Multiple STATCOM units in proximity have been adopted in power transmission systems in order to obtain better voltage regulation and share burdens. Throughout stability assessment in this dissertation, it is shown, for the first time, that STATCOMs could interact with each other in a negative way in the small-signal sense due to their control, causing voltage instability, while loads and transmission lines showed small effects. Since this voltage stability problem is induced by STATCOMs, d-q frame impedance-based stability analysis was used, for the first time, to explore the inherent power system instability problem with presence of STATCOMs as it provides an accurate understanding of the root cause of instability within the STATCOM control system. This dissertation first proposes the impedance model in d-q frame for STATCOMs, including dynamics from synchronization, current and voltage loops and reveals the significant features compared to other types of grid-tied converters that 1) impedance matrix strongly coupled in d and q channel due to nearly zero power factor, 2) different behaviors of impedances at low frequency due to inversed direction of reactive power and 3) coupled small-signal propagation paths on the voltage at point of common coupling from synchronization and ac voltage regulation. Using the proposed impedance model, this dissertation identifies the frequency range of interactions in a viewpoint of d-q frame impedances and pinpointed that the ac voltage regulation was the main reason of instability, masking the effects of PLL in power transmission systems. Due to the high impedance of STATCOMs compared to that of transmission lines around the frequency range of interactions, STATCOMs were seen to interact with each other through the transmission lines. A scaled-down 2-STATCOM power grid was built to verify the conclusions experimentally. / Ph. D. / STATCOMs have been proven a type of effective power electronics device for reactive power compensations and people are trying to install multiple STATCOMs in proximity in power systems in order to have better performances. This dissertation, for the first time, evaluates the operation of multiple STATCOMs in proximity and finds out that they could interact with each other in a negative way in the small-signal sense due to their control, causing voltage instability, while loads and transmission lines showed small effects. Since this voltage stability problem is induced by STATCOMs, d-q frame impedance-based stability analysis was used, for the first time, to explore the inherent power system instability problem with presence of STATCOMs as it provides an accurate understanding of the root cause of instability within the STATCOM control system. To this end, an impedance model of STATCOMs is proposed, which accurately explains the terminal behaviors of STATCOMs. Using the model, this dissertation identifies the frequency range of interactions in a viewpoint of d-q frame impedances and pinpointed that the ac voltage regulation was the main reason of instability, masking the effects of PLL in power transmission systems. All the above is validated experimentally in a scaled-down 2-STATCOM power system.

With development of renewable energies worldwide, power system is seeing higher penetration of Utility-scale photovoltaic (PV) farms at distributed level as well as transmission level. Power electronics converters present negative incremental impedance characteristics at their input while under regulated output control, which brings in the possibility of system instability. Recent evidence suggests that large-scale penetration of PV inverters increases the probability of instability. While IEEE standard 1547 newest version requires PV inverters to have reactive power control, there have been few investigations into the small-signal stability impact of PV inverters on distribution systems especially with reactive power control. In addition, the existing studies either use the conventional way of state space equations and eigenvalues or use time-domain simulation methodology, which are based on the assumptions that detailed models of the grid and the PV inverters are accessible. Different from the previous literatures, this research employs Generalized Nyquist Criterion (GNC) method based on measured impedances in d-q frames at connection interfaces. GNC method has the advantage that interconnection stability can be judged without knowing the grid and PV generator model details. This work first demonstrates the advantage of volt-var droop mode control among all different local reactive power control modes for PV inverters in the aspects of static impact on grid voltage profiles and power loss in a 12kV test-bed distribution system. Then it is discovered that d-q frame impedance of PV inverter under volt-var droop mode control shows a significant difference from other reactive power control modes. The d-q frame impedance derived from the small-signal model of PV generator is validated by both MATLAB simulation results and hardware experiments. Based on the d-q frame impedances, GNC is utilized to analyze the stability connection of a single PV farm and multiple PVs into the grid. GNC stability assessment results match with time-domain simulations and reveal the stability problem related to volt-var droop mode control. Furthermore, considering the unbalance of the distribution system, a new impedance model in d-q frame is proposed to capture both the dynamics of PV inverter operating in unbalanced points and the dynamics of three-phase unbalanced grid. The new impedance model is a combination of positive-negative sequence impedance and conventional d-q frame impedance. A procedure is designed for the measurement of the extended d-q frame impedance and the GNC application to predict small-signal stability of the unbalanced grid, which are justified by both time domain simulation and hardware experiments. / Doctor of Philosophy / To overcome the limited fossil fuel reserve on the earth and global warming, renewable energies become more and more popular worldwide. Centralized thermal power generators in the transmission system are gradually being replaced by distributed energy resources (DER) which are connection to the distribution system, bringing more challenges to the safe and stable operation of the power system. This work focuses on the small-signal stability impact of photovoltaic (PV) generators in the distribution system, which basically analyzes into whether the connection of PV generator to the distribution system will end up in an expected steady operation state with high resistance to any relatively small disturbances. The stability assessment tool is based on impedance measurement which treats both sides as black boxes and bridges the information gap between Utility operators and PV generator vendors. A major finding of this work is that while PV generators in the distribution system help to provide grid-support functions of voltage regulation, they may cause voltage small-signal stability problems due to the high grid impedance, which is worse if more PV inverters are put in parallel. Even PV farms connected to different branches of the complicated radial distribution system may have interactions with each other. So the design of control strategy and parameters of PV generator should consider the impact of other PV generators. GNC method based on impedances measurement is feasible and accurate for stability assessment of a distribution system with multiple PV farms. The impedance based method is upgraded and extended to be applied for the connection of power electronics devices to the three-phase unbalanced distribution systems.