**Overview:** This course covers the fundamentals of various optimization methods that are used in electricity markets. The course is split into three sections, each corresponding to one full day of lecture material. The sections cover (i) stochastic optimization, (ii) Benders decomposition and SDDP, and (iii) mixed integer programming and the EUPHEMIA algorithm. The course includes examples from the power industry that include adequacy analysis, capacity expansion planning, and hydro-thermal planning. Exercises accompany the material, in order to support the learning objectives.

**Prerequisites:** The course has been tailored for specialists in the power industry, such as transmission system operators. The following background is required for following the course.

- Basic background in mathematical programming
- Basic background in convex optimization
- Electric power systems and electricity markets

**Section 1: Stochastic optimization**

- Section 1.1: Mathematical foundations
- Section 1.2: Algorithms for linear optimization
- Section 1.3: Introduction to mathematical programming languages
- Section 1.4: Two-stage stochastic programming
- Section 1.5: Application of two-stage stochastic programming for planning a power system with an adequacy target
- Section 1.6: Solving the planning problem using scenario decomposition / reduction
- Section 1.7: Solving the planning problem using Lagrange relaxation

**Section 2: Benders decomposition and SDDP**

- Section 2.1: Solving two-stage problems using Benders decomposition
- Section 2.2: Solving two-stage stochastic programs using the L-Shaped method
- Section 2.3: Modeling multi-stage stochastic programs
- Section 2.4: Nested decomposition
- Section 2.5: SDDP
- Section 2.6: Special topics in SDDP

**Section 3: MIP and the EUPHEMIA algorithm**

- Section 3.1: Mixed integer linear programming
- Section 3.2: The EUPHEMIA products
- Section 3.3: Pricing in EUPHEMIA
- Section 3.4: EUPHEMIA as a problem with complementarity constraints
- Section 3.5: Algorithmic approach in EUPHEMIA
- Section 3.6: Representing a network in EUPHEMIA