Donald J Chmielewski and Benjamin P Omell. Department of Chemical & Biological Engineering Illinois Institute of Technology. Energy Value ($/MWhr)

Transcription

1 Donald J Chmielewski and Benjamin P Omell Department of Chemical & Biological Engineering 40 ACC 2013 H 2 in Energy Value ($/MWhr) Generated Power (MW) Storage (tonnes) Time (days)

2 Outline Economic MPC IGCC Case Study Issues with Finite-Horizon EMPC Infinite-Horizon EMPC Economic Linear Optimal Control Implementation with Imperfect Forecasting

3 Model Predictive Control xu, tt min g x, u, w t s. t. x f ( x, u, w) z h( x, u, w) min d z z( ) z max

4 Traditional MPC Quadratic Objective T T g x, u, w x Qx u Ru min g x, u, w xu, tt t s. t. x f ( x, u, w) z h( x, u, w) min max z z( ) z d

5 Economic MPC g x, u, w Economic Objective - (Instantaneous Profit) min g x, u, w xu, tt t s. t. x f ( x, u, w) z min max z z( ) z d h( x, u, w)

6 Literature on EMPC Conceptual Development and Stability Issues: Rawlings and Amrit (2009); Diehl, et al. (2011); Huang and Biegler (2011); Heidarinejad, et al. (2012) Process Scheduling: Karwana and Keblisb (2007); Baumrucker and Biegler (2010); Lima et al. (2011); Kostina et al. (2011) Power Systems: Zavala et al. (2009); Xie and Ilić (2009), Hovgaard, et al. (2011), Omell and Chmielewski (2011) HVAC Systems: Braun (1992); Morris et al. (1994); Kintner- Meyer and Emery (1995); Henze et al. (2003); Braun (2007); Oldewurtel et al. (2010), Ma et al. (2012); Mendoza and Chmielewski (2012)

7 Outline Economic MPC IGCC Case Study Issues with Finite-Horizon EMPC Infinite-Horizon EMPC Economic Linear Optimal Control Implementation with Imperfect Forecasting

8 Overview of Smart Grid Generators Transmission Consumer Demand Generator Dispatch Renewable Smart Homes Smart Manufacturing with Storage Commercial Buildings

9 Integrated Gasification Combined Cycle

10 Hydrogen Gas Storage Hydrogen Gas Storage Assume Carbon Capture Operations

11 Conventional IGCC v coal Gasification Unit v H2 v H2,G Power Block P G P G =βv H2,G

12 IGCC with Dispatch Capability v coal Gasification Unit v H2 v H2,S Storage Tank v H2,G M 0 0 H 2 H 2 G M P G M max H2 H2 P max G P / Power Block P G =βv H2,G P G

13 Economic MPC for IGCC min P G tt t 0 0 C P d e M P G G s. t. M P / H 2 H 2 G M max H2 H2 P max G C () e t is the cost (or value) of electricity

14 Economic MPC Simulation with Perfect Forecasting of C e (t) H 2 in Energy Value ($/MWhr) Generated Power (MW) Storage (tonnes) Time (days)

15 Impact of Horizon Size on EMPC Energy Value ($/MWhr) Generated Power (MW) H 2 in Storage (tonnes) hr horizon 6hr horizon Time (days)

16 Inventory Depletion Long-term scheduling of a single-unit multi-product continuous process to manufacture high performance glass Lima, Grossman and Jiao (2011) An additional time horizon of six months... on the future demand [is required] to avoid a myopic inventory policy at the end of the scheduling period of 18 months.

17 Outline Economic MPC IGCC Case Study Issues with Finite-Horizon EMPC Infinite-Horizon EMPC Economic Linear Optimal Control Implementation with Imperfect Forecasting

18 Infinite Horizon MPC min g( x, u, w) d xu, t s.. t x Ax Bu Gw z D x D u min x u max z z( ) z t

19 Infinite Horizon Finite Constrained MPC min g( x, u, w) d xu, t s.. t x Ax Bu Gw z D x D u min x u max z z( ) z t t T

20 Infinite Horizon Finite Constrained MPC min g( x, u, w) d g( x, u, w) d xu, t tt s. t. x Ax Bu Gw min tt z D x D u x u max z z( ) z t t T

21 Finite Horizon MPC with Terminal Cost min g( x, u, w) d ( x( t T )) xu, t s. t. x Ax Bu Gw min tt z D x D u x u max z z( ) z t t T

