A Hybrid System Approach to the Analysis and Design of Power Grid Dynamic Performance

Abstract

We describe an approach to the analysis and design of power grid dynamic performance based on hybrid systems theory. Power grid is a large-scale Cyber-Physical System for transmission of electrical energy. The joint dynamics of physical processes and cyber elements in power grids are typical of a mixture of continuous and discrete behaviors, that is, hybrid dynamics. We address problems on stability that are basic concerns in the performance of current and future power grids with the hybrid dynamics. Measures for stability of power grids are interpreted as safety specifications in hybrid system models and are translated into restrictions on the systems' reachable sets of states. Algorithmic reachability analysis of hybrid systems enables analysis of safe initial states and hence quantitative estimation of stability regions. Also it contributes to synthesis of safe initial states as well as switching conditions in order to satisfy safety specifications in a power grid. We demonstrate the approach for two problems on transient stability of the single machine-infinite bus system and on fault release control of a multi-machine power grid.

Research on Cyber-Physical Modeling for Smart Distribution Grid

“…However, due to the heterogeneity of physical system and cyber system, the modeling of the physical layer and cyber layer is fragmented, and building a fusion model is very difficult. The method of hybrid system modeling is adopted in reference [5], which embodies the characteristics of cyber-physical system, but it cannot fully reflect the fusion of physical system and cyber system. So far there is no unified modeling method of cyber-physical system.…”

Hybrid controller for safe microgrid operation

“…We refer to (q, x) ∈ Q × X as the state of H and to (σ, v) ∈ Σ × V as the input of H. Note that a simpler HA model is used for the analysis and design of power grids [20,21]. Properties (e.g., existence and uniqueness) of trajectories in H are a challenging subject by itself: see [10] and references therein.…”

“…A (backward) reachable set is defined as a collection of all possible trajectories of H arriving at G in some time. The reachable set is denoted by P re(G, H) in the same manner as [20,21]. A finite-time (backward) reachable set is also defined as a collection of all possible trajectories arriving at G in a prescribed finite time T , denoted by P re T (G, H).…”

“…, 5 and ω g(critical) stands for the critical value of ω g . The choice of G| X aims to avoid large deviations of rotor speed that potentially lose synchronism with respect to the infinite bus [21,29]. We also define the set Init(q i ) of initial states in X at the discrete state q i as…”

Compositional transient stability analysis of power systems via the computation of reachable sets

“…This makes it possible to estimate a region of attraction from which one can identify the initial states of the post-fault scenario that converge back to the equilibrium. Along the same lines, the contributions presented in [22], [23] formulate power systems as a hybrid automatan to compute forward reachable sets using techniques based on LSMs for hybrid systems.…”