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Supercapacitors in stand-alone PV systems with ... U ⎛ ⎜1 − e ⎜ ⎝ t − = RC C UO ⎞ ⎟ ⎟ ⎠ (2) and charge stored in a capacitor: 1 Q = CU C 2 2 (3) Owing to extremely high capacitance values of a SC of the order of many thousands of Farads, there exist in practice no capacitance meters. Thus, the capacitance is determined mainly by means of equation 1 while discharging an SC through a fixed resistor R of known resistance. As there is no capacitance meter capable of measuring large capacitances, both mathematical and computer-aided calculation methods were tested during Authors’ investigations carried out on a single SC as well as on the series supercapacitor banks. The effects and effort appeared to be similar, though each of the methods needed rather a large amount of time to be accomplished. The value of capacitance can be determined manually by applying the voltage values measured at t=0 and after an exactly set period of time to the equation. This process can also be automated by using computer-aided methods, which not only enable one to draw and store the complete discharge characteristics but also to observe existing slight capacitance dependence on applied voltage (Fig. 2). The problems already mentioned in the introduction concerning generally building the series SC banks have several technical aspects. The main of them is the equalisation of working voltages across each capacitor in the bank, as the excessive voltage even across one component threatens to destroy the entire bank. The dange- 110 Fig. 2. Exemplary computer graph of a SC discharge U = f(t) curve, calculated and drawn with MATHCAD software. Rys.2. Przykładowy wykres komputerowy funkcji rozładowania U = f(t) superkondensatora, sporządzony za pomocą programu MATHCAD.
W. Grzesiak, T. Maj, E. Radziemska rously excessive voltages across certain SC units constituting the series bank may occur not only while charging, but also during rapid discharging processes. The well-known passive method of connecting the capacitors in parallel with resistors, all of the same value, appears to be inadmissible, because of excessive power losses due to the extreme capacities and low time constants (Fig. 3). Fig. 3. Standard (a) and improved (b) methods of SC voltage equalisation [1]. Rys. 3. Metody konwencjonalna (a) i ulepszona (b) symetryzacji napięcia [1]. An improved method consisting in temporary use of switches also is not too attractive because of the necessity to control electrically the voltage across SCs and to switch appropriate contacts. Recently, purely active electronic systems are preferably used (Fig. 4) in the series SC banks. Examples are shown in Figs. 5 - 8. Fig. 4. Simplified active balancing method. Rys. 4. Uproszczona aktywna metoda symetryzacji napięć. 111
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INSTYTUT TECHNOLOGII MATERIAŁÓW E
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SPIS TREŚCI ARTYKUŁY WPŁYW PROMI
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6 Wpływ promieniowania jonizujące
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2. STRUKTURA I DEFEKTY W YAP I LN W
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Wpływ promieniowania jonizującego
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