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Photovoltaic fault detection using a parameter based model
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Solar Energy 96 (2013) 96–102 www.elsevier.com/locate/solener
Photovoltaic fault detection using a parameter based model Yihua Hu a, Bin Gao b,⇑, Xueguan Song c, Gui Yun Tian b, Kongjing Li c, Xiangning He a b
a College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China c School of Electrical and Electronic Engineering, Newcastle University, England, United Kingdom
Received 4 February 2013; received in revised form 28 June 2013; accepted 8 July 2013
Communicated by: Associate Editor Elias Stefanakos
Abstract Photovoltaic (PV) modules convert part of incident solar energy into electrical energy for commercial applications, with the rest being transferred to heat energy. The modelling of PV modules plays an important role in the fault diagnosis of a PV array. The object of this paper is to develop a parameter based model of a PV module. This model is sequentially coupled with an electrical model and energy balance equation. In order to establish the parameter based model, key parameters including the total effective solar energy, total heat exchange coefficient and ambient temperature are calculated from two working points on PV module along with the corresponding temperature from a thermal camera. Using the developed model, a fault diagnosis method based on the model is illustrated. Finally, model validation is carried out by the experiments. Ó 2013 Elsevier Ltd. All rights reserved. Keywords: PV module; Parameter based model; Fault diagnosis; Model validation
1. Introduction Solar energy is a green and renewable energy source, which has been widely exploited in grid-connected systems, PV-pumps and stand-alone systems. With most system requirements, a large number of PV modules are required to be connected in series to form a PV string. This enables the overall PV array to obtain a high input voltage whilst simultaneously producing high output power. A PV array is usually subject to faults in real application, which may significantly decrease power generation efficiency and reduce the array’s lifespan. As a result, fault detection is crucial and necessary for the PV array maintenance. The PV array fault is defined as the condition that those who causes decrement of PV array power output. ⇑ Corresponding author at: School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China. E-mail address: [email protected] (B. Gao).
0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.07.004
There are two types of fault, the first one is recoverable fault, and the second one is unrecoverable fault. The recoverable fault caused by clouds/dust can be recovered by human maintains; while the PV degradation and/or micro-cracks which is called unrecoverable fault cannot be recovered. In this paper, the recoverable fault is main subject. In general, a PV array requires modules to be spread across a large physical area, which will unavoidably result in the PV array suffering from non-uniform illumination when shadow or dust casts across the modules (Chouder and Silvestre, 2010; Simon and Meyer, 2010; Zegaoui et al., 2012; Takashima et al., 2009; Gautam and Kaushika,2002; Tonui and Tripanagnostopoulos, 2007; Ishaque et al., 2011a,b; Munoz et al., 2011). If a PV array is under non-uniform illumination, the transferred electricity drops sharply (Armstrong and Hurley, 2010; Patel and Agarwal, 2008; Hu et al., 2012; Bruendlinger et al., 2006) which lead to output power and generation efficiency considerably below the acceptable level, and the unrecoverable fault PV module may occurs in the long time fault condition.
Y. Hu et al. / Solar Energy 96 (2013) 96–102
Therefore, it has become important to build a fault diagnosis system to detect such PV array fault. Currently, thermal cameras become one of the main tools to perform PV array fault diagnosis. Many researchers (Kaplani, 2013; Acciani et al., 2010; Buerhopa et al., 2012; Parinya et al., 2007; Krenzinger and Andrade, 2007; Simon and Meyer, 2010; Ko¨ntges et al., 2011; Trupke et al., 2006; Kasemann et al., 2006; Ramspeck et al., 2007; Kontges et al., 2011) detected PV array faults and investigated the temperature characteristics of PV array under fault conditions by thermal cameras. Among these works, thermal cameras are used only to detect the temperature differences between the healthy PV cells and the fault cells, but the potential fault diagnosis based upon the connection between temperature and electrical characteristics is rarely mentioned. To eliminate the limit of fault detection only based on temperature characterises, a new fault diagnosis method attempting to couple the temperature and electrical characteristics are preferred to improve the fault detection. Many researchers (Luque et al. 1998; Mattei et al.,2006; Armstrong and Hurley, 2010; Tiwari et al. 2011; Usama et al., 2012; Tsai et al., 2012) have researched in coupled model of PV. For example, Usama et al. (2012) created a simulation model combining an electrical model with a thermal model to study the PV module’s characteristics; Tsai et al. (2012) presented a novel integrated PV model that simultaneously describes both electricity characteristics and thermal dynamics of a commercial PV module. However, these models suffer from one major limitation, the linkage of electrical model and temperature model is either too complicated to be built, or too weak to be accurate, hence impractical for on-line/real-time detection. In this paper, electrical and temperature characteristics are linked by the energy balance equation to establish parameter based model. Two working points of the current–voltage PV module curve and their corresponding temperatures are used to calculate parameters of the proposed model as shown in Fig. 1. Then, the model is used to realize fault diagnosis. This paper is organized as follows. The parameter based model is presented in Section II. In Section III, key parameters in the parameter based model are calculated based upon the connection thermal and electrical characteristics, and then the fault diagnosis method is also introduced. In Section IV, experiments are carried out to verify the proposed model and analyze the experiment results. Conclusions are drawn in Section V. 2. Parameter based model The electrical and thermal characteristics play important role in both the fault diagnosis of a PV array and the overall performance. In this work, a parameter based model of a PV module considers both the electrical and temperature characteristics through the energy balance equation. The following sections give a brief introduction of this model.
