Passive Monitoring of the Power Generated in Grid Connected PV Systems.

Available online at www.sciencedirect.com

ScienceDirect Energy Procedia 57 (2014) 235 – 244

2013 ISES Solar World Congress

Passive monitoring of the power generated in grid connected PV systems. A. Firmana,*, V. Toranzosa, L. Veraa, A. Bussoa, J. de la Casab a Grupo en Energías Renovables, University Nacional del Nordeste, Av. Libertad 5460, Corrientes 3400, Argentina IDEA (Investigación y Desarrollo de Energía Solar), University of Jaén, Campus las Lagunillas s/n, 23071 Jaén, Spain

b

Abstract This paper presents a methodology associated to a set of explicit equations aimed to translate point-to-point the generated power to standard test conditions and its application to a real situation. Such equations are employed for monitoring and diagnostic of grid connected photovoltaic systems. The proposed method is based in the data analysis through statistical methods and it allows diagnosis or detection of instant decreases of generated power. The Experimental results are compared with other procedure of characterization of the nominal power of large photovoltaic generators under real operation conditions which are based on protocols similar to the one proposed in this paper. Results show differences less to 3% between both methods. In conclusion, the methodology presented is useful for real time diagnose of power decrease, when variation of maximum power with temperature is not known or in cases where catalog parameters are not available. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2013 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and/or peer-review under responsibility of ISES Selection and/or peer-review under responsibility of ISES.

Keywords: Solar energy; photovoltaic; translation to standard test condition; grid connected photovoltaic systems.

1. Introduction This paper presents a method which allows determining the generator peak power in standard test conditions (STC) at the inverter terminals from experimental measurements taken under real operation conditions. The method assumes that the photovoltaic array (PV) is polarized at the maximum power point and includes DC losses intrinsic to this kind of system. Over the last years it has been observed a sustainable increase in grid connected photovoltaic systems (GCPS), in particular, the installation of photovoltaic plants or solar farms with generation power ranging from tens of kilowatts to some megawatts [1]. Therefore, the necessity of determining real generation

* Corresponding author. Tel.: +54-379-4473931 (129); E-mail address: [email protected]

1876-6102 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and/or peer-review under responsibility of ISES. doi:10.1016/j.egypro.2014.10.028

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capacity exists since the time these plants entered into operation. This capacity is marked by the power in STC of the already built generator and which may not agree with the value estimated by adding up the power of individual modules comprising the plant. Moreover, the development of methods to determine in a fast, simple and reliable way the peak power of a PV array could be interesting to assess decay processes of the generator after many years of duty or due to a wrongful operation of the system. Nomenclature P

Power

G

Irradiance

Tc

Cell temperature

γ

Power variation with temperature at the point of maximum power

Voc

Open circuit voltage

Isc

Short circuit current

Pm

Power at the point of maximum power

Im

Current at the point of maximum power

Vm

Voltage at the point of maximum power

p

proportionality constant between irradiance and current

N

Number of series cells

βm

Temperature coefficient of the maximum voltage

Rs

Series Resistance

m

Diode ideality index

Vt

Thermal voltage

k

Stefan-Boltzmann constant

q

Electron charge

a, b, c

Linear fit constants

This kind of assessment is generally made by means of the current vs. voltage (I-V) curve [2,3,4] which implies momentary disconnection of the PV generator from the grid. This procedure is not practical in large installations due to the power involved thus resulting dangerous for operator [5]. Furthermore, up until now there are no commercial capacitive charge capable to withstand more than 100 kW [6], although bibliography mentions experimental electronic charges able to overcome that figure [7,8]. Therefore, raises the need for tools and methodologies to meet the operating status of the modules that make up the photovoltaic field. In this regards, it may be pointed out that nowadays the existing methods to assess the generation capacity of GCPS follow the protocol described by the Grupo de Sistemas of the Universidad Politécnica

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de Madrid (IES-UPM) [9] (eq. 1). This method is based on equations described by Osterwald [10] and which have been generalized to be applied to modules and PV generators [11,12,13].

