- Email: [email protected]
A new method based on charge parameters to analyse the performance of stand-alone photovoltaic systems
ARTICLE IN PRESS
Solar Energy Materials & Solar Cells 90 (2006) 1750–1763 www.elsevier.com/locate/solmat
A new method based on charge parameters to analyse the performance of stand-alone photovoltaic systems F.J. Mun˜oz, G. Almonacid, G. Nofuentes, F. Almonacid Grupo IDEA, Departamento de Ingenierı´a Electro´nica, de Telecomunicacio´n y Automa´tica, Universidad de Jae´n, Campus las Lagunillas, 23071 Jae´n, Spain Received 5 July 2005; accepted 21 October 2005 Available online 13 December 2005
Abstract The monitored data in photovoltaic systems are processed to determine overall energy balances which, together with the energy efficiencies and indices of performance, give a good indication of the performance of PV systems. However, the analysis based on energy parameters shows some shortcomings when they are used to analyse the performance of stand-alone photovoltaic (SAPV) systems, especially those without Maximum Power Point Tracker (MPPT). This kind of systems represents a large percentage of the SAPV systems (e.g. demonstration projects, consumer and industrial applications, Solar Home Systems in developing countries, etc.). This paper tries to give an alternative method that manages to analyse this kind of systems in a better way. This method is based on a translation of the energy parameters given by the Joint Research Center and the IEC Standard 61724 into new charge-related parameters. It must be said that charge parameters can be used by themselves to evaluate the system performance. Therefore, it is not necessary to deduce energy parameters using the nominal battery voltage. The monitored data of two SAPV systems without MPPT are used to compare the performance of these systems based on energy parameters with the analysis provided by the new charge parameters. This study will highlight the advantages of the charge parameters method. r 2005 Elsevier B.V. All rights reserved. Keywords: Monitoring; Stand-alone PV systems; Performance
Corresponding author. Tel.: +34 953 212810; fax: +34 953 211967.
E-mail address: [email protected] (F.J. Mun˜oz). 0927-0248/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2005.10.020
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
1751
1. Approach. Charge parameters in the analysis of SAPV systems performance The analysis method, based on energy parameters, given by the JRC in their European Guidelines for the Assesment of Photovoltaic Plants [1,2] and the IEC Standard 61724 [3] do not reflect the proper operation of the stand-alone photovoltaic (SAPV) systems from a technical point of view as it is the case for grid connected systems. Therefore, some new coefficients (e.g. Production Factor, PF, and Matching Factor, MF) have already been introduced within IEA PVPS Task 2 [4,5]. However, we must consider that the normalised performance indicators such as the energy yields (e.g. Yr, YA, Yf, LC, LS) are normalised to the nominal power of the array, P0. Furthermore, other system performance indices (PR, PF and MF) also depend on this parameter. SAPV systems without Maximum Power Point Tracker (MPPT) cannot usually manage to reach the maximum power point as the array voltage is largely determined by the battery. For the battery voltage usually presents little variations, it will be the array current which determines the array power. Therefore, the estimation of the potential energy of the array from the in-plane irradiation, HI, and the nominal power of the array would represent the theoretical energy that can be delivered by the array, but it would not lead to a proper estimation of the real potential of this kind of systems. Furthermore, we have observed that if pulse-width modulation (PWM) charge regulators are used, the monitored energy provided by the array, EA, is overestimated. The more the PWM techniques are used by the charge regulator, the greater is the overestimation. For those reasons, it is intended to develop a new method to analyse the performance of SAPV systems without MPPT. This method will be based on charge parameters. Although JRC indicates that instead of energy balances, the time integral of the corresponding currents (Ah) may be recorded, and energy parameters can be deduced using the nominal battery voltage, it tells that this should be avoided as some parameters will be overestimated or underestimated [2] when trying to extrapolate the energy performance of the system from a charge point of view. However, the charge parameters presented here can be used by themselves to evaluate the system performance. As a result, the error mentioned above will not be introduced as it is not necessary to obtain energy parameters from charge parameters using the nominal battery voltage. The proposed charge parameters (charge balances and the charge indices of performance) together with their counterpart energy parameters, considering a daily reporting period, t, are given in Table 1. However, if necessary, it can be obtained weekly or monthly reports. This set of parameters constitutes a new method to analyse better the performance of SAPV systems. In Table 2 there have been defined the different parameters that must be measured and recorded to obtain the parameters given in Table 1. The energy balances of the system are calculated from their recorded monitoring power parameters over the reporting periods such as days, weeks, months or years. In the same way, charge balances can be obtained as the time integral of their corresponding measured current parameters over the reporting period. This new scope in the performance analysis of SAPV systems has taken the battery voltage as the system reference voltage. In this way, all the charge balances will be related to this one. This is true if SAPV systems without MPPT and no converters in the load side are considered. If the last ones are used and there is one element in the system operating at a different voltage, it should be only applied a correction factor to normalise its voltage to
Wh/d Wh/d Wh/d Wh/d Wh/d Wh/d Wh/d Wh/d Wh/d — Wh/d Wh/d — Wh/d Wh/(d Wp) Wh/(d Wp) Wh/(d Wp) Wh/(d Wp) Wh/(d Wp) —
ESI
ESO
ETS EFS EL EL,AC
EL,DC
EII
EIO
ZI
Ein Euse FA
Euse,PV Yr
YA
Yf
LC LS PR
PF
ZSYS
MF
Energy to storage
Energy from storage
Net energy to storage Net energy from storage Energy to loads Energy to AC loads
Energy to DC loads
DC-energy input to inverter
AC-energy output from inverter
Energy efficiency of the inverter
Total input energy Useful energy supplied by the system Array fraction
Direct PV contribution to Euse Reference yield
Array yield
Final yield
Capture losses System losses Performance ratio
Production factor
System efficiency
Matching factor
—
—
—
Potential array charge Array output charge
H I P0 R I A V A dt Rday I SI V S dt Rday day I SO V S dt
Wh/d Wh/d
EP EA
Potential array energy Array output energy
PR FA
¼
Matching factor
System efficiency
Production factor
PR PF
Yf YA
YA Yr
Yf Yr
Capture losses System losses Performance ratio
Final yield
Array yield
Direct PV contribution to Quse Reference yield
Total input charge Useful charge supplied by the system Array charge fraction
Charge efficiency of the inverter
AC-charge output from inverter
DC-charge input to inverter
Charge to DC loads
Net charge to storage Net charge from storage Charge to loads Charge to AC loads
Charge from storage
Yr YA YA Yf
E use;PV P0
ðE SI E SO Þþ ðE SO E SI Þþ E L;AC þ E L;DC R day PL;AC dt R day I L;DC V S dt R I II V S dt Rday day PIO dt E IO E II E FS þ E A þ E BU E L þ E TS EA E in F A E use EP PSH ¼ P0 EA P0
Parameter
Equation
Unit
Symbol
Parameter
Charge to storage
Charge parameters
Energy parameters
Ah/d Ah/d
QII QIO
MFQ
ZSYSQ
PFQ
LCQ LSQ PRQ
YfQ
YAQ
Quse,PV YrQ
Qin Quse FAQ
—
—
—
Ah/(d Ap) Ah/(d Ap) —
Ah/(d Ap)
Ah/(d Ap)
Ah/d Ah/(d Ap)
Ah/d Ah/d —
—
Ah/d
QL,DC
ZIQ
Ah/d Ah/d Ah/d Ah/d
Ah/d
QTS QFS QL QL,AC
Ah/d
QSO
Ah/d Ah/d
Unit
QSI
QP QA
Symbol
S
AQ
Y
¼ Y fQ
PRQ F AQ
