supercapacitor - arnabutilities/rbac-frontend GitHub Wiki

how many fully charged 400F 2.8V supercapacitor required to charge a 10000mah powerbank?

To determine the number of fully charged 400F 2.8V supercapacitors needed to charge a 10000mAh power bank, we need to compare the energy stored in the capacitors with the energy required by the power bank.

Calculate the energy stored in one supercapacitor:

The energy ( E ) stored in a capacitor is given by: [ E = \frac{1}{2} C V^2 ] where ( C ) is the capacitance in farads (F) and ( V ) is the voltage in volts (V).

For one 400F, 2.8V supercapacitor: [ E_{cap} = \frac{1}{2} \times 400 \times 2.8^2 ] [ E_{cap} = 0.5 \times 400 \times 7.84 ] [ E_{cap} = 1568 \text{ joules (J)} ]
Calculate the energy required to charge the power bank:

The energy required depends on the voltage of the power bank. Assuming the power bank operates at 3.7V (a common voltage for lithium-ion batteries):

The energy in watt-hours (Wh) for a 10000mAh, 3.7V power bank is: [ E_{pb} = \text{Capacity (Ah)} \times \text{Voltage (V)} ] [ E_{pb} = 10 \text{ Ah} \times 3.7 \text{ V} ] [ E_{pb} = 37 \text{ Wh} ]

Converting watt-hours to joules (since 1 Wh = 3600 J): [ E_{pb} = 37 \times 3600 ] [ E_{pb} = 133200 \text{ J} ]
Determine the number of supercapacitors required:

The number of supercapacitors ( N ) needed is: [ N = \frac{E_{pb}}{E_{cap}} ] [ N = \frac{133200}{1568} ] [ N \approx 84.94 ]

Since we cannot have a fraction of a supercapacitor, we'll need at least 85 fully charged 400F, 2.8V supercapacitors to charge a 10000mAh power bank.

ok this 10000mah powerbank required 4 hours to get fully charged. is there any chance I can re-use any number of supercapacitor?

If the power bank takes 4 hours to fully charge, we can explore the possibility of reusing the supercapacitors to provide the necessary energy over that time period. This would involve a setup that allows the supercapacitors to discharge into the power bank and then be recharged in cycles.

Here's an approach to evaluate if this is feasible:

Calculate the charging power required by the power bank:

If the power bank takes 4 hours to charge fully, the average charging power ( P ) can be calculated using the total energy required and the charging time.

[ P = \frac{E_{pb}}{\text{charging time (seconds)}} ]

The charging time in seconds is: [ 4 \text{ hours} \times 3600 \text{ seconds/hour} = 14400 \text{ seconds} ]

Thus, the average charging power: [ P = \frac{133200 \text{ J}}{14400 \text{ s}} ] [ P \approx 9.25 \text{ W} ]
Calculate the number of supercapacitors needed to provide continuous power:

To continuously provide 9.25 W of power using supercapacitors, we need to evaluate the energy they can provide in a single discharge cycle and how quickly they can be recharged.

Each 400F, 2.8V supercapacitor stores 1568 J of energy. If a capacitor is used in a continuous charge-discharge cycle, the discharge rate and recharging capability become crucial.

Assuming the supercapacitors can be recharged in a time much shorter than the discharge time, you might set up multiple supercapacitors in parallel to smooth the power delivery.
Estimate the reusability of supercapacitors:

Suppose you have a setup where a set of supercapacitors is discharging while another set is charging. This requires careful management of the charge-discharge cycles.

If each supercapacitor discharges over a period and is then recharged, you need to ensure that the recharge time is sufficiently short compared to the discharge time.
Simplified calculation for reuse feasibility:

If you have 10 sets of supercapacitors (each set providing energy for a portion of the charging time), the setup could allow for sequential discharge and recharge.

To determine the exact number of supercapacitors needed for a practical setup, consider factors like:
- The efficiency of the power transfer system.
- The recharge rate of the supercapacitors.
Practical Considerations:

Given practical limitations and inefficiencies, assume a conservative estimate. If we consider a 50% efficiency in recharging cycles and system losses, you might double the initial number of supercapacitors.

Therefore, instead of 85 supercapacitors, you might need: [ \text{Approximately } 170 \text{ supercapacitors to manage continuous charge-discharge cycles efficiently.} ]

Reusing supercapacitors is theoretically feasible but requires a sophisticated management system to ensure efficient cycling and recharging.

ok, here is the deal. I want to make a super capasitor setup along with the 10000mah powerbank, so that I want to spend minimal time to charge the powerbank.

how much time it will take to charge this set of supercapacitors?

