Master's Thesis

Mathematical optimization of a solar photovoltaic system for a single-family detached home

Final Thesis 11.18 MB

Author of thesis: Ing. Sheikh Omar Bah

Acad. year: 2019/2020

Supervisor: doc. Ing. Pavel Charvát, Ph.D.

Reviewer: Ing. Tomáš Mauder, Ph.D.


This paper presents a mathematical sizing algorithms of a grid-connected photovoltaic-battery system for a residential
house. The objective is to minimize the total storage capacity with cost of electricity. The proposed methodology
is based on a Linear and Non-linear programming.
We have presents results from a existing PV panel FS-4115-3  for the given climatic conditions and the electricity use profile.
Measurements for whole household electricity consumption have been obtained over a period of two months. They were all obtained at one hour interval. The algorithm jointly optimizes the sizes of the photovoltaic and the battery systems by adjusting the battery charge and discharge cycles according to the availability of solar resource and a time-of-use tariff structure for electricity. The results show that jointly optimizing the sizing of battery and photovoltaic systems can significantly reduce electricity imports and the cost of electricity for the


Mathematical Optimization, Solar Photovoltaic, Battery storage system, Linear programming and Non linear Programming

Date of defence


Result of the defence

Defended (thesis was successfully defended)




Process of defence

Student presented his Master's thesis. The verbal and overall classifications of supervisor and reviewer were read. The reviewer asked 3 questions and the student had prepared slides with answers to the questions. The state exam committee had additional questions: Prof. Šlapal asked for an additional explanation why the graphs 25 and 27 are different and student presented data in Excel. Prof. Druckmüller asked for a description of formula (4.11) on page 36, which is written vice-versa and therefore it is bad. Prof. Šlapal asked the student to shortly describe the results of the thesis by own words.

Language of thesis




Study programme

Applied Sciences in Engineering (M2A-A)

Study branch

Mathematical Engineering

Composition of Committee

prof. RNDr. Josef Šlapal, CSc. (předseda)
prof. RNDr. Miloslav Druckmüller, CSc. (místopředseda)
doc. Ing. Luděk Nechvátal, Ph.D. (člen)
doc. RNDr. Jiří Tomáš, Dr. (člen)
doc. Ing. Jiří Šremr, Ph.D. (člen)
Assoc. Prof. Massimiliano Giuli (člen)

Supervisor’s report
doc. Ing. Pavel Charvát, Ph.D.

Sheikh Omar Bah showed a genuine interest in the topic of his master’s thesis. From the beginning, he was enthusiastically getting familiar with the concepts of solar photovoltaics (PV) systems comprising battery storage and he intensively studied mathematical models of the system components (PV modules, batteries, invertors, etc.). Certain problems occurred when he tried to use the models in mathematical optimization of the PV system. Some models were too detailed to be used in mathematical optimization without adopting metaheuristic optimization methods. An alternative approach of using time series of the performance data was chosen instead. Nonetheless, this led to other problems as the time series had too many data points to be easily handled by optimization tools. As the deadline for the completion of master’s thesis approached, Sheikh Omar Bah had to further simplify the optimization task to be able to complete his master´s thesis in time. The simplification of the optimization task decreased the relevance of the results. The time pressure, under which the master’s thesis was written, had a negative effect on the overall quality of the thesis.
Evaluation criteria
Fulfilment of requirements and objectives of assignment
Working process, extent and suitability of applied methods
Scholarly contribution and originality
Ability to interpret achieved results and draw conclusions
Applicability of results in practice or theory
Logical arrangement of thesis and its layout
Grafic layout, used style and language level
Work with used sources including quotations
Student's independence when working on the topic

Grade proposed by supervisor: D

Reviewer’s report
Ing. Tomáš Mauder, Ph.D.

The master thesis aim to develop optimization model of a solar photovoltaic system. The thesis has six section including introduction and conclusion. The aim of thesis is relevant, because nowadays is strong effort in EU to reduce the ecological footprint.

The level of English is poor with many grammatical errors. In some cases is very hard to understand some authors statements.

Graphical style is terrible. Most of figures should be placed in better quality (see fig. 1, 3, 4, 5 etc.). In some cases, figures and equations overflow the edges of paper (see eq. 4.5, fig. 20). Many figures are just included in the thesis, but they are not commented nor described in text (e.g. Figures 1-5, 8-10, 17, 20, 26-27, 29, 31).

The work with literature here is little chaotic. The literature should be indexed based on first author name or based on occurrence in text.

In addition, the mathematical part of work is poor. In section 2.6 Modeling, there is no mathematical background. How the model is mathematically describe? Is Eq. (4.1) on page 29 an objective function? I do not think so. This kind of work where optimization and mathematical models are presented requires a proper mathematical description. The style of equation writing is not consistent.  

Some thesis goals are not fulfilled (island operation, year-round operation) and the overall quality of the thesis is low. The results from chapter 5 are not trustable to me. From my personal impression, I feel that it is more look like bachelor than diploma thesis.

I recommend the thesis for defence, but I have a lot of doubt about it due to the mentioned serious issues.
Evaluation criteria Mark
Fulfilment of requirements and objectives of assignment E
Working process, extent and suitability of applied methods D
Scholarly contribution and originality D
Ability to interpret achieved results and draw conclusions E
Applicability of results in practice or theory E
Logical arrangement of thesis and its layout F
Grafic layout, used style and language level F
Work with used sources including quotations D

Grade proposed by reviewer: E