Dear Dalia,
Supercapacitors occupy the gap between high power/low energy electrolytic capacitors and low power/high energy rechargeable batteries. The energy Wmax that can be stored in a capacitor is given by the formula:
Wmax = 1/2 . Ctotal. V2loaded
This formula describes the amount of energy stored and is often used to describe new research successes. However, only part of the stored energy is available to applications, because the voltage drop and the time constant over the internal resistance mean that some of the stored charge is inaccessible. The effective realized amount of energy Weff is reduced by the used voltage difference between Vmax and Vmin and can be represented as:
Weff = 1/2 . C. (V2max - V2min)
This formula also represents the energy asymmetric voltage components such as lithium ion capacitors.
The amount of energy that can be stored in a capacitor per mass of that capacitor is called its specific energy. Specific energy is measured gravimetrically (per unit of mass) inwatt-hours per kilogram (Wh/kg).
The amount of energy can be stored in a capacitor per volume of that capacitor is called its energy density. Energy density is measured volumetrically (per unit of volume) in watt-hours per litre (Wh/l).
As of 2013 commercial specific energies range from around 0.5 to 15 Wh/kg. For comparison, an aluminum electrolytic capacitor stores typically 0.01 to 0.3 Wh/kg, while a conventional lead-acid battery stores typically 30 to 40 Wh/kg and modern lithium-ion batteries 100 to 265 Wh/kg. Supercapacitors can therefore store 10 to 100 times more energy than electrolytic capacitors, but only one tenth as much as batteries. For reference, petrol fuel has an specific energy density of 44.4 MJ/kg or 12300 Wh/kg(in vehicle propulsion, the efficiency of energy conversions should be considered resulting in 3700 Wh/kg considering a typical 30% internal combustion engine efficiency).
Commercial volumetric energy densities vary widely but in general range from around 5 to 8 Wh/l. Units of liters and dm3 can be used interchangeably. In comparison, petrol fuel has a volumetric energy density of 32.4 MJ/l.
Although the energy densities of supercapacitors are insufficient compared with batteries, capacitors have the important advantage of the power density. Power density describes the speed at which energy can be delivered to/absorbed from the load. The maximum power is given by the formula:
Pmax = 1/4. V2/Ri
with V = voltage applied and Ri, the internal DC resistance of the capacitor.
Power density is measured either gravimetrically in kilowatts per kilogram (kW/kg) or volumetrically in kilowatts per litre (kW/l).
The described maximum power Pmax specifies the power of a theoretical rectangular single maximum current peak of a given voltage. In real circuits the current peak is not rectangular and the voltage is smaller, caused by the voltage drop. IEC 62391–2 established a more realistic effective power Peff for supercapacitors for power applications:
Peff = 1/8. V2/Ri
Supercapacitor power density is typically 10 to 100 times greater than for batteries and can reach values up to 15 kW/kg.
Ragone charts relate energy to power and are a valuable tool for characterizing and visualizing energy storage components. With such a diagram, the position of power density and energy density of different storage technologies is easily to compare.
Energy density is equal to 1/2*C*V2/weight, where C is the capacitance you computed and V should be your nominal voltage (i.e 2.7 V).
Power Density is V2/4/ESR/weight, where ESR is the equivalent series resistance.
For more information, please use the following link:
Please note: that energy and power densities are generally used for two-electrode cells. In the three-electrode cell, you should take into consideration that capacitance of the single electrode will be in 4-fold higher than capacitance of the two-electrode cell in case of the symmetrical supercapacitor (C1~C2) and in 2-fold higher in case of the asymmetrical one where C1>>C2. In addition, the resistance will be different as well.
How can I calculate the energy density and power density ? - ResearchGate. Available from: https://www.researchgate.net/post/How_can_I_calculate_the_energy_density_and_power_density [accessed Apr 9, 2016].
http://www.sciencedirect.com/science/article/pii/S2352152X15000079
For more answers on similar questions posted on Research Gate, please use the following links:
https://www.researchgate.net/post/How_to_calculate_the_energy_density_and_power_density_of_supercapacitor
https://www.researchgate.net/post/What_is_the_best_and_the_most_reliable_way_to_calculate_energy_density_and_power_density_of_a_supercapacitor
https://www.researchgate.net/post/How_can_I_calculate_the_energy_density_and_power_density
References:
Wen Lu, Carbon Nanotube Supercapacitors
Christen, T.; Ohler, C. (2002). "Optimizing energy storage components using Ragone plots". J. Power Sources 110: 107–116. doi:10.1016/S0378-7753(02)00228-8.
Dunn-Rankin, D.; Leal, E. Martins; Walther, D.C. (2005). "Personal power systems". Prog. Energy Combust. Sci. 31: 422–465. doi:10.1016/j.pecs.2005.04.001.