To determine the time it will take to charge the set of supercapacitors, we need to consider the total energy that needs to be stored in the supercapacitors and the power of the charging source.

Total Energy Required

The total energy required to charge 85 supercapacitors (each 400F, 2.8V) can be calculated as follows:

Each supercapacitor stores: [ E_{cap} = \frac{1}{2} C V^2 = \frac{1}{2} \times 400 \times 2.8^2 = 1568 \text{ J} ]

For 85 supercapacitors: [ E_{total} = 85 \times 1568 \text{ J} = 133280 \text{ J} ]

Charging Power and Time

The charging time depends on the power of the charger used. The power ( P ) provided by the charger (in watts) determines how quickly the energy ( E_{total} ) can be supplied to the capacitors.

The charging time ( t ) (in seconds) is given by: [ t = \frac{E_{total}}{P} ]

Example Calculations with Different Charger Powers:

Using a 100W Charger: [ t = \frac{133280 \text{ J}}{100 \text{ W}} = 1332.8 \text{ seconds} \approx 22.2 \text{ minutes} ]
Using a 50W Charger: [ t = \frac{133280 \text{ J}}{50 \text{ W}} = 2665.6 \text{ seconds} \approx 44.4 \text{ minutes} ]
Using a 200W Charger: [ t = \frac{133280 \text{ J}}{200 \text{ W}} = 666.4 \text{ seconds} \approx 11.1 \text{ minutes} ]

Practical Considerations

Charger Efficiency: Real-world charging efficiency might not be 100%, so the actual time might be slightly longer.
Capacitor Charging Characteristics: Charging capacitors can involve increasing resistance and reduced current as they charge, potentially extending the charging time slightly.
Heat Management: High-power charging can generate heat, so proper cooling and heat dissipation should be considered.

Summary

The time to charge the set of 85 supercapacitors will depend on the power of your charger. For example:

With a 100W charger, it will take approximately 22.2 minutes.
With a 50W charger, it will take approximately 44.4 minutes.
With a 200W charger, it will take approximately 11.1 minutes.

Using a higher power charger will reduce the charging time, but ensure that the charger and capacitors can handle the power safely.

how much time it takes to fully discharge one of this supercapacitor indipendently?

To calculate the time it takes to fully discharge one 400F, 2.8V supercapacitor independently, we need to consider the discharge current and the voltage drop over time. The discharge time depends on the load resistance or the constant current applied during discharge.

Discharge Through a Resistor

When discharging through a resistor, the voltage ( V(t) ) across the capacitor decreases exponentially according to the equation: [ V(t) = V_0 e^{-\frac{t}{RC}} ] where:

( V_0 ) is the initial voltage (2.8V),
( R ) is the resistance in ohms,
( C ) is the capacitance (400F),
( t ) is the time in seconds.

The time constant ( \tau ) is given by: [ \tau = RC ]

The time to discharge significantly (to a small fraction of the initial voltage) is typically considered as 5 times the time constant ((5\tau)), as at this point the voltage has dropped to near zero (less than 1% of the initial voltage).

Example Calculation

Assume we discharge through a resistor ( R ). Let's choose a reasonable resistance value for illustration:

Discharge through a 1-ohm resistor:

[ \tau = RC = 1 \times 400 = 400 \text{ seconds} ]

The time to discharge to near zero (5 time constants) is: [ t = 5 \times \tau = 5 \times 400 = 2000 \text{ seconds} \approx 33.3 \text{ minutes} ]

Discharge at a Constant Current

For constant current discharge, the voltage decreases linearly. The time ( t ) to fully discharge is given by: [ t = \frac{C \times V_0}{I} ] where ( I ) is the discharge current.

Example Calculation

Discharge at 1A:

[ t = \frac{400 \times 2.8}{1} = 1120 \text{ seconds} \approx 18.7 \text{ minutes} ]
Discharge at 2A:

[ t = \frac{400 \times 2.8}{2} = 560 \text{ seconds} \approx 9.3 \text{ minutes} ]

Practical Discharge Times

Discharging through a 1-ohm resistor: Approximately 33.3 minutes.
Discharging at a constant current of 1A: Approximately 18.7 minutes.
Discharging at a constant current of 2A: Approximately 9.3 minutes.

The actual discharge time will depend on the load resistance or the current draw. Using a higher current will decrease the discharge time but also requires appropriate handling of the increased power dissipation and heat.

###how to prevent these capacitors to get discharge?

To prevent supercapacitors from discharging unintentionally, you can implement several methods and practices to ensure they maintain their charge:

1. Use Diodes

Blocking Diodes: Place diodes in series with the capacitors. This will allow current to flow into the capacitors during charging but block current from flowing back out.
- Schottky Diodes are often used due to their low forward voltage drop.

