A Theory of Solvability for Lossless Power Flow Equations -- Part II: Conditions for Radial Networks
arXiv:1701.02047 · doi:10.1109/TCNS.2017.2711859
Abstract
This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derived a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is parameterized by several graph-theoretic matrices -- the power network stiffness matrices -- which quantify the internal coupling strength of the network. In Part II, we leverage the fixed-point power flow to study power flow solvability. For radial networks, we derive parametric conditions which guarantee the existence and uniqueness of a high-voltage power flow solution, and construct examples for which the conditions are also necessary. Our conditions (i) imply convergence of the fixed-point power flow iteration, (ii) unify and extend recent results on solvability of decoupled power flow, (iii) directly generalize the textbook two-bus system results, and (iv) provide new insights into how the structure and parameters of the grid influence power flow solvability.
References in corpus (8)
- A Necessary Condition for Power Flow Insolvability in Power Distribution Systems with Distributed Generators
- Multistability of Phase-Locking in Equal-Frequency Kuramoto Models on Planar Graphs
- Toward Topologically Based Upper Bounds on the Number of Power Flow Solutions
- Exploring Synchronization in Complex Oscillator Networks
- Explicit Conditions on Existence and Uniqueness of Load-Flow Solutions in Distribution Networks
- Simple Certificate of Solvability of Power Flow Equations for Distribution Systems
- Solving the power flow equations: a monotone operator approach
- Convexity of Energy-Like Functions: Theoretical Results and Applications to Power System Operations
Cited by in corpus (6)
- Physics-Guided Deep Neural Networks for Power Flow Analysis
- Lossy DC Power Flow
- Multistability and anomalies in oscillator models of lossy power grids
- Multistability in lossy power grids and oscillator networks
- A Framework for Robust Steady-State Voltage Stability of Distribution Systems
- A Polynomial-Time Method for Testing Admissibility of Uncertain Power Injections in Microgrids