Mathematical software for gas transmission networks

This thesis is concerned with the development of numerical software for the simulation of gas transmission networks. This involves developing software for the solution of a large system of stiff differential/algebraic equations (DAE) containing frequent severe disturbances. The disturbances arise due to the varying consumer demands and the operation of network controlling devices such as the compressors. Special strategies are developed to solve the DAE system efficiently using a variable-step integrator. Two sets of strategies are devised; one for the implicit methods such as the semi-implicit Runge-Kutta method, and the other for the linearly implicit Rosenbrock-type method. Four integrators, based on different numerical methods, have been implemented and the performance of each one is compared with the British Gas network analysis program PAN, using a number of large, realistic transmission networks. The results demonstrate that the variable-step integrators are reliable and efficient. An efficient sparse matrix decomposition scheme is developed to solve the large, sparse system of equations that arise during the integration of the DAE system. The decomposition scheme fully exploits the special structure of the coefficient matrix. Lastly, for certain networks, the existing simulation programs fail to compute a feasible solution because of the interactions of the controlling devices in the network. To overcome this difficulty, the problem is formulated as a variational inequality model and solved numerically using an optimization routine from the NAG library (NAGFLIB(l982)). The reliability of the model is illustrated using three test networks

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

Efficient Dynamic Compressor Optimization in Natural Gas Transmission Systems

The growing reliance of electric power systems on gas-fired generation to balance intermittent sources of renewable energy has increased the variation and volume of flows through natural gas transmission pipelines. Adapting pipeline operations to maintain efficiency and security under these new conditions requires optimization methods that account for transients and that can quickly compute solutions in reaction to generator re-dispatch. This paper presents an efficient scheme to minimize compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flow. The optimization scheme relies on a compact representation of gas flow physics, a trapezoidal discretization in time and space, and a two-stage approach to minimize energy costs and maximize smoothness. The resulting large-scale nonlinear programs are solved using a modern interior-point method. The proposed optimization scheme is validated against an integration of dynamic equations with adaptive time-stepping, as well as a recently proposed state-of-the-art optimal control method. The comparison shows that the solutions are feasible for the continuous problem and also practical from an operational standpoint. The results also indicate that our scheme provides at least an order of magnitude reduction in computation time relative to the state-of-the-art and scales to large gas transmission networks with more than 6000 kilometers of total pipeline

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

Impacts of plug-in hybrid vehicles and combined heat and power technologies on electric and gas distribution network losses

Distribution network operators (DNOs) require strategies that can offset the tradeoffs new embedded technologies have on their assets. This paper employs modelling to show that through control device manipulation, gas and electric (G&E) network operators can influence savings in energy losses under the presence of plug-in hybrid vehicles (PHEVs) and combined heat and power technologies (CHPs). An integrated gas and electric optimal power flow (OPF) tool is introduced to undertake various case studies. The OPF tool evaluates the technical impacts experienced in the networks when DNOs apply a "plug and forget" operation strategy and then compares the results against a "loss minimisation" strategy. Results show the benefits in applying different strategies are more considerable in electric networks than in gas networks. The study corroborates that an integrated G&E analysis offers a fresh perspective for stakeholders in evaluating energy service networks performance under different operation strategies

A mathematical framework for modelling and evaluating natural gas pipeline networks under hydrogen injection

This article presents the framework of a mathematical formulation for modelling and evaluating natural gas pipeline networks under hydrogen injection. The model development is based on gas transport through pipelines and compressors which compensate for the pressure drops by implying mainly the mass and energy balances on the basic elements of the network. The model was initially implemented for natural gas transport and the principle of extension for hydrogen-natural gas mixtures is presented. The objective is the treatment of the classical fuel minimizing problem in compressor stations. The optimization procedure has been formulated by means of a nonlinear technique within the General Algebraic Modelling System (GAMS) environment. This work deals with the adaptation of the current transmission networks of natural gas to the transport of hydrogen-natural gas mixtures. More precisely, the quantitative amount of hydrogen that can be added to natural gas can be determined. The studied pipeline network,initially proposed by Abbaspour et al. (2005) is revisited here for the case of hydrogen-natural gas mixtures. Typical quantitative results are presented, showing that the addition of hydrogen to natural gas decreases significantly the transmitted power : the maximum fraction of hydrogen that can be added to natural gas is around 6 mass percent for this example