energies Article
A Glowworm Swarm Optimization-Based Maximum Power Point Tracking for Photovoltaic/Thermal Systems under Non-Uniform Solar Irradiation and Temperature Distribution Yi Jin 1 , Wenhui Hou 1 , Guiqiang Li 2, * and Xiao Chen 3 1 2 3
*
Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, 96 Jinzhai Road, Hefei 230036, China;
[email protected] (Y.J.);
[email protected] (W.H.) Department of Thermal Science and Energy Engineering, University of Science and Technology of China, 96 Jinzhai Road, Hefei 230026, China State Key Laboratory of Fire Science, University of Science and Technology of China, 96 Jinzhai Road, Hefei 230026, China;
[email protected] Correspondence:
[email protected]; Tel./Fax: +86-551-6360-3512
Academic Editor: Tapas Mallick Received: 19 January 2017; Accepted: 11 April 2017; Published: 15 April 2017
Abstract: The output power of a photovoltaic (PV) system depends on the external solar irradiation and its own temperature. In order to obtain more power from the PV system, the maximum power point tracking (MPPT) is necessary. However, when the PV is partially shaded, there will be multiple peaks in the power-current (P-I) curve. The conventional MPPT methods may be invalid due to falling into the local peak. In addition, in a photovoltaic-thermal (PV/T) system, the non-uniform temperature distribution on PV will also occur, which complicates the situation. This paper presents a MPPT method with glowworm swarm optimization (GSO) for PV in a PV/T system under non-uniform solar irradiation and temperature distribution. In order to study the performance of the proposed method, the conventional methods including the perturbation and observe algorithm (P and O), and the fractional open-circuit voltage technique (FOCVT) are compared with it in this paper. Simulation results show that the proposed method can rapidly track the real maximum power point (MPP) under different conditions, such as the gradient temperature distribution, the fast variable solar irradiation and the variable partial shading. The outcome indicates the proposed method has obvious advantages, especially the performance being superior to the conventional methods under the partial shading condition. Keywords: maximum power point tracking (MPPT); glowworm swarm optimization (GSO); photovoltaic-thermal (PV/T); non-uniform solar irradiation; temperature distribution
1. Introduction With the sharp increasing global demand for energy, the shortage of the conventional fossil fuels and environmental pollution are becoming more and more serious. Thus, renewable energy resources are paid more and more attention from scholars due to their easy accessibility to humankind around the world. Renewable energy is meeting, at present, 13.5% of the global energy demand [1]. In recent years, there has been a rapid development in solar photovoltaic power generation systems due to various advantages of solar energy, including limitlessness, zero production of pollution, noiselessness, and good reliability. The output power of photovoltaic (PV) depends on the external environment and its own temperature. Thus, maximum power point tracking (MPPT) technology is necessary to control and keep the PV system working at the maximum power point (MPP) under any conditions. Energies 2017, 10, 541; doi:10.3390/en10040541
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Many MPPT techniques have been proposed. The most commonly used are the fractional open-circuit voltage technology (FOCVT) [2], perturbation and observation (P and O) [3–6], and incremental conductance (IncCond) [7–9]. The P and O method and IncCond method usually implement the perturbation on the control variable to search the MPP based on the feedback of the output power. The main advantages of these two methods are that they are compatible with any PV module, require no information about the PV module, and are easily implemented. However, the selection of the perturbation step size is difficult to meet the demand of efficiency and precision at the same time. Thus, the variable step-size P and O MPPT technique is proposed. The performance of different variable step-size P and O MPPT techniques is compared by Chen et al. [10]. In addition, there will be multiple peaks in the P-I characteristic curve under the partial shading condition in actual applications. These conventional methods reach the local MPP, but cannot analyze and compare all peaks to determine the true MPP [11]. Many advanced methods using artificial intelligence are presented, including artificial neural networks (ANN) [12,13] and fuzzy logic (FLC) [14–16]. Kofinas proposed an intelligent MPPT control scheme based on a direct neural control (DNC), which consists of a single adaptive neuron and a hybrid learning mechanism [17]. However, these methods usually need an enormous volume of data for training, professional experience, or a complex leaning process. Recently, bio-inspired algorithms have drawn considerable attention due to their excellent characteristics in dealing with the non-linear and stochastic optimization problems. Many algorithms, like genetic algorithms (GA) [18], particle swarm optimization (PSO) [19], and artificial bee colony (ABC) [20], have been utilized for MPPT application. Larbes et al. improved