zhao G. Maximum photovoltaic power tracking: an algorithm for rapidly changing atmospheric conditions. IEEE Proc 1995;142(1):59e64. [20] Mutoh N, Ohno M, Inoue T. A method for MPPT control while searching for parameters corresponding to weather conditions for PV generation systems. IEEE Trans Indus Electron 2006;53(4):1055e65. [21] Hua C, Lin J. An on-line MPPT algorithm for rapidly changing illuminations of solar arrays. Renew Energy 2003;28:1129e42. [22] Li Shaowu, Gao Xianwen, Wang Lina, Liu Sanjun. A novel maximum power point tracking control method with variable weather parameters for photovoltaic systems. Sol Energy 2013;97:529e36. [23] Moura Scott. A switched extremum seeking approach to maximum power point tracking in photovoltaic systems. Grid Integration Altern Energy Sources 2009.
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
A maximum power point tracking control strategy with variable weather parameters for photovoltaic systems with DC bus Shaowu Li a, *, Amine Attou b, Yongchao Yang a, Dongshan Geng a a b
Science and Technology College, and School of Information Engineering, Hubei University for Nationalities, Enshi, China Intelligent Control & Electrical Power Systems Laboratory, Djillali Liabes University of Sidi Bel-Abbes, Sidi Bel-Abbes, Algeria
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 April 2014 Accepted 21 August 2014 Available online
In photovoltaic (PV) system, the most commonly used DC/DC converter is the basic buck or boost circuit to implement the maximum point power tracking (MPPT) due to their simple structure and low cost while there are some MPPT constraint conditions. By contrast, the conventional buck/boost DC/DC converter without MPPT constraint condition is seldom used because of its high cost or poor performance. To keep the advantages of these three DC/DC converters while overcoming their shortcomings, in this paper, the constraint conditions of capturing the maximum power point (MPP) of PV systems with direct-current (DC) bus are found out. Then, on the basis of this work, a MPPT control strategy with variable weather parameters is proposed. In this strategy, a new buck/boost DC/DC converter is proposed, which not only avoids the MPPT constraint conditions of basic buck or boost DC/DC converter but also overcomes the shortcomings of conventional buck/boost DC/DC converter. Finally, lots of simulated experiments verify the accuracy of MPPT constraint conditions, test the feasibility and availability of proposed MPPT control strategy, analyze the MPPT performance of proposed PV system and compare the output transient-state performance with conventional perturb and observe (P&O) method. © 2014 Elsevier Ltd. All rights reserved.
Keywords: PV system MPPT DC bus Constraint condition DC/DC converter
1. Introduction To PV system with DC bus, in order to avoid power losses, different DC/DC converters can be usually used as the connectors between PV cells and DC bus to implement MPPT control. This topology has advantages of simple structure, low cost, convenient installment and maintenance and has been widely used by PV generation microgrid at present [1]. For them, some existing methods such as the constant voltage tracking [2], the P&O method [2e6], the incremental conductance (IncCond) method [2,6,7], the quadratic maximization method [8,9] and so on can be directly used, however other algorithms such as the predictive control technique [10], the fuzzy logic control method [11e14], the neural network method [15], the sliding mode control method [16] and so on need be modified properly to meet the requirements of these special topologies. Nowadays there are some MPPT methods which are specifically used to PV systems with DC bus, such as the variable weather parameters (VWP) method [17], which makes the use of these PV systems wider. In all these MPPT methods, the P&O and IncCond methods are used more widely than others. The
* Corresponding author. Tel.: þ86 13997799701. E-mail addresses: [email protected], [email protected] (S. Li). http://dx.doi.org/10.1016/j.renene.2014.08.056 0960-1481/© 2014 Elsevier Ltd. All rights reserved.
