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The impact of photovoltaic systems on distribution transformer: A case study
Energy Conversion and Management 47 (2006) 311–321 www.elsevier.com/locate/enconman
The impact of photovoltaic systems on distribution transformer: A case study Humberto Jimenez a, Hugo Calleja b,*, Rau´l Gonza´lez a, Jorge Huacuz a, Javier Lagunas a a
IIE, Non-Conventional Energy Sources Department, P.O. Box 1-475, Cuernavaca, Morelos 62091, Mexico b Cenidet, Electronics Department, P.O. Box 5-164, Cuernavaca, Morelos 62050, Mexico Received 21 October 2004; accepted 29 April 2005 Available online 10 August 2005
Abstract In this paper, the results obtained after monitoring a distribution transformer during an 18 months period are described and discussed. The transformer fed several households, each with a grid connected photovoltaic system, and it was found that the power factor at the transformer attained unusually low levels. This was due to the fact that under some conditions, the systems provided a large portion of the active power demanded by the households, while the grid supplied all the reactive and distortion powers. The operating temperature was used as an indicator of the stress on the transformer. The temperature was at its lowest when the systems were providing the maximum energy available from the solar cells. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Photovoltaic systems; Power factor; Power monitoring
1. Introduction In areas with warm weather, the consumption of electric energy increases during the summer due to air conditioning loads connected to the grid, but as shown in Fig. 1, the peak demand *
Corresponding author. Tel.: +52 (777) 318 77 41x151; fax: +52 (777) 312 24 34. E-mail address: [email protected] (H. Calleja).
0196-8904/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2005.04.007
312
H. Jimenez et al. / Energy Conversion and Management 47 (2006) 311–321
Fig. 1. Average energy consumption in a household.
occurs during the hours with the highest solar irradiance [1]. Therefore, the widespread installation of grid connected photovoltaic (PV) systems can help reduce the peak demand that the utility must satisfy. In order to assess its viability for peak demand reduction, several photovoltaic (PV) systems were installed in selected households. It was originally assumed that the monthly energy consumption, as recorded by a logging watt-hour meter, would suffice for evaluation purposes. However, when random measurements of other electrical variables were taken, it was found that the power factor exhibited unusually low values; much lower, in fact, than those commonly obtained prior to the installation of the PV systems. This occurred in spite of the fact that the systems provided a high quality waveform and raised concerns about the suitability of the PV systems and their effect on the grid. The energy saving that can be obtained with PV systems has already been described in the technical literature [2]. The large scale effect of a large number of grid connected PV systems has also been analysed [3]. The authors could not find, however, information about the small scale effect of the PV systems; specifically, describing the stresses on the distribution transformer. Therefore, systematic monitoring of the installed systems and the distribution transformer was implemented. The main objective was to determine if, due to the PV systems, the transformer operated under abnormal conditions. In this paper, the results obtained after an 18 months test period are presented and discussed [4].
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2. Test arrangement The site selected for the tests is00a suburban area in Mexicali (Baja California, Mexico), located 00 at 32°39 0 48 N latitude, 115°28 0 04 W longitude and 3 m above sea level. The weather is quite dry all year long, and summer temperatures can be as high as 45 °C. A distribution transformer was instrumented in order to monitor the long term behaviour of the active and reactive powers, the temperature and the power factor. The transformer feeds four households and is rated at 75 kVA. The input is obtained from a 13.8 kV line, and the output is 120 V + 120 V. This arrangement is needed because most appliances are energized at 120 V, but the air conditioning apparatus must be energized from a 240 V source. The measured variables are as shown in Fig. 2. If the voltages VL1 and VL2 are sinusoidal, then the active power per phase is given by P ¼ V RMS I 1RMS cosðh1Þ
ð1Þ
where VRMS is the corresponding effective voltage, I1RMS is the effective value of the fundamental current and h1 is the displacement angle between this current and the voltage. The apparent power S can also be calculated using: S ¼ V RMS I RMS
ð2Þ
where IRMS is the effective value of the current waveform, harmonics included. The power factor PF is calculated with: P ð3Þ PF ¼ S The apparent power can also be expressed as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S ¼ P 2 þ Q2 þ D2
ð4Þ
where Q and D are the reactive and distortion powers, respectively [5]. However, it is common practice to compute a quantity as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð5Þ R ¼ S2 P 2
Fig. 2. Transformer instrumentation prior to installation of the PV systems.
