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Section 3.4 Efficiency definitions work. According to the previously made power definition, the discharge capacity is denoted negatively. However, for convenience, the negative sign of the discharge capacity is omitted in the presentation. 3.4 Efficiency definitions A variety of efficiency definitions exist for battery systems. In this work, it is distinguished between the operation point and the round-trip efficiency. The round-trip efficiencies are deployed in Chapter 6 and Chapter 7 . The operation point efficiency is required for the novel flow rate optimization, presented in Section 8.6 starting on page 127. 3.4.1 Round-trip efficiency Round-trip efficiencies require a consecutive charging and discharging process. However, different operation modes are possible for both processes. First of all, we can determine either the charging and discharging current or the charging and discharging power. Also, the stack voltage or the tank SoC can be used to indicate if a charging or discharging process is finished. Table 3-1 gives an overview of the possibilities to determine a round-trip efficiency value. A combination of operation modes is also possible. We can charge the battery with a constant power or a constant current until we reach a certain voltage limit. We can then continue the charging process using a so-called constant voltage phase until we reach a certain SoC limit. During the constant voltage phase, the charging power or current, respectively, is constantly adapted to maintain the cell voltage at the given limit. Naturally, the obtained efficiency values will strongly depend on the chosen operation mode. Combined operation modes are not considered in this work. Table 3-1 Different efficiency definitions (bold – used in this work) Operation point efficiency Combination of Combination of power and SoC current and SoC Round-trip efficiency Limited by SoC Limited by voltage Constant Constant Constant Constant power current power current The term round-trip efficiency is further refined as follows: Coulombefficiency The Coulomb efficiency is the ratio of the electric charge, fed to the battery during the charging process, and the electric charge, extracted from the battery during the discharging process, as shown in Eq. (3-1). Herein, IPCS is the externally applied current by the power conditioning system (PCS). The Coulomb efficiency is mainly affected by side reactions such vanadium crossover and shunt currents. η Col tDischarge IPCStdt tCharge tCharge IPCStdt 0 (3-1) 58PDF Image | Model-based Design Vanadium Redox Flow Batteries
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