advantages of P&O method mainly include its good operation without solar irradiance and temperature varying quickly with time and its simple analog circuitry or very-low-cost microcontroller. By contrast, its shortcomings are the tracking slowness and the output power oscillation around the MPP. The IncCond method has better performance than P&O, however it requires differentiation, division circuitry and a relatively complex decision making process, and therefore requires a more complex microcontroller with more memory, which makes the implementation of this method difficult. In this paper, to study the output transient-state performance of proposed MPPT strategy, the P&O method is selected as the comparison object. To PV systems with three basic DC/DC converters, the buck/ boost topology is the only one which allows the follow-up of the PV module MPP regardless of temperature, irradiance and connected load [18]. However, either the overall cost of this circuit is still too high or the MPPT performance is poor at present, which makes its integration, application and extension difficult. For example, to the basic buck/boost DC/DC converter, the input and output currents are all discontinuous, which makes MPPT performance poor, meanwhile the Cuk, Sepic and Zeta DC/DC converters all need two inductances and two capacitors and lots of circuit components must withstand higher voltage or higher current, which makes the component cost higher. Therefore, in actual installment and
S. Li et al. / Renewable Energy 74 (2015) 478e488
application. the buck or boost DC/DC converter is still the main circuit selected to implement MPPT control while there are some constraint conditions for their MPPT implementation. It is obvious that the best way to solve these above-mentioned questions is the acquisition of a new circuit which keeps the advantages of buck, boost and buck/boost DC/DC converters as well as overcomes their shortcomings. To achieve this goal, in this paper, what conditions the MPPs of different PV systems with DC bus can be tracked successfully under will be studied firstly. Then a new buck/boost DC/ DC converter which a buck is cascaded by a boost is proposed, which can switch between buck circuit and boost circuit to meet the MPPT demand with changes of external parameters. With regard to the issue how the changing weather has some effects on MPPT control, some works have been done [19e21], and some MPPT methods such as the VWP methods have found out the direct relationships between control signals and variable weather parameters [17,22], which makes the study on the overall performance of PV systems more convenient. In this paper, the VWP method is studied continuously and specially for PV system with DC bus. This paper is divided into the following sections: Section 2 presents the MPPT constraint conditions of PV systems with different topologies and the proposition of MPPT control strategy. How this proposed MPPT strategy is implemented is presented in Section 3. The accuracy of these MPPT constraint conditions is certified and the feasibility, availability and advantages of this proposed MPPT control strategy are analyzed by simulation experiments in Section 4. Some discussions are had in Section 5. Finally, some conclusions are drawn in Section 6.
2. Principle of MPPT control strategy 2.1. Analysis of mathematical model of PV system The configuration of PV generation system with DC bus can be shown in Fig. 1. Where V and I represent the output voltage and current of PV panel, respectively; Vo and Io represent the output voltage and current of DC/DC converter, respectively; RL represents the equivalent load resistance. In PV system shown in Fig. 1, three different topologies can be divided as PV-buck-bus, PV-boost-bus and PV-buck/boost-bus corresponding to the basic buck, boost and buck/boost DC/DC converters, respectively. It is obvious that the theoretical basis studying the constrain conditions of capturing the MPP is the mathematical models of PV cell and three DC/DC converters. Therefore, our work will start from analyzing these models. Firstly, in the practical application, the mathematical model of PV cell can be expressed by Eq. (1) [20,23].
h V i I ¼ Isc 1 C1 eC2 Voc 1
(1)
Where C1¼(1Im/Isc)exp(Vm/C2Voc);C2¼(Vm/Voc1)/ln(1Im/ Isc);ISC, VOC, Im and Vm represent the short circuit current, the open circuit voltage, the maximum power point current and voltage at
Fig. 1. Configuration of PV system with DC bus.
479
standard conditions (1000 W/m2 and 25 C), respectively. All data above are given by the PV array manufacturer. Secondly, with regard to the models of three DC/DC converters, the boost circuit is firstly analyzed as an example, and the buck or buck/boost circuit can be also analyzed by analogy. Here, Fig. 1 can be represented by Fig. 2. To simplify the boost DC/DC converter, assuming that: (1) the switch, diode, inductance and capacitor are all ideal electronic components; (2) the wires have no resistance and the output equivalent load can be represented by pure resistance RL; (3) the values of inductance and capacitor are large enough to ensure the output current continuous. Now the circuit shown in Fig. 2 can be analyzed through laws of circuit and conservation of energy, and Eqs. (2)e(4) can be given.
Vo ¼ V=ð1 DÞ
(2)
VI ¼ Vo Io
(3)
. Po ¼ Vo Io ¼ Vo2 RL
(4)
Where D represents the duty cycle of pulse width modulation (PWM) control signal of the boost DC/DC converter;Po represents the output power. According to Eqs. (1)e(4), Eq. (5) can be given.
Po ¼ RL ð1
2 DÞ2 Isc
pffiffiffiffiffiffi Po RL 1D C Voc
1 C1 e
2
2 1
(5)
Eq. (5) shows the theoretical relationship between D and Po, which is the mathematical model of PV system with PV-boost-bus topology. Likewise, the mathematical models of PV system with PVbuck-bus topology and PV-buck/boost-bus topology can be given as Eq. (6) and Eq. (7), respectively.
Po ¼
pffiffiffiffiffiffi 2 Po RL 2 RL Isc C2 DVoc 1 C e 1 1 D2
2 Po ¼ RL Isc
pffiffiffiffiffiffi 2 Po RL ð1DÞ ð1 DÞ2 C2 Voc D 1 C e 1 1 D2
(6)
(7)
2.2. Analysis of MPPT constraint conditions According to Eq. (5), in order to obtain the duty cycle Dmboost o corresponding to the MPP, we take the equation dP ¼ 0 into acdD count and have.
Dmboost ¼ 1
C Vomax
Fig. 2. Structure of PV system with PV-boost-bus topology.