97
Fig. 1. Proposed fault diagnosis system.
2.1. Electrical model The electrical character is influenced by both temperature and illumination. The electrical model of PV cell is expressed in Eqs. (1)–(3) (Ishaque et al., 2011a,b; Kontges et al., 2011; Usama et al.,2012). q I cell ¼ I L I o fexp ðV cell þ I cell Rs Þ 1g AKT cell V cell þ I cell Rs ð1Þ þ Rsh I o ¼ I oref
IL ¼
T cell T cellref
3
exp
qEBG 1 1 AK T cellref T cell
G I Lref þ k i ðT cell T cellref Þ Gref
ð2Þ
ð3Þ
where Icell is the PV cell output current; IL is photo current; q is the quantity of electric charge; K is Boltzmann’s constant; A is diode characteristic factor; Tcell is PV cell temperature; Io is the direction saturated current; Rs is series resistance of PV cell; Rsh is shunt resistance of PV cell; Vcell is PV cell output voltage. Gref is the reference irradiance level (1000 W/m2); G is the real irradiance of the PV panel; the parameters ILref, Ioref are photo current IL, direction saturated current Io at the reference condition. Tcellref is PV panel at reference condition. The parameter ILref, Ioref, Rs and Rsh can be calculated by solar panel datasheet, ki is current temperature coefficient given in the datasheet. Considering a panel is composed of many PV cells connected in series, the overall PV panel electrical model can be expressed as follows, q V þ IRs V þ IRs I ¼ I L I o fexp ð4Þ 1g þ AKT m Ns Rsh
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The parameters Tm, I and V can be measured using thermography, current and voltage sensors, respectively. Other parameters such as S, Upv and Ta in the parameter base model should be estimated based on real applications. 3. Key parameters calculation and fault diagnosis
Fig. 2. Relationships of temperature and electrical characters.
where I is the PV panel output current; V is the PV panel output voltage; Ns is the number of series cells, Tm is the PV module temperature.
To demonstrate how to calculate the key parameters (S, Upv and Ta) and validate whether this parameter based model is suitable for fault detection, theory analysis is given in the following section, where two working points of the PV module under fault condition and their corresponding temperatures are used to fulfil the model. Firstly, paragraph discusses the electrical and temperature characteristics of a PV array under fault conditions. 3.1. PV array electrical and thermal characteristics analysis under fault condition
2.2. Energy balance equation The purpose of the energy balance equation is to connect the electrical and thermal characteristics. An energy balance equation for a PV panel has been established with the hypothesis below (Tsai et al., 2012; Mattei et al., 2006): (1) The temperature difference between PV cells and cover glass is neglected. (2) Temperature Tm = Tcell is uniform in a healthy module. (3) There is no thermal propagation across PV cells. As described by Mattei et al. (2006), the energy balance is expressed as S ¼ V I þ U pv Am ðT m T a Þ
ð5Þ
S ¼ G Am
ð6Þ
where S is the effective solar absorbed flux, Ta is ambient temperature; Upv is an overall heat exchange coefficient corresponding to the total surface area of the module, Am is the PV module area.
A PV array under fault condition is illustrated in Fig. 3. In the figure, the array is composed by a rows and b columns, and the second row as marked by red dashed box is under fault condition. The current of each PV module string is measured by a current sensor, where Impp and If are the current of a healthy and fault strings, respectively. Vmpp and Vf are the module voltages of a healthy and fault string, respectively. Because of the structure of a string, each module in the string has the same current; by using Eq. (4), the voltage of a healthy module (such as Number 22) in fault string can be calculated. For healthy string, because the PV modules in health string have the same voltage, the module voltage of a healthy string can be expressed as shown in Eq. (7). For unhealthy string, due to the paralleled bypass diode structure of a PV module, a faulty PV module is shorted by these bypass diodes and its output voltage will change to zero; the string output voltage is supported by the healthy modules. Because of the parallel structure of PV array, every PV string has Vmpp
Ih A
2.3. Parameter based model TH
Eqs. (4) and (5) form both the parameter based model, and the key parameters including I, V, Tm, S, Upv and Ta. Fig. 2 illustrates the multi-physics connecting aspects of the PV parameter based model; E presents the electrical output power of the PV module. The electrical model is mainly influenced by effective solar energy S and module temperature Tm as illustrated in Eqs. (2) and (3), while the temperature is mainly influenced by electrical power and effective solar energy S as shown in Eq. (5). The temperature Tm and total effective solar energy S parameter link the electrical and thermal characteristics. Under the condition of a given effective solar energy S, the module temperature depends on the electrical power of the PV module.
11
1b
12
Healthy PV module string
Vf
If A
Fault PV module
T 21
22
2b
Uuhealthy PV module string
A
a1
a2
ab
Varray Fig. 3. PV array at heavy fault conditions.
