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Solar irradiance and temperature influence on the photovoltaic cell equivalent-circuit models
Solar Energy 188 (2019) 1102–1110
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Solar irradiance and temperature influence on the photovoltaic cell equivalent-circuit models
T
Y. Chaibia, , A. Allouhib, M. Malvonic, M. Salhia, R. Saadanid ⁎
a
2EMI Team, ENSAM, Moulay Ismail University, B.P 15290 El Mansour, Meknes 50500, Morocco Ecole Supérieure de Technologie de Fès, U.S.M.B.A, Route d’Imouzzer, BP 2427, Fez, Morocco c School of Electrical and Computer Engineering, National Technical University of Athens, Greece d FS – EST Meknès, Université Moulay Ismail, Avenue Zitoune, BP 11201, Meknès, Morocco b
ARTICLE INFO
ABSTRACT
Keywords: Modelling of photovoltaic module PV cell equivalent-circuit model Single-diode Double-diode Parameters extraction
Various works investigated different photovoltaic (PV) cell equivalent-circuit models and several techniques were proposed to extract their unknown parameters. The present paper analyzes the current/voltage (I-V) characteristics for Si-crystalline PV modules under non-standard conditions of irradiance and temperature, by using single-diode and double-diode models. The Chaibi and Ishaque methods are employed to determine the parameters for each equivalent-circuit model. Then, the I-V curves provided by the manufacturers and the calculated I-V characteristics are compared at different levels of irradiance and temperature. The comparison suggests prioritizing one of the two equivalent-circuit models according to the prevailing meteorological inputs. As such, a hybrid approach is proposed in order to select the most appropriate model depending on the relevant climatic conditions. The presented approach accuracy is evaluated using real weather data of two PV plants located in two different climatic zones (Mediterranean and Semi-Continental). Results show that the doublediode model is more reliable for low-irradiance levels; however, the single-diode model performs well with lowtemperature fluctuations. An error reduction of 53.93% and 21.04% can be reached for the cloudy weather and for the sunny days, respectively. Accordingly, this approach can be easily implemented as a computing tool to achieve more accurate prediction in the PV systems simulations.
1. Introduction Grid-connected and standalone systems represent the two principal categories of solar PV applications (Allouhi et al., 2016; Malvoni et al., 2017, 2016). It is well established that the economic viability and social acceptance of both applications rely strongly on the overall performance of energy conversion of PV modules (Allouhi et al., 2019). In fact, the presently commercialized PV technologies have low efficiencies and their performances are affected due to the nonlinearity of the PV cell and the external parameters variation (Abbassi et al., 2018). For these reasons, accurate modeling of PV modules constitutes an important topic that attracts a lot of researchers. This modeling task is divided into two parts; first, the choice of equivalent-circuit model, then the parameters extraction of the chosen model (Chaibi and Salhi, 2019). The PV cell equivalent-circuit model is an electrical scheme which allows analyzing the electrical performance of the PV module. This model gives the corresponding current–voltage (I-V) and power-voltage (P-V) characteristics for different external changes such as irradiance
⁎
and temperature (Chaibi et al., 2018). The history of the PV cell equivalent-circuit models knows continuous progress. The first introduced formulation is the ideal single-diode model which is composed of a diode in parallel with a current source (Ebrahimi et al., 2019). However, the use of this model does not reflect the real behavior of the PV cell (Siddiqui and Abido, 2013; Suthar et al., 2013; Villalva et al., 2009). Thereby, for a more realistic PV cell design, the assessment of losses should be taken into account by adding a block of resistances to the ideal model (Ishaque and Salam, 2011). To design contacts between the silicon and electrodes surface, a resistance is added in series (Jordehi, 2016); this model is named as the simplified single-diode model (SSDM) and the number of the unknown parameters is increased to four by adding the series resistance Rs (Chtita et al., 2019). The mathematical solution requires four equations to find the unknown parameters. The derivative of power with respect to voltage ( P / V = 0) (Ding et al., 2012; Ulapane et al., 2011; Xiao et al., 2004) and the relative expressions of the temperature coefficients Ki and/or Kv (Chenni et al., 2007; Kou et al., 1998) are commonly used as the
Corresponding author. E-mail address: [email protected] (Y. Chaibi).
https://doi.org/10.1016/j.solener.2019.07.005 Received 11 January 2019; Received in revised form 24 May 2019; Accepted 1 July 2019 Available online 09 July 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.
Solar Energy 188 (2019) 1102–1110
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fourth equation. The SSDM has been used widely to study the performance of the PV cell (Chenni et al., 2007; Ding et al., 2012; Ismail et al., 2013; Ulapane et al., 2011; Walker, 2001), showing modest results, which implied its improvement by adding another parameter noted as the shunt resistance. Consequently, the number of parameters increases to five and the extraction process becomes complicated. This model is named as the detailed single-diode model (SDM) and is considered as the most used due to its better compromise between efficiency and simplicity (Gao et al., 2018a). Additionally, this model represents the main structure of the most PV systems modelling software such as PVsyst, SAM and HOMER (Blair et al., 2014; Suite and Co, 2016; Universidade De Genebra, 2012). In the literature, another version of the SDM was introduced, termed as the double-diode model (DDM) that presents the same structure as the SDM but in which a second diode is added to the circuit model of the PV cell. Thanks to its high performance, this model has been adopted lately by several authors (Alam et al., 2015; Attivissimo et al., 2013; Et-torabi et al., 2017; Gao et al., 2018b; Ishaque et al., 2011). The DDM assumes seven unknown parameters {IL, Ios1, Ios2, Rs ,Rsh , 1, 2 }, leading to more complicated extraction process since it needs a set of seven equations to be solved. To overcome the complexity of parameters’ determination process, various techniques can be employed. Analytical and metaheuristics methods are the most common approaches to solve the “PV cell model parameter estimation problem” (Haouari-Merbah et al., 2005; Stutenbaeumer and Mesfin, 1999). The curve fitting method of I-V curves is the earliest analytical method used to extract the parameters (Chan et al., 1986; Stutenbaeumer and Mesfin, 1999). Hadj et al. and De blas et al. used the initial equations given by the manufacturer and confirmed that the initial values of Rs0 and Rsh0 are respectively the slope of the open-circuit point Voc / I and the slope of the short circuit point ISC / V (De Blas et al., 2002; Hadj Arab et al., 2004). This approach resulted in a set of five equations whose accuracy depends totally on the choice of the initial conditions. Researchers used different approximations to simplify the calculation. Chaibi et al. employed experimental measurements to reduce the number of parameters (Chaibi et al., 2018). The parameters are extracted by using a measurement under a special condition with initial equations from the manufacturer datasheet. Applying this method to silicon PV cell technologies indicates higher performance for monocrystalline and low relative errors for polycrystalline (Chaibi et al., 2018). On the other hand, Villalva et al. estimated an arbitrary value of the ideality factor and used an iterative method of the series and the shunt resistances until the datasheet peak power (Pmax , e ) coincides with the mathematical peak power(Pmax , m) . At this condition (Pmax , m =Pmax , e ) , the corresponding resistances are displayed and the other parameters are calculated using explicit equations (Villalva et al., 2009). In the case of seven parameters determination, Ishaque et al. assumed that the saturation currents were equal and gave an arbitrary value to both ideality factors, hence the number of unknown parameters has been reduced. It was reported that this technique presents a good performance at low irradiance changes (Ishaque et al., 2011). PV cell model parameter estimation can be seen as an optimization problem that can be solved using metaheuristic algorithms (Saha et al., 2018). These algorithms include genetic algorithm (GA) (Jervase et al., 2001), particle swarm optimization (PSO) (Mughal et al., 2017), artificial bee colony (ABC) (Oliva et al., 2014; Chaibi et al., 2019), and shuffled complex evolution (SCE) etc (Gao et al., 2018b). The literature review shows that different PV cell equivalent-circuit configurations can be adopted to analyze the electrical performance in accordance with the model complexity. The various ways to figure out the unknown parameters, whatever the model is chosen, differ from a technique to another; whether it is an iterative, analytical, graphical, numerical method or metaheuristic approaches, implying the complexity of the parameters determination. The objective of this paper is to investigate the performance of the most popular PV cell equivalent-circuit models, using two accurate
