Accelerating the energy transition toward systems based on low-cost renewable feedstocks and diverse energy sources is imperative. Solid oxide fuel cell (SOFC) technology represent a promising solution, offering high conversion efficiency, fuel flexibility, and combined heat and power capabilities. While material development has reached maturity, the field still lacks systematic and comprehensive investigation across multiple scales: from fundamental electrochemical processes in single cells to system-level challenges including control optimization and degradation criteria in compact CHP units. This thesis systematically investigates the electrochemical performance of Ni-GDC electrolyte supported cells (ESCs) from single-cell to system levels, based on which the control optimization algorithm and the degradation criteria are developed. Chapter 1 introduces SOFC technology and its comparative advantages. Chapter 2 employs electrochemical impedance spectroscopy (EIS) with distribution of relaxation times, equivalent circuit model , and complex nonlinear least square fit to deconvolute single-cell processes, identifying dominant resistances in gas conversion (0.1-1 Hz), O$^{2-}$ surface exchange in GDC (0.1-10 Hz), coupled gas diffusion/surface exchange (1-50 Hz), and charge transfer (>50 Hz). Chapter 3 examines degradation mechanisms under biogas reformate conditions with and without sulfur poisoning. EIS analysis indicated that major degradation originated from ohmic resistance and electrode charge transfer resistances. Sulfur poisoning tests demonstrated H$_2$S causes irreversible degradation, while degradation caused by dimethyl sulfide were fully reversible. Active negatrode GDC surface reaction was identified as the main contributor of better sulfur resistance than the Ni-YSZ anode supported cell. At the system level (Chapter 4), a Ό-CHP SOFC system was characterized under operational extremes. EIS and total harmonic distortion analysis identified fuel starvation thresholds (safe utilization factor <81%) and diagnostic markers (0.01-0.1 Hz excitation). Carbon deposition tests and long-term operation confirmed system stability. The hierarchical analysis from single cell to compact system allowed for the control and optimization of the system with clear operating boundary. Chapter 5 presents a constraint-adaptation real-time optimization algorithm that reached set power target within 15 minutes and improved electrical efficiency by 5%. The algorithm showed satisfying robustness against natural gas grid fluctuations. Chapter 6 compares static control strategies (fixed power/voltage/temperature) based on different end-of-life (EoL) criteria, including power loss, voltage reduction, and cumulative energy degradation. Cumulative energy degradation was identified as a reliable EoL criteria under dynamic operation. This work provides fundamental insights into electrochemical process deconvolution for Ni-GDC ESCs and establishes diagnostic methodologies for fault conditions of stacks and systems. The integrated pathway---combining advanced characterization, real-time optimization algorithms, and novel EoL criteria---offers a universal framework to accelerate solid oxide cell technology deployment. The proposed approaches address critical challenges in performance optimization and lifetime prediction, advancing fuel cell and electrolysis technology toward commercial viability.