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The shape of an I-V curve is determined by the PV device and system properties. However, the magnitude and position of the curve are determined by solar irradiance and the temperature of the PV device. Varying irradiance and temperature produces different voltage-current operating points, which generate different I-V curves for the same PV device. Therefore, a given I-V curve represents only one set of operating conditions for a PV device, at a specified exposure to irradiance and temperature. Solar Irradiance Response Changes in solar irradiance have a small effect on voltage but a significant effect on the current output of PV devices. The current of a PV device increases proportionally with increasing solar irradiance. Consequently, since the voltage re mains nearly the same, the power also increases proportionally. The relation ships between irradiance, current, and power can be expressed by the following ratios: F = solar irradiance 2 (in W/m^2) E = solar irradiance 1 (in W/m^2) = current at irradiance 2 (in A) = current at irradiance 1 (in A) P = power at irradiance 2 (in W) P = power at irradiance 1 (in W) This relationship is used to estimate how short-circuit current, maximum power current, or maximum power changes with a change in irradiance: --19. Voltage increases rapidly up to about 200 W/m^2 and then is almost constant. Current and maximum power increase proportionally with irradiance. For example, a PV module has a rated short- circuit current of 6A and a maximum power of 150W at 1000 W/m^2 of solar irradiance. What is the short-circuit current and the maximum power at 600 W/m^2 of irradiance? A family of I-V curves is a group of I-V curves at various irradiance levels. A family of I-V curves represents the changing output of a PV device with a single changing variable, such as irradiance throughout the day, with others held constant. The family of I-V curves also shows that the maximum power points at various irradiance levels don’t follow a line of constant load resistance, which would have to intersect with the origin. Therefore, a resistive load matched to the maximum power point at one irradiance level won’t operate the device at maximum power at higher or lower irradiance. Temperature Response For most types of PV devices, high operating temperatures significantly reduce voltage output. Current increases with temperature, but only slightly, so the net result is a decrease in power and efficiency. 0. Long-term high temperatures can also lead to premature degradation of cells and module encapsulation. For these reasons, it’s desirable to install modules and arrays in a manner that allows them to operate as cool as possible. 0-C – 250 -- 50C -- VOLTAGE (V) --20. Increasing cell temperature de creases voltage, slightly increases current, and results in a net decrease in power. Temperature Response Cell Temperature. The cell temperature of a PV device refers to the internal temperature at the p-n junction. Cell temperature is influenced by ambient temperature, wind speed, solar irradiance, thermal characteristics of the device's packaging, and the way the cell or module is installed or mounted. A cell temperature value is used when calculating how voltage or power are affected by temperature. Cell temperature can be estimated by either directly measuring the cell or module surface temperature or applying the temperature-rise coefficient. The temperature-rise coefficient is a coefficient for estimating the rise in cell temperature above ambient temperature due to solar irradiance. When the temperature-rise coefficient has been established for a particular installation, cell temperature under various conditions can be estimated with the following formula: T = 7 + (CT. x E) where Tee = cell temperature (in °C) = ambient temperature (in °C) CTi = temperature-rise coefficient (in °C/kW/m E = solar irradiance (in kW/m) The mounting configuration of arrays has a strong influence on the temperature-rise coefficient. For modules with the back surfaces exposed to wind, the temperature-rise coefficient may be about 15 to 20°CIkWIm (27 to 36°F/kW/m For modules mounted close to or directly on a surface, with the back surface not exposed to wind, the temperature-rise co efficient may be as high as 25 to 30°C/kW/m (45 to 54°F/kW/m temperature rise of at 20°C to 25°C (36°F to 45°F) over ambient temperature is typical for most array installations at peak sun. For example, a rooftop-mounted array has a temperature-rise coefficient of 20°C/kW/m If the ambient temperature is 30°C and the solar irradiance is 1100 W/m (1.1 kW/m what is the cell temperature? T = Tb + (CTi x E) T 1.1) T --- T -52°C cell == Temperature-Rise Coefficient With so many factors influencing the magnitude of the effect of irradiance on cell temperature, it’s difficult to absolutely determine the temperature-rise coefficient. The coefficient is usually established through field measurements. Actual cell temperature, ambient temperature, and solar irradiance are measured for a particular installation and these values are used in the following formula to calculate the temperature-rise coefficient: The temperature-rise coefficient may be calculated many times under various conditions and averaged to determine an approximate value. This temperature-rise coefficient can then to be used to predict future cell temperature, though this value will be a good estimate only during typical weather conditions. Unusual weather variations, such as high winds, reduce the accuracy of these calculations. == Temperature Coefficients. A temperature coefficient is the rate of change in voltage, current, or power output from a PV device due to changing cell temperature. A negative coefficient means the parameter decreases with increasing cell temperature, while a positive coefficient means