Optimal sizing ratio of a solar PV inverter for minimizing the levelized cost of electricity in Finnish irradiation conditions

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Optimal sizing ratio of a solar PV inverter for minimizing the levelized cost of electricity in Finnish irradiation conditions

Väisänen Jami, Kosonen Antti, Ahola Jero, Sallinen Timo, Hannula Toni

Väisänen J., Kosonen A., Ahola J., Sallinen T., Hannula T. (2019). Optimal sizing ratio of a solar PV inverter for minimizing the levelized cost of electricity in Finnish irradiation conditions. Solar Energy, 185. pp. 350-362. DOI: 10.1016/j.solener.2019.04.064

Final draft Elsevier Solar Energy

10.1016/j.solener.2019.04.064

© 2019 International Solar Energy Society

* Corresponding author

E-mail address: jami.vaisanen@lut.fi (J. Väisänen). 1

Optimal sizing ratio of a solar PV inverter

1

for minimizing the levelized cost of electricity in

2

Finnish irradiation conditions

3

Jami Väisänen

, Antti Kosonen

, Jero Ahola

, Timo Sallinen

, Toni Hannula

4

a Lappeenranta University of Technology, P.O. Box 20, FI-53851, Lappeenranta, Finland 5

bEtelä-Savon Energia, P.O. Box 166, FI-50101 Mikkeli, Finland 6

__________________________________________________________

7 8

Abstract 9

The amount of installed solar power in Finland is increasing as a result of decreasing photovoltaic 10

(PV) system component prices. The growth is especially noticeable in residential systems, and 11

ways to make PV electricity a more competitive choice for Finnish residents are studied. One of 12

these ways is to decrease the solar PV electricity production costs by decreasing the investment 13

costs by undersizing the inverter of the PV system. The objective of undersizing is to find the 14

optimal array-to-inverter sizing ratio (AISR) where the ratio of the economic loss from the clipped 15

energy to the economic gain from the decreased system investment achieved by an undersized 16

inverter is lowest.

17

In this paper, the economically most optimal AISRs are determined for different residential 18

array sizes, orientations, and inclinations when operating in Finnish locations and conditions.

19

Calculations for each inverter size are carried out by using recorded Finnish meteorological data 20

and the current Finnish PV system cost distribution, and by analyzing existing 1-second resolution 21

production measurement data of a Finnish PV system. It is concluded that it is necessary to use 1- 22

second resolution data as the use of 1-hour resolution production data would lead to more 23

significant undersizing caused by the power clipping occurring within an hour.

24

The optimal AISRs presented in this study are higher than the optimal ratios reported in previous 25

studies for locations further south than Finland. This can be explained by the northern location of 26

Finland, where the irradiance above Standard Test Conditions (STC) is lower than in central 27

Europe, for example. This allows more significant undersizing as less energy is clipped even at 28

higher ratios. In the case of south-oriented arrays in a 30° installation angle, the optimal AISRs for 29

the 10 kW, 6 kW, and 3 kW inverters were 1.6, 1.8, and 2.08, respectively. Again, the AISRs for 30

the southwest-southeast facade installations were 1.8, 1.9, and 2.17 for the inverters under study.

31

They do not clip the produced energy as much as rooftop systems because their production is more 32

evenly distributed throughout the day, yet they do not achieve as low production costs either. It is 33

pointed out that if the PV self-consumption is optimized by using PV to heat water or batteries as 34

a storage, limitation of the PV generation might not be the correct solution.

35 36

Keywords: Photovoltaic power system, Optimization, system sizing, PV, Inverter, Nordic 37

conditions 38

2 1. Introduction

39

The prices of photovoltaic (PV) system components have significantly decreased, resulting in 40

an increase in the use of solar power in the world. In Finland, for instance, the installed grid- 41

connected PV capacity tripled in 2016 and increased further by 250% in 2017, reaching a total 42

installed capacity of 69.8 MW (Ahola, 2018). The growth is especially noticeable in residential 43

systems, where the PV system size is relatively small. However, it has been estimated that the PV 44

capacity of residential rooftops could be as high as 12 GWp in Finland, implying that the installed 45

capacity is still relatively small (Lassila et al., 2016). Generally, the PV inverter is sized to match 46

the nominal power of the PV array in Finnish commercial systems. This ensures that no available 47

energy is lost, all the energy of the PV array is exploited, and the maximum amount of energy is 48

produced. This, however, is not necessarily economically the most viable option in residential 49

cases where the inverters are smaller than 10 kVA. To encourage Finnish residential PV system 50

purchases, economic aspects should be taken into consideration. The investment, and further, the 51

production costs can be lowered by decreasing the investment costs by undersizing the inverter of 52

the PV system, which, in a traditional 1:1 installation ratio, covers from 15% to 27% of the costs 53

of a new residential size PV system. Undersizing means that the inverter power of the PV system 54

is smaller than the peak power of the solar PV array, which can be achieved by installing a smaller 55

PV inverter or by adding solar panels to an existing system (Lund et al., 1994; Good et al. 2016).

56

This solution reduces the proportion of the PV inverter in the total investment, yet does not 57

decrease the PV energy production too much by the limitation of the inverter power. This loss of 58

energy is termed clipping.

