Distributed Conditions for Small-Signal Stability of Power Grids and Local Control Design

Operating modern power grids with stability guarantees is markedly important. Typical methods for analyzing and certifying power grid stability are largely centralized relying on the ability of the system operator to gather network-wide information and accurately compute the system's eigenvalues. These methods are oftentimes not privacy-preserving and computationally burdensome. They are therefore, not well-suited to modern power grids where small-signal stability has to be evaluated timely, efficiently and in a privacy-preserving fashion. In this paper, we introduce a distributed methodology for certifying small-signal stability of power grids and designing the local controllers. First, we analytically derive distributed conditions for network-wide stability that bus agents can inspect using local information. By leveraging these conditions, we then introduce a distributed control design algorithm (DCDA) that can guide the local control design so that stability of the interconnected system is guaranteed. The agents that adopt the proposed distributed algorithm are responsible for tuning their local controllers, producing their local control commands and ensuring that their local stability condition is met. The system operator is only responsible for verifying network-wide stability upon receiving affirmative responses from all agents and, announcing, that the overall system is stable. The proposed DCDA algorithm is numerically validated via simulations using the IEEE 39-bus system.