the performance of the FLC controller by using genetic algorithms (GA) for optimization [21]. Sundareswaran combined the PSO algorithm and the P and O algorithm for MPPT application of PV under the partial shading condition [22]. Glowworm swarm optimization (GSO) is a novel bionic algorithm for the optimization of multimodal functions. It is firstly proposed by Krishnanand and Ghose, who were inspired from the natural phenomenon that glowworms exchange information of searching for food with their peers in 2005 [23]. The GSO algorithm shows outstanding performance in finding the optimal solution for the multimodal functions but, at present, it is still rarely used in MPPT for PV. Considering the characteristic of multiple peaks in a P-I curve caused by the non-uniform solar irradiation conditions, GSO may be very suitable for MPPT. In addition, the photovoltaic-thermal energy (PV/T) system has the common phenomenon of the non-uniform temperature distribution on PV. Thus, the conditions are complex for PV/T under the non-uniform solar irradiation and temperature distribution. Currently, there are much fewer studies using GSO under these conditions. Therefore, in this paper, the novel GSO algorithm is presented to track the PV maximum power point for the PV/T application. In addition, in order to study the performance of the proposed method, the P and O method and FOCVT method are compared with it under four different complex conditions. The results indicate that the novel algorithm GSO is suitable for PV/T MPPT applications under non-uniform solar irradiation and temperature distribution. 2. Characteristics of Solar Modules 2.1. PV Cell The characteristic curve (the voltage-current curve and the power-current curve) of the solar cell is nonlinear. From the equivalent circuit in Figure 1 [24], the output characteristic of the PV cell is given by Equations (1)–(9): (1) I ph − Id − Ish − I = 0 where Ish is the current of the parallel resistance and I ph is the light-generated current, which is proportional to the given solar irradiation. It can be calculated by:
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I ph [I sc (Tc Tr )] S / 1000
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where I sc is the short-circuit current at standard test condition (STC) ( T 25 °C, S 1000 W/m2 ) I = [ Isc + α · ( Tc − Tr )] · S/1000 (2) and is the current temperaturephcoefficient of the cell. Tc and Tr are the operating temperature 2 I d represents and theIscreference temperature of the cell, respectively. which is where is the short-circuit current at standard test condition (STC) (T = the 25 ◦diode C, S =current, 1000 W/m ) and α is the current temperature coefficient of the cell. Tc and Tr are the operating temperature and the given according to the Shockley equation: reference temperature of the cell, respectively. Id represents the diode current, which is given according Id IO [exp(qUd / AkTc ) 1] (3) to the Shockley equation: I = I [exp(qU /AkTc ) − 1] (3) where q is the electronic charge ( q d 1.6 O1019 ), kd is Boltzmann’s constant ( k 1.38 1023 ), A is 19 ), k is Boltzmann’s constant (k = 1.38 × 10−23 ), A is where q isfactor the electronic charge × 10−saturation I O (q the ideal of the diode, is = the1.6 reverse current of the diode, where I o varies with the ideal factor of the diode, I is the reverse saturation current of the diode, where Io varies with the O is given by: the change in temperature and change in temperature and is given by: I o Iro (Tc / Tr )3 exp[qEg (1 / Tc 1 / Tr ) / Ak] (4) Io = Iro ( Tc /Tr )3 exp[qEg (1/Tc − 1/Tr )/Ak] (4) where Eg is the band gap energy of the semiconductor and I ro is the saturation current of the diode where Egwhich is the band gap energy at 25 °C, is calculated by: of the semiconductor and Iro is the saturation current of the diode at ◦ 25 C, which is calculated by: qVococ /AkT / AkTr )) (5) IroIro=IIscsc//[[exp( exp(qV −1]1] (5) 2 2 where VVococisisthe open-circuit voltage of of thethe PVPV module at STC (T = C,°C, S =S1000 W/m ). U isdthe ◦25 the open-circuit voltage module at STC ( T25 ).d U is 1000 W/m voltage of the equivalent diode which is given by: the voltage of the equivalent diode which is given by:
U+ IR UU IRs s d d=U
(6) (6)
where RRs sisisthe theseries seriesresistance. resistance.
Figure cell. Figure 1. 1. Equivalent Equivalent circuit circuit of of the the solar solar cell.
I sh is the current of the parallel resistance, which is given by: Ish is the current of the parallel resistance, which is given by: I (U I R ) / R Ish sh= (U + I · Rs s )/Rshsh
(7) (7)
where Rsh is the parallel resistance. where Rsh is the parallel resistance. From the former analysis, the input-output characteristic of the PV cell is: From the former analysis, the input-output characteristic of the PV cell is: q(U I Rs ) (U I Rs ) S [ I sc (Tc Tr )]S I o [exp( (8) q(U + I · Rs )) 1] (U + I · RIs ) 0 1000 AkTc [ Isc + α · ( Tc − Tr )] · − Io [exp( ) − 1] − Rsh −I=0 (8) 1000 AkTc Rsh The output power of the PV cell is given by: The output power of the PV cell is given by: P UI (9) P=U·I (9) The parameters values of the silicon solar cell used in simulation are illustrated in Table 1.
The parameters values of the silicon solar cell used in simulation are illustrated in Table 1.
