Conference Paper

NREL/CP-520-46001

June 2009

Partially Shaded Operation of a 

Grid-Tied PV System 

Preprint

C. Deline

National Renewable Energy Laboratory

To be presented at the 34th IEEE Photovoltaic Specialists Conference

Philadelphia, Pennsylvania

June 7–12, 2009
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1 

PARTIALLY SHADED OPERATION OF A GRID-TIED PV SYSTEM

Chris Deline

National Renewable Energy Laboratory, Golden, CO

ABSTRACT

Partial shading of a PV installation has a disproportionate 

impact on its power production. This paper presents 

background and experimental results from a single string 

grid-tied PV system, operated under a variety of shading 

conditions. In this configuration a shadow can represent a 

reduction in power over 30 times its physical size. Results 

are presented relating size and positions of shading to 

power reduction of the PV system. A simulation method is 

also described that provides an accurate description of 

shade based on a single site survey. This process can 

provide the basis for an accurate simulation of power 

reduction in a partially shaded PV system.

INTRODUCTION

There is continued interest among photovoltaic installers, 

regulators and owners to obtain accurate information on 

photovoltaic (PV) systems operating under shaded or 

mismatched conditions. It is best to avoid shade where 

possible; while partially shaded installations can still 

produce useful power for a portion of the day, shading will 

generally result in a significant reduction in power. [1] This 

is particularly true for building-integrated PV which often

requires the integration of modules with existing structures 

in sometimes crowded urban environments. [2] In the 

interest of expanding the number of PV installations 

worldwide and providing maximum benefit from these 

systems, it is useful to consider in more detail the power 

loss from partially shaded PV systems. 

Regulatory agencies such as the California Energy 

Commission have a particular interest in obtaining 

information on shaded PV operation in order to accurately 

calculate rebate incentives for shaded systems. For 

incentive programs focused on installed capacity rather 

than actual kWh production, modeling the PV system and 

its access to the solar resource is required to obtain the 

expected performance of the system. Because shading of 

PV systems disproportionately reduces their power output, 

the rebate incentives need to be adjusted accordingly.

Prior experiments have been conducted investigating the 

effect of shade on various PV systems, many of which 

were cited in a comprehensive literature review by Woyte 

et al. [3] Other recent works include simulations of 

partially shaded PV cells [4,5], experimental results of 

different maximum power point tracking algorithms under 

shaded conditions [6] and the effect of shade on PV 

system performance [7,8

SHADED MODULES

]. 

Typically, a crystalline silicon module will contain bypass 

diodes to prevent damage from reverse bias on partially

shaded cells. These diodes are placed across 12-18 cells

in what will be termed a ‘group’ of cells here. (Fig. 1) The 

bypass diode across this group of cells will begin 

conducting before the power dissipated into the shaded 

cell is enough to evolve damaging temperatures. [9,10] 

While the main purpose of a bypass diode is not 

necessarily to improve module performance under shaded 

conditions, this is a useful byproduct. The bypass diode

allows current from non-shaded parts of the module to 

pass by the shaded part, and limits the effect of shading to 

only the neighboring group of cells protected by the same 

bypass diode. When a bypass diode begins conducting, 

the module voltage will drop by an amount corresponding 

to the sum of cell voltages protected by the bypass diode 

plus the diode forward voltage, but current from 

surrounding unshaded groups of cells continues around 

the group of shaded cells. 

+

- +

-

-

+

+

-

I

+

V

-

Shade

2 N-1 N

1

+

D1

Fig. 1: N modules are shown in series, each consisting of 

3 groups of 18 cells. Each group of cells is connected to a 

bypass diode that begins conducting if shading causes a 

cell to go far enough into reverse bias. In this example, 

shade causes diode D1 to short out its group of cells, 

reducing module 1’s voltage by 1/3.

The effect of shade on power output of typical PV 

installations is nonlinear in that a small amount of shade 

on a portion of the array can cause a large reduction in 

output power. For instance, completely shading one cell 

of an array will cause the bypass diode protecting that cell 

to begin conducting, reducing the power of the module by 
2 

as much as – (depending on the number of groups 

of cells in the module). An ongoing experiment at the 

National Renewable Energy Laboratory (NREL) is 

designed to quantify the effects of shade on the 

performance of typical grid-tied PV installations.

