PV cell chara.ppt
- 1. PV Cell Characteristics & Model PRESENTED BY, SUDARSHAN B S ASSISTANT PROFESSOR DEPT. OF EEE RVCE, BANGALORE
- 2. The P-N Junction As A Sink, Its Modification Into A Source A P-N junction is usually represented as a diode shown in the figure. The P-side is called the anode (a), and the N-side is called the cathode (k). The diode symbol is pointed to one direction. This pointed part represents the direction of current flow in a diode. In other words, current flow in a diode is from anode to cathode. Since a solar cell is made of P-type and N-type materials and there exists a junction, it can also be represented in the most basic sense as a diode.
- 3. Consider a diode connected as a part of the external circuit as shown. With the voltage polarity as shown (anode +ve and cathode reference) and the current flowing as shown, power flows from the external circuit to the diode. In other words, diode acts as a sink and not a source.
- 4. In the v-i characteristics (in previous slide), the 1st quadrant represents dissipation. For the diode to act as (a part of) the source, it should operate in the 4th quadrant where the voltage polarity remains the same while the current direction changes so that the power flows into the external circuit. To represent this condition (current flow direction negative in relation to the assumed positive direction), we add a current source in parallel with the diode as shown in this slide. Current ipv of the current source is the photocurrent. It depends on the incident radiation intensity. More the radiation intensity, more will be the current ipv and hence more will be the current i, leading to higher power output.
- 5. Under dark conditions (i.e., no sunlight), ip=0 and the source characteristics will be same as the diode forward characteristics. As the solar radiation increases, the current ip (and hence i) increases. Now the characteristics will shift to the 4th quadrant by the amount ip. Any operating point on the 4th quadrant will, therefore, indicate the PV cell generating power.
- 6. For the PV cell, the current therefore is taken as positive when flowing out of the cell. Hence, the characteristics can be re-drawn as shown in this slide. For some portion of the curve, the current is constant while for some portion the voltage is constant. Thus, a PV cell is a unique combination of a constant-current, constant-voltage sources.
- 7. The constant current line gives an idea of the slope of the constant current portion and therefore it implies the existence of a high value shunt resistance in parallel with the current source. The constant voltage line indicates the slope of the constant voltage portion and implies a series resistance in series with the terminal.
- 8. Equivalent Circuit Of A PV Cell The two nonidealities along with the PV source gives the practical equivalent circuit of the PV cell as shown here. This model is popularly known as the single-diode equivalent model. If we take the series resistance to be zero and shunt resistance to be infinite, we obtain the ideal equivalent circuit of a PV cell. The series resistance is indicative of the internal resistance to the flow of current. It depends on the P- N junction depth, impurities, and contact resistance. The shunt resistance indicates the leakage current.
- 9. Equivalent Circuit Of A PV Cell For a typical 1 sq. in. silicon cell, the series resistance varies from 0.05 – 0.10 ohm and shunt resistance is in the range of 200 – 300 ohm. The PV conversion efficiency is greatly affected by even small variations of the series resistance, while being insensitive to variations in shunt resistance. A small increase in the series resistance can reduce the PV output significantly.
- 10. Currents in the equivalent circuit The photocurrent is given by, 𝒊𝒑 = (𝒊𝒅 + 𝒊𝒔𝒉 + 𝒊) ------- (1) At node A, the voltage is, 𝑉𝐴 = 𝑉𝑎𝑘 + 𝑖𝑅𝑠𝑒 But, 𝑉𝐴 = 𝑖𝑠ℎ𝑅𝑠ℎ Therefore, 𝒊𝒔𝒉 = 𝑽𝒂𝒌 + 𝒊𝑹𝒔𝒆 𝑹𝒔𝒉 Substituting in (1), we get 𝑖𝑝 = 𝑖𝑑 + 𝑉𝑎𝑘+𝑖𝑅𝑠𝑒 𝑅𝑠ℎ + 𝑖 ------- (2)
- 11. Currents in the equivalent circuit The diode current can be written as, 𝑖𝐷 = 𝐼0 𝑒 𝑉+𝑖𝑅𝑠𝑒 η𝑉𝑇 − 1 -------- (3) Where I0 is the reverse saturation current η is the ideality factor (=2 for silicon) VT is the volt equivalent of temperature 𝑉𝑇 = 𝑘𝑇 𝑞 = 𝑇 11600 k is Boltzmann’s constant T is temperature of the junction
- 12. Currents in the equivalent circuit Substituting (3) in (2) and solving for the terminal current ‘i’, we get 𝒊 = 𝒊𝒑 − 𝑰𝟎 𝒆 𝑽+𝒊𝑹𝒔𝒆 𝜼𝑽𝑻 − 𝟏 − 𝑽𝒂𝒌 + 𝒊𝑹𝒔𝒆 𝑹𝒔𝒉 This is called the terminal current model. Note that the LHS current i depends on i (itself) on RHS, i.e., an acausal system which indicates that the present state of i depends on itself. However, in practice, the junction capacitance of the diode across it will be a state (having memory and history) and will take care of the causality problem.