the parameter increases with increasing cell temperature. Temperature coefficients can be expressed as a unit (absolute) change per degree of temperature change or a percentage (relative) change per degree of temperature change. Unit change temperature coefficients are generally specific to a PV device manufacturer, and may be based on an individual cell or an entire module. Typical temperature coefficient values for crystalline silicon cells are -2.25 mV/°C/cell (-0.00225 V/°C/cell) and 3.70 j. IA/°C/cm (0.0000037 A/°C/cm These temperature coefficients may be specified for certain I-V parameters. For example, a temperature coefficient for open-circuit voltage cannot accurately predict the effects of temperature at other voltages. Module or array coefficients are calculated from cell coefficients with the following formulas: cv = cv x n CC xnxA I I-rell p where C = module or array absolute temperature coefficient for voltage (in VI°C) C = cell absolute temperature coefficient for voltage (in V/°C/cell) n = number of series-connected cells C = module or array absolute temperature coefficient for current (in AI°C) C = cell absolute temperature coefficient for current (in A/°C/cm n = number of parallel-connected cell strings A = individual cell area in cm. For example, what are the module temperature coefficients for a module with 36 cells (each 144 cm in area) arranged in two parallel strings of 18 series-connected cells each? cv = C VcdI C x 18 C = -0.0405 V/°C C=C xnxA I I- p C 144 C, = 0.00011 A/°C Percentage change temperature coefficients for crystalline silicon cells are relatively constant among manufacturers or cell fabrication processes and are approximately equal to -0.4%I°C (-0.004/°C) for volt age, 0.1%/°C (0.0011°C) for current, and -0.5%I°C (-0.0051°C) for power. Unlike most unit change coefficients, percentage change coefficients can be used with any point on the I-V curve. The percentages are applied to reference (or rated) values to determine the unit change temperature coefficients using the following formulas: C = ef x C%V C, = I x C%J C,. = x C % p where C = absolute temperature coefficient for voltage (in VI°C) Vrei = reference (or rated) voltage (in V) C%V = relative temperature coefficient for voltage (in 1°C) C = absolute temperature coefficient for current (in AI°C) 'ref = reference (or rated) current (in A) C%J = relative temperature coefficient for current (in 1°C) C = absolute temperature coefficient for power (in W/°C) ref = reference (or rated) power (in W) C% = relative temperature coefficient for power (in 1°C) For example, if the open-circuit voltage for a PV module is 21.6 V at 25°C (77°F), what is the unit change temperature coefficient for voltage? C = x C%V C =21.6x-0.004 C = -0.086 V/°C Arrays installed in hot climates, such as deserts, are likely to produce less power than their rating because of high cell temperatures. Temperature Translations. Temperature translations use temperature coefficients to estimate the change in voltage, current, and power parameters due to cell temperature. Translations determine the potential range of operating voltages and power levels, which must be within certain limits for code compliance and connection to power processing equipment downstream, including batteries, charge controllers, and inverters. The small increases in voltage due to greater irradiance are often cancelled by small decreases in voltage due to the associated higher cell temperatures Therefore, voltage changes due to irradiance are not considered significant for most applications. Changes in cell temperature that are associated with changes in ambient temperatures, however, can have ill effects on voltage. Temperature translations can be applied across the entire I-V curve, though they are usually applied to open-circuit voltage, maxi mum power voltage, and maximum power, using reference values at 25°C (77°F). Because the cell temperature effect on current is very small, it’s often ignored in field measurements. Voltage and power translations can be calculated using the following formulas: V =V +( -TIxC) trans ref cell ref V P =P +( -TjxG) trans ref cell ref P where V = translated voltage at cell trans temperature (in V) Vf = reference (or rated) voltage corresponding to Tf (in V) T cell = cell temperature (in °C) Trf = reference (or rated) temperature (in °C) C = absolute temperature coefficient of voltage (in V/°C) trans = translated power at cell temperature (in W) = reference (or rated) power corresponding to Trf (in W) C = absolute temperature coefficient of power (in W/°C). For example, a PV module with 36 series- connected cells has a rated open-circuit voltage of 21.7 V at 25°C. The manufacturer provides a temperature coefficient for open-circuit volt age for individual cells of -2.1 mV/°C/cell (-0.0021 V/°C/cell). The ambient temperature is 30°C, the solar irradiance is 800 W/m (0.8 kW/m and temperature-rise coefficient is 25°C/kW/m What is the expected open- circuit voltage under these conditions? First, using ambient temperature and solar irradiance information, estimate the cell temperature using the temperature-rise coefficient formula: T = ' + (CTflSe X E) T = 30 + (25 x 0.8) T = 50°C Next, determine the temperature coefficient of open-circuit voltage for the entire module. CV = Cr X n C x36 C = -0.076 VI°C Finally, the voltage translation formula is used to determine the translated open-circuit voltage: ' = Vf + ( - Tre) x CV) Vtra = 21.7 + ( x -0.076) V = 21.7 + (25 x -0.076) trans V =21.7+(-1.9) trans V = 19.8 V Therefore, at operating temperatures 25°C (45°F) higher than the rated temperature, the voltage is reduced by about 10%. Power is similarly affected. Consequently, higher-than- rated temperatures are one of the primary factors causing arrays to operate at less than their rated power in the field. Next: Modules and Arrays |