• Energy Research

AbstractMeasurements on the diffusion coefficient of the neutral molecule N,N,N′,N′‐tetramethyl‐para‐phenylenediamine and the radical cation and dication generated by its one‐ and two‐electron oxidation, respectively, are reported over the range 298–348 K in both acetonitrile and four room temperature ionic liquids (RTILs). Data were collected using single and double potential step chronoamperometry at a gold disk electrode of micrometer dimension, and analysed via fitting to the appropriate analytical expression or, where necessary, to simulation. The variation of diffusion coefficient with temperature was found to occur in an Arrhenius‐type manner for all combinations of solute and solvent. For a given ionic liquid, the diffusional activation energies of each species were not only closely equivalent to each other, but also to the RTIL's activation energy of viscous flow. In acetonitrile supported with 0.1 M tetrabutylammonium perchlorate, the ratio in diffusion coefficients of the radical cation and dication to the neutral molecule were calculated as 0.89±0.05 and 0.51±0.03, respectively. In contrast, amongst the ionic liquids the same ratios were determined to be on average 0.53±0.04 and 0.33±0.03. The consequences of this dissimilarity are considered in terms of the modelling of voltammetric data gathered within ionic liquid solvents.

Optimisation and simulation models for the design and operation of grid-connected distributed energy systems (DES) often exclude the inherent nonlinearities related to power flow and generation and storage units, to maintain an accuracy-complexity balance. Such models may provide sub-optimal or even infeasible designs and dispatch schedules. In DES, optimal power flow (OPF) is often misrepresented and treated as a standalone problem. OPF consists of highly nonlinear and nonconvex constraints related to the underlying alternating current (AC) distribution network. This aspect of the optimisation problem has often been overlooked by researchers in the process systems and optimisation area. In this review we address the disparity between OPF and DES models, highlighting the importance of including elements of OPF in DES design and operational models to ensure that the design and operation of microgrids meet the requirements of the electrical grid. By analysing foundational models for both DES and OPF, we identify detailed technical power flow constraints that have been typically represented using oversimplified linear approximations in DES models. We also identify a subset of models, labelled DES-OPF, which include these detailed constraints and use innovative optimisation approaches to solve them. Results of these studies suggest that achieving feasible solutions with high-fidelity models is more important than achieving globally optimal solutions using less-detailed DES models. Recommendations for future work include the need for more comparisons between high-fidelity models and models with linear approximations, and the use of simulation tools to validate DES-OPF models. The review is aimed at a multidisciplinary audience of researchers and stakeholders who are interested in modelling DES to support the development of more robust and accurate optimisation models for the future. 32 pages, 2 figures, 3 tables

The optimal selection, sizing, and location of small-scale technologies within a grid-connected distributed energy system (DES) can contribute to reducing carbon emissions, consumer costs, and network imbalances. This is the first study to present an optimisation framework for obtaining discrete technology sizing and selection for grid-connected DES design, while simultaneously considering multiphase optimal power flow (MOPF) constraints to accurately represent unbalanced low-voltage distribution networks. An algorithm is developed to solve the resulting Mixed-Integer Nonlinear Programming (MINLP) formulation. It employs a decomposition based on Mixed-Integer Linear Programming (MILP) and Nonlinear Programming (NLP), and utilises integer cuts and complementarity reformulations to obtain discrete designs that are also feasible with respect to the network constraints. A heuristic modification to the original algorithm is also proposed to improve computational speed. Improved formulations for selecting feasible combinations of air source heat pumps (ASHPs) and hot water storage tanks are also presented. The algorithms outperform the existing state-of-the-art commercial MINLP solver, which fails to find any solutions in two instances. While feasible solutions were obtained for all cases, convergence was not achieved for all, especially for those involving the larger network. Where converged, the algorithm with the heuristic modification has achieved results up to 70% faster than the original algorithm. Results for case studies suggest that including ASHPs can support up to 16% higher renewable generation capacity compared to gas boilers, albeit with higher ASHP investment costs. The optimisation framework and results can be used to inform stakeholders such as policy-makers and network operators, to increase renewable energy capacity and aid the decarbonisation of domestic heating systems. 47 pages, 10 figures, 14 Tables

The design of grid-connected distributed energy systems (DES) has been investigated extensively as an optimisation problem in the past, but most studies do not include nonlinear constraints associated with unbalanced alternating current (AC) power flow in distribution networks. Previous studies that do consider AC power flow use either less complex balanced formulations applicable to transmission networks, or iterative linearisations derived from local power flow solutions and prior knowledge of the design. To address these limitations, this study proposes a new algorithm for obtaining DES design decisions subject to nonlinear power flow models. The use of regularised complementarity reformulations for operational constraints that contain binary variables is proposed. This allows the use of large-scale nonlinear solvers that can find locally optimal solutions, eliminating the need for linearisations and prior knowledge while improving accuracy. DES design models with either multiphase optimal power flow (MOPF), which captures inherent phase imbalances present in distribution networks, or balanced optimal power flow formulations (OPF) are tested using a modified version of the unbalanced IEEE EU low-voltage network. Results are compared with a popular linear DES design framework, which proposes an infeasible operational schedule when tested with MOPF, while the fixed design alone produces the highest annualised costs. Despite the increased complexity, DES with MOPF obtains the best solution, enabling a greater integration of solar capacity and reducing total annualised cost when compared to DES with OPF. The new algorithm achieves a 19% improvement when compared with solving a bi-level model for DES with OPF, where the entire binary topology in the nonlinear model is fixed. The study therefore enables the acquisition of DES designs that can work symbiotically within distribution networks. 20 pages, 5 figures