methods from the literature to extract the parameters. Thus, SDM and DDM are adopted and the methods proposed by Chaibi et al. (2018) and by Ishaque et al. (2011) are employed to determine the SDM and DDM parameters, respectively. The investigation aim is to analyze PV cell equivalent-circuit models for different Si-crystalline technologies under non-standard conditions, namely under variations of irradiation and temperature. Through this analysis, it is possible to prioritize the use of one model instead of the others according to the actual prevailing meteorological inputs; an approach that could enhance significantly the accuracy. Therefore, the novelty of this work is to assess the effectiveness of a hybrid approach, obtained by switching from the two equivalent-circuit configurations (the single and the double diode model) according to different levels of solar irradiance and temperature, in order to ensure high accuracy in the photovoltaic cell modelling. In addition, experimental validation of the proposed hybrid approach is carried out using real PV power generations of two PV plants located in different climate zones (Semi-Continental and Mediterranean climate zone). The reason is to investigate the performances of the outlined models under various climatic fluctuations for more representative results. The current paper is organized as follows: First, in Section 2, the description of different PV cell equivalent-circuit models is given. The PV cell parameters extraction methods are demonstrated in Section 3. The performance indices, together with climate conditions of the PV sites under examination are presented in Section 4. Results and discussions are presented in Section 5. Finally, the main conclusions are drawn based on the current analysis in Section 6. 2. PV cell models In order to evaluate the electrical performance of the PV cell, diverse equivalent-circuit models are simulated with the main objective is to plot the corresponding I-V and P-V characteristics for different values of irradiance and temperature. The output current of the simplified single-diode model is expressed by the following equation (Rauschenbach, 1980):
I = IL
Ios {exp [A (V + IRs )
(1)
1]}
where I and V are respectively the output current and voltage of the PV panel, IL is the photo-generated current, Ios is the saturation current, Rs is the series resistance and A is the thermal voltage. The detailed single-diode model (Fig. 1) adds the shunt resistance Rsh and the output current of the PV cell is given by (Rauschenbach, 1980):
I = IL
Ios {exp [A (V + IRs )
1]}
V + Rs I Rsh
(2)
For the double-diode model, shown in Fig. 2, both the circulated currents in the diodes are expressed separately; hence the output current is given by the following equation (Ishaque et al., 2011): I = IL
Ios1 {exp [A1 (V + IR s )
with Ai =
1]}
Ios2 {exp [A2 (V + IR s )
1]}
V + Rs I Rsh
q i kTNcell
Fig. 1. Single-diode equivalent circuit. 1103
(3)
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Ior =
Voc
Isc exp (AVoc )
Rs Isc Rsh
(7)
exp (AIsc Rs )
where, Vm and Im are the maximum voltage and current of the PV module, Voc is the open circuit voltage. By replacing the reverse saturation current of the diode in Eq. (8), the value of the diode saturation current Ios varies with each value of temperature (Lineykin et al., 2014).
Ios = Ior
Fig. 2. Double-diode equivalent circuit model.
The double-diode configuration depicted in Fig. 2 is another equivalent-circuit model used to evaluate the electrical performance of the PV panel. For this reason, several researchers have adopted some approximations to simplify the calculation process. As reported in Ishaque et al. (2011), Ishaque et al. assumed that the saturation currents were equal and used a modification on the equation given by (Villalva et al., 2009). The modified equation of the saturation current is represented as follows:
As can be seen in Eqs. (1)–(3), the output current equations are comprised of the electrical parameters and the outputs voltage of the PV module. These parameters are unknown which implies the use of an extraction technique with accurate performance. For this reason, the method proposed by Chaibi et al. (2018) is used to extract the parameters of the SDM, while the method suggested by Ishaque et al. (2011) is employed to determine the DDM parameters. In both methods, the current-generated value depends on the variation of irradiance and temperature. This current is calculated by using the following equation (Motahhir et al., 2018; Walker, 2001):
G 1000
Ios1 = Ios2 =
Isc + Ki (T exp [(Voc + Kv (T
(4)
I
exp (AVoc ) Im
exp (AIsc Rs ) Voc
=
Voc
Im
Vm Rs Im Rsh
exp (AVoc ) exp [A (Vm + Rs Im)
Vm Rs Im R sh
exp (AVoc ) exp [A (Vm + Rs Im)
=
Vm
Im Rs Im
1 Rsh
Aexp [A (Vm + Rs Im)]
kTNcell ] q
(9)
Vm + Im Rs
Ios exp
kTNcell q
+ exp
Vm + Im Rs (p
1)
kTNcell q
+2
Pm Vm
(10)
4. Methodology
This method consists of one measurement and the determination of the other parameters is effectuated by solving the mathematical equations extracted from datasheet characteristic points. This method is selected to extract the single-diode parameters. The methodology followed by this extraction technique is explained as follows: For the detailed single-diode model in Fig. 1, the number of unknown parameters is limited to four, i.e. the ideality factor , saturation current Ios , shunt resistance Rsh and series resistance Rs . As reported by Chaibi et al. (2018), when the PV panel is exposed to dark condition (IL = 0), the overall resistance of the PV module is extracted using the ohm relation between the measured output current and voltage of the PV panel. This resistance represents the sum of the shunt and the series resistances. Because of its very low value, the series resistance is considered negligible which means that the measured resistance is approximately the shunt resistance. Thereafter, the other parameters are extracted by using the characteristic equations from the datasheet. For this reason, the set of equations given by Eqs. (5) and (6) are solved to obtainRs and γ. Then, the determined values are replaced in Eq. (7) to find the reverse saturation current Ior (Chaibi et al., 2018). Rs Isc Rsh
2 / p}
Vm + Im RS
Rsh =
• Method of Chaibi et al. (2018)
Voc
298.15)
298.15))/{ 1 +
where, the values of the ideality factors 1 and 2 are taken respectively 1 and 1.2, p is a value that could be chosen ≥ 2.2 (Ishaque et al., 2011).Kv is the temperature coefficient of the PV module open circuit voltage. For Rs and Rsh estimation, the resistances are evaluated using an iteration process of the series resistance until achieving the peak power (Pm) of the datasheet, and this shunt resistance is represented by Eq. (10).
where, Ki is the temperature coefficient of the short circuit current Isc .
Isc
(8)
• Method of Ishaque et al. (2011)
3. PV cell parameters extraction methods
298.15)
1 T
EG0 is the band gap (1.22 eV).
where i is associated to the ideality factor ( ) of each diode, Ncell is the number of series cell that constitutes the PV module, q (=1.6·10−19C) and k (=1.4· 10−23 JK−1) are respectively the electron charge and the constant of Boltzmann. For the various levels of irradiance G (W/m2) and temperature T (K), the simulation of I-V and P-V curves requires the knowledge of the PV cell equivalent-circuit parameters.