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Table 1 Behaviour in summer and winter without PV systems Parameter
Summer July
Winter December
Power factor (pu)
Minimum Average Maximum
0.90 0.92 0.94
0.88 0.94 0.99
Transformer temperature (°C)
Minimum Maximum
35 50
23 34
Fig. 3. Measured variables after installation of the PV systems.
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi From Eq. (4), it is clear that R ¼ Q2 þ D2 and, therefore, includes the reactive and distortion powers. Nevertheless, the quantity R is usually referred to as the reactive power, and most instruments follow this approach (although a better term would be the non-active power). Prior to installation of the PV systems, the transformer was monitored during a 6-month period, long enough to include the summer and winter seasons. The reference values for a summer month and for a winter month, obtained prior to installation of the PV systems, are listed in Table 1. The PV systems were installed once the reference data were collected. The systems did not include battery banks, had identical power stages and generated high quality sinusoidal current waveforms. The cell arrays, however, were different, with an average power of 1.7 kW per household. The measured variables are illustrated in Fig. 3. H1 to H4 are the households, and both the active power Pj and the apparent power Sj in each one were recorded. Each house also had a watthour meter at the common coupling point CCP. Regarding the PV systems, only two were included in the measurement of the delivered power. In the transformer, the measured variables were the active power PAC, the apparent power SAC and its temperature TT. The ambient temperature TA was also measured in a point close to the transformer. Data for a full year was collected.
3. Measurements In all cases, the variables were recorded every 10 min (arithmetic average of 60 samples), and two averages were calculated: (a) The first one was an hourly average. It corresponded to the
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arithmetic average of six sequential values. (b) The second one was a monthly average. It corresponded to the arithmetic average of the hourly values, at the same hour, within a month. These values were used for evaluation purposes. The following graphs are based on these values. It should be pointed out that the data for October was lost. The handling of the missing data is indicated in the figuresÕ captions. When the systems were installed, it was found that they provided up to 45% of the energy consumed by the households during the summer. When this occurred, the power factor at the transformer was moderately degraded. That was not the case, however, during the period spanning from January through April. In this period, the power factor became severely degraded, even approaching zero. Fig. 4 shows the behaviour of the power factor PF and the maximum monthly irradiance Ir along the year, while Fig. 5 shows the behaviour of the minimum power factor and the maximum ambient temperature TA. The decrement in power factor was due to the fact that during the January–April period, the PV systems generate energy approaching the amount required by the households or in excess of that amount. During this period, the ambient temperature is below 30 °C, and most people refrain from using the air conditioning apparatus. The load is then comprised by other appliances, which might draw non-sinusoidal current waveforms. If the PV system injects a current at the fundamental frequency, with a magnitude such that the active power requirements of the load are exactly matched, then the grid must supply the reactive and distortion power, and the power factor will be at its minimum. Fig. 6 shows the monthly averages corresponding to March, the month with the lowest power factor (taken as an absolute value). The curve labelled PF corresponds to the power factor, Ir to the irradiance, TT to the transformer temperature and TA to the ambient temperature. The power factor reaches two minimums, at 9:00 in the morning and at 14:00 in the afternoon; therefore,
1
1000 900
0.9
Ir 0.8
700
PF
0.7
600
0.6
500
0.5
400
0.4
300
0.3
200
0.2
100
0.1
0
1
2
3
4
5
6 7 Month
8
9
10
11
12
PF (pu)
Irradiance (W/m2)
800
0
Fig. 4. Minimum power factor and maximum irradiance (data for October is extrapolated).
316
H. Jimenez et al. / Energy Conversion and Management 47 (2006) 311–321 1
10
0.9
9 8
0.8
7
0.7
6
0.6
5
0.5
4
0.4
TA
3
0.3
2
0.2
1
0.1
0
1
2
3
4
5
6 7 Month
8
9
10
11
PF (pu)
Temperature (ºC)
PF
0 12
Fig. 5. Minimum power factor and maximum temperature (data for October is extrapolated).
