90 citations · 1.1k across the 68 of their papers we have counts for
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On the Network Topology Dependent Solution Count of the Algebraic Load Flow Equations
Tianran Chen, Dhagash Mehta
A large amount of research activity in power systems areas has focused on developing computational methods to solve load flow equations where a key question is the maximum number o…
Recent Advances in Computational Methods for the Power Flow Equations
Dhagash Mehta, Daniel K Molzahn, Konstantin Turitsyn
The power flow equations are at the core of most of the computations for designing and operating electric power systems. The power flow equations are a system of multivariate nonli…
Toward Topologically Based Upper Bounds on the Number of Power Flow Solutions
Daniel K Molzahn, Dhagash Mehta, Matthew Niemerg
The power flow equations, which relate power injections and voltage phasors, are at the heart of many electric power system computations. While Newton-based methods typically find…
An index-resolved fixed-point homotopy and potential energy landscapes
Tianran Chen, Dhagash Mehta
Stationary points (SPs) of the potential energy landscapes can be classified by their Morse index, i.e., the number of negative eigenvalues of the Hessian evaluated at the SPs. In…
Statistics of Stationary Points of Random Finite Polynomial Potentials
Dhagash Mehta, Matthew Niemerg, Chuang Sun
The stationary points (SPs) of the potential energy landscapes (PELs) of multivariate random potentials (RPs) have found many applications in many areas of Physics, Chemistry and M…
A Collection of Challenging Optimization Problems in Science, Engineering and Economics
Dhagash Mehta, Crina Grosan
Function optimization and finding simultaneous solutions of a system of nonlinear equations (SNE) are two closely related and important optimization problems. However, unlike in th…