Mathematical Modelling in Civil Engineering
Vol. 15‐No. 3 : 13‐27‐2019
Doi: 10.2478/mmce‐2019‐0008
WIND LOAD DESIGN OF PHOTOVOLTAIC POWER PLANTS BY
COMPARISON OF DESIGN CODES AND WIND TUNNEL TESTS
Ovidiu BOGDAN - Lecturer, PhD, Technical University of Civil Engineering of Bucharest, Department of Strength
of Materials, Bridges and Tunnels, e-mail: obogdan@utcb.ro
Dan CREŢU - Professor, PhD, Technical University of Civil Engineering of Bucharest, Department of Strength of
Materials, Bridges and Tunnels
Abstract:Wind load design of the ground-mounted photovoltaic (PV) power plants requires
interpretation of the design code considering the particularities of these structures. The PV power
plants consist on systems of several solar panels. Wind load pressure coefficient evaluation, by design
code, for a single solar panel considered as a canopy roof, neglect the group effect and the air
permeability of the system. On the other hand, the canopy roofs are structures with medium
serviceability, but the PV power plants are structures with low serviceability. This paper discuss the
difficulties of the wind load design for the PV power plants ground mounted in Romania and
compares the Romanian, German, European and American wind design code specifications with the
parameters provided by the wind tunnel test, for this type of structures. For Romanian wind load
design an evolution of the 1990, 2004 and 2012 editions of the design codes specifications is also
studied. Evaluation of the internal resultants for the structural elements of the PV panel, considering
the pressure coefficients and the force coefficients, conducts to different results. Further code
explanations and design specifications are required for wind design of the PV power plants.
Keywords: wind pressure coefficient, wind force coefficient, photovoltaic panel, group effect
1. Introduction
The green energy is assumed by the European Union strategy to cover 20% of the total energy
production until 2020. Romania assumed 38% target by its national strategy, for green energy
only, till 2020. The Romanian national strategy on energy policy is based on green certificates
which are public paid to the investors in green energy facilities. Green energy represents around
one third of the total energy power produced in Romania. About 1400 MW is the total power
installed at 2016 by photovoltaic power plants, similar with the nuclear power provided by the two
operational nuclear reactors located at Cernavoda. If an installation cost of about 1 million euro is
considered for every MW, the total investments in photovoltaic energy reached 1.5 billion euro.
The total installation cost was even bigger, since for one MW was paid around 3 million euro in
2004 and decreased to 1 million euro in 2016. From the total installation cost, an important amount
represents the cost of the metallic support structure of the photovoltaic panels. The safe and
structural performance guided design of this structure to wind, and eventually snow load, conducts
to an eventually decrease of the structure cost.
This paper describes the difficulties of the wind load design of the photovoltaic power plants in
Romania and is based on a technical consultancy contract between the Strength of Materials,
Bridges and Tunnels Department of the Technical University of Civil Engineering of Bucharest
and a private investor and designer for PV power plants. In Romania, the wind design of the
photovoltaic power plants requires the wind pressure and force evaluation based on the recently
enforced Wind Load Design Code with the indicative CR 1-1-4-2012 [1]. This design code
replaced the old wind load design code,2004 version, having the indicative NP-082-04 [2] and
entitled „The fundamentals of design and loads on constructions. The wind load”. The new version
of the Wind Load Design Code is not completely overcoming the interpretation and evaluation
difficulties of the former design code.
Based on the specifications of the CR 1-1-4-2012 Wind Load Design Code [1], the photovoltaic
power plants needs wind load evaluation as for the canopy type structures. This assumption is
completely neglecting the group effect of photovoltaic power plant panels. On the other hand, the
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photovolatic power plants and the structural canopies have usually not the same life span. Since
the photovoltaic power plants are in use for an average of about 20 years, the canopies may be
used for the same duration as the main structure, if they are atached to structures. In this case, the
canopies are structures of about 50 years life span.
The paper is structured on subsections referring to the PV panel structural description, wind load
evaluation based on the Romanian design code, wind load comparison for different wind design
codes, a critical review of the Romanian wind design code regarding this type of structures, the
wind tunnel experiments description and the comparison of the measured wind coefficients and
forces with the design code obtained values, and the final conclusions and comments.
The consulted literature review referring to PV arrays is validating the influence of the tilt angle,
incidence angle of the wind, space between panels and sheltering effect of the arrays.
