arXiv subjects

Sleiman Mhanna

Publications and source records attributed to Sleiman Mhanna.

10 recordsLinked to original sources

arXiv2026

Volt-VAr-Watt Optimization in Four-Wire Low-Voltage Networks: Exact Nonlinear Models and Smooth Approximations - Extended Version

The proliferation of distributed energy resources is increasing the prevalence of both overvoltages and undervoltages in low-voltage (LV) distribution networks. Smart inverter functionalities, such as Volt-VAr and Volt-Watt control, can regulate voltage at the consumer level but are challenging to capture in optimization models due to their nondifferentiability. This paper proposes three nonlinear models for four-wire unbalanced optimal power flow that incorporate these nonsmooth functions without binary or integer variables. The first model encodes these nonsmooth functions directly as user-defined functions using control flow, a feat enabled by many state-of-the-art algebraic modeling languages. The second and third introduce bespoke smooth approximations with tunable approximation errors to address potential numerical issues arising from nondifferentiability, improving reliability while maintaining accuracy. All three methods are evaluated on real four-wire unbalanced LV networks with varying rooftop solar adoption levels, including a 539-bus system with 302 smart inverters. This paper is not only the first to demonstrate accurate, reliable, and tractable Volt-Var-Watt optimization (VVWO) on real four-wire unbalanced LV network models, but it also establishes that optimization-based, non-incremental methods offer superior reliability compared to commonly used incremental (quasi-steady-state) approaches.

eess.SY↗

arXiv2022

Towards Optimal Integrated Planning of Electricity and Hydrogen Infrastructure for Large-Scale Renewable Energy Transport

The imminent advent of large-scale green hydrogen (H2) production raises the central question of which of the two options, transporting "green" molecules, or transporting "green" electrons, is the most cost-effective one. This paper proposes a first-of-its-kind mathematical framework for the optimal integrated planning of electricity and H2 infrastructure for transporting large-scale variable renewable energy (VRE). In contrast to most existing works, this work incorporates essential nonlinearities such as voltage drops due to losses in high-voltage alternating current (HVAC) and high-voltage direct current (HVDC) transmission lines, losses in HVDC converter stations, reactive power flow, pressure drops in pipelines, and linepack, all of which play an important role in determining the optimal infrastructure investment decision. Capturing these nonlinearities requires casting the problem as a nonconvex mixed-integer nonlinear program (MINLP), whose complexity is further exacerbated by its large size due to the relatively high temporal resolution of RES forecasts. This work then leverages recent advancements in convex relaxations to instead solve a tractable alternative in the form of a mixed-integer quadratically constrained programming (MIQCP) problem. The impact of other fundamental factors such as transmission distance and RES capacity is also thoroughly analysed on a canonical two-node system. The integrated planning model is then demonstrated on a real-world case study involving renewable energy zones in Australia.

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arXiv2022

Fair Coordination of Distributed Energy Resources with Volt-Var Control and PV Curtailment

This paper presents a novel distributed optimal power flow (DOPF) method for fair distributed energy resource (DER) coordination in the context of mandated rooftop PV inverter control modes. In practice, inverter reactive power control is increasingly required by grid connection codes, which often unfairly curtail PV generation of prosumers towards the end of low-voltage feeders. Similarly, optimization-based DER coordination methods that aim solely for technically-efficient DER coordination do not consider the distribution of PV curtailment across customers. To address these concerns, we develop a tractable multi-objective DOPF method for optimal DER coordination that (i) curtails PV generation fairly across prosumers, and (ii) incorporates a standard piecewise-linear volt-var control reactive power control function without using integer variables. Three equity principles representing different interpretations of fairness are implemented in our coordination method; namely, egalitarian, proportional and uniform dynamic PV curtailment redistribution. The performance of our approach is demonstrated on low-voltage distribution feeders of different sizes (5, 10, 25, 50 and 100 prosumers) using two network topologies: line topology without lateral spurs and tree topology with lateral spurs. Each network considers three levels of PV penetration, giving 30 test systems in total. The results demonstrate the effectiveness of the proposed DOPF method for fair DER coordination: PV curtailment is equitably distributed among prosumers with a computational burden on par with conventional DOPF approaches. Moreover, different fairness methods result in different patterns of curtailment, which a regulator may choose between.