Y. Hu et al. / Solar Energy 96 (2013) 96–102
the same voltage Varray, as illustrated in Fig. 3; the relationship between healthy module voltage in healthy string (Vmpp) and healthy module voltage in unhealthy string (Vf) can be expressed as in Eq. (8). Influenced by the faulty module, the healthy modules in a faulty string work at nonmaximum power point (non-MPP), while the modules in the healthy strings remain at the maximum power point (MPP). V mpp ¼
V array b
V mpp b ¼ V f ðb xÞ
G¼
99
I mpp V mpp Am gr lðT m T ref Þ
ð12Þ
where Empp is the electrical output power at MPP; ge denotes the efficiency assessment of the PV module at a module temperature of Tm, gr denotes the efficiency assessment of the PV module at temperature Tref (25 °C). For silicon PV, The efficient temperature coefficient is l = 0.05/°C1.
ð7Þ
3.3. Non-MPP working point calculation
ð8Þ
The illumination intensity G can be used to calculate the healthy module voltage of faulty string. The unknown parameters in Eqs. (2)–(4) are those of illumination intensity G, module temperature, module current and voltage. Given the temperature T 0H which can be retrieved by using thermal image, the illumination intensity G calculated by Eq. (12) and fault string current If obtained from current senor, the voltage of the healthy module in fault string can be expressed as the function F(If) and can be calculated by using Eqs. (2)–(4). Thus, the electrical output of the healthy module in fault string can be written as follows.
where Varray is the array voltage which is measured as shown in Fig. 3; x is the number of faulty modules in the unhealthy module string. The working points of MPP and non-MPP modules are illustrated in Fig. 4, with a lesser electrical output power from a module in a fault string, meaning that more energy is transferred to heat, refers to T 0H > TH. Where TH and T 0H are the respective module temperatures of the healthy and faulty string. Based on the current, voltage and temperature of the module in the healthy string, the effective solar energy can be calculated by Eqs. (2)–(4).
Ef ¼ I f FðI f Þ
ð13Þ
3.2. Effective solar energy calculation
3.4. Key parameters calculation
In order to realize the Upv and Ta calculation, the effective solar energy should be calculated first. To start off, the output electrical energy of the module in the healthy string which is working at MPP can be expressed as Eq. (9). Next, the efficiency assessment of PV module can be expressed by using Eq. (10) (Sandnes and Rekstad,2002), the effective solar energy can be calculated from Eq. (11), and the corresponding illumination intensity can be expressed as in Eq. (12).
The electrical and thermal information of MPP and non-MPP modules, including current, voltage and temperature can be used to calculate the key parameters (Upv and Ta) of our parameter based model. At MPP, by combining Vmpp, Impp, TH, from Eqs. (5) and (11), the following equation can be written.
Empp ¼ I mpp V mpp
ð9Þ
ge ¼ gr lðT m T ref Þ
ð10Þ
Empp I mpp V mpp S¼ ¼ ge gr lðT m T ref Þ
ð11Þ
I mpp V mpp ð1 ge Þ ¼ Am U pv ðT H T a Þ ge lðT m T ref Þ
ð14Þ
At non-MPP, combining If, T 0H , and Eqs. (5), (11), and (13), the following equation can be written. I mpp V mpp I f FðI f Þ ¼ Am U pv ðT 0H T a Þ ge lðT m T ref Þ
ð15Þ
Deducing from Eqs. (14) and (15), the key parameters Upv and Ta can be expressed as follows. h i h i I mpp V mpp I mpp V mpp I F ðI Þ I V T T 0H f f H mpp mpp ge lðT m T ref Þ ge lðT m T ref Þ Ta ¼ I mpp V mpp I f FðI f Þ ð16Þ I mpp V mpp ge lðT m T ref Þ
U pv ¼
I mpp V mpp
fT m
ð
ge l T m T ref
Þ
I mpp V mpp
I f FðI f Þ T H
I mpp V mpp
ð
ge l T m T ref
I mpp V mpp I f FðI f Þ
Þ
I mpp V mpp
Am
T 0H
g ð17Þ
Fig. 4. Healthy and unhealthy PV module working points of fault PV module.
Once the key parameters, S, Upv and Ta are obtained in terms of Eqs. (11), (16), and (17), the parameter based
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model is established, and it thus can be used for fault diagnosis. 3.5. Fault diagnosis based on parameter based model Based on the parameter based model of a PV module, fault diagnosis can be undertaken. All of the healthy PV modules in a PV array are assumed have the same parameters such as effective solar illumination intensity S, ambient temperature Ta and total heat exchange coefficient Upv. Fault diagnosis can be carried out using Eq. (18). When the module is under a fault condition, the calculated Upv value will be different from that of a healthy module. In addition, the fault category can also be distinguished through the difference of heat exchange coefficients. SE ð18Þ U pv ¼ Am ðT m T a Þ
Table 2 PV module parameter. Parameters
Value
Open voltage (V) Short current (A) MPP current (A) MPP voltage (V) Current temperature coefficient (°C) Voltage temperature coefficient (°C) Power temperature coefficient (°C) Maximum power (W)
4.8 0.23 0.21 3.85 0.06%/K 0.36%/K 0.45%/K 0.8
4. Model validation In order to validate the proposed model, a scaled experimental example was constructed and the main specifications of the utilised thermal camera are shown in Table 1. The mini-PV module used in the experiment and its respective the datasheet is shown in Table 2. The type of the solar power meter used was TM-207, which was used to validate the PV model correction. 4.1. Experiment Fig. 5(a) denotes the experiment of the module at different load conditions including MPP load, heavy load, light load and shadow condition. The MPP load (35 X) module was used to simulate the module in a healthy string working at MPP, and the 50 X load was used to simulate the module in fault string working at non-MPP. The sun illumination was measured at 560 W/m2 using the TM-207, the voltage of MPP load and 50 X were 3.96 V and 4.37 V, respectively. The experiments were carried out at wind speed conditions of less than 5 m/s. Fig. 5(b) is the thermography image obtained from thermal camera. 4.2. Experiment results and discussion As mentioned above, the key parameters are first calculated by using the proposed method. The calculated Table 1 Thermal camera. Parameters
Value
Company Type IR resolution Thermal sensitivity/NETD Minimum focus distance Spatial resolution (IFOV) Image frequency Focus
FLIR FLIR i7 140 140 pixels <0.1 °C 0.6 m 3.7 mrad 9 Hz Focus free
Fig. 5. Thermography with different load condition.
