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Mismatch losses in PV power plants
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ScienceDirect Solar Energy 100 (2014) 42–49 www.elsevier.com/locate/solener
Mismatch losses in PV power plants Daniel Go´mez Lorente a, Simone Pedrazzi b,⇑, Gabriele Zini c, Alberto Dalla Rosa c, Paolo Tartarini b a
Department of Civil Engineering, Electrical Engineering Section (ETSICCP), University of Granada, Campus Fuentenueva, 18017 Granada, Spain b Department of Engineering “Enzo Ferrari”, University of Modena and Reggio Emilia, Via Vignolese 905, 41125 Modena, Italy c Amplio Solar s.r.l., Via Galliera 91, 40121 Bologna, Italy Received 5 September 2013; received in revised form 20 November 2013; accepted 22 November 2013
Communicated by: Associate Editor Nicola Romeo
Abstract In this paper, two different PV arrays have been simulated in order to quantify the electrical mismatch loss in each one of them. The simulations have been performed both in the standard condition (STC) and in the dynamic conditions which implement the meteorological data from the two different locations. Two methods have been applied to calculate the mismatch losses. The first one (the simplified method) assumes that all modules are at the tolerance limit and the second one (the I–V curve method) calculates the loss instead from the I–V characteristic of the modules or of the module series/parallel. Also an ordering procedure starting from the I mp value of the module has been evaluated. The results show a very small mismatch loss in the small PV plant of 40 modules, furthermore the ordering does not influence so much the loss in this case. Instead, the loss in the larger array of 320 modules is bigger and the ordering method presents a more significant influence. Ó 2013 Elsevier Ltd. All rights reserved. Keywords: Photovoltaics; Mismatch; PV array; Simulation
1. Introduction The depletion of fossil fuels and the pollution from conventional energy sources have required the exploitation of renewable energy sources, such as photovoltaic (PV). PV grid connected systems (PVGCSs) are used to supply the grid with energy produced by PV modules. The viability of a photovoltaic grid-connected plant (PVGCP) (Swanson, 2009) is determined by several factors (Swider et al., 2008), such as the initial capital cost of the system, the generation unit costs (Lee and Moore, 2010), the selling price of the generated energy and the PVGCP capital cost subsidization rate. Installation costs are decreasing due to the standardization of technology and rising demands, ⇑ Corresponding author. Tel.: +39 0592056229; fax: +39 0592056126.
E-mail address: [email protected] (S. Pedrazzi). 0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.11.026
but the premiums for the sale of electricity and the subsidies for the initial installation of PVGCSs are also becoming lower as well due to the inability of governments to maintain the initial level of high financial aid. Therefore, any project of PVGCSs which can optimize the energy output and reduce the cost of installation should be well-investigated and adopted. These PVGCs are composed of a large number of photovoltaic modules connected in series and parallel, forming a large number of strings and arrays (Elasser et al., 2010). In a central inverter architecture adopted in this work, all of these modules are connected to a power central DC–DC converter that performs maximum power point tracking (MPPT) and then to a DC–AC inverter to connect to the utility grid. These structures do not extract the maximum power that PV modules can provide due to several reasons, for
D.G. Lorente et al. / Solar Energy 100 (2014) 42–49
example the global maximum power point (MPP) is not the MPP for all individual modules in the cases of partial shading (Lehman, 2008), soiling and mismatches which lead to energy loss and power loss in the DC-distribution cables, etc. Advanced inverter setup are able to reduce these losses. For example, module-integrated PV and converter units is a good technique for achieving maximum power generation for mismatching and/or partially shaded PV modules. This technology increase power generation as much as 30%, compared to the conventional bypass diode structure (Chong and Zhang, 2013). The I–V mismatch occurring in PV arrays, which depends on tolerance, has dropped in the last ten years; the manufacturers of PV modules have refined the products by reducing the power tolerance from 10% down to 3% or less in particular cases (Spertino and Akilimali, 2009). Due to the changing weather conditions and the manufacture tolerance of the PV modules, the control system of the converter must place the system at the optimal power point. Nevertheless, the operating point of the generator on the I–V curve is dynamically modified; the MPPT must get the MPP at any moment and must maintain PVGCP power in the neighborhoods at this point and produce power with the higher efficiency (Abouobaida and Cherkaoui, 2012). Many MPP tracking (MPPT) methods have been developed and implemented (DeBrito et al., 2013; Esram and Chapman, 2007; Houssamo et al., 2013; Renaudineau et al., 2011). The methods vary in complexity, types of sensors required, convergence speed, cost, range of effectiveness, implementation hardware, popularity, and in other respects. The majority of these methods utilizes DC–DC converters (Taghvaee et al., 2013) of a PV module Ri that will change the apparent impedance value to match the RMPP. Many studies and many techniques (Iannone et al., 1997) have attempted to quantify the importance of mismatch loss in PV arrays (Charles et al., 1995; MacAlpine et al., 2012a,b; Spertino and Akilimali, 2009) and the power loss due this mismatch loss (Bucciarelli, 1979). In this paper we try to quantify the mismatch losses for different configurations of arrays, following different typologies. Forty standard PV modules have been selected to compose a PV array and the mismatch loss occurring in each different configuration has been quantified considering the characteristics of the modules in standard conditions. Furthermore, a comparison is conducted between the configuration of modules ordered by their I mp and that of modules randomly placed. The results obtained by different random disposition of the same modules are very similar because the power tolerance of the modules are less the 2% of the nominal power. Therefore, the random disposition do not modify substantially the simulation results. To estimate the mismatch losses, two different strategies have been adopted. First, we use the method described in Spertino and Akilimali (2009) where only two types of PV modules in the string are considered (the maximum and the minimal power PV modules), making this
43
approach more restrictive and obtaining higher mismatch loss with the calculation. The second method is to construct the I–V curve under standard test conditions (STC) with the data of V oc ; V mp ; I sc ; I mp ; Rs and Rsh (Pedrazzi et al., 2010). Using the curve of each PV module of the string we are able to obtain the operating voltage at STC for each module choosing the lowest current in the entire string. Similarly we proceed with the same method for the entire array. Similar to the previous methods, a further strategy has been applied to consider certain weather conditions. Manufacturers typically provide only limited operational data for photovoltaic panels, such as the open circuit voltage V oc , the short circuit current I sc , the maximum power current I mp and voltage V mp , the series resistance Rs , the shunt resistance Rsh , the temperature coefficients at open circuit voltage and short circuit current (bV oc and aI sc , respectively) and the nominal operating cell temperature NOCT. These data are available only at STC, for which the irradiance is 1000 W/m2, the cell temperature T c is 25 °C and the air mass is equal to AM ¼ 1:5. To study mismatch loss at operating conditions, we have followed the method introduced in DeSoto et al. (2006) using V oc ; V mp ; I sc and I mp . A mismatch loss study on an actual installation has been conducted on a real photovoltaic plant operating in the Italian region of Puglia. An annual simulation of both an ordered and a random PV array has been performed taking into account experimental solar irradiance, temperature and wind data. Using the method in DeSoto et al. (2006) mismatch losses were calculated in both cases. The rest of the paper is organized as follows: Section 2 gives the general information on PV modules, strings mismatch and arrays mismatch; Section 3 presents the use of new algorithms to quantify mismatch looses occurring in PVGCs; Section 4 discusses the experimental framework and presents the analysis of results, and finally in Section 5 we summarize our conclusions. 2. PV model for I–V curve simulation and mismatch losses 2.1. Solar module model The PV solar module converts the solar radiation into electrical power. We use the single diode model presented by Wenham et al. (2013) to simulate the I–V characteristics of each PV module. The equivalent circuit of the PV module is depicted in Fig. 1. Its I–V relationship is given by: V þ IRs V þ IRs I ¼ I L I 0 exp 1 ð1Þ a Rsh where I L is the photo current generated when the diode is radiated by solar energy, I 0 is the diode reverse saturation current, Rs is the series resistance, Rsh is the shunt resistance and a is a parameter that depends on diode technology and cell temperature. We need these five parameters in order to solve Eq. (1) to find the maximum power point. Manufactures provide only three operation point in
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D.G. Lorente et al. / Solar Energy 100 (2014) 42–49
of each module is referred to as mismatch losses (Gautam and Kaushika, 2001; Kaushika, 2003): P array ¼
n X P i mismatchlosses
ð5Þ
i¼1
Fig. 1. Single diode equivalent circuit for PV module characterization.
