能源問題是當今全球關注的焦點，燃料電池正是極具發展潛力的能源，然而對於燃料電池實際應用仍不廣泛。由於早期高溫燃料電池在製造與運作過程中面臨許多技術性問題，爾後轉向發展中、低溫燃料電池，不僅對於燃料電池電極材料與電解液的優化如火如荼的在進行，複合動力系統也是發展的重點之一。為了有效地模擬固態氧化物燃料電池與史特林引擎複合動力系統的功率與效率輸出，本文以基因演算法求出系統最大效率發生時的未知參數值。
本文設計一複合系統確保固態氧化物燃料電池始終處於運轉狀態且應用電化學、有限時間熱力學理論和考慮輻射熱傳的效應建立複合動力系統模型，並且與過往文獻相較加入熱傳過電壓對固態氧化物燃料電池的影響。除此之外為了使模型更貼近現實也建立包含高低溫熱儲之間的熱漏以及史特林引擎非理想回熱等不可逆損失。推導出複合系統功率與效率表示式，以系統效率作為基因演算法之目標函數、燃料電池與史特林熱機耦合之能量方程式作為非線性不等式限制式，求出系統在最大功率下的最佳化參數。
本研究得出的結論包含固態氧化物燃料電池工作電壓受到活性過電壓、歐姆過電壓、濃度過電壓以及熱傳過電壓四種不同因素造成的壓降後，最終輸出電壓在電流密度 5000、 10000、 15000(A/m^2)時分別只有理論最大電壓的 52.9%、 30.9%、 13.1%，並且隨著電流密度增加逐漸趨近於零；燃料利用率若高過0.75則混合動力系統無明顯之最佳效率存在，在熱交換器效率為0.7時燃料利用率以低於0.95為上限，否則燃料電池將無足夠能量保持持續運轉；此外，整體而言各項不可逆參數越低、熱交換器效率越高則系統會有較佳的性能表現，然而熱交換器效率一方面也影響史特林引擎高溫熱儲溫度進而影響史特林引擎一個完整循環所需時間，因此在不同電流密度時熱交換器效率對於系統的影響並非全然有助益的。

Energy is a main issue all over the world recently. Fuel cells are fast-growing energy which is still not applied widely. Due to many technical problems that take place in manufacturing and operating of high temperature fuel cells, medium and low temperature fuel cells are spring up gradually. The optimization of electrode and electrolyte materials of fuel cells is in full swing, and hybrid power systems are also being developing. Thus, a genetic algorithm is introduced in this research in order to simulate the solid oxide fuel cell (SOFC) and Stirling engine hybrid system effectively, and calculate the unknown parameters when the system efficiency is maximum.
A layout of hybrid power system is presented in this paper in order to ensure that the SOFC is always in operation. Moreover, electrochemistry, finite-time thermodynamics and radiation heat transfer are considered in this system. Compared with literatures, the influence of thermal overpotential is introduced. Heat loss between heat reservoirs and non-ideal regenerator heat loss are included to make the hybrid system close to reality. The power and efficiency equations of the hybrid system are derived, and the former is took as the objective function of genetic algorithm. The energy equation which coupled by the SOFC and the Stirling engine is used as a non-linear constraint to find the optimal parameters of the hybrid system at maximum efficiency.
The present study conclude that when the hybrid system is suffered from activation, ohmic, concentration and thermal overpotentials, the output voltage at current density 5000, 10000 and 15000(A/m^2) are 52.9%, 30.9% and 13.1% of theoretical maximum voltage respectively, and gradually approach zero as the current density increases. If fuel utilization is higher than 0.75, the hybrid system would be no maximum efficiency. Fuel utilization need to be lower than 0.95 when the heat exchanger efficiency is 0.7, or the SOFC cannot be able to operate continuously. Furthermore, in general, the lower the irreversible parameters and the higher the efficiency of the heat exchanger, the better the performance of the system will be. However, under low current density, the efficiency of the heat exchanger also affects the heat source temperature of the Stirling engine, which makes the cycle time required of the Stirling engine longer. Hence, the effect of heat exchanger efficiency on the system at different current densities is not entirely helpful.

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