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Improved Mixing and Pressure Loss Formulations for Gas Network Optimization

Geonhee Kim, Christopher Lourenco, Daphne Skipper, Luze Xu

TL;DR

This work tackles the challenging problem of nominating validation in gas networks with mixing and pressure-loss dynamics, using both a discrete MINLP and a continuous NLP formulation. It introduces three classes of cuts (McCormick, flow-direction, bilinear-bounds) to tighten the MINLP and two new smooth pressure-loss models (flow-splitting fs and smooth PKr) that leverage flow-splitting variables. Computational experiments with BARON on GasLib-582 show that the MINLP with cuts and the fs/PKr pressure-loss models achieves reliable, fast solves for all tested instances, while the NLP is more variable and can be slower or fail for some models. The results demonstrate that, with strengthened formulations, MINLP can be competitive with NLP for gas-network nomination problems, guiding practical optimization in large-scale networks with mixing and friction losses.

Abstract

Non-convex, nonlinear gas network optimization models are used to determine the feasibility of flows on existing networks given constraints on network flows, gas mixing, and pressure loss along pipes. This work improves two existing gas network models: a discrete mixed-integer nonlinear program (MINLP) that uses binary variables to model positive and negative flows, and a continuous nonlinear program (NLP) that implements complementarity constraints with continuous variables. We introduce cuts to expedite the MINLP and we formulate two new pressure loss models that leverage the flow-splitting variables: one that is highly accurate and another that is simpler but less accurate. In computational tests using the global solver BARON our cuts and accurate pressure loss improves: (1) the average run time of the MINLP by a factor of 35, (2) the stability of the MINLP by solving every tested instance within 2.5 minutes (the baseline model timed out on 25% of instances), (3) the stability of the NLP by solving more instances than the baseline. Our simpler pressure loss model further improved run times in the MINLP (by a factor of 48 versus the baseline MINLP), but was unstable in the context of the NLP.

Improved Mixing and Pressure Loss Formulations for Gas Network Optimization

TL;DR

This work tackles the challenging problem of nominating validation in gas networks with mixing and pressure-loss dynamics, using both a discrete MINLP and a continuous NLP formulation. It introduces three classes of cuts (McCormick, flow-direction, bilinear-bounds) to tighten the MINLP and two new smooth pressure-loss models (flow-splitting fs and smooth PKr) that leverage flow-splitting variables. Computational experiments with BARON on GasLib-582 show that the MINLP with cuts and the fs/PKr pressure-loss models achieves reliable, fast solves for all tested instances, while the NLP is more variable and can be slower or fail for some models. The results demonstrate that, with strengthened formulations, MINLP can be competitive with NLP for gas-network nomination problems, guiding practical optimization in large-scale networks with mixing and friction losses.

Abstract

Non-convex, nonlinear gas network optimization models are used to determine the feasibility of flows on existing networks given constraints on network flows, gas mixing, and pressure loss along pipes. This work improves two existing gas network models: a discrete mixed-integer nonlinear program (MINLP) that uses binary variables to model positive and negative flows, and a continuous nonlinear program (NLP) that implements complementarity constraints with continuous variables. We introduce cuts to expedite the MINLP and we formulate two new pressure loss models that leverage the flow-splitting variables: one that is highly accurate and another that is simpler but less accurate. In computational tests using the global solver BARON our cuts and accurate pressure loss improves: (1) the average run time of the MINLP by a factor of 35, (2) the stability of the MINLP by solving every tested instance within 2.5 minutes (the baseline model timed out on 25% of instances), (3) the stability of the NLP by solving more instances than the baseline. Our simpler pressure loss model further improved run times in the MINLP (by a factor of 48 versus the baseline MINLP), but was unstable in the context of the NLP.
Paper Structure (36 sections, 2 theorems, 33 equations, 4 figures, 5 tables)

This paper contains 36 sections, 2 theorems, 33 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Previous Work
  3. Our Contribution
  4. Organization
  5. Introduction to gas network optimization
  6. Gas network fundamentals
  7. Notation
  8. Optimization model template
  9. Gas mixing model
  10. Flow-Splitting
  11. Discrete flow-splitting
  12. Continuous flow-splitting
  13. Mixing and propogation
  14. Discrete mixing and propagation
  15. Continuous mixing and propagation
  16. ...and 21 more sections

Key Result

theorem 5.1

If $\frac{k_{u,v}}{D_{u,v}} < 1$, then eq:modelerparam_quadratic has two real solutions: one positive and one negative.

Figures (4)

  • Figure 1: Pressure loss models for a sample GasLib582 Pipe
  • Figure 2: Baseline NLP model dominates baseline MINLP
  • Figure 3: Effects of cuts on the computational performance of the NLP and MINLP.
  • Figure 4: Performance Profile All Pressure Loss Models

Theorems & Definitions (5)

  • theorem 5.1
  • proof
  • remark thmcounterremark
  • theorem 5.2
  • proof