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Table 1. Parameters of the silicon solar cell. Table 1. Parameters of the silicon solar cell. Table 1. Parameters of the silicon solar cell. Parameters Value Unit Parameters Value Unit Parameters Value Unit ◦ Current temp.temp. coefficient Current coefficient 0.002086 0.002086 A/ A/°C C Current temp.Voltage coefficient Open-circuit Voltage 0.53 VA/°C Open-circuit (Voc) (Voc ) 0.002086 0.53 V Open-circuit Voltage (V 0.53 Short-circuit Current 2.926 AV Short-circuit Current (Iocsc)) (Isc ) 2.926 A Short-circuit Current sc) 2.926 Factor - AIdealIdeal Factor (A) (I(A) 1.31.3 Electrical resistance 0.0277 Ω Ideal Factor (A) 1.3 Electrical resistance 0.0277 Ω Electrical resistance 0.0277 Ω
2.2. PV Module 2.2. PV Module The output power of one PV cell is limit, as shown in Figure 2. So in order to acquire the desired The output power ofusually one PV cell is limit, as shown ininFigure 2. Soparallel. in order tothis acquire desired power, PV are usually connected with each other series and In the series power,the the PVcells cells are connected with each other in series and parallel. Inpaper, thisthe paper, the power, the PV cells are usually connected with each other in series and parallel. In this paper, mode adopted. In PV/T there isthere the similar gradient temperature distribution on thethe PV series is mode is adopted. In application, PV/T application, is the similar gradient temperature distribution on series In PV/Texchange application, theretemperatures isThe the temperatures similarof gradient temperature distribution on module dueistoadopted. the exchange structure. The the water inlet the water the PVmode module dueheat to the heat structure. of the waterand inlet and the outlet water the PV module due to heat exchange structure. temperatures of that the water inlet the water are different in photovoltaic-thermal (PV/T) systems. Thus, we assume the temperature gradient outlet are different in the photovoltaic-thermal (PV/T)The systems. Thus, we assume that theand temperature ◦ ◦ outlet are different in photovoltaic-thermal (PV/T) systems. Thus, we assume that the temperature scope is 0.2 C. In the °C. simulation, the temperature of the first cell is set to cell 20 is C, set andtothe gradient scope is 0.2 In the simulation, the temperature of the first 20temperature °C, and the gradient scope is 0.2 0.2 ◦°C. Inshown the simulation, the temperature gradient scope is C, as in Figure 3. in temperature gradient scope is 0.2 °C, as shown Figure 3. of the first cell is set to 20 °C, and the temperature gradient scope is 0.2 °C, as shown in Figure 3. Output power of PV cell 1
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Figure 2. 2. Output Output power power of of the the photovoltaic photovoltaic (PV) (PV) cell. cell. Figure Figure 2. Output power of the photovoltaic (PV) cell.
Figure 3. The ideal temperature distribution on PV for a photovoltaic-thermal (PV/T) system. Figure 3. The ideal temperature distribution on PV for a photovoltaic-thermal (PV/T) system. Figure 3. The ideal temperature distribution on PV for a photovoltaic-thermal (PV/T) system.
The P-I curves of the PV module under different solar irradiation is shown in Figure 4. This Thethat P-I the curves of the PV module under different solar is by shown in Figure 4. This shows output is a under nonlinear function andirradiation is affected solar The P-I curves of the power PV module different solar irradiation is shown inthe Figure 4. irradiation. This shows shows that the output power is a nonlinear function and is affected by the solar irradiation. Additionally, electrical current corresponding toaffected maximum power ( Iirradiation. the solar that the outputthe power is a nonlinear function and is by the solar Additionally, mp ) varies with Additionally, the electrical current corresponding to maximum power ( I mp ) varies with the solar the electricalThus, current to maximum (Imp ) varies with the solarthe irradiation. Thus, irradiation. in corresponding order to find the real I mp aspower the reference operating point, application of irradiation. Thus, order the real Ioperating as the reference operating point, the application of in order to find theinreal Imptoasfind the reference point, the application of MPPT technology is mp MPPT technology is necessary. The P-I curves of the PV module under different partial shading necessary. The P-I is curves of the PV module under different partial shading conditions is shown in MPPT technology necessary. curves of the PV different partial shading conditions is shown in Figure 5.The TheP-I shading situation is module shown inunder Figure 6. In this situation, the Figure 5. The shading situation is shown in Figure 6. In this situation, the temperature distribution is conditions is distribution shown in Figure 5. The to shading situation is shown Figure In this situation, the temperature is assumed be unaltered with Figure 3insince the6.shading area is small. assumed to be unaltered with Figure 3 since the shading area is small. The curves are characterized by temperature distribution is assumed to be unaltered withcondition. Figure 3 since area is small. The curves are characterized by multiple peaks in this Mostthe of shading the traditional MPPT multiple peaks in this condition. Most of the traditional MPPT methods usually may converge into The curves are characterized by multiple peaks in this condition. Most of the traditional methods usually may converge into the LMPP (local maximum power point) instead of the MPPT global methods usually may converge the Thus, LMPPthis (local maximum point) instead the global GMPP (global maximum powerinto point). paper applies power the GSO algorithm to of complete the GMPP (global maximum power point). Thus, this paper applies the GSO algorithm to complete the MPPT. MPPT.
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the LMPP (local maximum power point) instead of the global GMPP (global maximum power point). Thus, Energiesthis 2017,paper 10, 541 applies the GSO algorithm to complete the MPPT. 5 of 13 Output power of PV module 40
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Current(A) Figure 4. under Figure 4. Output Output power power of of the the PV PV module module under different different levels levels of of solar solar irradiation. irradiation. Figure 4. Output power of the PV module under different levels of solar irradiation.
power of PV Module Figure 4. Output power of the Output PV module under Output power of PVdifferent Module levels of solar irradiation. 40 40
35 40 35
35 30 30
2 of PV Module Output power
Partial shading S=600W/m 2 Partial shading S=600W/m
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Figure 5. Output power of the PV module under partial shading. Figure 5. Output Output power of of the PV PV module under under partial partial shading. shading. Figure 5. Figure 5. Outputpower power ofthe the PV module module under partial shading.
Figure 6. The partial shading condition of PV for a PV/T system. Figure 6. The partial shading condition of PV for a PV/T system.
