(426b) Steel Production Scheduling With Optimization of Time-Sensitive Electricity Purchases
As more emphasis is placed on integration of distributed generation new automation technologies need to be introduced in order to meet the challenges on the supply side. One of these technologies is to involve the consumer side in active balancing of supply-demand within Industrial Demand Side Management (IDSM). IDSM is considered cost-effective since it involves low upfront hardware investments. Large electricity users such as process industry are foreseen to play an increasing role in the future electricity markets by active participation and shaping of electricity demand profiles for example during expensive peak consumption times, and also contributing to safe and reliable operation. This is relevant especially in recent economic crisis, which has resulted into reduced number of production orders. According to World Steel Association the apparent steel use of finished steel products in Europe decreased by 9,3 % in 2012, and it is likely to drop further in 2013 (World Steel Association 2013). Facing substantial underutilization of production capacity, the process industry is seeking for new ways of energy cost reductions. Production plant participation in volatile electricity markets brings new opportunities, but also challenges. Optimization of electricity consumption cost and energy purchase strategy may lead to significant savings since in electricity-intensive production electricity bill can account by far for most of the raw material cost.
Partly due to these reasons, and also due to recent advancements in production optimization methods, the topic of energy-aware scheduling is gaining attention in the literature. Recent work introduces volatile electricity markets in scheduling of continuous processes (Castro et al. 2009, Castro et al. 2011, Mitra et al. 2012). Less emphasis has been placed so far into scheduling of batch processes (Hadera & Harjunkoski 2013), which lies in the context of this work. Other aspects of energy-aware scheduling have been investigated in several studies such as energy and human resource constrained scheduling (Hait, A., & Artigues, 2011), scheduling under different electricity-tariffs (Ashok 2006), or tracking of pre-agreed electricity load profiles (Nolde & Morari 2010).
The focus of this work is on two aspects of Industrial Demand Side Management. One is the problem of load deviation. It is common practice that an energy-intensive plant commits its load in advance to get favorable prices for electricity. However, once committed to the local supplier, the plant is obligated to pay financial penalties in case the actual consumption deviates from the pre-agreed values by certain margin. The second aspect considered in this work is the possibility to participate in liberalized electricity markets. The plant is assumed to have the opportunity to buy electricity from the hourly-regulated day-ahead market, or to buy from a local supplier at a fixed price. Moreover, possibility to produce electricity on-site at a certain cost is considered as well. In addition to those electricity sources, the plant is allowed to benefit from selling the electricity back to the grid in case of a surplus. These aspects create a challenging optimization problem that has not been reported so far in this contex.
The resulting model has been formulated as Mixed Integer Linear Programming problem applied to a hybrid flow-shop model using continuous-time formulation based on global precedence variables (Harjunkoski & Grossmann 2001, Harjunkoski & Sand 2008, Hadera & Harjunkoski 2013). The model is applied to electricity-intensive Melt Shop section of a stainless steel plant with final product called heat. The plant is assumed to have parallel non-identical equipment at each stage of production. The production starts from the Electric Arc Furnace then a heat goes through Argon Oxygen Decarburization and Ladle Furnace stages. At the final stage, Continuous Casting, heats are combined into groups and casted subsequently in a predefined sequence. Strict production constraints include minimum transportation times, maximum hold-up time of heats between subsequent stages, and required setup times between heats with special rules for the last stage where setup times are enforced only between casting sequences. Electricity consumption is dependent both on the equipment used and a specific product to be processed.
The core of the formulation is to answer the question how to account for electricity consumption in continuous-time based scheduling. For this purpose we introduce discrete-time grid corresponding to both hourly varying electricity prices and hourly changing pre-agreed load values. The time horizon of the schedule is divided into equidistant time intervals called time slots. The consumption accounting is done using two event binaries denoting if a given task started or finished within a given time slot. In addition, a set of continuous variables based on the event binaries can keep track of the amount of time a given task spends within the time slot, which in turn allows to keep track of the electricity consumption. Knowledge of the consumption provides a way to optimize the electricity purchase contracts. Choosing different options is driven by an objective function that minimizes penalties paid for deviation from pre-agreed values, cost of electricity consumption (supplied either by local provider or bought at day-ahead market), and cost for electricity produced onsite substracted by revenues generated by potential sale of electricity to the grid.
The model is tested on various problem sizes. The results show that the formulaton is capable of optimizing the production schedule minimizing electricity bill while satisfying all critical production constraints. The purchase strategy can be optimally chosen, including the option of selling the electricity back to the grid. The part of the formulation dealing with electricity consumption and purchase optimization is generic, and thus it can be applied to discrete-time scheduling models for different industries. The main limitation of the model that should be addressed in further work is computational performance for large scale instances. In order to compute real-world cases the model can be decomposed using state-of-the-art methods for example such as Lagrangean, Benders or Bi-level decomposition.
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