ARRAY CONFIGURATION AND RESULTS

A 10-module series string of crystalline Si PV modules is 

mounted on the roof of NREL’s Outdoor Test Facility at 

180o (South) azimuth and 40o tilt. (Fig. 2) The 165W 

modules are series-connected to an SMA 1800U grid-tied 

inverter which provides peak power tracking for the entire 

10-module string. Each PV module consists of 3 groups 

of 18 cells, and each group of cells is protected by a 

bypass diode. The particular modules used in this 

experiment were from a prior experiment, comprised of

two sets of five matched modules, each with a different 

antireflective top coating. There are some differences in

power production of the modules due to different top

coatings, but the effect was found to be negligible except 

for very early or late in the day when the data will not be 

considered anyway. 

System performance and individual module voltages are 

tracked by current and voltage transducers connected to a 

Campbell Scientific datalogger. Additional plane-of-array 

(POA) irradiance is measured by Kipp & Zonen and Li-Cor 

pyranometers. Heat tape wrapped around the Li-Cor 

pyranometer limits snow and ice buildup under wintry 

conditions. [11] A digital camera automatically records the 

extent of shade on the modules throughout the day, and 

thermocouples measure module temperatures.

Fig. 2: Mounted solar modules and pyranometers. Shade 

obstructions for Test #2 are visible at the far right. 

Test #1: Direct shading of modules

The single string array is peak-power tracked throughout 

the day by the grid-tied inverter. Individual module voltage 

is recorded along with the series string current. Partial 

shade is introduced onto several modules by applying 

opaque masking tape directly to the module. The impact 

of partial shading is determined by comparison of the 

shaded module’s voltage with an unshaded ‘control’ 

module. Because current is continuous in this single 

string, a drop in module power is proportional to a drop in 

module voltage. Only a single group of cells in each 

module is shaded in this experiment, therefore module 

voltage will drop by up to 1/3 as one of three bypass 

diodes begins conducting. (Fig. 3) 

Fig. 3: Module voltages are shown for a typical day. One 

cell is completely shaded around 10 AM dropping that 

module’s voltage by 1/3. The voltage drop results from 

one of the three module bypass diodes turning on and 

conducting the entire system current around the shaded 

group of cells. 

Half of the modules are chosen as candidates for shading. 

One cell per module is shaded with opaque masking tape 

in the amount of 10%, 16%, 20%, 24%, 31%, 35% or 39% 

of a cell’s area. Twenty-five different cells were shaded in 

total at each of these shading levels to provide a 

distribution of the shading effect. Relative power output of 

the shaded group of cells is determined by the shaded 

module’s output voltage relative to an un-shaded control 

module. Data is only considered from sunny days within 

the 3-week data collection interval, while irradiance is 

greater than 400 W/m2

. 

A comparison of the effect of various cell shading 

percentages is shown in Fig. 4. As can be seen in this 

figure, the relative power output of the shaded group of 

cells decreases significantly when 25-40% of a single cell 

is shaded. Any shading coverage greater than 40% of one 

cell results in the total reduction of that 18-cell string’s 

power output. This huge power loss illustrates a worstcase scenario in the disproportionate reduction of power 

from a small shadow. Shading half of one cell negates all 

the power produced by the 18 cells in that bypass diode 

group. Therefore, the reduction in power from shading 

half of one cell is equivalent to removing a cell active area 

36 times the shadow’s actual size. 

0 5 10 15 20 25

-5

0

5

10

15

20

25

30

Time (h)

Voltage (V)

Shaded module

Unshaded modules
3 

Fig. 4: Impact of single-cell shading on the output power 

of the 18-cell string. Shading greater than 40% of any 

single cell leads to total loss of power for the group of cells 

protected by that bypass diode. Error bars represent +/- 

one standard deviation.

Very specific and distributed shading is required to 

achieve such a high multiplication in shading effect. The 

benefit of bypass diodes in shaded modules becomes 

clear when the cell becomes additionally shaded. Any 

further shading of the cell, or of any other cells in the same 

group yields no further reduction in module or system 

power. A useful measure of the relative impact of shading 

on a system is the Shade Impact Factor (SIF) [12

 

] which is 

a relationship between the spatial extent of shade on a 

module or system, and its resulting power reduction. The 

shade impact factor can be represented by: 

 (1)

where and are the nominal system power and 

area, is the shaded area, and is the power 

produced under shaded conditions. For the previously 

considered worst-case scenario of shade covering half of 

one cell, SIF = 36 because this size of shadow causes a 

power reduction 36x greater than the relative size of the 

shadow would suggest. In systems where individual cell 

bypass diodes are present or a shadow projects uniformly 

on all cells, SIF 1. 

