We are pleased to announce a MOSEK workshop on

*Semidefinite optimization in power flow problems*taking place on

**Tuesday,**

**February 28th, 2017**at the Symbion research park.

Optimal power flow is one of the major problems in optimization of electric power systems, asking for the minimization of operating costs in terms of a specified objective function in the presence of non-linear power flow equations. Three experts, Spyros Chatzivasileiadis (DTU), Cédric Josz (CNRS) and Martin Skovgaard Andersen (DTU) will discuss recent advanced based on convex relaxations and in particular on semidefinite programming.

The workshop is free and open to everyone. There will be coffee, refreshments and time for discussions. Please register through this form to help us with planning.

**Schedule:**

14:00 - 14:05 Welcome

14:05 - 14:50 Spyros Chatzivasileiadis

15:00 - 15:45 Cédric Josz

16:00 - 16:45 Martin Skovgaard Andersen

17:30+ optional dinner (Nørrebro Bryghus)

**Abstracts:**

- Spyros Chatzivasileiadis, DTU
**SDP Problems for Power System Stability and Optimization**

In recent years, semidefinite programming is met with increasing interest within the power systems community. Its most notable application to-date is on the convex formulation of the AC optimal power flow problem. At the same time, semidefinite programs can be used to derive Lyapunov functions that guarantee power system stability.

In this talk we will report on recent work both on power system stability and optimization. First, we will present a novel robust stability toolbox for power grids that can address uncertainties in equilibrium points and fault-on dynamics. In that, we bring in the quadratic Lyapunov functions approach to transient stability assessment.

Second, we will propose formulations for the integration of chance constraints for several uncertain variables in the optimal power flow problem. We demonstrate our method with numerical examples, and we investigate the conditions to achieve zero duality gap. - Cédric Josz, LAAS CNRS
**Application of Polynomial Optimization to Electricity Transmission Networks**

Multivariate polynomial optimization where variables and data are complex numbers is a non-deterministic polynomial-time hard problem that arises in various applications such as electric power systems, imaging science, signal processing, and quantum mechanics. We transpose to complex numbers the Lasserre hierarchy which aims to solve real polynomial optimization problems to global optimality. This brings complex semidefinite programming into the picture and calls for an interior-point algorithm in complex numbers. The Nesterov-Todd direction will be discussed and supplemented by numerical results on the European high-voltage electricity transmission network. - Martin Skovgaard Andersen, DTU
**Numerical Aspects of Semidefinite Relaxations of Optimal Power Flow Problems**

Power flow optimization plays an important role in power system operation and planning. It is used to find a cost-optimal operating point of a power system that consists of a set of power buses that are interconnected through a network of transmission lines. We discuss recent progress based on convex relaxation techniques for optimal power flow problems and investigate some numerical aspects through an empirical study.

**Essentials:**

- Time: 28.02.2017, from 2pm.
- Place: Fruebjergvej 3, 2100 Copenhagen, directions to the Symbion research park.
- Registration: use this form
- Contact: info@mosek.com