Energy 24 (1999) 93–102
Performance analysis of a grid-connected photovoltaic
system
M. Sidrach-de-Cardonaa,*, Ll. Mora Lópezb
a
Dpto. Fı́sica Aplicada II, E. T. S. De Ingenierı́a Informática, Campus de Teatinos, Universidad de Málaga,
Malaga, Spain
b
Dpto. Lenguajes y C. Computación, E. T. S. De Ingenierı́a Informática, Campus de Teatinos, Universidad de
Málaga, Malaga, Spain
Received 18 May 1998
Abstract
Grid-connected photovoltaic systems are required to introduce photovoltaic solar energy into urban areas.
To analyze these systems, a 2.0 kWp power system has been installed at the University of Málaga, Spain.
The array power output was estimated by using measured I–V curves for the installed modules with minimization of mismatch losses. The supplied grid energy and main performances are described. The effects
on system yield of threshold-inverter and coupling losses of the inverter to the grid have been studied.
During 1997, the system supplied 2678 kWh to the grid, i.e. the mean daily output, was 7.4 kWh. The
annual performance ratio was 64.5% and the optimal value 67.9%.  1999 Elsevier Science Ltd. All
rights reserved.
1. Introduction
Grid-connected photovoltaic systems represent important systems for potential use in all countries. Small grid-connected systems for use in detached or semi-detached houses are especially
promising developments. They will mean an important saving of conventional energy. The energy
produced by a grid-connected photovoltaic system depends on (i) climatic factors (incident
irradiation and module working temperature), (ii) inverter characteristics (yield, working point
and operation threshold, defined as the minimum required power to connect the inverter to the
grid) and (iii) the coupling system to the grid, which depends on the characteristics of the energy
* Corresponding author. Fax: 34-95-2132849; E-mail: msidrach@ctima.uma.es
0360-5442/99/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved.
PII: S 0 3 6 0 - 5 4 4 2 ( 9 8 ) 0 0 0 8 4 - X
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M. Sidrach-de-Cardona, Ll. Mora López / Energy 24 (1999) 93–102
produced by the inverter and on grid stability and availability. With the weather conditions in
Southern Spain, the adequate size of installation for a single-family housing is approximately 2
kWp. In order to study how the aforementioned parameters influence the operation of that installation, an experimental grid-connected photovoltaic system has been installed at the University
of Málaga, Spain.
The photovoltaic generator is composed of 42 I53 modules—the nominal power module is 53
Wp—connected in two branches in parallel, with 21 panels in series in each of them. The inverter
used is a Sirio PRM2 monophase: maximum power 2.2 kW, with input voltage ranging between
290 and 360 V DC and output of 230 V AC in phase with the grid. It uses the modulation system
by width of pulses, with a sinusoidal wave form. The working point follows the point of maximum
power of the photovoltaic generator. The integration of the system in the structure of the building
has forced us to install the modules with an inclination of 54° from the horizontal and with an
azimuth of 9° south-west (building orientation). Meteorological parameters and input–output
inverter data are recorded by the data acquisition system.
2. Characterization of the photovoltaic generator
In the manufacturer’s manual, the nominal power of the photovoltaic modules is referred to
standard conditions (STC): temperature of cell equal to 25°C, irradiance equal to 1000 W/m2,
and solar spectrum AM 1.5. It is well-known that manufacturers classify modules within the same
model according to their nominal power referred to standard conditions ⫾ 10%. As a result, it
is difficult to know, in practice, the real installed power and, hence, to quantify the mismatch
losses which are due to the dispersion of the module electrical characteristic parameters. The
steps followed to obtain the real installed power have been: (i) measurement, under outdoor conditions, of the characteristic I–V curve for the modules, (ii) correction of the curves to standard
conditions and determination of their electrical characteristic parameters, and (iii) following the
laws of modules association, determination of both the real peak power installed and the losses
due to dispersion of parameters.
When obtaining experimental measure of I–V curves, errors appear due to variations within
the solar spectrum and determination of module temperature. In order to minimize these errors,
the following measurement conditions have been imposed: global irradiance in the measure
plane > 750 W/m2; diffuse fraction ⬍ 10%; maximum variation of irradiance during time of
measurement ⬍ 1%; the measurement was made at solar noon (approximately); the temperature
sensor had good thermal coupling with the back face of module; maximum variation of module
temperature during time of measurement ⬍ 1°C; and wind speed ⬍ 1 m/s. With this method, the
estimated error on determining the maximum peak power point is 2.2%. Experimental curves
have been corrected to standard conditions, as in Ref. [1].
