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Session 11 Matching Array and Inverter
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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The design of a grid-connected PV system must take into consideration
local operating conditions such that the array and the inverter are
matched for those conditions.
The key parameters are:
1) Voltage
2) Current
3) Power
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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Grid Connected inverters
have a Maximum Power
Point Tracking range( MPPT)
with a specified mininum
and maximum input
voltages (DC voltages)
The inverter will track the
MPPT of the PV array to
provide the best
performance given the
prevailing irradance and
temperature
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LESSON 11. COPYRIGHT
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• If the array fails to produce the minimum voltage of the
inverter voltage window, inverter shuts down
• If the array open circuit voltage exceeds the inverters
maximum input voltage window , inverter may be damaged
224v
321 V
200
MPPT Range
9 modules
300
480v
443V
400
500
it is therefore imperative that these
calculations are correct
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LESSON 11. COPYRIGHT
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• Fronius IG 35/50/70 inverter data the MPPT range for all
inverter shown is 230 – 500 Vdc
• for effective operation the maximum power point voltage should
remain in this range
• Max dc voltage that the inverter can handle is 500 Vdc the o/cct
voltage of the array should not exceed this figure.
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LESSON 11. COPYRIGHT
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Temperature is a major de-rating
factor in calculating yield, a subject for a
future session
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LESSON 11. COPYRIGHT
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As temperature increases, the band gap of the intrinsic semiconductor
shrinks, and the open circuit voltage (Voc) decreases.
At the same time, the lower band gap allows more incident energy to be
absorbed because a greater percentage of the incident light has enough
energy to raise charge carriers from the valence band to the conduction
band. A larger photocurrent results.
The increase in the current for a given temperature rise however is
proportionately lower than the decrease in voltage. Hence the efficiency
of the cell is reduced.
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Solar Cell Operating Characteristics
The graph below shows that with constant irradiance the output voltage of a cell or
an array of cells falls as it is called upon to deliver more current.
Maximum power
delivery occurs the
voltage has dropped
to about 80% of open
circuit voltage.
The Fill Factor (FF) is
defined as the ratio
between the power at
the maximum power
point and the product
of the open circuit
voltage and short
circuit current. It is
typically better than
75% for good quality
solar cells.
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LESSON 11. COPYRIGHT
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The short circuit (SC) current is directly related to the number of photons
absorbed by the semiconducting material and is thus proportional to
light intensity.
The conversion efficiency is therefore reasonably constant so that the
power output is proportional to the irradiance down to fairly low levels,
however the efficiency is reduced if the cell temperature is allowed to
rise.
The open circuit (OC) voltage varies only slightly with light intensity
Currentά irradiance
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LESSON 11. COPYRIGHT
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DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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The open circuit voltage of PV modules depends on the cell
temperature and the solar irradiation. The highest open circuit
voltage occurs when the PV modules are at the coldest temperature
and in bright sun.
Because PV modules also have a reduction in voltage at high cell
temperatures, you must make sure the MPP voltage of the
strings will not drop below the minimum inverter DC input voltage of
200V DC in very hot temperature conditions, including
wire losses/voltage drop.
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LESSON 11. COPYRIGHT
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Solar Cell Efficiency
The following graphs show the same information as those above but in a
slightly different form showing how increased temperature reduces the
efficiency.
Output
power
decreasing
In real outdoor conditions the rated peak power Wp is seldom achieved, since
module temperature usually is more in the range of 40°C - 60°C. Efficiency can
be improved by cooling the cells and some systems have been designed to
make use of the heat absorbed by the cooling fluid in solar heating
applications.
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LESSON 11. COPYRIGHT
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Sunteck temp. coefficients Pmp or Pmax & Voc
Not all manufacture data is so helpful
Voltage temperature may be expressed %/°C, V °C ( or
mW/°C)
a conversion sheet will assist your calculations when
voltage co-effieffent V/ °C is required
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LESSON 11. COPYRIGHT
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Calculating temperature coefficients and changes in voltage due to temperature
When you are doing calculations with respect to temperature, you need to be careful of what
units your specifications are in. There are two main types of calculations that are done; one
requires the coefficient to be in %/°C and the other in V/°C (or mV/°C).