59

The objective of undersizing is to find the optimal array-to-inverter sizing ratio (AISR) where 60

the ratio of the economic loss from the clipped energy to the economic gain from the decreased 61

system investment achieved by an undersized PV inverter is lowest. This ratio is affected by the 62

technological aspects of the PV modules and the PV inverter applied, the weather and solar 63

radiation conditions in the location, and the applied data and their time resolutions (Kratzenberg et 64

al., 2014). Notton et al. (2009) studied the technological parameters that affect the AISR and found 65

that the inverter efficiency curve, that is, how the inverter efficiency behaves at different relative 66

loads, has the most significant effect on the relative size of the inverter, whereas the influence of 67

the PV module technology and the inclination of the PV array is minor.

68

In recent years, numerous studies have addressed inverter undersizing by using simulated and 69

actual 1-hour resolution data; it has been found that an AISR of 1.0–1.6 is optimal value. Of these 70

ratios, the most northern system location, and at the same time, the highest AISR 1.6, was reported 71

in Stockholm (59°N) (Notton et al., 2009; Stetz et al., 2010; Demoulias, 2010; Rodrigo, 2017;

72

Mondol et al., 2009). The ratio varies greatly depending on the location and climate of the site. For 73

Eugene, Oregon (44°N), the optimal AISR is 1.4, whereas for Las Vegas, Nevada (36°N), the ratio 74

is 1.0, meaning that the inverter should not be undersized at all (Chen et al., 2013). This clearly 75

demonstrates the effect of the installation location on the optimal AISR; the amount of direct 76

irradiance is much higher in Las Vegas than in Eugene. Kratzenberg et al. (2014) confirms that the 77

sizing ratio increases the further north the system is located. This is due to the fact that the amount 78

of direct sunlight is smaller and the intensity of the average irradiance is the lower, the further 79

north the system site is located, causing a smaller percentage of the total produced energy to be 80

clipped. Since the beginning of 2013, German PV systems have been required by law to participate 81

3

in the feed-in management; if one does not want to participate in the feed-in management, the 82

AISR of a new PV system has to be at least 1.42 (SMA, 2013). Wang et al. stated that if the natural 83

degradation rate of a PV module is considered for a 20-year lifetime, the optimal sizing ratio is 84

increased by 10%, because the annual average clipped energy decreases every year.

85

The objective of the present paper is to determine an ideal AISR in solar PV systems to 86

minimize the energy production costs for different array sizes, inclinations, and orientations in 87

Finnish conditions. In Finland, because of the geographic location, the amount of solar irradiation 88

is smaller and the climate is different from locations further south, which increases the influence 89

of undersizing. This means that in Finland, a higher AISR could be optimal than the AISRs 90

reported optimal in previous studies for locations with more irradiation. Further, the study uses 91

actual 1-second resolution production data gathered from a 51.5 kWp flat roof solar power plant 92

of Lappeenranta University of Technology (LUT) in the year 2015, which provides more accurate 93

results for the optimal AISR than 1-hour resolution data. Burger et al. (2006) studied the impact of 94

different time resolutions for solar radiation data and found that the use of 1-hour resolution data 95

hides important irradiation peaks; the use of 1-hour data results in about 6% of daytime hours with 96

irradiance ≥1000 W/m², and 1-minute data in about 9% of daytime hours.

97

Because of the structure of the cost distribution in a PV system, the cost proportions of a PV 98

inverter and its installation in the total investment are larger in smaller PV systems. This leads to 99

a situation where undersizing of a PV inverter in a PV system is more profitable in residential-size 100

systems than in larger systems. The purchase prices of new Finnish PV systems of different sizes 101

in 2017 is shown in Fig. 1. The inverter cost does not include replacement of the inverter, but it is 102

assumed that the cost of a new inverter would be on the same scale with the initial system.

103

104

Figure 1: Finnish PV system cost distribution in systems sized 1.3─62.4 kWp (Sallinen, 2017).

105

0 % 10 % 20 % 30 % 40 % 50 % 60 % 70 % 80 % 90 % 100 %

1300 2080 2080 3120 3120 5200 5200 7280 7280 10400 10400 15600 15600 20800 20800 31200 52000 62400

Percentage

Power (Wp)

Inverter Inverter freight

Panels freighted to Finland Mounting system

Minor accessories Installation

Travel, accomodation and freight costs

4

This paper focuses on residential PV systems sized under 10 kVA, where the cost of the PV inverter 106

is from 15% to 27% of the total investment, which includes replacement of the PV inverter once 107

during the system lifetime. Different AISRs for inverters of different sizes are calculated and the 108

best AISR is determined for each inverter by using the current Finnish PV system cost distribution 109

and analyzing actual 1-second-resolution production measurement data of a Finnish PV system 110

together with recorded Finnish weather data. The use of 1-second-resolution data instead of 1-hour 111

data is necessary to ensure that no production information is lost, as the production can vary greatly 112

within a production hour as a result of sudden changes in irradiance conditions.

113

This paper is organized as follows. First, the inverter characteristics that have an effect on 114

undersizing are introduced. Then, the weather conditions and the effects of the applied data are 115

presented by using data and knowledge available. Finally, different AISRs for three different 116

inverter sizes are calculated, the optimal AISRs are determined for each system, and their benefits 117

are compared with the 1:1 ratio.

