Contributed Session Thu.2.MA 550

Thursday, 13:15 - 14:45 h, Room: MA 550

Cluster 18: Optimization in energy systems [...]

Bilevel programming and housing retrofit


Chair: Mark Jennings



Thursday, 13:15 - 13:40 h, Room: MA 550, Talk 1

Eugene Zak
Bilevel Programming for combinatorial auctions in electricity markets

Coauthors: Sami Ammari, Kwok Cheung


In advanced electricity markets some bids and offers extend over a block of several consecutive time periods so that the block bid/offer has to be cleared entirely for all time periods comprising the block. According to a typical market rule a block bid can be cleared only if its price is not lower than the average market price. Similarly, a block offer can be cleared only if its price is not higher than the average market price. The dilemma occurs: block bids/offers selection as a primal solution cannot be properly exercised without knowing the prices as a dual solution, and the prices depend on the selection decisions. We propose a model harmonizing such complex "primal-dual'' market rules. The model, based on bilevel programming, ties together the primal and dual variables so that the "primal-dual'' market rules become a part of the overall model. The model is a non-linear Mixed Integer Program (MIP). We have implemented an exact algorithm to solve this model. The computational results demonstrate the adequacy of the modeling and algorithmic approaches and their practical value for several European electricity markets with combinatorial auctions.



Thursday, 13:45 - 14:10 h, Room: MA 550, Talk 2

Peter Gross
Risk averse bilevel problems in energy markets

Coauthors: Raimund M. Kovacevic, Georg Ch Pflug


Our work introduces risk averse bilevel problems as a special case of stochastic bilevel problems. These problems can for example arise at the pricing of energy delivery contracts, when instead of a replication approach a game-theoretic approach to pricing is chosen. In the latter case, the exercise price set by the seller anticipates the exercise strategy of the buyer that will be triggered by this particular exercise price. The special, case where constraints on the seller's risk are included in the model, we call risk averse bilevel problem.
This particular type of bilevel problem where the seller's constraints depend on the buyer's exercise strategy has so far received little attention, since in general it leads to a nonconvex optimization problems where the feasible set even may be nonconnected. We demonstrate the properties and particular difficulties of this problem and present algorithms suitable for solving it. We apply an iterative solution method on some real data and investigate the numerical behavior.



Thursday, 14:15 - 14:40 h, Room: MA 550, Talk 3

Mark Jennings
Optimization of technology investments and capital management in an urban energy system housing retrofit project: Use of rolling horizons in a London borough study

Coauthors: David Fisk, Nilay Shah


We consider formulations optimizing the technological and capital decisions taken when retrofitting urban energy systems at the large-scale. This study can be considered a minimum cost strategic capital management problem, incorporating a resource-task network representation of the housing stock's demand and supply side energy systems. We use real data on existing housing conditions from a London borough seeking to minimise its housing stocks's greenhouse gas emissions.
We seek to answer two research questions: (i) what is the effect of rolling horizons on investments which retrofit housing technologies?, and (ii) to what degree does the abstraction of the temporally dynamic technological operations in separate LP, MILP, and MINLP formulations impact upon the optimizations's fidelity, piecewise special ordered set branching error, and processing unit solution time respectively?
Initial insights suggest that expected reductions in energy demand may be adversely affected by investor attitudes to shorter time horizons. MILP formulations of housing retrofit projects may offer the best tradeoffs between fidelity/accuracy and reasonable solution times.


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