Some of the very first experimental studies were done by Radu [3] for PV panels located on flat
roofs. They used a pneumatic mediation technique to measure the pressure coefficients of the
exposed surface. Shelter effects due to the marginal attics and the successive PV panel parallel
rows were identified.
If mounted on flat roofs, Cao et all. [4] shows on 1:50 scale models that the single PV array
indicates comparable wind uplift forces for center or edge location of the array. For multiple arrays
the uplift forces are decreasing with distance from the edge of the roof. The sheltering effect is
indicated by larger forces for single PV array compared with multiple PV array. Mean and peak
force values are increased with tilting angle and distance between PV arrays due to the increased
turbulence. The building depth can be neglected, but the roof parapets decreased height are
conducting to increased turbulence on PV panels if they are close to the edge of the roof. Tests
and CFD simulation were compared for multiple PV arraysmounted on the roof of the parking
open structures by Axinte et all. [5]. Higher turbulence for roof edge located PV arrays and the
effect of the closing provided by the vehicles parked underneath were studied.
For ground mounted PV stand-alone panel, tilted by 25°, the study of Jubayer [6] evaluates the wind
pressure coefficients resulted from CFD analysis at full scale and compared the results with the
measured parameters obtained by experiments at 1:10 scale. Good agreement of the parameters were
observed, which indicates the independence of the wind pressure coefficients due to the scale model,
if large scale is considered (up to 1:50). 0° and 180° wind direction are responsible for maximum drag
and uplift forces, but the 45° and 135° for the maximum overturning moment. For the last, corner
vortices were observed. The ASCE code indicated values for monoslope free roofs were in good
agreement with mean values resulted from the numerical study. Extending the study to the PV arrays,
for the same tilting angle, and performing the CFD analysis, Jubayer [7] observed that first row is
always affected by the largest wind forces, independent on the wind direction, which indicates the
sheltering effect on the next rows. For these rows, the wind loads are higher for oblique wind direction
than for direct wind. Different tilting angles were studied by CFD analysis for PV arrays by Shademan
[8] and determined that the critical panels are those located on the corners due to the increased
turbulence, for all tilting angles. The tilting angle effects were also studied using CFD analysis by
Irtaza [9] for ground mounted single panel and PV array and increased turbulence was determined
when increasing the tilting angle. Single panel experiments were also performed by Velicu [10] and
observed that force coefficients are increasing with the tilting angle.
A comparison of the roof mounted to the ground mounted PV arrays was performed by
Stathopoulos [11] using 1:200 scale models experiments. They observed the critical wind acting
on 135° direction, with extreme values on the range 105° to 180°. For this range the panel tilting
angle may be significant. The building height and panel location is not very significant, but panels
located on the roof edge take the greatest net wind forces. A unified ground and roof mounted
panels net pressure coefficients diagram was proposed. Spacing parameters were studied by
Warsido [12] on 1:30 scale model of ground mounted and roof mounted PV arrays. Sheltering
effect, increased wind forces for edge located panels, higher for diagonal wind direction, are
15
observed. No significant effect of the lateral spacing between panels for roof mounted and
important variations of the wind coefficients for ground mounted were also measured. Force and
overturning moments for ground mounted panels are increasing when longitudinal spacing is
increased. For the roof mounted panels, the force and overturning moments are decreased if the
increasing of the gap between panels and roof edge.
The uncertainties of the wind measured forces as a result of the model scale were studied by Aly
[13] using CFD modeling of the ground mounted PV array. The uncertainties are more significant
for the ground mounted PV arrays, which are usually consider the 1:30 scale model, than for roof
mounted PV arrays, since they are using the building scale, usually 1:100 to 1:500. The numerical
analysis was calibrated on test available data and a hybrid experimental/computational procedure
was developed and performed. Mean pressure coefficients are not dependant on the scale model,
but the peak values are strongly determined by the model and turbulence scale. The commonly
used BLWT are indicating smaller peak pressure coefficients values than a CFD simulated more
accurate turbulence at high Reynolds numbers, like Large Eddy Simulation. Some insights of the
scale factor for roof mounted PV arrays were presented also by Kray [14], who mentioned the
increase of the peak pressure coefficients when reducing the model scale from 1:100 to 1:50.
2. Photovoltaic panel structural system description
A photovoltaic power plant consists by several PV panels emplaced in row and by several rows
(similar as in Fig. 1). A small gap, of centimeters length, is used in between panels in row. The PV
panel rows are parallel, at distances of meters determined based on the panel width and inclination,
so that the maximum solar exposure act on every panel.