1100
110 PF
Ir
100
900
90
800
80
700
70
600
60
500
50
400
40 TT
300
30
200
TA
100
20
Temperature (ºC) & P. F . (%)
Irradiance (W/m2)
1000
10
0
0
-100 1
2
3
4
5
6
7
8
9
-10 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hour
Fig. 6. Monthly average during March.
although it is plotted as a positive quantity, the power factor between these minimums is a negative quantity, meaning that the systems are dumping excess energy into the grid. Fig. 7 shows the monthly averages obtained during April. The curve labelled PF corresponds to the power factor, PAC to the active power, R to the non-active power and PE to the estimated active power, that is, the power that would be drawn if the PV systems were not installed. The
317
11
110
10
100
9
90
8
80 PF
7
70
6
60
5
50
PAC
4
40 PE
3
P.F. (%)
Active & reactive power (kW - kVAR)
H. Jimenez et al. / Energy Conversion and Management 47 (2006) 311–321
30
2
20
1
10 ℜ
0
0
-1
-10
-2
-20 1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
Fig. 7. Monthly averages during April.
non-active power remains fairly constant, but the active power exhibits a large swing. As can be readily appreciated, the systems inject energy into the grid from about 8:30 a.m. to 2:20 p.m. The rise in the transformer temperature above the ambient was used as an indicator of the thermal stress on the transformer. Assuming a constant energy consumption pattern with a seasonal 50 TT 45 40
Temperature (ºC)
35 30 TA
25 20 15 10 5 0
∆T Jan
Feb Mar
Apr
May Jun Jul Month
Aug
Sep
Nov Dec
Fig. 8. Daily averaged temperature throughout the year (data for October is omitted).
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variation due to the air conditioning equipment, the load at the transformer should be at a minimum when the irradiance is highest, and the ambient temperature is below or around 30 °C. According to Figs. 4 and 5, these conditions occur during April; therefore, the minimum temperature differential should be expected in this month. Fig. 8 shows the monthly average of the daily temperatures. The bottom trace, labelled DT, is the difference between the transformer temperature TT and the ambient temperature TA. As expected, DT is at a minimum, around 5 °C, when the PV systems are providing the maximum amount of energy. There is an increase in DT when the PV systems cease operating, up to 8 °C during the night. A similar behaviour was observed
Fig. 9. Equivalent circuit.
40
200 VAC
150
30
IPV
20
100
IL
0
0 -50
-10
-100
-20
-150
-30
-200
-40 0
0.002
0.004
0.006
0.008
0.01
Time (seconds)
Fig. 10. Waveforms.
0.012
0.014
0.016
Amps
Volts
10
IAC
50
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throughout the year. The maximum averaged DT was 9.83 °C, the minimum was 4.77 °C and the average was 7.69 °C.
4. Analysis of the power factor degradation Fig. 9 depicts the schematic diagram of a single PV system connected to the grid. The distribution transformer corresponds to the source VAC that generates a purely sinusoidal voltage waveform, and it is assumed that there is a non-linear load ZL connected to the mains. Fig. 10 shows the waveforms for the case described. The current IL corresponds to a lighting load comprised of fluorescent lamps with electromagnetic ballasts; as can be seen, it is fairly sinusoidal but includes some harmonics [6], as allowed by the standards [7]. On the other hand, the current IPV is a purely
1 0.8 0.6 0.4
PF
0.2 0
-0.2 -0.4 -0.6 -0.8 -1 0
250
500
750
1000 1250 1500 1750 2000 2250 2500 PPV(W)
Fig. 11. Power factor as a function of the power injected by the test system.
Table 2 Numerical values for a PV system matching the load active power Parameter
PV system idle
PV system operating
VAC IAC IPV PAC SAC FP
129.8 V 9.77 A 0 1.248 kW 1.269 kVA 0.983
129.8 V 1.86 A 9.6 A 0.1019 W 0.241 kVA 0.0004
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sinusoidal wave, and its amplitude matches the active power requirements of the load. It is readily appreciated that the current IAC does not include a component at the fundamental frequency. The numerical values are listed in Table 2, where both voltage and current are expressed as RMS values. Fig. 11 shows the behaviour of the power factor as a function of the power injected by the PV system and for the waveforms shown in Fig. 10. As can be seen, the power factor is null when the power supplied by the systems matches exactly the requirements of the load. The power factor becomes negative for higher values of PPV.