parameters (G and Ta) are then compared with their measured values. The calculated parameter (Upv), which cannot be measured, is compared to experimental formulation results from literature. Fault diagnosis can be validated by comparing the healthy total heat exchange coefficient Upv with the fault condition value. In Fig. 5 the electrical power and effective solar energy from the sun can be calculated by Eqs. (9)–(11). Appendix gives the detail calculation progress. The effective solar energy S is 3.94 W, corresponding to the illumination intensity 540/m2. The actual sun illumination intensity is 560 W/m2, and the error rate is approximately 3.45%. On the base of illumination value, the key parameters (Upv and Ta) can be testified. The temperature of the Tm and T 0m which denote temperature of the MPP load module and 50 X load module calculated by image process method, are 18.1 °C and 18.3 °C respectively. Furthermore, the voltage of both MPP load module and 50 X load module can be used to calculate electrical power. By the Eqs. (14) and (15), Upv and Ta can be obtained. The calculated results are that parameter of Upv is 45.2 W/m2°C, and the ambient temperature Ta is 7.52 °C. The ambient temperature is approximate to real temperature 8 °C with the error is less than 5%. The total exchange coefficient is close to the result gained from the experiment formulation mentioned by Mattei et al. (2006). By calculating the parameters (S, Upv and Ta), the parameter based model is established. Then, the fault diagnosis is checked by the proposed method. In Fig. 5 the covered module temperature is 8.8 °C, the calculated result of Upv by the using Eq. (18) is 421 W/m2°C, which is very different from that of the healthy module, where the Upv
Y. Hu et al. / Solar Energy 96 (2013) 96–102
(45.2 W/m2°C) corresponds to a material with a high rate of exchange coefficient. Overall, the calculated coefficients (S, Ta and Upv) are verified by the experiment, which testifies the correction of the proposed model. The fault diagnosis method presented here is also validated by the experiment. 5. Conclusion
Am ¼ 1:2 7:6 8 ¼ 72:96 cm2 gr ¼
P mppref ¼ 11% Am Gref
P mpp ¼
V 2mpp ¼ 0:448 W Rmpp
(1) The PV module electrical model and energy balance equation is coupled to establish a parameter based model. (2) The key parameters (S, Upv and Ta) of the model are calculated from two working points of the PV module and corresponding temperature. (3) Fault diagnosis is realized based on this parameter based model. Notwithstanding the fact that a parameter based model has been established and validated, the other existing factors such as wind and dust have not considered in this proposed model, both of which exist in real condition. The vortex and dust distribution caused by wind in real PV array, introduce non-uniform of temperature distribution in thermography; it is challenge to estimate the real temperature of PV module. The pattern and behaviors of historic information will be applied for wind and dust influence including non-uniform illustration and other defects’ detection and classification. In future work, different influencing factors such as wind speed and dust. will be analyzed for their effect upon defect classification. Acknowledgments The authors would like to thank the National Natural Science Foundation of China (51207138) and China Postdoctoral Science Foundation (2012M511363). The work is also partial supported by FP7 HEMOW project. The authors would also like to thank Dr. Cui Lei for her wonderful suggestion and finally S. Crichton for proof reading the manuscript. Appendix A. The mini PV module is composed by 8 PV cells; width and length of each cell are 1.2 cm and 7.6 cm, in which the width of bus bar is considered. The mini PV module area (Am) is calculated as following in Eq. (A1). The reference efficiency is presented in Eq. (A2). In test condition, the PV module efficiency is calculated by Eq. (A4); the Eq. (A5) calculates the effective solar absorbed flux in mini PV module; the corresponding illumination is calculated by Eq. (A6).