(8)
480
S. Li et al. / Renewable Energy 74 (2015) 478e488
Where Vomax represents the maximum value of Vo; C represents a variable weather parameter whose value is related with the parameters of solar cell, solar irradiance S and solar cell temperature T. The value of C can be calculated by Eq. (9). Meanwhile, it can be seen from Eq. (9) that C whose unit is “V” is really a voltage and its value is a constant under a certain weather condition.
1 þ C1 1 C ¼ C2 Voc lambertw e C1
(9)
To an ideal boost circuit, Eq. (8) can be described as Eq. (10) when its output terminal is directly connected with a DC bus. Where Vbus represents the voltage of DC bus.
Dmboost ¼
Vbus C Vbus
(10)
Eq. (10) shows the theoretical relationship between Dmboost and Vbus at the MPP of PV system with PV-boost-bus topology. Because Dmboost belongs to the interval [0, 1], Eq. (11) can be given according to Eq. (10).
0
Vbus C 1 Vbus
(11)
That is.
Vbus C
(12)
It is obvious that Eq. (12) is the constraint condition under which the MPP capture will be possible for PV system with PVboost-bus topology. Likewise, according to Eq. (6), the theoretical relationship between Dmbuck and Vbus at the MPP of PV system with PV-buck-bus topology can be given as Eq. (13). Where Dmbuck represents the duty cycle corresponding to the MPP.
Dmbuck ¼
Vbus C
(13)
According to Eq. (13), the constraint condition under which the MPP capture will be possible for PV system with PV-buck-bus topology is obtained:
0 < Vbus C
(14)
Likewise, according to Eq. (7), the theoretical relationship between Dmbuckboost and Vbus at the MPP of PV system with PV-buck/ boost-bus topology can be given as Eq. (15). Where Dmbuckboost represents the duty cycle corresponding to the MPP.
Dmbuckboost ¼
Vbus C þ Vbus
(15)
Eq. (15) shows that there is always an appropriate Dmbuckboost to make this equation work regardless of Vbus. Therefore, a conclusion can be drawn that the MPP of PV system with PV-buck/ boost-bus topology can be always captured. All in all, the constraint conditions of capturing the MPPs of PV systems with three topologies can be shown in Table 1.
Table 1 MPPT constraint conditions for PV systems with three topologies. Different topologies
Constraint conditions
PV-buck-bus PV-boost-bus PV-buck/boost-bus
0 < Vbus C Vbus C none
According to Table 1, we can answer this question: What are the appropriate Vbus ranges in which the MPPs of PV systems with three topologies can be captured successfully? That is to say, in actual installment and application, MPPT control can be implemented successfully by selecting the appropriate Vbus according to the calculated value of C or choosing the right topology of PV system according to the parameters C and Vbus. On the other hand, Table 1 shows that PV system with PV-buck/ boost-bus topology is the only one which allows the follow-up of the PV module MPP regardless of temperature, irradiance and connected load. However, the overall cost of this circuit is still too high at present, which makes its integration and extension difficult. In actual installment and application, the buck or boost DC/DC converter is still the main circuit used to implement MPPT control. Therefore, it is of great significance to find out the control strategy through using buck and boost DC/DC converters to implement MPPT control regardless of temperature, irradiance and connected load. 2.3. Proposition of MPPT control strategy According to these results and analysis in Section 2.2, an MPPT control strategy can be proposed that the MPP can be tracked successfully by selecting PV-buck-bus topology for 0
C ¼ 4:62 106 ðS 638:25Þ2 0:0516 T þ 18:577
(16)
Eq. (16) shows C is determined by S and T. Therefore, in actual application, the values of S andT must be measured by sensors or measuring devices, then the real-time value of C which will be compared with Vbus can be calculated by Eq. (16). 3.2. Proposition of PV system configuration After the value of C has been calculated, PV system may change its topology to match the corresponding MPPT condition according to the comparison between C and Vbus. To simplify the configuration and reduce the cost, a new buck/boost converter which is used as MPPT device in PV system with DC bus is proposed and shown in Fig. 3 and its work status can be switched by the switches S1 and S2. When the duty cycle of PWM2 keeps at 0, the PWM1 signal controls this converter to work at buck status. That is to say, the circuit in
S. Li et al. / Renewable Energy 74 (2015) 478e488
Fig. 3. PV system configuration to implement the proposed MPPT strategy.