The further described PV panel is one element of a photovoltaic power plant constructed in
Romania, on South of Bucharest, close to the Danube. The power plant has an installed capacity
of 120 MW, one of the largest in the country. The structure of one photovoltaic panel consists of
five transversal cantilever type steel frames and four longitudinal aluminum beams, supported
continuously on every transversal frame. The distances in between transversal steel frames are all
equal with 2.10 m. The size of the photovoltaic panel is 9740 mm by 3302 mm with an inclination
of 25 degrees from horizontal plane, for the analyzed case.
Fig. 1 – Photovoltaic power plant assemblage pattern (© Königsolar GmbH)
The transversal steel frames are constructed by assemblage of:
⁃
a vertical S355 steel column having a total height of 2800 mm, from which 1400 mm are
embedded in soil;
⁃
a 25 degrees inclined S355 steel beam having the length of 2600 mm, hinged to the top of
the column;
⁃
two S235 steel braces having 988 mm and 692 mm respectively, both hinged to the beam
and column.
16
The sizes of the transversal frame structural elements are indicated in Fig. 2. No foundation is
required to fix the vertical steel columns.
The four longitudinal aluminum beams have the same length as the photovoltaic panel, 9740 mm.
The beams are located at equal distances of 825 mm in between. From top, and bottom beam
respectively, to the end of the photovoltaic panel are 351 mm. On transversal direction, every panel
consists of two rows of photovoltaic cells, emplaced with a gap of 22 mm in between.
Fig. 2 – The sizes of transversal structural steel frame elements
3. Wind load evaluation for one panel
The considered photovoltaic power plant is located in category II terrain, with low vegetation and
isolated obstacles, as indicated by the Romanian Wind Load Design Code CR 1-1-4-2012 [1] and
the Eurocode EN 1991-1-4:2006 [15] respectively.
Based on the Romanian Wind Load Design Code [1], which basically follows the corresponding
Eurocode [15], the wind load may be evaluated either as an acting pressure, by the following
equation:
𝑤
𝛾
∙𝑐
∙𝑞 𝑧
(1)
or as a resultant force, by the following equation
𝐹
𝛾
∙𝑐 ∙𝑐 ∙𝑞 𝑧
∙𝐴
(2)
To evaluate the characteristic peak velocity wind pressure, the following equation is used, as
indicated by the former mentioned wind design codes
𝑞 𝑧
𝑐 ∙𝑐 𝑧
∙𝑐
𝑧
∙𝑞
(3)
For the considered photovoltaic power plant site location, the basic wind pressure indicated by the
Romanian wind map is evaluated as 𝑞
50 𝑑𝑎𝑁/𝑚 . If changes in terrain orography are
negligible 𝑐
1 and terrain roughness coefficient is determined as 𝑐 𝑧
0.496 and the peak
velocity coefficient as 𝑐 𝑧
2.988 for the site and reference height considered, the peak
velocity wind pressure results as 𝑞 𝑧
74.148 𝑑𝑎𝑁/𝑚 .
17
As indicated in the design code, to evaluate the wind load as a resultant force the dynamic
coefficient 𝑐 it may be neglected, if the structure of the PV panel vibrates with a fundamental
frequency larger than 5 Hz, which is the case of analyzed panel.
Then, to compare the magnitude of the wind load obtained based on a pressure distribution (Eq. 1)
with the one obtained based on a resultant force (Eq. 2), a comparison in between pressure coefficients
and force coefficient values is required. The single canopy case is considered, as indicated in CR 11-4-2012 Romanian Design Code [1]. The comparison is given in Table 1 where 𝜑 represents the
wind flow underneath panel blockage ratio. The pressure coefficients are mentioned for the two wind
directions, first conducting to the uplifting of the canopy (wind pressure upwards – suction) and then
conducting to the descent of the panel (wind pressure downwards). The second case wind load must
be added to the snow load and the panel self-weight respectively, which finally conducts to the design
load combination for the structural elements of the PV panel.