IL = Isc + Ki (T
3 qEG0 T 1 exp 298.15 k 298.15
The present work aims to analyze the performances of the SDM and the DDM under non-standard conditions in order to classify which model is the most appropriate model to adopt for different levels of solar irradiance and temperature. For achieving the aim, it is first essential to analyze each electrical circuit separately. Hence, the selected methods to extract the parameters, Chaibi et al. (2018); and Ishaque et al. (2011) are implemented in MATLAB environment and applied to two silicon PV modules of different technologies. These PV modules are the monocrystalline SM55 and the polycrystalline MSX60, respectively. The technical specifications of both models as given by the manufacturer are presented in Table 1 (BP MSX60, 2002; Shell SM55, 2002). It is interesting to note that the choice of the PV panels is based on their wide availability in the market as they account for a share of 80% (Sudhakar Babu et al., 2016). The obtained I-V curves are compared to the data delivered by manufacturers for different levels of irradiance and temperature by using the root mean square error (RMSE) and relative error Erel . These parameters can be calculated as follows:
Base case(i) Calculated(i) *100 Calculated(i)
(5)
Erel (%) =
(6)
RMSE(%) =
1104
1 N
(11)
N
(Base case(i) i=1
Calculated(i))2 *100
(12)
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normalized mean absolute error (NMAE), defined as the average of error between the exact value for the base case and the calculated values. This error can be represented as follows:
Table 1 Datasheet parameters of SM55 and MSX60 PV panels at STC (Standard Test Conditions). Parameters Pm [W] Vm [V] Im [A] Voc [V] Isc [A] KI [%/K] Kv [%/K] Ncell
Mono-Si SM55 55 17.4 3.15 21.7 3.45 0.04 −0.35 36
Poly-Si MSX60
NMAE(%) =
60 17.1 3.5 21.1 3.8 0.06 −0.37 36
1 N
N 1
Base case(i) Calculated(i) *100 Max1N (Base case(i))
(13)
where, N is the total number of samples. It measures the performance improvements achievable by using the hybrid approach with respect to the equivalent-circuit models SDM and DDM. 5. Results and discussion The results discussion is divided into two parts:
where, the base case represents the value extracted from PV module manufacturer datasheet and the calculated one is determined using the equivalent-circuit models. These errors are expressed for each i-th sample. A classification is introduced in order to identify which model to adopt for a given climate condition getting the best fit. So, a hybrid approach that combines the single and the double-diode models is suggested. It performs according to the climate variation and selects instantly one of the two models with the lowest error. This approach is explained in Fig. 3. Thereafter, an experimental validation is carried out by using real hourly values of titled irradiance G , cell temperature T and DC output powers (PDC ), recorded from 01/12/2017 to 23/12/2017 for a total of 529 samples, of two PV plants located in different climatic zones Mediterranean (Brindisi, Italy) and Semi-continental (Meknes, Morocco) with a nominal power of 2.2 kWp and 2 kWp, respectively. The reason behind using these two PV plants is to investigate the performances of the outlined models under various climate fluctuations. Fig. 4 shows the monthly averages of the horizontal plane irradiance and the ambient temperature over one year for each climate zone by using PVGIS website (“PVGIS,” n.d.). As observed in this figure, Semicontinental climate (SCC) presents higher irradiance and temperature than Mediterranean climate. The performances of the hybrid approach are assessed by the
- Comparison I-V curves, where the I-V characteristics for both MonoSi and Poly-Si PV panel given by the manufacturer datasheets and by both SDM and DDM are analyzed by a performance evaluation under different conditions of solar irradiance and temperature; - Implementation of the hybrid approach and its validation against real recorded data from two PV plants experiencing differences in hourly climatic variations, where the best combination of SDM and DDM is used. 5.1. Comparison of I-V curves The parameters of the single-diode models are determined using the method proposed by Chaibi et al. (2018) as given in Table. 2. The double-diode model parameters according to the method suggested by Ishaque et al. (2011) are displayed in Table 3. The photo-generated current is calculated using Eq. (4) and the extracted parameters are inserted in the PV output current equations {Eqs. (2) and (3)}.The corresponding I-V and P-V curves of the tested PV models are plotted to analyze the behavior of single-diode and double diode models. It is necessary to stress that the computed curves should agree well with those given by the manufacturer datasheets. Figs. 5–7 display the calculated and provided I-V characteristics from manufacturer datasheet of the Mono-Si and Poly-Si PV modules at various levels of irradiance and temperature. In addition, the corresponding RMSE calculated using Eq. (12) to investigate the fitting error between the estimated I-V curves and manufacturer is illustrated in Fig. 5. Low RMSE values demonstrate a good matching between the computed I-V curves for different levels of irradiance and fixed temperature (T = 25 °C) with the datasheet ones. Moreover, Chaibi et al. method seems to fit better for irradiance values above 600 W/m2. Otherwise, Ishaque et al. method gives better fitting for 200 W/m2 and 400 W/m2. In Fig. 6, I-V characteristics of the Mono-Si PV module are plotted for temperature in the range from 20 °C to 60 °C and a fixed irradiance at 1000 W/m2. It is observed that the provided I-V curves using both chosen methods fit well with manufacturer ones. However, a little difference is observed between Chaibi et al. method and manufacturer curves at the temperature value of 20 °C with a RMSE that exceeds 2%. In the same way, the plotted I-V curves of the Poly-Si PV module using Ishaque et al. and Chaibi et al. methods are evaluated. As displayed in Fig. 7, the obtained I-V curves using the examined methods and the manufacturer graphs are presented for various levels of temperature and a constant value of solar irradiance (G = 1000 W/m2). As can be seen, the Ishaque et al. I-V curves agrees well with the manufacturer for all temperature levels, except for 25 °C, Chaibi et al. method gives better results with a RMSE value less than 1%. Based on this, it seems that the single-diode model is more suitable to model the Mono-Si PV panels while the double-diode model is more appropriate for Poly-Si PV panels. Note that the I-V curves of the Poly-Si module for different irradiance levels are not provided due to the lack of information on the irradiance variation from the manufacturer. In order to compare the results achieved by two equivalent-circuit
Fig. 3. Diagram of the proposed hybrid approach. 1105
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Y. Chaibi, et al. 300
35
Mediterranean Semi-Continental
250
25
Temperature [°C]
GHI [kWh/m2 ]
Semi-Continental
30
200
150
100
20 15 10
50
0 Jan
Mediterranean
5
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
0 Jan
Dec
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Fig. 4. The monthly average values of the horizontal plane irradiance and the ambient temperature for the Mediterranean and the semi-continental climate zone.
where the base case represents the extracted value from manufacturer curves and the calculated one corresponds to the computed values using the SDM and the DDM. The results are displayed in Fig. 8. Based on this categorization, Fig. 8(a) gives the relative errors of the PV panel output power for each class of irradiance and temperature. As noticed in Fig. 8(a), the SDM is more reliable to model the PV panel for lowtemperature ranges. However, the double-diode model shows good results in medium and high-temperature ranges. Furthermore, it can be seen that the double-diode model performs well with low and medium irradiances whereas the single-diode model is more convenient with high irradiance variations. Besides, the open-circuit voltage relative errors associated with the equivalent-circuit models of both PV panel technologies are presented for different levels of temperature and irradiance (see Fig. 8(b)). As can be observed, the single-diode model seems to be very appropriate to model the Mono-Si modules because of its lower error compared to the double-diode model. On the opposite side, the double-diode model presents a key solution to model the PolySi PV panel especially for medium and high levels of temperature. Moreover, the SDM presents good results for low irradiance, while the DDM is more suitable for medium and high ranges of irradiance. For the short-circuit current, the chosen equivalent-circuit models are compared under the same variation of climate conditions and this is performed for both PV panel technologies. As can be seen in Fig. 8(c), the relative errors demonstrate that the single-diode model is more appropriate to model the PV panel under the variation of irradiance. Also, this model is more suitable for temperature variation except for the Poly-Si technology in high temperature changes. Briefly, these curves
Table 2 Extracted parameters using Chaibi et al. method for the single-diode model.
Mono-Si Poly-Si
Rsh [Ω]
Rs [Ω]
Io [μA]
γ
6500 7000
0.1124 0.1880
4.8244 1.1174
1.7409 1.5079
Table 3 Extracted parameters using Ishaque et al. method for the double-diode model.
Mono-Si Poly-Si
Rsh [Ω]
Rs [Ω]
γ1
γ2
Io1 = Io2 [A]
144.24 166.58
0.34 0.47
1 1
1.2 1.2
4.7039 0.10−10 2.2324 0.10−10
models and the electrical parameters of the PV panel {Isc, Voc, Pm} extracted from manufacturer datasheet for different weather conditions, three intervals (Low, Medium and High) of irradiance and temperature were identified for classification. For the irradiance, the low values class is below 400 W/m2, the medium one is between 400 W/m2 and 800 W/m2 and the high values class is above 800 W/m2. For the temperature changes, the low variations are below 25 °C, the medium one is between 25 °C and 40 °C and the last class is for temperatures above 40 °C. As a first step, the manufacturer I-V curves are used to calculate the corresponding power for each variation of the climatic variable. Based on the climate variations, the relative error is computed using Eq. (11), Mono-Si SM55 1000 W/m
3.5
Current [A]
3
800 W/m
1.5 1
600 W/m
2
400 W/m
2
200 W/m
Chaibi et al. Ishaque et al.