Y fQ Y rQ Y AQ Y rQ PRQ PFQ
Y rQ Y AQ Y AQ Y fQ
Quse;PV I0
QA I0
QFS þ QA þ QBU QL þ QTS QA Qin F AQ Quse Q PSH ¼ P I0
QIO QII
ðQSI QSO Þþ ðQSO QSI Þþ QL;AC þ QL;DC R 1 day PL;AC V S dt R V L;DC I L;DC V dt S Rday day I II dt R 1 day PIO V dt
HII 0 R I A dt Rday I SI dt Rday day I SO dt
Equation
Table 1 Energy and charge parameters for the analysis of the performance of SAPV systems without MPPT. It has been considered a daily reporting period. Furthermore, due to the relative low power of SAPV systems without MPPT, the energy parameters will be expressed in Wh instead of kWh 1752 F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
ARTICLE IN PRESS
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
1753
Table 2 Parameters to be measured and recorded to obtain the parameters given in Table 1 Parameter
Symbol (Unit)
Total irradiance (array plane) Array output voltage Array output current Battery voltage Current input to storage battery Current output from storage battery Load voltage Current to all dedicated AC loads Power to all dedicated AC loads Inverter DC current Inverter AC power
GI (W/m2) VA (V) IA (A) VS (V) ISI (A) ISO (A) VL (A) IL,DC (A) PL,AC (W) III (A) PIO (W)
the battery voltage (i.e. if a DC converter is used to power a load which operates at a different voltage Rthan the battery one, the charge given to the load by the DC converter R will be given by I L ðV L =V S Þ dt instead of I L dt). In the literature there are already design methods of SAPV without MPPT which are based on charge instead of energy parameters [6,7]. It would be very interesting to translate this idea to the analysis of the SAPV systems performance from the recorded monitoring data. 2. Experimental results The monitored data of two SAPV systems without MPPT and without any type of converter in the load side (with no inverter or DC/DC converter), Table 3, are used to compare the system performance based, respectively, on energy and charge parameters. The first system, denoted system 1, is a 200 Wp SAPV system which illuminates at night a pergola installed at the flat roof of the Escuela Polite´cnica Superior de Jae´n. The second one, denoted system 2, is a SAPV system which has been integrated in a health emergency vehicle [8]. This hybrid system has been designed as a juxtaposition of two energy sources: a 400 Wp PV system and the conventional alternator vehicle. Both systems have a 200 Ah lead–acid battery as the storage unit. 2.1. Potential energy of a SAPV without MPPT As it has been indicated above, a SAPV without MPPT cannot usually achieve the maximum power point. Therefore, the potential energy given by the array, EP, stated by the JRC and IEC 61724 will lead, in this kind of systems, to an overestimation of the potential of the array. EP indicates the maximum theoretical energy that can provide the array but it does not represent its real potential. In order to evaluate the real potential of these systems, the array charge potential, QP, can be considered. This one is obtained from the in-plane irradiation, HI, and the nominal current, I0. In normal operating conditions, the generated current will be between the
ARTICLE IN PRESS 1754
F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
Table 3 Components of systems 1 and 2 System 1 SAPV system which feeds the lamps that illuminates the pergola installed at the flat roof of the Escuela Politecnica Superior de Jae´n
System 2 SAPV system installed in a health emergency vehicle to charge its original and service battery
200 Wp PV array (4 50 Wp modules each containing 36 serial cells) ISC,array ¼ 13.08 A VOC,array ¼ 21.6 V 200 Ah valve regulated lead–acid (VRLA) battery VS ¼ 12 V 30 A PWM charge regulator 400 Wp PV generator (8 50 Wp, modules each containing 36 serial cells) ISC,array ¼ 26.16 A VOC,array ¼ 21.6 V 200 Ah VRLA battery (service battery) 95 Ah SLI battery (original battery) VS ¼ 12 V 30 A PWM charge regulator
shortcircuit current, ISC, and the maximum power point current. In order to consider the worst case it has been chosen this last one. Moreover, this consideration will correct the effect of high temperatures [9]. Anyway, due to the proximity between ISC and the maximum power point current, this underestimation involves an error much lower than the one associated with the overestimation given by EP. The daily performance of system 1 based, respectively, on an energy and a charge basis during different days is shown in Fig. 1. As it can be observed, during some days (e.g. days 2, 3 and 4), the array output energy, EA, is lower than the energy given to loads, EL, although the array potential energy, EP, is greater than this last one. On the other hand, the charge array potential, QP, gives a more realistic value, showing that this last one is lower than the charge given to the loads, QL, and justifying, in these circumstances, that the array could not cover completely the load demand. Furthermore, it can be pointed out that the relative difference between the estimated energy potential defined by EP and the energy given by the array is much greater than the difference between QP and QA. EP is not a good indicator of the real potential of the array for it considers the maximum power point voltage as the array voltage (the real array voltage is lower than this last one). Meanwhile, the array charge potential, QP, gives a more realistic value of the array potential as it is only calculated from the array maximum power point current which is very close to the current given by the array. ETS and EFS are the energy battery balances and indicate, respectively, the net energy supplied to storage, (ESI–ESO)+, and the net energy drawn from storage, (ESO–ESI)+, where x+ denotes a minimum value of 0. On the other hand, the battery charge balances are given by QTS and QFS, which indicate, respectively, the net charge to storage, (QSI–QSO)+, and the net charge drawn from storage, (QSO–QSI)+. Later, in Section 2.3 we will study and compare these parameters.
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
1755
Daily System Performance. Energy Parameters EP
1800 1600
EL
EA
ETS
EFS
1534.73
Wh/dWp
1400 1191.93
1200 1000
947.23 838.25
800
774.05
710.40
600
772.65
714.40 598.35 490.09 386.40
472.90
400
245.36
200
188.48
118.71 0.00
0
107.64 0.00
0.00
day 1
686.38 635.58
590.84
day 2
42.84
0.00
day 3
day 4
0.00
day 5
Ah/dAp
Daily System Performance. Charge Parameters 100 90 80 70 60 50 40 30 20 10 0
QP
QL
QA
QTS
QFS
88.18
68.48 61.94
61.30 56.19
55.86
54.42
50.93 51.25 44.38
44.47
40.33 35.14
34.38 29.44 21.07 17.57 10.89
5.44 0.00
day 1
0.00
day 2
0.00
day 3
0.00
day 4
0.33 0.00
day 5
Fig. 1. Daily performance of system 1 based, on an energy and a charge basis. EP is not a good indicator of the real potential of the array for it considers the maximum power point voltage as the array voltage (the real array voltage is lower than this one).
2.1.1. Charge and energy indices of performance We are going to study the effect of the overestimation of the array potential energy on the energy indices of performance. Furthermore, these last ones will be compared with the proposed charge indices of performance. The reference yield, Yr, represents the theoretically available energy per day per Wp (due to the relative low power of SAPV systems, we use Wp instead of kWp). On the other hand, the reference yield expressed in charge units, YrQ, indicates the theoretically available charge per day and Ap (peak-Ampere). Both parameters represent the number of peak sun-hours per day (or number of hours of the standard irradiance, 1 kW/m2, which would produce the same daily irradiation). The array yield, YA, and the one indicated in terms of charge, YAQ, show, respectively, the energy delivered by the array per day and Wp, and the charge given by the array per day and Ap. These yields represent the number of hours per day that the array would need to be operated at its rated output power/current to give the same output as the recorded integral value for that day.
