Thirty-five years of Pai and

Still Hungry for MorePete Sauer

Grainger Chair Professor of Electrical Engineering

October 15, 2015

First of all - welcome back!!

George Swenson (Head 1979-1985) withPetar Kokotovic and Les Fink

1981 - The first named professor in the UIUC College of Engineering

Mangalore Anantha PaiGrainger Professor

3.14159265358979323

In a 1988 report to the Grainger Foundation,M. E. VanValkenburg

(Grainger Professor and Dean of Engineering) presented:

Faculty change since 1978

Lost 4

P. R. Egbert (retired)M. S. Helm (retired)D. F. Hang (retired)R. W. Burtness (retired)

Gain 4

P. W. SauerM. A. PaiM. IlicP. T. Krein

1982 – 2014 (90 papers – next 14 slides)

K. D. Demaree, M. A. Pai and P. W. Sauer, "Trajectory Approximations and

Iterative PEBS Method in Direct Stability Analysis"

S. Ahmed-Zaid, P. W. Sauer, M. A. Pai and M. K. Sarioglu, "Reduced Order

Modelling of Synchronous Machines Using Singular Perturbations“

P. W. Sauer, I. N. Hajj, M. A. Pai and T. N. Trick, "Computer Methods in Electric

Network Analysis"

S. Ahmed-Zaid, P. V. Kokotovic, M. A. Pai and P. W. Sauer, "Dynamic

Aggregation in Higher Order Multi-machine Models"

P. W. Sauer, K. D. Demaree and M. A. Pai, "Stability Limited Load Supply and

Interchange Capability"

M. A. Pai, K. D. Demaree and P. W. Sauer, "Transient Energy Margins and

Sensitivity Models for Dynamic Security Assessment”

P. W. Sauer, S. Ahmed-Zaid and M. A. Pai, "Systematic Inclusion of Stator

Transients in Reduced Order Synchronous Machine Models"

M. A. Pai, P. W. Sauer and K. D. Demaree, "Direct Methods of Stability Analysis

in Dynamic Security Assessment"

P. W. Sauer and M. A. Pai, "Electric Utilities and Universities Staying Ten Years

Ahead-Together”

P. W. Sauer, J. P. Christensen and M. A. Pai, "Piecewise Linear Transient

Stability Analysis Using Direct Integration Energy Evaluation"

M. A. Pai, K. Khorasani and P. W. Sauer, "Multi-machine Stability Analysis Using

Time Scale Decomposition"

M. A. Pai, P. W. Sauer and K. Khorasani, "Singular perturbations and large scale

power system stability"

P. W. Sauer, S. Ahmed-Zaid and M. A. Pai, "Nonlinear decoupling in a class of

quadratic two-time-scale systems with applications to synchronous machines"

P. V. Kokotovic, P. W. Sauer and M. A. Pai, "The slow manifold in power system

dynamic models”

J. H. Chow, J. R. Winkelman, M. A. Pai and P. W. Sauer, "Application of singular

perturbations theory to power system modeling and stability analysis"

M. Martina, M. A. Pai and P. W. Sauer, "Torque-angle loop analysis of power

systems with improved machine model"

A. K. Behera, M. A. Pai and P. W. Sauer, "Analytical approaches to determine

critical clearing time in multi-machine power system"

K. Khorasani, M. A. Pai and P. W. Sauer, "Modal-based stability analysis of

power systems using energy functions"

P. W. Sauer, D. J. LaGesse, S. Ahmed-Zaid and M. A. Pai, "Reduced-order

modeling of interconnected multi-machine power systems using time-scale

decomposition"

P. W. Sauer, C. Rajagopalan, M. A. Pai and A. Varghese, "Critical modes and

voltage instability in power systems"

J. H. Chow, J. R. Winkelman, M. A. Pai and P. W. Sauer, "Model reduction and

energy function analysis of power systems using singular perturbation

techniques"

M. A. Pai, P. W. Sauer, H. Othman, J. H. Chow and J. R. Winkelman,

"Decoupled stability analysis of large scale power systems using integral

manifold approach"

M. A. Pai, H. Othman, P. W. Sauer, J. H. Chow and J. R. Winkelman,

"Application of integral manifold theory in large scale power system stability

analysis"

P. W. Sauer, A. K. Behera, M. A. Pai, J. R. Winkelman and J. H. Chow,

"Trajectory Approximations For Direct Methods That Use Sustained Faults With

Detailed Power System Models"

