Sharing Storage in a Smart Grid: A Coalitional Game Approach

Sharing economy is a transformative socio-economic phenomenon built around the idea of sharing underused resources and services, e.g., transportation and housing, thereby reducing costs and extracting value. Anticipating continued reduction in the cost of electricity storage, we look into the potential opportunity in electrical power system where consumers share storage with each other. We consider two different scenarios. In the first scenario, consumers are assumed to already have individual storage devices and they explore cooperation to minimize the realized electricity consumption cost. In the second scenario, a group of consumers is interested to invest in joint storage capacity and operate it cooperatively. The resulting system problems are modeled using cooperative game theory. In both cases, the cooperative games are shown to have non-empty cores and we develop efficient cost allocations in the core with analytical expressions. Thus, sharing of storage in cooperative manner is shown to be very effective for the electric power system

Array algorithms for H^2 and H^∞ estimation

Currently, the preferred method for implementing H^2 estimation algorithms is what is called the array form, and includes two main families: square-root array algorithms, that are typically more stable than conventional ones, and fast array algorithms, which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Using our recent observation that H^∞ filtering coincides with Kalman filtering in Krein space, in this chapter we develop array algorithms for H^∞ filtering. These can be regarded as natural generalizations of their H^2 counterparts, and involve propagating the indefinite square roots of the quantities of interest. The H^∞ square-root and fast array algorithms both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H^∞ filters. These conditions are built into the algorithms themselves so that an H^∞ estimator of the desired level exists if, and only if, the algorithms can be executed. However, since H^∞ square-root algorithms predominantly use J-unitary transformations, rather than the unitary transformations required in the H^2 case, further investigation is needed to determine the numerical behavior of such algorithms

An Approximately Optimal Algorithm for Scheduling Phasor Data Transmissions in Smart Grid Networks

In this paper, we devise a scheduling algorithm for ordering transmission of synchrophasor data from the substation to the control center in as short a time frame as possible, within the realtime hierarchical communications infrastructure in the electric grid. The problem is cast in the framework of the classic job scheduling with precedence constraints. The optimization setup comprises the number of phasor measurement units (PMUs) to be installed on the grid, a weight associated with each PMU, processing time at the control center for the PMUs, and precedence constraints between the PMUs. The solution to the PMU placement problem yields the optimum number of PMUs to be installed on the grid, while the processing times are picked uniformly at random from a predefined set. The weight associated with each PMU and the precedence constraints are both assumed known. The scheduling problem is provably NP-hard, so we resort to approximation algorithms which provide solutions that are suboptimal yet possessing polynomial time complexity. A lower bound on the optimal schedule is derived using branch and bound techniques, and its performance evaluated using standard IEEE test bus systems. The scheduling policy is power grid-centric, since it takes into account the electrical properties of the network under consideration

An Approximately Optimal Algorithm for Scheduling Phasor Data Transmissions in Smart Grid Networks

In this paper, we devise a scheduling algorithm for ordering transmission of synchrophasor data from the substation to the control center in as short a time frame as possible, within the realtime hierarchical communications infrastructure in the electric grid. The problem is cast in the framework of the classic job scheduling with precedence constraints. The optimization setup comprises the number of phasor measurement units (PMUs) to be installed on the grid, a weight associated with each PMU, processing time at the control center for the PMUs, and precedence constraints between the PMUs. The solution to the PMU placement problem yields the optimum number of PMUs to be installed on the grid, while the processing times are picked uniformly at random from a predefined set. The weight associated with each PMU and the precedence constraints are both assumed known. The scheduling problem is provably NP-hard, so we resort to approximation algorithms which provide solutions that are suboptimal yet possessing polynomial time complexity. A lower bound on the optimal schedule is derived using branch and bound techniques, and its performance evaluated using standard IEEE test bus systems. The scheduling policy is power grid-centric, since it takes into account the electrical properties of the network under consideration

A global identifiability condition for consensus networks on tree graphs

In this paper we present a sufficient condition that guarantees identifiability of linear network dynamic systems exhibiting continuous-time weighted consensus protocols with acyclic structure. Each edge of the underlying network graph G is defined by a constant parameter, referred to as the weight of the edge, while each node is defined by a scalar state whose dynamics evolve as the weighted linear combination of its difference with the states of its neighboring nodes. Following the classical definitions of identifiability and indistinguishability, we first derive a condition that ensures the identifiability of the edge weights of G in terms of the associated transfer function. Using this characterization, we propose a sensor placement algorithm that guarantees identifiability of the edge weights. We describe our results using illustrative examples

Online Algorithms for Dynamic Matching Markets in Power Distribution Systems

This letter proposes online algorithms for dynamic matching markets in power distribution systems. These algorithms address the problem of matching flexible loads with renewable generation, with the objective of maximizing social welfare of the exchange in the system. More specifically, two online matching algorithms are proposed for two generation-load scenarios: (i) when the mean of renewable generation is greater than the mean of the flexible load, and (ii) when the condition (i) is reversed. With the intuition that the performance of such algorithms degrades with increasing randomness of the supply and demand, two properties are proposed for assessing the performance of the algorithms. First property is convergence to optimality (CO) as the underlying randomness of renewable generation and customer loads goes to zero. The second property is deviation from optimality, which is measured as a function of the standard deviation of the underlying randomness of renewable generation and customer loads. The algorithm proposed for the first scenario is shown to satisfy CO and a deviation from optimality that varies linearly with the variation in the standard deviation. We then show that the algorithm proposed for the second scenario satisfies CO and a deviation from optimality that varies linearly with the variation in standard deviation plus an offset under certain condition