Message passing for optimization and control of a power grid: Model of a distribution system with redundancy

Abstract

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 pre-defined 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.

A decentralized algorithm for optimal resource allocation in smartgrids with communication network externalities

“…In addition, we see the sequence of power allocations for users 1 and 2 ({ 11 w user 11). This would be the actual power allocation to these two users since it satisfies more accurately the system's power capacity constraints 8 . Observe also that user 1 is given more resources than the rest users (the users not shown have similar behavior with user 2); this is because user 1's current demand α 1 is higher than the rest.…”

“…In [7], market models and distributed demand response schemes are studied that try to optimize the gap between power supply and demand in both competitive and oligopolistic markets. A message passing algorithm for optimization and control of the power grid is presented in [8].…”

Scalable Harmonization of Complex Networks With Local Adaptive Controllers

“…Different functions denoted by the same letter are distinguished by identifiers of their arguments and possibly by an additional decoration, often being the set to which concerns. 3 Individual admissible control laws are described by pds S(ut|w t−1 ) having their supports on admissible sets of inputs ut and conditioned by the available knowledge. For the system model (1) and the ideal closed loop model (2), the knowledge of w t−1 suffices.…”

“…Proposition 1 (FPD with Observed External Variables): The optimal strategy in the FPD sense (3), for the system model (1) and the ideal closed loop model (2), consists of the optimal control laws S O (u t |w t−1 ), w t−1 = (y t−1 , x t−1 ), t ∈ t,…”

“…The harmonisation can be supported by a message-passing. It is one of new decentralised methods for managing systems with large ensembles of interconnected nodes [3] where information is retrieved and disseminated in a consistent probabilistic fashion. The approach has emerged independently in a number of fields, including communications theory [4], artificial intelligence [5], and statistical physics [6].…”