We consider the decentralized control of radial distribution systems with controllable photovoltaic inverters and storage devices. For such systems, we consider the problem of designing controllers that minimize the expected cost of meeting demand, while respecting distribution system and resource constraints. Employing a linear approximation of the branch flow model, we formulate this problem as the design of a decentralized disturbance-feedback controller that minimizes the expected value of a convex quadratic cost function, subject to convex quadratic constraints on the state and input. As such problems are, in general, computationally intractable, we derive an inner approximation to this decentralized control problem, which enables the efficient computation of an affine control policy via the solution of a conic program. As affine policies are, in general, suboptimal for the systems considered, we provide an efficient method to bound their suboptimality via the solution of another conic program. A case study of a 12 kV radial distribution feeder demonstrates that decentralized affine controllers can perform close to optimal.

10aRM14-0021 aLin, Weixuan1 aBitar, Eilyan uhttps://certs.lbl.gov/publications/decentralized-control-distributed01539nas a2200145 4500008003900000245006400039210006400103260003800167300001600205520105500221653001301276100001701289700001801306856006901324 2016 d00aParameterized supply function equilibrium in power networks0 aParameterized supply function equilibrium in power networks aLas Vegas, NV, USAbIEEEc12/2016 a1542 - 15483 aWe 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-robust