1.5
2
2.5 2
2
Mono-Si SM55
2
Manufacturer data Chaibi et al. Ishaque et al.
RMSE [%]
4
1
0.5
2
0.5 0
0
5
10
Voltage [V]
15
20
25
0
200
400
600
Irradiance [W/m 2]
800
1000
Fig. 5. Comparison between the I-V characteristics using Chaibi et al., Ishaque et al. methods and manufacturer data related to the Mono-Si SM55 PV panel for different irradiances, T = 25 °C. 1106
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Mono-Si SM55
4 3.5
2 1.5
RMSE [%]
Current [A]
60 °C 50 °C 40 °C 30 °C 20 °C
Chaibi et al. Ishaque et al.
2
3 2.5
Mono-Si SM55
2.5
Manufacturer Chaibi et al. Ishaque et al.
1
1.5
1
0.5
0.5 0
0
5
10
Voltage [V]
15
20
0
25
20
30
40
Temperature [°C]
50
60
Fig. 6. Comparison of the I-V characteristics using Chaibi et al., Ishaque et al. methods and manufacturer data related to the Mono-Si SM55 PV panel for different temperatures, G = 1000 W/m2.
show that the low-irradiance levels engender high errors in the PV output power with a value of 8.40%. The lowest error closed to 0.10%. is presented at the short circuit currents. Such analysis enables the clustering of the performance for both single-diode and double-diode model in different range of irradiance and temperature according to the flowchart in Fig. 3. So, the classification tabulated in Table 4 proposes guidelines in selecting the model to be used in the simulation process with respect to the actual climate condition to achieve the lowest error.
of DC power based on the actual atmospheric condition of the two climate zones (Mediterranean and the Semi-continental climate). These powers are utilized to calculate the normalized absolute mean errors (see Eq. (13)) between experimental and calculated DC power using the hybrid approach for each one of the PV plants. These errors are displayed in Fig. 10. Fig. 10(a) shows the NMAE between the hybrid approach and the individual SDM and DDM. It is significantly high because of the fluctuated cloudy weather of the Mediterranean climate. Furthermore, a decreasing of the error up to 53.93% for irradiance variations and 49.52% for temperature variations can be achieved by the proposed approach. Fig. 10(b) shows that the NMAE related to the Semi-Continental PV plant, seems to be lower compared to Mediterranean PV plant, due to the sunny behavior of Meknes city. Moreover, in Continental climatic conditions the proposed approach can reduce the error by 21.04% and 14.66% due to irradiance and temperature variations, respectively.
5.2. Implementations of the hybrid approach and validation A comparison of predicted DC outputs and actual experimental data on an hourly basis is carried out. In order to investigate the impact of the climatic condition on the performance of both SDM and DDM, the experimental titled irradiance and modules temperature of two PV plants are utilized to compute the corresponding SDM and DDM powers. Thereafter, the obtained output data series is used to calculate the error between the real generated powers (base case) and the computed ones (SDM and DDM power) using the error formula given in Eq. (11). These errors are presented in Fig. 9. As can be observed in this figure, the mean error results support the findings of the previous subsection about the relationship between climate conditions and accuracy of single and double diode model which was summarized in Table 4. The previously classification introduced in Table 4 is used to build a hybrid approach which selects the most suitable model for computing
The paper evaluates the accuracy of the single-diode and the double-diode models as the most popular PV cell equivalent-circuit models under changes of solar irradiance and temperature. Two commercialized silicon PV module technologies, Monocrystalline SM55 and Polycrystalline MSX60, are considered to investigate the performance of two equivalent-circuit models with respect to the manufacturer data. The comparison demonstrates that the single-diode model seems to be more suitable for high fluctuations of irradiance. In turn, the double-
Poly-Si MSX60
5
Poly-Si MSX60
2
Manufacturer data Chaibi et al. Ishaque et al.
4
Chaibi et al. Ishaque et al.
1.5
T = 0°C T = 25°C T = 50°C T = 75°C
3
2
RMSE [%]
Current [A]
6. Conclusion
1
0.5
1
0
0
0
5
10
Voltage [V]
15
20
25
0
25
50
75
Temperature [°C]
Fig. 7. Comparison of the I-V characteristics using Chaibi et al., Ishaque et al. methods and manufacturer data related to the Poly-Si MSX60 PV panel for different temperatures, G = 1000 W/m2. 1107
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Output PV power
9
Low Temperature Medium Temperature High Temperature Low Irradiance Medium Irradiance High Irradiance
8 7
E rel [%]
6 5 4 3 2 1 0
Mono-Si (SDM)
Mono-Si (DDM)
Poly-Si (SDM)
Poly-Si (DDM)
Technology (ECM)
(a)
Open-circuit voltage
9
Low Temperature Medium Temperature High Temperature Low Irradiance Medium Irradiance High Irradiance
8 7
Low Temperature Medium Temperature High Temperature Low Irradiance Medium Irradiance High Irradiance
8 7 6
E rel [%]
E rel [%]
6 5 4
5 4
3
3
2
2
1
1
0
Short-circuit current
9
0 Mono-Si (SDM)
Mono-Si (DDM)
Poly-Si (SDM)
Mono-Si (SDM)
Poly-Si (DDM)
Technology (ECM)
Mono-Si (DDM)
Poly-Si (SDM)
Poly-Si (DDM)
Technology (ECM)
(b)
(c)
Fig. 8. Relative error of (a) PV output power, (b) open-circuit voltage, (c) short circuit current using the SDM and the DDM for different classes of solar irradiance and temperature. Base case: extracted values from Datasheet. 7
Table 4 Performance classification of the equivalent-circuit models for different levels of irradiance and temperature.
Medium
High
Low
Medium
High
DDM DDM SDM
DDM SDM SDM
SDM SDM SDM
SDM SDM SDM
DDM SDM SDM
DDM DDM DDM
[%]
5
Low
rel
Power Voltage Current
6
Temperature
E
Irradiance
Low Temperature Medium Temperature Low Irradiance Medium Irradiance High Irradiance
4 3 2
diode model is more reliable to predict the electrical parameters under the medium and low irradiance variations. Furthermore, the SDM performs well with low fluctuations of temperature and the DDM is more appropriate for medium and high variations. The results prove that the performance of the Photovoltaic Cell Equivalent-Circuit Models is influenced by solar irradiance and temperature. This suggests a new approach to enhance the accuracy of PV output prediction. The paper presents a more appropriate approach able to switch between the SDM and DDM according to the instantaneous variation of solar irradiance and temperature. The performance of the hybrid approach was assessed considering real data of two PV systems implemented in two sites of different climatic zones. An error analysis was performed between the proposed hybrid approach and the conventional SDM and DDM models.
1 0
SDM (MC)
DDM (MC)
SDM (SCC)
DDM (SCC)
ECM (Climate zone) Fig. 9. Normalized mean error of the SDM and the DDM under different classes of solar irradiance and temperature in Mediterranean climate (MC) and SemiContinental Climate (SCC) conditions.
The proposed approach can diminish the computing errors by up to 53.93% in the case of the cloudy weather conditions and up to 21.04% for sunny climatic conditions. 1108
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Mediterranean Climate
60
SDM DDM
50
NMAE [%]
NMAE [%]
40
30 20
30 20
10
10
Low
Medium
Irradiance Level
0
High
Temperature Level
Medium
Semi-Continental Climate
60
SDM DDM
50
SDM DDM
50
40
40
NMAE [%]
NMAE [%]
Low
(a)
Semi-Continental Climate
60
30 20 10 0
SDM DDM
50
40
0
Mediterranean Climate
60
30 20 10
Low
Medium
0
High
Irradiance Level
Low
Temperature Level
Medium
(b) Fig. 10. Relative error between the hybrid approach and the SDM and DDM of Mediterranean (a) and Semi-continental climate conditions (b) PV plant for different level of solar irradiance and temperature. Base case: Hybrid approach.