standard reference conditions for each module: maximum power, open circuit and short circuit. The value of Rs and Rsh at STC are also a given data. Starting from these informations, we implement a system of three equation Eq. (2). Solving this system, we find the I L ; I 0 and a values at STC. 8 I sc Rs I sc Rs > > I ¼ I I exp 1 sc L 0 > > a Rsh > > > < V oc 0 ¼ I L I 0 exp 1 VRshoc > a > > > > > V þ I mp Rs V mp þ I mp Rs > : I mp ¼ I L I 0 exp mp 1 a Rsh ð2Þ Thanks to the maximum power point tracker (MPPT) embedded in the system, the photovoltaic output solves the following system: 8 V mp þ I mp Rs V mp þ I mp Rs > > > I ¼ I I exp 1 mp L 0 > > a Rsh > > > > > dP dV dI dI > > ¼ I mp þ V mp ¼ I mp þ V mp ¼0 < dV P ¼P mp dV I¼I mp dV I¼I mp dV I¼I mp > > I0 V mp þ I mp Rs 1 > > exp > > dI Rs a a > > ¼ > > I R V þ I R Rs > dV 0 s mp mp s > I¼I mp : 1þ exp þ a a Rsh ð3Þ which gives the operating maximum power output I mp –V mp of the module. String voltage, string current, array voltage and array current have been calculated taking into account the mismatch loss discussed in the next paragraph. 2.2. Mismatch losses As we know, a PV array consists of a number N p of strings in parallel, while each of these strings is composed of a number N s of modules in series. Hence, the nominal power of the array should be: P array ¼
n X
Pi
ð4Þ
i¼1
where n ¼ N p N s and P i is the output power of each PV module. However, the power output of the array is always less than this value. The difference between the maximum power of the array and the sum of the maximum powers
Mismatch losses can come from permanent or temporary sources. The modules composing a same array usually have different characteristics even if they are manufactured with the same power rating. Mismatch losses are essentially caused by the dispersion of the modules electrical characteristics in an array. Indeed, generally modules within a same array do not have the exact same electrical properties because of the intrinsic module parameters. Aside from these manufacturing defects, degradation of the PV cells in the modules also occurs during their lifetime. Therefore, permanent sources include manufacturing tolerance, performance degradation, and module cracking. A temporary source of mismatch loss is a change in the irradiance level received by PV modules. The mismatch caused by the changes in irradiance level is called partial shading of the PV array. Furthermore, partial shading sources include those which are easy to predict and those that are not. Easy-to-predict sources include nearby PV arrays, buildings and trees;whereas clouds, soiling, and snow are examples of sources difficult to predict. In series-connected modules, the current flowing through each module is the same. In the case of a partially shaded string, the modules that cannot provide the string current are short-circuited by bypass diodes to enable proper string current flow and protect the shaded modules from operating in reverse bias voltages. But if the problem is manufacturing variability, the whole string current will be reduced to the lowest common. In a multistring system, the mismatch loss has a higher level of complexity because in addition to the current constraint in each series string, each parallel string must operate at the same voltage. 3. Methodologies for calculating mismatch losses on PV plants For the calculation of mismatch loss two different methods have been used and the results obtained by each of them have been compared. These methods are explained in the following. 3.1. Simplified method One new method to calculate mismatch loss is to assume that all modules are at the built-in tolerance limit (Spertino and Akilimali, 2009). In a string of N s modules, this method assumes that the modules with a maximum tolerance are N s1 , while all other modules N s N s1 have the minimum tolerance level. The mismatch loss for a string is therefore calculated by Eq. (6):
D.G. Lorente et al. / Solar Energy 100 (2014) 42–49
lmis;string ¼ l¼
N s1 Ns
2 2l 1 1þ
2 NNs1s þ 1
V oc 1 V mp
ð6Þ ð7Þ
where is the module maximum tolerance and l is the series-parameters. The typical values of the parameter l lie within the range of 0.2–0.45 for all the modules produced by silicon technologies. As one can see, this method is very restrictive since it assumes the worst case, namely the photovoltaic modules are at the tolerance limit. Obviously, with a high number of PV modules on the limit of tolerance, the mismatch loss will be greater. In the same way, we proceed to calculate the mismatch loss in N p strings in parallel. In this case, the number of strings at the maximum power limit will be N p1 , while the other N p N p1 strings will be considered as the minimum limit power strings. The mismatch losses value for a array is calculated by Eq. (8): N p1 1 2 2k 1þ Np lmis;array ¼ ð8Þ N p1 2 N p þ 1 k¼
I sc 1 I mp
45
Fig. 2. I–V curve of two different module.
ð9Þ
The typical results of the parallel-parameters k lie within the range of 0.06–0.3 for all modules manufactured with silicon technologies. 3.2. I–V curve method at STC This method to calculate mismatch loss in photovoltaic array is based on the displacement of the operating point for each PV module working at STC. This new operating point will be imposed by the lower current in the string. To perform this procedure, we must know the I–V curve of each module from the flash report. The I–V curve is calculated using the tabulated values of V mp ; V oc ; I sc ; I mp ; Rs and Rsh at STC. With these data, using the method shown by Pedrazzi et al. (2010), we can obtain the values of the photocurrent I L , concurrent dark ideality factor I 0 and diode factor a at STC. Then, using the method expressed by Jain and Kapoor (2004), King et al. (2004) and Wenham et al. (2013) we can calculate the I–V curve of the PV module. Once we have the I–V curve of each module in the string, we only need to impose the lowest current of all modules in the string to get the operating point of each one, and hence, the output voltage of each PV module, as it is shown in Figs. 2 and 3. Therefore, on the basis of the flash reports, the intrinsic I–V mismatch is expressed as relative power losses. Pn i¼1 P M;i P M;array Pn lmis ¼ ð10Þ i¼1 P M;i
Fig. 3. I–V curve method.