ARTICLE IN PRESS 1756
F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
The final yield, Yf, represents the actually used PV energy per day per Wp while YfQ indicates the actually used PV charge per day and per Ap. These yields represent the number of hours per day that the array would need to operate at its rated output power or current to equal its monitored contribution to the daily load. Finally, the normalised losses are defined as the differences between yields. In that way, the array capture losses expressed in terms of energy and charge are defined, respectively, by LC ¼ Yr–YA and YCQ ¼ YrQ–YAQ. LCQ represent the same capture losses as LC except for the maximum power point losses (i.e. operating cell temperature higher than 25 1C, partial shading, low irradiance, reduction of array current when the battery is fully charged and wiring losses). The wiring losses can be calculated if the charge balances are normalised to the battery voltage considering the different system voltages. The system losses can be defined, in the same way, in terms of energy or charge by LS ¼ YA–Yf and LSQ ¼ YAQ–YfQ. Both parameters show the storage losses in the battery, the inverter or DC–DC converter losses and the wiring losses from the battery to the loads. In Fig. 2 are shown the energy and charge system yields and the normalised losses during different days. As it can be observed, the energy capture losses are, in percentage, much higher than the charge ones. This is due to the overestimation of the array potential given by EP: the energy capture losses includes maximum power point losses, which are intrinsic losses in SAPV systems without MPPT. Moreover, the capture losses due to the maximum power point losses can overestimate the total capture losses, making, in some occasions, more difficult the identification of other capture losses (low irradiance, wiring losses, partial shading, etc.). If we compare the system losses, we can also see, on a percentage basis, how the energy ones are slightly higher than the charge ones. As it will be explained later in Section 2.2, this is due to the overestimation of the energy provided by the array, EA, when PWM charge regulators are used. Moreover, both systems losses, LS and LSQ, are very low as there are no converters in the load side and the wiring losses between the battery and the loads are negligible. The charge performance ratio, PRQ, is the ratio of the PV charge actually used to the charge theoretically available (i.e. YfQ/YrQ), while the charge production factor, PFQ, is the ratio between the charge provided by the array and the charge theoretically available (i.e. YAQ/YrQ). If we compare the energy indices of performance (denoted PR and PF), with the charge ones, PRQ and PFQ, Fig. 3, we observe that the energy indices of performance are lower than their charge counterparts. This can be explained as the energy indices of performance are related to the reference yield, Yr, which depends on EP (see Table 1). As it has been mentioned before, in SAPV systems without MPPT there is an overestimation of the potential array energy where the maximum power point losses are included in the calculations of the energy indices of performance. This will lead to an underestimation of the real performance of SAPV systems without MPPT. On the other hand, the charge indices of performance (PRQ and PFQ) give better information about the performance of the system as they consider the charge reference yield, YrQ, which take into account the real potential of the array provided by QP. In Fig. 3, the system efficiencies from an energy and charge point of view, Zsys and ZsysQ (Table 1) have also been included. As the system losses are negligible, both parameters are close to one.
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
1757
Energy Indices of Performance YF LS LC 100% 90% 80%
3.17
1.37
0.96
1.62
0.01
0.02
2.30
Wh/(day Wp)
70% 0.01
60% 50%
0.04
0.04
40% 30%
3.77
2.14
1.74
2.66
3.08
2
3 day
4
5
20% 10% 0% 1
Charge Indices of Performance YFQ LSQ LCQ 100% 90% 2.13 80% Ah/(day Ap)
70%
0.74
0.39 0.00
0.00
0.79
1.36
0.00 0.00
0.00
60% 50% 40% 4.85
2.78
2.33
3.51
4.05
30% 20% 10% 0% 1
2
3 day
4
5
Fig. 2. Daily energy indices of performance versus daily charge indices of performance. Data obtained from system 1.
2.2. Overestimation of E A in SAPV systems We have observed that if PWM charge regulators are used, the monitored array output energy, EA, can be much higher than the product of the array output charge, QA, and the nominal battery voltage. This control regime, used by a great number of charge controllers, is based on delivering current pulses, which width is controlled by a pulsewidth modulator, to the battery. It is applied when the battery voltage approaches the endof-charge voltage. When this occurs, the battery voltage is kept constant while the current
ARTICLE IN PRESS 1758
F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
Energy Indices of Performance PR
PF
ηsys
1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 day 1
day 2
day 3
day 4
day 5
day Charge Indices of Performance PRQ
PFQ
ηsysq
1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 day 1
day 2
day 3
day 4
day 5
day Fig. 3. Daily indices of performance (e.g. performance ratio and production factor) based on an energy and charge basis. Data obtained from system 1. In SAPV systems without MPPT there is an overestimation of the potential array energy, which will lead to an underestimation of the real performance ratio, PR, and production factor, PF, of the system.
delivered to the battery is slowly diminished by reducing the duty cycle. These current pulses have associated voltage pulses in the array, providing, when monitoring, high array voltage samples, and they can be much higher than the battery voltage, Fig. 4. In these conditions, the energy delivered by the array, calculated as the time integral of the product of the array current and the array voltage, will lead to a greater value than the real one. This error could be avoided if we sample at the same time and considering a high sampling frequency the two channels corresponding to the array current and voltage, and consequently obtain the power given by the array as the product of these two parameters. One solution to this problem would be to use advanced and much more expensive data
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
1759
18.00 Array Voltage (VA) Battery Voltage (VS)
16.00
Alternator Voltage 14.00 12.00
V
10.00 8.00 6.00 4.00 2.00
23:15:00
22:30:00
21:45:00
21:00:00
20:15:00
19:30:00
18:45:00
18:00:00
17:15:00
16:30:00
15:45:00
15:00:00
14:15:00
13:30:00
12:45:00
12:00:00
11:15:00
9:45:00
10:30:00
9:00:00
8:15:00
7:30:00
6:45:00
6:00:00
5:15:00
4:30:00
3:45:00
3:00:00
2:15:00
1:30:00
0:45:00
0:00:00
0.00
time
Fig. 4. Array voltage versus battery voltage. If PWM charge regulators are used, the energy delivered by the array, calculated as the product of the array current and the array voltage, will be overestimated. Data obtained from system 2: a health emergency vehicle with a 400 Wp PV array integrated in its roof. The daily vehicle load demand can be supplied by the vehicle alternator and the PV array.
loggers that could sample simultaneously the array current and voltage. Another solution would be to measure directly with a power sensor. However, with the analysis method proposed in this paper none of these solutions are necessary as the array output charge does not suffer any overestimation as it does not use the array voltage, it only considers the array current. A more representative value of the energy delivered by the array is provided by the time integral of the product of the array current and the battery voltage. This is true if a SAPV without MPPT is considered. We can compare R R the array output energy defined as I A V A dt with the array output energy given by I A V S dt, and calculate the relative error defined by the following equation: R R day I A V A dt day I A V S dt R relative error ¼ 100: (1) day I A V S dt We have measured this error considering a daily reporting period and different use levels of the PWM techniques by the charge regulator: high, medium and low. A medium use of the PWM techniques is considered when the charge regulator applies this type of control between the 30% and 70% of the daily generating period. On the other hand, a high and low use will be taken into account when the PWM techniques are applied, respectively, more than 70% and below the 30% of the daily generating period. As it can be observed in Fig. 5, which shows for system 2 the relative error in the estimation of the array output energy when using PWM charge regulators, the more the charge regulator uses the PWM
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
%
relative error
PR
20.00
0.50
15.00
0.40 0.30
10.00
0.20
5.00
PR
1760
0.10 0.00
0.00 High PWM Level
Medium PWM Level
Low PWM Level
Fig. 5. Relative error in the estimation of the array energy, EA, when using PWM charge regulators versus the mean daily performance ratio. A daily reporting period and different use levels of the PWM techniques, high, medium and low, have been considered. Data obtained from system 2.
techniques, the higher is the error. If the charge regulator applies this type of control almost all the time during the generating period, the relative error can reach 18%. If a medium use of this technique is considered, the error can be around 12%. Finally, if there is a little use of the PWM techniques, the error is reduced to 4%. A possible solution to estimate the array energy in SAPV systems without MPPT would be to take EA as the time integral of the product of the array current and the battery voltage. However, this idea would be equivalent to considering the array output charge, QA. It must be remembered that if we use charge parameters they are related to the battery voltage. In Fig. 5 the mean daily performance ratio has also been included. As it could be expected, the higher the use of the PWM techniques, the lower is the PR. This indicates that professional photovoltaic systems, which have been oversized to provide low Loss of Load Probability (LLP), and therefore will generally report low PR values, are going to be more susceptible to this overestimation of the energy given by the array. The overestimation of the total array output energy, EA, is spread over the rest of related parameters: Ein (total input energy), FA (PV array fraction of total input energy), Euse,PV, (direct PV energy contribution to Euse), YA, (array yield), Yf, (final yield), LC (capture losses), LS (system losses), PF (production factor) and PR (performance ratio). The relative error in each performance index due to the overestimation of the array energy, EA, when using PWM charge regulators, is shown in Fig. 6. That is, we are comparing the daily performance indices obtained from EA considering the array voltage with those calculated from the array energy obtained from the battery voltage. As it can be observed, the relative error in the performance indices generally increases as there is a higher use in the PWM techniques. The overestimation of EA generally produces an overestimation of the indices of performance. This is true except for the capture losses, which suffers an underestimation. The high relative error given by the system losses, LS, is due to the low absolute value of this kind of losses obtained from the analysis performance of system 2. 2.3. Charge and energy balances When the two methods are compared, the information level that can be offered from these two scopes must be considered. In this way, the daily energy and charge balances are shown in Fig. 1 to illustrate the performance of system 1.
