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Power minimization of gas transmission network in fully transient state using metaheuristic methods

  • Hamid Reza Moetamedzadeh EMAIL logo and Hossein Khodabakhshi Rafsanjani
Published/Copyright: October 17, 2022
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 23 Issue 7-8

Abstract

In gas transmission networks, the pressure drop caused by friction is one of the main operation costs that is compensated through consuming energy in the compressors. In the competitive market of energy, considering the demand variation is inevitable. Hence, the power minimization should be carried out in transient state. Since the minimization problem is severely nonlinear and nonconvex subjected to nonlinear constraints, utilizing a powerful minimization tool with a straightforward procedure is very helpful. In this paper, a novel approach is proposed based on metaheuristic algorithms for power minimization of a gas transmission network in fully transient conditions. The metaheuristic algorithms, unlike the gradient dependent method, can solve the complicated minimization problem without simplification. In the proposed strategy, the cost function is not expressed explicitly as a function of minimization variables; therefore, the transient minimization can be as precise as possible. The minimization is carried out by a straightforward methodology in each time sample, which leads to more precise solutions as compared to the quasi transient minimization. The metaheuristic minimizer, called the particle swarm optimization gravitational search algorithm (PSOGSA), is utilized to find the optimum operating set points. The numerical results also confirm the accuracy and well efficiency of the proposed method.

Keywords: gas transmission; metaheuristic algorithm; minimization; transient analysis
Corresponding author: Hamid Reza Moetamedzadeh, University of Applied Science and Technology, Yazd Branch, Yazd, Iran, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix A

In this section the procedure of the transient analysis for a simple gas transmission network (illustrated in Figure A.1) is presented. This methodology could be extended for more complicated networks.

Figure A.1: Simple gas pipeline network.
Figure A.1:

Simple gas pipeline network.

The transient analysis can be accomplished by constituting the system of equations and solving it by the numerical algorithms such as Newton–Raphson. The goal is to find the pressure and flowrates of all space nodes of the network at all time.

Figure A.2 shows the system of equations of the network illustrated in Figure A.1 for computing the pressure and flowrate of each node at time sample n + 1. These quantity at time sample n have been computed previously and n = 1 belongs to the initial conditions. In this pseudo code P{1} and Q{1} are pressure and flowrate of the first pipe (Pipe{1}). Also, P{2}and Q{2} are pressure and flowrate of the second pipe (Pipe{2}). The external boundary values in this network are the input pressure (Pin) and the output flowrate (Q out) used in lines 9 and 24, respectively. As shown in Figure A.1, P d is the discharge pressure and Q s is the suction flowrate. The parameter J is the number of nodes in each pipeleg. Lines 1–8 are the momentum and continuity equations for the first pipeleg. Line 9 indicates to the external boundary values for the first pipeleg which is input pressure. Line 10 calculates the suction pressure according to Eq. (2). Also, Line 11 computes the discharge pressure regarding to Eq. (7). These values are used as the internal boundary values for the second pipeleg. In lines 12 and 13, EI and VI are the equation and variable indexes used to keep the system of equations straightforward. Lines 14–21 are the momentum and continuity equations for the second pipeleg. Line 22–24 indicates the boundary values where lines 22–23 are the internal boundary values and line 24 is the external boundary value (the output flowrate). As shown in Figure A.2, the system of equation has 2J + EI + 3 = 4J + 4 equations (F(1) to F(2J + EI + 3)) and 2J + 2 + VI = 4J + 4 unknowns (X(1) to X(2J + 2 + VI)) which can be easily solved by numerical method such as Newton–Raphson algorithm. Using the same procedure the system of equations of more complicated networks could be considered and solved for transient analysis.

Figure A.2: The system of equations of a simple pipeline network illustrated in Figure A.1 to compute the pressure and flowrate of each node at time sample n + 1.
Figure A.2:

The system of equations of a simple pipeline network illustrated in Figure A.1 to compute the pressure and flowrate of each node at time sample n + 1.

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Received: 2020-03-12
Revised: 2022-05-17
Accepted: 2022-09-29
Published Online: 2022-10-17
Published in Print: 2022-12-16

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2020-0057
Keywords for this article
gas transmission; metaheuristic algorithm; minimization; transient analysis

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Coordinated target tracking in sensor networks by maximizing mutual information
  4. Legendre wavelet residual approach for moving boundary problem with variable thermal physical properties
  5. Computational study of intravenous magnetic drug targeting using implanted magnetizable stent
  6. Extended logistic map for encryption of digital images
  7. Valuation of the American put option as a free boundary problem through a high-order difference scheme
  8. Power minimization of gas transmission network in fully transient state using metaheuristic methods
  9. A priori error estimates for finite element approximations to transient convection-diffusion-reaction equations in fluidized beds
  10. Higher order rogue waves for the(3 + 1)-dimensional Jimbo–Miwa equation
  11. Dynamic characteristics of supersonic turbulent free jets from four types of circular nozzles
  12. New insights into singularity analysis
  13. Chaos and bifurcations in a discretized fractional model of quasi-periodic plasma perturbations
  14. Wavelet collocation methods for solving neutral delay differential equations
  15. Numerical solution of highly non-linear fractional order reaction advection diffusion equation using the cubic B-spline collocation method
  16. Solving nonlinear third-order boundary value problems based-on boundary shape functions
  17. Positive radial solutions for Dirichlet problems involving the mean curvature operator in Minkowski space
  18. Effect of outlet impeller diameter on performance prediction of centrifugal pump under single-phase and cavitation flow conditions
  19. A fractional-order ship power system: chaos and its dynamical properties
  20. Graphical structure of extended b-metric spaces: an application to the transverse oscillations of a homogeneous bar
  21. Hypergeometric fractional derivatives formula of shifted Chebyshev polynomials: tau algorithm for a type of fractional delay differential equations
  22. Modelling and numerical synchronization of chaotic system with fractional-order operator
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