where P M;i is the maximum output power of the ith module (from the flash test) before the connection with the other modules, and P M;array is the actual maximum output power on the resulting I–V characteristic after the array connection. Similarly we proceed to calculate the mismatch losses in parallel strings. In this case we use the same procedure to calculate the curve I–V of the entire string. Once we have the curves of each string, we choose the lower voltage and current of the operating point for each string. 3.3. Dynamic method As it is known, the electrical power output from a photovoltaic panel depends on the incident solar radiation, the cell temperature, the solar incidence angle and the load resistance. Therefore, to make a better approximation of the mismatch loss in a photovoltaic array we must know the behavior of the PV module under certain weather
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D.G. Lorente et al. / Solar Energy 100 (2014) 42–49
conditions. In DeSoto et al. (2006) a study of the dependence of the parameters on operating conditions is done. The value of the parameters needed to construct the curve on operating conditions I–V can be obtained from the parameters V oc ; V mp ; I sc ; I mp ; Rs and Rsh on STC and the values of the irradiation and the cell temperature using equations above taking from DeSoto et al. (2006). IL ¼
G M ½I L;STC þ aI sc ðT T STC Þ GSTC M STC
ð11Þ
where I L is the light current, G is the absorbed solar irradiance, M is the air mass modifier, aI sc is the short circuit current temperature coefficient and T is the cell temperature all of them at operating conditions, while GSTC ; M STC ; I L;STC , and T STC are the values for reference conditions. Eg ¼ Eg;STC ½1 0:0002677ðT T STC Þ
ð12Þ
Rs ¼ Rs;STC
ð13Þ
Rsh ¼ Rsh;STC a ¼ aSTC
S STC S
T T STC
ð14Þ ð15Þ
Once we have the values of I L ; I 0 ; a; Rs and Rsh for operating conditions, we are able to calculate the I–V curve of each module for operating conditions. Then we can proceed to calculate the mismatch loss for the entire PV array as explained in the previous sections. Therefore, we adopt both the simplified and the I–V curve method to calculate the mismatch losses. To simulate the energy production, solar irradiance data on the considered PV plant have been taken into account and the cell temperature has been evaluated using the method proposed by King et al. (2004) as it considers also ambient temperature and wind speed. 4. Simulations and results In this section we discuss the elements and issues related to the simulated study. We provide the details of the modules chosen for the static simulations and the parameters of the possible configurations in Section 4.1. Section 4.2 shows the results of the dynamic simulations and subsequently Section 4.3 compares them and identifies the best classification. 4.1. Static simulation In this subsection, we summarize the mismatch losses in two PV power plants in STC condition. The first plant is composed by 40 modules of Yingli Solar YL225P-29b with a nominal power of 225 W. The maximum modules tolerance of the array is positive and equal to 1.8%, the minimum modules tolerance is 0.2%. Tables 1 and 2 summarize the mismatch losses. The losses have been calculated using the simplified method in Table 1 and the I–V curve method in Table 2. We consider different plant configuration using 1 MMPT or 2 MMPT. Furthermore both
randomly and systematically arranged I mp based PV arrays have been included in the study. The second plant consists of 320 modules of Yingli Solar YL225P-29b with a nominal power of 225 W. The maximum module tolerance of the array is positive and equal to 1.9% while the minimum module tolerance is 0%. This array is composed by 16 20-module strings. Both the simplified and static methods are applied to randomly and orderly arranged I mp based PV arrays. Tables 1 and 2 report the mismatch losses in this plant. 4.2. Dynamic simulation Simulations over a one-year long period with 1 h time step have been done for these arrays. We adopt the dynamic method to calculate the values of I L ; I 0 ; a; Rs and Rsh for every hour and use the simplified and I–V curve methods to evaluate the hourly mismatch losses. For the plant of 40 modules, we implement meteorological data from Albuquerque (Sandia, 2013). Randomly and systematically arranged PV arrays with different configuration have been considered, furthermore the results of these simulations have been shown in Tables 3 and 4. The meteorological data of “Pallara” are adopted for the plant of 320 modules. A schematic of the electric architecture of the large-scale PV power plant is shown in Fig. 4. The PV modules are connected in series to form strings; all strings are connected in parallel by means of connection boxes that host the necessary electrical protections to insure that no inverse current is running in a string as a result of malfunctions or partial shadings and to protect cables from over-currents in case of short-circuits. Within the connection boxes, DC circuit breakers give the user the possibility to disconnect the PV field even under solar irradiation, for maintenance or safety purposes, and surge protection devices (SPD) protect strings and the inverters from voltage surges resulting i.e. from lightings hitting the installation directly or indirectly. Downstream the inverter, on the AC side, a number of SPDs, circuit breakers, switches and relays protect the AC lines from over-currents and over-voltages. The transformer provides the voltage increase for low to medium voltage (MV); downstream, switches and fuses protect the cables and the grid from over-currents, while an electronic interface relay ensures that in case the grid be disconnected, the PV field does not inject energy in the grid itself for safety reasons. The large array here considered is depicted in Fig. 5. Again this applies to both randomly and orderly arranged PV arrays. 4.3. Analysis and comparison The simplified method gives a greater mismatch loss compared to the static one because it adopts the worst case. However, the difference between these methods is smaller in the bigger plant. In the static simulations, the mismatch loss is very small for the 40-module plant and the module ordering does not influence significantly loss values. The
D.G. Lorente et al. / Solar Energy 100 (2014) 42–49
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Table 1 Results of the static simulations with simplified method at STC of the 40 and 320 modules arrays. Module
Ordination
String
MMPT
lmis;series [%]
lmis;par [%]
lmis;tot [%]
40 40 40 40 40 40 40 40
Random Random Random Random I mp I mp I mp I mp
2 2 4 4 2 2 4 4
1 2 1 2 1 2 1 2
0.14 0.14 0.18 0.18 0.07 0.07 0.09 0.09
0.51 – 0.28 0.25 0.59 – 0.31 0.29
0.65 0.14 0.46 0.43 0.66 0.07 0.40 0.38
320 320
Random I mp
16 16
1 1
0.16 0.02
0.07 0.8
0.23 0.10
Table 2 Results of the static simulations with I–V curve method at STC of the 40 and 320 modules arrays. Module
MMPT
lmis;series [%]
lmis;par [%]
lmis;tot [%]
40 40 40 40 40 40 40 40
Random Random Random Random I mp I mp I mp I mp
Ordination
String 2 2 4 4 2 2 4 4
1 2 1 2 1 2 1 2
0.02 0.03 0.03 0.02 0.01 0.01 0.01 0.01
0.03 – 0.07 0.04 0.03 – 0.03 0.03
0.05 0.03 0.10 0.06 0.05 0.01 0.05 0.04
320 320
Random I mp
16 16
1 1
0.08 0.01
0.03 0.06
0.11 0.07
Table 3 Results of the dynamic simulations with simplified method of the 40 and 320 modules arrays. Module
MMPT
Enom [kW h]
Emis [kW h]
lmis;tot [%]
40 40 40 40 40 40 40 40
Random Random Random Random I mp I mp I mp I mp
Ordination
String 2 2 4 4 2 2 4 4
1 2 1 2 1 2 1 2
18,529 18,529 18,529 18,529 18,529 18,529 18,529 18,529
18,408 18,503 18,444 18,449 18,406 18,516 18,455 18,459
0.65 0.14 0.46 0.43 0.66 0.07 0.40 0.38
320 320
Random I mp
16 16
1 1
136,230 136,230
135,916 136,099
0.23 0.10
Table 4 Results of the dynamic simulations with I–V curve method of the 40 and 320 modules arrays. Module
MMPT
lmis;series [%]
lmis;par [%]
lmis;tot [%]
40 40 40 40 40 40 40 40
Random Random Random Random I mp I mp I mp I mp
Ordination
String 2 2 4 4 2 2 4 4
1 2 1 2 1 2 1 2
18,529 18,529 18,529 18,529 18,529 18,529 18,529 18,529
18,518 18,518 18,517 18,520 18,519 18,522 18,521 18,524
0.06 0.06 0.07 0.05 0.05 0.04 0.04 0.03
320 320
Random I mp
16 16
1 1
136,230 136,230
136,080 136,147
0.11 0.06
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D.G. Lorente et al. / Solar Energy 100 (2014) 42–49
Fig. 4. Electric architecture for the PV system (Zini and Tartarini, 2012).