Fig. 4 also shows a relatively large distribution of output 

power for cells shaded near 30%. One reason for the 

diversity in power levels can be attributed to differences 

between the shaded response of various cells. Previous 

experiments have shown that differences in the reverse 

bias characteristic of cells can lead to dissimilar shaded 

and hot-spot response of cells that have otherwise similar 

forward characteristics. [13, 14, 15] Because of this 

variation in reverse characteristic, some cells are more 

susceptible to shade than others. In particular, Type A or 

high shunt resistance cells have a flat reverse bias 

characteristic [16] and as such are particularly susceptible 

to biasing to high negative voltages with small amounts of 

shade. If a Type A cell is shaded, it will dissipate more 

power within itself than a lower shunt resistance Type B 

cell would. A Type A cell will also bias to a greater

negative voltage than a Type B cell for the same reverse 

current, and therefore has a lower shade tolerance before

its group’s bypass diode begins conducting. 

A second contribution to the wide distribution of output 

power for cells shaded near 30% comes from differences 

in irradiance levels. Fig. 4 shows data for a variety of 

irradiance levels between 400 W/m2 and 1100 W/m2

. 

When data is evaluated for different irradiance levels, it 

becomes clear that the same percentage of shade results 

in a greater shade impact factor at higher irradiance. This 

trend is shown in Fig. 5. 

Fig. 5: Partially shaded power output for different plane-ofarray irradiances. Shaded impact on power output 

increases at higher irradiance as the system current 

increases. 

All of the partially shaded cells yield similar power output

at low irradiance. However, as irradiance and therefore 

the series string current is increased, power in the more 

highly shaded cells quickly drops. The power from a 

group of cells eventually reaches zero at high irradiance 

as the protecting bypass diode begins to conduct current. 

For the group of cells containing the 39% shaded cell, 

output power drops to zero at >500 W/m2 irradiance. The 

same is true of the 30% shaded cell group at >800 W/m2

. 

For the 24% shaded cell group, the power never drops 

much even at high irradiance. The relative output power 

remains high for this partially shaded condition because 

the reverse bias power dissipated within the 24% shaded 

cell is not great enough to result in the bypass diode 

turning on. The voltage of the module does drop, meaning 

that the cell is reverse biased and dissipating power to 

some extent, just not enough to reduce the output power 

to zero. 

5 10 15 20 25 30 35 40

-0.2

0

0.2

0.4

0.6

0.8

1

Cell shade percentage

Relative string power
4 

Test #2: Nearby shade obstructions

A second type of shade was applied to the same array 

configuration. Two different opaque shading objects were 

placed near two of the modules in order to cast a shadow 

at different times of the day. A flat plate measuring 60 cm 

x 60 cm was positioned 50 cm to the east of the last 

module in the array. The second shade obstruction is a 4” 

diameter PVC pipe attached at the bottom right corner of 

another module in the array. The cylindrical obstruction

extends above the bottom edge of the module by 35 cm. 

The layout of the shade obstructions is shown in Fig. 6.

Fig. 6: Flat plate and pole shade obstructions installed 

near two modules in Test #2. Shading simulation is shown

here for 8:00 on April 7th. 

Examples of the shadows cast by the two shade 

obstructions can also be seen in Fig. 6. The flat plate

obstruction casts a rectangular shadow extending all the 

way across the module at its maximum extent. The 

cylindrical post casts a long, thin shadow that tracks 

across the module throughout the day. By monitoring the 

module voltages and recording the extent of the shadows, 

an estimate of the power lost due to shade and therefore 

the shade impact factor can be determined. The results 

for both the pole and the flat plate obstruction over a 2-

hour period beginning at 7:30 AM are shown in Fig. 7.

It is clear from Fig. 7 that a small amount of shade e.g. 

from 2-3 partially shaded cells leads to a large SIF and a 

disproportionate loss in power. As the shadow of either 

the pole or the flat plate covers a greater portion of a 

module, the Shade Impact Factor (Eq. 1) decreases. In 

fact, the best fit line to the flat plate shading data follows 

SIF ∝ (Shade %)-1. For a module that is covered by shade 

over 15-50% of its area, the Shade Impact Factor 

approaches SIF = 2. A shadow that covered the entirety 

of one module would have the value SIF = 1. The value 

SIF = 2 has been adopted by the California Energy 

Commission as a constant shade penalty factor for its 

Expected Performance Based Incentive program. [12] It 

would appear that this value is consistent with shade of 

moderate extent (15%-50%) covering parts of one or more 

modules in the array.

Fig. 7: Shade Impact Factor for a pole shadow (◊) or flat 

plate shadow (o) falling on a single module. (··): Leastsquares fit to the data following y = 31.9 x-1. (– ·): Constant 

SIF = 2 value.

