A model predictive control strategy for load shifting in a water pumping scheme with maximum demand charges

Abstract

The aim of this research is to affirm the application of closed-loop optimal control for load shifting in plants with electricity tariffs that include time-of-use (TOU) and maximum demand (MD) charges. The water pumping scheme of the Rietvlei water purification plant in the Tshwane municipality (South Africa) is selected for the case study. The objective is to define and simulate a closed-loop load shifting (scheduling) strategy for the Rietvlei plant that yields the maximum potential cost saving under both TOU and MD charges. The control problem is firstly formulated as a discrete time linear open loop optimal control model. Thereafter, the open loop optimal control model is converted into a closedloop optimal control model using a model predictive control technique. Both the open and closed-loop optimal control models are then simulated and compared with the current (simulated) level based control model. The optimal control models are solved with integer programming optimization. The open loop optimal control model is also solved with linear programming optimization and the result is used as an optimal benchmark for comparisons. Various scenarios with different simulation timeouts, switching intervals, control horizons, model uncertainty and model disturbances are simulated and compared. The effect of MD charges is also evaluated by interchangeably excluding the TOU and MD charges. The results show a saving of 5.8% to 9% for the overall plant, depending on the simulated scenarios. The portion of this saving that is due to a reduction in MD varies between 69% and 92%. The results also shows that the closed-loop optimal control model matches the saving of the open loop optimal control model, and that the closed-loop optimal control model compensates for model uncertainty and model disturbances whilst the open loop optimal control model does not. AFRIKAANS : Die doel van hierdie navorsing is om die applikasie van geslote-lus optimale beheer vir las verskuiwing in aanlegte met elektrisiteit tariewe wat tyd-van-gebruik (TVG) en maksimum aanvraag (MA) kostes insluit te bevestig. Die water pomp skema van die Rietvlei water reiniging aanleg in die Tshwane munisipaliteit (Suid-Afrika) is gekies vir die gevalle studie. Die objektief is om 'n geslote-lus las verskuiwing (skedulering) strategie vir die Rietvlei aanleg te definieer en te simuleer wat die maksimum potensiaal vir koste besparing onder beide TVG en MA kostes lewer. Die beheer probleem is eerstens gevormuleer as 'n diskreet tyd lineêre ope-lus optimale beheer model. Daarna is die ope-lus optimale beheer model aangepas na ‘n geslote-lus optimale beheer model met behulp van 'n model voorspellende beheer tegniek. Beide die ope- en geslote-lus optimale beheer modelle is dan gesimuleer en vergelyk met die huidige (gesimuleerde) vlak gebaseerde beheer model. Die optimisering van optimale beheer modelle is opgelos met geheeltallige programmering. Die optimisering van die ope-lus optimale beheer model is ook opgelos met lineêre programmering en die resultaat is gebruik as 'n optimale doelwit vir vergelykings. Verskeie scenarios met verskillende simulasie stop tye, skakel intervalle, beheer horisonne, model onsekerheid en model versteurings is gesimuleer en vergelyk. Die effek van MA kostes is ook geevalueer deur inter uitruiling van die TVG en MA kostes. Die resultate toon 'n besparing van 5. 8% tot 9% vir die algehele aanleg, afhangend van die gesimuleerde scenarios. Die deel van die besparing wat veroorsaak is deur 'n vermindering in MA wissel tussen 69% en 92%. Die resultate toon ook dat die geslote-lus optimale beheer model se besparing dieselfde is as die besparing van die ope-lus optimale beheer model, en dat die geslote-lus optimale beheer model kompenseer vir model onsekerheid en model versteurings, terwyl die ope-lus optimale beheer model nie kompenseer nie. Copyright