An alternative optimal strategy for stochastic model predictive control of a residential battery energy management system with solar photovoltaic

Scenario-based stochastic model predictive control traditionally considers the optimal strategy to be the expectation of the optimal strategies across all scenarios. However, while the stochastic problem involving uncertainties can be substantiated by a large number of scenarios, the expectation of...

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Veröffentlicht in:	Applied energy Jg. 283; S. 116289
Hauptverfasser:	van der Meer, Dennis, Wang, Guang Chao, Munkhammar, Joakim
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Elsevier Ltd 01.02.2021
Schlagworte:	autocorrelation batteries case studies energy Engineering Science with specialization in Civil Engineering and Built Environment Gradient boosting management systems Multivariate forecasting prediction Quantile regression Scenario based solar collectors solar energy Stochastic model predictive control stochastic processes Sweden Teknisk fysik med inriktning mot byggteknik och byggd miljö variance covariance matrix Sweden Stochastic model predictive control Scenario based Quantile regression Multivariate forecasting Gradient boosting
ISSN:	0306-2619, 1872-9118, 1872-9118
Online-Zugang:	Volltext
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Abstract	Scenario-based stochastic model predictive control traditionally considers the optimal strategy to be the expectation of the optimal strategies across all scenarios. However, while the stochastic problem involving uncertainties can be substantiated by a large number of scenarios, the expectation of the respective optimal control strategies derived from all scenarios as the optimal control strategy to the problem is challenging to justify. We therefore propose a different approach in which we artfully have the optimization program find the common optimal strategy across all scenarios for the first prediction step at each sample time, which, if it exists, yields the true optimal strategy with greater confidence. We demonstrate the efficacy of the proposed formulation through a case study of a research villa in Borås, Sweden, that is equipped with a battery and a photovoltaic system. We compute a covariance matrix that contains time-dependent information of the data and use it to generate autocorrelated scenarios from the probabilistic forecasts that serve as the uncertain input to the energy management system. We justify the credibility of the optimal solution derived from the proposed formulation with compelling reasoning and quantitative results such as improved self-consumption of photovoltaic power. •We reformulate the scenario-based stochastic model predictive control algorithm.•We add a constraint that forces the control strategy to be equal across scenarios.•The reformulation is tested on a system with a battery, load and PV system.•The probabilistic forecasts and multivariate forecasts are thoroughly evaluated.•The reformulation results in increased profit, self-consumption and self-sufficiency.
AbstractList	Scenario-based stochastic model predictive control traditionally considers the optimal strategy to be the expectation of the optimal strategies across all scenarios. However, while the stochastic problem involving uncertainties can be substantiated by a large number of scenarios, the expectation of the respective optimal control strategies derived from all scenarios as the optimal control strategy to the problem is challenging to justify. We therefore propose a different approach in which we artfully have the optimization program find the common optimal strategy across all scenarios for the first prediction step at each sample time, which, if it exists, yields the true optimal strategy with greater confidence. We demonstrate the efficacy of the proposed formulation through a case study of a research villa in Borås, Sweden, that is equipped with a battery and a photovoltaic system. We compute a covariance matrix that contains time-dependent information of the data and use it to generate autocorrelated scenarios from the probabilistic forecasts that serve as the uncertain input to the energy management system. We justify the credibility of the optimal solution derived from the proposed formulation with compelling reasoning and quantitative results such as improved self-consumption of photovoltaic power. Scenario-based stochastic model predictive control traditionally considers the optimal strategy to be the expectation of the optimal strategies across all scenarios. However, while the stochastic problem involving uncertainties can be substantiated by a large number of scenarios, the expectation of the respective optimal control strategies derived from all scenarios as the optimal control strategy to the problem is challenging to justify. We therefore propose a different approach in which we artfully have the optimization program find the common optimal strategy across all scenarios for the first prediction step at each sample time, which, if it exists, yields the true optimal strategy with greater confidence. We demonstrate the efficacy of the proposed formulation through a case study of a research villa in Borås, Sweden, that is equipped with a battery and a photovoltaic system. We compute a covariance matrix that contains time-dependent information of the data and use it to sample autocorrelated scenarios from the probabilistic forecasts that serve as the uncertain input to the energy management system. We justify the credibility of the optimal solution derived from the proposed formulation with compelling reasoning and quantitative results such as improved self-consumption of photovoltaic power. Scenario-based stochastic model predictive control traditionally considers the optimal strategy to be the expectation of the optimal strategies across all scenarios. However, while the stochastic problem involving uncertainties can be substantiated by a large number of scenarios, the expectation of the respective optimal control strategies derived from all scenarios as the optimal control strategy to the problem is challenging to justify. We therefore propose a different approach in which we artfully have the optimization program find the common optimal strategy across all scenarios for the first prediction step at each sample time, which, if it exists, yields the true optimal strategy with greater confidence. We demonstrate the efficacy of the proposed formulation through a case study of a research villa in Borås, Sweden, that is equipped with a battery and a photovoltaic system. We compute a covariance matrix that contains time-dependent information of the data and use it to generate autocorrelated scenarios from the probabilistic forecasts that serve as the uncertain input to the energy management system. We justify the credibility of the optimal solution derived from the proposed formulation with compelling reasoning and quantitative results such as improved self-consumption of photovoltaic power. •We reformulate the scenario-based stochastic model predictive control algorithm.•We add a constraint that forces the control strategy to be equal across scenarios.•The reformulation is tested on a system with a battery, load and PV system.•The probabilistic forecasts and multivariate forecasts are thoroughly evaluated.•The reformulation results in increased profit, self-consumption and self-sufficiency.
ArticleNumber	116289
Author	Munkhammar, Joakim Wang, Guang Chao van der Meer, Dennis
Author_xml	– sequence: 1 givenname: Dennis orcidid: 0000-0002-9473-4536 surname: van der Meer fullname: van der Meer, Dennis email: dennis.vandermeer@angstrom.uu.se organization: Department of Civil and Industrial Engineering, Uppsala University, Sweden – sequence: 2 givenname: Guang Chao surname: Wang fullname: Wang, Guang Chao organization: Mechanical and Aerospace Engineering, University of California, San Diego, USA – sequence: 3 givenname: Joakim surname: Munkhammar fullname: Munkhammar, Joakim organization: Department of Civil and Industrial Engineering, Uppsala University, Sweden
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Keywords	Stochastic model predictive control Scenario based Quantile regression Multivariate forecasting Gradient boosting
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Snippet	Scenario-based stochastic model predictive control traditionally considers the optimal strategy to be the expectation of the optimal strategies across all...
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SubjectTerms	autocorrelation batteries case studies energy Engineering Science with specialization in Civil Engineering and Built Environment Gradient boosting management systems Multivariate forecasting prediction Quantile regression Scenario based solar collectors solar energy Stochastic model predictive control stochastic processes Sweden Teknisk fysik med inriktning mot byggteknik och byggd miljö variance covariance matrix
Title	An alternative optimal strategy for stochastic model predictive control of a residential battery energy management system with solar photovoltaic
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