dashed frame is just a buck DC/DC converter. On the other hand, when the duty cycle of PWM1 keeps at 1, the PWM2 signal just controls this circuit to work at boost DC/DC converter status. In Fig. 3, the main function of MPPT controller is to use the control signals (PWM1 and PWM2) to make PV system always operating at the MPP. Here, the duty cycles of PWM1 and PWM2 are calculated by Eq. (13) and Eq. (10), respectively, according to the sampling values of parameters S, T and Vbus. The main flow chart of controller can be shown in Fig. 4. Where DPWM1 and DPWM2 represent the duty cycles of PWM1 and PWM2, respectively. It is obvious that, to the proposed new buck/boost converter, DPWM1 is equal to Dmbuck for buck status while DPWM2 is equal to Dmboost for boost status. In addition, to make the MPPT control more convenient, the proposed buck/boost converter is kept at buck status when C¼Vbus. 4. Simulation experiments and results analysis 4.1. Verification experiments of MPPT constraint conditions To verify the accuracy of constraint conditions shown in Table 1, many simulation experiments are conducted by MATLAB. Where PV cell model whose parameters are the same as Section 3.1 is built by Simulink according to Eq. (1); the inductances, capacitors, switches and diodes are all ideal components; the frequency of
Fig. 4. Flow chart of MPPT control.
481
PWM control signal is 20 kHz. On the one hand, at standard conditions, the PoD curves of PV-buck-bus, PV-boost-bus and PVbuck/boost-bus modules with various Vbus are shown in Figs. 5e7, respectively. Here, the value of C is calculated as 17.91 by Eq. (9) and the ideal MPPs of all modules are about 150.6 W. It can be seen from Fig. 5 that, at standard conditions, to PV system with PV-buck-bus topology, Po has an available MPP which can be tracked by an appropriate MPPT method when Vbus such as 17 V is less than C; Po does just reach its MPP when D and Vbus (17.91 V in Fig. 5) is just equal to 1 and C, respectively; Po has not an available MPP when Vbus such as 19 V is more than C, therefore no method can make PV system implement MPPT control. Fig. 6 shows that, at standard conditions, to PV system with PV-boost-bus topology, Po has not an available MPP when Vbus such as 17 V is less than C, therefore MPPT control can not be implemented; Po does just reach its MPP when D and Vbus (17.91 V in Fig. 6) is just equal to 0 and C, respectively; Po has an available MPP which can be tracked by an appropriate MPPT method when Vbus such as 19 V is more than C. Fig. 7 shows, to PV system with PV-buck/boost-bus topology, MPPT control can always be implemented at standard conditions. Therefore, to PV system with three topologies, the constraint conditions shown in Table 1 are all accurate at standard conditions. By the way, it can be seen from Figs. 5 and 6 that there is a critical value of Vbus which is represented by Vbusth. It is the voltage of DC bus for ideal PV-buck-bus module with D¼1 or ideal PV-boost-bus module with D¼0. According to the above-mentioned analysis, the ideal value of Vbusth is just equal to C. On the other hand, at non-standard conditions, some experiments are done by MATLAB simulation and results can be shown in Figs. 8e11. Figs. 8 and 9 show the DmbuckS and DmbuckT curves of PV-buck-bus module, respectively, and 17.287 and 17.13 represent the minimum values of C in these two experiments, respectively. Figs. 10 and 11 show the DmboostS and DmboostT curves of PV-boost-bus module, respectively, and 19.15 and 19.2 represent the maximum values of C in these two experiments, respectively. To simplify the analysis of these experiments, the ranges of T andS are set as 0e40 C0 and 0e1276.5 W/m2, respectively. It can be seen from Fig. 8 that, to PV system with PV-buck-bus topology, the DmbuckS curves are eventually cut their tops with the increment of Vbus, which illustrates the MPPT control can not be implemented in these corresponding S range (such asS2½249; 1027 when Vbus¼18 V); these curves are just cut their
Fig. 5. PoD curves of PV-buck-bus module at various Vbus.
482
S. Li et al. / Renewable Energy 74 (2015) 478e488
Fig. 6. PoD curves of PV-boost-bus module at various Vbus.
Fig. 9. S ¼ 1000 W/m2,DmbuckT curves at various Vbus.
Fig. 7. PoD curves of PV-buck/boost-bus module at various Vbus.
Fig. 10. T¼25 C, DmboostS curves at various Vbus.
Fig. 8. T¼25 C,DmbuckS curves at various Vbus.
Fig. 11. S¼1000 W/m2, DmboostT curves at various Vbus.
