# Super Capacitor Balancing System

Supercapacitors (SCs) generally operate at a low voltage of about 2.7 volts. To achieve a higher operating voltage, it is necessary to build a series of SC cells connected in series. Due to differences in capacitance and insulation resistance caused by production or aging, the voltage drop across individual capacitors may exceed the rated voltage limit. Therefore, a balancing system is required to prevent accelerated aging of the capacitor cell. In the following, the effect of uneven voltage division in such serial circuits will be explained in principle. For a better understanding, balancing strategies for using a series connection of two capacitors are discussed. The imbalance of supercapacitors connected in a series capacitor A can be modeled by parallel connection of an RC element and a dielectric resistor. For now, we can neglect the insulation resistance and consider the series connection of two capacitors with capacitances C1 and C2. The amount of energy in such a case is the charge q on the capacitor, that is, on its internal interfaces. With the help of the law of conservation of charge is the voltage drop across and with each capacitor as the total voltage. In the following, we can consider the case where C1 is greater than C2. In this case the voltage drop across each capacitor is and with the voltage of each capacitor set to Vr = V1 = V2, the charge on Capacitor 1 should be increased and the voltage on Capacitor 2 reduced. Using the definition of amperage (I = dq/dt), the voltage can be written as and Interpret current I1,2 as the electric current that must flow for a period of time Δt to balance this system. The constant current required to balance the voltage ΔV at a given time period t is balancing strategies The literature classifies balancing strategies according to various characteristics such as: dissipative behavior of power Speed ​​balancing Type of technology used Pricing Therefore, when choosing the right balancing strategy, it is important to know all parameters and limitations of the specific application to make the right decision. Here, we distinguish between active equilibrium and passive equilibrium. Measurements The series connection of two SCs from Würth Elektronik was tested: Capacitor 1: C1 = 10 F Capacitor 2: C2 = 15 F This corresponds to the deviations from a theoretical capacitor with a nominal capacitance Cr = 12.5 F. For charging we used a charging voltage Vg = 5.4 V and a maximum charging current Ic = 2 A. In order to design a reliable circuit we would like to stress that a combination of SCs with different nominal capacitances is not recommended. This mixture has been selected for experimental purposes only. 1-kΩ Resistor For negative balancing, we used a resistor with 1 kΩ (1%) and was rated for 0.6 W. The resistor was chosen in favor of a short balancing time rather than low power dissipation. The measured voltages V1 and V2 and the output voltage V1 – V2, shown in Figure 1, indicate complete equilibration after about 600 minutes. V1 and V2 come close to Vr. The total power dissipation (calculated from the effective leakage current, Iloss) after 12 hours is 2.8 mA x 5.4 V ≈ 15 mW. For low-power applications or backup solutions, this compensation speed can be fast enough and the power dissipation is acceptable. For standalone battery-powered applications, the resistance must be increased to reduce losses. To be on the safe side, it is also advised to reduce the operating voltage to avoid overvoltage. Written by René Kalbitz, Product Manager at Würth Elektronik eiSos GmbH & Co. KGP, please visit the e-book for the full article.

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