5. Conclusions According to the results obtained, it can be concluded that a low power factor does not translate as an over stress in the distribution transformer. This is true as long as the PV systems provide a high quality current waveform. When this is the case, the non-active power in the transformer remains the same, and the reduction in the power factor is due to a reduction in the active power. This is confirmed by the temperature measurements, which show that the transformer operates at lower temperatures when the PV systems are injecting the maximum power onto the grid. Therefore, besides the obvious advantage of peak demand reduction, in the case tested, the PV systems should also contribute to a longer operational life of the distribution transformers. Regarding the actual value of the power factor, if a high value is desired under all operating conditions, then two possible solutions exist. The first one is to have loads that behave linearly; however, current standards leave enough room for a fairly high harmonic content, especially for low power loads. The second solution consists of adding active filtering capabilities to the PV systems. This is an attractive solution, and several systems with this capability have already been reported [8]. Another issue to consider is that the power factor, by itself, might be somewhat misleading in regard to the actual stress on a distribution transformer. An accurate evaluation should take into account all the powers involved.
Acknowledgements We received help from many people during the development of the project. We wish to thank Mr Enrique Guzman, Mr. Carlos Gonzalez and Ms. Lina Castillo from the Baja California Division, CFE utility company; Mr. Marco Vilchis from the Baja California University and Mrs. Laura Morales from the PAESE divisional office.
References [1] Ramos G, Diaz R, Fiscal R, Alquicira C, Martinez S, Maqueda M. The change to summer time: savings in energy consumption and demand and reduction in pollution. Boletı´n IIE 1997;21(2):91–100 [in Spanish]. [2] Al-Hasan A, Ghoneim A, Abdullah A. Optimizing electrical load pattern in Kuwait using grid connected photovoltaic systems 2004. Energy Convers Manage 2004;45:483–94.
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[3] Faaborg A. Impacts of power penetration from photovoltaic power system in distribution networks. International Energy Agency Report IEA PVPS T5–10. 2002. [4] Gonza´lez R., Jime´nez H., Lagunas J. Behaviour of grid-connected PV systems: Its impact on household demand, and on the distribution transformer [in Spanish]. Electrical Research Institute Report IIE/01/14/11779/I002/AIII. 2002. [5] Sun S, Kiyokawa H. Decomposition of voltage current and power 1991. IEE Proc-B 138(1):35–9. [6] Kim H-S, Okada N, Takigawa K. A study on utility interactive PV system in harmony with utility, IEEE PESC 2000, June 2000, Ireland. [7] IEC International Standard 61000-3-2. Limits for harmonic current emissions (equipment input current 616 A per phase). 2001. [8] Calleja H, Jimenez H. Performance of a grid connected PV system used as active filter. Energy Convers Manage 2004;45:2417–28.
The impact of photovoltaic systems on distribution transformer: A case study Humberto Jimenez a, Hugo Calleja b,*, Rau´l Gonza´lez a, Jorge Huacuz a, Javier Lagunas a a
IIE, Non-Conventional Energy Sources Department, P.O. Box 1-475, Cuernavaca, Morelos 62091, Mexico b Cenidet, Electronics Department, P.O. Box 5-164, Cuernavaca, Morelos 62050, Mexico Received 21 October 2004; accepted 29 April 2005 Available online 10 August 2005
Abstract In this paper, the results obtained after monitoring a distribution transformer during an 18 months period are described and discussed. The transformer fed several households, each with a grid connected photovoltaic system, and it was found that the power factor at the transformer attained unusually low levels. This was due to the fact that under some conditions, the systems provided a large portion of the active power demanded by the households, while the grid supplied all the reactive and distortion powers. The operating temperature was used as an indicator of the stress on the transformer. The temperature was at its lowest when the systems were providing the maximum energy available from the solar cells. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Photovoltaic systems; Power factor; Power monitoring
1. Introduction In areas with warm weather, the consumption of electric energy increases during the summer due to air conditioning loads connected to the grid, but as shown in Fig. 1, the peak demand *
Corresponding author. Tel.: +52 (777) 318 77 41x151; fax: +52 (777) 312 24 34. E-mail address: [email protected] (H. Calleja).