S. Li et al. / Renewable Energy 74 (2015) 478e488
tops when Vbus is equal to 17.287 V which is the critical value of implementing the MPPT. Under these conditions which the MPP can be captured (such as Vbus17.287 V), the maximum value of Dmbuck is reached when S ¼ 638.25W/m2, which means the easiest appearance of “cut top” phenomenon here. Fig. 9 shows that the DmbuckT curves are eventually cut their tops with the increment of Vbus, which illustrates the MPPT control can not be implemented in these corresponding T range; these curves are just cut their tops when Vbus is equal to 17.13 V which is the critical value of implementing the MPPT. Therefore, to PV system with PV-buck-bus topology, the constraint condition shown in Table 1 is accurate at non-standard conditions. It can be seen from Fig. 10 that, to PV system with PV-boost-bus topology, the DmboostS curves are eventually cut their bottoms with the decrement of Vbus, which illustrates the MPPT control can not be implemented in these corresponding S range (such asS2½0; 249∪½1027; 1276:5 when Vbus¼18 V); these curves are just cut their bottoms when Vbus is equal to 19.15 V which is the critical value of implementing the MPPT. Under these conditions which the MPP can be captured (such as Vbus19.15 V), the minimum value of Dmboost is reached when S¼0 or 1276.5W/m2, which means the easiest appearance of “cut bottom” phenomenon here. Fig. 11 shows that theDmboostT curves are eventually cut their bottoms with the decrement of Vbus, which illustrates the MPPT control can not be implemented in these corresponding T range; these curves are just cut their tops when Vbus is equal to 19.2 V which is the critical value of implementing the MPPT. Therefore, to PV system with PV-boost-bus topology, the constraint condition shown in Table 1 is accurate at non-standard conditions. 4.2. Feasibility and availability experiments of proposed control strategy To test the feasibility and availability of the proposed MPPT control strategy, lots of experiments for PV system shown in Fig. 3 are conducted by MATLAB simulation. Where PV cell model whose parameters are the same as Section 3.1 is built by Simulink according to Eq. (1); the inductance (L) and capacitor (C) whose values are 1 mH and 1 mF, respectively, are the ideal components;
483
the internal and snubber resistance of switches (S1 and S2) are 1 mU and 100 kU, respectively; the internal resistance, snubber resistance and forward voltage of diodes (D1 and D2) are 1 mU, 0.5 kU and 0.8 V, respectively; the internal resistance of DC bus is 1 mU; the frequency of control signals (PWM1 and PWM2) is 20 kHz. The experimental results under various (S,T) and various Vbus conditions are shown in Table 2 and Table 3, respectively. Where C and Cc represent the calculated values according to Eq. (9) and Eq. (16), respectively; Dpwm1c and Dpwm1p represent the duty cycles of PWM1 while the proposed PV system is operating at its MPP through the proposed MPPT control strategy and P&O method, respectively; Dpwm2c and Dpwm2p represent the duty cycles of PWM2 at MPP corresponding to the proposed MPPT control strategy and P&O method, respectively; Pmax represents the maximum output power of PV cell; Pomax and Pomp represent the maximum output powers of proposed buck/boost converter with proposed MPPT control strategy and P&O method, respectively; Pbuck and Pboost represent the maximum output powers of PV systems with PV-buck-bus and PV-boost-bus topologies through using the P&O method, respectively; “/” in Tables 2 and 3 represents the failure of capturing the MPP. It can be seen from Table 2 that, on the one hand, the values of Pomax are approximately equal to those of Pomp under a given (S,T) conditions when Vbus keeps at 18 V, which illustrates the proposed MPPT strategy is controlling PV system to operate around its MPP. On the other hand, the errors between Dpwm1c and Dpwm1p or between Dpwm2c and Dpwm2p are small and have little influence on accuracy of Pomax. Meanwhile, Table 2 also shows that, because of the internal and snubber resistance of switches and diodes in Fig. 3, there are some errors between Pomax and Pbuck or Pboost, which are all less than 7 W. It is obvious that these errors owing to circuit component parameters can be ignored in verifying MPPT theoretical analysis. Therefore, a conclusion can be drawn that the MPP can be tracked well by proposed MPPT control strategy. That is to say, the proposed MPPT control strategy is feasible and available under various S,T and invariable Vbus conditions. It can be seen from Table 3 that, under various Vbus and standard S,T conditions, the errors between Pomax and corresponding Pomp are all less than 5 W, which illustrates that the values of Pomax are