Hoping this will be helpful,
Rafik
Dear Dalia,
Supercapacitors occupy the gap between high power/low energy electrolytic capacitors and low power/high energy rechargeable batteries. The energy Wmax that can be stored in a capacitor is given by the formula:
Wmax = 1/2 . Ctotal. V2loaded
This formula describes the amount of energy stored and is often used to describe new research successes. However, only part of the stored energy is available to applications, because the voltage drop and the time constant over the internal resistance mean that some of the stored charge is inaccessible. The effective realized amount of energy Weff is reduced by the used voltage difference between Vmax and Vmin and can be represented as:
Weff = 1/2 . C. (V2max - V2min)
This formula also represents the energy asymmetric voltage components such as lithium ion capacitors.
The amount of energy that can be stored in a capacitor per mass of that capacitor is called its specific energy. Specific energy is measured gravimetrically (per unit of mass) inwatt-hours per kilogram (Wh/kg).
The amount of energy can be stored in a capacitor per volume of that capacitor is called its energy density. Energy density is measured volumetrically (per unit of volume) in watt-hours per litre (Wh/l).
As of 2013 commercial specific energies range from around 0.5 to 15 Wh/kg. For comparison, an aluminum electrolytic capacitor stores typically 0.01 to 0.3 Wh/kg, while a conventional lead-acid battery stores typically 30 to 40 Wh/kg and modern lithium-ion batteries 100 to 265 Wh/kg. Supercapacitors can therefore store 10 to 100 times more energy than electrolytic capacitors, but only one tenth as much as batteries. For reference, petrol fuel has an specific energy density of 44.4 MJ/kg or 12300 Wh/kg(in vehicle propulsion, the efficiency of energy conversions should be considered resulting in 3700 Wh/kg considering a typical 30% internal combustion engine efficiency).
Commercial volumetric energy densities vary widely but in general range from around 5 to 8 Wh/l. Units of liters and dm3 can be used interchangeably. In comparison, petrol fuel has a volumetric energy density of 32.4 MJ/l.
Although the energy densities of supercapacitors are insufficient compared with batteries, capacitors have the important advantage of the power density. Power density describes the speed at which energy can be delivered to/absorbed from the load. The maximum power is given by the formula:
Pmax = 1/4. V2/Ri
with V = voltage applied and Ri, the internal DC resistance of the capacitor.
Power density is measured either gravimetrically in kilowatts per kilogram (kW/kg) or volumetrically in kilowatts per litre (kW/l).
The described maximum power Pmax specifies the power of a theoretical rectangular single maximum current peak of a given voltage. In real circuits the current peak is not rectangular and the voltage is smaller, caused by the voltage drop. IEC 62391–2 established a more realistic effective power Peff for supercapacitors for power applications:
Peff = 1/8. V2/Ri
Supercapacitor power density is typically 10 to 100 times greater than for batteries and can reach values up to 15 kW/kg.
Ragone charts relate energy to power and are a valuable tool for characterizing and visualizing energy storage components. With such a diagram, the position of power density and energy density of different storage technologies is easily to compare.
Energy density is equal to 1/2*C*V2/weight, where C is the capacitance you computed and V should be your nominal voltage (i.e 2.7 V).
Power Density is V2/4/ESR/weight, where ESR is the equivalent series resistance.
For more information, please use the following link:
Please note: that energy and power densities are generally used for two-electrode cells. In the three-electrode cell, you should take into consideration that capacitance of the single electrode will be in 4-fold higher than capacitance of the two-electrode cell in case of the symmetrical supercapacitor (C1~C2) and in 2-fold higher in case of the asymmetrical one where C1>>C2. In addition, the resistance will be different as well.
How can I calculate the energy density and power density ? - ResearchGate. Available from: https://www.researchgate.net/post/How_can_I_calculate_the_energy_density_and_power_density [accessed Apr 9, 2016].
http://www.sciencedirect.com/science/article/pii/S2352152X15000079
For more answers on similar questions posted on Research Gate, please use the following links:
https://www.researchgate.net/post/How_to_calculate_the_energy_density_and_power_density_of_supercapacitor
https://www.researchgate.net/post/What_is_the_best_and_the_most_reliable_way_to_calculate_energy_density_and_power_density_of_a_supercapacitor
https://www.researchgate.net/post/How_can_I_calculate_the_energy_density_and_power_density
References:
Wen Lu, Carbon Nanotube Supercapacitors
Christen, T.; Ohler, C. (2002). "Optimizing energy storage components using Ragone plots". J. Power Sources 110: 107–116. doi:10.1016/S0378-7753(02)00228-8.
Dunn-Rankin, D.; Leal, E. Martins; Walther, D.C. (2005). "Personal power systems". Prog. Energy Combust. Sci. 31: 422–465. doi:10.1016/j.pecs.2005.04.001.
Hoping this will be helpful,
Rafik
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