برنامه ریزی تولید بهینه با قیمت های برق حساس به زمان برای فرآیندهای قدرت فشرده پیوسته

Power-intensive processes can lower operating expenses when adjusting production planning according to time-dependent electricity pricing schemes. In this paper, we describe a discrete-time, deterministic MILP model that allows optimal production planning for continuous power-intensive processes. We emphasize the systematic modeling of operational transitions, that result from switching the operating modes of the plant equipment, with logic constraints. We prove properties on the tightness of several logic constraints. For the time horizon of 1 week and hourly changing electricity prices, we solve an industrial case study on air separation plants, where transitional modes help us capture ramping behavior. We also solve problem instances on cement plants where we show that the appropriate choice of operating modes allows us to obtain practical schedules, while limiting the number of changeovers. Despite the large size of the MILPs, the required solution times are small due to the explicit modeling of transitions.

The profitability of industrial power-intensive processes is affected by the availability and pricing of electricity supply. Nowadays, two major trends increase the complexity of managing power-intensive processes. First, deregulation in the 1990s introduced hourly as well as seasonal variations. Second, the environmental pressure to reduce CO2 emissions and diminishing natural resources lead to an increasing share of renewable energies, which intensifies the aforementioned problem. These trends have added a considerable amount of uncertainty and variability in the daily operating expenses of power-intensive industries, which in turn affect their competitiveness. One important component of the current and future power system is the concept of Demand Side Management (DSM), consisting of Energy Efficiency (EE) and Demand Response (DR). A report released by The World Bank (Charles River Associates, 2005) defines DSM as the “systematic utility and government activities designed to change the amount and/or timing of the customer's use of electricity for the collective benefit of the society, the utility and its customers.” While EE aims for permanently reducing demand for energy, DR focuses on the operational level (Voytas et al., 2007). The official classification of DR by the North American Electric Reliability Corporation (NERC) distinguishes between dispatchable and non-dispatchable programs (see Fig. 1). Full-size image (43 K) Fig. 1. Illustration of DR applications for chemical processes according to the classification of DR programs by NERC (Voytas et al., 2007); reduced diagram. Figure options Dispatchable DR programs include any kind of demand response that is according to instructions from a grid operator's control center. They are divided into capacity services, such as load control and interruptible demand, and ancillary services, such as spinning and nonspinning reserves as well as regulation. The control actions, which balance the electricity supply and demand, differ on the time scale and usually range from a few seconds to one hour. Hence, participation in one of these dispatchable DR programs requires the process to be highly flexible, while process feasibility and safety have to be maintained. Nowadays, chemical companies, which operate flexible processes like chlor-alkali synthesis, market already a few percent of their total load as operative capacity reserve (e.g. in Germany; Paulus & Borggrefe, 2011). The potential of ancillary services for aluminum production was recently evaluated in a case study by ALCOA (Todd et al., 2009). However, both processes, chlor-alkali synthesis and aluminum production, are examples of capital-intensive processes that are operated at a high level of capacity utilization. Thus, these processes usually only shift production on a minute level around a predefined setpoint. In contrast to dispatchable DR programs, non-dispatchable DR programs do not involve instructions from a control center. Instead, the electricity consumption of industrial customers is influenced by the market price of electricity. Typical examples of time-sensitive electricity prices are time-of-use (TOU) rates and real-time prices (RTP). While TOU rates are usually specified in terms of on-peak, mid-peak and off-peak hours, real-time prices vary every hour and are quoted either on a day-ahead or hourly basis. Other pricing models exist but strongly depend on the characteristics of the regional market (NERC study; (Voytas et al., 2007)). Non-dispatchable DR programs allow industrial customers to perform production planning based on predefined hourly prices. At first glance it may seem that production planning due to price fluctuations is only attractive for processes that are operated significantly below the process capacity, and therefore have operational flexibility. However, major demand drops due to economic changes, such as the 2008 recession, can lead to over-capacities, which in turn make a systematic production planning more attractive. Promising examples can be found in the industrial gases sector (cryogenic air separation plants) and in the cement industry. The purpose of this paper is to describe a general model that helps decision-makers for power-intensive production processes to optimize their production schedules with respect to operating costs that are due to fluctuations in electricity prices, which are in turn caused by non-dispatchable DR programs.

In this paper, we have presented a model for the optimal operational production planning for continuous power-intensive processes that participate in non-dispatchable demand response programs. We described a deterministic MILP model that allows an accurate and efficient modeling of transitions between operating modes using a discrete time representation. Properties on the tightness of several logic constraints were proved. We successfully applied the model to two different real-world air separation plants that supply to the liquid merchant market, as well as cement plants. In the air separation case study, the operational optimization model produced savings of more than 10% when compared to a simple heuristic. We also learned that operational flexibility, in terms of production and storage capacity, is the key to lower operating expenses. For the same demand profile, a plant with two liquefiers was able to save 5% on costs when compared with a single liquefier plant. We observed in the case of the cement plant that the introduction of transitional modes resulted in a large-scale model. Nevertheless, the model was superior compared to a smaller model that only had single product modes, and thus lacked the capability of limiting the number of occurring transitions, and could not be solved to optimality. Despite the large size of the MILP model with transitional modes, the required solution times to obtain the optimal solution were small for all test cases. Furthermore, the obtained schedules were practical to implement because we were able to limit the number of occurring transitions. Future work will examine the impact of long-term capital investments in additional production or storage capacity that increase process flexibility and potentially facilitate savings on the operational level. We also intend to model the effect of uncertainty in the problem data.