PV Characteristics

Cheatsheet Content

### Photovoltaic (PV) Basics A photovoltaic cell (solar cell) converts light energy directly into electrical energy. The fundamental principle is the photovoltaic effect. #### Key Parameters: - **Short-Circuit Current ($I_{SC}$):** The maximum current produced by the cell when the voltage across it is zero (i.e., terminals are shorted). - **Open-Circuit Voltage ($V_{OC}$):** The maximum voltage produced by the cell when the current flowing through it is zero (i.e., terminals are open-circuited). - **Maximum Power Point ($P_{MPP}$):** The point on the I-V curve where the product of current and voltage (power) is maximized. - **Current at MPP ($I_{MPP}$):** The current at the maximum power point. - **Voltage at MPP ($V_{MPP}$):** The voltage at the maximum power point. ### I-V Characteristics The Current-Voltage (I-V) curve describes the relationship between the current ($I$) and voltage ($V$) of a PV device under specific illumination and temperature conditions. #### Ideal Diode Model: The current-voltage characteristic of an ideal PV cell can be approximated by: $$ I = I_{L} - I_0 \left[ \exp\left(\frac{qV}{nkT}\right) - 1 \right] $$ Where: - $I_L$: Light-generated current (proportional to irradiance) - $I_0$: Diode saturation current (temperature dependent) - $q$: Electron charge ($1.602 \times 10^{-19}$ C) - $V$: Voltage across the diode - $n$: Diode ideality factor (typically 1 to 2) - $k$: Boltzmann's constant ($1.381 \times 10^{-23}$ J/K) - $T$: Cell temperature in Kelvin #### Key Points on I-V Curve: - **Short-Circuit Point (0, $I_{SC}$):** Occurs when $V=0$. The current is approximately $I_L$. - **Open-Circuit Point ($V_{OC}$, 0):** Occurs when $I=0$. - **Maximum Power Point ($V_{MPP}$, $I_{MPP}$):** The knee of the curve where the largest rectangle can be inscribed. #### Effect of Irradiance: - Increasing irradiance primarily increases $I_{SC}$ (shifts the curve vertically). - $V_{OC}$ increases slightly with irradiance. #### Effect of Temperature: - Increasing temperature primarily decreases $V_{OC}$ (shifts the curve horizontally to the left). - $I_{SC}$ increases very slightly with temperature. - Overall, power output decreases significantly with increasing temperature. ### P-V Characteristics The Power-Voltage (P-V) curve shows the relationship between the output power ($P = V \cdot I$) and voltage ($V$) of a PV device. #### Curve Shape: - The P-V curve typically has a single distinct peak, which corresponds to the Maximum Power Point ($P_{MPP}$). - At $V=0$ (short circuit), $P=0$. - At $I=0$ (open circuit), $P=0$. #### Maximum Power Point (MPP): - The peak of the P-V curve. - $P_{MPP} = V_{MPP} \cdot I_{MPP}$. - MPPT (Maximum Power Point Tracking) algorithms are used to continuously operate the PV system at this point to maximize energy harvest. #### Effect of Irradiance and Temperature: - **Irradiance:** Higher irradiance shifts the entire P-V curve upwards, significantly increasing $P_{MPP}$. $V_{MPP}$ changes slightly. - **Temperature:** Higher temperature shifts the P-V curve downwards and to the left, significantly decreasing $P_{MPP}$ and $V_{MPP}$. ### Performance Metrics - **Fill Factor (FF):** Represents the "squareness" of the I-V curve, indicating the quality of the cell. $$ FF = \frac{V_{MPP} \cdot I_{MPP}}{V_{OC} \cdot I_{SC}} $$ - **Efficiency ($\eta$):** The ratio of electrical power output ($P_{MPP}$) to the incident solar power ($P_{in}$). $$ \eta = \frac{P_{MPP}}{P_{in}} = \frac{V_{MPP} \cdot I_{MPP}}{A \cdot G} $$ Where: - $A$: Surface area of the PV cell/module - $G$: Irradiance (solar power per unit area, e.g., W/m$^2$)