•Calculating the change in voltage due to temperature
When calculating your maximum and minimum voltages for a system, you need your temperature
coefficient to be in V/°C. If it is given as %/°C, then you will need to convert it. Have a look at the
two examples below, which are calculating the minimum VMP of a module:
•Temperature Coefficient given in mV/°C
VMP= 35.4V
Temperature coefficient = 160mV/°C
(Note: 160mV/°C = 0.16V/°C)
If the cell was at 70°C, then the VMP would be
35.4 - [0.16 x (70-25)] = 28.V
•Temperature Coefficient given in %/°C
VMP = 35.4V
Temperature Coefficient = 0.5% is 35.4V.
35.4 x 0.5 ÷ 100 = 0.177V
Then use this figure in your calculations.
If the cell was at 70°C, then the VMP would be
35.4 - [0.177 x (70-25)] = 27.44V
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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• Calculating a temperature coefficient, ftemp
If you need to calculate ftemp (for example to work out the yearly energy yield of a system), then you
need to have your specification in %/°C. If it is given as mV/°C, then you will need o convert it.
Remember that if you are working out a fraction, you need to divide any percentages by 100 (as 25% =
0.25 etc.). Have a look at the examples below:
•Temperature Coefficient given in mV/°C
Cell Temperature = 55°C
Temperature Coefficient = 160mV/°C
VMP = 35.4V
Firstly work out, in percentage, how much 160mV is of 35.4V: 0.16 ÷ 35.4 x 100 = 0.45%/°C (or 0.0045 as
a fraction)
Then use this value in your calculation: ftemp = 1 - [0.0045 x (55 – 25)] = 0.865
•Temperature Coefficient given in %/°C
Temperature Coefficient = 0.5%/°C
Cell Temperature = 55°C
f temp would then be:
1 – [0.005 x (55 – c25)] = 0.85
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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224v
MPPT Range
480v
Inverter MPPT range
Figures 1a-d shows examples , matching modules to
inverter, cell temp 0°C to 75° C Fig 1a max. input
voltage assumed 480V
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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224v
205V
200
MPPT Range
8 modules
480v
324V
300
voltage
400
500
1b MPP voltage of the array falls below MPPT range/ inverter shuts down
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224v
MPPT Range
257V
200
480v
10 modules
300
400
492V
500
1cMPP voltage of the PV array exceeds inverter input voltage
with ten modules in series at low temperature
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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224v
321 V
200
MPPT Range
9 modules
300
480v
443V
400
500
• This voltage range will be determined by the inverter
chosen for the job
• 9 modules in series suits the MPPT range of the
inverter
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LESSON 11. COPYRIGHT
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• The inverter has a maximum input voltage limit that is
higher than the maximum MPPT range
• Max input dc voltage should be used when calculating
the maximum allowable array Voc
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LESSON 11. COPYRIGHT
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Solar modules each have different
temperature coefficients. These
typically range from -0.2%/°C to
0.5%/°C dependant on module
technology. (Refer to the
manufacturer’s datasheet for exact
values).
The de-rating of the array due to
temperature will be dependent on the
type of module installed and the
average ambient maximum
temperature for the location.
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LESSON 11. COPYRIGHT
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DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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The three different solar modules currently available
on the market each have different temperature
coefficients.
These are:
A) Monocrystalline Modules
Monocrystalline Modules typically have a temperature
coefficient of –0.45%/°C. That is for every degree above
25°C the output power is derated by 0.45%
B) Polycrystalline Modules
Polycrystalline Modules typically have a temperature
coefficient of –0.5%/°C.
C) Amorphous Modules
These types of modules have a different temperature
characteristic, resulting in a lower coefficient , typically
around - 0.2%/° C.
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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The temperature de-rating factors is calculated
as follows
Note: The absolute value of temperature is
applied – the formula determines whether the
temperature factor is greater or less than 1
due to actual effective temperature of the cell.
