Thermal performance of a steady state physical pipe model for simulating district heating grids with variable flow

Duquette, Jean; Rowe, Andrew; Wild, Peter

doi:10.1016/j.apenergy.2016.06.092

Cited by 117 publications

(48 citation statements)

References 14 publications

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“…are distributed according to µ 1 and µ 2 respectively. Constraint (3b) ensures that µ 1 is a valid probability 2 The notation M(C) + denotes the cone of non-negative Borel measures on a semi-algebraic set C.…”

Section: A Generalized Moment Problem For Two-stage Programs With Recmentioning

confidence: 99%

“…Most older district heating networks are controlled using VT-CF, whereas newer networks use CT-VF [2].…”

Section: Optimal Operating Strategiesmentioning

confidence: 99%

“…The network constraints described in Section 5 cannot be directly integrated into the polynomial optimization framework (1)- (2). Whereas the polynomial approximation (17) is valid for positive and negative mass flow values, we need to determine the flow direction in advance to remove the absolute value operator in (13) and to establish equations (18) and (19).…”

Section: Optimal Operating Strategiesmentioning

confidence: 99%

“…Theorem. Two-stage problem (1)- (2) and the GMP (3) are equivalent, in that (a) ρ 12 = ρ, and (b) if x * 1 is an optimal solution of (1), then (3) has an optimal solution that includes the Dirac measure µ * 1 = δ x * 1 .…”

Section: Appendix a Proof Of Theoremmentioning

confidence: 99%

“…We report that the performance of an optimally-parameterized fixed-temperature variable-mass-flow strategy can approach that of a fully variable strategy. systems tend to have variable mass flow control [2]. Each strategy is subject to a trade-off in terms of losses; higher supply and return temperatures lead to increased heat losses, whereas higher mass flow rates increase the hydraulic losses in the pipes.…”

mentioning

confidence: 99%

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A two-stage polynomial approach to stochastic optimization of district heating networks

Hohmann

Warrington

Lygeros

2019

Sustainable Energy, Grids and Networks

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In this paper, we use stochastic polynomial optimization to derive high-performance operating strategies for heating networks with uncertain or variable demand. The heat flow in district heating networks can be regulated by varying the supply temperature, the mass flow rate, or both simultaneously, leading to different operating strategies. The task of choosing the set-points within each strategy that minimize the network losses for a range of demand conditions can be cast as a two-stage stochastic optimization problem with polynomial objective and polynomial constraints. We derive a generalized moment problem (GMP) equivalent to such a two-stage stochastic optimization problem, and describe a hierarchy of moment relaxations approximating the optimal solution of the GMP. Under various network design parameters, we use the method to compute (approximately) optimal strategies when one or both of the mass flow rate and supply temperature for a benchmark heat network. We report that the performance of an optimally-parameterized fixed-temperature variable-mass-flow strategy can approach that of a fully variable strategy. systems tend to have variable mass flow control [2]. Each strategy is subject to a trade-off in terms of losses; higher supply and return temperatures lead to increased heat losses, whereas higher mass flow rates increase the hydraulic losses in the pipes. This trade-off has been studied in different contexts. A comparison of strategies for primary networks 1 can be found in [3]. Hydraulic control strategies for the primary and secondary network were optimized in [4]. New mass flow regulation schemes using pumps were compared to the traditional strategy of controlling the consumer side heat flow using valves in [5]. The performance of district heating networks with multiple sources was studied in [6].Significant effort has also been invested in simplified models of these systems. The steady-state thermal losses of a network can be modelled as an exponential temperature drop along a pipe segment [6,7,8,9].By replacing the exponential by its first order Taylor approximation, the authors of [7] and [9] obtain a polynomial representation of the pipe output temperature. The hydraulic losses, namely the pressure drop along pipes and substations, are mass flow rate dependent and can be characterised implicitly by the nonlinear Colebrook-White equation [6]. To simplify this representation, it is often assumed that a pipe segment has a constant coefficient of resistance [7,9,10], making the absolute pressure losses quadratic in the mass flow rate. Thus, both types of network loss can be modelled using polynomial functions. Two-stage stochastic programsIf the operating strategy keeps a control variable fixed (either temperature or mass flow rate), it is desirable that the fixed choice leads to acceptable performance over a range of demand conditions. Here we define this performance as the expected operational cost incurred by hydraulic and thermal losses with respect to a probability distribution of the heat de...

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Section: A Generalized Moment Problem For Two-stage Programs With Recmentioning

confidence: 99%

“…Most older district heating networks are controlled using VT-CF, whereas newer networks use CT-VF [2].…”

Section: Optimal Operating Strategiesmentioning

confidence: 99%

Section: Optimal Operating Strategiesmentioning

confidence: 99%

Section: Appendix a Proof Of Theoremmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

A two-stage polynomial approach to stochastic optimization of district heating networks

Hohmann

Warrington

Lygeros

2019

Sustainable Energy, Grids and Networks

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Various disturbances propagation analysis of district heating system based on the standardized thermal resistance method

Chen,

Wang,

Hao

et al. 2023

Energy Science & Engineering

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Various heating disturbances and faults in the heating network are necessary to be controlled and handled by some intelligent heating strategies with the increasing complexity of the heating network. This paper constructed the dynamic modeling of the heating system using standard thermal resistance and obtained a dynamic heat current model of the heating system. On this basis, we analyzed the heat transfer performance of the heating system. Five disturbances are selected, including the behavior of users, indoor heat source, heat exchanger heat transfer performance deterioration, pipe blockage, and pipe leakage. The effects of different disturbances on the overall system and user side water supply temperature were obtained by establishing a dynamic model for segmented heating pipelines. Feasible control methods for the heating network and load side are sorted out, mainly changing the water supply's temperature and the water supply's flow rate to reduce the water supply's fluctuation. Five specific control strategies are proposed for five types of disturbances. Comparing the case without control and the case with control, the results show that the fluctuation of water supply temperature is significantly reduced, and the control strategies can reduce the impact of disturbances on the heat network system and customers and improve the comfort of customers in the presence of disturbances. under the disturbance of pipeline leakage, the method proposed in this article reduces the temperature fluctuation amplitude by 75% and the fluctuation duration by 60%.

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Flow Process Models for Pipeline Diagnosis

Kowalczuk

Tatara

2020

Studies in Systems, Decision and Control

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Thermal performance of a steady state physical pipe model for simulating district heating grids with variable flow

Cited by 117 publications

References 14 publications

A two-stage polynomial approach to stochastic optimization of district heating networks

A two-stage polynomial approach to stochastic optimization of district heating networks

Various disturbances propagation analysis of district heating system based on the standardized thermal resistance method

Flow Process Models for Pipeline Diagnosis

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