Fig. 5. 320 Modules array schematic.
minimum value it is obtained for 2 string of 10 modules connected to 2 MPPT. In this case, the losses for the non-organized 40-module plant are calculated as 0.14% with the simplified method and 0.10% with the I–V curve method. Instead, for the aligned 40-module plant the minimum loss is 0.07% calculated with the simplified method and 0.05% with the I–V curve one. In the 320-module plant, the mismatch loss is higher compared to the small plant because of its parallel connection of 16 strings. Furthermore, the effect of how ordering the modules can reduce the loss is more noteworthy because the loss in the non-organized array is definitely higher. The minimum loss in the non-organized 320-module plant is 0.23% calculated by the simplified method and 0.11% by the I–V curve method. Instead, the minimum loss for the organized 320-module plant is calculated at 0.10% with the simplified method and 0.07% with the I–V curve method.
The simulations on the annual operation of the small plant show a negligible loss similar to that in the static simulation. Here, the results show a minimum value again reached for 2 string of 10 modules connected to 2 MPPT. The loss in the randomly arranged 320-module plant is 0.14% with the simplified calculation and 0.06% with I–V curve method. Instead the minimum loss for the arranged 320-module plant is 0.07% with the simplified calculation and 0.04% with I–V curve method. In the big plant, using the simplified approach we note that there is an average mismatch loss of 0.23% and 0.10% for non-arranged and ordered arrays respectively, and the numbers become 0.11% and 0.06% respectively using the simplified method. 5. Conclusions This analysis concerns electrical mismatch phenomena of the PV arrays. Two different arrays of 40 and 320
D.G. Lorente et al. / Solar Energy 100 (2014) 42–49
modules are studied and two different calculation methods compared. The more conservative method is the simplified approach which assumes that all modules are at the tolerance limit. The tolerance is small and reaches 1.9% of the nominal power of the module at STC. Therefore, the small array of 40 modules has a negligible loss while the 320-module array has a more significant mismatch loss at about 0.23% of the nominal power. Module ordering decreases this value to 0.10% and increases the calculated energy by about 83 kW h every year. For a large PV plant composed of 14 arrays of 320 modules with 1 MW of peak power, the energy increased by module ordering is equal to 1162 kW h, Therefore, a very small amount of energy is obtained with the module ordering compared to the economical effort invested to organize the module array. These calculations do not take into account shading, different inclination or soiling effect; an ulterior analysis can include these aspects as well as the power tolerance vs. electrical mismatch relation. In any case, the electrical mismatch loss in the modules is very small compared to the ohmic loss in the cables (from 0.5% to 1.5%) (Almonacid et al., 2011) and in the inverters (from 5% to 10%) (Durisch et al., 1998). Acknowledgements The authors wish to thank Pei-Shu Wu from Amplio Solar SrL for her assistance in editing the paper. References Abouobaida, H., Cherkaoui., M., 2012. Comparative study of maximum power point trackers for fast changing environmental conditions. In: Multimedia Computing and Systems (ICMCS) International Conference. Almonacid, F., Rus, C., Prez-Higueras, P., Hontoria, L., 2011. Calculation of the energy provided by a {PV} generator. Comparative study: conventional methods vs. artificial neural networks. Energy 36, 375– 384. Bucciarelli Jr., L.L., 1979. Power loss in photovoltaic arrays due to mismatch in cell characteristics. Sol. Energy 23, 277–288. Charles, E., Lehman, E., Zoellick, J., Pauletto, G., 1995. Effects of mismatch losses in photovoltaic arrays. Sol. Energy 54 (3), 165–171. Chong, B., Zhang, L., 2013. Controller design for integrated PV-converter modules under partial shading conditions. Sol. Energy 92, 123–138. DeBrito, M.A.G., Galotto, L., Sampaio, L.P., de Azevedo e Melo, G., Canesin, C.A., 2013. Evaluation of the main MPPT techniques for photovoltaic applications. IEEE Trans. Ind. Electron. 60 (3), 1156– 1167. DeSoto, W., Klein, S., Beckman, W., 2006. Improvement and validation of a model for photovoltaic array performance. Sol. Energy 80, 78–88. Durisch, W., Leutenegger, S., Tille, D., 1998. Comparison of small inverters for grid-independent photovoltaic systems. Renew. Energy 15, 585–589 (Renewable Energy Energy Efficiency, Policy and the Environment).