P





G 1  J Tc  Tco Po Go



(1)

P is the power measured at irradiance G and at cell temperature Tc with γ accounting for the power variation with temperature at the point of maximum power. The sub-index zero in the equation indicates values at standard conditions. This method needs the knowledge beforehand of the value of γ which it is typically a parameter presented in the manufacturer catalogs. Generally the γ supplied by the manufacturer represent the average behavior of a set of modules and there is no mention to the deviations that might be expected. Moreover, methodologies that relate to manufacturer data may present differences due to problems not linked to the module itself and which affect energy production, such as wiring, losses by mismatch or simply by dust accumulation. With this in mind, the methodology proposed hereby is capable to determine peak power at STC of a PV system under real operation conditions independently of characteristic parameter provided by the manufacturer and relying on variables usually monitored in PV installations. Such methodology can also be employed as real time diagnostic tool for detection of generation problems. 2. Numerical methodology Due to the fact that in these systems the inverter already includes a set of mathematical algorithms for maximum power point tracking (MPPT) there are no traditional characteristics parameters such as short circuit current (Isc) available therefore any simple translation to STC of the GCPS under real operation conditions is unviable, hence, other options must be analyzed. The energy injection by the inverters is produced as soon as the open circuit voltage (Voc) lies within a certain range. This situation generally takes place at low levels of irradiance compared with normal operation conditions, therefore, the determination of standard Voc and the voltage variation with temperature (β) under these conditions can not be done with precision, besides the fact that β varies according to whether the system is polarized at the point of maximum power or at the open circuit [14,15]. For these reasons it is sought to develop equations for point-to-point translation of the generated power to STC which rely only on voltage and current polarization data of the inverter over the PV array together with the value of irradiance and cell temperature. In this purpose it is considered that the polarization always is takes place at the point of maximum power determined by the product of current and voltage of maximum power (Pm=Im.Vm). Due the fact that nowadays inverters MPPT algorithms have efficiencies higher than 99% [16,17] it may be consider that the system is always polarized at this point. Considering that Im is not very sensitive with temperature and voltage variation and only varies directly proportional to irradiance G, for a finite interval ∆G it can be developed in Taylor series written according to eq. 2:

I m (G)

I m (Go ) 

GI m (Go ) G 2 I m (Go ) (G  Go )  GG Tc, V GG 2 m

(G  Go ) 2  ... Tc, Vm

(2)

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Neglecting terms of order higher than one leads to eq. 3. In this equation p represents the proportionality constant between irradiance and current.

I m (G)

I m (Go )  p(G  Go )

I m (Go ) 

I m (Go ) (G  Go ) Go

I m (Go ) G Go

(3)

Equation 4 is obtained operating on eq. 3. The temperature correction term is neglected due the fact that for silicon cells the variation of the current with temperature is at least three orders of magnitude lower than Im for each degree centigrade [15,18].

I m (Go )

G I m (G) o G

(4)

The Taylor series for Vm considering for the time being that it is independent of irradiance and current and that it only depends on temperature is expressed by eq. 5.

Vm (Tc) Vm (Tco ) 

GVm (Tco ) G 2Vm (Tco ) (Tc  Tco )  GT GTc2 G, I m

(Tc  Tco ) 2  ... G, I m

(5)

Neglecting terms of order higher than one and taking into account the relation in eq. 6, eq. 7 can be written as:

GV m # Em N GTc

(6)

Vm (Tc) Vm (Tco )  E m N (Tc  Tco )

(7)

where N represents the number of cells electrically interconnected in series and βm represents the voltage variation with temperature at the point of maximum power. The ohmic effect is accounted for by adding a term to eq. 7 which is function of the series resistance (Rs). Given that the parallel resistance is normally two or more orders of magnitude higher than Rs only ohmic effects are considered. The series resistance Rs accounts for the voltage drop in the cells and in the connection wiring and terminals. Rs produce a voltage drop Im.Rs which affects the translation procedure when the current between any two states is modified. Taking this effect into consideration leads to eq. 8.

V (Tc) V (Tco )  E m N (Tc  Tco )  Rs( I m (Go )  I m (G))

(8)

Equation 8 might be corrected to account for variations in the irradiance thus leading to eq. 9. This equation along with eq. 4 are used to perform voltage translations to STC. The relationships developed this far have been previously employed for modeling and simulation of PV devices [19]. In these equations the ideality index of the diode m and the thermal voltage Vt are also included.