Summary data are given in Table 1 for standard conditions. The mean value of the power of
the modules is 9.4% lower than the nominal power. Previous papers [2,3] have obtained similar
deviations between nominal power of the modules (given by manufacturers) and power measured
in outdoor conditions. The standard deviations of parameters shown in Table 1 are also similar
to those obtained in other papers (see, for example, Ref. [4]). The frequency distribution of the
experimental maximum power values is shown in Fig. 1. With standard statistical test, it is poss-
M. Sidrach-de-Cardona, Ll. Mora López / Energy 24 (1999) 93–102
95
Table 1
Electrical characteristics of the photovoltaic modules under standard conditions
Parameter
Short circuit current Isc (A)
Open circuit voltage Voc (V)
Peak power Pm (W)
Peak-power voltage Vm (V)
Peak-power current Im (A)
Fill factor FF (%)
Mean
3.1
21.5
48.1
17.3
2.8
71.5
Maximun
3.2
22.1
50.8
17.8
2.9
73.5
Minimun
3.0
21.2
46.5
17.0
2.7
70.2
STD
0.04
0.22
0.93
0.19
0.04
0.79
Fig. 1. Frequency histogram for the peak power of the modules assuming a normal distribution.
ible to accept that these values follow a normal distribution with mean 48.1 W and standard
deviation 0.97 (significance level ⫽ 0.05). Hence, the estimated maximum peak power of the
photovoltaic generator would be 2016 W. To minimize mismatch losses, modules have been
sorted according to their peak-power current [5]. Modules with similar values of this parameter
have been connected in the same series. Photovoltaic array characteristics and mismatch losses
are reported in Table 2. The ohmic power losses under standard conditions have been calculated
by multiplying the cable resistance with the square of the current in the maximum power point.
The estimated array power is 1957 W, far from the manufacture power of the modules (53 Wp
⫻ 42 ⫽ 2226 W).
3. Evaluation of results
The experimental data from 1997 have been used. The evaluation has been carried out computing daily energy balances of the different parts in the installation. These balances allow us to
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M. Sidrach-de-Cardona, Ll. Mora López / Energy 24 (1999) 93–102
Table 2
Characteristics of the photovoltaic array under standard conditions
Parameter
Short circuit current (A)
Open circuit voltage (V)
Maximun power point current (A)
Maximun power point voltage (V)
Estimated array peak power (W)
Mismatch losses (%)
Ohmic losses (%)
Array area (m2)
Array efficiency (%)
6.1
450
5.4
362
1957
3
1.0
17.4
11.0
compute the mean daily yields of photovoltaic array, inverter and system. To compute these
efficiencies, two different types of data have been used: on the one hand, the energy received
when the inverter is working, on the other hand, all the daily energy incident on the generator
has been considered.
The daily photovoltaic array yield is given by
␩PV,d ⫽ EPV,d/Er,d,
(1)
where EPV,d is the daily energy (in kWh) supplied by the modules and Er,d the available daily
energy, defined as the daily irradiation on the plane of the array surface during the time when
the inverter is connected to the grid. Here,
冘
n
Er,d ⫽
(Ei ⫻ C),
(2)
i⫽1
where C ⫽ 0 if the inverter is out and C ⫽ 1 if the inverter is operating; n is the total number
of values recorded daily and Ei the total energy received on the plane of the array surface during
one measurement interval. Therefore, C ⫽ 0 for ‘Ei ⬍ the inverter threshold’ and ‘Ei ⱖ the
inverter threshold, while the inverter is disconnected from the grid’. For each month, the mean
daily value of the daily photovoltaic array yield is
冘␩
D
␩PV,m ⫽
PV,d
/D,
(3)
d⫽1
where D is the total number of days with data. Similarly, the monthly mean daily inverter yield is
冘␩
D
␩inv,m ⫽
inv,d
/D,
(4)
d⫽1
where ␩inv,d is the inverter daily yield, defined as the ratio between the daily active energy at the
output of the inverter and the daily energy at the input of the inverter.
The monthly average daily system yield is
M. Sidrach-de-Cardona, Ll. Mora López / Energy 24 (1999) 93–102
冘␩
97
D
␩sys,m ⫽
sys,d
/D,
(5)
d⫽1
where ␩sys,d is the daily system yield, computed as
␩sys,d ⫽ Egrid,d/Er,d,
(6)
where Egrid, d is the daily active energy at the output of the inverter and consequently, to the grid.
If the whole incident energy is considered, global yields can be defined. The global photovoltaic
array yield (␩G,PV,m) is the yield of the generator, using all the daily energy (Ei,d) received on the
plane of the array surface, that is
冘
D
␩G,PV,m ⫽
(EPV,d/Ei,d),
(7)
d⫽1
where d stands for daily value and m stands for daily monthly average. Hence, the global system
yield is computed as:
冘
D
␩G,sys,m ⫽
(Egrid,d/Ei,d).