22 Unconstrained Value Function ( x( t T)) min g( x, u, w) d xu, tt s. t. x Ax Bu Gw

23 Unconstrained Value Function ( x( t T)) min g( x, u, w) d xu, tt s. t. x Ax Bu Gw If g x, u, w - (Instantaneous Profit)

24 Unconstrained Value Function ( x( t T)) min g( x, u, w) d xu, tt s. t. x Ax Bu Gw If g x, u, w - (Instantaneous Profit) Then () does not exist

25 Statistically Constrained Value Function ( x( t T )) min g( x, u, w) d ELOC xu, tt s. t. x Ax Bu Gw z D x D u x 2 min max E[ z ] min z, z u 2

26 Outline Economic MPC IGCC Case Study Issues with Finite-Horizon EMPC Infinite-Horizon EMPC Economic Linear Optimal Control Implementation with Imperfect Forecasting

27 ELOC Development 1. Stochastic Electricity Price Model 2. Constrained Stochastic Control 3. Analytic Expression for Revenue 4. Controller Synthesis

28 Electricity Price Model White Noise Input Shaping Filter Sequence with Electricity Price Characteristics

29 Realization of Electricity Spectral Density (($/MW) 2 /hr) Elecriticy Value ($/MW hr) Frequence (rad/hr) Time (days)

30 Scaled Electricity Prices White Noise Input a Shaping Filter Sequence with Electricity Price Characteristics Overall Process Model: x Ax Bu agw

31 ELOC Development 1. Stochastic Electricity Price Model 2. Constrained Stochastic Control 3. Analytic Expression for Revenue 4. Controller Synthesis

32 Stochastic Constrained Control z 1 Assumeu Lx and find L such that 0 ( A BL) j j 2 ( D j j z j max j x x u x D L) and * ( A BL) x 2 ( D j x z T D L) u min j 2 a GS, T T j w j 1... n G Based on standard deviations j 's z T z j z Constraints min and max j z 2

33 ELOC Development 1. Stochastic Electricity Price Model 2. Constrained Stochastic Control 3. Analytic Expression for Revenue 4. Controller Synthesis

34 G G G G G e e e e e P P P P P C C C C C, ~, ~ ELOC Objective Function G e G e G e T G e T P C P C E P C E dt P C T ] ~ ~ [ ] [ 1 lim 0 where

35 ELOC Objective Function G e G e T G e T C P P E C dt C P T ] ~ ~ [ 1 lim 0 Then, enforce the condition e P G C ~ ~ a Ce e e e G e C E C C E P C E a a a ] ~ [ )] ~ ( ~ [ ] ~ ~ [ 2

36 ELOC Development 1. Stochastic Electricity Price Model 2. Constrained Stochastic Control 3. Analytic Expression for Revenue 4. Controller Synthesis

37 ELOC Synthesis z j j j j j j T j T u x x u x j j T w T x x n j z z D L D D L D G GS BL A BL A s t 1..., 2 and 2 ) ( ) ( ) ( ) ( 0.. min max 2 a G e Ce L P C j j x a a,, 0,, min x L u ELOC Can be solved using Convex Optimization

38 Comparison of ELOC and EMPC Power Generated (MW) ELOC EMPC Time (days) 2000 H 2 in Storage (tonnes) Time (days)

39 Outline Economic MPC IGCC Case Study Issues with Finite-Horizon EMPC Infinite-Horizon EMPC Economic Linear Optimal Control Implementation with Imperfect Forecasting

40 Linear Quadratic Optimal Control ( x( t T)) min g( x, u, w) d xu, t T s. t. x Ax Bu

41 Linear Quadratic Optimal Control If ( x( t T)) min g( x, u, w) d xu, t T s. t. x Ax Bu Q M x g( x, u, w) = x T u T T M R u ( x( t T)) x( t T) T P x( t T) LQR u L LQR x

42 Inverse Optimality on ELOC ( x( t T)) min g( x, u, w) d xu, t T s. t. x Ax Bu Gw T T QELOC MELOC x g( x, u, w) = x u T MELOC R ELOC u ( x( t T)) x( t T) T P x( t T) ELOC u L ELOC x

43 Inverse Optimality Chmielewski & Manthanwar (2004): If there exists P > 0 and R > 0 such that A T P PA Q L R 1 L PB T RL A L T 1 T PB M R PB M 0 M R PB T T P PA T L T R PB T T T Then M ( L R PB) and Q L RL A P PA are such that Q M T M R 0 R 0 and P and L satisfy