Acknowledgment
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Solar irradiance and temperature influence on the photovoltaic cell equivalent-circuit models
T
Y. Chaibia, , A. Allouhib, M. Malvonic, M. Salhia, R. Saadanid ⁎
a
2EMI Team, ENSAM, Moulay Ismail University, B.P 15290 El Mansour, Meknes 50500, Morocco Ecole Supérieure de Technologie de Fès, U.S.M.B.A, Route d’Imouzzer, BP 2427, Fez, Morocco c School of Electrical and Computer Engineering, National Technical University of Athens, Greece d FS – EST Meknès, Université Moulay Ismail, Avenue Zitoune, BP 11201, Meknès, Morocco b
ARTICLE INFO
ABSTRACT
Keywords: Modelling of photovoltaic module PV cell equivalent-circuit model Single-diode Double-diode Parameters extraction
Various works investigated different photovoltaic (PV) cell equivalent-circuit models and several techniques were proposed to extract their unknown parameters. The present paper analyzes the current/voltage (I-V) characteristics for Si-crystalline PV modules under non-standard conditions of irradiance and temperature, by using single-diode and double-diode models. The Chaibi and Ishaque methods are employed to determine the parameters for each equivalent-circuit model. Then, the I-V curves provided by the manufacturers and the calculated I-V characteristics are compared at different levels of irradiance and temperature. The comparison suggests prioritizing one of the two equivalent-circuit models according to the prevailing meteorological inputs. As such, a hybrid approach is proposed in order to select the most appropriate model depending on the relevant climatic conditions. The presented approach accuracy is evaluated using real weather data of two PV plants located in two different climatic zones (Mediterranean and Semi-Continental). Results show that the doublediode model is more reliable for low-irradiance levels; however, the single-diode model performs well with lowtemperature fluctuations. An error reduction of 53.93% and 21.04% can be reached for the cloudy weather and for the sunny days, respectively. Accordingly, this approach can be easily implemented as a computing tool to achieve more accurate prediction in the PV systems simulations.
1. Introduction Grid-connected and standalone systems represent the two principal categories of solar PV applications (Allouhi et al., 2016; Malvoni et al., 2017, 2016). It is well established that the economic viability and social acceptance of both applications rely strongly on the overall performance of energy conversion of PV modules (Allouhi et al., 2019). In fact, the presently commercialized PV technologies have low efficiencies and their performances are affected due to the nonlinearity of the PV cell and the external parameters variation (Abbassi et al., 2018). For these reasons, accurate modeling of PV modules constitutes an important topic that attracts a lot of researchers. This modeling task is divided into two parts; first, the choice of equivalent-circuit model, then the parameters extraction of the chosen model (Chaibi and Salhi, 2019). The PV cell equivalent-circuit model is an electrical scheme which allows analyzing the electrical performance of the PV module. This model gives the corresponding current–voltage (I-V) and power-voltage (P-V) characteristics for different external changes such as irradiance
⁎
and temperature (Chaibi et al., 2018). The history of the PV cell equivalent-circuit models knows continuous progress. The first introduced formulation is the ideal single-diode model which is composed of a diode in parallel with a current source (Ebrahimi et al., 2019). However, the use of this model does not reflect the real behavior of the PV cell (Siddiqui and Abido, 2013; Suthar et al., 2013; Villalva et al., 2009). Thereby, for a more realistic PV cell design, the assessment of losses should be taken into account by adding a block of resistances to the ideal model (Ishaque and Salam, 2011). To design contacts between the silicon and electrodes surface, a resistance is added in series (Jordehi, 2016); this model is named as the simplified single-diode model (SSDM) and the number of the unknown parameters is increased to four by adding the series resistance Rs (Chtita et al., 2019). The mathematical solution requires four equations to find the unknown parameters. The derivative of power with respect to voltage ( P / V = 0) (Ding et al., 2012; Ulapane et al., 2011; Xiao et al., 2004) and the relative expressions of the temperature coefficients Ki and/or Kv (Chenni et al., 2007; Kou et al., 1998) are commonly used as the
Corresponding author. E-mail address: [email protected] (Y. Chaibi).
https://doi.org/10.1016/j.solener.2019.07.005 Received 11 January 2019; Received in revised form 24 May 2019; Accepted 1 July 2019 Available online 09 July 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.
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fourth equation. The SSDM has been used widely to study the performance of the PV cell (Chenni et al., 2007; Ding et al., 2012; Ismail et al., 2013; Ulapane et al., 2011; Walker, 2001), showing modest results, which implied its improvement by adding another parameter noted as the shunt resistance. Consequently, the number of parameters increases to five and the extraction process becomes complicated. This model is named as the detailed single-diode model (SDM) and is considered as the most used due to its better compromise between efficiency and simplicity (Gao et al., 2018a). Additionally, this model represents the main structure of the most PV systems modelling software such as PVsyst, SAM and HOMER (Blair et al., 2014; Suite and Co, 2016; Universidade De Genebra, 2012). In the literature, another version of the SDM was introduced, termed as the double-diode model (DDM) that presents the same structure as the SDM but in which a second diode is added to the circuit model of the PV cell. Thanks to its high performance, this model has been adopted lately by several authors (Alam et al., 2015; Attivissimo et al., 2013; Et-torabi et al., 2017; Gao et al., 2018b; Ishaque et al., 2011). The DDM assumes seven unknown parameters {IL, Ios1, Ios2, Rs ,Rsh , 1, 2 }, leading to more complicated extraction process since it needs a set of seven equations to be solved. To overcome the complexity of parameters’ determination process, various techniques can be employed. Analytical and metaheuristics methods are the most common approaches to solve the “PV cell model parameter estimation problem” (Haouari-Merbah et al., 2005; Stutenbaeumer and Mesfin, 1999). The curve fitting method of I-V curves is the earliest analytical method used to extract the parameters (Chan et al., 1986; Stutenbaeumer and Mesfin, 1999). Hadj et al. and De blas et al. used the initial equations given by the manufacturer and confirmed that the initial values of Rs0 and Rsh0 are respectively the slope of the open-circuit point Voc / I and the slope of the short circuit point ISC / V (De Blas et al., 2002; Hadj Arab et al., 2004). This approach resulted in a set of five equations whose accuracy depends totally on the choice of the initial conditions. Researchers used different approximations to simplify the calculation. Chaibi et al. employed experimental measurements to reduce the number of parameters (Chaibi et al., 2018). The parameters are extracted by using a measurement under a special condition with initial equations from the manufacturer datasheet. Applying this method to silicon PV cell technologies indicates higher performance for monocrystalline and low relative errors for polycrystalline (Chaibi et al., 2018). On the other hand, Villalva et al. estimated an arbitrary value of the ideality factor and used an iterative method of the series and the shunt resistances until the datasheet peak power (Pmax , e ) coincides with the mathematical peak power(Pmax , m) . At this condition (Pmax , m =Pmax , e ) , the corresponding resistances are displayed and the other parameters are calculated using explicit equations (Villalva et al., 2009). In the case of seven parameters determination, Ishaque et al. assumed that the saturation currents were equal and gave an arbitrary value to both ideality factors, hence the number of unknown parameters has been reduced. It was reported that this technique presents a good performance at low irradiance changes (Ishaque et al., 2011). PV cell model parameter estimation can be seen as an optimization problem that can be solved using metaheuristic algorithms (Saha et al., 2018). These algorithms include genetic algorithm (GA) (Jervase et al., 2001), particle swarm optimization (PSO) (Mughal et al., 2017), artificial bee colony (ABC) (Oliva et al., 2014; Chaibi et al., 2019), and shuffled complex evolution (SCE) etc (Gao et al., 2018b). The literature review shows that different PV cell equivalent-circuit configurations can be adopted to analyze the electrical performance in accordance with the model complexity. The various ways to figure out the unknown parameters, whatever the model is chosen, differ from a technique to another; whether it is an iterative, analytical, graphical, numerical method or metaheuristic approaches, implying the complexity of the parameters determination. The objective of this paper is to investigate the performance of the most popular PV cell equivalent-circuit models, using two accurate