- 13. PV Cell Parameters from V-I and P-V Characteristics Consider the equivalent circuit of the PV cell and the corresponding v-I characteristics as shown below. V-I Characteristics of a PV Cell
- 14. PV Cell Parameters The terminal current is given by, 𝒊 = 𝒊𝒑 − 𝑰𝟎 𝒆 𝑽+𝒊𝑹𝒔𝒆 𝜼𝑽𝑻 − 𝟏 − 𝑽𝒂𝒌 + 𝒊𝑹𝒔𝒆 𝑹𝒔𝒉 The three significant points on the I-V characteristics are marked in the graph. Point-1 Consider the case when the terminals a and k are short circuited. Across these terminals, the voltage is zero due to the short circuit. The y-axis intercept when the terminal voltage is zero (short-circuited) is called the short circuit current (Isc). At this point, Vak = 0 and I = Isc. Therefore, 𝑰𝒔𝒄 = 𝒊𝒑 − 𝑰𝟎 𝒆 𝟎+𝑰𝒔𝒄𝑹𝒔𝒆 𝜼𝑽𝑻 − 𝟏 − 𝟎 + 𝑰𝒔𝒄𝑹𝒔𝒆 𝑹𝒔𝒉
- 15. PV Cell Parameters Generally, Rse <<<< Rsh. Therefore, IscRse -> 0. In such case, Isc = ip Since the ip is proportional to the irradiance (incident solar radiation), we can write Isc α Irradiance This means that whenever irradiance changes, the short-circuit current changes linearly. Ponit-2 Now consider the case when there is no load connected to the PV cell. This represents the open circuit condition. In this case, current is zero. When the current is zero, the terminal voltage is called the open-circuit voltage (Voc). Here, Vak = Voc, and i = 0. This means, 𝟎 = 𝒊𝒑 − 𝑰𝟎 𝒆 𝑽𝒐𝒄+𝟎𝑹𝒔𝒆 𝜼𝑽𝑻 − 𝟏 − 𝑽𝒐𝒄 + 𝟎𝑹𝒔𝒆 𝑹𝒔𝒉
- 16. PV Cell Parameters 𝟎 = 𝒊𝒑 − 𝑰𝟎 𝒆 𝑽𝒐𝒄 𝜼𝑽𝑻 − 𝟏 − 𝑽𝒐𝒄 𝑹𝒔𝒉 Numerically, Rsh >>> Voc. Thus we can approximate the above equation as, 𝟎 = 𝒊𝒑 − 𝑰𝟎 𝒆 𝑽𝒐𝒄+𝟎𝑹𝒔𝒆 𝜼𝑽𝑻 − 𝟏 𝑖𝑝 𝐼0 = 𝒆 𝑽𝒐𝒄 𝜼𝑽𝑻 − 𝟏 𝒆 𝑽𝒐𝒄 𝜼𝑽𝑻 = 𝟏 + 𝑖𝑝 𝐼0 Taking natural logarithm on both sides, we get 𝑽𝒐𝒄 𝜼𝑽𝑻 = ln 1 + 𝑖𝑝 𝐼0
- 17. PV Cell Parameters 𝑽𝒐𝒄 = 𝜼𝑽𝑻 ∗ 𝒍𝒏 𝟏 + 𝒊𝒑 𝑰𝟎 Thus, Voc is related to ip (and hence the irradiance), but in a logarithmic manner. Whenever there is any increase in irradiance, the open-circuit voltage increases logarithmically. Parameter Change in irradiance Open-Circuit Voltage Logarithmic change (small value) Short-Circuit Current Linear change (proportionally large)
- 18. Effect Of Change In Irradiance
- 19. BYD Panel Datasheet Curve
- 20. PV Cell Parameters Third Point The third point of significance relates to the maximum power t hat can be transferred from the PV cell. At the origin, V = 0 and I = 0, implying P = 0. At Voc point, P = 0 as the current is zero. At Isc point, P = 0 as the voltage is zero. Hence there will be a hill-shaped power curve in between these two points. This curve is called the P-V Curve of solar cell.