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
100.00 80.00
1761
Low PWM level Medium PWM Level High PWM level
%
60.00 40.00 20.00 0.00 -20.00
YA
YF
LC
LS
PR
PF
Fig. 6. Relative error in each performance index due to overestimation of array energy, EA, when using PWM charge regulators. Data obtained from system 2. A daily reporting period and different use levels of the PWM techniques, high, medium and low, have been considered.
As it has been mentioned before, the array potential shown by QP is more realistic than the estimation given by EP. Furthermore, the charge given by the array, QA, is also more realistic than its counterpart EA, which, as it has been mentioned above, suffers from overestimation when PWM charge regulators are used. If we pay attention to the charge given to the loads, QL, there is nothing to point out as this one gives the same information as its relative, energy one. However, if we pay attention to the battery energy balances, given by ETS (net energy supplied to storage) and EFS (net energy drawn from storage), and the battery charge balances, provided by QTS (net charge to storage) and QFS (net charge from storage), we observe that, in most cases, the net energy given to the battery is higher than the net energy given to the battery calculated as the product of QTS and the nominal battery voltage. On the other hand, the net energy provided by the battery is lower than the one calculated from the net charge provided by the battery and the battery voltage. In short, the energy balances of the battery provide a more generous estimation of the State of Charge (SOC) of the battery than the one offered by the charge battery balances. However, this estimation is not realistic as the energy efficiency of a battery is lower than the charge efficiency. The energy efficiency is around 70–80%, while the charge efficiency can even reach the 95% [10] for lead–acid batteries. Although lead acid charge efficiency is affected by factors such as the battery SOC, battery design, battery grid alloy, charge rate, battery history, battery age and cycle Depth of Discharge (DOD) [11], the charge efficiency will be generally higher than the energy efficiency. Therefore, the charge parameters would lead to a better estimation of the SOC of the battery. Besides, the low-energy efficiency not only can give erroneous values of EFS and ETS but can affect the other system performance parameters such as Ein, FA, Euse,PV, Yf, LS and PR. For long reporting periods (i.e. several months) in which the net energy supplied or drawn from storage are much greater than the energy storage capacity (by more than a factor of 10), EFS and ETS are worthless in the calculations of the system performance, as any difference between these two parameters is primarily due to the efficiency of the battery. On the other hand, for short reporting periods (1 day or just a few days), in which
ARTICLE IN PRESS 1762
F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
EFS and ETS are at least ten times lower than the energy storage of the battery, ETS and EFS become important terms in the system performance calculations as, in this case, any difference between ETS and EFS is due to the change in the amount of energy stored in the battery [3]. Although the IEC 61724 indicates that the effect of the efficiency of the battery can be assumed negligible, it is clear that this assumption becomes more real if we consider charge battery balances, as the charge efficiency is higher than the energy efficiency. Therefore, the charge battery balances will provide a better estimation of the battery SOC and, hence, of the system performance too. The Ah balance management assumes that all current supplied is used for the battery charge. Although, the charge efficiency for a discharged battery is initially about 99%, the efficiency will drop off as the battery approaches higher SOC, and approach zero near 100% SOC. In that way, the battery is recharged with coefficients varying from 105% for valve regulated lead–acid (VRLA) to 130% for vented batteries to compensate for the energy used by the hydrolysis of water at the end of the charge. Furthermore, the Amperehours needed for water electrolysis increases when the battery gets old because of the internal resistance. Although the counting system may not be precise enough and the value obtained may change after a few cycles, this method enables a short-term evaluation that consequently avoids deep discharge and overcharges [12]. Furthermore, batteries are key elements in SAPV systems as they account for more than 30% of the lifecycle costs of solar off-grid systems [13]. In SHS it can even reach 50% [14]. Therefore, it would be very important not only to pay attention to the system performance but to keep an eye on the battery performance too, watching if there are overcharges and deep discharges, and if they are frequent or not. Short reporting reports, together with a more accurate information about the SOC of the battery, given by the charge battery balances, will help not only to know better the system performance but to keep the system’s batteries in good SOC as it will permit to take right decisions when necessary. 3. Conclusions We have presented a new method to analyse the performance of SAPV systems without MPPT. In this way, the results of the analysis of two SAPV systems have been shown. The analysis has been made from two different scopes, the one given by the energy parameters as the JRC and the IEC 61724 indicate, and the other provided by the new charge parameters. It has been proved that the method based on charge parameters is more accurate and gives better information about the performance of the system as:
The array charge potential, QP, gives a more realistic value of the array potential. QP is only calculated from the array maximum power point current which is very close to the current given by the array. On the other hand, the method based on energy parameters leads to an overestimation of the real potential of SAPV systems without MPPT. Moreover, this can lead to an overestimation of the capture losses and an underestimation of the performance ratio and the production factor. The array output charge, QA, is not overestimated if the charge regulator uses PWM techniques, as it is the case with the total array output energy, EA. As only the array current is considered, the high value that can reach the array voltage under PWM
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
1763
techniques is not taken into account. Therefore, there is no error that can be spread over other related parameters. The battery charge balances provide a better estimation of the SOC of the battery as the charge efficiency of a battery is larger than the energy efficiency. The energy battery balances offer a worse estimation of the battery SOC, which will give a poorer analysis of the system’s performance, especially for short reporting periods.
Furthermore, it must be remembered that the battery SOC and most of the information related to the battery offered by the battery manufacturer is given in Ampere-hour. This is one more reason, in addition to the ones mentioned above, for considering conveniently operating with the charge parameters instead of energy parameters in SAPV systems, especially in those without MPPT. References [1] Commission of the European Communities, Photovoltaic System Monitoring, Guidelines for the Assesement of Photovoltaic Plants, Document A, version 4.3, March 1997. [2] Commission of the European Communities, Photovoltaic System Monitoring, Guidelines for the Assesement of Photovoltaic Plants, Document B, version 4.3, March 1997. [3] International Standard IEC 61724. Photovoltaic System Performance Monitoring—Guidelines for Measurement, Data Exchange and Analysis, first ed., International Electrotechnical Commission (IEC), Geneve, April 1998. [4] D. Mayer, M. Heidenreich, Performance analysis of stand-alone PV Systems from a rational use of energy point of view, in: Proceedings of the Third World Conference on Photovoltaic Energy Conversion, Osaka, Japan, June 2003. [5] A. Sobirey, H. Riess, P. Sprau, Matching factor—a new tool for the assesment of stand-alone systems, in: Proceedings of the Second World Conference and Exhibition, Vienna, Austria, July 1998. [6] PV Design Center, Stand-Alone Photovoltaic Systems, A Handbook of Recommended Design Practices, Sandia National Laboratories Albuquerque, NM, USA, 1993. [7] R. Messenger, J. Ventre, Photovoltaic Systems Engineering, CRC Press, Boca Raton, FL, 2000, pp. 193–235. [8] G. Almonacid, et al., Integration of PV Systems on health emergency vehicle, The FIVE Project, Prog. Photovoltaics 12 (2004) 609. [9] M.A. Abella, Sistemas Fotovoltaicos, Inroduccio´n al Disen˜o y Dimensionado de Instalaciones de Energı´ a Solar Fotovoltaica, S.A.P.T Publicaciones Te´cnicas S.L.: Madrid, 2001, p. 244. [10] T. Markvart, L. Castan˜er, Practical Handbook of Photovoltaics, Elsevier Science, Oxford, 2003, p. 594. [11] IEEE Standard 1361, IEEE Guide for Selection, Charging and Evaluation of Lead–Acid Batteries uses in Stand-Alone Photovoltaic (PV) Systems, IEEE, New York, December 2003, p. 18. [12] Report IEA PVPS Task 3, Management of Storage Batteries used in Stand-Alone Photovoltaic Power Systems. [13] A. Luque, S. Hegedus S. Handbook of Photovoltaic Science and Engineering, Wiley, Chichester, 2003, p. 785. [14] Report IEA-PVPS T3-18:2004, Evaluation of Energy Storage Devices in Stand-Alone PV Power Systems, p. 9.