Table 1
Pressure and force coefficients for 𝛂
zone
𝜑 0
𝑎𝑛𝑦 𝜑
𝟐𝟓°inclination
A
B
C
𝑐
-2.6 -3.2 -3.2 -1.6
+2.0 +3.1 +2.3 +1.0
Fig. 3 – Pressure zones for a single canopy
A significant increase is observed for pressure based wind design load compared with the resultant
force based wind load. For the photovoltaic panel size described above, the wind resultant load for
a current transversal steel frame structure is determined in the two cases:using pressure coefficients
and the resultant force coefficient respectively, as indicated in Table 1. The two resultant forces
acting on a current transversal steel frame are then compared. By using the resultant force
coefficients, the resultant force on the transversal frame for the uplifting effect of the panel is
obtained 𝐹
8.23 𝐾𝑁 and for the descending effect of the panel is obtained 𝐹
5.142 𝐾𝑁. In
comparison, the same resultant force acting on a current transversal frame determined by using the
pressure coefficients indicates significantly increased values: 𝐹 ∗ 14 𝐾𝑁 for the force
conducting to the uplifting effect of the PV panel and 𝐹 ∗ 10.6 𝐾𝑁 for the descending effect.
The star index shows the case of the resultant force obtained based on the pressure coefficients.
This significant difference for the same load,acting to a current transversal steel frame and
basically used for the design of the structural members of the frame, requires further and clear
explanations in the wind design code. These remarks are missing from the CR 1-1-4-2012
Romanian Design Code [1]. Recommendations about what coefficients are needed to be used for
the design of the PV panel structural system components (transversal frame, longitudinal beams)
are required for a safe and cost efficient design.
A second observation results from the additional moment obtained in the case of using the resultant
force coefficients. At the steel column of every transversal frame, an additional moment will be
produced by the eccentricity of the load, applied at 𝑑/4, where 𝑑represents the width of the
18
panel.This moment is not considered for the pressure coefficients case, since the obtained resultant
load will act on the centroid of the PV panel.
If the group effect is considered, for multiple connected canopies and several rows, a reduction
factor is indicated in the design code. This factor goes to a maximum of 0.7 for all rows beyond
the third, for both uplifting or descending effect of the panel. Since this reduction is applied to
both cases of resultant load, the one obtained based on pressure coefficients and the one obtained
based on the resultant force coefficients, no change of the above observations are to be considered.
4. Wind load comparison for different design codes
The wind pressure coefficients are basically determined based on the wind tunnel tests made on real
or reduced scale specimens. As a consequence, the coefficients should reveal same values,
independent on the design code edition or country. Change of the pressure coefficients from code to
code may be explained only if the probabilistic approach is used to determine the indicated values
of the coefficients. Different safety factors conduct to different pressure coefficients even if the same
structures or reduced scale models are considered. The Romanian CR 1-1-4-2012 Design Code [1]
doesn’t explain clearly what assumption is used to determine the pressure coefficients.
To have a complete image of the basis and evolution of the pressure coefficients for consecutive
editions of the Romanian Wind Load Design Codes, a comparison with the different countries
versions of the same code is done. The pressure coefficients are indicated in Fig. 4 to Fig.7 and
their values are then compared for the following design codes: STAS 10101/20-90,the Romanian
1990 version [16], EN 1991-1-4, the Eurocode [15], SR EN 1991-1-4, the Romanian translation
of the Eurocode [17], NP-082-04, the Romanian 2004 former version [2], CR-1-1-4-2012, the
Romanian actual version in use [1], DIN 1055-4:2005-03, the German code [18] and ASCE 7-10,
the American code [19]. The 10 degrees inclination of the panel is considered for the comparison,
since the German design code is not indicating pressure coeficients for larger inclinations.
On the other hand, it can be observed by code comparison that the Eurocodes [15,17], and the
recent Romanian code versions [1,2], are both indicating pressure coeficients, to be used for the
design of the roof structural members, and resultant force coefficients respectively, to be used for
the eccentric applied resultant wind load and design of the steel supporting column. The German
[18], the American [19] and the old 1990 version of the Romanian [16] design codes are indicating
values for pressure coefficients only, for different inclination of the canopies, to be used for design
of all structural members.
d
0.8
0.4
1.4
0.2
h=ze
or
Fig. 4 – Pressure coefficients indicated by STAS 10101/20-90 [16]
19
-0.3
0.7
0.3
-0.6
0
0.3
-0.7
h=ze
or
Fig. 5 – Pressure coefficients indicated byDIN 1055-4:2005-03 [18]
1.6
2.1
1.2
1.5
1.6
2.1
d/10
d/10
or
Fig. 6 – Pressure coefficients indicated byNP-082-04 [2], EN 1991-1-4 [15],
SR EN 1991-1-4 [17] and CR 1-1-4-2012 [1]
1.53 (0.4)
-0.7 (-1.57)
1.05 (1.67)
1.1 (0)
case A (case B)
h=ze
or
Fig. 7 – Pressure coefficients indicated byASCE 7-10 [19]
The mechanical torsor of the external loads is then determined, at the top level of the column, for
a current transversal structural steel frame, and the comparison with its values for the indicated list
of the design codes is made in Table 2. The mechanical torsor components, resultant force and
moment, 𝐹 and 𝑀 , normalized with the panel length and peak velocity wind pressure, are determined
for the photovoltaic panel size described above, d parameter referring to the width of the panel. 10
degrees inclination of the panel cases are compared, since the German Wind Design Code [18] is
not indicating pressure coefficients values for larger inclination of canopies.
