## Christopher DeMarco

**Grainger Professor of Power Engineering**

2544 Engineering Hall

1415 Engineering Drive

Madison, WI 53706

Ph: (608) 262-5546

Fax: (608) 262-1267

demarco@engr.wisc.edu

**Primary Affiliation**:

Electrical and Computer Engineering

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### Profile Summary

My research interests center on nonlinear stability and control theory, with particular emphasis on applications in electric power systems.My work in this area has focused on a number of topics. The first was the problem of identifying region-of-attraction estimates in systems described by ordinary differential equations with algebraic constraints, sometimes referred to as "semi-implicit" systems, but only recently have received attention in the literature on direct methods of transient stability analysis.Region-of-attraction estimates have important practical application in determining the ability of a power system to recover from line faults, load disturbances , and loss of generation. A second area of research in electric power systems involves illuminating the relationship between stability properties of deterministic models for the power system and exit-time statistics in a stochastic differential equation model having broad-band random disturbances in the load term. Using results from optimal control theory, we have demonstrated a closed form expression for the so-called "quasi potential" function for the power system, and shown its relationship to a standard deterministic Lyapunov function.This result offers considerable promise in yielding practically implementable algorithms to indicate in real time the vulnerability of the power system to such phenomena as voltage collapse. A third area of my research that ties developments in modern control theory with power systems applications, is the topic of "robust stability."A power system is a highly nonlinear system, whose operating point is continually changing in time.We are extending results in robust control theory to obtain a means of guaranteeing stable operation of the system over a whole range of operating points, and examining the development of algorithms for application to large scale systems.

- BS 1980, EE, Massachusetts Institute of Technology
- MS 1982, EE, University of California--Berkeley
- PhD 1985, EE, University of California--Berkeley

- computational complexity in computer-aided control analysis
- nonlinear dynamics
- electric power system stability
- control systems, power systems

#### Summer 2016

- ECE 699 - Advanced Independent Study

My research interests center on nonlinear stability and control theory, with particular emphasis on applications in electric power systems.My work in this area has focused on a number of topics. The first was the problem of identifying region-of-attraction estimates in systems described by ordinary differential equations with algebraic constraints, sometimes referred to as "semi-implicit" systems, but only recently have received attention in the literature on direct methods of transient stability analysis.Region-of-attraction estimates have important practical application in determining the ability of a power system to recover from line faults, load disturbances , and loss of generation. A second area of research in electric power systems involves illuminating the relationship between stability properties of deterministic models for the power system and exit-time statistics in a stochastic differential equation model having broad-band random disturbances in the load term. Using results from optimal control theory, we have demonstrated a closed form expression for the so-called "quasi potential" function for the power system, and shown its relationship to a standard deterministic Lyapunov function.This result offers considerable promise in yielding practically implementable algorithms to indicate in real time the vulnerability of the power system to such phenomena as voltage collapse. A third area of my research that ties developments in modern control theory with power systems applications, is the topic of "robust stability."A power system is a highly nonlinear system, whose operating point is continually changing in time.We are extending results in robust control theory to obtain a means of guaranteeing stable operation of the system over a whole range of operating points, and examining the development of algorithms for application to large scale systems.