Solar Energy Materials & Solar Cells 90 (2006) 1750–1763 www.elsevier.com/locate/solmat
A new method based on charge parameters to analyse the performance of stand-alone photovoltaic systems F.J. Mun˜oz, G. Almonacid, G. Nofuentes, F. Almonacid Grupo IDEA, Departamento de Ingenierı´a Electro´nica, de Telecomunicacio´n y Automa´tica, Universidad de Jae´n, Campus las Lagunillas, 23071 Jae´n, Spain Received 5 July 2005; accepted 21 October 2005 Available online 13 December 2005
Abstract The monitored data in photovoltaic systems are processed to determine overall energy balances which, together with the energy efficiencies and indices of performance, give a good indication of the performance of PV systems. However, the analysis based on energy parameters shows some shortcomings when they are used to analyse the performance of stand-alone photovoltaic (SAPV) systems, especially those without Maximum Power Point Tracker (MPPT). This kind of systems represents a large percentage of the SAPV systems (e.g. demonstration projects, consumer and industrial applications, Solar Home Systems in developing countries, etc.). This paper tries to give an alternative method that manages to analyse this kind of systems in a better way. This method is based on a translation of the energy parameters given by the Joint Research Center and the IEC Standard 61724 into new charge-related parameters. It must be said that charge parameters can be used by themselves to evaluate the system performance. Therefore, it is not necessary to deduce energy parameters using the nominal battery voltage. The monitored data of two SAPV systems without MPPT are used to compare the performance of these systems based on energy parameters with the analysis provided by the new charge parameters. This study will highlight the advantages of the charge parameters method. r 2005 Elsevier B.V. All rights reserved. Keywords: Monitoring; Stand-alone PV systems; Performance
Corresponding author. Tel.: +34 953 212810; fax: +34 953 211967.
E-mail address: [email protected] (F.J. Mun˜oz). 0927-0248/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2005.10.020
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
1751
1. Approach. Charge parameters in the analysis of SAPV systems performance The analysis method, based on energy parameters, given by the JRC in their European Guidelines for the Assesment of Photovoltaic Plants [1,2] and the IEC Standard 61724 [3] do not reflect the proper operation of the stand-alone photovoltaic (SAPV) systems from a technical point of view as it is the case for grid connected systems. Therefore, some new coefficients (e.g. Production Factor, PF, and Matching Factor, MF) have already been introduced within IEA PVPS Task 2 [4,5]. However, we must consider that the normalised performance indicators such as the energy yields (e.g. Yr, YA, Yf, LC, LS) are normalised to the nominal power of the array, P0. Furthermore, other system performance indices (PR, PF and MF) also depend on this parameter. SAPV systems without Maximum Power Point Tracker (MPPT) cannot usually manage to reach the maximum power point as the array voltage is largely determined by the battery. For the battery voltage usually presents little variations, it will be the array current which determines the array power. Therefore, the estimation of the potential energy of the array from the in-plane irradiation, HI, and the nominal power of the array would represent the theoretical energy that can be delivered by the array, but it would not lead to a proper estimation of the real potential of this kind of systems. Furthermore, we have observed that if pulse-width modulation (PWM) charge regulators are used, the monitored energy provided by the array, EA, is overestimated. The more the PWM techniques are used by the charge regulator, the greater is the overestimation. For those reasons, it is intended to develop a new method to analyse the performance of SAPV systems without MPPT. This method will be based on charge parameters. Although JRC indicates that instead of energy balances, the time integral of the corresponding currents (Ah) may be recorded, and energy parameters can be deduced using the nominal battery voltage, it tells that this should be avoided as some parameters will be overestimated or underestimated [2] when trying to extrapolate the energy performance of the system from a charge point of view. However, the charge parameters presented here can be used by themselves to evaluate the system performance. As a result, the error mentioned above will not be introduced as it is not necessary to obtain energy parameters from charge parameters using the nominal battery voltage. The proposed charge parameters (charge balances and the charge indices of performance) together with their counterpart energy parameters, considering a daily reporting period, t, are given in Table 1. However, if necessary, it can be obtained weekly or monthly reports. This set of parameters constitutes a new method to analyse better the performance of SAPV systems. In Table 2 there have been defined the different parameters that must be measured and recorded to obtain the parameters given in Table 1. The energy balances of the system are calculated from their recorded monitoring power parameters over the reporting periods such as days, weeks, months or years. In the same way, charge balances can be obtained as the time integral of their corresponding measured current parameters over the reporting period. This new scope in the performance analysis of SAPV systems has taken the battery voltage as the system reference voltage. In this way, all the charge balances will be related to this one. This is true if SAPV systems without MPPT and no converters in the load side are considered. If the last ones are used and there is one element in the system operating at a different voltage, it should be only applied a correction factor to normalise its voltage to
Wh/d Wh/d Wh/d Wh/d Wh/d Wh/d Wh/d Wh/d Wh/d — Wh/d Wh/d — Wh/d Wh/(d Wp) Wh/(d Wp) Wh/(d Wp) Wh/(d Wp) Wh/(d Wp) —
ESI
ESO
ETS EFS EL EL,AC
EL,DC
EII
EIO
ZI
Ein Euse FA
Euse,PV Yr
YA
Yf
LC LS PR
PF
ZSYS
MF
Energy to storage
Energy from storage
Net energy to storage Net energy from storage Energy to loads Energy to AC loads
Energy to DC loads
DC-energy input to inverter
AC-energy output from inverter
Energy efficiency of the inverter
Total input energy Useful energy supplied by the system Array fraction
Direct PV contribution to Euse Reference yield
Array yield
Final yield
Capture losses System losses Performance ratio
Production factor
System efficiency
Matching factor
—
—
—
Potential array charge Array output charge
H I P0 R I A V A dt Rday I SI V S dt Rday day I SO V S dt
Wh/d Wh/d
EP EA
Potential array energy Array output energy
PR FA
¼
Matching factor
System efficiency
Production factor
PR PF
Yf YA
YA Yr
Yf Yr
Capture losses System losses Performance ratio
Final yield
Array yield
Direct PV contribution to Quse Reference yield
Total input charge Useful charge supplied by the system Array charge fraction
Charge efficiency of the inverter
AC-charge output from inverter
DC-charge input to inverter
Charge to DC loads
Net charge to storage Net charge from storage Charge to loads Charge to AC loads
Charge from storage
Yr YA YA Yf
E use;PV P0
ðE SI E SO Þþ ðE SO E SI Þþ E L;AC þ E L;DC R day PL;AC dt R day I L;DC V S dt R I II V S dt Rday day PIO dt E IO E II E FS þ E A þ E BU E L þ E TS EA E in F A E use EP PSH ¼ P0 EA P0
Parameter
Equation
Unit
Symbol
Parameter
Charge to storage
Charge parameters
Energy parameters
Ah/d Ah/d
QII QIO
MFQ
ZSYSQ
PFQ
LCQ LSQ PRQ
YfQ
YAQ
Quse,PV YrQ
Qin Quse FAQ
—
—
—
Ah/(d Ap) Ah/(d Ap) —
Ah/(d Ap)
Ah/(d Ap)
Ah/d Ah/(d Ap)
Ah/d Ah/d —
—
Ah/d
QL,DC
ZIQ
Ah/d Ah/d Ah/d Ah/d
Ah/d
QTS QFS QL QL,AC
Ah/d
QSO
Ah/d Ah/d
Unit
QSI
QP QA
Symbol
S
AQ
Y
¼ Y fQ
PRQ F AQ
Y fQ Y rQ Y AQ Y rQ PRQ PFQ
Y rQ Y AQ Y AQ Y fQ
Quse;PV I0
QA I0
QFS þ QA þ QBU QL þ QTS QA Qin F AQ Quse Q PSH ¼ P I0
QIO QII
ðQSI QSO Þþ ðQSO QSI Þþ QL;AC þ QL;DC R 1 day PL;AC V S dt R V L;DC I L;DC V dt S Rday day I II dt R 1 day PIO V dt
HII 0 R I A dt Rday I SI dt Rday day I SO dt
Equation
Table 1 Energy and charge parameters for the analysis of the performance of SAPV systems without MPPT. It has been considered a daily reporting period. Furthermore, due to the relative low power of SAPV systems without MPPT, the energy parameters will be expressed in Wh instead of kWh 1752 F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
ARTICLE IN PRESS
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
1753
Table 2 Parameters to be measured and recorded to obtain the parameters given in Table 1 Parameter
Symbol (Unit)
Total irradiance (array plane) Array output voltage Array output current Battery voltage Current input to storage battery Current output from storage battery Load voltage Current to all dedicated AC loads Power to all dedicated AC loads Inverter DC current Inverter AC power
GI (W/m2) VA (V) IA (A) VS (V) ISI (A) ISO (A) VL (A) IL,DC (A) PL,AC (W) III (A) PIO (W)
