Fernando Paganini

Charalampos Avraam, Jesse Rines, Aurik Sarker et al.

Voltage collapse is a type of blackout-inducing dynamic instability that occurs when the power demand exceeds the maximum power that can be transferred through the network. The traditional (preventive) approach to avoid voltage collapse is based on ensuring that the network never reaches its maximum capacity. However, such an approach leads to inefficiencies as it prevents operators to fully utilize the network resources and does not account for unprescribed events. To overcome this limitation, this paper seeks to initiate the study of voltage collapse stabilization. More precisely, for a DC network, we formulate the problem of voltage stability as a dynamic problem where each load seeks to achieve a constant power consumption by updating its conductance as the voltage changes. We show that such a system can be interpreted as a dynamic game, where each player (load) seeks to myopically maximize their utility, and where every stable power flow solution amounts to a Local Nash Equilibrium. Using this framework, we show that voltage collapse is equivalent to the non-existence of a Local Nash Equilibrium in the game and, as a result, it is caused by the lack of cooperation between loads. Finally, we propose a Voltage Collapse Stabilizer (VCS) controller that uses (flexible) loads that are willing to cooperate and provides a fair allocation of the curtailed demand. Our solution stabilizes voltage collapse even in the presence of non-cooperative loads. Numerical simulations validate several features of our controllers.

Fernando Paganini, Enrique Mallada

The issue of synchronization in the power grid is receiving renewed attention, as new energy sources with different dynamics enter the picture. Global metrics have been proposed to evaluate performance and analyzed under highly simplified assumptions. In this paper, we extend this approach to more realistic network scenarios and more closely connect it with metrics used in power engineering practice. In particular, our analysis covers networks with generators of heterogeneous ratings and richer dynamic models of machines. Under a suitable proportionality assumption in the parameters, we show that the step response of bus frequencies can be decomposed in two components. The first component is a {system-wide frequency} that captures the aggregate grid behavior, and the residual component represents the individual bus frequency deviations from the aggregate. Using this decomposition, we define --and compute in closed form-- several metrics that capture dynamic behaviors that are of relevance for power engineers. In particular, using the \emph{system frequency}, we define industry-style metrics (Nadir, RoCoF) that are evaluated through a representative machine. We further use the norm of the residual component to define a \emph{synchronization cost} that can appropriately quantify inter-area oscillations. Finally, we employ robustness analysis tools to evaluate deviations from our proportionality assumption. We show that the system frequency still captures the grid steady-state deviation, and becomes an accurate reduced-order model of the grid as the network connectivity grows. Simulation studies with practically relevant data are included to validate the theory and further illustrate the impact of network structure and parameters on synchronization. Our analysis gives conclusions of practical interest, sometimes challenging the conventional wisdom in the field.

Fernando Paganini, Enrique Mallada

A recent trend in control of power systems has sought to quantify the synchronization dynamics in terms of a global performance metric, compute it under very simplified assumptions, and use it to gain insight on the role of system parameters, in particular, inertia. In this paper, we wish to extend this approach to more realistic scenarios, by incorporating the heterogeneity of machine ratings, more complete machine models, and also to more closely map it to classical power engineering notions such as Nadir, Rate of Change of Frequency (RoCoF), and inter-area oscillations. We consider the system response to a step change in power excitation, and define the system frequency as a weighted average of generator frequencies (with weights proportional to each machine's rating); we characterize Nadir and RoCoF by the $L_\infty$ norm of the system frequency and its derivative, respectively, and inter-areas oscillations by the $L_2$ norm of the error of the vector of bus frequencies w.r.t. the system frequency. For machine models where the dynamic parameters (inertia, damping, etc.) are proportional to rating, we analytically compute these norms and use them to show that the role of inertia is more nuanced than in the conventional wisdom. With the classical swing dynamics, inertia constant plays a secondary role in performance. It is only when the turbine dynamics are introduced that the benefits of inertia become more prominent.