(8)
d⫽1
The mean daily values for each month of the parameters are shown in Tables 3 and 4. The
daily mean values of both temperature of the modules (Tm) and ambient temperature (Ta)—computed during the hours of sun—are also shown. The system supplied 2678 kWh to the grid during
259 days, i.e. the daily mean energy was 7.4 kWh. In February and March the installation reaches
its greatest global daily yield. These are months with high values of daily irradiation and low
values of daily ambient temperature—and hence low values for the temperature of the modules.
Table 3
Mean daily values of ambient temperature, module temperature, energy received on the plane of array, input inverter
energy and output inverter energy
Month
Ta (°C)
Tm (°C)
January
February
March
April
May
June
July
August
September
October
November
December
13.3
16.5
17.4
19.5
21.2
25.2
26.2
27.6
25.5
23.0
17.7
14.8
22.3
32.2
33.6
34.8
37.0
42.0
43.6
45.2
42.2
36.6
29.0
25.3
Ei,d (kWh/m2)
3.3
6.0
6.6
5.8
5.9
6.3
6.5
6.6
6.3
5.6
4.3
3.8
EPV,d (kWh)
5.0
10.0
10.9
8.7
8.8
9.6
9.5
9.4
9.6
8.6
6.8
6.0
Egrid,d (kWh)
4.3
8.7
9.4
7.5
7.6
8.4
8.3
8.3
8.4
7.5
5.9
5.2
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M. Sidrach-de-Cardona, Ll. Mora López / Energy 24 (1999) 93–102
Table 4
Mean daily values of the main yield in the analyzed system
Month
␩PV,m (%)
␩inv,m (%)
␩sys,m (%)
␩G,PV,m (%)
␩G,sys,m (%)
Days with data
January
February
March
April
May
June
July
August
September
October
November
December
9.8
10.3
10.2
9.7
9.5
9.4
9.2
8.8
9.6
9.5
9.6
9.7
85.5
86.6
86.9
86.5
87.2
87.3
87.8
87.8
87.5
87.2
86.7
86.3
8.4
8.9
8.9
8.4
8.3
8.2
8.1
7.7
8.4
8.3
8.3
8.4
7.1
9.2
9.2
8.1
8.0
8.1
8.1
7.9
8.6
8.3
7.9
7.3
6.1
7.9
8.0
7.0
7.0
7.1
7.2
7.0
7.5
7.2
6.9
6.4
31
28
31
28
31
29
31
31
27
31
30
31
The mean daily yield of the inverter is about 85–88%, hence, its behaviour is good during the
periods of operation. However, some of the received energy is not used by the installation due
to operation threshold, see Table 4. On average, the system yield ranges between 7.7 and 8.9%
when the inverter is working (␩sys,m), but only between 6.1 and 8.0% if the whole daily energy
received on the plane of the array surface (␩G,sys,m) is considered. The reason why these differences
appear is twofold: on the one hand, the losses due to inverter–grid connection problems have
been, on average, 4.8% of the daily global incident energy, and these losses do not depend on
the daily irradiation; on the other hand, the results show that the inverter threshold losses strongly
depend on the incoming level of daily global irradiation, reaching levels close to 100% when this
irradiation in the array plane is below 750 Wh/m2. On clear days, these losses represent 3% of
the daily global irradiation [6]. These differences are greater on days with low irradiation.
The normalized frequency distribution of daily irradiation on the plane of the array surface is
shown in Fig. 2. The normalized frequency distribution of the daily energy supplied to the grid
is shown in Fig. 3. These distribution functions are clearly different. This shows that the efficiency
of the system strongly depends on the value of daily irradiation. For high values of irradiation,
these differences are due to the effect of the temperature on the system yield. For low irradiation
levels, these differences are due to the increase of the system losses. In previous papers [7,8],
grid-connected photovoltaic systems are examined assigning constant values to the yield of the
system components. These values are calculated during a specific operation period. However, our
results show that these yields must be quantified taking into account the received daily irradiation.
Only under these conditions is it justified to extrapolate these results to locations with a different
distribution of daily irradiation.
In order to compare the yield of the photovoltaic system with another PV system, two new
parameters are defined. The final yield is defined as the annual or daily system energy output
divided by Wp,e, where Wp,e denotes the previously estimated peak power of the array under
standard conditions:
Yf,d ⫽ Egrid,d/Wp,e,
(9)
M. Sidrach-de-Cardona, Ll. Mora López / Energy 24 (1999) 93–102
99
Fig. 2. Normalized frequency distribution for the daily global irradiation on the plane of the array surface.
Fig. 3. Normalized frequency distribution for the daily energy to the grid.
In other papers [9,10], the final yield is defined using the nominal peak power given by the
manufacturer. In this way, the real installed power is usually overestimated.