Table 2 Experimental results under various (S,T) and Vbus ¼ 18 V conditions. (S,T)
C
Cc
Dpwm1c
Dpwm1p
Dpwm2c
Dpwm2p
Pmax(W)
Pomax(W)
Pomp(W)
Pbuck(W)
Pboost(W)
(500,0) (500,10) (800,10) (500,20) (800,20) (1000,20) (500,30) (800,30) (1000,30) (1200,30) (1000,40) (1200,40)
18.630 18.129 18.165 17.629 17.663 18.164 17.128 17.162 17.648 18.475 17.133 17.935
18.665 18.149 18.182 17.633 17.666 18.150 17.117 17.150 17.634 18.487 17.118 17.971
0.964 0.992 0.990 1 1 0.992 1 1 1 0.974 1 1
0.971 0.996 0.993 1 1 0.993 1 1 1 0.973 1 1
0 0 0 0.0203 0.0186 0 0.0490 0.0472 0.0204 0 0.0490 0.0016
0 0 0 0.024 0.0187 0 0.0498 0.0481 0.0250 0 0.054 0.0036
73.7 73.3 117.9 72.8 117.4 150.9 72.4 117.0 150.5 188.7 150.1 188.3
68.8 68.8 110.4 69.0 110.8 141.8 68.76 110.4 141.9 176.7 141.2 177.1
69.3 69.1 110.9 69.0 110.8 142.8 68.78 110.5 142.3 177.7 141.6 177.3
72.4 72.3 115.8 / / 148.4 / / / 184.7 / /
/ / / 69.3 111.4 / 69.2 111.2 143.4 / 142.8 179.4
Table 3 Experimental results under various Vbus and standard S,T conditions. Vbus(V)
C
Cc
Dpwm1c
Dpwm1p
Dpwm2c
Dpwm2p
Pmax(W)
Pomax(W)
Pomp(W)
Pbuck(W)
Pboost(W)
12 15 17 18 20 24
17.91 17.91 17.91 17.91 17.91 17.91
17.89 17.89 17.89 17.89 17.89 17.89
0.671 0.838 0.950 1 1 1
0.710 0.868 0.962 1 1 1
0 0 0 0.006 0.105 0.255
0 0 0 0.012 0.128 0.275
150.7 150.7 150.7 150.7 150.7 150.7
132.9 136.3 140.2 141.6 142.4 143.6
137.7 140.6 141.7 142.6 144.2 145.0
143.9 147.5 148.4 / / /
/ / / 143.5 144.4 145.2
484
S. Li et al. / Renewable Energy 74 (2015) 478e488
Table 4 Values of experimental parameters under standard conditions. Range of time (s)
From 0 to 0.1
From 0.1 to 0.25
From 0.25 to 0.5
Experiment Experiment Experiment Experiment
19 17.5 18.5 17
18.5 17 17 19
18.75 17.25 19 17.5
1 2 3 4
Vbus(V) Vbus(V) Vbus(V) Vbus(V)
approximately equal to those of Pomp. Meanwhile, the errors between Dpwm1c and Dpwm1p or between Dpwm2c and Dpwm2p are also small. According to these analysis, we know that PV system can operate around MPP through using proposed MPPT control strategy. Therefore, a conclusion can be drawn that the proposed MPPT control strategy is feasible and available under various Vbus and invariable S,T conditions. By the way, because the built PV system according to Fig. 3 is not ideal, there are some errors between Pmax and Pomax,Pomp,Pbuck,Pboost. Meanwhile, according to Table 3, these errors will become bigger with the decrement of Vbus. However, the verification of feasibility and availability of proposed MPPT strategy is not influenced by them. 4.3. MPPT performance analysis To analyze the MPPT performance of proposed control strategy, some experiments are also done by MATLAB. Here, the parameters of PV system are all same as Section 4.2. Meanwhile, in these experiments, PV system is assumed to operate under invariable S,T conditions, invariable S,Vbus conditions and invariable S,Vbus conditions, respectively. Here, to make a MPPT performance comparison between proposed MPPT strategy and conventional P&O method, their corresponding maximum powers Pomax and Pomp are shown together in all following figures. Note that Pomp shown in these figures only represent the steady-state values at MPP for P&O method. 4.3.1. Experiments under invariable S,T conditions When S and S are selected as 1000 W/m2 and 25 C0, respectively, four experiments are conducted. In these experiments, the changing values of Vbus and its corresponding ranges of time are shown in Table 4 and the MPPT performance is analyzed under Vbus>Cc, 0
Fig. 12. Output power curves under experiment 1 condition.
Fig. 13. Output power curves under experiment 2 condition.
the value of Cc is 17.89. Therefore, according to Table 4, experiment 1, experiment 2 and experiment 3 or 4 correspond respectively with Vbus>Cc, 0
4.3.2. Experiments under invariable T and Vbus conditions When the proposed PV system is operating under T ¼ 25 C and Vbus ¼ 18 V conditions, four experiments are still conducted. In these experiments, the changing ranges of S and corresponding Cc (represented byS(W/m2)/Cc) are shown in Table 5 and the MPPT performance is still analyzed under 0
Fig. 14. Output power curves under experiment 3 condition.
S. Li et al. / Renewable Energy 74 (2015) 478e488
Fig. 15. Output power curves under experiment 4 condition.
Fig. 16. Output power curves under experiment 1 condition.
0
Fig. 17. Output power curves under experiment 2 condition.
Table 5 Values of experimental parameters under T¼25 C and Vbus¼18 V conditions. Range of time (s) Experiment Experiment Experiment Experiment
1 2 3 4
S(W/m2)/Cc S(W/m2)/Cc S(W/m2)/Cc S(W/m2)/Cc
From 0 to 0.1
From 0.1 to 0.25
From 0.25 to 0.5
800/17.41 1200/18.74 800/17.41 1200/18.74
1000/17.89 1150/18.5 1200/18.74 800/17.41
900/17.6 1300/19.31 1000/17.89 1150/18.5
Fig. 18. Output power curves under experiment 3 condition.
