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area of each stack in system C is one "nth" the area of the single stack in system A. For simplicity, each stack is considered to contain only one cell. Since each system achieves the same total fuel utilization (90 percent) across the same total area, each stack has the same average current density. Irreversible voltage loss is mainly a function of current density and stack temperature. Since these parameters are equivalent in each stack, it is assumed that the Nernst potential of each stack would be reduced by the same amount. In system A, 90 percent of the fuel is utilized in a single stack, and all the current is generated at a single voltage. The power that this system can achieve is represented by the graph's shaded region. In system B, three stacks in series each utilize 30 percent of the fuel. The current generated by each stack in system B is one third of the current generated in system A. Each stack in system B produces a different voltage. At the exit of the first stack, a high Nernst potential is generated because 70 percent of the fuel is still unburned. Likewise, at the exit of the second stack, 40 percent of the fuel remains unburned, generating another improved Nernst potential. Only ten percent of the fuel remains at the exit of the third stack, yielding the same Nernst potential that the single stack in system A produced. The three stack network can produce more power because two-thirds of the total charge is transferred at increased voltages. Comparing the shaded areas of the graphs illustrates the additional power that can be produced by arranging stacks in series. In system C, many stacks are connected in series. Very small currents are generated at still higher voltages. As the number of stacks in series is increased, the maximum achievable power quickly approaches the power which a reversible system would generate, i.e. complete conversion of the available free energy. (A reversible system is reversible at every point in each stack, not just at the stack outlets.) The shaded area in the graph nearly fills the entire area under the curve - the reversible power. Each system in Figure 8-38 converts an equivalent amount of free energy (90 percent fuel utilization) into heat and electrical work. The key difference, however, is that the systems with MCFC stacks networked in series transfer charge at higher voltages, thus converting more of the free energy directly into electrical work, and less into heat. As the number of stacks in series is increased, a reversible process is approached which would convert all the free energy into work and none into heat. Although heat that is produced from free energy can be reconverted into electrical work (e.g. via a steam turbine), an MCFC stack's direct conversion of free energy is intrinsically more efficient. Therefore, networking MCFC stacks in series results in more efficient power production even when waste heat is recovered. Although each stack added to a series network would improve the system's efficiency, the incremental benefit obtained with each additional stack diminishes. A finite number of stacks could adequately, but not exactly, approach a reversible process. In a practical network, the number of stacks would be limited by economic, space, and design constraints. 8-85PDF Image | Fuel Cell Handbook (Seventh Edition)
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