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LESSON 11. COPYRIGHT
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For the worked example, assume the average
ambient temperature is 25 º C (Ta.day ) and the module is polycrystalline.
The average daily effective cell temperature is:
Tcell.eff = Ta.day + 25
= 25 + 25
= 50
Where :Tcell.eff = average daily effective cell temperature,
in degrees C
Ta.day = daytime average ambient temperature
(for the month of interest), in degrees
In the above formula the absolute value of the temperature coefficient [γ] is applied, this
is 0.5%/oC and cell temperature at Standard Test Conditions is 25 ° C [ Tstc) ]
Therefore the effective derating factor due to temperature is:
1 - (50 – 25) x 0.5% = 100 -12.5% = 87.5% = 0.875
The de-rating then for 1,2 and 3 above
is 87.5% of 144.4 W, = 126.3 Watts
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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MINIMUM ARRAY SIZE
The number of modules required in the array =
the peak power required by the array divided by
the adjusted output of the PV module
In the worked example,
the number of 160W modules required is
2.01kW 126.3 W 15.9
always round up to the next full module
i.e. 16 in this case
The 16 modules
will provide an array with a peak rating of
16 x 160W = 2.56 kW
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LESSON 11. COPYRIGHT
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FINAL ARRAY CONFIGURATION
The array must be matched to the voltage window
of the inverter and therefore the final array
configuration will be dependent on the inverter
selected and the allowable operating voltage
window.
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LESSON 11. COPYRIGHT
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MATCHING ARRAY VOLTAGE TO THE MAXIMUM INVERTER
VOLTAGE AND VOLTAGE WINDOW OF THE INVERTER
The output power of a solar module is affected by the
temperature of the solar cells. In crystalline PV modules
this effect can be as much as 0.5% for every 1 degree
variation in temperature. (NOTE: for other PV cell
technologies the manufacturers data must be used).
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Many of the inverters available will have a voltage
operating window. If the solar voltage is outside this
window the inverter will not operate and in the case
where a maximum input voltage is specified and the
array voltage is above the maximum specified then
the inverter could be damaged.
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LESSON 11. COPYRIGHT
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DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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Matching an PV array to Inverter
Worked example shown explains how to size an PV array
to specific inverter.
It will follow the following steps
•Minimum number of modules per string
•Maximum number of modules per string
•Maximum number of strings
•Checking the power rating
•Checking the array/inverter match
Follow the handout sheet
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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Worked Example
Assume the maximum effective cell temperature recorded at site is
75°C, and the minimum temperature is 0°C. It is proposed to install
a Fronius IG60 inverter and Sunteck 205 PV modules. Assume
there is a 2% voltage drop across the dc cables, allowance of a 10%
safety margin on the inverter lower input voltage window and 5% on
the upper voltage window.
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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Aim to calculate the number of Sunteck Pluto Ade PV modules (in
terms of number of modules in each string and the number of
strings). required to match the Fronius IG60 inverter in parameters
of voltage, current and power.