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Elasser, A., Agamy, M., Sabate, J., Steigerwald, R., Fisher, R., HarfmanTodorovic, M., 2010. A comparative study of central and distributed mppt architectures for megawatt utility and large scale commercial photovoltaic plants. In: IECON 36th Annual Conference on IEEE Industrial Electronics Society. Esram, T., Chapman, P.L., 2007. Comparison of photovoltaic array maximum power point tracking techniques. IEEE Trans. Energy Convers. 22 (2), 439–449. Gautam, N., Kaushika, N., 2001. Network analysis of fault-tolerant solar photovoltaic arrays. Sol. Energy Mater. Sol. Cells 69, 25–42. Houssamo, I., Locment, F., Sechilariu, M., 2013. Experimental analysis of impact of MPPT methods on energy efficiency for photovoltaic power systems. Electr. Power Energy Syst. 46, 98–107. Iannone, F., Noviello, G., Sarno, A., 1997. Monte Carlo techniques to analyse the electrical mismatch losses. Sol. Energy 62 (2), 85–92. Jain, A., Kapoor, A., 2004. Exact analytical solutions of the parameters of real solar cells using Lambert w-function. Sol. Energy Mater. Sol. Cells 81, 269–277. Kaushika, N., 2003. Energy yield simulations of interconnected solar PV arrays. IEEE Trans. Energy Convers. 18 (1), 127–134. King, D.L., Boyson, W.E., Kratochvil, J.A., 2004. Photovoltaic Array Performance Model. Sandia. Lee, K., Moore, J., 2010. Configuration optimization of a photovoltaic power plant in relation to cost and performance. In: ASME Conference 4th International Conference on Energy Sustainability. Lehman, D.N.B., 2008. An adaptive solar photovoltaic array using modelbased reconfiguration algorithm. IEEE Trans. Ind. Electron. 55 (7), 980–986. MacAlpine, S., Brandemuehl, M., Erickson, R., 2012a. Beyond the module model and into the array: mismatch in series strings. In: 38th IEEE Photovoltaic Specialists Conference (PVSC). MacAlpine, S., Deline, C., Erickson, R., Brandemuehl, M., 2012b. Module mismatch loss and recoverable power in unshaded PV installations. In: 38th IEEE Photovoltaic Specialists Conference. Pedrazzi, S., Zini, G., Tartarini, P., 2010. Complete modeling and software implementation of a virtual solar hydrogen hybrid system. Energy Convers. Manage. 51, 122–129. Renaudineau, H., Houari, A., Martin, J.P., Pierfederici, S., MeibodyTabar, F., Gerardin, B., 2011. A new approach in tracking maximum power under partially shaded conditions with consideration of converter losses. Sol. Energy 85 (11), 2580–2588. Sandia, 2013. PV Performance Modeling Collaborative.
ScienceDirect Solar Energy 100 (2014) 42–49 www.elsevier.com/locate/solener
Mismatch losses in PV power plants Daniel Go´mez Lorente a, Simone Pedrazzi b,⇑, Gabriele Zini c, Alberto Dalla Rosa c, Paolo Tartarini b a
Department of Civil Engineering, Electrical Engineering Section (ETSICCP), University of Granada, Campus Fuentenueva, 18017 Granada, Spain b Department of Engineering “Enzo Ferrari”, University of Modena and Reggio Emilia, Via Vignolese 905, 41125 Modena, Italy c Amplio Solar s.r.l., Via Galliera 91, 40121 Bologna, Italy Received 5 September 2013; received in revised form 20 November 2013; accepted 22 November 2013
Communicated by: Associate Editor Nicola Romeo
Abstract In this paper, two different PV arrays have been simulated in order to quantify the electrical mismatch loss in each one of them. The simulations have been performed both in the standard condition (STC) and in the dynamic conditions which implement the meteorological data from the two different locations. Two methods have been applied to calculate the mismatch losses. The first one (the simplified method) assumes that all modules are at the tolerance limit and the second one (the I–V curve method) calculates the loss instead from the I–V characteristic of the modules or of the module series/parallel. Also an ordering procedure starting from the I mp value of the module has been evaluated. The results show a very small mismatch loss in the small PV plant of 40 modules, furthermore the ordering does not influence so much the loss in this case. Instead, the loss in the larger array of 320 modules is bigger and the ordering method presents a more significant influence. Ó 2013 Elsevier Ltd. All rights reserved. Keywords: Photovoltaics; Mismatch; PV array; Simulation
1. Introduction The depletion of fossil fuels and the pollution from conventional energy sources have required the exploitation of renewable energy sources, such as photovoltaic (PV). PV grid connected systems (PVGCSs) are used to supply the grid with energy produced by PV modules. The viability of a photovoltaic grid-connected plant (PVGCP) (Swanson, 2009) is determined by several factors (Swider et al., 2008), such as the initial capital cost of the system, the generation unit costs (Lee and Moore, 2010), the selling price of the generated energy and the PVGCP capital cost subsidization rate. Installation costs are decreasing due to the standardization of technology and rising demands, ⇑ Corresponding author. Tel.: +39 0592056229; fax: +39 0592056126.
E-mail address: [email protected] (S. Pedrazzi). 0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.11.026
but the premiums for the sale of electricity and the subsidies for the initial installation of PVGCSs are also becoming lower as well due to the inability of governments to maintain the initial level of high financial aid. Therefore, any project of PVGCSs which can optimize the energy output and reduce the cost of installation should be well-investigated and adopted. These PVGCs are composed of a large number of photovoltaic modules connected in series and parallel, forming a large number of strings and arrays (Elasser et al., 2010). In a central inverter architecture adopted in this work, all of these modules are connected to a power central DC–DC converter that performs maximum power point tracking (MPPT) and then to a DC–AC inverter to connect to the utility grid. These structures do not extract the maximum power that PV modules can provide due to several reasons, for
D.G. Lorente et al. / Solar Energy 100 (2014) 42–49
example the global maximum power point (MPP) is not the MPP for all individual modules in the cases of partial shading (Lehman, 2008), soiling and mismatches which lead to energy loss and power loss in the DC-distribution cables, etc. Advanced inverter setup are able to reduce these losses. For example, module-integrated PV and converter units is a good technique for achieving maximum power generation for mismatching and/or partially shaded PV modules. This technology increase power generation as much as 30%, compared to the conventional bypass diode structure (Chong and Zhang, 2013). The I–V mismatch occurring in PV arrays, which depends on tolerance, has dropped in the last ten years; the manufacturers of PV modules have refined the products by reducing the power tolerance from 10% down to 3% or less in particular cases (Spertino and Akilimali, 2009). Due to the changing weather conditions and the manufacture tolerance of the PV modules, the control system of the converter must place the system at the optimal power point. Nevertheless, the operating point of the generator on the I–V curve is dynamically modified; the MPPT must get the MPP at any moment and must maintain PVGCP power in the neighborhoods at this point and produce power with the higher efficiency (Abouobaida and Cherkaoui, 2012). Many MPP tracking (MPPT) methods have been developed and implemented (DeBrito et al., 2013; Esram and Chapman, 2007; Houssamo et al., 2013; Renaudineau et al., 2011). The methods vary in complexity, types of sensors required, convergence speed, cost, range of effectiveness, implementation hardware, popularity, and in other respects. The majority of these methods utilizes DC–DC converters (Taghvaee et al., 2013) of a PV module Ri that will change the apparent impedance value to match the RMPP. Many studies and many techniques (Iannone et al., 1997) have attempted to quantify the importance of mismatch loss in PV arrays (Charles et al., 1995; MacAlpine et al., 2012a,b; Spertino and Akilimali, 2009) and the power loss due this mismatch loss (Bucciarelli, 1979). In this paper we try to quantify the mismatch losses for different configurations of arrays, following different typologies. Forty standard PV modules have been selected to compose a PV array and the mismatch loss occurring in each different configuration has been quantified considering the characteristics of the modules in standard conditions. Furthermore, a comparison is conducted between the configuration of modules ordered by their I mp and that of modules randomly placed. The results obtained by different random disposition of the same modules are very similar because the power tolerance of the modules are less the 2% of the nominal power. Therefore, the random disposition do not modify substantially the simulation results. To estimate the mismatch losses, two different strategies have been adopted. First, we use the method described in Spertino and Akilimali (2009) where only two types of PV modules in the string are considered (the maximum and the minimal power PV modules), making this