P. W. Sauer, M. A. Pai, M. Ilic and P. T. Krein, "The Electric Power Engineering

Program at UIUC"

P. W. Sauer, A. K. Behera, M. A. Pai, J. R. Winkelman and J. H. Chow, "A Direct

Method for Transient Stability Analysis of Power Systems With Detailed Models"

C. Rajagopalan, P. W. Sauer and M. A. Pai, "Steady-State Stability Analysis in

Power Systems: Comparison of Algorithms”

F. Dobraca, M. A. Pai and P. W. Sauer, "Dynamic Security Assessment Including

Relay Performance"

A. Varghese, P. W. Sauer and M. A. Pai, "Time Scale Analysis of Excitation

Control"

M. A. Pai, P. W. Sauer and F. Dobraca, "A New Approach to Transient Stability

Evaluation in Power Systems"

M. A. Pai and P. W. Sauer, "Stability Analysis of Power Systems by Lyapunov's

Direct Method"

A. Varghese, P. W. Sauer and M. A. Pai, "Synchronous Machine Block Diagram

Analysis With Fast Dynamics"

C. Rajagopalan, P. W. Sauer and M. A. Pai, "An Integrated Approach to Dynamic

and Static Voltage Stability"

P. W. Sauer and M. A. Pai, "Power System Steady-State Stability and the Load-

Flow Jacobian"

M. A. Pai and P. W. Sauer, "New Approaches to Dynamic Security Assessment“

P. W. Sauer and M. A. Pai, "Steady-State Stability and Load Flow“

M. A. Pai and P. W. Sauer, "A Framework for Application of Generalized

Kharitonov's Theorem in the Robust Stability Analysis of Power Systems"

P. W. Sauer, C. Rajagopalan and M. A. Pai, "An Explanation and Generalization

of the AESOPS and PEALS Algorithms"

J. H. Chow, J. R. Winkelman, M. A. Pai and P. W. Sauer, "Singular Perturbation

Analysis of Large-Scale Power Systems“

M. A. Pai, A. Y. Kulkarni and P. W. Sauer, "Parallel Dynamic Simulation of Power

Systems“

P. W. Sauer, R. J. Evans, Jr. and M. A. Pai, "Maximum unconstrained loadability

of power systems"

M. A. Pai, P. W. Sauer and K. R. Padiyar, "Direct methods in stability analysis in

power systems: future directions for research"

F. Dobraca, M. A. Pai and P. W. Sauer, "Fast dynamic simulation of power

systems for security assessment"

F. Dobraca, M. A. Pai and P. W. Sauer, "Relay margins as a tool for dynamic

security assessment"

J. T. Sterling, M. A. Pai and P. W. Sauer, "A methodology of secure and optimal

operation of a power system for dynamic contingencies“

P. W. Sauer and M. A. Pai, "Power system security in a less regulated

environment“

C. Rajagopalan, B. C. Lesieutre, P. W. Sauer and M. A. Pai, "Dynamic aspects of

voltage/power characteristics"

P. W. Sauer, B. C. Lesieutre and M. A. Pai, "Dynamic vs. static aspects of

voltage problems"

M. A. Pai and P. W. Sauer, "Mathematical issues in security enhancement of

large scale power systems,"

P. W. Sauer, B. C. Lesieutre and M. A. Pai, "Transient algebraic circuit models of

power systems

P. W. Sauer and M. A. Pai, "Modeling and simulation of multi-machine power

system dynamics”

M. A. Pai, P. W. Sauer and F. Dobraca, "A new trajectory approximation

technique for transient stability studies"

M. A. Pai, P. W. Sauer and R. K. Ranjan, "Robust Control Theory Application In

Power System Stability"

M. A. Pai, P. W. Sauer, A. Y. Kulkarni, "Conjugate Gradient Approach to Parallel

Processing in Dynamic Simulation of Power Systems"

M. A. Pai, P. W. Sauer, A. Y. Kulkarni, "Conjugate Gradient Approach to Parallel

Processing in Dynamic Simulation of Power Systems"

T. J. Overbye, M. A. Pai and P. W. Sauer, "A Composite Framework for

Synchronous and Voltage Stability in Power Systems"

B. C. Lesieutre, P. W. Sauer and M. A. Pai, "Sufficient Conditions on Static Load

Models for Network Solvability"

R. K. Ranjan, M. A. Pai and P. W. Sauer, "Steady State Stability In Power

Systems With Nonlinear Voltage Dependent Loads"

T. J. Overbye, M. A. Pai and P. W. Sauer, "Some Aspects of the Energy Function

Approach to Angle and Voltage Stability Analysis in Power Systems"