the battery voltage (i.e. if a DC converter is used to power a load which operates at a different voltage Rthan the battery one, the charge given to the load by the DC converter R will be given by I L ðV L =V S Þ dt instead of I L dt). In the literature there are already design methods of SAPV without MPPT which are based on charge instead of energy parameters [6,7]. It would be very interesting to translate this idea to the analysis of the SAPV systems performance from the recorded monitoring data. 2. Experimental results The monitored data of two SAPV systems without MPPT and without any type of converter in the load side (with no inverter or DC/DC converter), Table 3, are used to compare the system performance based, respectively, on energy and charge parameters. The first system, denoted system 1, is a 200 Wp SAPV system which illuminates at night a pergola installed at the flat roof of the Escuela Polite´cnica Superior de Jae´n. The second one, denoted system 2, is a SAPV system which has been integrated in a health emergency vehicle [8]. This hybrid system has been designed as a juxtaposition of two energy sources: a 400 Wp PV system and the conventional alternator vehicle. Both systems have a 200 Ah lead–acid battery as the storage unit. 2.1. Potential energy of a SAPV without MPPT As it has been indicated above, a SAPV without MPPT cannot usually achieve the maximum power point. Therefore, the potential energy given by the array, EP, stated by the JRC and IEC 61724 will lead, in this kind of systems, to an overestimation of the potential of the array. EP indicates the maximum theoretical energy that can provide the array but it does not represent its real potential. In order to evaluate the real potential of these systems, the array charge potential, QP, can be considered. This one is obtained from the in-plane irradiation, HI, and the nominal current, I0. In normal operating conditions, the generated current will be between the
ARTICLE IN PRESS 1754
F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
Table 3 Components of systems 1 and 2 System 1 SAPV system which feeds the lamps that illuminates the pergola installed at the flat roof of the Escuela Politecnica Superior de Jae´n
System 2 SAPV system installed in a health emergency vehicle to charge its original and service battery
200 Wp PV array (4 50 Wp modules each containing 36 serial cells) ISC,array ¼ 13.08 A VOC,array ¼ 21.6 V 200 Ah valve regulated lead–acid (VRLA) battery VS ¼ 12 V 30 A PWM charge regulator 400 Wp PV generator (8 50 Wp, modules each containing 36 serial cells) ISC,array ¼ 26.16 A VOC,array ¼ 21.6 V 200 Ah VRLA battery (service battery) 95 Ah SLI battery (original battery) VS ¼ 12 V 30 A PWM charge regulator
shortcircuit current, ISC, and the maximum power point current. In order to consider the worst case it has been chosen this last one. Moreover, this consideration will correct the effect of high temperatures [9]. Anyway, due to the proximity between ISC and the maximum power point current, this underestimation involves an error much lower than the one associated with the overestimation given by EP. The daily performance of system 1 based, respectively, on an energy and a charge basis during different days is shown in Fig. 1. As it can be observed, during some days (e.g. days 2, 3 and 4), the array output energy, EA, is lower than the energy given to loads, EL, although the array potential energy, EP, is greater than this last one. On the other hand, the charge array potential, QP, gives a more realistic value, showing that this last one is lower than the charge given to the loads, QL, and justifying, in these circumstances, that the array could not cover completely the load demand. Furthermore, it can be pointed out that the relative difference between the estimated energy potential defined by EP and the energy given by the array is much greater than the difference between QP and QA. EP is not a good indicator of the real potential of the array for it considers the maximum power point voltage as the array voltage (the real array voltage is lower than this last one). Meanwhile, the array charge potential, QP, gives a more realistic value of the array potential as it is only calculated from the array maximum power point current which is very close to the current given by the array. ETS and EFS are the energy battery balances and indicate, respectively, the net energy supplied to storage, (ESI–ESO)+, and the net energy drawn from storage, (ESO–ESI)+, where x+ denotes a minimum value of 0. On the other hand, the battery charge balances are given by QTS and QFS, which indicate, respectively, the net charge to storage, (QSI–QSO)+, and the net charge drawn from storage, (QSO–QSI)+. Later, in Section 2.3 we will study and compare these parameters.
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
1755
Daily System Performance. Energy Parameters EP
1800 1600
EL
EA
ETS
EFS
1534.73
Wh/dWp
1400 1191.93
1200 1000
947.23 838.25
800
774.05
710.40
600
772.65
714.40 598.35 490.09 386.40
472.90
400
245.36
200
188.48
118.71 0.00
0
107.64 0.00
0.00
day 1
686.38 635.58
590.84
day 2
42.84
0.00
day 3
day 4
0.00
day 5
Ah/dAp
Daily System Performance. Charge Parameters 100 90 80 70 60 50 40 30 20 10 0
QP
QL
QA
QTS
QFS
88.18
68.48 61.94
61.30 56.19
55.86
54.42
50.93 51.25 44.38
44.47
40.33 35.14
34.38 29.44 21.07 17.57 10.89
5.44 0.00
day 1
0.00
day 2
0.00
day 3
0.00
day 4
0.33 0.00
day 5
Fig. 1. Daily performance of system 1 based, on an energy and a charge basis. EP is not a good indicator of the real potential of the array for it considers the maximum power point voltage as the array voltage (the real array voltage is lower than this one).
2.1.1. Charge and energy indices of performance We are going to study the effect of the overestimation of the array potential energy on the energy indices of performance. Furthermore, these last ones will be compared with the proposed charge indices of performance. The reference yield, Yr, represents the theoretically available energy per day per Wp (due to the relative low power of SAPV systems, we use Wp instead of kWp). On the other hand, the reference yield expressed in charge units, YrQ, indicates the theoretically available charge per day and Ap (peak-Ampere). Both parameters represent the number of peak sun-hours per day (or number of hours of the standard irradiance, 1 kW/m2, which would produce the same daily irradiation). The array yield, YA, and the one indicated in terms of charge, YAQ, show, respectively, the energy delivered by the array per day and Wp, and the charge given by the array per day and Ap. These yields represent the number of hours per day that the array would need to be operated at its rated output power/current to give the same output as the recorded integral value for that day.
ARTICLE IN PRESS 1756
F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
The final yield, Yf, represents the actually used PV energy per day per Wp while YfQ indicates the actually used PV charge per day and per Ap. These yields represent the number of hours per day that the array would need to operate at its rated output power or current to equal its monitored contribution to the daily load. Finally, the normalised losses are defined as the differences between yields. In that way, the array capture losses expressed in terms of energy and charge are defined, respectively, by LC ¼ Yr–YA and YCQ ¼ YrQ–YAQ. LCQ represent the same capture losses as LC except for the maximum power point losses (i.e. operating cell temperature higher than 25 1C, partial shading, low irradiance, reduction of array current when the battery is fully charged and wiring losses). The wiring losses can be calculated if the charge balances are normalised to the battery voltage considering the different system voltages. The system losses can be defined, in the same way, in terms of energy or charge by LS ¼ YA–Yf and LSQ ¼ YAQ–YfQ. Both parameters show the storage losses in the battery, the inverter or DC–DC converter losses and the wiring losses from the battery to the loads. In Fig. 2 are shown the energy and charge system yields and the normalised losses during different days. As it can be observed, the energy capture losses are, in percentage, much higher than the charge ones. This is due to the overestimation of the array potential given by EP: the energy capture losses includes maximum power point losses, which are intrinsic losses in SAPV systems without MPPT. Moreover, the capture losses due to the maximum power point losses can overestimate the total capture losses, making, in some occasions, more difficult the identification of other capture losses (low irradiance, wiring losses, partial shading, etc.). If we compare the system losses, we can also see, on a percentage basis, how the energy ones are slightly higher than the charge ones. As it will be explained later in Section 2.2, this is due to the overestimation of the energy provided by the array, EA, when PWM charge regulators are used. Moreover, both systems losses, LS and LSQ, are very low as there are no converters in the load side and the wiring losses between the battery and the loads are negligible. The charge performance ratio, PRQ, is the ratio of the PV charge actually used to the charge theoretically available (i.e. YfQ/YrQ), while the charge production factor, PFQ, is the ratio between the charge provided by the array and the charge theoretically available (i.e. YAQ/YrQ). If we compare the energy indices of performance (denoted PR and PF), with the charge ones, PRQ and PFQ, Fig. 3, we observe that the energy indices of performance are lower than their charge counterparts. This can be explained as the energy indices of performance are related to the reference yield, Yr, which depends on EP (see Table 1). As it has been mentioned before, in SAPV systems without MPPT there is an overestimation of the potential array energy where the maximum power point losses are included in the calculations of the energy indices of performance. This will lead to an underestimation of the real performance of SAPV systems without MPPT. On the other hand, the charge indices of performance (PRQ and PFQ) give better information about the performance of the system as they consider the charge reference yield, YrQ, which take into account the real potential of the array provided by QP. In Fig. 3, the system efficiencies from an energy and charge point of view, Zsys and ZsysQ (Table 1) have also been included. As the system losses are negligible, both parameters are close to one.