 

SITE SURVEY & SHADE SIMULATION

PV performance estimation becomes more accurate with 

the incorporation of data from a shading site survey. 

Present site survey devices provide information on the 

available solar resource based on the surrounding shade 

obstructions at the survey site. However, this calculation 

does not account for the partial shade conditions on 

different parts of the array. Following the method of Drif et 

al. [17] it is possible to take one site survey measurement 

and to predict what the shade extent would look like at any 

arbitrary point on the array. By calculating the spatial 

extent of the shadow on a PV array and using example 

Shade Impact Factor data from Fig. 7, an accurate time-ofday shadow derating for the particular installation can be 

determined.

Several site survey products are available that provide the 

azimuth angle and elevation angle from surrounding 

obstructions in graphical and tabular format. An example

output taken from the Test #2 experiment setup is shown 

in Fig. 8. If the i shade vertex azimuth and elevation

points are known along with the distance from the 

survey site to the ith shade obstruction , Cartesian 

coordinates for the shade points can be determined: 

( ) via coordinate transform. Here positive x

and y are taken to be east and north, respectively. The 

(0,0,0) origin coincides with where the site survey 

measurement was taken.
5 

Fig. 8: Azimuth and elevation coordinates for a sample 

site survey. Green polygons represent the shading 

objects present in Test #2. A sun path diagram displays 

the time of day when shading is apparent at the site 

survey location. 

A set of j coordinates for the photovoltaic system is also 

generated: ( ) relative to the site survey 

location. The position of each shading point relative to 

each PV point can be determined by the following 

coordinate transforms: [17] 

 (2)

 

 (3)

 

At any given point j on the PV array, the azimuth and 

elevation of the surrounding shading obstructions are

known. This provides a useful estimate of shade 

conditions at a given PV point and time of day if the solar 

azimuth and elevation are known. By comparing

with at a given azimuth, where i is chosen such 

that , shade will be present at array vertex j if 

. 

A numerical simulation can be conducted where the shade 

present on the array is calculated for each time of day 

throughout the year. Depending on the spatial resolution 

desired in the simulation, the j coordinates for the 

photovoltaic system may be chosen to match the vertices 

of each module, the vertices of each cell in each module, 

or any other value, limited only by the processor memory 

and speed. The and apparent shade vertices are 

calculated for each PV coordinate and compared with the 

sun’s position at each time of day, providing a picture of 

shade on the PV system. For a single grid-tied PV string, 

the relative string power and shade impact factor of Fig. 4 

and Fig. 7 can then be used to translate shade percentage 

into power reduction for the system. Multiple shaded 

vertices on a group of cells or module indicate that the 

bypass diodes for that group are conducting and reducing 

the system output power by an equivalent amount. 

A comparison between experimental results from Test #2 

and the simulation method described here are shown in 

Fig. 9. This plot shows the relative reduction in power of a 

single module as shadow crosses it over one day. The 

simulation input is the site survey details shown in Fig. 8. 

The particular module being monitored is the last module 

in the array, visible to the right of Fig. 6. Shade from the 

flat plate shade obstruction covers most of the module 

early in the morning, reducing power output between 7 

and 10 AM. Shade from the pole obstruction is apparent 

on this module by 3 PM. 

Fig. 9: Shaded module power relative to an unshaded 

control over a cloudless day. Simulation data comes from 

a site survey and shade simulation utilizing 150 PV array 

datapoints, 171 shade obstruction datapoints and 5 minute 

solar positions. 

Some timing differences are visible between the 

experiment and simulation data. This discrepancy may 

partly be due to the low spatial resolution of the simulation 

– using on average one PV datapoint per cell – and 

partially due to the shade obstructions being so close to 

the array. The close shade obstructions result in much 

greater spatial error when the shade coordinates are 

translated to other PV locations. A more typical shade 

condition would have greater distance to the shade 

obstructions, which would likely translate to greater 

accuracy in the simulation. 

CONCLUSIONS

Partial shading of PV installations has a disproportionate

impact on power production. For a single-string grid-tied 

PV system, a shadow can represent a reduction in power 

over 30 times its physical size. In order to accurately 

predict the power lost due to shaded conditions, it is 

necessary to identify the bypass diode placement in the 
6 

PV modules, as bypass diodes regulate the impact of 

shading on a particular module or group of cells. With an 

accurate description of the PV module layout, a single site 

survey can provide an estimate of shade conditions at one

position, and geometric transforms can translate that 

shade description to any point in the PV array. This 

process can provide the basis for an accurate simulation 

of power reduction in a partially shaded PV system.