20
Table 2
Comparison of the mechanical torsor components for 𝛂
Design code
𝑐
CR 1-1-4-2012
a.o.
𝑐
STAS 10101/90
DIN 1055
case A
ASCE
case B
Descending effect
𝐹
𝑀
1.28d
0
0.5d
0.125d2
0.9d
0.083d2
0.65d
0.0875d2
1.29d
0.06d2
1.035d
0.159d2
𝟏𝟎° panel inclination
Uplifting effect
𝐹
𝑀
1.62d
0
0.9d
0.225 d2
0.5d
0.05 d2
0.85d
0.0375 d2
0.2d
0.225 d2
0.785d
0.196 d2
The recent Romanian versions of the wind load design codes NP-082-04 [2], CR-1-1-4-2012 [1]
and SR EN 1991-1-4 [17], as well as the Eurocode EN 1991-1-4 [15], are all presented at the same
row of the table, since all are indicating same pressure coefficients for the photovoltaic panel.
Moreover, they are the codes which are mentioning both pressure coefficients and resultant force
coefficients for the wind load design.
Comparing the mechanical torsor components, the resultant force and moment values, for the
uplifting effect of the panel case, and for the descending effect respectively, it can be observed
that the old Romanian version of the wind design code STAS 10101/90 [16] conducts to similar
values as the German design code [18], but the Romanian recent versions of the design code
[1,2,17] and the Eurocode [15] are getting closer to the American code [19]. The conclusion is that
the European and the Romanian wind design codes are following the American codes in increasing
the pressure coefficients values. This can be accepted only if superior level of safety is assumed,
which conducts to a probabilistic approach. As a consequence, the values indicated by design
codes for pressure coefficients are to be accepted as maximum expected values. They are always
indicating larger values than the ones determined based on wind tunnel tests.
On the other hand, the pressure coefficients values indicated by the design codes are given for the
canopy type structures, which basically are individual structures with medium life, but the
photovoltaic power plants are comprised on several number of individual panels and they have
reduced life. Therefore, the group effect should be considered for this type of structures, which
results to a reduction factor applied to the pressure coefficients values, with a maximum reduction
of 30% starting with the third row of panels. By this reduction, the pressure coefficients values, as
well as the resultant force and moment values, are getting closer to the old version of the Romanian
code, or the German code values. This applies only for the panels located on the third row and
more, which makes the first row and the second located panels to be designed for the maximum
loads indicated by the code. Changing the structural solution or increasing the size of the structural
members, for the supporting structure of the panels located on one row, compared with the ones
located on the others, may increase the cost of the structure. The comparison of the pressure
coefficients indicated by the design code with the ones measured at wind tunnel tests may reveal
also important findings.
5. Wind load evaluation difficulties existent in the Romanian design code
The importance of the structure designed by wind load is considered by 𝛾 importance coefficient.
The Romanian wind load design code [1], as well as the Eurocode [15], is not mentioning explicitly
the photovolatic power plants. If these structures are considered as constructions with class III or IV
for importance, the importance coefficient shoult be taken as 1, which makes no change of the wind
design load. As it was explained in the introduction of the paper, the investment cost for a photovolatic
power plant construction is about 10 million euros for a 10 MW power. This is why the importance
factor should be specified and take into account the investment cost and the risk involved.
21
When determining the wind load as a resultant force by Eq. (2), using the corresponding coefficient
values, the Romanian and the Eurocode wind load design code [1,15] are indicating the refference
area 𝐴
to be used. The Romanian code explains the reference area as the area “normal
orientated to the wind direction, for buildings or for structural components”. This creates
confusion since for a horizontal canopy, as example, the uplift wind effect conducts to an uplifting
resultant force. Using the Romanian design code definition of the reference area, if the canopy is
horizontal and wind acts laterally, the reference area “normal orientated to the wind direction” is
getting zero, which results to no wind load. The mistake comes to the designer eyes if the original
version of the Romanian design code, the Eurocode [15], is consulted. There is no mention of the
is the reference area of
direction of the refference area, relative to the wind flow direction: “𝐴
the structure or structural element, given in Section 7 or Section 8” -subchapter 5.3 point (2) and
respectively “𝐴
is the area of the individual surface” - subchapter 5.3 point (3). The same is
mentioned in the Romanian translation of the Eurocode, SR EN 1991-1-4 [17]. The conclusion is
that the Romanian wind load design code CR-1-1-4-2012 [1], which follows the Eurocode EN
1991-1-4 [15], is using a poor translation, missing relevant terms and explanations. This is the
origin of the confusion created by the Romanian code.