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§G · ¸¸ Vm (Tc) Vm (Tco )  E m N (Tc  Tco )  Rs( I m (Go )  I m (G))  m.N .Vt ln¨¨ © Go ¹

(9)

The ideality index of the diode is hard to determine if the polarization of inverter on the PV array is the only data available nonetheless, the effect produced by the ideality index can be approximated to the effect produced by the series resistance since in both cases there exists a change in the slope of I-V curve towards the open circuit voltage zone (eq. 10) thus lowering the maximum power [20,21].



wV wI Voc

Rs 

m.N .Vt Isc

(10)

For this reason, according to literature, m is assumed be equal to 1 for mono-crystalline silicon and equal to 1.2 for poly-crystalline silicon cells [22]. Therefore, Rs is taken as fitting parameter since their effects are related. Rearrangement of eq. 9 leads to eq. 11 which can be interpreted as a bi-dimensional equation describing a plane that crosses the origin and can be simply described by eq. 12.

'Vm  m.N .Vt.' lnG E m N .'Tc  Rs.'I m

c.z

a.x  b. y

(11) (12)

where a = βmN and –b = Rs. As stated previously Rs includes ohmic losses from both the PV module and connection wiring and terminals. Hence, the unknown parameters βm y Rs can be determined by linear regression using this simple relationship along with measurements of current, voltage, irradiance and temperature. Once these coefficients were fitted with experimental data they are used to translate current and voltage to STC and subsequent determination of nominal power and quantification of peak power of the PV generator under this standard condition. 3. Experimental methodology In order to apply the methodology previously explained it is necessary to have a set of experimental measurements of Vm, Im, G and Tc. These measurements must be obtained simultaneously, stored at a sampling interval of 30 s along a continuous period of time during a clear sky day thus assuring that the system operates in a vast spectrum of irradiances. Voltage and current measurements (Vm, Im) are made at the input side of the inverter by means of a wattmeter or data-logger with precision below 1%. Given Im measurements should be made indirectly the use of a shunt resistance (0.1 %) is recommended. Although a DC Hall effect probe is of simpler implementation its use is unadvisable for a process of calibration because the uncertainty level associated to this kind of sensor. Measurement of G and Tc are performed using as probes two modules of similar characteristics to those comprising the PV plant. These probes must be calibrated by a recognized laboratory, installed coplanar to the PV generator thus cancelling any uncertainties associated to spectral losses or to incidence angle. Measuring open circuit voltage on one module and short circuit current on the other one, cell

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temperature and irradiance in the plane of generator may be obtained applying eq. 13 and eq. 14. [23]. In these equations the sub-index ms indicates measured values and the sub-index ref indicates reference values obtained from calibration.

G

Tc

I sc, ms Gref I sc, ref

(13)

Voc, ms  Voc, ref  βref .N ref .Tref § mref .k G N ref ¨ βref  Ln ¨ q G ref ©

· ¸ ¸ ¹

(14)

where βref is the variation with temperature of the open circuit voltage corresponding to the reference module, mref is the diode index of ideality, k is the Boltzman constant and q the electron charge. 4. Results As an example, the bi-dimensional monitoring methodology proposed was applied to analyze experimental data from a 100 kWp PV plant located in the South of Europe. The data was gathered under real operation condition by the Research Group and Solar Energy Development (I+DEA) of the University of Jaén, Spain. The PV plant is conformed by 220 Wp mono-crystalline silicon modules comprising of 96 cells each presenting a γ coefficient (power variation with temperature) of -0.45%/°C (according to the technical specification reported by the manufacturer). The generator is made up of 46 branches in parallel each comprising 12 modules connected in series. Taking as calculation base technical specs provided by the manufacturer, this arrangement supplies an installed nominal power of 121.44 kWp. The generator connects to the grid by means of a 100kW inverter. Figure 1 show the time evolution of the irradiance and current for a particular day. From the plot it can be observed that during noon hours the current diminishes due to saturation of the inverter caused by the excess in generated power with respect to its nominal power. In order not to exceed design limits the inverter displaces the polarization point of the PV array. For this reason, as a first approach in the evaluation, data between the two vertical lines is discarded. In this region the device reaches the threshold where the point of maximum power begins to displace thus increasing the electric noise. Moreover, given that any translation introduces deviations and these are higher as farther is the departure from destination conditions only data gathered under irradiation higher than 500 W/m2 is employed. The proposed bi-dimensional monitoring methodology is based on ∆Vm, ∆Im, ∆Tc, ∆ln(G) calculated from measured data. Because these data are affected by uncertainties originated by the MPPT algorithm it is necessary to determine which is these incremental differences maximizes the correlation coefficient (R2) in the fitting process to determine βm and Rs. Once determined these parameters are employed to translate the selected data to STC by applying the equations presented previously. The results obtained indicate an average power of 113.6 kWp, a total series resistance for the system Rs = 0.395Ω, a voltage variation with temperature at the point of maximum power βm = -1.81 mV/°C and a correlation coefficient R2 = 0.94. Figure 2 plots the time evolution of the peak power resulting from the application of the translation methodology proposed.