118 119

2. Solar PV inverter 120

2.1 Efficiency of a PV inverter 121

The energy efficiency of a PV inverter is affected by the DC-side voltage and the relative load 122

(Baumgartner et al., 2007). The dependence of efficiency and voltage is caused by the DC-DC 123

converter. The commercial PV inverters generally consist of two stages; a DC-DC converter that 124

performs the maximum power point tracking (MPPT) and boosts the voltage if it is less than the 125

required 340 VDC and 565 VDC in single-phase and three-phase PV inverters, respectively, and 126

a DC-AC converter that transforms DC power into AC power. The DC-DC converter degrades the 127

efficiency of the PV inverter if it has to increase or decrease the circuit voltage. However, the 128

voltage produced by the solar panels is relatively constant regardless of irradiance, while the 129

current is more dependent on changes in irradiance. The dependence between the voltage at the 130

MPP and the irradiance is depicted in Fig. 2.

131

132

Figure 2: Voltage of the MPP and its dependence on irradiance (Kivimäki, 2014).

133

5

Fig. 2 shows that the voltage of the MPP at lower irradiance is about half of the voltage of the open 134

circuit at higher irradiance. For example, this causes the MPP voltage to be over 565 V virtually 135

all the time if the solar array is sized for a maximum DC input voltage of 1000 V open circuit 136

voltage at a certain local coldest temperature.

137

The efficiency of a PV inverter is heavily dependent on the relative load. Fig. 3 shows the 138

behavior of the efficiency curve of a PV inverter, where the efficiency almost reaches its maximum 139

value when the power is 30% of the nominal. This value varies depending on the DC voltage.

140

141

Figure 3: Efficiency curve of a 12 kW, three-phase commercial inverter (SMA tripower).

142

The efficiency decrease in lower power points can be explained by the technical losses in the 143

system and the self-operation power of the inverter.

144

It might be possible to increase the efficiency of power conversion at lower powers by optimally 145

undersizing the inverter of the PV system as the efficiency of a PV inverter is not constant but 146

dependent on the inverter loading ratio instead. The same load appears as a higher relative load for 147

a smaller PV inverter, which increases the efficiency because of the efficiency curve operation of 148

the inverter. This means that a larger inverter operates most of its load hours at a lower efficiency 149

(Sallinen, 2017; Malamaki et al., 2017).

150

On the other hand, from the viewpoint of a solar PV inverter, the annual operating hours at each 151

power level are of interest. Fig. 4 shows an annual power histogram of a 51.5 kW system, where 152

the hours below 10% power production are much more common than the higher ones. The inverter 153

in question operates under 10% nominal power for 48% of its annual running time, whereas it 154

operates only for about 1% of the time above 90% nominal power.

155

6 156

Figure 4: Histogram of the production power hours of a 51.5 kW system.

157

Because of the nature of the inverter efficiency curve, if the 51.5 kW system in Fig. 4 were sized 158

with a 35 kW inverter, the annual energy produced at powers below 5 kW would increase by 159

approximately one percentage unit.

160

Sangwongwanich et al. (2018) studied the effect of undersizing on the reliability of an inverter 161

in a Danish PV system and found that even at an AISR of two, the lifetime of an inverter does not 162

decrease below 20 years, but the probability that the tested inverter fails after 20 years of usage 163

increases drastically. The study also showed that the lifetime of an inverter is the longer, the lower 164

is the annual irradiation, but the effect of undersizing on the inverter reliability is stronger. In this 165

paper, this effect is negated, because the inverter is replaced once during the lifetime of the system, 166

as the typical lifetime of an inverter in a residential Finnish PV system is about 15 years.

167

2.2 MPP tracker 168

The MPP tracker is one of the most important features of a solar PV inverter. It maximizes the 169

power coming from the solar panels at every instant by adjusting the PV string voltage. If the 170

irradiance decreases while the PV inverter loads the PV array with the initial power, the voltage of 171

the array collapses. As a result, the MPP tracker changes its operating point and seeks a new MPP 172

by decreasing the load current. The MPP trackers of PV inverters work at different speeds and at 173

steps of different sizes when altering the voltage. If the step is large, a quicker reaction to the 174

changing circumstances is achieved. Alternatively, if the step is small, the power will reach its 175

maximum point faster, but the reaction to faster changes is slower(Kivimäki, 2014).

176

The voltage is changed by adjusting the current pulse length coming from the solar PV array, 177

most of the modern PV inverters apply Pulse Width Modulation (PWM) as a basic principle and 178

change this pulse length regularly during a grid frequency period. The pulse length can also be 179

0 10 20 30 40 50 60 70 80 90 100

- 2.00 4.00 6.00 8.00 10.00 12.00 14.00

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 24000 26000 28000 30000 32000 34000 36000 38000 40000 42000 44000 46000 48000 50000 52000 Total produced energy (%)

Percentage of produced energy (%)

Power (kW)

Amount Cumulative

7

used to decrease the power of the DC side, if the power that the inverter feeds into the grid is 180

greater than the nominal power of the PV inverter. This prevents the inverter from overloading, 181

which assists in the PV inverter undersizing by increasing the reliability of the inverter over time.

182 183

8 3. Conditions and Data

184

3.1 Weather and irradiation conditions in Finland 185

Irradiation can be direct or diffuse irradiation. Direct irradiation describes solar irradiation that 186

has travelled a straight line from the sun to the surface of a PV module. Diffuse irradiation means 187

irradiation that has been reflected or scattered by some other surface or air molecules before 188

reaching the PV module surface. All the irradiation in cloudy days as well as at sunrise and sunset 189

is diffuse irradiation, the amount of which is affected by the climate and weather conditions of the 190

location.