Figure 6. The partial shading condition of PV for a PV/T system. 3. MPPT Algorithm Figure 6. The partial shading condition of PV for a PV/T system. 3. MPPT Algorithm algorithm is used for finding the current, the voltage, or the duty cycle corresponding to 3. MPPTMPPT Algorithm 3. MPPTMPPT Algorithm algorithm is used for theon current, theThis voltage, orapplies the duty to the maximum power, keeping thefinding PV work the MPP. paper thecycle GSOcorresponding algorithm to the MPPT algorithm is used for finding the current, the voltage, or the duty cycle corresponding to the maximum power, keeping the PV work on the MPP. This paper applies the GSO algorithm to the PV for the PV/T application. In finding order tothe evaluate the the performance of the this duty method, thecorresponding P and O and to MPPT algorithm is used for current, voltage, or cycle the maximum power, keeping the PV work on the MPP. This paper applies the GSO algorithm to the PV for the PV/T application. In order to evaluate the performance of this method, the P and O and FOCVT methods are appliedthe for PV comparison. the maximum power, keeping work on the MPP. This paper applies the GSO algorithm to the FOCVT methods are appliedInfor comparison. PV for the PV/T application. order to evaluate the performance of this method, the P and O and
PV for the PV/T application. In order to evaluate the performance of this method, the P and O and 3.1. The Proposed MPPT FOCVT methods areGSO-Based applied for comparison. FOCVT methods areGSO-Based applied for comparison. 3.1. The Proposed MPPT This algorithm uses glowworms with a luminescent quantity, called luciferin, as their agents. In This algorithm uses glowworms with a luminescent quantity, called luciferin, as their agents. In the beginning, glowworms, as initial solutions, are randomly distributed in the problem space, then 3.1. The Proposed GSO-Based MPPT the beginning, glowworms, as initial solutions, are randomly distributed in the problem space, then
This algorithm uses glowworms with a luminescent quantity, called luciferin, as their agents. In the beginning, glowworms, as initial solutions, are randomly distributed in the problem space, then
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3.1. The Proposed GSO-Based MPPT This algorithm uses glowworms with a luminescent quantity, called luciferin, as their agents. In the beginning, glowworms, as initial solutions, are randomly distributed in the problem space, then they move to a brighter state in their own sensor range. Finally, they gather around the brightest ones, which correspond to the optimized solution of the problem. There are three phases in this process: luciferin update phase, movement phase, and the local-decision range update phase [23]. 3.1.1. Luciferin Update Phase The value of luciferin glowworms carry mainly depends on the objective function value of the current position. The formula for updating luciferin is given by: Ii (t + 1) = (1 − ρ) ∗ Ii (t) + γ ∗ F ( xi (t + 1))
(10)
where ρ is the luciferin decay constant (0 < ρ < 1) set as 0.4, (1 − ρ) ∗ Ii (t) to simulate the decay of the luciferin with time. γ is the luciferin enhancement constant set as 0.6, Ii (t) and Ii (t + 1) are the luciferins at iterations t and t + 1, respectively, and F ( xi (t + 1)) represents the objective function which is the output power of the PV module in this paper, given by: F = Ppv = VPV ∗ I
(11)
where VPV is the total voltage of the PV cells in series. The voltage of each PV cell can be expressed as a function of the current I by deriving from Equations (1) to (8) in Section 2. Thus, F is the function of solar irradiation S, the current I, and the temperature T. In this study, the temperature distribution is set as shown in Figure 3, I is the parameter to be optimized through this algorithm, which is regarded as the location of the glowworm, and S is the input variable. 3.1.2. Movement Phase Each agent decided to move to a superior individual according to a probability mechanism. The probability of the agent i moving to the agent j is calculated by: pij =
Ij (t) − Ii (t) Im (t) − Ii (t)
(12)
∑
m∈ Ni (t)
where Ni (t) is the neighborhood group of the agent i: Ni (t) =
n
j : di,j (t) < rdi , Ii (t) < Ij (t)
o
(13)
di,j (t) = k xi − x j k is the Euclidean distance between glowworms i and j at iteration t. rdi represents the variable neighborhood range associated with glowworm i at time t. Glowworms are attracted by neighbors that glow brighter; that is, glowworms will move to the neighbors that have larger luciferin values than the other neighbors. The movement is decided by the probability given by Equation (12). If pij0 (t) = max( pij (t)), set the position of glowworm i equal to j
the position of glowworm j. Then glowworms update their position. The movement update rule can be stated as follows: x i ( t + 1) = x i ( t ) + s ∗ (
x j ( t ) − xi ( t ) ) k x j (t) − xi (t)k
(14)
where s is the step size and xi (t) and xi (t + 1) are the locations of agent i at iteration t and t + 1, respectively.
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The decision radius should be updated according to the number of individuals in the current range: n n oo i i min{ ,max{0, β*∗((nnt t−N| N (t) )}} (15) rdi (t +rd1(t) =1)min rs ,rmax 0, rdri d((tt)) + (15) s i i ( t )|)
whereβis the is the variation coefficient of the decision radius isnumber the number of individuals with where variation coefficient of the decision radius andand nt isnthe of individuals with high t luciferin valuesvalues in thein local-decision range.range. high luciferin the local-decision The flowchart of this algorithm The flowchart of this algorithmisisshown shownin inFigure Figure7.7.
Figure 7. 7. The The flowchart flowchart of of the the glowworm glowworm swarm swarm optimization optimization (GSO) (GSO)algorithm. algorithm. Figure
The algorithm parameters work well for a wide range of simulation scenarios and that only n The algorithm parameters work well for a wide range of simulation scenarios and that only n and and rs are parameters that influence the algorithm’s behavior [23]. Therefore, if the setting rs are parameters that influence the algorithm’s behavior [23]. Therefore, if the setting conditions are conditions are algorithm changed, these algorithm will remain and not needtuned to be changed, these parameters will parameters remain the same and do the not same need to be do specifically rs reduce specifically tuned for every problem. need tothe becomputing selected totime reduce computing n and to for every problem. Only n and rs need Only to be selected andthe obtain higher peak-capture levels. Thepeak-capture values of maximum iteration and glowworm number in the time and obtain higher levels. The valuesnumber of maximum iteration number andused glowworm simulation of the GSO algorithm are set as 20 and 50 respectively. number used in the simulation of the GSO algorithm are set as 20 and 50 respectively.
