Chair: David Wozabal, Technical University of Munich, Germany
A dynamic programming approach to the ramp constrained intra-hour stochastic single-unit commitment problem
Ditte Heide-Jørgensen (firstname.lastname@example.org), Pierre Pinson (email@example.com), Trine Krogh Boomsma (firstname.lastname@example.org)
Renewable energy sources, such as wind power, are characterized by unpredictable and fluctuating generation. The increasing share of renewables in many power systems therefore makes it relevant to consider the stochastic unit commitment (UC) problem. Here, we consider the sub-problem of single-unit commitment that arises from applying Lagrangian relaxation to the demand constraints of the UC problem. Our sub-problem is likewise stochastic, however, with uncertainty in the cost coefficients. To appropriately account for fluctuations in renewable generation, we assume a fine time resolution of the scheduling horizon. Furthermore, due to the additional flexibility requirements in a power system with a significant share of renewables, we solve the ramp-constrained version of the scheduling problem. Current research has primarily focused on two-stage stochastic programming formulations of this problem, the reason being that multi-stage formulations increase exponentially in size with the number of time periods. To capture the gradual updating of information throughout the planning horizon, we maintain focus on the multi-stage version. As an alternative to mixed-integer linear programming formulations, we rely on the dynamic programming literature for deterministic unit commitment problems. This approach has been shown to easily handle discrete decisions such as start-up and shut-downs of the generating units subject to minimum up- and down-times, and under certain assumptions, further allow for ramping decisions without discretizing continuous generation levels. Our main idea is to extend the dynamic programming formulation of the ramp-constrained deterministic single-unit problem to include stochastic electricity prices. In doing so, we will consider how and when to account for updates of information, and put special efforts into modeling uncertainty in electricity prices as a Markov chain.
Keywords: Unit commitment, Stochastic Programming, Dynamic Programming
On the generation of optimal scenario trees
Georg Pflug (email@example.com)
Scenario trees for optimizing energy production and trading should reflect realistic models for prices, demands, water inflow etc. We discuss how optimal trees can be generated from identified stochastic models using recursive estimation techniques. The approach minimized the distance between the tree and the underlying real world process. The algorithms are illustrated on a larger example for hydrostorage optimization.
Keywords: Scenario generation, distance minimzation, stochastic approximation
Valuing Gas Storages with Approximate Dual Dynamic Progamming
David Wozabal (firstname.lastname@example.org), Nils Löhndorf (email@example.com)
We consider the problem of gas storage valuation under price uncertainty. To model long term as well as short term price dynamics, we fit a two-factor model to historical spot market prices. To compute of the true value of storage, we propose an approach based on approximate dynamic dual programming. Our approximation strategy relies on efficient discretization of the price process combined with learning a piecewise-linear approximation of the value function of the dynamic program. To assess the benefit of our approach, we compare the approximated value against the (rolling) intrinsic value. Since storage valuation is often done monthly whereas prices change on a daily basis, we additionally study the effect of using a finer time granularity on the value of storage. Finally, we include the conditional value at risk into the optimization problem which provides a measure to calibrate the degree of risk-sensitivity and compare resulting profit distribution to the case where risk is not taken into account.
Keywords: Stochastic Dynamic Programming, Energy,