191

The solar electricity production potential in solar PV systems is dependent on the amount and 192

direction of irradiance in a location. In Finland, most of the solar energy is gained during summer 193

months, when the days are longer and the irradiance is higher, whereas the average temperatures 194

still remain relatively low. In winter, snow often covers the panels and fewer daylight hours 195

decrease the energy production. If the snow is not cleaned off from the panels, there is no 196

production during the winter months. However, less than 5% of the yearly irradiation is captured 197

during the winter months, meaning that the significance of snow cover is low. Nevertheless, the 198

snow coverage may have some effect in late February and March, causing a slight decrease in the 199

annual electricity production, and thereby, somewhat increasing the percentage of annual clipped 200

energy caused by undersizing.

201

The annual horizontal irradiation on a level surface in Jyväskylä (62°N) is around 850 kWh/m²,

202

the hour distribution of which is shown in Fig. 5. The distribution is also presented in two other 203

locations, which demonstrates the irradiation variation in Finland. Most of the irradiation is gained 204

after midday because of the difference between the solar time and the Finnish time. On average, 205

the local time is 30 min behind the solar time (Flowingdata, 2014) 206

9

207 208 209 210 211 212 213 214 215 216 217 218 219 220

Figure 5: Distribution of solar irradiation of on a level surface by hour in three different Finnish locations in the year 221

2015 (Finnish Meteorological Institute, 2015).

222

caused by different inclinations is shown in Fig. 6; it includes both direct and diffuse radiation.

224

The higher the inclination is, the more energy is lost from the eastern and western directions; on 225

the other hand, irradiance from south is increased. Up to a certain point, the gain from the southern 226

direction is greater than the loss from the eastern and western directions. The best fixed inclination 227

in southern Finland is 45°.

228

229

Figure 6: Irradiation on a solar PV panel in different inclinations in Finnish conditions in the year 2015. 0, −90, and 230

90 refer to irradiation from southern, eastern, and western directions, respectively (Finnish Meteorological Institute, 231

2015).

232

0 10 20 30 40 50 60

-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80

Irradiation (kWh/m2 )

Angle (°)

60 Degrees 40 Degrees 20 Degrees 0.00

20.00 40.00 60.00 80.00 100.00 120.00

00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22 22-23

Irradiation (kWh/m2)

Time (h)

Jyväskylä Helsinki-Vantaa Sotkamo

10

At 60°, 40°, and 20° inclinations, the annual global irradiations on solar panels in southern Finland 233

are 1060 kWh/m², 1080 kWh/m², and 990 kWh/m², respectively. This means that a 27% increase 234

in the amount of irradiation can be achieved by tilting the panels 40° compared with a horizontal 235

installation. However, it should be noted that increasing the inclination causes several problems, 236

for example, the modules will require more space because of the longer shadows, meaning that 237

fewer panels can be fitted on the roof area. Further, the panel inclination affects the wind load on 238

the panels, increasing the costs of the mounting system.

239

Inclining the panels towards south also increases the maximum irradiance and the amount of 240

higher irradiance that reaches the module compared with a horizontal installation. The irradiance 241

intensity histograms of 0° and 40° inclination in Jyväskylä are presented in Fig. 7. Even with a 40°

242

inclination, the irradiance above the Standard Test Conditions (STC) of 1000 W/m² is achieved 243

only for 84 hours in a year, and often, when such intensities are achieved, the panel temperature 244

exceeds the STC temperature. Nevertheless, 90% of the annual energy is obtained at irradiance 245

levels below 700 W/m². This leads to a situation where undersizing the PV inverter does not clip 246

the energy production as much as similar undersizing would do in a geographic location with a 247

greater amount of higher irradiance, thus allowing more significant undersizing.

248

11 249

250 (a)

251 252 (b)

Figure 7: Histogram of annual irradiance in Jyväskylä with an installation angle of (a) 0° and (b) 40° (Finnish 253

Meteorological Institute, 2015).

254

The number of diffuse irradiance minutes is so high that, despite the low intensity, they cover 255

25.5% of the total annual irradiation in Finland. As stated in previous chapters, during times of 256

diffuse irradiance, some gains can be achieved in the electricity production by optimally 257

undersizing the PV inverter owing to the nature of the efficiency curves of the PV inverter. In wall 258

mountings, diffuse irradiance production is important, because no direct irradiance reaches the 259

41.80

20.21 13.31

8.88

6.21 4.06

2.80 1.62 0.80 0.24 0.05 0.00 0.00 0 10 20 30 40 50 60 70 80 90 100

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00

1 100 200 300 400 500 600 700 800 900 1000 1100 1200

Cumulative percentage (%)

Percentage of annual irradiance (%)

Power (W/m²)

Amount Cumulative

34.19

18.83 13.10

9.30 7.27

5.30 4.39

2.93 2.25

1.42 0.73 0.23 0.05 0.01 0.00 0 10 20 30 40 50 60 70 80 90 100

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00

1 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Cumulative percentage (%)

Percentage of annual irradiance (%)

Power (W/m²)

Amount Cumulative

12

module, if the module is shadowed. In the future, the usage of panels as a facade material may 260

become more common, meaning that the orientation of panels would not play as great a role. As a 261

result, the modules would get only a little if no direct irradiance, and their production would consist 262

mostly of diffuse irradiance.

