##
470221 A Demand Response Strategy for Continuous Processes Using Stochastic Optimal Scheduling

Demand Response has been studied extensively in the literature for residential applications [3], however chemical processes nearly always obey nonlinear dynamics making their control notoriously difficult to optimize [4]. Adjusting the production set-point brings about a transition period during which product quality is uncontrolled. Unlike linear systems commonly modeled for classical control theory, the length of this transition period depends not only on the difference between the current state and the target but also on the current state itself. To work around the difficulty involved in determining arbitrary nonlinear transient profiles, a discrete set of stable operating points for the reactor are identified a priori by algebraically solving for values of control variables at as many equilibrium points as the user desires and tabulating the specific transition profiles between all possible pairs of equilibrium points. Once a sufficient number of the stable operating modes and their transitions have been tabulated, a clique wandering Dynamic Programming (DP) algorithm can be used to calculate the optimal schedule. [5] To do this, a clique (a fully connected graph) is generated for each time step using the stable operating points as the nodes, and weighting each edge according to the cost of the transition from the source to the set-point plus the cost of operating at the set-point for the remainder of the time after the transition. For each time step and each mode at each time step, every possible path from the previous feasible states is evaluated. Any of these new paths which both cost more and have less storage available than some other path or violate any constraint are then removed from the feasible set of this time step, preventing the number of computations from becoming exponential in time.

By using this clique wandering algorithm, the optimal scheduling policy was found for four case studies of CSTR operation. In the first case a CSTR was considered to be powered solely by the grid, and the envelope of pricing conditions which optimally lead to steady-state operation was found. The analysis was then repeated for the second case with on-site renewable energy generating units providing power to the plant. The results of using the DP algorithm on this case study matched or improved performance as compared to previous results of CSTR studied in the literature [5] [6]. Then the natural ability of Dynamic Programming to handle stochasticity was utilized for the third case, where uncertainty was introduced in the weather forecast and thus renewable power availability. In the fourth and final case the degree of stochasticity was increased further by adding random noise to the hourly electricity price. The results of the stochastic simulation for our case study show that the effects of taking the stochasticity are significant. Operating cost reductions above 10% compared to the steady state operation could be found in the best case, while savings of 4% are found for the average case.

**References**

[1] |
N. Li , L. Chen, S. H. Lowe, “Optimal demand response based on utility maximization in power networks," |

[2] |
I. Harjunkoski , E. Scholtz. X. Feng, "Industry Meets the Smart Grid," |

[3] |
R. Deng , Z. Yang. M. Chow, J. Chen, "A Survey on Demand Response in Smart Grids: Mathematical Models and Approaches," |

[4] |
M.A. Javinsky & R. H. Kadlec, "Optimal Control of a Continuous Flow Stirred Tank Chemical Reactor," |

[5] |
C. Tong, N. El-Farra, A. Palazoglu, X. Yan, "Energy Demand Response of Process Systems through Production Scheduling and Control," |

[6] |
T. Feital et al., "Modeling and Performance Monitoring of Multivariate Multimodal Processes," |

**Extended Abstract:**File Not Uploaded

See more of this Group/Topical: Computing and Systems Technology Division