0196-8904/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2005.04.007
312
H. Jimenez et al. / Energy Conversion and Management 47 (2006) 311–321
Fig. 1. Average energy consumption in a household.
occurs during the hours with the highest solar irradiance [1]. Therefore, the widespread installation of grid connected photovoltaic (PV) systems can help reduce the peak demand that the utility must satisfy. In order to assess its viability for peak demand reduction, several photovoltaic (PV) systems were installed in selected households. It was originally assumed that the monthly energy consumption, as recorded by a logging watt-hour meter, would suffice for evaluation purposes. However, when random measurements of other electrical variables were taken, it was found that the power factor exhibited unusually low values; much lower, in fact, than those commonly obtained prior to the installation of the PV systems. This occurred in spite of the fact that the systems provided a high quality waveform and raised concerns about the suitability of the PV systems and their effect on the grid. The energy saving that can be obtained with PV systems has already been described in the technical literature [2]. The large scale effect of a large number of grid connected PV systems has also been analysed [3]. The authors could not find, however, information about the small scale effect of the PV systems; specifically, describing the stresses on the distribution transformer. Therefore, systematic monitoring of the installed systems and the distribution transformer was implemented. The main objective was to determine if, due to the PV systems, the transformer operated under abnormal conditions. In this paper, the results obtained after an 18 months test period are presented and discussed [4].
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2. Test arrangement The site selected for the tests is00a suburban area in Mexicali (Baja California, Mexico), located 00 at 32°39 0 48 N latitude, 115°28 0 04 W longitude and 3 m above sea level. The weather is quite dry all year long, and summer temperatures can be as high as 45 °C. A distribution transformer was instrumented in order to monitor the long term behaviour of the active and reactive powers, the temperature and the power factor. The transformer feeds four households and is rated at 75 kVA. The input is obtained from a 13.8 kV line, and the output is 120 V + 120 V. This arrangement is needed because most appliances are energized at 120 V, but the air conditioning apparatus must be energized from a 240 V source. The measured variables are as shown in Fig. 2. If the voltages VL1 and VL2 are sinusoidal, then the active power per phase is given by P ¼ V RMS I 1RMS cosðh1Þ
ð1Þ
where VRMS is the corresponding effective voltage, I1RMS is the effective value of the fundamental current and h1 is the displacement angle between this current and the voltage. The apparent power S can also be calculated using: S ¼ V RMS I RMS
ð2Þ
where IRMS is the effective value of the current waveform, harmonics included. The power factor PF is calculated with: P ð3Þ PF ¼ S The apparent power can also be expressed as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S ¼ P 2 þ Q2 þ D2
ð4Þ
where Q and D are the reactive and distortion powers, respectively [5]. However, it is common practice to compute a quantity as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð5Þ R ¼ S2 P 2
Fig. 2. Transformer instrumentation prior to installation of the PV systems.
314
H. Jimenez et al. / Energy Conversion and Management 47 (2006) 311–321
Table 1 Behaviour in summer and winter without PV systems Parameter
Summer July
Winter December
Power factor (pu)
Minimum Average Maximum
0.90 0.92 0.94
0.88 0.94 0.99
Transformer temperature (°C)
Minimum Maximum
35 50
23 34
Fig. 3. Measured variables after installation of the PV systems.
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi From Eq. (4), it is clear that R ¼ Q2 þ D2 and, therefore, includes the reactive and distortion powers. Nevertheless, the quantity R is usually referred to as the reactive power, and most instruments follow this approach (although a better term would be the non-active power). Prior to installation of the PV systems, the transformer was monitored during a 6-month period, long enough to include the summer and winter seasons. The reference values for a summer month and for a winter month, obtained prior to installation of the PV systems, are listed in Table 1. The PV systems were installed once the reference data were collected. The systems did not include battery banks, had identical power stages and generated high quality sinusoidal current waveforms. The cell arrays, however, were different, with an average power of 1.7 kW per household. The measured variables are illustrated in Fig. 3. H1 to H4 are the households, and both the active power Pj and the apparent power Sj in each one were recorded. Each house also had a watthour meter at the common coupling point CCP. Regarding the PV systems, only two were included in the measurement of the delivered power. In the transformer, the measured variables were the active power PAC, the apparent power SAC and its temperature TT. The ambient temperature TA was also measured in a point close to the transformer. Data for a full year was collected.
