Optimal Combinatorial Electricity Markets

The deregulation of the electricity industry in many countries has created a number of marketplaces in which producers and consumers can operate in order to more effectively manage and meet their energy needs. To this end, this paper develops a new model for electricity retail where end-use customers choose their supplier from competing electricity retailers. The model is based on simultaneous reverse combinatorial auctions, designed as a second-price sealed-bid multi-item auction with supply function bidding. This model prevents strategic bidding and allows the auctioneer to maximise its payoff. Furthermore, we develop optimal single-item and multi-item algorithms for winner determination in such auctions that are significantly less complex than those currently available in the literature

Designing Coalition-Proof Reverse Auctions over Continuous Goods

This paper investigates reverse auctions that involve continuous values of different types of goods, general nonconvex constraints, and second stage costs. We seek to design the payment rules and conditions under which coalitions of participants cannot influence the auction outcome in order to obtain higher collective utility. Under the incentive-compatible Vickrey-Clarke-Groves mechanism, we show that coalition-proof outcomes are achieved if the submitted bids are convex and the constraint sets are of a polymatroid-type. These conditions, however, do not capture the complexity of the general class of reverse auctions under consideration. By relaxing the property of incentive-compatibility, we investigate further payment rules that are coalition-proof without any extra conditions on the submitted bids and the constraint sets. Since calculating the payments directly for these mechanisms is computationally difficult for auctions involving many participants, we present two computationally efficient methods. Our results are verified with several case studies based on electricity market data

Market-Based Task Allocation Mechanisms for Limited Capacity Suppliers

This paper reports on the design and comparison of two economically-inspired mechanisms for task allocation in environments where sellers have finite production capacities and a cost structure composed of a fixed overhead cost and a constant marginal cost. Such mechanisms are required when a system consists of multiple self-interested stakeholders that each possess private information that is relevant to solving a system-wide problem. Against this background, we first develop a computationally tractable centralised mechanism that finds the set of producers that have the lowest total cost in providing a certain demand (i.e. it is efficient). We achieve this by extending the standard Vickrey-Clarke-Groves mechanism to allow for multi-attribute bids and by introducing a novel penalty scheme such that producers are incentivised to truthfully report their capacities and their costs. Furthermore our extended mechanism is able to handle sellers' uncertainty about their production capacity and ensures that individual agents find it profitable to participate in the mechanism. However, since this first mechanism is centralised, we also develop a complementary decentralised mechanism based around the continuous double auction. Again because of the characteristics of our domain, we need to extend the standard form of this protocol by introducing a novel clearing rule based around an order book. With this modified protocol, we empirically demonstrate (with simple trading strategies) that the mechanism achieves high efficiency. In particular, despite this simplicity, the traders can still derive a profit from the market which makes our mechanism attractive since these results are a likely lower bound on their expected returns

Optimal Topology Design for Disturbance Minimization in Power Grids

The transient response of power grids to external disturbances influences their stable operation. This paper studies the effect of topology in linear time-invariant dynamics of different power grids. For a variety of objective functions, a unified framework based on $H_2$ norm is presented to analyze the robustness to ambient fluctuations. Such objectives include loss reduction, weighted consensus of phase angle deviations, oscillations in nodal frequency, and other graphical metrics. The framework is then used to study the problem of optimal topology design for robust control goals of different grids. For radial grids, the problem is shown as equivalent to the hard "optimum communication spanning tree" problem in graph theory and a combinatorial topology construction is presented with bounded approximation gap. Extended to loopy (meshed) grids, a greedy topology design algorithm is discussed. The performance of the topology design algorithms under multiple control objectives are presented on both loopy and radial test grids. Overall, this paper analyzes topology design algorithms on a broad class of control problems in power grid by exploring their combinatorial and graphical properties.Comment: 6 pages, 3 figures, a version of this work will appear in ACC 201