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Master's Thesis
Author of thesis: Bc. Alena Večeřová
Acad. year: 2025/2026
Supervisor: doc. Ing. Jakub Kůdela, Ph.D.
Reviewer: RNDr. Pavel Popela, Ph.D.
This master’s thesis deals with the optimal control of an energy system with a photovoltaic power plant and battery storage. The aim of the thesis is to develop a model enabling the minimization of electricity costs by optimal battery charging and discharging while considering time-varying electricity prices, photovoltaic generation, and household consumption. The thesis first describes the considered energy system and provides a review of optimization methods used for battery storage management. Subsequently, a mathematical model of the system is formulated on a discrete-time horizon with a fifteen-minute time step. Uncertainty of input variables is modeled using discrete scenarios. A stochastic dynamic programming approach based on the Bellman equation is used to solve the optimization problem. The implemented model takes into account operational constraints of the battery storage, such as charging power limits and minimum delay between charging and discharging blocks. The thesis also includes a Python implementation of the algorithm, simulation of the system operation, and economic evaluation of different photovoltaic and battery configurations. The results show that properly controlled battery storage can significantly reduce electricity costs and increase the utilization of locally generated photovoltaic energy.
photovoltaic system, battery storage, dynamic programming, stochastic optimization, Bellman equation, energy management, optimal control, uncertainty modeling
Date of defence
08.06.2026
Result of the defence
Defended (thesis was successfully defended)
Grading
A
Process of defence
Studentka prezentovala práci, byl přečten posudek školitele, oponent přečetl svůj posudek. K otázkám oponenta: Zahrnutí degradace bateriového úložiště a dopad na optimalizační strategii: pomocí penalizace - bez vlivu, ne moc dobrá cesta nebo zavést další stavovou proměnnou - zvýšení náročnosti. Téma diskretizace baterie - ukázána citlivost výsledků Rozšíření pro komunitní energetiku - využití dvoustupňového modelu lepší dr.Eryganov - Co se děje s baterií na konci v rámci denního modelu? Je tam terminální podmínka - je jedno, kde skončí. dr.Rozehnalová - Jsou do modelu zahrnuty i záporné burzovní ceny odkupu? - nejsou, zahrnutí fixní nasmlouvané ceny - šlo by to snadno zahrnout doc. Kolář - jednotka kW peak - vysvětleno
Language of thesis
Czech
Faculty
Fakulta strojního inženýrství
Department
Institute of Mathematics
Study programme
Mathematical Engineering (N-MAI-P)
Composition of Committee
doc. Mgr. Petr Vašík, Ph.D. (předseda) doc. RNDr. Martin Kolář, Ph.D. (místopředseda) prof. Aleksandre Lomtatidze, DrSc. (člen) Ing. Ivan Eryganov, Ph.D. (člen) Ing. Petra Rozehnalová, Ph.D. (člen)
Supervisor’s reportdoc. Ing. Jakub Kůdela, Ph.D.
Grade proposed by supervisor: A
Reviewer’s reportRNDr. Pavel Popela, Ph.D.
Grade proposed by reviewer: A
Responsibility: Mgr. et Mgr. Hana Odstrčilová