Contributed Session Mon.1.MA 550

Monday, 10:30 - 12:00 h, Room: MA 550

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

Unit commitment and inventory problems


Chair: Tim Schulze



Monday, 10:30 - 10:55 h, Room: MA 550, Talk 1

Ali Koc
Parallel branch-cut-price for solving multistage stochastic unit commitment problems

Coauthor: Jayant Kalagnanam


Unit commitment (UC) lies in the heart of future smart grid. Independent system operators and utilities aim to solve various forms of the problem that handle such contemporary concepts as renewable generation, energy storage, power purchase agreements, future power markets, demand response, etc. These concepts induce various forms of uncertainty into the problem. We use multistage stochastic programming framework to incorporate these uncertainties, and present a parallel decomposition algorithm based on a branch-cut-price framework. We bring together several advancements in the UC literature, stochastic programming, mixed integer programming, large-scale optimization, and parallel computing. We develop a new weighting scheme and a lower bounding method to improve the decomposition algorithm, and a constructive heuristic method to restore near-optimal solutions. The serial algorithm solves problem instances as efficient as highly sophisticated commercial solvers, and the parallel algorithm solves large-scale nonlinear stochastic UC problem instances with up to 3000 generators, 24 hours, and 200 scenarios on a 32-processor cluster, obtaining almost linear speedups.



Monday, 11:00 - 11:25 h, Room: MA 550, Talk 2

Kin Keung Lai
A stochastic approach to power inventory optimization

Coauthors: Qiang Wang, Qian Zhang


Rooted in the airline industry, inventory management systems have been applied for 40 years since the first paper by Beckmann. This involves application of information systems and pricing strategies to allocate the right capacity to the right customer at the right price at the right time. Also there are some salient differences between airlines and power plants. For example: (i) electric power has to be generated, transmitted and consumed at the same time; and (ii) safety of power grid is also an important factor to be considered, implying more strict requirements for cancellations, no-shows and overbooking problems. Also, unlike the airline industry, orders for electricity power usually last for a period of time such as one day, one week, one month and even one year, and the price varies with quantity and time periods. Advance bookings are encouraged even one day or even half-an-hour in advance in order to guarantee safety and efficiency of the power grid and the power plant.
This study is developed on the basis of power plants facing stochastic demand with varied prices. A network optimization mode is proposed for power plant inventory management under an uncertain environment.



Monday, 11:30 - 11:55 h, Room: MA 550, Talk 3

Tim Schulze
Decomposition methods for stochastic unit commitment

Coauthors: Andreas Grothey, Kenneth I.m. Mckinnon


In recent years the expansion of energy supplies from volatile renewable sources has triggered an increased interest in stochastic optimization models for generation unit commitment. Several studies have modelled the problem as a stochastic mixed-integer (piecewise linear or convex quadratic) multi-stage problem. Solving this problem directly is computationally intractable for large instances and many alternative approaches have been proposed. However, few of them exploit the structure of the multi-stage formulation. In this talk we outline how decomposition and coordination methods can be applied to exploit the structure of the underlying scenario tree. It has been shown that progressive hedging can yield good solutions for this problem, and we give a short review of our findings from applying it. However, this method is not guaranteed to converge for mixed-integer problems. Therefore the focus of the talk is on a branch & price framework which guarantees convergence. Numerical results are given to illustrate the behaviour of the method.


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