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This paper considers the problem of optimally dispatching a set of generators in a power system; these generators are interconnected to some loads via a network of buses. We consider scenarios when the power network is operating at a steady state, and a small change in the load occurs at some of the load buses. Upon occurrence of this event, the network seeks to find the change in generator injections...
This paper studies an electricity market consisting of an independent system operator (ISO) and a group of generators. The goal is to solve the DC optimal power flow (DC-OPF) problem: have the generators collectively meet the power demand while minimizing the aggregate generation cost and respecting line flow limits. The ISO by itself cannot solve the DC-OPF problem as the generators are strategic...
This paper studies the projected saddle-point dynamics for a twice differentiable convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and (projected) gradient ascent in variables corresponding to concavity. We provide a novel characterization of the omega-limit set of the trajectories of these...
This paper studies a class of network optimization problems where the objective function is the summation of individual agents' convex functions and their decision variables are coupled by linear equality constraints. These constraints are not sparse, meaning that they do not match the pattern of the network adjacency matrix. We propose two approaches to design efficient distributed algorithms to...
This paper studies an electricity market consisting of an independent system operator (ISO) and a group of generators. The goal is to solve the economic dispatch (ED) problem, i.e., make the generators collectively meet a given amount of power demand while minimizing the aggregate generation cost. The ISO by itself cannot solve the ED problem as the generators are strategic and do not share their...
This paper considers the dynamic economic dispatch problem for a group of generators with storage that communicate over a weight-balanced strongly connected digraph. The objective of the generators is to collectively meet a certain load profile, specified over a finite time horizon, while minimizing the aggregate cost. At each time slot, each generator decides on the amount of generated power and...
This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics (gradient-descent in the first variable and gradient-ascent in the second one). We identify a suite of complementary conditions under which the set of saddle points is asymptotically...
This paper considers the economic dispatch problem for a group of power generating units. The collective aim is to meet a power demand while respecting individual generator constraints and minimizing the total generation cost. Assuming that the units communicate over a strongly connected, weight-balanced digraph, we propose a distributed coordination algorithm that provably converges to the solution...
This paper considers the economic dispatch problem for a group of power generating units communicating over an arbitrary strongly connected, weight-balanced digraph. The goal of the group is to collectively meet a specified load while respecting individual generation bounds and minimizing the total generation cost, which corresponds to the sum of individual arbitrary convex functions. We introduce...
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