本文提出兩種先進能源系統之動態模型建立方法，其中包含： (i)自由活塞發電機之物理模型。此模型共包含17個狀態，其中包括活塞動態、發電機電流、歧管與汽缸之流體動態及熱動態模型。系統亦採用電子閥門與缸內直噴裝置使系統最佳化及降低汙染物排放。模擬結果顯示可透過切換進排氣時機、負載及燃油質量，使系統由SI模式切換至HCCI模式。(ii)含熱效應之超級電容等效電路模型。文獻中顯示超級電容之充放電特性受到端電壓、溫度及操作頻率之影響，因此本論文提出一個包含熱效應及電壓效應之超級電容模型。此模型以超級電容在不同操作電壓及溫度之交流阻抗為基礎，鑑別出電容模型之參數。建立超級電容之動態模型後，擴展型卡爾曼濾波器則使用於對超級電容系統之充電狀態及溫度之估測。實驗結果得知由卡爾曼濾波器對充電狀態及溫度進行估測，可消除超級電容動態模型之誤差及量測雜訊並提供更精確的預測。

For the purpose of model-based analysis and control design, this thesis proposes two dynamic model of advanced electric energy system. (i): SI/HCCI free-piston engine generators (FPEGs). The physics-based model contains 17 states, which includes piston dynamics, alternator current, runners and cylinder gas filling dynamics and thermal dynamics. Homogeneous charge compression ignition (HCCI) combustion is employed for better efficiency and reduced emissions, whereas spark ignition (SI) combustion can be used quick start for the FPEG and higher power demand. Equipped with electric mechanical valves (EMVs) and direct injection, the free-piston engine generator is deemed to achieve optimized and clean combustion. Key features in this dynamic model include the runners and cylinder filling dynamics and cycle-to-cycle coupling between the piston motion and combustion process. Simulation results demonstrate that during a transition from SI to HCCI mode the scavenging process needs to be properly maintained so as to achieve trapped mass balance between the opposite cylinders and thus regulation of the compression ratio. (ii): Ultracapacitor (UC) model including thermal behavior. The performance and life expectancy of ultracapacitors depend heavily on the operating voltage and temperature. At this part, simultaneous estimation of state-of-charge (SOC) and temperature is achieved by applying extended Kalman filter (EKF) algorithm with only the terminal measurement of voltage and current. For the application of EKF algorithm, a nonlinear model which consists of a voltage-and-thermal-dependent equivalent circuit model and a thermal model is first developed. The parameters in the equivalent circuit model are identified by applying least squares method with weightings at different frequencies so as to achieve satisfactory prediction over the whole applicable frequency ranges. Experimental results demonstrate that the EKF-based estimator is crucial in providing accurate and consistent prediction of SOC and temperature in existence of modeling errors and measurement noises, especially during dynamic charge/discharge cycles at low temperature. The accurate estimation of SOC and temperature enables optimum energy and thermal management of ultracapacitors.

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