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Fig. 1.- Time evolution curves of irradiance and current for a 100 kW GCPS

Fig. 2.- Time evolution of peak power as determined using the translation to STC of monitored data

The same selected set of data is analyzed applying the procedure proposed by the IES-UPM (eq. 1) and the results obtained with the two methods were compared. The slope (a) determined from the linear fitting of eq. 1 represents the power under STC (Po). The value of γ used in eq. 1 is that recommended by the manufacturer. The results are shown in figure 3. The deviation between methodologies is 2.8%. On the other hand, when these results are compared against the nominal power of the PV array there is exists a deviation of 3.7% for IES-UPM method and a 6.5% deviation for the proposed bi-dimensional methodology. It should be stressed the latter method does not rely on any parameter informed by the manufacturer.

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Fig. 3.- Results of data analysis using the protocol developed by IES-UPM. Superimposed is the resulting linear fitting line

Fig. 4.- Time evolution of peak power under standard conditions of measurement. The presence of a generation anomaly is observed in the test consistent with the saturation of the inverter. The dotted line represents the power threshold of 10% below the nominal power of the generator

A particular feature of the bi-dimensional methodology developed is that it may be used as a tool for detection of generation problems. It is worth mentioning that the proposed method does not make use of the maximum power variation with temperature (J). Figure 4 depicts the results obtained from monitoring and translation to standard conditions when applied to the entire data set which includes the saturation region of the inverter. The values of Rs and βm, used in this calculation are those previously determined for the case in which the data corresponding to the saturation region of the inverter was not included. As a result it is observed that the power decrease caused by the change of polarization of the inverter over its

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saturation region becomes evident reaching a minimum in power production of 109.0 kWp, power which is 10.2% below the nominal power of the PV array as determined taking into account only catalog information (121.44 kWp). This anomaly could be detected by incorporating a power failure warning functionality to the data monitoring routine, for example for powers lower than 10% (dotted line) compared to nominal power of PV array, which sets an advantage with respect to other evaluation methods. 5. Conclusion It is concluded that the bi-dimensional methodology developed is useful in different cases, when the maximum power variation with temperature is not precisely known, when catalog parameters are inexistent or not reliable or when conditions in the PV generator might affect these parameters. It should be pointed out that the method allows the determination of parameters which represent the best fit to the proposed model an advantage over relying just on figures provided by the manufacturer. In general, parameters supplied by the manufacturer cover a wide range of modules or sometimes they just constitute generic figures useful for design purposes. Furthermore, another advantage presented by this method is that once the parameters were determined and the equations adjusted they can be used to detect anomalies in power generation. The potentiality of the method was tested comparing its results against those predicted by other method of frequent use for diagnosis of large PV plants. When reliable information on the PV array is available the application of the methodology based on the protocol developed by IES-UPM is implemented easily as compared to the methodology based in bidimensional adjustment shown in this paper. The bi-dimensional fitting method presents the possibility of analyzing the PV array and establish the peak power under STC over the entire day and not only over a brief instant such is the case of testing by means of the I-V curve. Furthermore, I-V curve testing implies the momentary disconnection of the generator. More exhaustive assessment of the bi-dimensional methodology requires testing it on a larger number of PV systems, a matter for future work. Acknowledgements The authors wish to thank Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT), Argentina, for providing financial assistance for the research projects: PICTO CIN 0144/2010 and PICT 0300/2008. The authors also wish like to thank the support from Ministerio de Ciencia y Técnica through the binational research project CAPES- MINCyT BR11 Red07 and FONARSEC through the research project Fits Energía 008/2010. References [1] http://www.sunenergysite.eu. Available on-line at May-2013. [2] IEC 1829. Crystalline silicon photovoltaic PV array on-site measurement of I–V characteristics. Geneve. International Electrotechnical Commission IEC, 1995 [3] Blesser G and Munro D. Guidelines for Assessment of Photovoltaic Plants. Document A. Initial and periodic test on PV plants. Report EUR 16340 EN. Issue 2, 1995.

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