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
1757
Energy Indices of Performance YF LS LC 100% 90% 80%
3.17
1.37
0.96
1.62
0.01
0.02
2.30
Wh/(day Wp)
70% 0.01
60% 50%
0.04
0.04
40% 30%
3.77
2.14
1.74
2.66
3.08
2
3 day
4
5
20% 10% 0% 1
Charge Indices of Performance YFQ LSQ LCQ 100% 90% 2.13 80% Ah/(day Ap)
70%
0.74
0.39 0.00
0.00
0.79
1.36
0.00 0.00
0.00
60% 50% 40% 4.85
2.78
2.33
3.51
4.05
30% 20% 10% 0% 1
2
3 day
4
5
Fig. 2. Daily energy indices of performance versus daily charge indices of performance. Data obtained from system 1.
2.2. Overestimation of E A in SAPV systems We have observed that if PWM charge regulators are used, the monitored array output energy, EA, can be much higher than the product of the array output charge, QA, and the nominal battery voltage. This control regime, used by a great number of charge controllers, is based on delivering current pulses, which width is controlled by a pulsewidth modulator, to the battery. It is applied when the battery voltage approaches the endof-charge voltage. When this occurs, the battery voltage is kept constant while the current
ARTICLE IN PRESS 1758
F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
Energy Indices of Performance PR
PF
ηsys
1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 day 1
day 2
day 3
day 4
day 5
day Charge Indices of Performance PRQ
PFQ
ηsysq
1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 day 1
day 2
day 3
day 4
day 5
day Fig. 3. Daily indices of performance (e.g. performance ratio and production factor) based on an energy and charge basis. Data obtained from system 1. In SAPV systems without MPPT there is an overestimation of the potential array energy, which will lead to an underestimation of the real performance ratio, PR, and production factor, PF, of the system.
delivered to the battery is slowly diminished by reducing the duty cycle. These current pulses have associated voltage pulses in the array, providing, when monitoring, high array voltage samples, and they can be much higher than the battery voltage, Fig. 4. In these conditions, the energy delivered by the array, calculated as the time integral of the product of the array current and the array voltage, will lead to a greater value than the real one. This error could be avoided if we sample at the same time and considering a high sampling frequency the two channels corresponding to the array current and voltage, and consequently obtain the power given by the array as the product of these two parameters. One solution to this problem would be to use advanced and much more expensive data
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
1759
18.00 Array Voltage (VA) Battery Voltage (VS)
16.00
Alternator Voltage 14.00 12.00
V
10.00 8.00 6.00 4.00 2.00
23:15:00
22:30:00
21:45:00
21:00:00
20:15:00
19:30:00
18:45:00
18:00:00
17:15:00
16:30:00
15:45:00
15:00:00
14:15:00
13:30:00
12:45:00
12:00:00
11:15:00
9:45:00
10:30:00
9:00:00
8:15:00
7:30:00
6:45:00
6:00:00
5:15:00
4:30:00
3:45:00
3:00:00
2:15:00
1:30:00
0:45:00
0:00:00
0.00
time
Fig. 4. Array voltage versus battery voltage. If PWM charge regulators are used, the energy delivered by the array, calculated as the product of the array current and the array voltage, will be overestimated. Data obtained from system 2: a health emergency vehicle with a 400 Wp PV array integrated in its roof. The daily vehicle load demand can be supplied by the vehicle alternator and the PV array.
loggers that could sample simultaneously the array current and voltage. Another solution would be to measure directly with a power sensor. However, with the analysis method proposed in this paper none of these solutions are necessary as the array output charge does not suffer any overestimation as it does not use the array voltage, it only considers the array current. A more representative value of the energy delivered by the array is provided by the time integral of the product of the array current and the battery voltage. This is true if a SAPV without MPPT is considered. We can compare R R the array output energy defined as I A V A dt with the array output energy given by I A V S dt, and calculate the relative error defined by the following equation: R R day I A V A dt day I A V S dt R relative error ¼ 100: (1) day I A V S dt We have measured this error considering a daily reporting period and different use levels of the PWM techniques by the charge regulator: high, medium and low. A medium use of the PWM techniques is considered when the charge regulator applies this type of control between the 30% and 70% of the daily generating period. On the other hand, a high and low use will be taken into account when the PWM techniques are applied, respectively, more than 70% and below the 30% of the daily generating period. As it can be observed in Fig. 5, which shows for system 2 the relative error in the estimation of the array output energy when using PWM charge regulators, the more the charge regulator uses the PWM
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
%
relative error
PR
20.00
0.50
15.00
0.40 0.30
10.00
0.20
5.00
PR
1760
0.10 0.00
0.00 High PWM Level
Medium PWM Level
Low PWM Level
Fig. 5. Relative error in the estimation of the array energy, EA, when using PWM charge regulators versus the mean daily performance ratio. A daily reporting period and different use levels of the PWM techniques, high, medium and low, have been considered. Data obtained from system 2.
techniques, the higher is the error. If the charge regulator applies this type of control almost all the time during the generating period, the relative error can reach 18%. If a medium use of this technique is considered, the error can be around 12%. Finally, if there is a little use of the PWM techniques, the error is reduced to 4%. A possible solution to estimate the array energy in SAPV systems without MPPT would be to take EA as the time integral of the product of the array current and the battery voltage. However, this idea would be equivalent to considering the array output charge, QA. It must be remembered that if we use charge parameters they are related to the battery voltage. In Fig. 5 the mean daily performance ratio has also been included. As it could be expected, the higher the use of the PWM techniques, the lower is the PR. This indicates that professional photovoltaic systems, which have been oversized to provide low Loss of Load Probability (LLP), and therefore will generally report low PR values, are going to be more susceptible to this overestimation of the energy given by the array. The overestimation of the total array output energy, EA, is spread over the rest of related parameters: Ein (total input energy), FA (PV array fraction of total input energy), Euse,PV, (direct PV energy contribution to Euse), YA, (array yield), Yf, (final yield), LC (capture losses), LS (system losses), PF (production factor) and PR (performance ratio). The relative error in each performance index due to the overestimation of the array energy, EA, when using PWM charge regulators, is shown in Fig. 6. That is, we are comparing the daily performance indices obtained from EA considering the array voltage with those calculated from the array energy obtained from the battery voltage. As it can be observed, the relative error in the performance indices generally increases as there is a higher use in the PWM techniques. The overestimation of EA generally produces an overestimation of the indices of performance. This is true except for the capture losses, which suffers an underestimation. The high relative error given by the system losses, LS, is due to the low absolute value of this kind of losses obtained from the analysis performance of system 2. 2.3. Charge and energy balances When the two methods are compared, the information level that can be offered from these two scopes must be considered. In this way, the daily energy and charge balances are shown in Fig. 1 to illustrate the performance of system 1.
