We consider the setting in which generators compete in scalar-parameterized supply functions to serve an inelastic demand spread throughout a transmission constrained power network. The market clears according to a locational marginal pricing mechanism, in which the independent system operator (ISO) determines the generators' production quantities so as to minimize the revealed cost of meeting demand, subject to transmission and generator capacity constraints. Under the assumption that both the ISO and generators choose their strategies simultaneously, we establish the existence of Nash equilibria for the underlying game, and derive a tight bound on its price of anarchy. Under the more restrictive setting of a two-node power network, we present a detailed comparison of market outcomes predicted by the simultaneous-move formulation of the game against those predicted by the more plausible sequential-move formulation, where the ISO observes the generators' strategy profile prior to determining their production quantities.

10aRM14-0021 aLin, Weixuan1 aBitar, Eilyan uhttps://certs.lbl.gov/publications/parameterized-supply-function01356nas a2200145 4500008003900000245005600039210005600095260003500151300001600186520089500202653001301097100001701110700001801127856006501145 2016 d00aPerformance bounds for robust decentralized control0 aPerformance bounds for robust decentralized control aBoston, MA, USAbIEEEc08/2016 a4323 - 43303 aWe consider the decentralized output feedback control of stochastic linear systems, subject to robust linear constraints on both the state and input trajectories. For problems with partially nested information structures, we establish an upper bound on the minimum achievable cost by computing the optimal affine decentralized control policy as a solution to a finite-dimensional conic program. For problems with general (possibly nonclassical) information structures, we construct another finite-dimensional conic program whose optimal value stands as a lower bound on the minimum achievable cost. With this lower bound in hand, one can bound the suboptimality incurred by any feasible decentralized control policy. A study of a partially nested system reveals that affine policies can be close to optimal, even in the presence state/input constraints and non-Gaussian disturbances.

10aRM14-0021 aLin, Weixuan1 aBitar, Eilyan uhttps://certs.lbl.gov/publications/performance-bounds-robust01414nas a2200217 4500008003900000245007900039210006900118260004400187300001000231520069000241653001000931653002200941653002600963653002800989653002801017100002601045700001801071700001501089700001801104856007401122 2014 d00aPiecewise affine dispatch policies for economic dispatch under uncertainty0 aPiecewise affine dispatch policies for economic dispatch under u aNational Harbor, MD, USAbIEEEc07/2014 a1 - 53 aStochastic optimization has become one of the fundamental mathematical frameworks for modeling power systems with important sources of uncertainty in the demand and supply sides. In this framework, a main challenge is to find optimal dispatch policies and settlement schemes that support a market equilibrium. In this paper, the economic dispatch under linear network constraints and resource uncertainty is revisited. Piece-wise affine continuous dispatch policies and locational prices that support a market equilibrium using a two-settlement scheme are derived. We find that the ex-post locational prices are piecewise affine continuous functions of the system uncertainties.

10aCERTS10aeconomic dispatch10aPower system modeling10areliability and markets10astochastic optimization1 aMunoz-Alvarez, Daniel1 aBitar, Eilyan1 aTong, Lang1 aWang, Jianhui uhttps://certs.lbl.gov/publications/piecewise-affine-dispatch-policies