My work focuses on the theory and application of networked dynamical systems with a special emphasis on power-system physics, machine learning, and graph-based modeling. I study how flows, constraints, and feedback interact across physical, computational, and economic layers of modern energy infrastructures, and how these interactions shape system behavior across different temporal and spatial scales.
1. Mathematical and Graph-Theoretic Foundations
I develop mathematical tools that unify the study of complex networks across physical, cyber, and economic domains.
My work includes:
- Graph and multigraph representations of energy and infrastructure systems
- Incidence matrices, weighted Laplacians, and reduced forms
- Linearized flow operators such as power transfer distribution factors and line outage distribution factors
- Convex analysis, duality, and operator-theoretic formulations
- Multi-layer graph structures for modeling interactions among physical, informational, and economic layers
These methods provide a unified framework for understanding stability, controllability, and global behavior in large-scale networks.
2. Physical Network Dynamics and Power-Flow Structure
I study how physical laws determine the movement of energy across a network and how disturbances propagate through the grid.
Areas of focus include:
- Linear and nonlinear power-flow relations
- Dynamics derived from conservation laws and graph structure
- Modal analysis of oscillatory behavior and electromechanical interactions
- Sensitivity of flows to contingencies, switching actions, and topology changes
- Flow–potential relationships and the geometry underlying system response
This work builds a systematic understanding of how physical constraints shape real-time grid behavior.
3. Optimization, Control, and Multi-Scale Coordination
Modern power grids operate as equilibria of interconnected optimization and control processes.
I investigate both the mathematical structure and the practical algorithms that govern these systems:
- Network-constrained optimization and relaxations
- Distributed and decomposition-based coordination
- Feedback control as dynamic optimization
- Multi-rate operation across physical, operational, and economic time scales
- Learning-enabled optimization under changing system conditions
These ideas connect the mathematics of optimization with real-world grid operations.
4. Machine Learning, Phasor Measurement Intelligence, and Data-Driven Methods
I develop machine learning and statistical methods for real-time situational awareness using high-frequency data from phasor measurement units.
Event Identification and Oscillation Analysis
- End-to-end event detection based on modal structure and machine learning
- Semi-supervised techniques that reduce reliance on labeled data
- Localization of forced oscillations using sparse and subspace-based methods
- Signal processing pipelines for operational intelligence
Inertia and System Strength Forecasting
- Inertia estimation and spatial strength metrics from high-resolution data
- Continual learning and meta-learning for evolving topology
- Robust algorithms for uncertainty in load, renewable generation, and dispatch
This work integrates physics-informed modeling with modern learning techniques.
5. Electricity Markets, Congestion Geometry, and Economic Coordination
I study how physical network constraints shape economic outcomes in electricity markets and how market mechanisms interact with grid physics.
- Simulation and analysis of large-scale market operations
- Formation of locational marginal prices as dual variables of network-constrained optimization
- Modeling of congestion, redispatch, and economic efficiency
- Intertemporal scheduling and operational limitations
- Geometric interpretation of congestion based on network sensitivity structure
This unifies physical flow modeling with economic decision processes.
6. Resilience, Reliability, and Extreme-Event Modeling
I investigate how networks respond to uncertainty, rare events, and structural disruptions.
- Quantification of resilience under uncertainty
- Validation using high-fidelity Monte Carlo simulation
- Graph-theoretic analysis of islanding, restoration, and survivability
- Modeling of distributed energy resources and microgrid coordination
This work integrates uncertainty modeling with the structure of physical networks.
7. Cyber-Physical Networks and Multi-Layer Interactions
Energy systems operate through tightly coupled physical, communication, and computational processes.
I study how these layers interact and how risk propagates across them.
- Communication network modeling for grid applications
- Mapping between communication demands and computational resources
- Coupling among physical flows, communication delays, and control decisions
- System-level risk arising from interconnected cyber-physical processes
This work builds an integrated view of infrastructure that spans multiple layers of operation.
8. Broader Systems and Cross-Domain Network Insights
Beyond energy systems, I explore general principles that govern complex networks in many domains.
- Emergence of collective behavior from local interactions
- Interplay among information flow, influence, and resource exchange
- Stability, resilience, and adaptation in interconnected dynamical systems
These insights support the analysis and design of complex engineered, social, and natural systems.