When calculating the wind design resultant load for a structure, based on the pressure coefficient,
and comparing with the one determined based on the resultant force coefficient, the first has
significant larger values than the second. This was proven above in Section 4. The difference come
from the much larger pressure coefficients indicated by the code, compared with the resultant force
coefficients, for same type of structure. The pressure coefficients must be considered as maximum
expected values, and the code assume they should be used for roof structural members design and
for local connections design. Is the structural support members design, like for the transversal steel
frame components of the analysed structure, not so safe like design of the roof components and
connections, since the first should use in design the resultant force coefficients and the second the
pressure coefficients? This requires further explanations and comments on the Romanian design
code, which at this moment are missing from the code text.
Anyway, is difficult to explain why the Romanian code version CR-1-1-4-2012 [1] was created and is
used, since the Romanian translation of the Eurocode SR EN 1991-1-4 [17] follows the original code
with no change. The Romanian National Annex, which is also done, may be used together with the
Romanian translation version of Eurocode [17], for wind design of any structure located in Romania.
6. Wind tunnel tests
The wind tunnel tests are done by Wacker Ingenieure GmbH from Germany [20] and a significant
excerpt of their technical report is presented forward. The wind tunnel model represents a group of
photovoltaic panels with 3.30 meters width and 25 degrees inclination from horizontal plane. The
panels are considered to be located in category II terrain as indicated by the Romanian Wind Load
Design Code CR 1-1-4-2012 [1], on rows at equal distances of 7.5 meters, as indicated in Fig. 8. The
edges of the panel are located at 0.75 m (bottom) and 2.18 m respectively (top) to the ground level.
Fig. 8 –The consecutive rows parameters of the PV panels
22
Fig. 9 –The reduced scale wind tunnel model of the PV panels
The 1:40 reduced scale wind tunnel model is indicated in Fig. 9 and is comprised by eight
consecutive panel rows. The small gaps between panels in row are completely neglected by the
wind tunnel model. The access roads provided terrain roughness is also neglected by the model.
The width of the property is about 50 meters and allows relevant wind observations to be done.
No other panel arrangements were considered for the study.
The real wind effects simulation must model a limit layer turbulent wind over the ground with
similar terrain roughness. For this purpose, the reduced scale model is fixed on a plate with similar
asperities as for the wind category II terrain, also indicated in Fig. 9. These boundary conditions
are decisevely changing the wind average velocity profile and the turbulence parameters.
The wind velocity variation 𝑣 𝑧 on heigth depends on terrain roughness and existent obstacles as
buildings, trees and orography changes. On the wind tunnel is simulated the wind for a free field model,
as for current locations, and the wind velocity profile on heigth is then obtained by the equation:
.
(4)
where 𝑣 is the average wind velocity and 𝑧 is the heigth measured from the ground level.
The velocity variations about the wind average velocity are required for the model. For these, the
turbulence intensity 𝑇 𝑧 and the average standard deviation 𝜎 𝑧 of the wind velocity variations
on 𝑧 heigth profile, as a function of average wind velocity 𝑣 𝑧 are considered. This distribution
should model the real one.
The wind average velocity distribution by heigth and turbulence wind variation are modeled by
several rough plane elements fixed at the bottom of the wind tunnel model. The wind tunnel crosssection is 2.50 m in width and 1.85 m in heigth, and the length of the tunnel is 12 m.
Fig. 10 –Wind pressure zones measured for the model
23
The wind average velocity is measured using Prandtl tubes and the turbulence wind variation
velocities are measured using anemometers.
The similarity of the Reynolds numbers, indicating the inertia to the viscoelastic force ratios, of
the reduced scale and real model respectively, is used to corectly assume the conversion and flux
over an obstacle. The intensity of the wind pressure is related with the Reynolds number.
Measurements are done for every 15 degrees of the wind direction incidence angle variation. The wind
pressure parameters are determined as difference in between measured positive and negative values.