263

The temperature of the solar panel and the irradiance on the solar panel primarily affect the 264

electricity production of the PV system. When the temperature rises, the voltage of the panel 265

decreases, but the current increases. However, the decrease in voltage is greater than the increase 266

in the current, and thus, the total power decreases. The solar panel temperature is affected by the 267

ambient temperature and the irradiance. For example, the temperature coefficient of a 268

polycrystalline Panda 60 Cell solar panel is 275 Wp ± 0.38 %/°C, and the temperature coefficient 269

of a monocrystalline YGE 60 Cell solar panel is 275 Wp ± 0.42 %/°C.

270

Because of the northern location of Finland, the average ambient temperatures are lower than 271

in leading solar energy production countries, such as China or Germany. This increases the 272

production, which can be further enhanced by lowering the temperature of solar panels even more 273

with sufficient cooling. Cooling implemented with ventilation can increase the module power by 274

around 2%. An air gap behind the panels is sufficient to achieve the required ventilation for the 275

potential benefit (Sallinen, 2017).

276

When the irradiance suddenly spikes, the modules produce the highest power. This is caused 277

by the heat capacity of the solar panels: the delay to heat up from a sudden increase in irradiance 278

gives them time to produce in a lower temperature with a higher irradiance. This is on condition 279

that the MPPT can find the maximum power point faster than the solar panels heat up. The effect 280

of the heating up of solar panels can be seen in Fig. 8.

281

282

Figure 8: Solar panel production during and after an increase in irradiance.

283

These kinds of spikes occur always when irradiance changes from diffuse to direct. However, the 284

amount of energy these spikes produce is low; they cover only 0.05‰ of the annual solar energy 285

production at Lappeenranta University of Technology (LUT). It is worth noting that these spikes 286

are cut out first when downsizing the PV inverter.

287

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Power (W)

Time (min)

13 3.2 Meters and measured data

288

The recorded data provide valuable information for future plant dimensioning, as they give 289

accurate and concrete information about the production potential in a location. The resolution of 290

the measured data also plays a key role; the shorter the measuring interval is, the more information 291

is gained. Some of the solar energy simulation programs provide data at an hourly level, whereas 292

real recorded data can be in a 1-second resolution, for example. Simulation programs can nowadays 293

achieve better than the 1-hour resolution, but the data are not as accurate as actual measured data 294

would be. Here, the 1-second resolution data used in the study were gathered from the 51.5 kWp 295

flat roof solar power plant of Lappeenranta University of Technology (LUT) in the year 2015. The 296

values are output values, meaning that the losses are taken into account. The PV inverters of the 297

plant are not undersized, meaning that no energy is lost by clipping, and the slope of the array is 298

angled at 15° towards south. Fig. 9 shows the recorded production of the LUT solar PV plant on a 299

clear and an overcast day with 1-second and 1-hour resolutions. In the location, shading affects the 300

production of the PV modules.

301

302 303 (a)

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000

5 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Power (W)

Time (h)

Second Hour

14 304

305 (b)

Figure 9: Productions of the LUT 51.5 kWp solar PV plant (south oriented with 15° inclination) with 1-second and 306

1-hour resolutions. (a) Clear day 6.7.2015. (b) Overcast day 9.7.2015.

307

Fig. 9 shows that the difference between the resolutions is not as noticeable on clear days as it is 308

on overcast days. This is due to the sudden spikes in the production that are caused by rapid changes 309

in irradiance. Using 1-second resolution data ensures that no information is lost, which is extremely 310

important when the sizing of the PV inverter is considered; using 1-hour resolution could 311

potentially lead to skewed results and a nonideally sized PV inverter. Table 1 shows the differences 312

in annual clipped energies when undersizing the LUT 51.5 kWp plant with different-sized inverters 313

based on 1-second and 1-hour resolution data.

314

Table 1: Clipped energy (kWh) of the LUT 51.5 kWp power plant in the year 2015 based on 1-second and 1-hour 315

resolution data. The annual production is 38345 kWh with no clipping.

316

Inverter Power (kW)

20.0 25.0 30.0 35.0 40.0 45.0 50.0

Second (kWh)

7884.8 4743.7 2398.8 906.3 216.7 34.3 1.8 Hour

(kWh)

4984.5 2599.7 1004.0 192.3 0.0 0.0 0.0

317

Table 1 shows that not a single full hour of energy has been produced with a power of over 40 kW.

318

If the undersizing was to be carried out by using 1-hour data, the results would be skewed and 319

would not give the right picture about the lost production because of the clipping occurring during 320

the irradiance changes within an hour. For example, a 35 kW inverter in the system would lead to 321

a 0.5% loss of energy when using 1-hour data, whereas the use of 1-second data the loss would be 322

about 2.5%. By using these data and values of Table 1, coefficients for fixing 1-hour data into 1- 323

second data are formed and used in the calculations in this paper.

324

In Fig. 10, the production histogram of the LUT 51.5 kWp solar plant for the year 2015 is 325

plotted with different hypothetical system inverter sizes.

326

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000

5 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Power (W)

Time (h)

Second Hour

15 327

Figure 10: Production histogram of 2015 using 1-second resolution data. 51.5 kWp array and different inverter sizes.