3. Measurements In all cases, the variables were recorded every 10 min (arithmetic average of 60 samples), and two averages were calculated: (a) The first one was an hourly average. It corresponded to the
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arithmetic average of six sequential values. (b) The second one was a monthly average. It corresponded to the arithmetic average of the hourly values, at the same hour, within a month. These values were used for evaluation purposes. The following graphs are based on these values. It should be pointed out that the data for October was lost. The handling of the missing data is indicated in the figuresÕ captions. When the systems were installed, it was found that they provided up to 45% of the energy consumed by the households during the summer. When this occurred, the power factor at the transformer was moderately degraded. That was not the case, however, during the period spanning from January through April. In this period, the power factor became severely degraded, even approaching zero. Fig. 4 shows the behaviour of the power factor PF and the maximum monthly irradiance Ir along the year, while Fig. 5 shows the behaviour of the minimum power factor and the maximum ambient temperature TA. The decrement in power factor was due to the fact that during the January–April period, the PV systems generate energy approaching the amount required by the households or in excess of that amount. During this period, the ambient temperature is below 30 °C, and most people refrain from using the air conditioning apparatus. The load is then comprised by other appliances, which might draw non-sinusoidal current waveforms. If the PV system injects a current at the fundamental frequency, with a magnitude such that the active power requirements of the load are exactly matched, then the grid must supply the reactive and distortion power, and the power factor will be at its minimum. Fig. 6 shows the monthly averages corresponding to March, the month with the lowest power factor (taken as an absolute value). The curve labelled PF corresponds to the power factor, Ir to the irradiance, TT to the transformer temperature and TA to the ambient temperature. The power factor reaches two minimums, at 9:00 in the morning and at 14:00 in the afternoon; therefore,
1
1000 900
0.9
Ir 0.8
700
PF
0.7
600
0.6
500
0.5
400
0.4
300
0.3
200
0.2
100
0.1
0
1
2
3
4
5
6 7 Month
8
9
10
11
12
PF (pu)
Irradiance (W/m2)
800
0
Fig. 4. Minimum power factor and maximum irradiance (data for October is extrapolated).
316
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10
0.9
9 8
0.8
7
0.7
6
0.6
5
0.5
4
0.4
TA
3
0.3
2
0.2
1
0.1
0
1
2
3
4
5
6 7 Month
8
9
10
11
PF (pu)
Temperature (ºC)
PF
0 12
Fig. 5. Minimum power factor and maximum temperature (data for October is extrapolated).
1100
110 PF
Ir
100
900
90
800
80
700
70
600
60
500
50
400
40 TT
300
30
200
TA
100
20
Temperature (ºC) & P. F . (%)
Irradiance (W/m2)
1000
10
0
0
-100 1
2
3
4
5
6
7
8
9
-10 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hour
Fig. 6. Monthly average during March.
although it is plotted as a positive quantity, the power factor between these minimums is a negative quantity, meaning that the systems are dumping excess energy into the grid. Fig. 7 shows the monthly averages obtained during April. The curve labelled PF corresponds to the power factor, PAC to the active power, R to the non-active power and PE to the estimated active power, that is, the power that would be drawn if the PV systems were not installed. The
317
11
110
10
100
9
90
8
80 PF
7
70
6
60
5
50
PAC
4
40 PE
3
P.F. (%)
Active & reactive power (kW - kVAR)
H. Jimenez et al. / Energy Conversion and Management 47 (2006) 311–321
30
2
20
1
10 ℜ
0
0
-1
-10
-2
-20 1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
Fig. 7. Monthly averages during April.
non-active power remains fairly constant, but the active power exhibits a large swing. As can be readily appreciated, the systems inject energy into the grid from about 8:30 a.m. to 2:20 p.m. The rise in the transformer temperature above the ambient was used as an indicator of the thermal stress on the transformer. Assuming a constant energy consumption pattern with a seasonal 50 TT 45 40
Temperature (ºC)
35 30 TA
25 20 15 10 5 0
∆T Jan
Feb Mar
Apr
May Jun Jul Month
Aug
Sep
Nov Dec
Fig. 8. Daily averaged temperature throughout the year (data for October is omitted).