Five zones on panel rows, indicated in Fig. 10, are identified by wind pressure measurements: first,
second, middle, second last and last row respectively. No changes for wind pressure parameters
were measured starting with the third row. Six lateral zones with variable width like 1.0 m (A
zone), 2.0 m (B zone), 3.0 m (C zone), 4.0 m (D zone), 6.0 m (E zone) and variable width
respectively (F zone), were also measured.
Measured maximum values of the resultant force 𝑐 , moment 𝑐 coefficient and eccentricity of
the resultant equivalent force are indicated in Table 3 for every zone on rows and lateral direction
respectively. Positive values are indicating the descending wind action on panel, and negative the
ascending wind action.
Fig. 11 - Definition of moment 𝑐 and resultant force 𝑐 coefficients
Fig. 12 - Distribution and pressure coefficient evaluation for one panel
24
Table 3
Maximum values of the measured coefficients for the wind zones indicated in Fig. 10
1st row
2nd row
Descending
wind action
Middle
row
2nd last
row
Last row
1st row
2nd row
Ascending
wind action
Middle
row
2nd last
row
Last row
𝑐
𝑐
𝑒
𝑐
𝑐
𝑒
𝑐
𝑐
𝑒
𝑐
𝑐
𝑒
𝑐
𝑐
𝑒
𝑐
𝑐
𝑒
𝑐
𝑐
𝑒
𝑐
𝑐
𝑒
𝑐
𝑐
𝑒
𝑐
𝑐
𝑒
A
1.05
0.12
0.11
1.05
0.10
0.10
1.05
0.10
0.10
1.25
0.10
0.08
1.45
0.11
0.08
1.70
0.21
-0.12
-1.45
0.17
-0.12
-1.35
0.13
-0.10
-1.35
0.15
-0.11
-1.45
0.20
-0.14
B
0.90
0.11
0.12
0.80
0.09
0.11
0.85
0.09
0.11
0.90
0.10
0.11
1.10
0.10
0.09
-1.15
0.19
-0.17
-1.00
0.15
-0.15
-0.90
0.13
-0.14
-0.95
0.14
-0.15
-1.25
0.19
-0.15
Lateral wind zone
C
D
0.85
0.85
0.11
0.11
0.13
0.13
0.70
0.50
0.07
0.06
0.10
0.12
0.65
0.45
0.07
0.07
0.11
0.15
0.70
0.55
0.07
0.07
0.10
0.13
0.80
0.60
0.09
0.08
0.11
0.13
-0.85
-0.80
0.13
0.13
-0.15
-0.16
-0.75
-0.65
0.12
0.12
-0.16
-0.18
-0.70
-0.65
0.12
0.11
-0.17
-0.17
-0.85
-0.70
0.11
0.11
-0.13
-0.16
-1.10
-0.95
0.15
0.12
-0.14
-0.13
E
0.80
0.11
0.14
0.30
0.05
0.17
0.30
0.04
0.13
0.40
0.05
0.13
0.45
0.05
0.11
-0.75
0.11
-0.15
-0.65
0.10
-0.15
-0.65
0.10
-0.15
-0.65
0.11
-0.17
-0.90
0.11
-0.12
F
0.80
0.11
0.14
0.30
0.05
0.17
0.30
0.04
0.13
0.40
0.04
0.10
0.45
0.05
0.11
-0.70
0.11
-0.16
-0.65
0.10
-0.15
-0.60
0.10
-0.17
-0.65
0.10
-0.15
-0.90
0.11
-0.12
𝑐 neg
-0.07
-0.06
-0.04
-0.04
-0.04
Measured maximum values of the resultant force 𝑐 , moment 𝑐 coefficient and eccentricity of
the resultant equivalent force are indicated in Table 3 for every zone on rows and lateral direction
respectively. Positive values are indicating the descending wind action on panel, and negative the
ascending wind action.
The resultant forces on the PV panel surface are then determined by the following equations
𝐹
𝑐 ∙𝑏∙𝑞 𝐻
𝑀
𝑐 ∙𝑏 ∙𝑞 𝐻
𝑘𝑁/𝑚
𝐹∙𝑒
(5)
𝑘𝑁𝑚/𝑚
(6)
where
𝑞 𝐻 represents the basic wind pressure at the maximum heigth 𝐻 of the structure, measured on
free field and taken from the design code wind map depending on the site location and terrain
category
𝑏 represents the PV panel width
𝑒 represents the eccentricity of the resultant equivalent force 𝑒
as function of the width 𝑏.