328

Fig. 10 shows that even if the PV inverter was significantly undersized, the energy losses would 329

stay relatively low. This is due to the low energy production at higher power points. For example, 330

with an undersized 30 kW inverter, only about 6% of the annual energy production would be 331

clipped, yet the inverter investment would be substantially reduced. Fig. 10 also shows that the 332

production spikes are at 55─85% and 20% of the nominal power of the array. The spike at 20%

333

comes from the production during diffuse irradiance, whereas the spike at 55–80% is caused by 334

the average productions during direct irradiation. Peak powers are absent because of the warming 335

of the panel and the unideal installation slope of 15°. In addition, the peak powers are limited by 336

the low amount of irradiance over 1000 W/m², as can be seen in Fig. 7, as the nominal power of 337

the panels is rated at an irradiance of 1000 W/m². 338

339

4. Techno-economic analysis 340

The irradiance on the surface of the array is calculated for every hour by using 1-hour resolution 341

weather data, which cover both diffuse and direct radiation. The irradiance used in the study 342

represents an average year, and every year’s production is assumed identical in terms of weather 343

and irradiance conditions. For an oriented surface, the angle of incidence 𝜃 (°) is required. It is 344

calculated as follows:

345

cos 𝜃 = sin 𝛿 sin 𝜙 cos 𝛽 − sin 𝛿 cos 𝜙 sin 𝛽 cos 𝛾 346

+ cos 𝛿 cos 𝜙 cos 𝛽 cos 𝜔 + cos 𝛿 sin 𝜙 sin 𝛽 cos 𝛾 cos 𝜔 (1) 347

+ cos 𝛿 sin 𝛽 sin 𝛾 sin 𝜔 , 348

0.65 0.675 0.7 0.725 0.75 0.775 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700

0 5 10 15 20 25 30 35 40 45 50 53 Portion of available annual PV energy

Energy (kWh)

Power (kW)

Energy (25 kW) Energy (30 kW) Energy (35 kW)

Energy (40 kW) Energy (45 kW) Energy (unlimited)

Cumulative (25 kW) Cumulative (30 kW) Cumulative (35 kW)

Cumulative (40 kW) Cumulative (45 kW) Cumulative (unlimited)

16

where 𝛽 is the slope of the surface (°), 𝛾 is the azimuth of the surface (°), 𝜙 is the latitude (°), 𝛿 is 349

the solar declination (°), and 𝜔 is the hour angle (°). The Zenith angle 𝜃_z (°) is obtained by setting 350

𝛽 = 0° in the above equation, which yields:

351

cos 𝜃_z= cos 𝜙 cos 𝛿 cos 𝜔 + sin 𝜙 sin 𝛿 (2)

352

Direct irradiance on a surface (W/m²) tracking the sun is calculated by 353

𝐺_bs = { 𝐺_b

cos 𝜃_z, cos 𝜃_z> 0 0, cos 𝜃_z≤ 0

, (3)

354

where 𝐺_b is the amount of direct irradiance (W/m²) obtained from the weather data. This value has 355

to be fixed to correspond to the air mass value (AM) in the production hour. The AM is calculated 356

for every production hour as follows:

357

AM = 1

cos 𝜃_z, (4)

358

for which the maximum 𝐺_bsvalues at set AMs are defined as:

359

AM 𝑮_{𝐛𝐬,𝐦𝐚𝐱}/𝑮_𝐛𝐬

2.0 0.84

3.8 0.62

5.6 0.47

10 0.27

360

This means that the real direct radiation (W/m²) on a surface is 361

𝐺_bsr= {𝐺_bs, 𝐺_bs < 𝐺_bs,max

𝐺_bs,max, 𝐺_bs ≥ 𝐺_bs,max . (5) 362

Some of the irradianceis reflected and lost because of the angle of incidence. This is considered 363

with the following reflection-fixing coefficients:

364

𝑅 = {

0.95, 𝜃 ≤ 57°

0.7, 57° < 𝜃 ≤ 78°

0.3, 78° < 𝜃 ≤ 85°

0.1, 𝜃 > 85°

. (6)

365

From these coefficients, we can calculate the irradiance on an oriented module surface (W/m²):

366

𝐸_e= {cos 𝜃 ∙ 𝐺_bsr∙ 𝑅 + 𝐺_d, cos 𝜃 > 0

𝐺_d, cos 𝜃 ≤ 0 , (7) 367

where 𝐺_d is the amount of diffuse irradiance (W/m²) obtained from the weather data.

368

17 369

The DC power output (W) is calculated for every production hour of a year as follows:

370

𝑃_DC = 𝐸_e∙ 𝐴_a∙ 𝜂_mod∙ (1 + 𝛼_p∙ (𝑇 − 𝑇_STC) , (8) 371

where 𝐴_a is the PV array area (m²), 𝜂_mod is the module efficiency (%), 𝛼_P is the temperature 372

coefficient of power (%/K) that accounts for the change in production relative to the module 373

temperature, 𝑇 is the module temperature (K), and 𝑇_STC is the STC temperature (25 °C). To 374

consider module degradation, the DC power output in year 𝑛 of operation (W) is given as 375

𝑃_DC,𝑛 = 𝑃_DC∙ (1 − 𝑣_deg )^𝑛−1 , (9)

376

where 𝑣_deg is the effective PV module degradation rate (%/a). From this, the AC power output 377

(W) is calculated as follows:

378

𝑃_AC,𝑛 = 𝑃_AC,𝑛∙ 𝜂_inv , (10)

379

where 𝜂_inv is the PV inverter efficiency (%), which is affected by partial loads. However, the 𝑃_AC,𝑛 380

cannot exceed the inverter maximum power, which results in 381

𝑃_AC.n = {𝑃_AC,𝑛, 𝑃_AC,𝑛< 𝑃_inv

𝑃_inv, 𝑃_AC,𝑛 ≥ 𝑃_inv , (11)

