Convex Relaxations for Gas Expansion Planning

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutions to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal soluutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solutions

A cost function for the natural gas transmission industry: further considerations

This article studies the cost function for the natural gas transmission industry. In addition to a tribute to H.B. Chenery, it firstly offers some further comments on a recent contribution (Yépez, 2008): a statistical characterization of long-run scale economies, and a simple reformulation of the long-run problem. An extension is then proposed to analyze how the presence of seasonally-varying flows modifies the optimal design of a transmission infrastructure. Lastly, the case of a firm that anticipates a possible random rise in its future output is also studied to discuss the optimal degree of excess capacity to be built into a new transmission infrastructure

Optimization of the long-term planning of supply chains with decaying performance

This master's thesis addresses the optimization of supply and distribution chains considering the effect that equipment aging may cause over the performance of facilities involved in the process. The decaying performance of the facilities is modeled as an exponential equation and can be either physical or economic, thus giving rise to a novel mixed integer non-linear programming (MINLP) formulation. The optimization model has been developed based on a typical chemical supply chain. Thus, the best long-term investment plan has to be determined given production nodes, their production capacity and expected evolution; aggregated consumption nodes (urban or industrial districts) and their lumped demand (and expected evolution); actual and potential distribution nodes; distances between the nodes of the network; and a time horizon. The model includes the balances in each node, a general decaying performance function, and a cost function, as well as constraints to be satisfied. Hence, the investment plan (decision variables) consists not only on the start-up and shutdown of alternative distribution facilities, but also on the sizing of the lines satisfying the flows. The model has been implemented using GAMS optimization software. Results considering a variety of scenarios have been discussed. In addition, different approaches to the starting point for the model have been compared, showing the importance of initializing the optimization algorithm. The capabilities of the proposed approach have been tested through its application to two case studies: a natural gas network with physical decaying performance and an electricity distribution network with economic decaying performance. Each case study is solved with a different procedure to obtain results. Results demonstrate that overlooking the effect of equipment aging can lead to infeasible (for physical decaying performance) or unrealistic (for economic decaying performance) solutions in practice and show how the proposed model allows overcoming such limitations thus becoming a practical tool to support the decision-making process in the distribution secto

Robust Multi-Objective Sustainable Reverse Supply Chain Planning: An Application in the Steel Industry

In the design of the supply chain, the use of the returned products and their recycling in the production and consumption network is called reverse logistics. The proposed model aims to optimize the flow of materials in the supply chain network (SCN), and determine the amount and location of facilities and the planning of transportation in conditions of demand uncertainty. Thus, maximizing the total profit of operation, minimizing adverse environmental effects, and maximizing customer and supplier service levels have been considered as the main objectives. Accordingly, finding symmetry (balance) among the profit of operation, the environmental effects and customer and supplier service levels is considered in this research. To deal with the uncertainty of the model, scenario-based robust planning is employed alongside a meta-heuristic algorithm (NSGA-II) to solve the model with actual data from a case study of the steel industry in Iran. The results obtained from the model, solving and validating, compared with actual data indicated that the model could optimize the objectives seamlessly and determine the amount and location of the necessary facilities for the steel industry more appropriately.This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problem

Distributed Resources Shift Paradigms on Power System Design, Planning, and Operation: An Application of the GAP Model

Power systems have evolved following a century-old paradigm of planning and operating a grid based on large central generation plants connected to load centers through a transmission grid and distribution lines with radial flows. This paradigm is being challenged by the development and diffusion of modular generation and storage technologies. We use a novel approach to assess the sequencing and pacing of centralized, distributed, and off-grid electrification strategies by developing and employing the grid and access planning (GAP) model. GAP is a capacity expansion model to jointly assess operation and investment in utility-scale generation, transmission, distribution, and demand-side resources. This paper conceptually studies the investment and operation decisions for a power system with and without distributed resources. Contrary to the current practice, we find hybrid systems that pair grid connections with distributed energy resources (DERs) are the preferred mode of electricity supply for greenfield expansion under conservative reductions in photovoltaic panel (PV) and energy storage prices. We also find that when distributed PV and storage are employed in power system expansion, there are savings of 15%-20% mostly in capital deferment and reduced diesel use. Results show that enhanced financing mechanisms for DER PV and storage could enable 50%-60% of additional deployment and save 15 /MWh in system costs. These results have important implications to reform current utility business models in developed power systems and to guide the development of electrification strategies in underdeveloped grids