485
486
S. Li et al. / Renewable Energy 74 (2015) 478e488
Fig. 19. Output power curves under experiment 4 condition.
Fig. 20. Output power curves under experiment 1 condition.
strategy can always control the proposed PV system to operate around its MPP regardless of irradiance, temperature and DC bus voltage. 4.4. Performance comparison The MPPT performance has been analyzed and compared in Section 4.3, however, the transient performance of P&O method is not considered. Here, an experiment is done to make the transient performance comparison between proposed MPPT strategy and conventional P&O method and its result can be shown in Fig. 24. Where the parameters of PV system are all same as Section 4.2 and S, T, Vbus and step-size increment of duty cycle D in P&O method are selected as 1000 W/m2, 25 C 17.5 V and 0.005, respectively. The settling time of the output power is about 22 ms when the proposed MPPT control strategy is used in PV system, just as the solid line has been showing in Fig. 24. By contrast, the settling time is about 215 ms when the conventional P&O method is used, just as the dotted line has been showing in Fig. 24. When the step-size increments of P&O method are various, some experiments are done to make a further comparison of the settling time. Experiments results show that, when the step-size increments of P&O method are selected 0.003, 0.006, 0.007, 0.008 and 0.01, the settling times are about 350 ms, 184 ms, 165 ms, 142 ms and 118 ms, respectively, and that, with regard to output power curve, the oscillation around MPP will become bigger with the increment of step size. Therefore, it is obvious that the proposed MPPT strategy has better transient-state performance than the conventional P&O method.
Fig. 21. Output power curves under experiment 2 condition.
5. Discussions Whether the MPP of PV system with DC bus can be captured or not is constrained by conditions shown in Table 1 when the output
Table 6 Values of experimental parameters under S¼1000 W/m2 and Vbus¼18 V conditions. Range of time (s) Experiment Experiment Experiment Experiment
1 2 3 4
T( C)/Cc T( C)/Cc T( C)/Cc T( C)/Cc
From 0 to 0.15
From 0.15 to 0.3
From 0.3 to 0.5
25/17.89 10/18.67 25/17.89 10/18.67
40/17.12 20/18.15 10/18.67 25/17.89
30/17.64 0/19.18 30/17.64 0/19.18
Fig. 22. Output power curves under experiment 3 condition.
S. Li et al. / Renewable Energy 74 (2015) 478e488
487
system can be proposed and designed as follows: Firstly, according to the paper [17], the ideal output power at MPP (represented by Pomax) can be calculated by the measured values of S and T. Secondly, in Fig. 3, Io must be sampled by MPPT controller, then the real-time output power (represented by Po) and difference (represented by Ep) between Pomax and steady-state value of Po can be calculated out. Lastly, a threshold value can be set and represented by ε. Meanwhile, in Fig. 4, a judgment must be added in flow chart. If Ep>ε, which means that PV system fails to operate around MPP, a reserve MPPT method such as P&O method will be switched and operated. 6. Conclusions
Fig. 23. Output power curves under experiment 4 condition.
In this paper, to different PV systems with DC bus, on the basis of finding out the constraint conditions of capturing their MPPs, a MPPT control strategy with variable weather parameters has been proposed. Meanwhile, to implement this MPPT method, a new buck/boost DC/DC converter has been proposed, which has avoided the high-cost and difficult-application problems of basic buck/ boost DC/DC converter. Finally, through lots of simulation experiments, the accuracy of these constraint conditions has been verified, the feasibility and availability of proposed MPPT control strategy have been tested, the MPPT performance has been analyzed and the output transient-state performance has been compared. Acknowledgment This work was supported by guidance project of Hubei Department of Education (No. B2014244 and B2013076). References
Fig. 24. Performance comparison between proposed strategy and P&O method.
