Simple certificate for power distribution network security assessment

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2017.Cataloged from PDF version of thesis.Includes bibliographical references (pages 53-54).The integration of volatile renewable energy sources, non-traditional load managements, and unforeseen natural disasters introduce uncertainties that could easily jeopardize the security of power systems. Meanwhile, constructing the real solvable boundary-crucial for contingency analysis, security assessment, and planning network processes-in multidimensional parameter space is burdensome and time consuming; hence there is an urgent need for a tool to identify the security region, or the set of viable injections. This thesis presents fast and reliable inner approximation techniques for solvable boundaries of power distribution systems based on Banach fixed point theorem and Kantorovich theorem. The novel method is in a simple "certificate" form-a single lined inequality condition that involves the system variables and parameters. Our certificate is noniterative, therefore computationally efficient, and the simulation results confirm that the presented approach constructs regions that are sufficiently large for most security-constrained functions. The construction for our "certificates" begins with re-formulating power-flow equations into appropriate forms such that they are applicable to the aforementioned two major theorems. Practical applications of the proposed technique include fast screening tool for feasible injection change, certified solvability margins, and new computationally robust continuation power flow algorithms.by Suhyoun Yu.S.M

Fixed-point theorem-based voltage stability margin estimation techniques for distribution systems with renewables

The future distribution systems expose to an unprecedented level of uncertainties due to renewable resources, nontraditional loads, aging infrastructure, etc., posing potential risks to secure operation of the system.This article proposes a new technique to estimate the voltage stability margin of the distribution systems with high penetration of renewables.Its convergence and robustness under complex and stressed working conditions are guaranteed in theory. This technique is handy for the operation as it features self-adaptive step size and is applicable to general system topology. It leverages a newly derived analytical solvability certificate based on the Kantorovich fixed-point theorem. A fast version of the proposed technique is duly proposed to speed up the computation up to 8 times while maintaining high accuracy, which lends itself to online and time-sensitive emergency tasks. Numerical simulations with various IEEE test feeders verify the performance of the techniques.Ministry of Education (MOE)Nanyang Technological UniversityNational Research Foundation (NRF)This work was supported in part by NTU SUG, MOE AcRF TIER 1- 2019-T1-001-119 (RG 79/19), and in part by EMA & NRFEMA-EP004-EKJGC-0003

Unpacking the computations of human spatial search under uncertainty: noisy utility maximization, discounting, and probability warping

Humans navigate daily decision-making by flexibly choosing appropriate approximations of what ought to be done. Which mental algorithms do people use, and when? We use behavioural experiments and modelling to investigate three computational principles known to influence decision making: noisy utility maximization, discounting, and the probability warping principle of Prospect Theory. While these principles have been shown to separately influence human behaviour in simple laboratory tasks, such as bandits and gambles, we evaluate their combined use in the context of a naturalistic spatial search that required sequential decision-making. We found that while aggregate human behaviour can be reasonably well explained by an optimal planner with noisy utility maximization, individual-level behaviour exhibits consistent irregularities, that deviate from expected utility theory. We show that model-based prediction of individual-level behaviours in our experiment is significantly improved by combining the three computational principles, and benefits particularly strongly from probability warping. Furthermore, our results suggest that probability warping may be a common factor of human decision making, that generalizes beyond the gambles explored in Prospect Theory, to natural human behaviours such as spatial search and navigation

Unpacking the computations of human spatial search under uncertainty: noisy utility maximization, discounting, and probability warping

Humans navigate daily decision-making by flexibly choosing appropriate approximations of what ought to be done. Which mental algorithms do people use, and when? We use behavioural experiments and modelling to investigate three computational principles known to influence decision making: noisy utility maximization, discounting, and the probability warping principle of Prospect Theory. While these principles have been shown to separately influence human behaviour in simple laboratory tasks, such as bandits and gambles, we evaluate their combined use in the context of a naturalistic spatial search that required sequential decision-making. We found that while aggregate human behaviour can be reasonably well explained by an optimal planner with noisy utility maximization, individual-level behaviour exhibits consistent irregularities, that deviate from expected utility theory. We show that model-based prediction of individual-level behaviours in our experiment is significantly improved by combining the three computational principles, and benefits particularly strongly from probability warping. Furthermore, our results suggest that probability warping may be a common factor of human decision making, that generalizes beyond the gambles explored in Prospect Theory, to natural human behaviours such as spatial search and navigation