- 21. PV Cell Parameters The point on the power-voltage curve where maximum power can be extracted is called the maximum power point (Pm). The projection of this point on the V-I curve gives the third significant point as the operating point corresponding to maximum power generation. The voltage at maximum power point is denoted by Vm and the current at maximum power point by Im. It is necessary to operate the solar cell at the operating point corresponding to the maximum power point in order to supply maximum possible power to the load and use the solar cell to its fullest. V-I and P-V Curves of PV Cell
- 22. Effect Of Change In Irradiance
- 23. Solar Cell Parameters – A Datasheet
- 24. Solar Cell Parameters – A Datasheet Solar cell efficiency is, η = 𝑃0 𝑃𝑖𝑛 = 𝑃𝑚 𝑃𝑖𝑛 = 𝑉 𝑚𝐼𝑚 𝑃𝑖𝑛 Consider the panel with 6*10 pieces of polycrystalline solar cell series, with each cell having dimensions of 156mm*156mm. Standard insolation = 1kW/m2. Then, Pin = (1kW/m2) * (area of the panel) = (1 kW/m2) * (60 * 156mm * 156mm) = (1kW/m2) * (1.46 m2) Pin = 1.46kW For this panel, efficiency is 16.5% (from datasheet)
- 25. Solar Cell Parameters – A Datasheet Thus, Po = Pm = efficiency of cell * Pin = (16.5/100) * (1.46*1000) Po = 240W If G is the irradiance (in kW/m2) and Ac is the area of cell (in m2), then 𝜼 = 𝑽𝒎𝑰𝒎 𝑮𝑨𝒄 Thus, efficiency of cell is inversely proportional to its area. Effective area available in a module decreases due to spacing between cells. Therefore always, ηcell > ηmodule The datasheet ratings are usually given for the cell itself and not the module.
- 26. Effect Of Temperature on Isc Temperature change affects three parameters namely, the short-circuit current (Isc), the open- circuit voltage (Voc) and the maximum power point (Pm). Effect of temperature on Isc Earlier, it was shown that the short-circuit current is directly proportional to the photocurrent (ip). The photocurrent is directly proportional to the irradiance or insolation (power/m2 of the incident solar radiations) With increase in temperature, the photocurrent will increase. This is because the forbidden band gap energy reduces, enabling more electrons to jump from the valance band to the conduction band, giving more free electrons. Therefore, the short circuit current increases as temperature increases. That is, Isc has a positive temperature coefficient. The increase is very small (around 0.1% per Kelvin rise in temperature). This is represented in the datasheet by the parameter temperature coefficient of ISC.
- 27. Effect Of Temperature on Voc Effect of temperature on Voc The equation of Voc is given by, 𝑽𝒐𝒄 = 𝜼𝑽𝑻 ∗ 𝒍𝒏 𝑰𝟎 + 𝒊𝒑 𝑰𝟎 since I0 <<< ip, we can say I0+ip = ip. Therefore, 𝑽𝒐𝒄 = 𝜼𝑽𝑻 ∗ 𝒍𝒏 𝒊𝒑 𝑰𝟎 In the above equation, VT = T/11600 is a function of temperature, and I0 is an exponential function of temperature. Considering these two effects, Voc will be inversely proportional to temperature. The dependence of I0 on temperature can be expressed as, 𝐼0 ∝ 𝑇𝑚 𝑒 − 𝑉𝐺𝑜 𝑛𝑉𝑇 Using a constant of proportionality, we can write, 𝐼0 = 𝐾𝑇𝑚𝑒 − 𝑉𝐺𝑜 𝑛𝑉𝑇
- 28. Effect Of Temperature on Voc 𝐼0 = 𝐾𝑇𝑚 𝑒 − 𝑉𝐺𝑜 𝑛𝑉𝑇 Taking natural logarithm on both sides, we get ln(𝐼0) = ln(𝐾𝑇𝑚 ) + ln 𝑒 − 𝑉𝐺𝑜 𝑛𝑉𝑇 = 𝑚 ln 𝐾𝑇 − 𝑉𝐺𝑂 𝑛𝑉𝑇 = 𝑚 ln 𝐾 + 𝑚 ln 𝑇 − 𝑉𝐺𝑂 (𝑛𝑇/11600) Differentiating with respect to T and simplifying, we get 𝑑 𝑑𝑇 ln 𝐼0 = 𝑚 𝑇 + 𝑉𝐺𝑂 𝑛𝑇𝑉𝑇 ---------- (1) We know that, 𝑉 𝑜𝑐 = 𝜂𝑉𝑇 ∗ 𝑙𝑛 𝑖𝑝 𝐼0 Differentiating with respect to T, we get
- 29. Effect Of Temperature on Voc 𝑑 𝑑𝑇 𝑉 𝑜𝑐 𝑛𝑉𝑇 = 𝑑 𝑑𝑇 ln 𝐼𝑝 − 𝑑 𝑑𝑇 (ln 𝐼0) −𝑉 𝑜𝑐 𝑛𝑇𝑉𝑇 + 1 𝑛𝑉𝑇 𝑑𝑉 𝑜𝑐 𝑑𝑇 = − 𝑚 𝑇 + 𝑉𝐺𝑂 𝑛𝑇𝑉𝑇 Simplifying, we get 𝑑𝑉𝑂𝐶 𝑑𝑇 = 𝑉 𝑜𝑐 𝑇 − 𝑚𝑛𝑉𝑇 𝑇 + 𝑉𝐺𝑂 𝑇 Or, 𝑑𝑉𝑂𝐶 𝑑𝑇 = 𝑉 𝑜𝑐 − (𝑚𝑛𝑉𝑇 + 𝑉𝐺𝑂) 𝑇 This shows that the rate of change of Voc with respect to temperature is inversely proportional to temperature. In other words, an increase in temperature will reduce the open-circuit voltage. That is, Voc has a negative temperature coefficient.