P. W. Sauer, B. C. Lesieutre and M. A. Pai, "Maximum Loadability and Voltage

Stability in Power Systems"

P. W. Sauer, B. C. Lesieutre and M. A. Pai, "Transient Algebraic Circuits for

Power System Dynamic Modeling“

M. A. Pai, P. W. Sauer, B. C. Lesieutre and R. Adapa, "Structural Stability in

Power Systems: Effect of Load Models"

M. A. Pai, M. Laufenberg and P. W. Sauer, "Evaluation of Path Dependent

Integrals in the Energy Function Method"

B. C. Lesieutre, P. W. Sauer and M. A. Pai, "Why Power/Voltage Curves Are Not

Necessarily Bifurcation Diagrams“

P. W. Sauer, M. A. Pai and S. J. Zhao, "Phasor Representations of Power

System Transients"

R. K. Ranjan, M. A. Pai and P. W. Sauer, "Analytical Formulation of Small Signal

Stability Analysis of Power Systems with Nonlinear Load Models"

M. A. Pai, R. K. Ranjan and P. W. Sauer, "Robust Stability In Power Systems

With Nonlinear Loads Using Generalized Kharitonov's Theorem”

B. C. Lesieutre, P. W. Sauer and M. A. Pai, "Development and Comparative

Study of Induction Machine Based Dynamic P, Q Load Models"

P. W. Sauer and M. A. Pai, "A Comparison of Discrete vs Continuous Dynamic

Models of Tap-Changing-Under-Load Transformers”

M. A. Pai, P. W. Sauer, and A. Y. Kulkarni, "A preconditioned iterative solver for

dynamic simulation of power systems”

C. D. Vournas, M. A. Pai, P. W. Sauer, "The Effect of Automatic Voltage

Regulation on the Bifurcation Evolution in Power Systems”

M. A. Pai, P. W. Sauer, and B. C. Lesieutre, "Static and dynamic nonlinear loads

and structural stability in power systems“

C. D. Vournas, P. W. Sauer, and M. A. Pai, "Time-scale decomposition in voltage

stability analysis of power systems”

M. A. Pai, M. Laufenberg and P. W. Sauer, "Some Clarifications in the transient

energy function method“

C. D. Vournas, P. W. Sauer, and M. A. Pai, "Relationships between voltage and

angle stability of power systems”

A. Y. Kulkarni, M. A. Pai, and P. W. Sauer, "Power System Dynamic Response

Calculations Using Krylov Subspace Method“

C. D. Vournas, P. W. Sauer, and M. A. Pai, "Critical Eigenvalue Computation in

Partly Regulated Power Systems“

C. D. Vournas, M. A. Pai, and P. W. Sauer, "Power System Stability Analysis

Using Singular Perturbation”

A. Y. Kulkarni, M. A. Pai, and P. W. Sauer, "Parameter Tuning of the GMRES

Method for Dynamic Simulation of Power Systems“

S. R. Fernandes, P. W. Sauer, and M. A. Pai, "Quantification of Parameter

Importance in Power Systems Steady-State Stability Analysis”

P. W. Sauer and M. A. Pai, "Power System Dynamics and Stability"

I. Hiskens, M. A. Pai and P. W. Sauer, "An Iterative Approach to Calculating

Dynamic ATC”

B. C. Lesieutre, P. W. Sauer and M. A. Pai, "Existence of Solutions for the

Network/Load Equations in Power Systems“

P. W. Sauer, C. Kammin, T. B. Nguyen, and M. A. Pai, "Transmission Line

Eigenvalues - Two to Infinity“

C. D. Vournas, G. Manos, P. W. Sauer and M. A. Pai, "Effect of Overexcitation

Limiters on Power System Long-Term Modeling”

A. Y. Kulkarni, M. A. Pai, and P. W. Sauer, "Iterative Solver Techniques in

Fast Dynamic Calculations of Power Systems“

P W. Sauer and M. A. Pai, “Relationships between power system dynamic

equilibrium, load flow, and operating point stability”

E. H. Abed, N. S. Namachchivaya, T. J. Overbye, M. A. Pai, P. W. Sauer and A.

Sussman, “Data-Driven Power System Operations”

S. Liu, Peter W. Sauer, D. Chaniotis and M. A. Pai, “Krylov Subspace and

Balanced Truncation Methods for Power System Model Reduction”

2001

2006

Energy

VPE + VKE = constant

dVPE /dt + dVKE /dt = 0