Synchronous machines (SMs) are a vital part of today's world, and precise modeling is important for studying their stability. In this thesis, a small-signal analysis is done on the d-q frame for the AC SM. Starting from formulating the SM's abc frame equations, a d-q transformation is done based on the SM rotor frame so that the inductance from the abc frame representation will be fixed. Then, the SM's fundamental parameters are obtained from standstill frequency response testing. In the interest of having the most complete model possible, a governor controller and an exciter controller have been designed, and their performance has been evaluated according to the International Standard ISO-8628. A d-q steady-state analysis has been carried out and the resulting small-signal perturbation has been added to the steady-state equations. The model has been analyzed with exciter control only, with governor control only, and with both controllers, and in the end, the small-signal d-q impedance model for the SM has been verified by simulations and experiments in the Center for Electronics Systems (CPES) at Virginia Tech. The impedance measurement unit (IMU) was built by CPES. It is designed for measuring three-phase AC power systems and DC systems. Nevertheless, even though the single-phase system can be connected to the IMU, the impedance result in the end is not correct. Modifications have been made to the IMU so that it is able to calculate the single-phase AC power system impedance. The experimental results demonstrate that implementation has been completed. / Master of Science / Emergency diesel generators are critical in the event of widespread blackouts. Generators are typically synchronous machines (SMs), and stability studies are crucial from the standpoint of the power system. With knowledge gained through stability analysis, if instability occurs, a solution can be quickly formulated based on phenomena that has been observed during the event. In order to study the system stability, an accurate model is essential. The small-signal d-q impedance model will be derived by the Center for Power Electronics Systems (CPES) at Virginia Tech based on an AC generator that is rated at 28 kW, and the impedance results will be verified by both MATLAB/Simulink simulations and experiments. The impedance measurement unit (IMU) will serve as the equipment to do the measurement. However, the IMU can only correctly calculate impedance for a three-phase power system. For the single-phase AC power system, due to the three-phase phase locker loop (PLL) calculating the wrong angle, the IMU cannot properly determine the impedance. However, modifications have been applied to the IMU so that it can automatically calculate the impedance for a single-phase AC power system.