2. Isolation Switches

Mechanical Switches: Manually controlled switches can be used to disconnect the capacitors from the circuit when they are not in use.
Relays: Electromechanical relays can be used to disconnect the capacitors electronically.
MOSFETs or Solid State Relays: These can be controlled by a microcontroller to disconnect the capacitors automatically.

3. Low Leakage Circuit Design

High-quality Capacitors: Use capacitors with low self-discharge rates.
Proper PCB Design: Ensure that the printed circuit board (PCB) design minimizes leakage paths by keeping the board clean and using proper insulation techniques.

4. Protective Circuits

Battery Management Systems (BMS): Implement a BMS that includes features to isolate the supercapacitors when not in use.
Charge Controllers: Use charge controllers that can disconnect the capacitors from the load once fully charged.

5. Temperature Control

Temperature Management: Store and operate the supercapacitors within their specified temperature range. High temperatures can increase leakage currents.
Heat Sinks or Cooling: Use heat sinks or cooling methods to maintain optimal temperature.

6. Encapsulation

Encapsulation: Encapsulate the capacitors in a protective casing to prevent contamination and physical damage which can lead to leakage.

7. Regular Monitoring

Voltage Monitoring: Regularly monitor the voltage across the capacitors using a microcontroller or monitoring system. If the voltage drops below a threshold, the system can alert or take corrective action.

Example Circuit for Isolation

Here’s a simple example circuit using a MOSFET for isolating a supercapacitor:

Components:

P-channel MOSFET (e.g., IRF9540)
Control circuitry (e.g., microcontroller or manual switch)

Circuit Description:

Source of the MOSFET connects to the positive terminal of the capacitor.
Drain of the MOSFET connects to the load.
Gate is controlled by the microcontroller or switch. When the gate is pulled to ground, the MOSFET conducts, connecting the capacitor to the load. When the gate is at a higher potential, the MOSFET is off, isolating the capacitor.

Gate Control:

Use a voltage divider to ensure the gate voltage is appropriately controlled.
Add a pull-up resistor to keep the gate at a high potential when not actively driven by the control circuit.

This method ensures that the supercapacitors remain isolated from the load when not needed, thus preventing unintended discharge.

Summary

By implementing a combination of diodes, switches, protective circuits, and careful design, you can effectively prevent your supercapacitors from discharging unintentionally. This will help maintain their charge and ensure they are ready for use when needed.

ok I want to understand if I want replace this 10000mah power bank with a set of supercapacitors, what will be the advantages and disadvantages?

Replacing a 10000mAh power bank with a set of supercapacitors has both advantages and disadvantages. Here’s a detailed comparison to help you understand the implications:

Advantages of Using Supercapacitors

Fast Charging and Discharging:
- Supercapacitors can be charged and discharged much faster than batteries. This means you can quickly recharge your power source and deliver high bursts of power to devices.
Long Cycle Life:
- Supercapacitors can endure hundreds of thousands to millions of charge-discharge cycles without significant degradation, whereas lithium-ion batteries typically last for a few hundred to a few thousand cycles.
High Power Density:
- They have a high power density, making them ideal for applications requiring quick bursts of energy.
Wide Operating Temperature Range:
- Supercapacitors can operate effectively in a wider temperature range compared to batteries, making them suitable for extreme environments.
Low Maintenance:
- They require less maintenance compared to batteries, which may need periodic recalibration and monitoring.
Safety:
- Supercapacitors are less prone to thermal runaway and do not catch fire or explode under normal operating conditions, unlike lithium-ion batteries.

Disadvantages of Using Supercapacitors

Lower Energy Density:
- Supercapacitors have a much lower energy density compared to lithium-ion batteries. This means they store less energy per unit volume or weight, making them bulkier for the same amount of stored energy.
Self-Discharge:
- Supercapacitors have a higher self-discharge rate compared to batteries, meaning they lose their charge over time even when not in use.
Voltage Fluctuation:
- The voltage of a supercapacitor drops linearly with the discharge, unlike batteries that maintain a relatively constant voltage. This requires additional circuitry to regulate voltage for devices.
Higher Initial Cost:
- Supercapacitors can be more expensive upfront compared to lithium-ion batteries for the same energy capacity.
Energy Storage Efficiency:
- Supercapacitors can be less efficient in terms of energy storage capacity per unit weight or volume, making them impractical for applications requiring large amounts of stored energy in a compact form.

Practical Considerations

Application Suitability:
- Supercapacitors are ideal for applications requiring quick charge and discharge cycles, high power output, and durability over many cycles. They are often used in applications such as regenerative braking systems, uninterruptible power supplies (UPS), and power smoothing in electronics.
Energy Requirement:
- If your primary need is long-term energy storage with moderate power output, lithium-ion batteries might be more suitable due to their higher energy density.