44 IGCC Example L ELOC Q ELOC e5 6.37e e e ELOC M P ELOC 7.26e R ELOC

45 Predictive Form of ELOC tt T T QELOC MELOC x T min x u d x( t T ) PELOC x( t T ) xu, T M t ELOC R ELOC u s. t. x Ax Bu Gw z D x D u x u min max z z( ) z t t T

46 Infinite Horizon EMPC tt T T QELOC MELOC x T min x u d x( t T ) PELOC x( t T ) xu, T M t ELOC R ELOC u s. t. x Ax Bu Gw z D x D u x u min max z z( ) z t t T

47 IH-EMPC vs. EMPC 24-hr horizon Energy Value ($/MWhr) Generated Power (MW) H 2 in Storage (tonnes) IH-EMPC 1500 EMPC Time (days)

48 Horizon Size Sensitivity Power Generated (MW) 1500 Difference 1000 in computation times for 30 day simulation: 500 EMPC 24 hr horizon~ 22.8 sec IH-EMPC 1 hr horizon~ 0.02 sec Reduction of 99.9% Power Generated (MW) Time (days) Time (days) 6 hr horizon 24 hr horizon 24 hr horizon 1 hr horizon

49 Outline Economic MPC IGCC Case Study Issues with Finite-Horizon EMPC Infinite-Horizon EMPC Economic Linear Optimal Control Implementation with Imperfect Forecasting

50 Prediction of Electricity Price White Noise Input Shaping Filter Sequence with Electricity Price Characteristics Measured Electricity Price State Estimator and/or Predictor Prediction of Electricity Price

51 Imperfect Forecast Simulation Energy Value ($/MWhr) Generated Power (MW) H 2 in Storage (tonnes) IH-EMPC EMPC Time (days)

52 Revenue Case Revenue (10 3 $/day) Revenue Increase No Dispatch EMPC: Perfect Forecast % EMPC: Imperfect Forecast % IH-EMPC: Imperfect Forecast %

53 Acknowledgements Current and Former Students: David Mendoza-Serrano Ming Yang (Taiwan Electric) Amit Manthanwar Personal Communications: Ignacio E. Grossman and Ricardo M Lima Funding: National Science Foundation (CBET )

54 AIChE Workshop on Smart Grid for the Chemical Process Industry September 25-27, 2013 Chicago Will explore the opportunities and challenges associated with demand response in the chemical process industry. Co-sponsored by AIChE Computing and Systems Technology (CAST) Division and IIT Wanger Institute for Sustainable Energy Research (WISER) Collocated with the Great Lakes Symposium on Smart Grid and the New Energy Economy (September 23-25, 2013, Co-sponsored by IEEE Power and Energy Society and IIT Galvin Center for Electricity Innovation)

55 AIChE Workshop on Smart Grid for the Chemical Process Industry September 25-27, 2013 Chicago Confirmed Speakers Large Industrials and Demand Response in the United States David Heitzer, EDF Energy Services Economic Dispatch of a Combined Heat and Power Plant Jong S. Kim and Thomas F. Edgar, University of Texas at Austin Flexible and Efficient Operation for Power Generation and Process Industry A GE Perspective Aditya Kumar, GE Global Research A Distributed Control Framework for Smart Grid Development Jinfeng Liu University of Alberta and Panagiotis D. Christofides University of California, Los Angeles Supply Driven-Operation of Processes Alexander Mitsos, Ganzhou Wang and Wolfgang Marquardt, RWTH Aachen University; Amin Ghobeity and Chris Williams, Massachusetts Institute of Technology Use of Low Cost Electrical Power in Petrochemical Process Units Dennis O Brien, Jacobs Consultancy and Donald J. Chmielewski, Active participation of Industry in the Smart Grid Ernst Scholtz, Xiaoming Feng, and Iiro Harjunkoski, ABB Corporate Research Assessing the Benefits of Stochastic Market Clearing Victor M. Zavala, Argonne National Laboratory Multiscale Optimization for Demand Side Management of Industrial Power-intensive Processes Qi Zhang Ignacio Grossmann, Carnegie Mellon University

56 Conclusions Illustrated issues with Finite Horizon EMPC Inventory creep Manipulated variable chattering Proposed a Infinite Horizon Formulation Provided IH-EMPC tuning methods Sensitivity to horizon size nearly eliminated IH-EMPC less sensitive to forecast errors.