(22b) Moving Horizon Closed-Loop Scheduling of Processes Operating Under Dynamic Constraints
Richard C. Pattison1, Cara R. Touretzky1, Iiro Harjunkoski2, Michael Baldea1
1McKetta Department of Chemical Engineering, The University of Texas at Austin, Austin, TX
2ABB Corporate Research, Ladenburg, Germany
The deregulation of electricity markets has brought new challenges and opportunities in the operation of electricity-intensive chemical processes. Day-ahead/real-time electricity tariffs feature fast changes in energy prices, and it is desirable to impose frequent changes in production targets (e.g., hourly changes in production rate) to capitalize on these fluctuations. In general, production levels (and electricity consumption) are increased at times when prices are low, and the excess product is stored or buffered. As a result, when electricity prices are at a peak, the production levels (and electricity consumption) can be decreased. From the perspective of the electric grid, this operating paradigm effectively amounts to storing energy in the form of chemical products as a means of providing demand response service. However, this constitutes a significant departure from the traditional operation of chemical processes, where setpoint changes are assumed to be infrequent (compared to the process time constant) and the process operates chiefly at steady state. Under the latter conditions, scheduling calculations do not require knowledge of the process dynamics. However, in the more dynamic operating paradigm associated with fast fluctuations in market conditions and prices, transient operations become the norm and the process may never reach steady state in between production target changes. Thus, it is crucial to ensure that a schedule is dynamically feasible, which motivates incorporating a representation of the process dynamics in the scheduling model.
The resulting scheduling problem is in the form of a mixed-integer dynamic optimization (MIDO), and its solution poses several practical challenges. When a first-principles, detailed dynamic process model is used, the problem is often difficult (if not impossible) to solve in a practical amount of time. This challenge is amplified by the fact that, in practical applications, the schedule must likely be recalculated periodically to account for updated price- and demand forecasts, and disturbances. In our previous work  we addressed this challenge by constructing low-order dynamic â??scale bridgingâ? models (SBMs) . The SBMs predict the closed-loop evolution of variables relevant to the scheduling calculation in response to production target changes, and alleviate the computational challenges associated with embedding the dynamic model in the scheduling calculation.
In this talk, we present a new approach to accounting for changes in market conditions and disturbances to the process . To this end, we close the scheduling loop with feedback based on measurements of the identified scheduling-relevant process variables, in conjunction with an observer structure that is used to update the SBM states. The feedback mechanism is implemented using, i) periodic updates of the schedule over a moving horizon to incorporate the updated price and demand forecasts, and, ii) event-driven updates that account for measurable process and market disturbances.
The theoretical developments are then demonstrated on an industrial-scale cryogenic air separation unit (ASU) model. A system identification routine, based on using transient historical production data, was used to construct SBMs. The ASU is outfitted with a liquid nitrogen storage tank, which enables the process to adjust the production rate in response to variable electricity prices while satisfying product demand by re-gasifying the liquid nitrogen inventory. The optimal schedule is solved using a sequential dynamic optimization framework, and results in a 4.8% savings in electricity cost over the course of 4 days in comparison to a scenario where the production rate is constant. We also evaluate disturbance scenarios comprising, i) a planned, ii) an unplanned, and, iii) a random drop in demand due to a failure at the customer site. In all cases, the moving horizon framework successfully manages the production and inventory levels without any dynamic of product constraint violations.
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 R. C. Pattison, C. R. Touretzky, T. Johansson, I. Harjunkoski, and M. Baldea. Optimal process operations in fast-changing electricity markets: Framework for scheduling with low-order dynamic models and an air separation application. Ind. Eng. Chem. Res., 55(16):4562â??4584, 2016.
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 R. C. Pattison, C. R. Touretzky, I. Harjunkoski, M. Baldea. Moving Horizon Production Scheduling using Dynamic Process Models. Submitted to AIChE J, 2016.