Future work on this project includes investigating the 

impact of shade on thin film modules, and their shade 

tolerance relative to crystalline silicon modules. Parallelstring PV systems will also be investigated and compared 

with the single-string results presented here.

Acknowledgment

This work was supported by the U.S. Department of 

Energy under Contract No. DOE-AC36-08GO28308 with 

the National Renewable Energy Laboratory.

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[1] K. Kurokawa, “Realistic values of various parameters 

for PV system design”, Renewable Energy 15, 1998, pp. 

157-164

[2] U. Jahn, “Operational performance of grid-connected 

PV systems on buildings in Germany”, Progress in 

Photovoltaics 12, 2004, pp. 441-448

[3] A. Woyte, J. Nijs, and R. Belmans, “Partial shadowing 

of PV arrays with different system configurations: literature 

review and field test results”, Solar Energy 74, 2003, pp. 

217-233

[4] N. Kaushika and N. Gautam, “Energy yield simulations 

of interconnected solar PV arrays”, IEEE trans. energy 

conversion 18, 2003 pp.127-134

[5] H. Kawamura et al., “Simulations of I-V characteristics 

of a PV module with shaded PV cells”, Solar energy 

materials & solar cells 75, 2003 pp. 613-621

[6] R. Bruendlinger et al., “Maximum power point tracking 

performance under partially shaded PV array conditions”, 

21st European PV energy conference 4-8 Sept. 2006

[7] M. Garcia et al., “Partial shadowing, MPPT 

performance and inverter configurations: observations at 

tracking PV plants”, Prog. Photovolt: Res. Appl. 16, 2008,

pp. 529-536

[8] N. Chaintreuil et al., “Effects of shadow on a grid 

connected PV system”, 23rd European PV energy 

conference, 2008, p.3417

 

[9] J. Bishop, “Microplasma breakdown and hot-spots in 

silicon solar cells”, Solar Cells 26, 1989, pp. 335-349

[10] G. Bhattacharya and C. Neogy, “Removal of the hotspot problem in photovoltaic modules and arrays”, Solar 

Cells 31, 1991, pp. 1-12

[11] B. Marion, J. Rodriguez, J. Pruett, “Instrumentation 

for evaluating PV system performance losses from snow”, 

ASES Solar 2009 Conference, May 2009

[12] California Energy Commission SB1 Guidelines 2008 

pg. 56: http://www.energy.ca.gov/2008publications/CEC300-2008-007/CEC-300-2008-007-CMF.PDF 

[13] E. Molenbroek, D. Waddington and K. Emery, “Hot 

spot susceptibility and testing of PV modules”, 22nd IEEE 

Photovoltaic Specialists Conference, 1991, pp. 547-552

[14] W. Herrmann, W. Wiesner and W. Vaassen, “Hot spot 

investigations on PV modules-new concepts for a test 

standard and consequences for module design with 

respect to bypass diodes” 26th IEEE Photovoltaic 

Specialists Conference,1997, pp. 1129–1132

[15] M. Alonso-Garcia, J. Ruiz and F. Chenlo, 

“Experimental study of mismatch and shading effects in 

the IV characteristic of a photovoltaic module”, Solar 

Energy Materials & Solar Cells 90, 2006, pp. 329-340 

[16] International Electrotechnical Commission (IEC) 

61215, "Crystalline silicon terrestrial photovoltaic (PV) 

modules - design qualification and type approval", pp. 55-

64 (2005)

[17] M. Drif, P. Perez, J. Aguilera and J. Aguilar, “A new 

estimation method of irradiance on a partially shaded PV 

generator in grid-connected photovoltaic systems”, 

Renewable Energy 33, 2008, pp. 2048-2056
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Partially Shaded Operation of a Grid-Tied PV System: Preprint

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14. ABSTRACT (Maximum 200 Words)

Partial shading of a photovoltaic (PV) installation has a disproportionate impact on its power production. This paper 

presents background and experimental results from a single-string grid-tied PV system, operated under a variety of 

shading conditions. In this configuration, a shadow can represent a reduction in power over 30 times its physical 

size. Results are presented relating size and positions of shading to power reduction of the PV system. A simulation 

method is also described that provides an accurate description of shade based on a single site survey. This process 

can provide the basis for an accurate simulation of power reduction in a partially shaded PV system.

15. SUBJECT TERMS

PV; partially shading; grid-tied system; power reduction; crystalline silicon; module; simulation method; bypass diode;

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