cs.CE↗

arXiv2022

Practical Considerations of DER Coordination with Distributed Optimal Power Flow

The coordination of prosumer-owned, behind-the-meter distributed energy resources (DER) can be achieved using a multiperiod, distributed optimal power flow (DOPF), which satisfies network constraints and preserves the privacy of prosumers. To solve the problem in a distributed fashion, it is decomposed and solved using the alternating direction method of multipliers (ADMM), which may require many iterations between prosumers and the central entity (i.e., an aggregator). Furthermore, the computational burden is shared among the agents with different processing capacities. Therefore, computational constraints and communication requirements may make the DOPF infeasible or impractical. In this paper, part of the DOPF (some of the prosumer subproblems) is executed on a Raspberry Pi-based hardware prototype, which emulates a low processing power, edge computing device. Four important aspects are analyzed using test cases of different complexities. The first is the computation cost of executing the subproblems in the edge computing device. The second is the algorithm operation on congested electrical networks, which impacts the convergence speed of DOPF solutions. Third, the precision of the computed solution, including the trade-off between solution quality and the number of iterations, is examined. Fourth, the communication requirements for implementation across different communication networks are investigated. The above metrics are analyzed in four scenarios involving 26-bus and 51-bus networks.

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arXiv2021

Iterative LP-based Methods for the Multiperiod Optimal Electricity and Gas Flow Problem

In light of the increasing coupling between electricity and gas networks, this paper introduces two novel iterative methods for efficiently solving the multiperiod optimal electricity and gas flow (MOEGF) problem. The first is an iterative MILP-based method and the second is an iterative LP-based method with an elaborate procedure for ensuring an integral solution. The convergence of the two approaches is founded on two key features. The first is a penalty term with a single, automatically tuned, parameter for controlling the step size of the gas network iterates. The second is a sequence of supporting hyperplanes together with an increasing number of carefully constructed halfspaces for controlling the convergence of the electricity network iterates. Moreover, the two proposed algorithms use as a warm start the solution from a novel polyhedral relaxation of the MOEGF problem, for a noticeable improvement in computation time as compared to a cold start. Unlike the first method, which invokes a branch-and-bound algorithm to find an integral solution, the second method implements an elaborate steering procedure that guides the continuous variables to take integral values at the solution. Numerical evaluation demonstrates that the two proposed methods can converge to high-quality feasible solutions in computation times at least two orders of magnitude faster than both a state-of-the-art nonlinear branch-and-bound (NLBB) MINLP solver and a mixed-integer convex programming (MICP) relaxation of the MOEGF problem. The experimental setup consists of five test cases, three of which involve the real electricity and gas transmission networks of the state of Victoria with actual linepack and demand profiles.

math.OC↗

arXiv2018

Accelerated Methods for the SOCP-relaxed Component-based Distributed Optimal Power Flow

In light of the increased focus on distributed methods, this paper proposes two accelerated subgradient methods and an adaptive penalty parameter scheme to speed-up the convergence of ADMM on the component-based dual decomposition of the second-order cone programming (SOCP) relaxation of the OPF. This work is the first to apply an adaptive penalty parameter method along with an accelerated subgradient method together in one scheme for distributed OPF. This accelerated scheme is demonstrated to reach substantial speed-ups, as high as 87%, on real-world test systems with more than 9000 buses, as well as on other difficult test cases.

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arXiv2017

A Component-Based Dual Decomposition Method for the OPF Problem

This paper proposes a component-based dual decomposition of the nonconvex AC optimal power flow (OPF) problem, where the modified dual function is solved in a distributed fashion. The main contribution of this work is that is demonstrates that a distributed method with carefully tuned parameters can converge to globally optimal solutions despite the inherent nonconvexity of the problem and the absence of theoretical guarantees of convergence. This paper is the first to conduct extensive numerical analysis resulting in the identification and tabulation of the algorithmic parameter settings that are crucial for the convergence of the method on 72 AC OPF test instances. Moreover, this work provides a deeper insight into the geometry of the modified Lagrange dual function of the OPF problem and highlights the conditions that make this function differentiable. This numerical demonstration of convergence coupled with the scalability and the privacy preserving nature of the proposed method makes it well suited for smart grid applications such as multi-period OPF with demand response (DR) and security constrained unit commitment (SCUC) with contingency constraints and multiple transmission system operators (TSOs).

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arXiv2016

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.

math.OC↗

arXiv2016

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 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.

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arXiv2016

A Distributed Algorithm for Demand Response with Mixed-Integer Variables

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

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