ðA1Þ ðA2Þ ðA3Þ
ge ¼ gr lðT m T ref Þ ¼ 11% 0:05%ð18:1 25Þ 11:35%
This paper built a parameter based model for PV modules, with the model applied in fault diagnosis. The main contribution of this paper includes:
101
ðA4Þ
S¼
P mpp 0:448 ¼ ¼ 3:94 W 11:35% ge
ðA5Þ
G¼
S 3:94 2 ¼ ¼ 540 W=m Am 72:96 104
ðA6Þ
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Solar Energy 96 (2013) 96–102 www.elsevier.com/locate/solener
Photovoltaic fault detection using a parameter based model Yihua Hu a, Bin Gao b,⇑, Xueguan Song c, Gui Yun Tian b, Kongjing Li c, Xiangning He a b
a College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China c School of Electrical and Electronic Engineering, Newcastle University, England, United Kingdom
Received 4 February 2013; received in revised form 28 June 2013; accepted 8 July 2013
Communicated by: Associate Editor Elias Stefanakos
Abstract Photovoltaic (PV) modules convert part of incident solar energy into electrical energy for commercial applications, with the rest being transferred to heat energy. The modelling of PV modules plays an important role in the fault diagnosis of a PV array. The object of this paper is to develop a parameter based model of a PV module. This model is sequentially coupled with an electrical model and energy balance equation. In order to establish the parameter based model, key parameters including the total effective solar energy, total heat exchange coefficient and ambient temperature are calculated from two working points on PV module along with the corresponding temperature from a thermal camera. Using the developed model, a fault diagnosis method based on the model is illustrated. Finally, model validation is carried out by the experiments. Ó 2013 Elsevier Ltd. All rights reserved. Keywords: PV module; Parameter based model; Fault diagnosis; Model validation
1. Introduction Solar energy is a green and renewable energy source, which has been widely exploited in grid-connected systems, PV-pumps and stand-alone systems. With most system requirements, a large number of PV modules are required to be connected in series to form a PV string. This enables the overall PV array to obtain a high input voltage whilst simultaneously producing high output power. A PV array is usually subject to faults in real application, which may significantly decrease power generation efficiency and reduce the array’s lifespan. As a result, fault detection is crucial and necessary for the PV array maintenance. The PV array fault is defined as the condition that those who causes decrement of PV array power output. ⇑ Corresponding author at: School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China. E-mail address: [email protected] (B. Gao).
0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.07.004
There are two types of fault, the first one is recoverable fault, and the second one is unrecoverable fault. The recoverable fault caused by clouds/dust can be recovered by human maintains; while the PV degradation and/or micro-cracks which is called unrecoverable fault cannot be recovered. In this paper, the recoverable fault is main subject. In general, a PV array requires modules to be spread across a large physical area, which will unavoidably result in the PV array suffering from non-uniform illumination when shadow or dust casts across the modules (Chouder and Silvestre, 2010; Simon and Meyer, 2010; Zegaoui et al., 2012; Takashima et al., 2009; Gautam and Kaushika,2002; Tonui and Tripanagnostopoulos, 2007; Ishaque et al., 2011a,b; Munoz et al., 2011). If a PV array is under non-uniform illumination, the transferred electricity drops sharply (Armstrong and Hurley, 2010; Patel and Agarwal, 2008; Hu et al., 2012; Bruendlinger et al., 2006) which lead to output power and generation efficiency considerably below the acceptable level, and the unrecoverable fault PV module may occurs in the long time fault condition.
Y. Hu et al. / Solar Energy 96 (2013) 96–102
Therefore, it has become important to build a fault diagnosis system to detect such PV array fault. Currently, thermal cameras become one of the main tools to perform PV array fault diagnosis. Many researchers (Kaplani, 2013; Acciani et al., 2010; Buerhopa et al., 2012; Parinya et al., 2007; Krenzinger and Andrade, 2007; Simon and Meyer, 2010; Ko¨ntges et al., 2011; Trupke et al., 2006; Kasemann et al., 2006; Ramspeck et al., 2007; Kontges et al., 2011) detected PV array faults and investigated the temperature characteristics of PV array under fault conditions by thermal cameras. Among these works, thermal cameras are used only to detect the temperature differences between the healthy PV cells and the fault cells, but the potential fault diagnosis based upon the connection between temperature and electrical characteristics is rarely mentioned. To eliminate the limit of fault detection only based on temperature characterises, a new fault diagnosis method attempting to couple the temperature and electrical characteristics are preferred to improve the fault detection. Many researchers (Luque et al. 1998; Mattei et al.,2006; Armstrong and Hurley, 2010; Tiwari et al. 2011; Usama et al., 2012; Tsai et al., 2012) have researched in coupled model of PV. For example, Usama et al. (2012) created a simulation model combining an electrical model with a thermal model to study the PV module’s characteristics; Tsai et al. (2012) presented a novel integrated PV model that simultaneously describes both electricity characteristics and thermal dynamics of a commercial PV module. However, these models suffer from one major limitation, the linkage of electrical model and temperature model is either too complicated to be built, or too weak to be accurate, hence impractical for on-line/real-time detection. In this paper, electrical and temperature characteristics are linked by the energy balance equation to establish parameter based model. Two working points of the current–voltage PV module curve and their corresponding temperatures are used to calculate parameters of the proposed model as shown in Fig. 1. Then, the model is used to realize fault diagnosis. This paper is organized as follows. The parameter based model is presented in Section II. In Section III, key parameters in the parameter based model are calculated based upon the connection thermal and electrical characteristics, and then the fault diagnosis method is also introduced. In Section IV, experiments are carried out to verify the proposed model and analyze the experiment results. Conclusions are drawn in Section V. 2. Parameter based model The electrical and thermal characteristics play important role in both the fault diagnosis of a PV array and the overall performance. In this work, a parameter based model of a PV module considers both the electrical and temperature characteristics through the energy balance equation. The following sections give a brief introduction of this model.