3.2. 3.2. Perturbation Perturbation and and Observe Observe Algorithm Algorithm The The traditional traditional perturb perturb and and observe observe algorithm algorithm imposed imposed aa fixed-size fixed-size disturbance disturbance on on the the control control variables variables (voltage), (voltage), and and judged judged the the next next direction direction of of the the disturbance disturbance by by observing observing the the change change of of the the power. In this method, the operating voltage is perturbed in a given direction; if the power increased power. In this method, the operating voltage is perturbed in a given direction; if the power increased (the toto thethe MPP), thethe direction would be maintained, otherwise the (theoperating operatingpoint pointisismoving movingtowards towards MPP), direction would be maintained, otherwise direction would be thebe opposite. This method is impossible to considerate of the tracking the direction would the opposite. This method is impossible to considerate of theefficiency tracking and the steady state accuracy at the same time. In this paper, the step-size is set 0.5 V. The flow of efficiency and the steady state accuracy at the same time. In this paper, the step-size is set 0.5chart V. The the P and O algorithm is shown in Figure 8. If P > P , it means that the operating point is moving old8. If P P , it means that the operating point flow chart of the P and O algorithm is shown in Figure old towards the MPP. Further voltage perturbations will be provided in the same direction as earlier in is moving towards the MPP. Further voltage perturbations will be provided in the same direction as order to move operating point much closer to the MPP. If P < Pold , it means that the operating point is earlier in order to move operating point much closer to the MPP. If P Pold , it means that the moving away from the MPP. Further voltage perturbations will be provided in the reverse direction in operating point is moving away fromcloser the MPP. Further order to move operating point much to the MPP. voltage perturbations will be provided in the reverse direction in order to move operating point much closer to the MPP.
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Figure Theflowchart flowchartof ofthe theperturbation perturbation and observe Figure 8.8.The observe(P (Pand andO) O)algorithm. algorithm.
Fractional Open-CircuitVoltage VoltageTechnique Technique 3.3.3.3. Fractional Open-Circuit this method, thevoltage voltageatatthe theMPP MPPis is considered considered proportional voltage of of In In this method, the proportionaltotothe theopen-circuit open-circuit voltage the PV. The relation is given by: the PV. The relation is given by:
Vmp = Kv · Vococ Vmp mp Kvv Voc
(16)(16)
where VmpVis the voltage corresponding to MPP, Kv is Kthe coefficient of proportionality, usually ranging where mp is the voltage corresponding to MPP, mp vv is the coefficient of proportionality, usually from 0.65 tofrom 0.8. 0.65 Voc is voltage which can be calculated by analyzing the PV the system. ranging to the 0.8. open-circuit Vococ is the open-circuit voltage which can be calculated by analyzing PV system.
4. Simulation Results 4. In Simulation order to Results compare the tracking performance of different methods mentioned above, the PV
system In is order simulated in MATLAB/Simulink (R2015b, Natick, MA, USA). Thethesystem to compare the tracking performance of MathWorks, different methods mentioned above, PV consist of a PV module, a DC-DC boost converter, a battery, the MPPT algorithm, and the pulse width system is simulated in MATLAB/Simulink (R2015b, MathWorks, Natick, MA, USA). The system modulation module. The boost used forthe MPPT toalgorithm, adjust theand operating voltage consist of a(PWM) PV module, a DC-DC boostconverter converter,is a battery, MPPT the pulse widthby using PWM technique to control the opening and closing metal-oxide field-effect modulation (PWM) module. The boost converter is used of forthe MPPT to adjust semiconductor the operating voltage by transistor (MOSFET) switch at 10 kHZ. The inductor is set of to the 10 mH. The PWM technique uses using PWM technique to control the opening and closing metal-oxide semiconductor field-the effect transistor switch at 10 kHZ. The inductor is setThe to 10structure mH. Thediagram PWM technique deviation of the V(MOSFET) to form the closed-loop control. with theuses GSO mp and VPV mp and 9. PV the deviation of the mp VPV form to thethe closed-loop The structure the GSO algorithm is shown inVFigure Intoorder study thecontrol. performance and thediagram suitablewith occasion of the algorithm is shown Figure 9. is In implemented order to the study performance proposed method, the in simulation in thethe following cases:and the suitable occasion of the proposed method, the simulation is implemented in the following cases:
Case 1: Gradient temperature distribution condition Case Gradient temperature distribution condition Case 2: 1: Fast variation in solar irradiation Case 2: Fast variation in solar irradiation Case 3: Partial shading condition Case 3: Partial shading condition Case 4: Variation in the degree of shading. Case 4:
Variation in the degree of shading.
Figure The structurediagram diagramofofthe thesystem. system. PWM: pulse maximum Figure 9. 9. The structure pulse width widthmodulation; modulation;and andMPPT: MPPT: maximum power point tracking. power point tracking.
