In this work, we propose a computationally feasible approachtodetect severe multiple contingencie... more In this work, we propose a computationally feasible approachtodetect severe multiple contingencies. We pose a contingency analysisproblem using a nonlinear optimization framework, which enables ustodetect the fewest possible transmission line outages resulting ina systemfailure of specified severity, and the most severe system failure causedby removing a specified number of transmission lines from service.Illustrations using a three bus system and the
The Self Consistent Field (SCF) iteration, widely used forcomputing the ground state energy and t... more The Self Consistent Field (SCF) iteration, widely used forcomputing the ground state energy and the corresponding single particlewave functions associated with a many-electronatomistic system, is viewedin this paper as an optimization procedure that minimizes the Kohn-Shamtotal energy indirectly by minimizing a sequence of quadratic surrogatefunctions. We point out the similarity and difference between the totalenergy and the surrogate, and show how the SCF iteration can fail whenthe minimizer of the surrogate produces an increase in the KS totalenergy. A trust region technique is introduced as a way to restrict theupdate of the wave functions within a small neighborhood of anapproximate solution at which the gradient of the total energy agreeswith that of the surrogate. The use of trust region in SCF is not new.However, it has been observed that directly applying a trust region basedSCF(TRSCF) to the Kohn-Sham total energy often leads to slowconvergence.We propose to use TRSCF with...
Object-oriented programming is becoming a popular way of developing new software. The promise of ... more Object-oriented programming is becoming a popular way of developing new software. The promise of this new programming paradigm is that software developed through these concepts will be more reliable and easier to re-use, thereby decreasing the time and cost of the software development cycle. This report describes the development of a C++ class library for nonlinear optimization. Using object-oriented techniques,
In this work, we propose a computationally feasible approachtodetect severe multiple contingencie... more In this work, we propose a computationally feasible approachtodetect severe multiple contingencies. We pose a contingency analysisproblem using a nonlinear optimization framework, which enables ustodetect the fewest possible transmission line outages resulting ina systemfailure of specified severity, and the most severe system failure causedby removing a specified number of transmission lines from service.Illustrations using a three bus system and the
The Self Consistent Field (SCF) iteration, widely used forcomputing the ground state energy and t... more The Self Consistent Field (SCF) iteration, widely used forcomputing the ground state energy and the corresponding single particlewave functions associated with a many-electronatomistic system, is viewedin this paper as an optimization procedure that minimizes the Kohn-Shamtotal energy indirectly by minimizing a sequence of quadratic surrogatefunctions. We point out the similarity and difference between the totalenergy and the surrogate, and show how the SCF iteration can fail whenthe minimizer of the surrogate produces an increase in the KS totalenergy. A trust region technique is introduced as a way to restrict theupdate of the wave functions within a small neighborhood of anapproximate solution at which the gradient of the total energy agreeswith that of the surrogate. The use of trust region in SCF is not new.However, it has been observed that directly applying a trust region basedSCF(TRSCF) to the Kohn-Sham total energy often leads to slowconvergence.We propose to use TRSCF with...
Object-oriented programming is becoming a popular way of developing new software. The promise of ... more Object-oriented programming is becoming a popular way of developing new software. The promise of this new programming paradigm is that software developed through these concepts will be more reliable and easier to re-use, thereby decreasing the time and cost of the software development cycle. This report describes the development of a C++ class library for nonlinear optimization. Using object-oriented techniques,
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