Applying Piecewise Linear Characteristic Curves in District Energy Optimisation. Pickering, B. & Choudhary, R. 07 2017. ![Applying Piecewise Linear Characteristic Curves in District Energy Optimisation [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper abstract bibtex Representing nonlinear curves as piecewise elements allows complex systems to be optimised by linear programs. Piecewise linearisation has been recently introduced in the context of distributed energy system optimisation. It is an efficient technique for representing non-linear technology behaviours in linear optimisation models, which are favourable in district energy optimisation models, owing to their speed and ability to handle large numbers of design variables. This paper describes a method of automating the creation of piecewise elements of technology performance curves for minimum fit error. The results show an objective function value improvement at a relatively large penalty in solution time: from 1.6 times to 58 times longer than describing technologies as having a single value for efficiency (SVE). We show that within the context of common technology performance curves, three breakpoints yield sufficiently accurate results and any returns are diminishing beyond that. Even at three breakpoints, it is evident that the placement of breakpoints along a curve significantly influences solution time, in a way for which it is not possible to account in automation. But, large savings can be made by automation by including a constraint to ensure piecewise curves have a strictly increasing/decreasing gradient. This avoids the use of special ordered sets, simplifying model generation and the number of non-continuous variables. SVE models provide a less realistic solution and application of nonlinear consumption curves ex-post shows them to be ultimately more expensive systems than their piecewise counterparts. However, this ex-post analysis applied to SVE models is a good compromise for feasibility level analyses, where whole system cost is key. However, investment decisions and operation schedules are markedly affected by consumption curve representation. Thus, the use of piecewise linearisation is beneficial for detailed design, particularly if automation of breakpoint allocation can help solve the issue of model convergence.
@conference{Pickering2017ApplyingPiecewise,
author = {Bryn Pickering and Ruchi Choudhary},
booktitle = {The 30th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS)},
address = {San Diego, California, USA},
title = {Applying Piecewise Linear Characteristic Curves in District Energy Optimisation},
year = {2017},
month = {07},
abstract = {Representing nonlinear curves as piecewise elements allows complex systems to be optimised by linear programs. Piecewise linearisation has been recently introduced in the context of distributed energy system optimisation. It is an efficient technique for representing non-linear technology behaviours in linear optimisation models, which are favourable in district energy optimisation models, owing to their speed and ability to handle large numbers of design variables. This paper describes a method of automating the creation of piecewise elements of technology performance curves for minimum fit error. The results show an objective function value improvement at a relatively large penalty in solution time: from 1.6 times to 58 times longer than describing technologies as having a single value for efficiency (SVE). We show that within the context of common technology performance curves, three breakpoints yield sufficiently accurate results and any returns are diminishing beyond that. Even at three breakpoints, it is evident that the placement of breakpoints along a curve significantly influences solution time, in a way for which it is not possible to account in automation. But, large savings can be made by automation by including a constraint to ensure piecewise curves have a strictly increasing/decreasing gradient. This avoids the use of special ordered sets, simplifying model generation and the number of non-continuous variables. SVE models provide a less realistic solution and application of nonlinear consumption curves ex-post shows them to be ultimately more expensive systems than their piecewise counterparts. However, this ex-post analysis applied to SVE models is a good compromise for feasibility level analyses, where whole system cost is key. However, investment decisions and operation schedules are markedly affected by consumption curve representation. Thus, the use of piecewise linearisation is beneficial for detailed design, particularly if automation of breakpoint allocation can help solve the issue of model convergence.},
url = {https://www.researchgate.net/publication/319334427_Applying_Piecewise_Linear_Characteristic_Curves_in_District_Energy_Optimisation},
keywords = {District energy, Mixed Integer Linear Programming, Optimisation, Piecewise Linearisation},
project = {District_energy}
}
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It is an efficient technique for representing non-linear technology behaviours in linear optimisation models, which are favourable in district energy optimisation models, owing to their speed and ability to handle large numbers of design variables. This paper describes a method of automating the creation of piecewise elements of technology performance curves for minimum fit error. The results show an objective function value improvement at a relatively large penalty in solution time: from 1.6 times to 58 times longer than describing technologies as having a single value for efficiency (SVE). We show that within the context of common technology performance curves, three breakpoints yield sufficiently accurate results and any returns are diminishing beyond that. Even at three breakpoints, it is evident that the placement of breakpoints along a curve significantly influences solution time, in a way for which it is not possible to account in automation. But, large savings can be made by automation by including a constraint to ensure piecewise curves have a strictly increasing/decreasing gradient. This avoids the use of special ordered sets, simplifying model generation and the number of non-continuous variables. SVE models provide a less realistic solution and application of nonlinear consumption curves ex-post shows them to be ultimately more expensive systems than their piecewise counterparts. However, this ex-post analysis applied to SVE models is a good compromise for feasibility level analyses, where whole system cost is key. However, investment decisions and operation schedules are markedly affected by consumption curve representation. 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