382

where 𝑃_inv is the rated power of the PV inverter (W). The clipped power 𝑃_c,𝑛 (W) is obtained from 383

the power exceeding the rated power of the PV inverter 384

As the production data are in 1-hour averages, the hourly energy yield is the same as the average 385

hourly production power. Thus, the total AC electricity yield (Wh) in year 𝑛 of operation is 386

calculated as follows:

387

𝐸_𝑛 = ∑ 𝐸_AC,𝑛,𝑖

8760

𝑖=1

, (12)

388

where 𝑖 is the production hour of the year in question and 𝐸_AC,𝑛,𝑖 is the hourly energy yield (Wh) 389

obtained from the average production power. From this, the total energy yield in the system 390

lifetime (Wh) is calculated as 391

𝐸_tot= ∑ 𝐸_𝑛

𝑘

𝑛=1

, (13)

392

where 𝑘 is the lifetime of the system. In the same way, the total clipped energy in year 𝑛 (Wh) is 393

calculated by 394

𝐸_c,𝑛 = ∑ 𝐸_c,𝑛,𝑖,

8760

𝑖=1

(14) 395

and the total clipped energy during the system lifetime (Wh) is 396

18 𝐸_c,tot= ∑ 𝐸_c,𝑛

𝑘

𝑛=1

. (15)

397

Finally, the levelized cost of electricity (LCOE) is used to estimate the total electricity 398

production costs of the system during its lifetime. LCOE ^c

kWh is calculated by 399

LCOE = 𝐼_t∙ 100

𝐸_tot/1000, (16)

400

where 𝐼_t is the cost of the total PV system investment (€).

401

5. Results 402

Jyväskylä weather data provided by the Finnish Meteorological Institute are used in the 403

irradiation and temperature calculations. The weather data are from the city of Jyväskylä, because 404

it is the closest weather data point to the LUT solar power plant. Jyväskylä is geographically and 405

climatically similar to Lappeenranta and the distance between the two cities is relatively short, 406

meaning that similar temperatures, number of daylight hours, and conditions of partial cloudiness 407

can be assumed. The 1-hour resolution weather data from Jyväskylä are used to obtain 1-hour 408

production data. These production data are then correlated with the 1-second resolution production 409

data by using the coefficients formed by applying the results presented in Table 1. As both the 410

weather and production data are from the year 2015, this correlation can be done. In addition, the 411

use of data over one year only can be justified by the fact that the factors affecting the production 412

during the year 2015 do not significantly differ from average conditions. According to the weather 413

data of Jyväskylä, the annual global irradiation on a horizontal surface in the year 2015 was 859 414

kWh/m², while the average annual global irradiation in Jyväskylä is about 850 kWh/m². Table 2 415

presents the average monthly mean temperatures in Jyväskylä and the monthly mean temperatures 416

in the year 2015.

417 418

Table 2: Average monthly mean temperatures and monthly mean temperatures in the year 2015 (Finnish 419

Meteorological Institute, 2015).

420

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVG

(°C)

−7.9 −8.2 −3.4 2.5 9.3 13.9 16.7 14.3 9.1 4.9 −1.6 −3.8 2015

(°C)

−6.5 −2.1 −0.4 3.4 8.7 12.2 14.7 15.6 10.9 4.0 2.7 0.1 421

The differences in mean temperatures and annual global radiation in the year 2015 compared with 422

the average values cannot be considered significant. The other characteristics used in the 423

production calculations are shown in Table 3, and the efficiency of the inverter is defined in 424

accordance with the efficiency curve seen in Fig. 3.

425

19 426

Table 3: System STC characteristics used in the calculations.

427

Characteristic Value

Module area 6.49 m²/kWp

Maximum module power 250 W

MPP voltage 29.8 V

MPP current 8.39 A

Open-circuit voltage 37.6 V

Short-circuit current 8.92 A

Module efficiency 15.4 %

Temperature coefficient of 𝑃_max −0.42 %/K Temperature coefficient of 𝐼𝑠𝑐 0.05 %/K Temperature coefficient of 𝑈𝑜𝑐 −0.33 %/K

Module degradation rate 0.89 %/year

System lifetime 25 years

System latitude 62°

System longitude 25.7°

428

The system investment calculations are performed with the following initial values: PV inverter 429

price, including replacement of the PV inverter once during the system lifetime, 20 ^c

W for a 10 kW 430

inverter, 25 ^c

W for a 6 kW inverter, 33 ^c

W for a 3 kW inverter, the panel price including a mounting 431

system 1000 ^€

kWp, and other fixed costs of 1500 €, for instance panel maintenance. The values are 432

obtained by using Fig. 1 and by including the installation equipment, the installation costs, and the 433

travel costs in the inverter and panel prices. The cost distribution in Table 4 is obtained by using 434

these prices.

435

Table 4: PV system cost distribution used in the simulations.