97
Fig. 1. Proposed fault diagnosis system.
2.1. Electrical model The electrical character is influenced by both temperature and illumination. The electrical model of PV cell is expressed in Eqs. (1)–(3) (Ishaque et al., 2011a,b; Kontges et al., 2011; Usama et al.,2012). q I cell ¼ I L I o fexp ðV cell þ I cell Rs Þ 1g AKT cell V cell þ I cell Rs ð1Þ þ Rsh I o ¼ I oref
IL ¼
T cell T cellref
3
exp
qEBG 1 1 AK T cellref T cell
G I Lref þ k i ðT cell T cellref Þ Gref
ð2Þ
ð3Þ
where Icell is the PV cell output current; IL is photo current; q is the quantity of electric charge; K is Boltzmann’s constant; A is diode characteristic factor; Tcell is PV cell temperature; Io is the direction saturated current; Rs is series resistance of PV cell; Rsh is shunt resistance of PV cell; Vcell is PV cell output voltage. Gref is the reference irradiance level (1000 W/m2); G is the real irradiance of the PV panel; the parameters ILref, Ioref are photo current IL, direction saturated current Io at the reference condition. Tcellref is PV panel at reference condition. The parameter ILref, Ioref, Rs and Rsh can be calculated by solar panel datasheet, ki is current temperature coefficient given in the datasheet. Considering a panel is composed of many PV cells connected in series, the overall PV panel electrical model can be expressed as follows, q V þ IRs V þ IRs I ¼ I L I o fexp ð4Þ 1g þ AKT m Ns Rsh
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The parameters Tm, I and V can be measured using thermography, current and voltage sensors, respectively. Other parameters such as S, Upv and Ta in the parameter base model should be estimated based on real applications. 3. Key parameters calculation and fault diagnosis
Fig. 2. Relationships of temperature and electrical characters.
where I is the PV panel output current; V is the PV panel output voltage; Ns is the number of series cells, Tm is the PV module temperature.
To demonstrate how to calculate the key parameters (S, Upv and Ta) and validate whether this parameter based model is suitable for fault detection, theory analysis is given in the following section, where two working points of the PV module under fault condition and their corresponding temperatures are used to fulfil the model. Firstly, paragraph discusses the electrical and temperature characteristics of a PV array under fault conditions. 3.1. PV array electrical and thermal characteristics analysis under fault condition
2.2. Energy balance equation The purpose of the energy balance equation is to connect the electrical and thermal characteristics. An energy balance equation for a PV panel has been established with the hypothesis below (Tsai et al., 2012; Mattei et al., 2006): (1) The temperature difference between PV cells and cover glass is neglected. (2) Temperature Tm = Tcell is uniform in a healthy module. (3) There is no thermal propagation across PV cells. As described by Mattei et al. (2006), the energy balance is expressed as S ¼ V I þ U pv Am ðT m T a Þ
ð5Þ
S ¼ G Am
ð6Þ
where S is the effective solar absorbed flux, Ta is ambient temperature; Upv is an overall heat exchange coefficient corresponding to the total surface area of the module, Am is the PV module area.
A PV array under fault condition is illustrated in Fig. 3. In the figure, the array is composed by a rows and b columns, and the second row as marked by red dashed box is under fault condition. The current of each PV module string is measured by a current sensor, where Impp and If are the current of a healthy and fault strings, respectively. Vmpp and Vf are the module voltages of a healthy and fault string, respectively. Because of the structure of a string, each module in the string has the same current; by using Eq. (4), the voltage of a healthy module (such as Number 22) in fault string can be calculated. For healthy string, because the PV modules in health string have the same voltage, the module voltage of a healthy string can be expressed as shown in Eq. (7). For unhealthy string, due to the paralleled bypass diode structure of a PV module, a faulty PV module is shorted by these bypass diodes and its output voltage will change to zero; the string output voltage is supported by the healthy modules. Because of the parallel structure of PV array, every PV string has Vmpp
Ih A
2.3. Parameter based model TH
Eqs. (4) and (5) form both the parameter based model, and the key parameters including I, V, Tm, S, Upv and Ta. Fig. 2 illustrates the multi-physics connecting aspects of the PV parameter based model; E presents the electrical output power of the PV module. The electrical model is mainly influenced by effective solar energy S and module temperature Tm as illustrated in Eqs. (2) and (3), while the temperature is mainly influenced by electrical power and effective solar energy S as shown in Eq. (5). The temperature Tm and total effective solar energy S parameter link the electrical and thermal characteristics. Under the condition of a given effective solar energy S, the module temperature depends on the electrical power of the PV module.
11
1b
12
Healthy PV module string
Vf
If A
Fault PV module
T 21
22
2b
Uuhealthy PV module string
A
a1
a2
ab
Varray Fig. 3. PV array at heavy fault conditions.