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Power(W) Power(W)
4.1. Gradient Temperature Temperature Distribution Distribution Condition Condition 4.1. 4.1. Gradient Temperature Distribution Condition In In this this condition, condition, the the solar solar irradiance irradiance isissupposed supposedtotobe beconstant constant(S( S=1000 the 1000 W/m W/m22 ), while the In this condition, the solar irradiance is supposed to be constant ( S 1000 W/m2 ), while the temperature distribution of the PV module for PV/T system is shown in Figure 3. The simulation temperature distribution of the PV module for PV/T system is shown in Figure 3. The simulation temperature distribution of the PVand moduleFOCVT for PV/T system is rapidly shown track in Figure 3. Thecomparison simulation results thethe proposed GSO methods can the MPP results show showthat that proposed GSO the and the FOCVT methods can rapidly trackinthe MPP in results show that the proposed GSO and 10. theThe FOCVT methods can rapidly track the aMPP in with the P and O algorithm shown in Figure output power of PV module can reach steady comparison with the P and O algorithm shown in Figure 10. The output power of PV module can comparison with the P and O algorithm shown in Figure 10. The output power of PV module can state by using the GSO and FOCVT methods in lessmethods than halfinof thethan settling using reachina 0.0018 steady sstate in 0.0018 s by using the GSO and FOCVT less half time of thebysettling reach a steady state in 0.0018 s by using the GSO and FOCVT methods in less than half of the settling the andusing O algorithm. timeP by the P and O algorithm. time by using the P and O algorithm. 50 50 45 45 40 40 35 35 30 30 25 25 20 20 15 15 10 10 5 5 0 00 0
Output power of PV module Output power of PV module
P&O P&O GSO GSO FOCVT FOCVT
0.002 0.002
0.004 0.004
0.006
Time(s)0.006 Time(s)
0.008 0.008
0.01 0.01
Figure 10. Output Output power power under under a gradient temperature temperature distribution. Figure Figure 10. 10. Output power under aa gradient gradient temperature distribution. distribution.
Irradiance (W/m Irradiance (W/m 2 ) 2 )
4.2. Fast Fast Variation Variation in in Solar Solar Irradiation Irradiation 4.2. The temperature is assumed to be constant ( T 25 ◦°C), while there is a fast variation in the solar The temperature 25 °C), C), while 25 temperature is is assumed assumed to be constant (T (T= while there there is is aa fast variation in the solar irradiation, as shown in Figure 11. irradiation, as shown in Figure 11. Figure 11. 1100 1100 1000 1000 900 900 800 800 700 700 600 600 500 500 400 400 300 300 200 200 100 100 0 00 0
0.005 0.005
0.01 0.01
0.015 0.015
0.02 0.02 Time(s) Time(s)
0.025 0.025
0.03 0.03
0.035 0.035
0.04 0.04
Figure 11. Variation of the solar irradiation. Figure 11. Variation of the the solar solar irradiation. irradiation. Figure 11. Variation of
This shows that the GSO algorithm and the FOCVT method can rapidly and correctly track the This shows that the GSO algorithm and the FOCVT method can rapidly and correctly track the MPPThis under the that condition of fast variation solar irradiation in can comparison withcorrectly the P and O shows the GSO algorithm andinthe FOCVT method rapidly and track MPP under the condition of fast variation in solar irradiation in comparison with the P and O algorithm, as shown in Figure 12. As Figure 12 shows, it is obvious that the GSO algorithm can the MPP under the condition of fast variation in solar irradiation in comparison with the P and O algorithm, as shown in Figure 12. As Figure 12 shows, it is obvious that the GSO algorithm can improve the maximum tracking power by128% and it 13.3% compared to GSO the conventional and Oalgorithm, as shown in Figure 12. As Figure shows, is obvious that the algorithm canPimprove improve the maximum tracking power by 8% and 13.3% compared to the conventional P and O2 to 800 W/m2 based MPPT controller, respectively, when the solar irradiation from 600 W/m the maximum tracking power by 8% and 13.3% compared to thechanges conventional P and O-based MPPT based MPPT controller, respectively, when the solar irradiation changes from 600 W/m22 to 800 W/m2 2 to 1000 W/m2 at 0.03 s, respectively. It can be seen 2 at 0.02s and from 800 W/m that the GSO algorithm controller, respectively, when the solar irradiation changes from 600 W/m to 800 W/m at 0.02 s and at 0.02s and from 800 W/m2 to 1000 W/m2 at 0.03 s, respectively. It can be seen that the GSO algorithm 2 to 1000 W/m 2 at 0.03 s,than has the performance the FOCVT method. The steady statealgorithm errors of using P from 800better W/msteady-state respectively. It can be seen that the GSO has the has the better steady-state performance than the FOCVT method. The steady state errors of using P and Osteady-state will increaseperformance obviously with irradiation When theerrors solar of irradiation is 600 better thanthe thesolar FOCVT method.increase. The steady state using P and O and O will increase obviously with the solar irradiation increase. When the solar irradiation is 600 2, the RMSE of the output power by using P and O, GSO, and FOCVT are 0.9623, 0.4528, and W/mincrease will obviously with the solar irradiation increase. When the solar irradiation is 600 W/m2 , W/m2, the RMSE of the output power by using P and O, GSO, and FOCVT are 0.9623, 0.4528, and 0.5701, respectively. It can be seen that the GSO algorithm has the better steady-state performance 0.5701, respectively. It can be seen that the GSO algorithm has the better steady-state performance than the FOCVT and P and O methods. than the FOCVT and P and O methods.