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LESSON 11. COPYRIGHT
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DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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Step One: Minimum number of modules in a string (maximum cell temperature)
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Vmp_cell.eff
= Vmp-stc – [ V x ( Tcell_eff - Tstc ) ]
Where:
Vmp_cell.eff = Maximum Power Point Voltage at effective cell temperature, Volts
Vmp-stc
= Maximum Power Point Voltage at STC, Volts
= voltage temperature co-efficient, V per degree Celsius
v
Tcell_eff
= cell temperature at specified temperature, in degrees Celsius
Tstc
= cell temperature at standard test conditions, in degrees Celsius
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Calculation Steps
Calculate the difference between the cell temperature and STC
75-25=50°C
Convert the PMAX coefficient into V/°C
0.38%/°C x 38.1 = 0.145 V/°C
Multiply difference in temp by the PMAX
50 X 0.145 = 7.25V
Temp. coefficient (in V/°C)
Take this away from the rated VMP
(as the cell temperature is well above 25/°C)
38.1 – 7.25 = 30.85V
Multiply this by 0.98 allow 2% voltage drop
30.85V x 0.98 = 30.23V
Multiply the inverter min. voltage by 1.1 (10%safety margin)
150 x 1.1 = 165V
Divide the module voltage into the inverter voltage
165 ÷ 30.23 = 5.46 modules
Round this number UP
Round up to 6 modules
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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Step 2: Maximum number of modules in series (minimum temperature)
Vmax_oc = Voc_STC – [ V x ( Tmin - T STC )]
Where:
Vmax_oc = Open Circuit Voltage at minimum cell temperature, Volts
Voc_STC = Open Circuit Voltage at STC, Volts
= voltage temperature co-efficient, V per degree Celsius
v
Tcell_eff
= expected minimum daily cell temperature, in degrees Celsius
T STC
= cell temperature at standard test conditions, in degrees Celsius
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Calculation Steps
Calculate the difference between the cell temperature and STC
0 – 25 =25°C
Convert the VOC coefficient into V/°C
0.29%/°C X 45.8V = 0.133V/°C
Multiply the difference in temp. by
VOC temp. coefficient (in V//°C)
25 x 0.133 = 3.32V
Add this figure to original voltage`
( as the cell temp is below 25°C)
45.8 + 3.32 =49.12 V
No voltage drop (maximum o/cct, no current no Vd)
49.12 V
Multiply the max. inverter voltage
by 0.95 to give a 5% safety margin
500 x 0.95 =475V
Divide the max. inverter voltage (incl. safety margin)
475 ÷ 49.12 = 9.67 modules
by the max module voltage
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Round this figure down
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Round down to 9 modules
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Step 3: Maximum number of Strings
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ISC cell eff = ISC-STC + [ ISC X ( Tcell eff- T STC )]
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Where:
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ISC cell eff = ISC at effective cell temp, Amps
ISC-STC = ISC at STC Amps
ISC = ISC temperature coefficient, A/°C
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Tcell eff = cell temperature at specified temperature, in °c
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T STC = cell temperature at standard test conditions, in °c
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Calculation Steps:
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1. Calculate the difference between the cell temperature and STC
0 – 25 =25°C
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2.Convert the Isc coefficient into A/°C
0.046%/°C X 5.73A = 0.0026A/°C
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3. Multiply the difference in temp. by ISC temp. coefficient (in A//°C)
50 x0.0026 = 0.132A
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4. Add this figure to the rated ISC
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( as the cell temp is above 25°C)
5.73A + 0.132 = 5.86A
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5. Divide this current into the maximum dc inverter input current
35.8/5.86 = 6.11 strings
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6.Round this figure down
Round down to 6 strings
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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Step 4: Checking the Power Ratings
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Inverter manufactures may give a number of ratings for their inverter
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Maximum (Recommended) PV array rated power: recommendation from the
manufacture on how much power the inverter can process. Usually rated in Watt/
kWs
Maximum dc input power: maximum amount of dc power that the inverter can
convert into AC (this rating is lower than dc array power as there are PV array losses)
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Maximum AC output power : Maximum rated AC power that the PV array can
deliver
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Calculation must ensure voltage, current and power match a
module/array to the inverter.
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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From the example, primary calculations suggest 6 parallel strings of 9 modules in
series. This is 54 modules at 205 watts = 11070 watts, however this well above the
recommended inverter power range 4600 to 6700 watts.
Therefore the number of modules that can be used in the system based on power
would be:
Minimum No. = 4600/205w = 22.44 modules = 23 modules
Maximum No. 6700/205w = 32.68 modules = 32 modules
NB: if 4 strings of 9 modules were used this would mean 36
modules and 7380w which will not fit within the power rating of
the inverter, even according the earlier calculations such an
array may be ok.
From the table highest output would be 4 strings of eight
modules and output wattage 6560 watts.
DAMON FYSON GRID CONNECT
LESSON 11. COPYRIGHT
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