Research Papers: Energy Systems Analysis

Topology Optimization of Robust District Heating Networks

[+] Author and Article Information
Alberto Pizzolato

Department of Energy,
Politecnico di Torino,
Torino 10129, Italy
e-mail: alberto.pizzolato@polito.it

Adriano Sciacovelli

Birmingham Centre for Energy Storage (BCES),
School of Chemical Engineering,
University of Birmingham,
Birmingham B15 2TT, UK
e-mail: a.sciacovelli@bham.ac.uk

Vittorio Verda

Department of Energy,
Politecnico di Torino,
Torino 10129, Italy
e-mail: vittorio.verda@polito.it

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received February 1, 2017; final manuscript received September 18, 2017; published online November 14, 2017. Assoc. Editor: George Tsatsaronis.

J. Energy Resour. Technol 140(2), 020905 (Nov 14, 2017) (9 pages) Paper No: JERT-17-1054; doi: 10.1115/1.4038312 History: Received February 01, 2017; Revised September 18, 2017

Large district heating networks greatly benefit from topological changes brought by the construction of loops. The overall effects of malfunctions are smoothed, making existing networks intrinsically robust. In this paper, we demonstrate the use of topology optimization to find the network layout that maximizes robustness under an investment constraint. The optimized design stems from a large ground structure that includes all the possible looping elements. The objective is an original robustness measure, that neither requires any probabilistic analysis of the input uncertainty nor the identification of bounds on stochastic variables. Our case study on the Turin district heating network confirms that robustness and cost are antagonist objectives: the optimized designs obtained by systematically relaxing the investment constraint lay on a smooth Pareto front. A sudden steepness variation divides the front in two different regions. For small investments topological modifications are observed, i.e., new branches appear continuously in the optimized layout as the investment increases. Here, large robustness improvements are possible. However, at high investments no topological modifications are visible and only limited robustness gains are obtained.

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Fig. 1

Schematic of the one-dimensional model of the network

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Fig. 2

Original and smoothed cost function

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Fig. 3

Finite difference check on the accuracy of the adjoint approach: (a) first-order sensitivities and (b) second-order sensitivities

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Fig. 4

Original network and ground structure

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Fig. 5

Performance of the current network in design conditions: (a) mass flow rate and directions in each branch of the network and (b) pressure field

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Fig. 6

(a) Pareto front expressing the trade-off between robustness and cost and (b) marginal cost of robustness

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Fig. 7

Minimum investment required for each branch to exist. Black branches are never found to be economically convenient.

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Fig. 8

Optimized network layout at selected Pareto points. (a) 20 k€ investment, (b) 200 k€ investment, (c) 1000 k€ investment.

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Fig. 9

Local robustness field for the Pareto point at C*=200k€

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Fig. 10

Supply pressure field at selected Pareto points: (a) 20 k€ investment, (b) 200 k€ investment, (c) 1000 k€ investment

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Fig. 11

(a) Pressure drop reduction obtained in the PHs at selected Pareto points and (b) supply pressure in the PHs at selected Pareto points



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