(601g) Representative Energy Costs for Optimization of Industrial Process Design and Operations – Systematic Comparison of Clustering Methodologies

Representative energy costs for optimization of industrial process design and operations – Systematic comparison of clustering methodologies

Holger Teichgraeber¹ Adam Brandt¹

¹Department of Energy Resources Engineering, Stanford University, Stanford, California 94305-2220, USA

The optimization of process synthesis and design problems is concerned with the optimal design and operation of an industrial system consisting of several components and subcomponents. Often, these components consume or generate power. This optimization problem requires that operations scheduling be solved for multiple model years. Because this is computationally expensive, it is of interest to represent input data using as few days or weeks as possible. Input data clustering can help obtain practical solutions to problems that we are not able to solve for the full set of input data on reasonable timescales. Input data examined here include hourly or sub-hourly electricity prices, wind speed, and solar irradiation (one can think of other data as well such as hourly demand, hourly temperature etc.).

Both Brodrick et al. [1] and Bahl et al. [2] have proposed using k-means clustering for finding representative periods in the optimization of process synthesis and design problems. They measure the accuracy of representative periods based on the objective function (net present value or total annualized cost). A similar approach has been proposed by Nahmmacher et al. [3] and Merrick [4] for electricity generation extension planning models using hierarchical clustering. The process synthesis and design problems thus far considered solved large-scale optimization problems for which the objective function and solution structure for the full set of input data is unknown.

We formulate several example problems that capture characteristics of real world applications, but are solvable for a whole year of input data. We use these problems to systematically investigate which information is lost and kept in the operational stage of the optimization problem during input data clustering. We test different clustering methodologies systematically. This information has implications for the design decisions. For different problem types, different kind of information is important: Variability is important for storage arbitrage problems, whereas average cut-off price is important for power generation problems with operational on-off decision. We investigate these systematic relationships between clustering methodologies and problem type.

Amongst others, we formulate an electricity storage problem to optimally take advantage of energy price arbitrage, a scheduling problem to perform energy-intensive tasks in times of low electricity prices, and a gas turbine power generation problem.
In addition, we also use an oxy-combustion combined cycle design and operational optimization problem [5] as an example for a large scale optimization problem to investigate clustering effects.

We use these example problems to investigate which information loss and inaccuracy occurs due to clustering for each of these problems. Methods that are subject to investigation are clustering method, normalization, cluster centroid vs. closest day, and application to multi-timescale input data.

[1] Brodrick, Philip G., Charles A. Kang, Adam R. Brandt, and Louis J. Durlofsky. "Optimization of carbon-capture-enabled coal-gas-solar power generation." Energy79 (2015): 149-162.

[2] Bahl, Björn, Alexander Kümpel, Matthias Lampe, André Bardow. “Time-series aggregation for synthesis of distributed energy supply systems by bounding error in operational expenditure.” Computer Aided Chemical Engineering 38 (2016): 793-798

[3] Nahmmacher, Paul, Eva Schmid, Lion Hirth, and Brigitte Knopf. "Carpe diem: A novel approach to select representative days for long-term power system modeling." Energy112 (2016): 430-442.

[4] Merrick, James H. "On representation of temporal variability in electricity capacity planning models." Energy Economics59 (2016): 261-274.

[5] Teichgraeber, Holger, Philip G. Brodrick, and Adam R. Brandt., “Optimal Design and Operation of a Semi-Closed Oxy-Combustion Combined Cycle Power Plant”. 2016 American Institute of Chemical Engineers Annual Meeting. San Francisco, CA. November 2016.