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the RMSE of the output power by using P and O, GSO, and FOCVT are 0.9623, 0.4528, and 0.5701, respectively. It can be seen that the GSO algorithm has the better steady-state performance than the FOCVT and10, P 541 and O methods. Energies 2017, 2017, 10, 541 10 of of 13 13 Energies 10
Figure 12. 12. Output Output power power under under variable variable solar solar irradiation. irradiation. Figure Figure 12. Output power under variable solar irradiation.
4.3. Partial Partial Shading Shading Condition Condition 4.3. 4.3. Partial Shading Condition Under this this condition, condition, the the temperature temperature distribution distribution and and the the shaded shaded condition condition are are shown shown in in Under Under this condition, the temperature distribution and the shaded condition are shown in 22 Figures 3 and 6, respectively. The solar irradiance of the shaded part is and that of the Figures 3 and 6, respectively. The solar irradiance of the shaded part is and that of the 600 W/m 600 W/m 2 Figures 3 and 6, respectively. The solar irradiance of the shaded part is 600 W/m and that of the other 22 otherispart part is normal normal It is is obvious obvious that thealgorithm GSO algorithm algorithm can determine determine the GMPP GMPP other is ((SS W/m It that the GSO can the 10002W/m W/m 1000 part normal (S = 1000 ). It is).).obvious that the GSO can determine the GMPP in this condition, whereas the P and algorithms convergeconverge to the LMPP from Figure 13.Figure The GSO in this this condition, condition, whereas theOPPand andFOCVT O and and FOCVT FOCVT algorithms algorithms converge to the the LMPP from Figure 13. in whereas the and O to LMPP from 13. algorithm can improve the output byvalue 12.5% to P and andOFOCVT-based The GSO GSO algorithm algorithm can improve improve thepower outputvalue power value bycompared 12.5% compared compared toOand Oand FOCVTFOCVTThe can the output power by 12.5% to PP and and MPPT controllers under under partialpartial shading conditions. In addition, the P the and algorithm has a has slow based MPPT MPPT controllers under partial shading conditions. In addition, addition, the PPOand and O algorithm algorithm has based controllers shading conditions. In O aa speed and greater fluctuation in the steady state. slow speed speed and and greater greater fluctuation fluctuation in in the the steady steady state. state. slow Output power power of of PV PV module module Output 40 40 P&O P&O 35 35
GSO GSO FOCVT FOCVT
30 30
Power(W)
25 25 20 20 15 15 10 10 55 00 00
0.002 0.002
0.004 0.004
0.006 0.006
0.008 0.008
0.01 0.01
Time(s) Time(s)
Figure 13. 13. Output Output power power under under partial partial shading. shading. Figure Figure 13. Output power under partial shading.
4.4. Variation Variation in in the the Degree Degree of of Shading Shading 4.4. 4.4. Variation in the Degree of Shading Under this this condition, condition, the the situation situation of of the the temperature temperature distribution distribution and and shading shading are are the the same same Under Under this condition, the situation of the temperature distribution and shading are the same with with case case 3, 3, however however the the solar solar irradiance irradiance of of the the shaded shaded part part changes, changes, as as shown shown in in Figure Figure 14. 14. The The solar solar with case 3, however the solar irradiance of the shaded part changes, as shown in Figure 14. The solar 22 irradiance of of the the other other part part is isnormal normal(S It is can be seen that the the GSO GSO algorithm algorithm can can 1000 W/m W/m 2).).). It irradiance of the other part is normal ((SS= can 1000 irradiance 1000 W/m It is is can can be be seen seen that that the GSO algorithm rapidly track track the the GMPP GMPP even even when when the the shading shading degree degree varies, varies, whereas whereas the the FOCVT FOCVT method method converge converge rapidly track rapidly the GMPP even when the shading degree varies, whereas the FOCVT method converge to the LMPP, the P and O algorithm diverged from the MPP in the limited time, as shown in Figure Figure to the LMPP, the P and O algorithm diverged from the MPP in the limited time, as shown in to the LMPP, the P and O algorithm diverged from the MPP in the limited time, as shown in Figure 15. 15. 15.
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Irradiance (W/m2 ) 2 ) Irradiance (W/m
800 700 700 600 600 500 500 400 400 300 300 200 200 100 100 0 0 0 0
1
2
3
4
5
6
1
2
3 Time(s) Time(s)
4
5
-3 x 10 6
x 10
-3
Figure 14. The solar irradiation of the shading part. Figure Figure 14. 14. The The solar solar irradiation irradiation of of the the shading shading part. part. Output power of PV module Output power of PV module
40 40
P&O
35 35
GSO P&O FOCVT GSO
30
FOCVT
30
Power(W) Power(W)
25 25 20 20 15 15 10 10 5 5 0
0 0 0
1
2
3
4
5
6
1
2
3 Time(s) Time(s)
4
5
-3 x 10 6
x 10
-3
Figure 15. Output power under the variable degree of shading. Figure 15. Output power under the variable degree of shading. Figure 15. Output power under the variable degree of shading.
