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Mathmatical Modeling for expansion and dispatch planning in modern energy systems

Module EI7468

This Module is offered by Chair of Renewable and Sustainable Energy Systems (Prof. Hamacher).

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2016/7 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2016/7WS 2015/6

Basic Information

EI7468 is a semester module in German language at Master’s level which is offered in winter semester.

This module description is valid from WS 2015/6 to SS 2021.

Total workloadContact hoursCredits (ECTS)
150 h 60 h 5 CP

Content, Learning Outcome and Preconditions


Fundamental problems of unit commitment, expansion planning and optimal power flow, theoretical background for solving these problems:
Nonlinear Optimization ((Un-)Constrained Optimization, Lagrange function), Lagrangian Duality (primal and dual problem, strong and weak duality), Graph theory, Mixed-Integer optimization (Fundamentals, Solution algorithms), Application of theory to typical problems of energy system analysis

Learning Outcome

Upon successful completion of the module the participants understand the fundamentals of unit commitment and expansion planning with help of optimization methods. Additionally, they can set up (non-)linear optimization problems in the application of energy system analysis (e.g. Optimal Power Flow). Mixed-integer formulations for unit commitment can be drawed and suitable solution algorithms can be applied and characterized.


Fundamentals of higher mathematics and physics,
Modul EI7448 Modeling of energy systems

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

Typical problems of expansion and dispatch planning are discussed during the lecture. Concepts for solving these problems with using optimization theory are presented during the lecture and emphasized with help of examples. Solving the tutorial sheets the students learn the usage of typical problems. During the tutorial the solution steps are highlighted.


Slides, blackboard, tutorial sheets


Linear Programming and Network Flows; M. Bazaraa, J. Jarvis, H. Sherali; Third Edition; 2011;

A Textbook of Graph Theory; R. Balakrishnan, K. Ranganathan; 2012;

Integer Programming; M. Conforti, G. Cornuéjols, G. Zambelli; 2014;

Module Exam

Description of exams and course work

The exam will be written (90 min). The focus lies on arithmetic and math word problems to test the teached methods in the context of energy systems analysis.

Exam Repetition

There is a possibility to take the exam in the following semester.

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