The annual final yield is,
冘
T
Yf,y ⫽
Yf,d,
d⫽1
(10)
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M. Sidrach-de-Cardona, Ll. Mora López / Energy 24 (1999) 93–102
where T is the number of days of the year with data.
The daily performance ratio (PRd) is defined [9] as the ratio between the daily final yield and
the daily global irradiation on the plane of the array surface Ei,d,
PRd ⫽ Yf,d ⫻ GSTC/Ei,d,
(11)
where GSTC is the irradiance under standard conditions. This ratio allows to compare our results
with those of other grid-connected photovoltaic systems, irrespective of their location, tilt angle,
orientation and nominal power.
The annual performance ratio is:
冘
T
PRy ⫽
冘
T
Yf,d ⫻ GSTC/
d⫽1
Ei,d,
(12)
d⫽1
The annual final yield of our installation is 1361 kWh/kWp. This value is, approximately, twice
as big as the one reported by B. Decker and U. Jahn [9], for grid-connected photovoltaic installations in Germany. This result shows how good the conditions of irradiation in Southern Spain
are for the use of solar energy systems. In our installation, the annual performance ratio is 64.5%.
Other authors have obtained values ranging between 57% and 73% for grid connected photovoltaic
systems [7–11].
The optimal daily performance ratio can be computed using the system yield and the energy
received on the plane of the array surface. This parameter shows how this installation would have
worked if the connection to the grid had been perfect. To obtain this parameter, it is necessary
to calculate the energy E⬘grid,d which would have been produced if there had not been any energy
losses due to connection problems with the grid. Thus,
E⬘grid,d ⫽ ␩sys,d ⫻ E⬘r,d,
(13)
where E⬘r,d is the daily energy received on the plane of the array surface, when condition ‘Ei ⬍
inverter threshold’ is met. Similarly, the optimal daily final yield (Y⬘f,d) is defined as Eq. (9) but
replacing Egrid,d by E⬘grid,d and the optimal annual final yield is defined as Eq. (10) but replacing
Yf,d by Y⬘f,d. The daily optimal performance ratio (PR⬘d) and the annual optimal performance ratio
are defined as Eq. (11) and Eq. (12), respectively, but replacing Yf,d by Y⬘f,d.
In our case, the optimal annual final yield is 1424 kWh/kWp. The improvement amounts to
4.4% with respect to the annual final yield.
Fig. 4 shows normalized frequency distributions for the daily performance ratio and the daily
optimal performance ratio. The performance ratio is greater that 60% in 84% of days. PRd is zero
when the daily irradiation has been below the inverter threshold. Small PRd values correspond to
days in which losses due to the inverter threshold have had a significant influence on the behaviour
of the system. When losses due to connection problems with the grid are ignored, this figure
shows that PR⬘d is greater than 60% on 90% of days. The annual optimal performance ratio
is 67.9%.
M. Sidrach-de-Cardona, Ll. Mora López / Energy 24 (1999) 93–102
101
Fig. 4. Normalized frequency distribution for the daily performance ratio PRd and the optimal performance ratio PR⬘d.
4. Conclusions
A photovoltaic system has been installed and analyzed at the University of Málaga in order to
examine the behaviour of grid-connected photovoltaic systems in the climatic conditions of Southern Spain. The real installed peak power has been determined previously. This parameter is essential to know the final yield and the performance ratio of the system. It has been found that, on
average, the real power of the modules is 9.4% lower than the nominal power given by the manufacturer.
The mean daily energy generated by our installation has been 7.4 kWh. This means 3.8
kWh/kWp. On monthly average, the system yield ranges between 7.7 and 8.9% when the inverter
is working, but only between 6.1 and 8.0% if the whole daily irradiation is considered. These
differences are greater in winter months. They are due, basically, to the strong dependence of the
inverter threshold losses on daily irradiation. Thus, on days with low irradiation, the inverter is
not able to make connection with the grid. Apart from these losses, it is also necessary to take
into account losses due to problems of connection with the grid—the mean value of these losses
is 4.7% of the daily irradiation.
The final yield and the performance ratio of the system have been calculated. These parameters
have been optimized in order to remove the influence on the system yield of losses due to problems
in the grid. The obtained optimal annual final yield of the system is 1424 kWh/kWp. The improvement amounts to 4.4% with respect to the annual final yield of the system, 1361 kWh/kWp. The
annual performance ratio of this system is 64.5%, and its annual optimal performance ratio is
67.9%. This means that simply by solving the coupling problems between inverter and grid, it is
possible to obtain, with the same installation, daily values close to 4.0 kWh/kWp.
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M. Sidrach-de-Cardona, Ll. Mora López / Energy 24 (1999) 93–102
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