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
100.00 80.00
1761
Low PWM level Medium PWM Level High PWM level
%
60.00 40.00 20.00 0.00 -20.00
YA
YF
LC
LS
PR
PF
Fig. 6. Relative error in each performance index due to overestimation of array energy, EA, when using PWM charge regulators. Data obtained from system 2. A daily reporting period and different use levels of the PWM techniques, high, medium and low, have been considered.
As it has been mentioned before, the array potential shown by QP is more realistic than the estimation given by EP. Furthermore, the charge given by the array, QA, is also more realistic than its counterpart EA, which, as it has been mentioned above, suffers from overestimation when PWM charge regulators are used. If we pay attention to the charge given to the loads, QL, there is nothing to point out as this one gives the same information as its relative, energy one. However, if we pay attention to the battery energy balances, given by ETS (net energy supplied to storage) and EFS (net energy drawn from storage), and the battery charge balances, provided by QTS (net charge to storage) and QFS (net charge from storage), we observe that, in most cases, the net energy given to the battery is higher than the net energy given to the battery calculated as the product of QTS and the nominal battery voltage. On the other hand, the net energy provided by the battery is lower than the one calculated from the net charge provided by the battery and the battery voltage. In short, the energy balances of the battery provide a more generous estimation of the State of Charge (SOC) of the battery than the one offered by the charge battery balances. However, this estimation is not realistic as the energy efficiency of a battery is lower than the charge efficiency. The energy efficiency is around 70–80%, while the charge efficiency can even reach the 95% [10] for lead–acid batteries. Although lead acid charge efficiency is affected by factors such as the battery SOC, battery design, battery grid alloy, charge rate, battery history, battery age and cycle Depth of Discharge (DOD) [11], the charge efficiency will be generally higher than the energy efficiency. Therefore, the charge parameters would lead to a better estimation of the SOC of the battery. Besides, the low-energy efficiency not only can give erroneous values of EFS and ETS but can affect the other system performance parameters such as Ein, FA, Euse,PV, Yf, LS and PR. For long reporting periods (i.e. several months) in which the net energy supplied or drawn from storage are much greater than the energy storage capacity (by more than a factor of 10), EFS and ETS are worthless in the calculations of the system performance, as any difference between these two parameters is primarily due to the efficiency of the battery. On the other hand, for short reporting periods (1 day or just a few days), in which
ARTICLE IN PRESS 1762
F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
EFS and ETS are at least ten times lower than the energy storage of the battery, ETS and EFS become important terms in the system performance calculations as, in this case, any difference between ETS and EFS is due to the change in the amount of energy stored in the battery [3]. Although the IEC 61724 indicates that the effect of the efficiency of the battery can be assumed negligible, it is clear that this assumption becomes more real if we consider charge battery balances, as the charge efficiency is higher than the energy efficiency. Therefore, the charge battery balances will provide a better estimation of the battery SOC and, hence, of the system performance too. The Ah balance management assumes that all current supplied is used for the battery charge. Although, the charge efficiency for a discharged battery is initially about 99%, the efficiency will drop off as the battery approaches higher SOC, and approach zero near 100% SOC. In that way, the battery is recharged with coefficients varying from 105% for valve regulated lead–acid (VRLA) to 130% for vented batteries to compensate for the energy used by the hydrolysis of water at the end of the charge. Furthermore, the Amperehours needed for water electrolysis increases when the battery gets old because of the internal resistance. Although the counting system may not be precise enough and the value obtained may change after a few cycles, this method enables a short-term evaluation that consequently avoids deep discharge and overcharges [12]. Furthermore, batteries are key elements in SAPV systems as they account for more than 30% of the lifecycle costs of solar off-grid systems [13]. In SHS it can even reach 50% [14]. Therefore, it would be very important not only to pay attention to the system performance but to keep an eye on the battery performance too, watching if there are overcharges and deep discharges, and if they are frequent or not. Short reporting reports, together with a more accurate information about the SOC of the battery, given by the charge battery balances, will help not only to know better the system performance but to keep the system’s batteries in good SOC as it will permit to take right decisions when necessary. 3. Conclusions We have presented a new method to analyse the performance of SAPV systems without MPPT. In this way, the results of the analysis of two SAPV systems have been shown. The analysis has been made from two different scopes, the one given by the energy parameters as the JRC and the IEC 61724 indicate, and the other provided by the new charge parameters. It has been proved that the method based on charge parameters is more accurate and gives better information about the performance of the system as:
The array charge potential, QP, gives a more realistic value of the array potential. QP is only calculated from the array maximum power point current which is very close to the current given by the array. On the other hand, the method based on energy parameters leads to an overestimation of the real potential of SAPV systems without MPPT. Moreover, this can lead to an overestimation of the capture losses and an underestimation of the performance ratio and the production factor. The array output charge, QA, is not overestimated if the charge regulator uses PWM techniques, as it is the case with the total array output energy, EA. As only the array current is considered, the high value that can reach the array voltage under PWM
ARTICLE IN PRESS F.J. Mun˜oz et al. / Solar Energy Materials & Solar Cells 90 (2006) 1750–1763
1763
techniques is not taken into account. Therefore, there is no error that can be spread over other related parameters. The battery charge balances provide a better estimation of the SOC of the battery as the charge efficiency of a battery is larger than the energy efficiency. The energy battery balances offer a worse estimation of the battery SOC, which will give a poorer analysis of the system’s performance, especially for short reporting periods.
Furthermore, it must be remembered that the battery SOC and most of the information related to the battery offered by the battery manufacturer is given in Ampere-hour. This is one more reason, in addition to the ones mentioned above, for considering conveniently operating with the charge parameters instead of energy parameters in SAPV systems, especially in those without MPPT. References [1] Commission of the European Communities, Photovoltaic System Monitoring, Guidelines for the Assesement of Photovoltaic Plants, Document A, version 4.3, March 1997. [2] Commission of the European Communities, Photovoltaic System Monitoring, Guidelines for the Assesement of Photovoltaic Plants, Document B, version 4.3, March 1997. [3] International Standard IEC 61724. Photovoltaic System Performance Monitoring—Guidelines for Measurement, Data Exchange and Analysis, first ed., International Electrotechnical Commission (IEC), Geneve, April 1998. [4] D. Mayer, M. Heidenreich, Performance analysis of stand-alone PV Systems from a rational use of energy point of view, in: Proceedings of the Third World Conference on Photovoltaic Energy Conversion, Osaka, Japan, June 2003. [5] A. Sobirey, H. Riess, P. Sprau, Matching factor—a new tool for the assesment of stand-alone systems, in: Proceedings of the Second World Conference and Exhibition, Vienna, Austria, July 1998. [6] PV Design Center, Stand-Alone Photovoltaic Systems, A Handbook of Recommended Design Practices, Sandia National Laboratories Albuquerque, NM, USA, 1993. [7] R. Messenger, J. Ventre, Photovoltaic Systems Engineering, CRC Press, Boca Raton, FL, 2000, pp. 193–235. [8] G. Almonacid, et al., Integration of PV Systems on health emergency vehicle, The FIVE Project, Prog. Photovoltaics 12 (2004) 609. [9] M.A. Abella, Sistemas Fotovoltaicos, Inroduccio´n al Disen˜o y Dimensionado de Instalaciones de Energı´ a Solar Fotovoltaica, S.A.P.T Publicaciones Te´cnicas S.L.: Madrid, 2001, p. 244. [10] T. Markvart, L. Castan˜er, Practical Handbook of Photovoltaics, Elsevier Science, Oxford, 2003, p. 594. [11] IEEE Standard 1361, IEEE Guide for Selection, Charging and Evaluation of Lead–Acid Batteries uses in Stand-Alone Photovoltaic (PV) Systems, IEEE, New York, December 2003, p. 18. [12] Report IEA PVPS Task 3, Management of Storage Batteries used in Stand-Alone Photovoltaic Power Systems. [13] A. Luque, S. Hegedus S. Handbook of Photovoltaic Science and Engineering, Wiley, Chichester, 2003, p. 785. [14] Report IEA-PVPS T3-18:2004, Evaluation of Energy Storage Devices in Stand-Alone PV Power Systems, p. 9.