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approach more restrictive and obtaining higher mismatch loss with the calculation. The second method is to construct the I–V curve under standard test conditions (STC) with the data of V oc ; V mp ; I sc ; I mp ; Rs and Rsh (Pedrazzi et al., 2010). Using the curve of each PV module of the string we are able to obtain the operating voltage at STC for each module choosing the lowest current in the entire string. Similarly we proceed with the same method for the entire array. Similar to the previous methods, a further strategy has been applied to consider certain weather conditions. Manufacturers typically provide only limited operational data for photovoltaic panels, such as the open circuit voltage V oc , the short circuit current I sc , the maximum power current I mp and voltage V mp , the series resistance Rs , the shunt resistance Rsh , the temperature coefficients at open circuit voltage and short circuit current (bV oc and aI sc , respectively) and the nominal operating cell temperature NOCT. These data are available only at STC, for which the irradiance is 1000 W/m2, the cell temperature T c is 25 °C and the air mass is equal to AM ¼ 1:5. To study mismatch loss at operating conditions, we have followed the method introduced in DeSoto et al. (2006) using V oc ; V mp ; I sc and I mp . A mismatch loss study on an actual installation has been conducted on a real photovoltaic plant operating in the Italian region of Puglia. An annual simulation of both an ordered and a random PV array has been performed taking into account experimental solar irradiance, temperature and wind data. Using the method in DeSoto et al. (2006) mismatch losses were calculated in both cases. The rest of the paper is organized as follows: Section 2 gives the general information on PV modules, strings mismatch and arrays mismatch; Section 3 presents the use of new algorithms to quantify mismatch looses occurring in PVGCs; Section 4 discusses the experimental framework and presents the analysis of results, and finally in Section 5 we summarize our conclusions. 2. PV model for I–V curve simulation and mismatch losses 2.1. Solar module model The PV solar module converts the solar radiation into electrical power. We use the single diode model presented by Wenham et al. (2013) to simulate the I–V characteristics of each PV module. The equivalent circuit of the PV module is depicted in Fig. 1. Its I–V relationship is given by: V þ IRs V þ IRs I ¼ I L I 0 exp 1 ð1Þ a Rsh where I L is the photo current generated when the diode is radiated by solar energy, I 0 is the diode reverse saturation current, Rs is the series resistance, Rsh is the shunt resistance and a is a parameter that depends on diode technology and cell temperature. We need these five parameters in order to solve Eq. (1) to find the maximum power point. Manufactures provide only three operation point in
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of each module is referred to as mismatch losses (Gautam and Kaushika, 2001; Kaushika, 2003): P array ¼
n X P i mismatchlosses
ð5Þ
i¼1
Fig. 1. Single diode equivalent circuit for PV module characterization.
standard reference conditions for each module: maximum power, open circuit and short circuit. The value of Rs and Rsh at STC are also a given data. Starting from these informations, we implement a system of three equation Eq. (2). Solving this system, we find the I L ; I 0 and a values at STC. 8 I sc Rs I sc Rs > > I ¼ I I exp 1 sc L 0 > > a Rsh > > > < V oc 0 ¼ I L I 0 exp 1 VRshoc > a > > > > > V þ I mp Rs V mp þ I mp Rs > : I mp ¼ I L I 0 exp mp 1 a Rsh ð2Þ Thanks to the maximum power point tracker (MPPT) embedded in the system, the photovoltaic output solves the following system: 8 V mp þ I mp Rs V mp þ I mp Rs > > > I ¼ I I exp 1 mp L 0 > > a Rsh > > > > > dP dV dI dI > > ¼ I mp þ V mp ¼ I mp þ V mp ¼0 < dV P ¼P mp dV I¼I mp dV I¼I mp dV I¼I mp > > I0 V mp þ I mp Rs 1 > > exp > > dI Rs a a > > ¼ > > I R V þ I R Rs > dV 0 s mp mp s > I¼I mp : 1þ exp þ a a Rsh ð3Þ which gives the operating maximum power output I mp –V mp of the module. String voltage, string current, array voltage and array current have been calculated taking into account the mismatch loss discussed in the next paragraph. 2.2. Mismatch losses As we know, a PV array consists of a number N p of strings in parallel, while each of these strings is composed of a number N s of modules in series. Hence, the nominal power of the array should be: P array ¼
n X
Pi
ð4Þ
i¼1
where n ¼ N p N s and P i is the output power of each PV module. However, the power output of the array is always less than this value. The difference between the maximum power of the array and the sum of the maximum powers
Mismatch losses can come from permanent or temporary sources. The modules composing a same array usually have different characteristics even if they are manufactured with the same power rating. Mismatch losses are essentially caused by the dispersion of the modules electrical characteristics in an array. Indeed, generally modules within a same array do not have the exact same electrical properties because of the intrinsic module parameters. Aside from these manufacturing defects, degradation of the PV cells in the modules also occurs during their lifetime. Therefore, permanent sources include manufacturing tolerance, performance degradation, and module cracking. A temporary source of mismatch loss is a change in the irradiance level received by PV modules. The mismatch caused by the changes in irradiance level is called partial shading of the PV array. Furthermore, partial shading sources include those which are easy to predict and those that are not. Easy-to-predict sources include nearby PV arrays, buildings and trees;whereas clouds, soiling, and snow are examples of sources difficult to predict. In series-connected modules, the current flowing through each module is the same. In the case of a partially shaded string, the modules that cannot provide the string current are short-circuited by bypass diodes to enable proper string current flow and protect the shaded modules from operating in reverse bias voltages. But if the problem is manufacturing variability, the whole string current will be reduced to the lowest common. In a multistring system, the mismatch loss has a higher level of complexity because in addition to the current constraint in each series string, each parallel string must operate at the same voltage. 3. Methodologies for calculating mismatch losses on PV plants For the calculation of mismatch loss two different methods have been used and the results obtained by each of them have been compared. These methods are explained in the following. 3.1. Simplified method One new method to calculate mismatch loss is to assume that all modules are at the built-in tolerance limit (Spertino and Akilimali, 2009). In a string of N s modules, this method assumes that the modules with a maximum tolerance are N s1 , while all other modules N s N s1 have the minimum tolerance level. The mismatch loss for a string is therefore calculated by Eq. (6):
D.G. Lorente et al. / Solar Energy 100 (2014) 42–49
lmis;string ¼ l¼
N s1 Ns
2 2l 1 1þ
2 NNs1s þ 1
V oc 1 V mp
ð6Þ ð7Þ
where is the module maximum tolerance and l is the series-parameters. The typical values of the parameter l lie within the range of 0.2–0.45 for all the modules produced by silicon technologies. As one can see, this method is very restrictive since it assumes the worst case, namely the photovoltaic modules are at the tolerance limit. Obviously, with a high number of PV modules on the limit of tolerance, the mismatch loss will be greater. In the same way, we proceed to calculate the mismatch loss in N p strings in parallel. In this case, the number of strings at the maximum power limit will be N p1 , while the other N p N p1 strings will be considered as the minimum limit power strings. The mismatch losses value for a array is calculated by Eq. (8): N p1 1 2 2k 1þ Np lmis;array ¼ ð8Þ N p1 2 N p þ 1 k¼
I sc 1 I mp
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Fig. 2. I–V curve of two different module.
