# A Stochastic Control Approach to Optimal Power System Operation

**Researchers:** Magnus Perninge

**Funding: **VR

One of the main challenges when operating a power system is the economic re-dispatch performed to meet the continuously changing consumption patterns. When assuming the market structure of most deregulated power markets, with a specific power market designated to re-dispatch, the re-dispatch problem becomes an optimal switching problem with delays.

This aim of this project is therefore devoted to numerical solution techniques for large-scale stochastic optimal switching problems with delays.

Stochastic optimal switching problems are a subset of stochastic optimal control problems where the control set is finite and there is a fixed cost (or reward) associated to switching between the different points of the control set.

Stochastic optimal switching has a number of other important applications, such as mineral extraction, electricity generation optimization, gas storage, traffic control, etc. Almost all of which have switching delays.

Although the stochastic optimal switching problem has been solved in a rather general setting, most numerical methods suffer from the curse of dimensionality (which becomes even more apparent in the presence of delays).

### Publications

**Magnus Perninge:**
"A Limited-Feedback Approximation Scheme for Optimal Switching Problems with Execution Delays".
In: *Optimization and Control (math.OC)*,
arXiv.org,
2016.

**Magnus Perninge, Robert Eriksson:**
"A stochastic control formulation of the continuous-time power system operation problem".
In *2016 IEEE 16th International Conference on Environment and Electrical Engineering*,
2016.

**Camille Hamon, Magnus Perninge, Lennart Soder:**
"An importance sampling technique for probabilistic security assessment in power systems with large amounts of wind power".
*Electric Power Systems Research,*
**
131**,
pp. 11–18, 2016.

**Magnus Perninge:**
"A Control-variable Regression Monte Carlo Technique for Short-term Electricity Generation Planning".
In: *Optimization and Control (math.OC)*,
arXiv.org,
2015.

2017-02-14