Y. Hu et al. / Solar Energy 96 (2013) 96–102
the same voltage Varray, as illustrated in Fig. 3; the relationship between healthy module voltage in healthy string (Vmpp) and healthy module voltage in unhealthy string (Vf) can be expressed as in Eq. (8). Influenced by the faulty module, the healthy modules in a faulty string work at nonmaximum power point (non-MPP), while the modules in the healthy strings remain at the maximum power point (MPP). V mpp ¼
V array b
V mpp b ¼ V f ðb xÞ
G¼
99
I mpp V mpp Am gr lðT m T ref Þ
ð12Þ
where Empp is the electrical output power at MPP; ge denotes the efficiency assessment of the PV module at a module temperature of Tm, gr denotes the efficiency assessment of the PV module at temperature Tref (25 °C). For silicon PV, The efficient temperature coefficient is l = 0.05/°C1.
ð7Þ
3.3. Non-MPP working point calculation
ð8Þ
The illumination intensity G can be used to calculate the healthy module voltage of faulty string. The unknown parameters in Eqs. (2)–(4) are those of illumination intensity G, module temperature, module current and voltage. Given the temperature T 0H which can be retrieved by using thermal image, the illumination intensity G calculated by Eq. (12) and fault string current If obtained from current senor, the voltage of the healthy module in fault string can be expressed as the function F(If) and can be calculated by using Eqs. (2)–(4). Thus, the electrical output of the healthy module in fault string can be written as follows.
where Varray is the array voltage which is measured as shown in Fig. 3; x is the number of faulty modules in the unhealthy module string. The working points of MPP and non-MPP modules are illustrated in Fig. 4, with a lesser electrical output power from a module in a fault string, meaning that more energy is transferred to heat, refers to T 0H > TH. Where TH and T 0H are the respective module temperatures of the healthy and faulty string. Based on the current, voltage and temperature of the module in the healthy string, the effective solar energy can be calculated by Eqs. (2)–(4).
Ef ¼ I f FðI f Þ
ð13Þ
3.2. Effective solar energy calculation
3.4. Key parameters calculation
In order to realize the Upv and Ta calculation, the effective solar energy should be calculated first. To start off, the output electrical energy of the module in the healthy string which is working at MPP can be expressed as Eq. (9). Next, the efficiency assessment of PV module can be expressed by using Eq. (10) (Sandnes and Rekstad,2002), the effective solar energy can be calculated from Eq. (11), and the corresponding illumination intensity can be expressed as in Eq. (12).
The electrical and thermal information of MPP and non-MPP modules, including current, voltage and temperature can be used to calculate the key parameters (Upv and Ta) of our parameter based model. At MPP, by combining Vmpp, Impp, TH, from Eqs. (5) and (11), the following equation can be written.
Empp ¼ I mpp V mpp
ð9Þ
ge ¼ gr lðT m T ref Þ
ð10Þ
Empp I mpp V mpp S¼ ¼ ge gr lðT m T ref Þ
ð11Þ
I mpp V mpp ð1 ge Þ ¼ Am U pv ðT H T a Þ ge lðT m T ref Þ
ð14Þ
At non-MPP, combining If, T 0H , and Eqs. (5), (11), and (13), the following equation can be written. I mpp V mpp I f FðI f Þ ¼ Am U pv ðT 0H T a Þ ge lðT m T ref Þ
ð15Þ
Deducing from Eqs. (14) and (15), the key parameters Upv and Ta can be expressed as follows. h i h i I mpp V mpp I mpp V mpp I F ðI Þ I V T T 0H f f H mpp mpp ge lðT m T ref Þ ge lðT m T ref Þ Ta ¼ I mpp V mpp I f FðI f Þ ð16Þ I mpp V mpp ge lðT m T ref Þ
U pv ¼
I mpp V mpp
fT m
ð
ge l T m T ref
Þ
I mpp V mpp
I f FðI f Þ T H
I mpp V mpp
ð
ge l T m T ref
I mpp V mpp I f FðI f Þ
Þ
I mpp V mpp
Am
T 0H
g ð17Þ
Fig. 4. Healthy and unhealthy PV module working points of fault PV module.
Once the key parameters, S, Upv and Ta are obtained in terms of Eqs. (11), (16), and (17), the parameter based
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model is established, and it thus can be used for fault diagnosis. 3.5. Fault diagnosis based on parameter based model Based on the parameter based model of a PV module, fault diagnosis can be undertaken. All of the healthy PV modules in a PV array are assumed have the same parameters such as effective solar illumination intensity S, ambient temperature Ta and total heat exchange coefficient Upv. Fault diagnosis can be carried out using Eq. (18). When the module is under a fault condition, the calculated Upv value will be different from that of a healthy module. In addition, the fault category can also be distinguished through the difference of heat exchange coefficients. SE ð18Þ U pv ¼ Am ðT m T a Þ
Table 2 PV module parameter. Parameters
Value
Open voltage (V) Short current (A) MPP current (A) MPP voltage (V) Current temperature coefficient (°C) Voltage temperature coefficient (°C) Power temperature coefficient (°C) Maximum power (W)
4.8 0.23 0.21 3.85 0.06%/K 0.36%/K 0.45%/K 0.8
4. Model validation In order to validate the proposed model, a scaled experimental example was constructed and the main specifications of the utilised thermal camera are shown in Table 1. The mini-PV module used in the experiment and its respective the datasheet is shown in Table 2. The type of the solar power meter used was TM-207, which was used to validate the PV model correction. 4.1. Experiment Fig. 5(a) denotes the experiment of the module at different load conditions including MPP load, heavy load, light load and shadow condition. The MPP load (35 X) module was used to simulate the module in a healthy string working at MPP, and the 50 X load was used to simulate the module in fault string working at non-MPP. The sun illumination was measured at 560 W/m2 using the TM-207, the voltage of MPP load and 50 X were 3.96 V and 4.37 V, respectively. The experiments were carried out at wind speed conditions of less than 5 m/s. Fig. 5(b) is the thermography image obtained from thermal camera. 4.2. Experiment results and discussion As mentioned above, the key parameters are first calculated by using the proposed method. The calculated Table 1 Thermal camera. Parameters
Value
Company Type IR resolution Thermal sensitivity/NETD Minimum focus distance Spatial resolution (IFOV) Image frequency Focus
FLIR FLIR i7 140 140 pixels <0.1 °C 0.6 m 3.7 mrad 9 Hz Focus free
Fig. 5. Thermography with different load condition.