ð9Þ
The typical results of the parallel-parameters k lie within the range of 0.06–0.3 for all modules manufactured with silicon technologies. 3.2. I–V curve method at STC This method to calculate mismatch loss in photovoltaic array is based on the displacement of the operating point for each PV module working at STC. This new operating point will be imposed by the lower current in the string. To perform this procedure, we must know the I–V curve of each module from the flash report. The I–V curve is calculated using the tabulated values of V mp ; V oc ; I sc ; I mp ; Rs and Rsh at STC. With these data, using the method shown by Pedrazzi et al. (2010), we can obtain the values of the photocurrent I L , concurrent dark ideality factor I 0 and diode factor a at STC. Then, using the method expressed by Jain and Kapoor (2004), King et al. (2004) and Wenham et al. (2013) we can calculate the I–V curve of the PV module. Once we have the I–V curve of each module in the string, we only need to impose the lowest current of all modules in the string to get the operating point of each one, and hence, the output voltage of each PV module, as it is shown in Figs. 2 and 3. Therefore, on the basis of the flash reports, the intrinsic I–V mismatch is expressed as relative power losses. Pn i¼1 P M;i P M;array Pn lmis ¼ ð10Þ i¼1 P M;i
Fig. 3. I–V curve method.
where P M;i is the maximum output power of the ith module (from the flash test) before the connection with the other modules, and P M;array is the actual maximum output power on the resulting I–V characteristic after the array connection. Similarly we proceed to calculate the mismatch losses in parallel strings. In this case we use the same procedure to calculate the curve I–V of the entire string. Once we have the curves of each string, we choose the lower voltage and current of the operating point for each string. 3.3. Dynamic method As it is known, the electrical power output from a photovoltaic panel depends on the incident solar radiation, the cell temperature, the solar incidence angle and the load resistance. Therefore, to make a better approximation of the mismatch loss in a photovoltaic array we must know the behavior of the PV module under certain weather
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conditions. In DeSoto et al. (2006) a study of the dependence of the parameters on operating conditions is done. The value of the parameters needed to construct the curve on operating conditions I–V can be obtained from the parameters V oc ; V mp ; I sc ; I mp ; Rs and Rsh on STC and the values of the irradiation and the cell temperature using equations above taking from DeSoto et al. (2006). IL ¼
G M ½I L;STC þ aI sc ðT T STC Þ GSTC M STC
ð11Þ
where I L is the light current, G is the absorbed solar irradiance, M is the air mass modifier, aI sc is the short circuit current temperature coefficient and T is the cell temperature all of them at operating conditions, while GSTC ; M STC ; I L;STC , and T STC are the values for reference conditions. Eg ¼ Eg;STC ½1 0:0002677ðT T STC Þ
ð12Þ
Rs ¼ Rs;STC
ð13Þ
Rsh ¼ Rsh;STC a ¼ aSTC
S STC S
T T STC
ð14Þ ð15Þ
Once we have the values of I L ; I 0 ; a; Rs and Rsh for operating conditions, we are able to calculate the I–V curve of each module for operating conditions. Then we can proceed to calculate the mismatch loss for the entire PV array as explained in the previous sections. Therefore, we adopt both the simplified and the I–V curve method to calculate the mismatch losses. To simulate the energy production, solar irradiance data on the considered PV plant have been taken into account and the cell temperature has been evaluated using the method proposed by King et al. (2004) as it considers also ambient temperature and wind speed. 4. Simulations and results In this section we discuss the elements and issues related to the simulated study. We provide the details of the modules chosen for the static simulations and the parameters of the possible configurations in Section 4.1. Section 4.2 shows the results of the dynamic simulations and subsequently Section 4.3 compares them and identifies the best classification. 4.1. Static simulation In this subsection, we summarize the mismatch losses in two PV power plants in STC condition. The first plant is composed by 40 modules of Yingli Solar YL225P-29b with a nominal power of 225 W. The maximum modules tolerance of the array is positive and equal to 1.8%, the minimum modules tolerance is 0.2%. Tables 1 and 2 summarize the mismatch losses. The losses have been calculated using the simplified method in Table 1 and the I–V curve method in Table 2. We consider different plant configuration using 1 MMPT or 2 MMPT. Furthermore both
randomly and systematically arranged I mp based PV arrays have been included in the study. The second plant consists of 320 modules of Yingli Solar YL225P-29b with a nominal power of 225 W. The maximum module tolerance of the array is positive and equal to 1.9% while the minimum module tolerance is 0%. This array is composed by 16 20-module strings. Both the simplified and static methods are applied to randomly and orderly arranged I mp based PV arrays. Tables 1 and 2 report the mismatch losses in this plant. 4.2. Dynamic simulation Simulations over a one-year long period with 1 h time step have been done for these arrays. We adopt the dynamic method to calculate the values of I L ; I 0 ; a; Rs and Rsh for every hour and use the simplified and I–V curve methods to evaluate the hourly mismatch losses. For the plant of 40 modules, we implement meteorological data from Albuquerque (Sandia, 2013). Randomly and systematically arranged PV arrays with different configuration have been considered, furthermore the results of these simulations have been shown in Tables 3 and 4. The meteorological data of “Pallara” are adopted for the plant of 320 modules. A schematic of the electric architecture of the large-scale PV power plant is shown in Fig. 4. The PV modules are connected in series to form strings; all strings are connected in parallel by means of connection boxes that host the necessary electrical protections to insure that no inverse current is running in a string as a result of malfunctions or partial shadings and to protect cables from over-currents in case of short-circuits. Within the connection boxes, DC circuit breakers give the user the possibility to disconnect the PV field even under solar irradiation, for maintenance or safety purposes, and surge protection devices (SPD) protect strings and the inverters from voltage surges resulting i.e. from lightings hitting the installation directly or indirectly. Downstream the inverter, on the AC side, a number of SPDs, circuit breakers, switches and relays protect the AC lines from over-currents and over-voltages. The transformer provides the voltage increase for low to medium voltage (MV); downstream, switches and fuses protect the cables and the grid from over-currents, while an electronic interface relay ensures that in case the grid be disconnected, the PV field does not inject energy in the grid itself for safety reasons. The large array here considered is depicted in Fig. 5. Again this applies to both randomly and orderly arranged PV arrays. 4.3. Analysis and comparison The simplified method gives a greater mismatch loss compared to the static one because it adopts the worst case. However, the difference between these methods is smaller in the bigger plant. In the static simulations, the mismatch loss is very small for the 40-module plant and the module ordering does not influence significantly loss values. The