5. Conclusions 5. Conclusions 5. Conclusions In this paper, a novel MPPT method based on the GSO algorithm is proposed and its In this paper, a novel MPPT method based on the GSO algorithm is proposed and its performance is compared with Pmethod and O based and FOCVT methods. The simulations three different In this paper, a novel MPPT on the GSO algorithm is proposed used and its performance performance is compared with P and O and FOCVT methods. The simulations used three different methods and are implemented through MATLAB/Simulink under four conditions (gradient is compared with P and O and FOCVT methods. The simulations used three different methods and are methods and are implemented through MATLAB/Simulink under four conditions (gradient temperature condition, fast variation in solar irradiation, partialtemperature shading condition, and implementeddistribution through MATLAB/Simulink under four conditions (gradient distribution temperature distribution condition, fast variation in solar irradiation, partial shading condition, and variation thevariation degree ofinshading). The output power of thecondition, photovoltaic system affected condition,infast solar irradiation, partial shading and(PV) variation in is the degreeby of variation in the degree of shading). The output power of the photovoltaic (PV) system is affected by the external solar irradiation and its own temperature. Additionally, there will be multiple peaks in shading). The output power of the photovoltaic (PV) system is affected by the external solar irradiation the external solar irradiation and its own temperature. Additionally, there will be multiple peaks in the curves under theAdditionally, partial shading In addition, non-uniform temperature and P-I its own temperature. there condition. will be multiple peaks in the the P-I curves under the partial the P-I curves under the partial shading condition. In addition, the non-uniform temperature distribution appears on PV for PV/T applications. Taking into account the superiority in multi-peak shading condition. In addition, the non-uniform temperature distribution appears on PV for PV/T distribution appears on PV for PV/T applications. Taking into account the superiority in multi-peak function optimization, theaccount GSO isthe applied to theinMPPT controlfunction algorithm. It is confirmed by is a applications. Taking into superiority multi-peak optimization, the GSO function optimization, the GSO is applied to the MPPT control algorithm. It is confirmed by a simulation study thatcontrol the GSO algorithm better P and Ostudy and FOCVT. It canalgorithm track the applied to the MPPT algorithm. It performs is confirmed by athan simulation that the GSO simulation study that the GSO algorithm performs better than P and O and FOCVT. It can track the real MPP under different solar irradiation and temperature distributions with high accuracy, as well performs better than P and O and FOCVT. It can track the real MPP under different solar irradiation real MPP under different solar irradiation and temperature distributions with high accuracy, as well as partially-shaded conditions. However, the P and O and FOCVT will converge into the LMPP under and temperature distributions with high accuracy, as well as partially-shaded conditions. However, as partially-shaded conditions. However, the P and O and FOCVT will converge into the LMPP under the condition. Moreover, GSO algorithm has a bettercondition. time response in the Ppartially-shaded and O and FOCVT will converge into thethe LMPP under the partially-shaded Moreover, the partially-shaded condition. Moreover, the GSO algorithm has a better time response in comparison with the P and O algorithm, and its convergence speed is higher than the two other the GSO algorithm has a better time response in comparison with the P and O algorithm, and its comparison with the P and O algorithm, and its convergence speed is higher than the two other algorithms. convergence speed is higher than the two other algorithms. algorithms. Acknowledgments: The sponsored by the Science Foundation of Chinaof(Grant 51408578, Thestudy studywas was sponsored by National the National Science Foundation ChinaNos. (Grant Nos. Acknowledgments: The study was sponsored by the NationalFoundation Science Foundation of China (Grant Nos. 51605464, 51476159),51476159), Anhui Provincial Natural Science Foundation (1508085QE96, 1508085QE83). 51408578, 51605464, Anhui Provincial Natural Science (1508085QE96, 1508085QE83). 51408578, 51605464, 51476159), Anhui Provincial Natural Science Foundation (1508085QE96, 1508085QE83). Author Contributions: Yi Yi Jin Jin designed designed and and developed developed the the main main parts parts of of the the research research work, work, including including simulation simulation Author Contributions: model and analyses of the obtained results. Wenhui Hou contributed in the simulation and writing parts.simulation Guiqiang Author Contributions: Yi Jin designed and developed the main parts of research work, including model and analyses of the obtained Wenhui contributed in simulation Guiqiang Li contributed in theoretical analysis.results. Xiao Chen alsoHou involved in verifying the workand andwriting activelyparts. contributed to model and analyses of the obtained results. Wenhui Hou contributed in simulation and writing parts. Guiqiang Li contributed in theoretical analysis. Xiao Chen also involved in verifying the work and actively contributed to finalize the manuscript. Li contributed in theoretical analysis. Xiao Chen also involved in verifying the work and actively contributed to finalize the manuscript. finalize the manuscript. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.
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Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature A dij Eg F I Id Ii Imp IO Ish I ph Iro Isc k Kv nt Ni (t) P Pij Pmax Pij Ppv
Diode ideality factor Euclidean distance between i and j Band gap energy of semiconductor Objective function PV cell output current (A) Diode current (A) Luciferin of glowworm i Current corresponding to the MPP Diode reverse saturation current (A) Parallel resistance current (A) Light-generated current (A) Diode reverse saturation current at STC (A) Short-circuit current (A) Boltzmann’s constant (J/K) The coefficient of the proportionality Number of outstanding individuals Neighborhood of agen PV cell output power Probability of glowworm i moving to j PV maximum power (W) Probability of glowworm i PV module output power (W)
q rdi rs Rsh Rs s S t T Tc Tr U Ud VPV Vmp Vo Voc xi α β γ ρ
Electronic charge (C) Local decision radius Largest sensing radius Parallel resistance Series resistance Movement step size Solar radiation (W/m2 ) Iteration number Temperature Operating temperature (K) Reference temperature (K) PV cell output voltage (V) Diode voltage Voltage of the PV module Voltage corresponding to the MPP Boost converter output voltage (V) Open-circuit voltage Location of glowworm i Greek symbols The current temperature coefficient Variation coefficient of decision radius Luciferin enhancement constant Luciferin decay constant
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