Automatic Derivation of Optimal Piecewise Affine Approximations of Nonlinear Systems

Kvasnica, Michal; Szűcs, Alexander; Fikar, Miroslav

doi:10.3182/20110828-6-it-1002.01104

Cited by 13 publications

(12 citation statements)

References 6 publications

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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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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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“…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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“…They use neural networks with predefined basis functions to obtain the nonlinear functions. At the second stage they obtain the PWA approximation for the nonlinear functions obtained in the first stage using the approaches in Kvasnica etal . Kvasnica etal .…”

Section: Integration Of Scheduling and Control Based On Pwa Modelmentioning

confidence: 99%

“…However, for general multiple dimension functions that cannot be put into the form of case 1 and 2, Kvasnica etal . did not provide any approximation approaches.…”

Section: Integration Of Scheduling and Control Based On Pwa Modelmentioning

confidence: 99%

An integrated framework for scheduling and control using fast model predictive control

Zhuge

Ierapetritou

2015

AIChE Journal

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in Wiley Online Library (wileyonlinelibrary.com) Integration of scheduling and control involves extensive information exchange and simultaneous decision making in industrial practice (Engell and Harjunkoski, Comput Chem Eng. 2012;47:121-133; Baldea and Harjunkoski I, Comput Chem Eng. 2014;71:377-390). Modeling the integration of scheduling and dynamic optimization (DO) at control level using mathematical programming results in a Mixed Integer Dynamic Optimization which is computationally expensive (Flores-Tlacuahuac and Grossmann, Ind Eng Chem Res. 2006;45(20):6698-6712). In this study, we propose a framework for the integration of scheduling and control to reduce the model complexity and computation time. We identify a piece-wise affine model from the first principle model and integrate it with the scheduling level leading to a new integration. At the control level, we use fast Model Predictive Control (fast MPC) to track a dynamic reference. Fast MPC also overcomes the increasing dimensionality of multiparametric MPC in our previous study (Zhuge and Ierapetritou, AIChE J. 2014;60(9):3169-3183). Results of CSTR case studies prove that the proposed approach reduces the computing time by at least two orders of magnitude compared to the integrated solution using mp-MPC. V C 2015 American Institute of Chemical Engineers AIChE J, 61: 3304-3319, 2015 Keywords: integration of scheduling and control, piece-wise affine approximation, fast model predictive control, Multiparametric model predictive control, mixed integer nonlinear programming

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Automatic Derivation of Optimal Piecewise Affine Approximations of Nonlinear Systems

Cited by 13 publications

References 6 publications

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

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 †

An integrated framework for scheduling and control using fast model predictive control

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