currents of DC/DC converters are continuous. Therefore, in practical application, the inductor and capacitor selected as filter of DC/DC converter should be large enough to make the output current continuous. In Sections 4.2e4.4, there are some errors between Pomax and Pomp. However, in practical application, these small errors whose values are all less than 2 W can be ignored. If we need to make the MPPT control more accurate for considering the influence on change of circuit element parameters and inaccuracy measurement, the correction terms E1 and E2 can be added to Eq. (13) and Eq. (10), respectively. Where the average difference between Dpwm1p and Dpwm1c can be selected as E1 and the average difference between Dpwm2p and Dpwm2c can be selected asE2. In Tables 2 and 3, the errors between Pomax and Pbuck are always bigger than these between Pomax and Pboost, because, to the circuit shown in Fig. 3, the influence of the switch S2 and diode D2 at buck status is larger than that of S1 and D1 at boost status. It is obvious that the switch or diode with bigger snubber resistance and smaller internal resistance can be used to reduce these errors. In practical application, the parameter uncertainties of PV system maybe make MPPT control failed. To settle this issue, a reserve
[1] Sun Kai, Zhang Li, Xing Yan, Guerrero Josep M. A distributed control strategy based on DC bus signaling for modular photovoltaic generation systems with battery energy storage. IEEE Trans Power Electron 2011;26(10):3032e45. [2] Salas V, Barrado A. Review of the maximum power point tracking algorithms for stand-alone photovoltaic systems. Sol Energy Mater Sol Cells 2006;90(10): 1555e78. [3] Femia N, Petrone G, Spagnuolo G, Vitelli M. Optimization of perturb and observe maximum power point tracking method. IEEE Trans Power Electron 2005;20(4):963e73. [4] Abdelsalam Ahmed K, Massoud Ahmed M, Ahmed Shehab, Enjeti Prasad N. High-performance adaptive perturb and observe MPPT technique for photovoltaic-based microgrids. IEEE Trans Power Electron 2011;26(4): 1010e21. [5] Femia N, Petrone G, Spagnuolo G, Vitelli M. A technique for improving P&O MPPT performances of double stage grid-connected photovoltaic systems. IEEE Trans Indus Electron 2009;56(11):4473e82. [6] Zegaoui A, Aillerie M, Petit P, Sawicki JP, Jaafar A, Salame C, et al. Comparison of two common maximum power point trackers by simulating of PV generators. Energy Procedia 2011;6:678e87. [7] Liu F. A variable step size INC MPPT method for PV systems. IEEE Trans Indus Electron 2008;55(7):2622e8. [8] Ko Shih- Hung, Chao Ru-Min. Photovoltaic dynamic MPPT on a moving vehicle. Sol Energy 2012;86:1750e60. [9] Moradi Mohammad H, Reisi Ali Reza. A hybrid maximum power point tracking method for photovoltaic systems. Sol Energy 2011;85:2965e76. [10] Kakosimos Panagiotis E, Kladas Antonios G. Implementation of photovoltaic array MPPT through fixed step predictive control technique. Renew Energy 2011;36:2508e14. [11] Messai A, Mellit A, Guessoum A, Kalogirou SA. Maximum power point tracking using a GA optimized fuzzy logic controller and its FPGA implementation. Sol Energy 2011;85:265e77. [12] Larbes C, A€It Cheikh SM, Obeidi T, Zerguerras A. Genetic algorithms optimized fuzzy logic control for the maximum power point tracking in photovoltaic system. Renew Energy 2009;34:2093e100. [13] Gounden N Ammasai, Ann Peter Sabitha, Nallandula Himaja, Krithiga S. Fuzzy logic controller with MPPT using line-commutated inverter for three-phase grid-connected photovoltaic systems. Renew Energy 2005;30:909e15. [14] Patcharaprakiti Nopporn, Premrudeepreechacharn Suttichai, Sriuthaisiriwong Yosanai. Maximum power point tracking using adaptive
488
[15]
[16]
[17]
[18]
S. Li et al. / Renewable Energy 74 (2015) 478e488 fuzzy logic control for grid-connected photovoltaic system. Renew Energy 2009;34:1771e88. Lin Whei-Min, Hong Chih-Ming, Chen Chiung-Hsing. Neural-network-based MPPT control of a stand-alone hybrid power generation system. IEEE Trans Power Electron 2011;26(12):3571e81. Chiu Chian-Song, Ouyang Ya-Lun, Ku Chan-Yu. Terminal sliding mode control for maximum power point tracking of photovoltaic power generation systems. Sol Energy 2012;86:2986e95. Gao Xianwen, Li Shaowu, Gong Rongfen. Maximum power point tracking control strategies with variable weather parameters for photovoltaic generation systems. Sol Energy 2013;93:357e67. Enrique JM, Duran E, Sidrach-de-Cardona M, Andujar JM. Theoretical assessment of the maximum power point tracking efficiency of photovoltaic facilities with different converter topologies. Sol Energy 2007;81(8):31e8.
[19] Hussion KH, Zhao G. Maximum photovoltaic power tracking: an algorithm for rapidly changing atmospheric conditions. IEEE Proc 1995;142(1):59e64. [20] Mutoh N, Ohno M, Inoue T. A method for MPPT control while searching for parameters corresponding to weather conditions for PV generation systems. IEEE Trans Indus Electron 2006;53(4):1055e65. [21] Hua C, Lin J. An on-line MPPT algorithm for rapidly changing illuminations of solar arrays. Renew Energy 2003;28:1129e42. [22] Li Shaowu, Gao Xianwen, Wang Lina, Liu Sanjun. A novel maximum power point tracking control method with variable weather parameters for photovoltaic systems. Sol Energy 2013;97:529e36. [23] Moura Scott. A switched extremum seeking approach to maximum power point tracking in photovoltaic systems. Grid Integration Altern Energy Sources 2009.