Sleiman Mhanna

A Fast Distributed Algorithm for Large-Scale Demand Response Aggregation

A major challenge to implementing residential demand response is that of aligning the objectives of many households, each of which aims to minimize its payments and maximize its comfort level, while balancing this with the objectives of an aggregator that aims to minimize the cost of electricity purchased in a pooled wholesale market. This paper presents a fast distributed algorithm for aggregating a large number of households with a mixture of discrete and continuous energy levels. A distinctive feature of the method in this paper is that the nonconvex demand response (DR) problem is decomposed in terms of households as opposed to devices, which allows incorporating more intricate couplings between energy storage devices, appliances, and distributed energy resources. The proposed method is a fast distributed algorithm applied to the double smoothed dual function of the adopted DR model. The method is tested on systems with up to 2560 households, each with 10 devices on average. The proposed algorithm is designed to terminate in 60 iterations irrespective of system size, which can be ideal for an on-line version of this problem. Moreover, numerical results show that with minimal parameter tuning, the algorithm exhibits a very similar convergence behavior throughout the studied systems and converges to near-optimal solutions, which corroborates its scalability.

A Faithful Distributed Mechanism for Demand Response Aggregation

A faithful distributed mechanism is proposed in this paper for sharing the cost of electricity among a large number of strategic and distributed household agents that have private information, and discrete and continuous energy levels. In contrast to mechanisms in prior works, which charge the agents based on their day-ahead allocation, the proposed mechanism charges the agents based on their day-ahead allocation and their actual consumption. The mechanism is proven to be asymptotically dominant strategy incentive compatible, weakly budget balanced, and fair in charging the agents. However, the proposed mechanisms payment function, which requires computing a marginal allocation problem for each agent, renders the mechanism intractable for a large number of household agents if it is computed centrally. Thus, a distributed implementation of the mechanism is proposed, in which the agents share the computational burden with the aggregator. The distributed implementation is based on a penalty/reward scheme inspired by the prisoners dilemma that brings faithful computation to a dominant strategy equilibrium.

Towards a realistic implementation of mechanism design in demand response aggregation

In the quest for a realistic implementation of mechanism design in demand response, a two-stage mechanism is proposed in this paper for sharing the cost of electricity among strategic, rational, and selfish household agents that have private information about their preferences. Whereas mechanisms in prior works charge the agents based on their day-ahead allocations, the proposed mechanism charges the agents based on their actual consumption and the degree of deviation from their day-ahead allocations. The mechanisms payment rule is a function of the inverse of the strictly proper spherical scoring rule multiplied by a quadratic term that is independent of the agents reports. The mechanism is proven to be asymptotically incentive compatible and ex-ante weakly budget balanced under further conditions. The results of simulations also corroborate that, in the context of energy cost sharing, the mechanism is fair in allocating the payments from the agents as it assigns lower payments from agents that are more precise and more accurate in following the day-ahead appliance schedule allocated to them.

Tight LP approximations for the optimal power flow problem

DC power flow approximations are ubiquitous in the electricity industry. However, these linear approximations fail to capture important physical aspects of power flow, such as the reactive power and voltage magnitude, which are crucial in many applications to ensure voltage stability and AC solution feasibility. This paper proposes two LP approximations of the AC optimal power flow problem, founded on tight polyhedral approximations of the SOC constraints, in the aim of retaining the good lower bounds of the SOCP relaxation and relishing the computational efficiency of LP solvers. The high accuracy of the two LP approximations is corroborated by rigorous computational evaluations on systems with up to 9241 buses and different operating conditions. The computational efficiency of the two proposed LP models is shown to be comparable to, if not better than, that of the SOCP models in most instances. This performance is ideal for MILP extensions of these LP models since MILP is computationally more efficient than MIQCP.

A Distributed Algorithm for Demand Response With Mixed-Integer Variables

This letter presents a distributed algorithm for aggregating a large number of households with mixed-integer variables and intricate couplings between devices. The proposed distributed gradient algorithm is applied to the double smoothed dual function of the adopted demand response model. Numerical results show that, with minimal parameter adjustments, the convergence of the dual objective exhibits a very similar behavior irrespective system size.

Guidelines for realistic grounding of mechanism design in demand response

Paradigm-shifting changes in the electric power industry, such as high renewable energy penetration and advancements in infrastructure technologies, have prompted more focus on demand response (DR). This paper highlights four impediments associated with a realistic implementation of mechanism design for aggregator-coordinated DR, focusing in particular on the Vickrey-Clarke-Groves (VCG) mechanism, and describes the necessary assumptions for a realistic grounding to the implementation of mechanism design in DR. Additionally, we propose a two-stage distributed mechanism in which the agents share the computational burden with the aggregator and faithfully implement their intended computations.

A Faithful and Tractable Distributed Mechanism for Residential Electricity Pricing

Demand response (DR) programs incentivize consumers for using their elastic demand for demand shaping, supply-demand balancing, and other ancillary and network support services. This paper proposes a dynamic nonlinear pricing scheme for behind-the-meter distributed energy resources (DERs), such as residential batteries, plug-in electric vehicles, and smart appliances, participating in a DR program, based on distributed mechanism design concepts. The underlying method is a faithful mechanism that can overlay any tractable dual-decomposition algorithm that solves the DER management and coordination problem in a distributed fashion. Since electricity is a continuously produced and divisible commodity that cannot be invariably allocated or stored, the pricing scheme is designed to couple the negotiated allocations and the actual consumption in a proportionally fair way, which means that it assigns lower payments to consumers who require less energy and are more accurate in following these requirements. Specifically, this pricing scheme is based on the Lagrange multipliers, which are the byproducts of any dual-decomposition algorithm that solves the nonconvex DER management and coordination problem. As a result, and in contrast to most existing time-varying pricing schemes, this pricing strategy does not suffer from rebound peaks repercussions. Furthermore, the proposed distributed mechanism is proven to be asymptotically faithful, i.e., faithful when the number of households grows large, collusion proof and weakly budget balanced.