TY - JOUR

T1 - Message passing for optimization and control of a power grid

T2 - Model of a distribution system with redundancy

AU - Zdeborová, Lenka

AU - Decelle, Aurélien

AU - Chertkov, Michael

PY - 2009/10/19

Y1 - 2009/10/19

N2 - We use a power grid model with M generators and N consumption units to optimize the grid and its control. Each consumer demand is drawn from a predefined finite-size-support distribution, thus simulating the instantaneous load fluctuations. Each generator has a maximum power capability. A generator is not overloaded if the sum of the loads of consumers connected to a generator does not exceed its maximum production. In the standard grid each consumer is connected only to its designated generator, while we consider a more general organization of the grid allowing each consumer to select one generator depending on the load from a predefined consumer dependent and sufficiently small set of generators which can all serve the load. The model grid is interconnected in a graph with loops, drawn from an ensemble of random bipartite graphs, while each allowed configuration of loaded links represent a set of graph covering trees. Losses, the reactive character of the grid and the transmission-level connections between generators (and many other details relevant to realistic power grid) are ignored in this proof-of-principles study. We focus on the asymptotic limit, N→ and N/M→D=O (1) >1, and we show that the interconnects allow significant expansion of the parameter domains for which the probability of a generator overload is asymptotically zero. Our construction explores the formal relation between the problem of grid optimization and the modern theory of sparse graphical models. We also design heuristic algorithms that achieve the asymptotically optimal selection of loaded links. We conclude discussing the ability of this approach to include other effects such as a more realistic modeling of the power grid and related optimization and control algorithms.

AB - We use a power grid model with M generators and N consumption units to optimize the grid and its control. Each consumer demand is drawn from a predefined finite-size-support distribution, thus simulating the instantaneous load fluctuations. Each generator has a maximum power capability. A generator is not overloaded if the sum of the loads of consumers connected to a generator does not exceed its maximum production. In the standard grid each consumer is connected only to its designated generator, while we consider a more general organization of the grid allowing each consumer to select one generator depending on the load from a predefined consumer dependent and sufficiently small set of generators which can all serve the load. The model grid is interconnected in a graph with loops, drawn from an ensemble of random bipartite graphs, while each allowed configuration of loaded links represent a set of graph covering trees. Losses, the reactive character of the grid and the transmission-level connections between generators (and many other details relevant to realistic power grid) are ignored in this proof-of-principles study. We focus on the asymptotic limit, N→ and N/M→D=O (1) >1, and we show that the interconnects allow significant expansion of the parameter domains for which the probability of a generator overload is asymptotically zero. Our construction explores the formal relation between the problem of grid optimization and the modern theory of sparse graphical models. We also design heuristic algorithms that achieve the asymptotically optimal selection of loaded links. We conclude discussing the ability of this approach to include other effects such as a more realistic modeling of the power grid and related optimization and control algorithms.

UR - http://www.scopus.com/inward/record.url?scp=70449124108&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.80.046112

DO - 10.1103/PhysRevE.80.046112

M3 - Article

C2 - 19905395

AN - SCOPUS:70449124108

VL - 80

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 4

M1 - 046112

ER -