The resultant force coefficient 𝑐 is obtained by simultaneous measuring of the descending and
respectively ascending effect at the top and bottom edge of the PV panel. The friction forces on
25
panel surface are determined based on the design codes. No safety coefficients were considered
for the resultant coefficients indicated in Table 3. The resultant coefficients are also used to design
the support structure elements of the PV panel.
Table 4
Maximum and minimum measured resultant force coefficients
Wind action effect
Desc.
Asc.
+2.45
-3.00
+1.95
-1.95
+2.00
-2.10
+1.60
-1.65
1𝑚
10𝑚
1𝑚
10𝑚
Zone A-B
Zone C-F
Top edge of the panel
Desc.
Asc.
+0.90
-2.70
+0.75
-1.95
+0.90
-2.00
+0.70
-1.65
Bottom edge
Desc.
Asc.
+0.85
-2.60
+0.60
-1.80
+0.85
-1.90
+0.60
-1.50
The maximum and minimum values of the resultant force coefficients, obtained for every indicated
wind zone as a function of the reference exposed area, 𝐴
1 𝑚 or 𝐴
10 𝑚 , are
indicated in Table 4. The resultant forces are acting perpendicular to the panel plane and
intermediate values are determined by equation
𝐹
𝐹
𝐹
𝐹
𝑙𝑔𝐴
(8)
The values indicated by tables are considering the static component of the wind action and are not
including the dynamic variable component. Change of the geometrical parameters may result to
change of the wind load.
Based on the measured values of the pressure coefficients indicated above, a comparison of the
mechanical torsor components, resultant force and moment at the top of the panel supporting
column, for European design code [15] and for tunnel test is presented below, in Table 5. The
pannel inclination is 25 degrees from ground plane.
The maximum measured values for the wind tunnel pressure coefficients are considered for a
lateral A zone of 1.0 m width, and the minimum values for a central F zone. Significant differences
between wind tunnel based resultant forces and moments, and the corresponding forces and
moments obtained from the wind design code, are indicated by the comparison done in Table 5.
Table 5
Resultant forces comparison for European design code and wind tunnel test
Descending wind effect
𝐹
𝑀
EN 1991-1-4
Wind tunnel
pressure
coeff.
force
coeff. 𝑐
Max.
Min.
Ascending wind effect
𝐹
𝑀
2.06d
0
2.72d
0
1.00d
0.2500d2
1.60d
0.400 d2
1.45d
0.30d
0.1160d2
0.039d2
1.70d
0.60d
0.204 d2
0.102 d2
The reduced pressure coefficients measured by wind tunnel tests, compared with the design code,
results to a reduction of the PV panel supporting structure elements, like columns and beams crosssection, and finnally to a reduction of the investment cost.
The PV panels group effect, clearly identified by wind tunnel tests, and the significant reduction
for the pressure coefficients, observed by measurements, makes the wind tunnel tests a relevant
approach for the design of this category of structures.
26
7. Conclusions
The photovoltaic power plants are structures with an important investment cost, which translates
into the cost of the structural support also. The Romanian wind load design code, as the Eurocode
which was followed, is not mentioning explicitly the importance factor value for this type of
structures. If they are considered as low importance structures, based on their life duration which
is about 20 years, the investment cost is not assumed at his real size. The American design codes
are now using risk categories to evaluate the size of the probable loss. The Romanian wind load
design code should consider an importance factor for the photovoltaic power plants or similar
structures evaluating correctly the risk and the loss of the investment.
The Romanian wind load design code, and the Eurocode, is recommending the use of both pressure
and resultant force coefficients to evaluate the wind design load. Pressure coefficients are
maximum expected parameters and their value is significantly larger than the resultant force
coefficients. The German, American and older version of the Romanian wind load design code are
using only pressure coefficients for the wind design. This choice might be better than using two
categories of coefficients, with different safety expectation for different structural members.
Finding the pressure coefficients, for photovoltaic power plants and similar structures, using the
wind tunnel tests represents a valuable and safe procedure which should be recommended in this
case by the Romanian wind load design code. This procedure may overcome and clarify the
ambiguity of the code about what type of coefficients to be used for a safe design.
The authors are acknowledging the contribution of the Romanian company Alukönigstahl srl, and
German companies Königsolar GmbH and Wacker Ingenieure GmbH at the technical documents
used in this paper.
The study was presented on the 2nd Romanian National Conference on Wind Engineering
sessions, held in Bucharest on June, 6-7.
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