methods from the literature to extract the parameters. Thus, SDM and DDM are adopted and the methods proposed by Chaibi et al. (2018) and by Ishaque et al. (2011) are employed to determine the SDM and DDM parameters, respectively. The investigation aim is to analyze PV cell equivalent-circuit models for different Si-crystalline technologies under non-standard conditions, namely under variations of irradiation and temperature. Through this analysis, it is possible to prioritize the use of one model instead of the others according to the actual prevailing meteorological inputs; an approach that could enhance significantly the accuracy. Therefore, the novelty of this work is to assess the effectiveness of a hybrid approach, obtained by switching from the two equivalent-circuit configurations (the single and the double diode model) according to different levels of solar irradiance and temperature, in order to ensure high accuracy in the photovoltaic cell modelling. In addition, experimental validation of the proposed hybrid approach is carried out using real PV power generations of two PV plants located in different climate zones (Semi-Continental and Mediterranean climate zone). The reason is to investigate the performances of the outlined models under various climatic fluctuations for more representative results. The current paper is organized as follows: First, in Section 2, the description of different PV cell equivalent-circuit models is given. The PV cell parameters extraction methods are demonstrated in Section 3. The performance indices, together with climate conditions of the PV sites under examination are presented in Section 4. Results and discussions are presented in Section 5. Finally, the main conclusions are drawn based on the current analysis in Section 6. 2. PV cell models In order to evaluate the electrical performance of the PV cell, diverse equivalent-circuit models are simulated with the main objective is to plot the corresponding I-V and P-V characteristics for different values of irradiance and temperature. The output current of the simplified single-diode model is expressed by the following equation (Rauschenbach, 1980):
I = IL
Ios {exp [A (V + IRs )
(1)
1]}
where I and V are respectively the output current and voltage of the PV panel, IL is the photo-generated current, Ios is the saturation current, Rs is the series resistance and A is the thermal voltage. The detailed single-diode model (Fig. 1) adds the shunt resistance Rsh and the output current of the PV cell is given by (Rauschenbach, 1980):
I = IL
Ios {exp [A (V + IRs )
1]}
V + Rs I Rsh
(2)
For the double-diode model, shown in Fig. 2, both the circulated currents in the diodes are expressed separately; hence the output current is given by the following equation (Ishaque et al., 2011): I = IL
Ios1 {exp [A1 (V + IR s )
with Ai =
1]}
Ios2 {exp [A2 (V + IR s )
1]}
V + Rs I Rsh
q i kTNcell
Fig. 1. Single-diode equivalent circuit. 1103
(3)
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Y. Chaibi, et al.
Ior =
Voc
Isc exp (AVoc )
Rs Isc Rsh
(7)
exp (AIsc Rs )
where, Vm and Im are the maximum voltage and current of the PV module, Voc is the open circuit voltage. By replacing the reverse saturation current of the diode in Eq. (8), the value of the diode saturation current Ios varies with each value of temperature (Lineykin et al., 2014).
Ios = Ior
Fig. 2. Double-diode equivalent circuit model.
The double-diode configuration depicted in Fig. 2 is another equivalent-circuit model used to evaluate the electrical performance of the PV panel. For this reason, several researchers have adopted some approximations to simplify the calculation process. As reported in Ishaque et al. (2011), Ishaque et al. assumed that the saturation currents were equal and used a modification on the equation given by (Villalva et al., 2009). The modified equation of the saturation current is represented as follows:
As can be seen in Eqs. (1)–(3), the output current equations are comprised of the electrical parameters and the outputs voltage of the PV module. These parameters are unknown which implies the use of an extraction technique with accurate performance. For this reason, the method proposed by Chaibi et al. (2018) is used to extract the parameters of the SDM, while the method suggested by Ishaque et al. (2011) is employed to determine the DDM parameters. In both methods, the current-generated value depends on the variation of irradiance and temperature. This current is calculated by using the following equation (Motahhir et al., 2018; Walker, 2001):
G 1000
Ios1 = Ios2 =
Isc + Ki (T exp [(Voc + Kv (T
(4)
I
exp (AVoc ) Im
exp (AIsc Rs ) Voc
=
Voc
Im
Vm Rs Im Rsh
exp (AVoc ) exp [A (Vm + Rs Im)
Vm Rs Im R sh
exp (AVoc ) exp [A (Vm + Rs Im)
=
Vm
Im Rs Im
1 Rsh
Aexp [A (Vm + Rs Im)]
kTNcell ] q
(9)
Vm + Im Rs
Ios exp
kTNcell q
+ exp
Vm + Im Rs (p
1)
kTNcell q
+2
Pm Vm
(10)
4. Methodology
This method consists of one measurement and the determination of the other parameters is effectuated by solving the mathematical equations extracted from datasheet characteristic points. This method is selected to extract the single-diode parameters. The methodology followed by this extraction technique is explained as follows: For the detailed single-diode model in Fig. 1, the number of unknown parameters is limited to four, i.e. the ideality factor , saturation current Ios , shunt resistance Rsh and series resistance Rs . As reported by Chaibi et al. (2018), when the PV panel is exposed to dark condition (IL = 0), the overall resistance of the PV module is extracted using the ohm relation between the measured output current and voltage of the PV panel. This resistance represents the sum of the shunt and the series resistances. Because of its very low value, the series resistance is considered negligible which means that the measured resistance is approximately the shunt resistance. Thereafter, the other parameters are extracted by using the characteristic equations from the datasheet. For this reason, the set of equations given by Eqs. (5) and (6) are solved to obtainRs and γ. Then, the determined values are replaced in Eq. (7) to find the reverse saturation current Ior (Chaibi et al., 2018). Rs Isc Rsh
2 / p}
Vm + Im RS
Rsh =
• Method of Chaibi et al. (2018)
Voc
298.15)
298.15))/{ 1 +
where, the values of the ideality factors 1 and 2 are taken respectively 1 and 1.2, p is a value that could be chosen ≥ 2.2 (Ishaque et al., 2011).Kv is the temperature coefficient of the PV module open circuit voltage. For Rs and Rsh estimation, the resistances are evaluated using an iteration process of the series resistance until achieving the peak power (Pm) of the datasheet, and this shunt resistance is represented by Eq. (10).
where, Ki is the temperature coefficient of the short circuit current Isc .
Isc
(8)
• Method of Ishaque et al. (2011)
3. PV cell parameters extraction methods
298.15)
1 T
EG0 is the band gap (1.22 eV).
where i is associated to the ideality factor ( ) of each diode, Ncell is the number of series cell that constitutes the PV module, q (=1.6·10−19C) and k (=1.4· 10−23 JK−1) are respectively the electron charge and the constant of Boltzmann. For the various levels of irradiance G (W/m2) and temperature T (K), the simulation of I-V and P-V curves requires the knowledge of the PV cell equivalent-circuit parameters.