D.G. Lorente et al. / Solar Energy 100 (2014) 42–49
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Table 1 Results of the static simulations with simplified method at STC of the 40 and 320 modules arrays. Module
Ordination
String
MMPT
lmis;series [%]
lmis;par [%]
lmis;tot [%]
40 40 40 40 40 40 40 40
Random Random Random Random I mp I mp I mp I mp
2 2 4 4 2 2 4 4
1 2 1 2 1 2 1 2
0.14 0.14 0.18 0.18 0.07 0.07 0.09 0.09
0.51 – 0.28 0.25 0.59 – 0.31 0.29
0.65 0.14 0.46 0.43 0.66 0.07 0.40 0.38
320 320
Random I mp
16 16
1 1
0.16 0.02
0.07 0.8
0.23 0.10
Table 2 Results of the static simulations with I–V curve method at STC of the 40 and 320 modules arrays. Module
MMPT
lmis;series [%]
lmis;par [%]
lmis;tot [%]
40 40 40 40 40 40 40 40
Random Random Random Random I mp I mp I mp I mp
Ordination
String 2 2 4 4 2 2 4 4
1 2 1 2 1 2 1 2
0.02 0.03 0.03 0.02 0.01 0.01 0.01 0.01
0.03 – 0.07 0.04 0.03 – 0.03 0.03
0.05 0.03 0.10 0.06 0.05 0.01 0.05 0.04
320 320
Random I mp
16 16
1 1
0.08 0.01
0.03 0.06
0.11 0.07
Table 3 Results of the dynamic simulations with simplified method of the 40 and 320 modules arrays. Module
MMPT
Enom [kW h]
Emis [kW h]
lmis;tot [%]
40 40 40 40 40 40 40 40
Random Random Random Random I mp I mp I mp I mp
Ordination
String 2 2 4 4 2 2 4 4
1 2 1 2 1 2 1 2
18,529 18,529 18,529 18,529 18,529 18,529 18,529 18,529
18,408 18,503 18,444 18,449 18,406 18,516 18,455 18,459
0.65 0.14 0.46 0.43 0.66 0.07 0.40 0.38
320 320
Random I mp
16 16
1 1
136,230 136,230
135,916 136,099
0.23 0.10
Table 4 Results of the dynamic simulations with I–V curve method of the 40 and 320 modules arrays. Module
MMPT
lmis;series [%]
lmis;par [%]
lmis;tot [%]
40 40 40 40 40 40 40 40
Random Random Random Random I mp I mp I mp I mp
Ordination
String 2 2 4 4 2 2 4 4
1 2 1 2 1 2 1 2
18,529 18,529 18,529 18,529 18,529 18,529 18,529 18,529
18,518 18,518 18,517 18,520 18,519 18,522 18,521 18,524
0.06 0.06 0.07 0.05 0.05 0.04 0.04 0.03
320 320
Random I mp
16 16
1 1
136,230 136,230
136,080 136,147
0.11 0.06
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D.G. Lorente et al. / Solar Energy 100 (2014) 42–49
Fig. 4. Electric architecture for the PV system (Zini and Tartarini, 2012).
Fig. 5. 320 Modules array schematic.
minimum value it is obtained for 2 string of 10 modules connected to 2 MPPT. In this case, the losses for the non-organized 40-module plant are calculated as 0.14% with the simplified method and 0.10% with the I–V curve method. Instead, for the aligned 40-module plant the minimum loss is 0.07% calculated with the simplified method and 0.05% with the I–V curve one. In the 320-module plant, the mismatch loss is higher compared to the small plant because of its parallel connection of 16 strings. Furthermore, the effect of how ordering the modules can reduce the loss is more noteworthy because the loss in the non-organized array is definitely higher. The minimum loss in the non-organized 320-module plant is 0.23% calculated by the simplified method and 0.11% by the I–V curve method. Instead, the minimum loss for the organized 320-module plant is calculated at 0.10% with the simplified method and 0.07% with the I–V curve method.
The simulations on the annual operation of the small plant show a negligible loss similar to that in the static simulation. Here, the results show a minimum value again reached for 2 string of 10 modules connected to 2 MPPT. The loss in the randomly arranged 320-module plant is 0.14% with the simplified calculation and 0.06% with I–V curve method. Instead the minimum loss for the arranged 320-module plant is 0.07% with the simplified calculation and 0.04% with I–V curve method. In the big plant, using the simplified approach we note that there is an average mismatch loss of 0.23% and 0.10% for non-arranged and ordered arrays respectively, and the numbers become 0.11% and 0.06% respectively using the simplified method. 5. Conclusions This analysis concerns electrical mismatch phenomena of the PV arrays. Two different arrays of 40 and 320
D.G. Lorente et al. / Solar Energy 100 (2014) 42–49
modules are studied and two different calculation methods compared. The more conservative method is the simplified approach which assumes that all modules are at the tolerance limit. The tolerance is small and reaches 1.9% of the nominal power of the module at STC. Therefore, the small array of 40 modules has a negligible loss while the 320-module array has a more significant mismatch loss at about 0.23% of the nominal power. Module ordering decreases this value to 0.10% and increases the calculated energy by about 83 kW h every year. For a large PV plant composed of 14 arrays of 320 modules with 1 MW of peak power, the energy increased by module ordering is equal to 1162 kW h, Therefore, a very small amount of energy is obtained with the module ordering compared to the economical effort invested to organize the module array. These calculations do not take into account shading, different inclination or soiling effect; an ulterior analysis can include these aspects as well as the power tolerance vs. electrical mismatch relation. In any case, the electrical mismatch loss in the modules is very small compared to the ohmic loss in the cables (from 0.5% to 1.5%) (Almonacid et al., 2011) and in the inverters (from 5% to 10%) (Durisch et al., 1998). Acknowledgements The authors wish to thank Pei-Shu Wu from Amplio Solar SrL for her assistance in editing the paper. References Abouobaida, H., Cherkaoui., M., 2012. Comparative study of maximum power point trackers for fast changing environmental conditions. In: Multimedia Computing and Systems (ICMCS) International Conference. Almonacid, F., Rus, C., Prez-Higueras, P., Hontoria, L., 2011. Calculation of the energy provided by a {PV} generator. Comparative study: conventional methods vs. artificial neural networks. Energy 36, 375– 384. Bucciarelli Jr., L.L., 1979. Power loss in photovoltaic arrays due to mismatch in cell characteristics. Sol. Energy 23, 277–288. Charles, E., Lehman, E., Zoellick, J., Pauletto, G., 1995. Effects of mismatch losses in photovoltaic arrays. Sol. Energy 54 (3), 165–171. Chong, B., Zhang, L., 2013. Controller design for integrated PV-converter modules under partial shading conditions. Sol. Energy 92, 123–138. DeBrito, M.A.G., Galotto, L., Sampaio, L.P., de Azevedo e Melo, G., Canesin, C.A., 2013. Evaluation of the main MPPT techniques for photovoltaic applications. IEEE Trans. Ind. Electron. 60 (3), 1156– 1167. DeSoto, W., Klein, S., Beckman, W., 2006. Improvement and validation of a model for photovoltaic array performance. Sol. Energy 80, 78–88. Durisch, W., Leutenegger, S., Tille, D., 1998. Comparison of small inverters for grid-independent photovoltaic systems. Renew. Energy 15, 585–589 (Renewable Energy Energy Efficiency, Policy and the Environment).
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