Inexact Convex Relaxations for AC Optimal Power Flow: Towards AC Feasibility

Convex relaxations of AC optimal power flow (AC-OPF) problems have attracted significant interest as in several instances they provably yield the global optimum to the original non-convex problem. If, however, the relaxation is inexact, the obtained solution is not AC-feasible. The quality of the obtained solution is essential for several practical applications of AC-OPF, but detailed analyses are lacking in existing literature. This paper aims to cover this gap. We provide an in-depth investigation of the solution characteristics when convex relaxations are inexact, we assess the most promising AC feasibility recovery methods for large-scale systems, and we propose two new metrics that lead to a better understanding of the quality of the identified solutions. We perform a comprehensive assessment on 96 different test cases, ranging from 14 to 3120 buses, and we show the following: (i) Despite an optimality gap of less than 1%, several test cases still exhibit substantial distances to both AC feasibility and local optimality and the newly proposed metrics characterize these deviations. (ii) Penalization methods fail to recover an AC-feasible solution in 15 out of 45 cases, and using the proposed metrics, we show that most failed test instances exhibit substantial distances to both AC-feasibility and local optimality. For failed test instances with small distances, we show how our proposed metrics inform a fine-tuning of penalty weights to obtain AC-feasible solutions. (iii) The computational benefits of warm-starting non-convex solvers have significant variation, but a computational speedup exists in over 75% of the cases

Developing Integrated Waste Management Systems: Information Needs and the Role of Locally Based Data

No abstract available

Developing measures for valuing changes in biodiversity : final report

This document reports the findings from the DEFRA funded research project 'Developing measures for valuing changes in biodiversity'. The aim of the research was to develop an appropriate framework that will enable cost-effective and robust valuations of the total economic value of changes to biodiversity in the UK countryside. The research involved a review of ecological and economic literature on the valuation of biodiversity changes. The information gathered from this review, along with the findings from a series of public focus groups and an expert review of valuation methodologies, were used to develop a suite of valuation instruments that were used to measure the economic value of different aspects of biodiversity. Contingent valuation and choice experiment studies were administered to households in Cambridgeshire and Northumberland, while valuation workshops were conducted in Northumberland only. The data from these studies were also used to test for benefits transfer