IL = Isc + Ki (T
3 qEG0 T 1 exp 298.15 k 298.15
The present work aims to analyze the performances of the SDM and the DDM under non-standard conditions in order to classify which model is the most appropriate model to adopt for different levels of solar irradiance and temperature. For achieving the aim, it is first essential to analyze each electrical circuit separately. Hence, the selected methods to extract the parameters, Chaibi et al. (2018); and Ishaque et al. (2011) are implemented in MATLAB environment and applied to two silicon PV modules of different technologies. These PV modules are the monocrystalline SM55 and the polycrystalline MSX60, respectively. The technical specifications of both models as given by the manufacturer are presented in Table 1 (BP MSX60, 2002; Shell SM55, 2002). It is interesting to note that the choice of the PV panels is based on their wide availability in the market as they account for a share of 80% (Sudhakar Babu et al., 2016). The obtained I-V curves are compared to the data delivered by manufacturers for different levels of irradiance and temperature by using the root mean square error (RMSE) and relative error Erel . These parameters can be calculated as follows:
Base case(i) Calculated(i) *100 Calculated(i)
(5)
Erel (%) =
(6)
RMSE(%) =
1104
1 N
(11)
N
(Base case(i) i=1
Calculated(i))2 *100
(12)
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normalized mean absolute error (NMAE), defined as the average of error between the exact value for the base case and the calculated values. This error can be represented as follows:
Table 1 Datasheet parameters of SM55 and MSX60 PV panels at STC (Standard Test Conditions). Parameters Pm [W] Vm [V] Im [A] Voc [V] Isc [A] KI [%/K] Kv [%/K] Ncell
Mono-Si SM55 55 17.4 3.15 21.7 3.45 0.04 −0.35 36
Poly-Si MSX60
NMAE(%) =
60 17.1 3.5 21.1 3.8 0.06 −0.37 36
1 N
N 1
Base case(i) Calculated(i) *100 Max1N (Base case(i))
(13)
where, N is the total number of samples. It measures the performance improvements achievable by using the hybrid approach with respect to the equivalent-circuit models SDM and DDM. 5. Results and discussion The results discussion is divided into two parts:
where, the base case represents the value extracted from PV module manufacturer datasheet and the calculated one is determined using the equivalent-circuit models. These errors are expressed for each i-th sample. A classification is introduced in order to identify which model to adopt for a given climate condition getting the best fit. So, a hybrid approach that combines the single and the double-diode models is suggested. It performs according to the climate variation and selects instantly one of the two models with the lowest error. This approach is explained in Fig. 3. Thereafter, an experimental validation is carried out by using real hourly values of titled irradiance G , cell temperature T and DC output powers (PDC ), recorded from 01/12/2017 to 23/12/2017 for a total of 529 samples, of two PV plants located in different climatic zones Mediterranean (Brindisi, Italy) and Semi-continental (Meknes, Morocco) with a nominal power of 2.2 kWp and 2 kWp, respectively. The reason behind using these two PV plants is to investigate the performances of the outlined models under various climate fluctuations. Fig. 4 shows the monthly averages of the horizontal plane irradiance and the ambient temperature over one year for each climate zone by using PVGIS website (“PVGIS,” n.d.). As observed in this figure, Semicontinental climate (SCC) presents higher irradiance and temperature than Mediterranean climate. The performances of the hybrid approach are assessed by the
- Comparison I-V curves, where the I-V characteristics for both MonoSi and Poly-Si PV panel given by the manufacturer datasheets and by both SDM and DDM are analyzed by a performance evaluation under different conditions of solar irradiance and temperature; - Implementation of the hybrid approach and its validation against real recorded data from two PV plants experiencing differences in hourly climatic variations, where the best combination of SDM and DDM is used. 5.1. Comparison of I-V curves The parameters of the single-diode models are determined using the method proposed by Chaibi et al. (2018) as given in Table. 2. The double-diode model parameters according to the method suggested by Ishaque et al. (2011) are displayed in Table 3. The photo-generated current is calculated using Eq. (4) and the extracted parameters are inserted in the PV output current equations {Eqs. (2) and (3)}.The corresponding I-V and P-V curves of the tested PV models are plotted to analyze the behavior of single-diode and double diode models. It is necessary to stress that the computed curves should agree well with those given by the manufacturer datasheets. Figs. 5–7 display the calculated and provided I-V characteristics from manufacturer datasheet of the Mono-Si and Poly-Si PV modules at various levels of irradiance and temperature. In addition, the corresponding RMSE calculated using Eq. (12) to investigate the fitting error between the estimated I-V curves and manufacturer is illustrated in Fig. 5. Low RMSE values demonstrate a good matching between the computed I-V curves for different levels of irradiance and fixed temperature (T = 25 °C) with the datasheet ones. Moreover, Chaibi et al. method seems to fit better for irradiance values above 600 W/m2. Otherwise, Ishaque et al. method gives better fitting for 200 W/m2 and 400 W/m2. In Fig. 6, I-V characteristics of the Mono-Si PV module are plotted for temperature in the range from 20 °C to 60 °C and a fixed irradiance at 1000 W/m2. It is observed that the provided I-V curves using both chosen methods fit well with manufacturer ones. However, a little difference is observed between Chaibi et al. method and manufacturer curves at the temperature value of 20 °C with a RMSE that exceeds 2%. In the same way, the plotted I-V curves of the Poly-Si PV module using Ishaque et al. and Chaibi et al. methods are evaluated. As displayed in Fig. 7, the obtained I-V curves using the examined methods and the manufacturer graphs are presented for various levels of temperature and a constant value of solar irradiance (G = 1000 W/m2). As can be seen, the Ishaque et al. I-V curves agrees well with the manufacturer for all temperature levels, except for 25 °C, Chaibi et al. method gives better results with a RMSE value less than 1%. Based on this, it seems that the single-diode model is more suitable to model the Mono-Si PV panels while the double-diode model is more appropriate for Poly-Si PV panels. Note that the I-V curves of the Poly-Si module for different irradiance levels are not provided due to the lack of information on the irradiance variation from the manufacturer. In order to compare the results achieved by two equivalent-circuit
Fig. 3. Diagram of the proposed hybrid approach. 1105
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35
Mediterranean Semi-Continental
250
25
Temperature [°C]
GHI [kWh/m2 ]
Semi-Continental
30
200
150
100
20 15 10
50
0 Jan
Mediterranean
5
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
0 Jan
Dec
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Fig. 4. The monthly average values of the horizontal plane irradiance and the ambient temperature for the Mediterranean and the semi-continental climate zone.
where the base case represents the extracted value from manufacturer curves and the calculated one corresponds to the computed values using the SDM and the DDM. The results are displayed in Fig. 8. Based on this categorization, Fig. 8(a) gives the relative errors of the PV panel output power for each class of irradiance and temperature. As noticed in Fig. 8(a), the SDM is more reliable to model the PV panel for lowtemperature ranges. However, the double-diode model shows good results in medium and high-temperature ranges. Furthermore, it can be seen that the double-diode model performs well with low and medium irradiances whereas the single-diode model is more convenient with high irradiance variations. Besides, the open-circuit voltage relative errors associated with the equivalent-circuit models of both PV panel technologies are presented for different levels of temperature and irradiance (see Fig. 8(b)). As can be observed, the single-diode model seems to be very appropriate to model the Mono-Si modules because of its lower error compared to the double-diode model. On the opposite side, the double-diode model presents a key solution to model the PolySi PV panel especially for medium and high levels of temperature. Moreover, the SDM presents good results for low irradiance, while the DDM is more suitable for medium and high ranges of irradiance. For the short-circuit current, the chosen equivalent-circuit models are compared under the same variation of climate conditions and this is performed for both PV panel technologies. As can be seen in Fig. 8(c), the relative errors demonstrate that the single-diode model is more appropriate to model the PV panel under the variation of irradiance. Also, this model is more suitable for temperature variation except for the Poly-Si technology in high temperature changes. Briefly, these curves
Table 2 Extracted parameters using Chaibi et al. method for the single-diode model.
Mono-Si Poly-Si
Rsh [Ω]
Rs [Ω]
Io [μA]
γ
6500 7000
0.1124 0.1880
4.8244 1.1174
1.7409 1.5079
Table 3 Extracted parameters using Ishaque et al. method for the double-diode model.
Mono-Si Poly-Si
Rsh [Ω]
Rs [Ω]
γ1
γ2
Io1 = Io2 [A]
144.24 166.58
0.34 0.47
1 1
1.2 1.2
4.7039 0.10−10 2.2324 0.10−10
models and the electrical parameters of the PV panel {Isc, Voc, Pm} extracted from manufacturer datasheet for different weather conditions, three intervals (Low, Medium and High) of irradiance and temperature were identified for classification. For the irradiance, the low values class is below 400 W/m2, the medium one is between 400 W/m2 and 800 W/m2 and the high values class is above 800 W/m2. For the temperature changes, the low variations are below 25 °C, the medium one is between 25 °C and 40 °C and the last class is for temperatures above 40 °C. As a first step, the manufacturer I-V curves are used to calculate the corresponding power for each variation of the climatic variable. Based on the climate variations, the relative error is computed using Eq. (11), Mono-Si SM55 1000 W/m
3.5
Current [A]
3
800 W/m
1.5 1
600 W/m
2
400 W/m
2
200 W/m
Chaibi et al. Ishaque et al.
