Anticipatory Power Flow
Creators: name: Cahig, Christian
Publisher: name: Zenodo
Year: 2022
Subjects: Power systems computation
Power systems

description: This thesis presents <em>anticipatory power flow (APF)</em>, a two-stage computational framework for finding a set of supply injections and bus voltages that are power-flow feasible under the conditions of an upcoming dispatch (<em>e.g.</em>, upcoming power demands, scheduled supply limits, estimated system parameters), considering information from the preceding system snapshot (<em>e.g.</em>, bus voltages, powers demanded and supplied). The first stage—anticipating the supply injections—is formulated as a convex program called <em>extended economic dispatch</em> which modifies the standard economic dispatch model (i) by accounting for reactive supply injections; (ii) by adjusting the required power demand with an estimation of the system loss; and (iii) by using an objective that is a linear combination of the system loss and a regularizer representing the influence of the previous-snapshot supply injections. The second stage—finding the corresponding bus voltages—amounts to solving the <em>APF equations</em>, modifying the standard bus-injection model of the power flow equations (i) to have a user-specified <em>reference bus</em> (whose voltage phase angle is fixed to an arbitrary value) for avoiding rotational degeneracy; and (Ii) to have a <em>distributed slack variable</em> (compensating for inexactness of the anticipated supply injections) for maintaining well-determinedness. APF can be regarded as <em>an extension of the standard power flow problem</em>, deviating from the traditional classification of buses (<em>i.e.</em>, into PQ, PV, and slack) which assumes predetermination of a subset of supply injections and bus voltage magnitudes. APF can also be viewed as <em>a special case of continuation power flow</em> where the demand draws and the entire system parameters are the continuation parameters, and the two APF stages are analogous to a predict-correct cycle that lands on the target values of the continuation parameters. Experimental results suggest that the APF subproblems are amply handled by existing off-the-shelf solvers. Specifically, simulated scenarios based on a 3374-bus, 4161-branch, 596-generator portion of Poland's transmission network show that the extended economic dispatch subproblem and the APF equations can both be solved <em>in sub-second run times</em> on a consumer-grade machine. We also demonstrate the use of APF notions as auxiliary tools in two optimal power flow (OPF) scenarios: (i) <em>warm-starting OPF solvers</em> with initial iterates set according to the anticipated supply injections and the solution to their corresponding APF equations; and (ii) <em>finding the nearest power-flow feasible values</em> of a set of supply injections and bus voltages that optimize some approximated OPF model. Lastly, we derive and verify methods for <em>differentiating through the APF equations</em>, enabling computation of derivatives/sensitivities of the bus voltages, distributed slack, and arbitrary functions thereof, with respect to the corresponding anticipated supply injections. This lays the groundwork for the use of the APF equations to enforce structure in differentiable programming pipelines.
description: Please see `README.txt`.