- 30. Effect Of Temperature On Pm Effect of temperature on Pm Power is a product of voltage and current. Since Voc has a negative temperature coefficient of temperature and Isc has a positive temperature coefficient of temperature, and considering that the temperature coefficient of Isc is very small, the power will also have a negative temperature coefficient of temperature. This means that Pm would decrease with an increase in temperature. Parameter Effect of temperature Open-Circuit Voltage Negative temperature coefficient Short-Circuit Current Positive temperature coefficient Maximum Power Point Negative temperature coefficient
- 31. Effect Of Change In Temperature Parameter Effect of temperature Open-Circuit Voltage Negative temperature coefficient Short-Circuit Current Positive temperature coefficient Maximum Power Point Negative temperature coefficient
- 32. Effect Of Change In Temperature
- 34. Temperature Change Effect The values in the datasheet have been given for STC: Irradiance 1000W/m2, Module Temperature 25℃. Let us calculate the values for 40 ℃ temperature. 𝐼 𝑆𝐶 40℃ = 𝐼𝑆𝐶 25℃ + ∆𝑖 𝑉 𝑂𝐶 40℃ = 𝑉𝑂𝐶 25℃ + ∆𝑣𝑎𝑘 𝑃 𝑚 40℃ = 𝑃𝑚 25℃ + ∆𝑃 The percentage temperature coefficient of Isc is given by, %𝛼𝐼 = 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝐼𝑠𝑐 𝐼𝑠𝑐 25℃ ∆𝑇 = 0.045%/K Therefore, change in Isc is, ∆𝑖 = 𝛼𝐼 ∗ 𝐼𝑠𝑐 25℃ ∗ ∆𝑇 100 = 0.045 ∗8.99 ∗(40−25) 100 = 0.0606825 A
- 35. Temperature Change Effect Therefore, the temperature at 40 degree Celsius is, 𝐼𝑠𝑐 40℃ = 8.996 𝐴 Similarly we can calculate ΔV and ΔP as, ∆𝑣 = 𝛼𝑣 ∗ 𝑉𝑜𝑐 25℃ ∗ ∆𝑇 100 ∆𝑃 = 𝛼𝑝 ∗ 𝑃𝑚 25℃ ∗ ∆𝑇 100 And calculate the open-circuit voltage and power to be, 𝑉𝑜𝑐 40℃ = 34.85 𝐴 𝑃𝑚 40℃ = 223 𝑊 Parameter Value at 25℃ Value at 40℃ Voc 36.72 V 34.85 V Isc 8.99 A 8.9968 A Pm 240 Wp 223 Wp Parameter Effect of temperature Open-Circuit Voltage Negative temperature coefficient Short-Circuit Current Positive temperature coefficient Maximum Power Point Negative temperature coefficient
- 36. Concept of Fill Factor The Fill Factor (FF) is a figure of merit of a PV cell. In other words, the FF tells how ‘good’ or ‘bad’ the PV cell is. Consider the intersecting perpendiculars drawn at Voc and Isc that represents the maximum possible voltage and current that can theoretically be obtained by the cell. It is impossible to obtain this point practically. This point would be the operating point of an ideal cell, but not of a practical cell. The point (Vm, Im) is the practically achievable operating point due to the effects of Rsh and Rse. The fill factor represents how close the rectangle of (Vm, Im) bound point goes to the rectangle bound by (Voc, Isc) point.
- 37. Concept of Fill Factor The area as encompassed by the practically achievable maximum power point with respect to the idealized maximum power area is called the fill factor (FF). Mathematically, it is expressed as, 𝑭𝑭 = 𝑽𝒎𝑰𝒎 𝑽𝑶𝑪𝑰𝑺𝑪 For the BYD 240 Wp panel, Vm = 30.18V, Im = 7.96A Voc = 36.72V. Isc = 8.99A The fill factor is, 𝐹𝐹 = 30.18 ∗ 7.96 36.72 ∗ 8.99 = 𝟎. 𝟕𝟐