1.5
2
2.5 2
2
Mono-Si SM55
2
Manufacturer data Chaibi et al. Ishaque et al.
RMSE [%]
4
1
0.5
2
0.5 0
0
5
10
Voltage [V]
15
20
25
0
200
400
600
Irradiance [W/m 2]
800
1000
Fig. 5. Comparison between the I-V characteristics using Chaibi et al., Ishaque et al. methods and manufacturer data related to the Mono-Si SM55 PV panel for different irradiances, T = 25 °C. 1106
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Mono-Si SM55
4 3.5
2 1.5
RMSE [%]
Current [A]
60 °C 50 °C 40 °C 30 °C 20 °C
Chaibi et al. Ishaque et al.
2
3 2.5
Mono-Si SM55
2.5
Manufacturer Chaibi et al. Ishaque et al.
1
1.5
1
0.5
0.5 0
0
5
10
Voltage [V]
15
20
0
25
20
30
40
Temperature [°C]
50
60
Fig. 6. Comparison of the I-V characteristics using Chaibi et al., Ishaque et al. methods and manufacturer data related to the Mono-Si SM55 PV panel for different temperatures, G = 1000 W/m2.
show that the low-irradiance levels engender high errors in the PV output power with a value of 8.40%. The lowest error closed to 0.10%. is presented at the short circuit currents. Such analysis enables the clustering of the performance for both single-diode and double-diode model in different range of irradiance and temperature according to the flowchart in Fig. 3. So, the classification tabulated in Table 4 proposes guidelines in selecting the model to be used in the simulation process with respect to the actual climate condition to achieve the lowest error.
of DC power based on the actual atmospheric condition of the two climate zones (Mediterranean and the Semi-continental climate). These powers are utilized to calculate the normalized absolute mean errors (see Eq. (13)) between experimental and calculated DC power using the hybrid approach for each one of the PV plants. These errors are displayed in Fig. 10. Fig. 10(a) shows the NMAE between the hybrid approach and the individual SDM and DDM. It is significantly high because of the fluctuated cloudy weather of the Mediterranean climate. Furthermore, a decreasing of the error up to 53.93% for irradiance variations and 49.52% for temperature variations can be achieved by the proposed approach. Fig. 10(b) shows that the NMAE related to the Semi-Continental PV plant, seems to be lower compared to Mediterranean PV plant, due to the sunny behavior of Meknes city. Moreover, in Continental climatic conditions the proposed approach can reduce the error by 21.04% and 14.66% due to irradiance and temperature variations, respectively.
5.2. Implementations of the hybrid approach and validation A comparison of predicted DC outputs and actual experimental data on an hourly basis is carried out. In order to investigate the impact of the climatic condition on the performance of both SDM and DDM, the experimental titled irradiance and modules temperature of two PV plants are utilized to compute the corresponding SDM and DDM powers. Thereafter, the obtained output data series is used to calculate the error between the real generated powers (base case) and the computed ones (SDM and DDM power) using the error formula given in Eq. (11). These errors are presented in Fig. 9. As can be observed in this figure, the mean error results support the findings of the previous subsection about the relationship between climate conditions and accuracy of single and double diode model which was summarized in Table 4. The previously classification introduced in Table 4 is used to build a hybrid approach which selects the most suitable model for computing
The paper evaluates the accuracy of the single-diode and the double-diode models as the most popular PV cell equivalent-circuit models under changes of solar irradiance and temperature. Two commercialized silicon PV module technologies, Monocrystalline SM55 and Polycrystalline MSX60, are considered to investigate the performance of two equivalent-circuit models with respect to the manufacturer data. The comparison demonstrates that the single-diode model seems to be more suitable for high fluctuations of irradiance. In turn, the double-
Poly-Si MSX60
5
Poly-Si MSX60
2
Manufacturer data Chaibi et al. Ishaque et al.
4
Chaibi et al. Ishaque et al.
1.5
T = 0°C T = 25°C T = 50°C T = 75°C
3
2
RMSE [%]
Current [A]
6. Conclusion
1
0.5
1
0
0
0
5
10
Voltage [V]
15
20
25
0
25
50
75
Temperature [°C]
Fig. 7. Comparison of the I-V characteristics using Chaibi et al., Ishaque et al. methods and manufacturer data related to the Poly-Si MSX60 PV panel for different temperatures, G = 1000 W/m2. 1107
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Output PV power
9
Low Temperature Medium Temperature High Temperature Low Irradiance Medium Irradiance High Irradiance
8 7
E rel [%]
6 5 4 3 2 1 0
Mono-Si (SDM)
Mono-Si (DDM)
Poly-Si (SDM)
Poly-Si (DDM)
Technology (ECM)
(a)
Open-circuit voltage
9
Low Temperature Medium Temperature High Temperature Low Irradiance Medium Irradiance High Irradiance
8 7
Low Temperature Medium Temperature High Temperature Low Irradiance Medium Irradiance High Irradiance
8 7 6
E rel [%]
E rel [%]
6 5 4
5 4
3
3
2
2
1
1
0
Short-circuit current
9
0 Mono-Si (SDM)
Mono-Si (DDM)
Poly-Si (SDM)
Mono-Si (SDM)
Poly-Si (DDM)
Technology (ECM)
Mono-Si (DDM)
Poly-Si (SDM)
Poly-Si (DDM)
Technology (ECM)
(b)
(c)
Fig. 8. Relative error of (a) PV output power, (b) open-circuit voltage, (c) short circuit current using the SDM and the DDM for different classes of solar irradiance and temperature. Base case: extracted values from Datasheet. 7
Table 4 Performance classification of the equivalent-circuit models for different levels of irradiance and temperature.
Medium
High
Low
Medium
High
DDM DDM SDM
DDM SDM SDM
SDM SDM SDM
SDM SDM SDM
DDM SDM SDM
DDM DDM DDM
[%]
5
Low
rel
Power Voltage Current
6
Temperature
E
Irradiance
Low Temperature Medium Temperature Low Irradiance Medium Irradiance High Irradiance
4 3 2
diode model is more reliable to predict the electrical parameters under the medium and low irradiance variations. Furthermore, the SDM performs well with low fluctuations of temperature and the DDM is more appropriate for medium and high variations. The results prove that the performance of the Photovoltaic Cell Equivalent-Circuit Models is influenced by solar irradiance and temperature. This suggests a new approach to enhance the accuracy of PV output prediction. The paper presents a more appropriate approach able to switch between the SDM and DDM according to the instantaneous variation of solar irradiance and temperature. The performance of the hybrid approach was assessed considering real data of two PV systems implemented in two sites of different climatic zones. An error analysis was performed between the proposed hybrid approach and the conventional SDM and DDM models.
1 0
SDM (MC)
DDM (MC)
SDM (SCC)
DDM (SCC)
ECM (Climate zone) Fig. 9. Normalized mean error of the SDM and the DDM under different classes of solar irradiance and temperature in Mediterranean climate (MC) and SemiContinental Climate (SCC) conditions.
The proposed approach can diminish the computing errors by up to 53.93% in the case of the cloudy weather conditions and up to 21.04% for sunny climatic conditions. 1108
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Mediterranean Climate
60
SDM DDM
50
NMAE [%]
NMAE [%]
40
30 20
30 20
10
10
Low
Medium
Irradiance Level
0
High
Temperature Level
Medium
Semi-Continental Climate
60
SDM DDM
50
SDM DDM
50
40
40
NMAE [%]
NMAE [%]
Low
(a)
Semi-Continental Climate
60
30 20 10 0
SDM DDM
50
40
0
Mediterranean Climate
60
30 20 10
Low
Medium
0
High
Irradiance Level
Low
Temperature Level
Medium
(b) Fig. 10. Relative error between the hybrid approach and the SDM and DDM of Mediterranean (a) and Semi-continental climate conditions (b) PV plant for different level of solar irradiance and temperature. Base case: Hybrid approach.
Acknowledgment
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