318
H. Jimenez et al. / Energy Conversion and Management 47 (2006) 311–321
variation due to the air conditioning equipment, the load at the transformer should be at a minimum when the irradiance is highest, and the ambient temperature is below or around 30 °C. According to Figs. 4 and 5, these conditions occur during April; therefore, the minimum temperature differential should be expected in this month. Fig. 8 shows the monthly average of the daily temperatures. The bottom trace, labelled DT, is the difference between the transformer temperature TT and the ambient temperature TA. As expected, DT is at a minimum, around 5 °C, when the PV systems are providing the maximum amount of energy. There is an increase in DT when the PV systems cease operating, up to 8 °C during the night. A similar behaviour was observed
Fig. 9. Equivalent circuit.
40
200 VAC
150
30
IPV
20
100
IL
0
0 -50
-10
-100
-20
-150
-30
-200
-40 0
0.002
0.004
0.006
0.008
0.01
Time (seconds)
Fig. 10. Waveforms.
0.012
0.014
0.016
Amps
Volts
10
IAC
50
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throughout the year. The maximum averaged DT was 9.83 °C, the minimum was 4.77 °C and the average was 7.69 °C.
4. Analysis of the power factor degradation Fig. 9 depicts the schematic diagram of a single PV system connected to the grid. The distribution transformer corresponds to the source VAC that generates a purely sinusoidal voltage waveform, and it is assumed that there is a non-linear load ZL connected to the mains. Fig. 10 shows the waveforms for the case described. The current IL corresponds to a lighting load comprised of fluorescent lamps with electromagnetic ballasts; as can be seen, it is fairly sinusoidal but includes some harmonics [6], as allowed by the standards [7]. On the other hand, the current IPV is a purely
1 0.8 0.6 0.4
PF
0.2 0
-0.2 -0.4 -0.6 -0.8 -1 0
250
500
750
1000 1250 1500 1750 2000 2250 2500 PPV(W)
Fig. 11. Power factor as a function of the power injected by the test system.
Table 2 Numerical values for a PV system matching the load active power Parameter
PV system idle
PV system operating
VAC IAC IPV PAC SAC FP
129.8 V 9.77 A 0 1.248 kW 1.269 kVA 0.983
129.8 V 1.86 A 9.6 A 0.1019 W 0.241 kVA 0.0004
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sinusoidal wave, and its amplitude matches the active power requirements of the load. It is readily appreciated that the current IAC does not include a component at the fundamental frequency. The numerical values are listed in Table 2, where both voltage and current are expressed as RMS values. Fig. 11 shows the behaviour of the power factor as a function of the power injected by the PV system and for the waveforms shown in Fig. 10. As can be seen, the power factor is null when the power supplied by the systems matches exactly the requirements of the load. The power factor becomes negative for higher values of PPV.
5. Conclusions According to the results obtained, it can be concluded that a low power factor does not translate as an over stress in the distribution transformer. This is true as long as the PV systems provide a high quality current waveform. When this is the case, the non-active power in the transformer remains the same, and the reduction in the power factor is due to a reduction in the active power. This is confirmed by the temperature measurements, which show that the transformer operates at lower temperatures when the PV systems are injecting the maximum power onto the grid. Therefore, besides the obvious advantage of peak demand reduction, in the case tested, the PV systems should also contribute to a longer operational life of the distribution transformers. Regarding the actual value of the power factor, if a high value is desired under all operating conditions, then two possible solutions exist. The first one is to have loads that behave linearly; however, current standards leave enough room for a fairly high harmonic content, especially for low power loads. The second solution consists of adding active filtering capabilities to the PV systems. This is an attractive solution, and several systems with this capability have already been reported [8]. Another issue to consider is that the power factor, by itself, might be somewhat misleading in regard to the actual stress on a distribution transformer. An accurate evaluation should take into account all the powers involved.
Acknowledgements We received help from many people during the development of the project. We wish to thank Mr Enrique Guzman, Mr. Carlos Gonzalez and Ms. Lina Castillo from the Baja California Division, CFE utility company; Mr. Marco Vilchis from the Baja California University and Mrs. Laura Morales from the PAESE divisional office.
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