Summary

Advantages:

Fast charging/discharging
Long cycle life
High power density
Wide operating temperature range
Low maintenance
Improved safety

Disadvantages:

Lower energy density
Higher self-discharge rate
Voltage fluctuation
Higher initial cost
Less efficient for energy storage

Conclusion

Replacing a 10000mAh power bank with supercapacitors can be beneficial if you need quick charging and discharging capabilities, high cycle life, and can manage the higher self-discharge and lower energy density. If you require sustained energy storage with less frequent recharging and a stable voltage output, a lithium-ion battery might still be the better choice. Your decision should be based on the specific requirements of your application and the trade-offs you are willing to accept.

ok do you think if it is a right choice to use combination of supercapacitor and Li batteries for a electric car 5seater car? waht could be advantage and disadvantages?

Using a combination of supercapacitors and lithium-ion batteries in a 5-seater electric car can offer a balanced approach to energy storage, leveraging the strengths of both technologies. Here’s a detailed analysis of the advantages and disadvantages of such a hybrid energy storage system:

Advantages

Enhanced Performance:
- Quick Energy Delivery: Supercapacitors can provide rapid bursts of power for acceleration, which can enhance the car's performance and responsiveness.
- Regenerative Braking: Supercapacitors are excellent for capturing and storing energy from regenerative braking due to their fast charge and discharge capabilities.
Extended Battery Life:
- Load Levelling: Supercapacitors can handle the high peak power demands, reducing the stress on the lithium-ion batteries. This can lead to a longer lifespan for the batteries by avoiding high current spikes.
- Thermal Management: By handling high power demands, supercapacitors can help manage the thermal load on batteries, reducing the risk of overheating.
Improved Efficiency:
- Energy Recovery: The rapid charge-discharge cycle of supercapacitors makes energy recovery from braking more efficient, which can improve overall energy efficiency and extend the driving range.
Increased Safety:
- Reduced Heat Generation: Supercapacitors generate less heat compared to batteries during high power discharges, improving the overall safety of the energy storage system.

Disadvantages

Complexity and Cost:
- System Complexity: Integrating supercapacitors with lithium-ion batteries requires sophisticated power management and control systems to ensure smooth operation and coordination between the two types of energy storage.
- Higher Initial Cost: The addition of supercapacitors increases the initial cost of the energy storage system. Advanced control systems also add to the cost.
Space and Weight:
- Space Constraints: Supercapacitors have a lower energy density compared to lithium-ion batteries, which means they take up more space for the same amount of energy stored.
- Weight Considerations: Adding supercapacitors increases the weight of the vehicle, which can affect its overall efficiency and performance.
Self-Discharge:
- Energy Loss: Supercapacitors have a higher self-discharge rate compared to batteries. This means that if the vehicle is not used for extended periods, there can be significant energy loss from the supercapacitors.

Practical Considerations

Application Suitability:
- Urban vs. Long-Distance Driving: Supercapacitors are particularly useful in urban driving conditions with frequent stop-and-go traffic and regenerative braking opportunities. For long-distance driving with steady speeds, the benefit of supercapacitors may be less pronounced.
System Integration:
- Control Systems: Effective integration requires advanced battery management systems (BMS) and power electronics to manage the charge and discharge cycles of both supercapacitors and batteries efficiently.
- Cooling Systems: Proper thermal management systems are needed to handle the different thermal characteristics of supercapacitors and batteries.

Example of a Hybrid System

A hybrid energy storage system might involve:

Supercapacitors: Used for short-term high power demands, such as acceleration and regenerative braking.
Lithium-ion Batteries: Used for steady energy supply, ensuring a consistent driving range.

The control system would ensure that:

During acceleration, the supercapacitors supply the high current required.
During cruising, the lithium-ion batteries provide the steady power needed.
During braking, the energy is quickly captured by the supercapacitors and then slowly transferred to the lithium-ion batteries if needed.

Summary

Advantages:

Enhanced performance due to quick energy delivery
Extended battery life by reducing peak loads
Improved energy efficiency, especially in urban driving
Increased safety with reduced heat generation

Disadvantages:

Increased system complexity and initial cost
Additional space and weight requirements
Higher self-discharge rates leading to potential energy loss

Conclusion

A hybrid system combining supercapacitors and lithium-ion batteries can offer significant performance and efficiency benefits for a 5-seater electric car, especially in urban environments. However, the increased complexity, cost, and space requirements must be carefully considered and managed. This approach is suitable if the goal is to maximize vehicle performance, efficiency, and battery life while managing peak power demands effectively.