436

Array power (kWp)

Inverter power (kW)

Inverter (%)

Array and mounting (%)

Other fixed costs (%)

3.0 3.0 18.18 54.55 27.27

6.25 3.0 11.43 71.43 17.14

6.5 3.0 11.11 72.22 16.67

6.0 6.0 16.67 66.67 16.67

11.0 6.0 10.71 78.57 10.71

11.5 6.0 10.34 79.31 10.34

10.0 10.0 14.81 74.07 11.11

16.0 10.0 10.26 82.05 7.69

18.0 10.0 9.30 83.72 6.98

27.0 10.0 6.56 88.52 4.92

30.0 10.0 5.97 89.55 4.48

437

The calculation results are at 1-hour resolution and fixed into 1-second resolution by using the 438

coefficient obtained by using the LUT production data. Inverters of three different sizes are 439

undersized by adding more solar panels to the system located in Jyväskylä, and the economically 440

best PV inverter to PV array power ratio is determined for rooftop and facade installations. Rooftop 441

20

installations are mounted in a 30° angle towards south, and facade installations are divided between 442

the southwestern and southeastern walls. For the 10 kW inverter, also an east-west facade 443

installation is simulated. The fact that facade installations are likely to be more expensive to install 444

is not taken into account in the calculations, neither is the fact that a smaller inverter would have 445

a better efficiency, but as it has been stated in chapter 2.1, the effect would only increase the 446

possible optimal AISR. The following sizes were chosen, because the highest benefit of 447

undersizing is gained with smaller residential systems with the nominal power under 10 kW, where 448

the cost of a PV inverter is up to 20% of the total investment.

449 450

5.1 10 kW inverter 451

Fig. 11 shows results for the production costs with different rooftop PV array sizes for a 10 kW 452

inverter and the effect of changing the array size on the LCOE. At a 1:1 inverter to array ratio, the 453

peak load time is 968 hours in the first year, production per panel power is 968 ^kWh

kWp, and the LCOE 454

is 6.25 ^c

kWh. An optimal AISR of 1.6 was determined for the 10 kW inverter, meaning that the 455

optimal installed PV array size is 16 kWp. At the 1.6 ratio, the values have changed to 1478 hours, 456

891 ^kWh

kWp, and 5.92 ^c

kWh, respectively, while the clipped energy is 7.3% (1075 kWh) of the total 457

production on the first year. This means that by finding the optimal AISR, the production costs 458

can be reduced by 5% compared with the 1.0 ratio.

459

21 460

461 462 (a)

463 464 (b)

Figure 11: Production costs of (a) 10 kW inverter with 10 kWp panels centered and (b) 10 kW inverter with 16 kWp 465

panels centered and the effect of changing the array size.

466 467

It is worth noting that due to the PV array degradation caused by aging, which decreases the 468

production power during the system lifetime, the total clipped energy during the 25-year lifetime 469

of the system is 5.1%, which is less than in the first year alone.

470

If the array were split between the southwestern and southeastern facades, the optimal AISR 471

would be 1.8, meaning an 18 kWp array and a 10 kW inverter. In this case, the peak load hours, 472

the LCOE, and the clipped energy would be 1557 hours, 6.37 ^c

kWh, and 9.2% in the first year and 473

7.2% during the system lifetime, respectively.

474

An optimal east-west installation on a building facade would include a 15 kWp PV array on 475

both the eastern and western sides, meaning an installation ratio of 3. In this case, the peak load 476

time would increase to 1711 hours, and the clipped energy would be only 3% despite the AISR of 477

three. However, the LCOE would be as high as 7.64 ^c

kWh, even though the energy would be 478

5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6

-15 -10 -5 0 5 10 15

LOCE (c/kWh)

Array size change (%)

5.89 5.9 5.91 5.92 5.93 5.94 5.95 5.96 5.97 5.98

-15 -10 -5 0 5 10 15

LCOE (c/kWh)

Array size change (%)

22

produced over a much longer time period, making a 100% self-consumption more realistic than 479

with a rooftop installation, where the production peaks at midday.

480

The best array placement depends on the customer’s needs. In residential buildings, the loads 481

are usually higher in the morning and evening, and thus, a split installation would be more efficient.

482

In commercial buildings, the load usually peaks during working hours, and therefore, a rooftop 483

installation would be the most beneficial solution. The simulated AISRs for each of the most 484

common installation type along with their characteristics are compiled in Table 5.

485 486

Table 5: Simulated 10 kW inverter productions with different PV generator sizes.

487

10 kW inverter

Peak load time year 1 (h)

Produced energy in the 1st year (kWh/kWp)

Clipped energy

in the 1st year

(kWh)

Clipped energy

in the 1st year

(%)

Produced energy during lifetime

(kWh)

Clipped energy during lifetime

(kWh)

Clipped energy during lifetime (%)

LCOE without interest

(c/kWh) AISR 10 kWp

rooftop 30°

968 968 0 0 215968 0 0 6.25 1.0

16 kWp rooftop

30°

1442 891 1076 7.28 325625 16732 5.14 5.92 1.6

18 kWp facade

(SE/SW) 1505 820 1435 9.22 337300 24280 7.20 6.37 1.8

30 kWp facade

(E/W) 1908 568 513 3.00 387678 4487 1.16 8.64 3.0

18 kWp facade (SE/SW) and 9 kWp

south 30° 2002 960 560 3.00 423886 4608 1.08 7.19 2.7

30 kWp facade

(SE/S/SW) 2078 631 600 3.16 430385 5487 1.27 7.78 3.0

488

Table 5 shows that the best option for minimizing the production costs is to install 16 kWp of 489

panels on a rooftop towards south. Systems split between different facades clip less energy than 490

systems oriented towards one direction, because the production takes place over a longer period 491

and more energy can be produced throughout the day. This effect can be seen in Fig. 12.

492