The goal of this study was to evaluate the small signal and transient stability of the Western Electricity Coordinating Council (WECC) under high penetrations of renewable energy, and to identify control technologies that would improve the system performance. The WECC is the regional entity responsible for coordinating and promoting bulk electric system reliability in the Western Interconnection. Transient stability is the ability of the power system to maintain synchronism after a large disturbance while small signal stability is the ability of the power system to maintain synchronism after a small disturbance. Transient stability analysis usually focuses on the relative rotor angle between synchronous machines compared to some stability margin. For this study we employed generator speed relative to system speed as a metric for assessing transient stability. In addition, we evaluated the system transient response using the system frequency nadir, which provides an assessment of the adequacy of the primary frequency control reserves. Small signal stability analysis typically identifies the eigenvalues or modes of the system in response to a disturbance. For this study we developed mode shape maps for the different scenarios. Prony analysis was applied to generator speed after a 1.4 GW, 0.5 second, brake insertion at various locations. Six different WECC base cases were analyzed, including the 2022 light spring case which meets the renewable portfolio standards. Because of the difficulty in identifying the cause and effect relationship in large power system models with different scenarios, several simulations were run on a 7-bus, 5-generator system to isolate the effects of different configurations. Based on the results of the study, for a large power system like the WECC, incorporating frequency droop into wind/solar systems provides a larger benefit to system transient response than replacing the lost inertia with synthetic inertia. From a small signal stability perspective, the increase in renewable penetration results in subtle changes to the system modes. In general, mode frequencies increase slightly, and mode shapes remain similar. The system frequency nadir for the 2022 light spring case was slightly lower than the other cases, largely because of the reduced system inertia. However, the nadir is still well above the minimum load shedding frequency of 59.5 Hz. Finally, several discrepancies were identified between actual and reported wind penetration, and additional work on wind/solar modeling is required to increase the fidelity of the WECC models.
This report contains the results of a research effort on advanced robot locomotion. The majority of this work focuses on walking robots. Walking robot applications include delivery of special payloads to unique locations that require human locomotion to exo-skeleton human assistance applications. A walking robot could step over obstacles and move through narrow openings that a wheeled or tracked vehicle could not overcome. It could pick up and manipulate objects in ways that a standard robot gripper could not. Most importantly, a walking robot would be able to rapidly perform these tasks through an intuitive user interface that mimics natural human motion. The largest obstacle arises in emulating stability and balance control naturally present in humans but needed for bipedal locomotion in a robot. A tracked robot is bulky and limited, but a wide wheel base assures passive stability. Human bipedal motion is so common that it is taken for granted, but bipedal motion requires active balance and stability control for which the analysis is non-trivial. This report contains an extensive literature study on the state-of-the-art of legged robotics, and it additionally provides the analysis, simulation, and hardware verification of two variants of a proto-type leg design.