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Capacitor in series problem resolution

by:SMiLer     2022-01-10
Series capacitors are widely used in power transmission and distribution system, especially the long distance, large capacity of power transmission system, improve the transportation capacity, improve the stability of the system to improve system voltage regulation, at the same time improve the power factor of system, reduce the loss of line. After analytical capacitor in series capacitor in series problem, all of the charge on the capacitor anode quantity, the amount of charge is equal to the cathode plate. That is the best 10 u capacitance can charge 5 u, now 10 u capacitor voltage because the charge is reduced by half, so the voltage fell by half, to 25 v. Series a total pressure of 75 v. Capacity by one times the same capacitor in series and pressure, the partial pressure of large capacitance is half of small capacitance partial pressure, if the resistance is the partial pressure of terms, small capacitance is equivalent to high value resistance, large capacitor is equal to the minimum resistance, we put the series circuit current is equal to the principle of change is the series of charge on the capacitor plates of equal everywhere, the charge of electric potential of relatively rare large capacity must is very low. And charge density of small capacitance, high potential. So when a 10 & Omega; Resistance and 5 & Omega; Resistance in series, in 10 & Omega; Resistance is the partial pressure of 5 & Omega; The partial pressure of double resistance. So, the series is the total pressure of 75 v. Under the 75 v voltage, small capacitance 50 v full pressure, big capacitance half 25 v voltage on both ends. If the supply voltage U = 1000 volts, choose the withstand voltage of 600 v two capacitor used together, when C1 bear 750 volts, C2 bear 250 v voltage, two capacitors? In theory, with the capacity of series capacitor voltage should be equal, but in the actual measure the voltage is not equal. Whether in an ideal world, capacitor without leakage current ( The insulation resistance for infinite) , but in fact all of the capacitor have different degree of leakage current, ranging performance for their insulation resistance value. Rc1 and Rc2 respectively in this picture is the insulation resistance of the two capacitors are equivalent and shunt capacitors. Under steady state, After the charging process) , there is no current through the capacitor branch, and the resistance of branch current is: IR = U/( Rc1+Rc2) No matter how much they insulation resistance, as long as they are of limited value, the leakage current. So each capacitor on the voltage: U1 = IRRc1 = Rc1U/( Rc1+Rc2) U2 = IRRc2 = Rc2U / ( Rc1+Rc2) Under normal circumstances, the capacitor insulation resistance is different, so the voltage U1 is not the same as U2. If Rc1 = 3 rc2, U1 = 750 volts, U2 = 250 volts, U1 exceeds the working voltage of capacitor, such as capacitor is punctured ( Short circuit) , whole voltage is added to another capacitor, it will then be breakdown. In order to solve this problem, should be next to each capacitor in parallel a resistance R. The value of the R is about hundreds of thousands of European should be much smaller than insulation resistance ( General R should be less than 10% of the Rc) 。 In this way, each capacitor on the voltage is roughly the same, not far. Therefore, the resistance R is called the equalizing resistance.
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