parameters (G and Ta) are then compared with their measured values. The calculated parameter (Upv), which cannot be measured, is compared to experimental formulation results from literature. Fault diagnosis can be validated by comparing the healthy total heat exchange coefficient Upv with the fault condition value. In Fig. 5 the electrical power and effective solar energy from the sun can be calculated by Eqs. (9)–(11). Appendix gives the detail calculation progress. The effective solar energy S is 3.94 W, corresponding to the illumination intensity 540/m2. The actual sun illumination intensity is 560 W/m2, and the error rate is approximately 3.45%. On the base of illumination value, the key parameters (Upv and Ta) can be testified. The temperature of the Tm and T 0m which denote temperature of the MPP load module and 50 X load module calculated by image process method, are 18.1 °C and 18.3 °C respectively. Furthermore, the voltage of both MPP load module and 50 X load module can be used to calculate electrical power. By the Eqs. (14) and (15), Upv and Ta can be obtained. The calculated results are that parameter of Upv is 45.2 W/m2°C, and the ambient temperature Ta is 7.52 °C. The ambient temperature is approximate to real temperature 8 °C with the error is less than 5%. The total exchange coefficient is close to the result gained from the experiment formulation mentioned by Mattei et al. (2006). By calculating the parameters (S, Upv and Ta), the parameter based model is established. Then, the fault diagnosis is checked by the proposed method. In Fig. 5 the covered module temperature is 8.8 °C, the calculated result of Upv by the using Eq. (18) is 421 W/m2°C, which is very different from that of the healthy module, where the Upv
Y. Hu et al. / Solar Energy 96 (2013) 96–102
(45.2 W/m2°C) corresponds to a material with a high rate of exchange coefficient. Overall, the calculated coefficients (S, Ta and Upv) are verified by the experiment, which testifies the correction of the proposed model. The fault diagnosis method presented here is also validated by the experiment. 5. Conclusion
Am ¼ 1:2 7:6 8 ¼ 72:96 cm2 gr ¼
P mppref ¼ 11% Am Gref
P mpp ¼
V 2mpp ¼ 0:448 W Rmpp
(1) The PV module electrical model and energy balance equation is coupled to establish a parameter based model. (2) The key parameters (S, Upv and Ta) of the model are calculated from two working points of the PV module and corresponding temperature. (3) Fault diagnosis is realized based on this parameter based model. Notwithstanding the fact that a parameter based model has been established and validated, the other existing factors such as wind and dust have not considered in this proposed model, both of which exist in real condition. The vortex and dust distribution caused by wind in real PV array, introduce non-uniform of temperature distribution in thermography; it is challenge to estimate the real temperature of PV module. The pattern and behaviors of historic information will be applied for wind and dust influence including non-uniform illustration and other defects’ detection and classification. In future work, different influencing factors such as wind speed and dust. will be analyzed for their effect upon defect classification. Acknowledgments The authors would like to thank the National Natural Science Foundation of China (51207138) and China Postdoctoral Science Foundation (2012M511363). The work is also partial supported by FP7 HEMOW project. The authors would also like to thank Dr. Cui Lei for her wonderful suggestion and finally S. Crichton for proof reading the manuscript. Appendix A. The mini PV module is composed by 8 PV cells; width and length of each cell are 1.2 cm and 7.6 cm, in which the width of bus bar is considered. The mini PV module area (Am) is calculated as following in Eq. (A1). The reference efficiency is presented in Eq. (A2). In test condition, the PV module efficiency is calculated by Eq. (A4); the Eq. (A5) calculates the effective solar absorbed flux in mini PV module; the corresponding illumination is calculated by Eq. (A6).
ðA1Þ ðA2Þ ðA3Þ
ge ¼ gr lðT m T ref Þ ¼ 11% 0:05%ð18:1 25Þ 11:35%
This paper built a parameter based model for PV modules, with the model applied in fault diagnosis. The main contribution of this paper includes:
101
ðA4Þ
S¼
P mpp 0:448 ¼ ¼ 3:94 W 11:35% ge
ðA5Þ
G¼
S 3:94 2 ¼ ¼ 540 W=m Am 72:96 104
ðA6Þ
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