Optimal Piecewise Affine Approximations of Nonlinear Functions Obtained from Measurements

Szűcs, Alexander; Kvasnica, Michal; Fikar, Miroslav

doi:10.3182/20120606-3-nl-3011.00061

Cited by 12 publications

(7 citation statements)

References 10 publications

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“…To locate the optimal breakpoints for creating a linear‐piecewise function, a nonlinear programming problem (NLP) must be solved for each operation point. For this purpose, we used a toolbox created in previous studies,() which uses MATLAB's symbolic toolbox and fmincon solver to solve the NLP. For candidate operation points, we have selected two data points for C r ∈ {0,1} and 500 logarithmically distributed data points (from 10 −4 to 5·10 3 ) for FEC 0 .…”

Section: Methodsmentioning

confidence: 99%

Design and analysis of an aging‐aware energy management system for islanded grids using mixed‐integer quadratic programming

et al. 2019

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Summary The rapid increase of renewable energy sources made coordinated control of the distributed and intermittent generation units a more demanded task. Matching demand and supply is particularly challenging in islanded microgrids. In this study, we have demonstrated a mixed‐integer quadratic programming (MIQP) method to achieve efficient use of sources within an islanded microgrid. A unique objective function involving fuel consumption of diesel generator, degradation in a lithium‐ion battery energy storage system, carbon emissions, load shifting, and curtailment of the renewable sources is constructed, and an optimal operating point is pursued using the MIQP approach. A systematic and extensive methodology for building the objective function is given in a sequential and explicit manner with an emphasis on a novel model‐based battery aging formulation. Performance of the designed system and a sensitivity analysis of resulting battery dispatch, diesel generator usage, and storage aging against a range of optimization parameters are presented by considering real‐world specifications of the Semakau Island, an island in the vicinity of Singapore.

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Section: Methodsmentioning

confidence: 99%

Design and analysis of an aging‐aware energy management system for islanded grids using mixed‐integer quadratic programming

et al. 2019

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“…In this study, to determine vertices optimally, the approach used in [7], [54]- [56] is adapted to handle 3 dimensional data: assuming that the system can be approximated by a gridded data (i.e., not randomly scattered in the three dimensional input space). Hence, only the data points lying at the axes were optimally selected with the help of MATLAB's fmincon solver and griddedInterpolant functions.…”

Section: F Approximation Of Other Nonlinearitiesmentioning

confidence: 99%

Energy Arbitrage Optimization With Battery Storage: 3D-MILP for Electro-Thermal Performance and Semi-Empirical Aging Models

et al. 2020

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Dispatch of battery storage systems for stationary grid applications is a topic of increasing interest: due to the volatility of power system's energy supply relying on variable renewable energy sources, one foresees a rising demand and market potential for both short-and long-term fluctuation smoothing via energy storage. While the potential revenue attainable via arbitrage trading may yet surpass the steadily declining cost of lithium-ion battery storage systems, profitability will be constrained directly by the limited lifetime of the battery system and lowered by dissipation losses of both battery and power electronic components. In this study, we present a novel three-dimensional mixed-integer program formulation allowing to model power, state of charge (SOC), and temperature dependence of battery dynamics simultaneously in a three dimensional space leveraging binary counting and union-jack triangulation. The inclusion of a state-of-the-art electro-thermal degradation model with its dependence on most influential physical parameters to the arbitrage revenue optimization allows to extend the battery lifetime by 2.2 years (or 40%) over a base scenario. By doing a profitability estimation over the battery's lifetime and using 2018 historical intraday market trading prices, we have shown that profitability of the system increases by 11.14% via introducing SOC awareness and another significant 12.64% via introducing thermal sensitivity, resulting in a total 25.19% increase over the base case optimization formulation. Lastly, through the open source publication of the optimization routines described herein, an adaption and development of the code to individual needs is facilitated.

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“…After obtaining an appropriate form for approximation, the coefficients a i and b i , and the breakpoints r i , in Equation (A1), can be found by solving a nonlinear programming problem, defined by Equation (A4) for a pre-defined N number of pieces [52]. Therefore, an open-source toolbox, developed by Alexander Szücs et al [64][65][66], is used to determine the unknown parameters. Solutions are given in Tables A4 and A5.…”

Section: Abbreviationsmentioning

confidence: 99%

Ageing and Efficiency Aware Battery Dispatch for Arbitrage Markets Using Mixed Integer Linear Programming †

et al. 2019

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To achieve maximum profit by dispatching a battery storage system in an arbitrage operation, multiple factors must be considered. While revenue from the application is determined by the time variability of the electricity cost, the profit will be lowered by costs resulting from energy efficiency losses, as well as by battery degradation. In this paper, an optimal dispatch strategy is proposed for storage systems trading on energy arbitrage markets. The dispatch is based on a computationally-efficient implementation of a mixed-integer linear programming method, with a cost function that includes variable-energy conversion losses and a cycle-induced battery capacity fade. The parametrisation of these non-linear functions is backed by in-house laboratory tests. A detailed analysis of the proposed methods is given through case studies of different cost-inclusion scenarios, as well as battery investment-cost scenarios. An evaluation with a sample intraday market data set, collected throughout 2017 in Germany, offers a potential monthly revenue of up to 8762 EUR/MWh cap installed capacity, without accounting for the costs attributed to energy losses and battery degradation. While this is slightly above the revenue attainable in a reference application—namely, primary frequency regulation for the same sample month (7716 EUR/MWh cap installed capacity)—the situation changes if costs are considered: The optimisation reveals that losses in battery ageing and efficiency reduce the attainable profit by up to 36% for the most profitable arbitrage use case considered herein. The findings underline the significance of considering both ageing and efficiency in battery system dispatch optimisation.

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Optimal Piecewise Affine Approximations of Nonlinear Functions Obtained from Measurements

Cited by 12 publications

References 10 publications

Design and analysis of an aging‐aware energy management system for islanded grids using mixed‐integer quadratic programming

Design and analysis of an aging‐aware energy management system for islanded grids using mixed‐integer quadratic programming

Energy Arbitrage Optimization With Battery Storage: 3D-MILP for Electro-Thermal Performance and Semi-Empirical Aging Models

Ageing and Efficiency Aware Battery Dispatch for Arbitrage Markets Using Mixed Integer Linear Programming †

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