Integrating Scheduling and Control for Optimal Process...
Transcript of Integrating Scheduling and Control for Optimal Process...
Integrating Scheduling and Control forOptimal Process Operations in Fast-Changing Markets
Michael BaldeaMcKetta Department of Chemical Engineering &
Institute for Computational Engineering and SciencesThe University of Texas at Austin
Contributors: Dr. Juan Du (UT, now at PPG), Cara R. Touretzky (UT), Richard C. Pattison (UT), Jungup Park (UT), Ted Johansson (KTH/UT), Dr. Iiro Harjunkoski (ABB)
Enterprise-Wide Optimization Seminar Carnegie Mellon University, February 3, 2016
Process and Energy Systems Engineering
Outline
Background and Motivation
EWO Challenges
Integrating Scheduling and Control• Scale-bridging Principle• Model Predictive Control• Data-driven Models
Case Study
Conclusions and Perspective
Process and Energy Systems Engineering
Background and Motivation
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• Significant expansion of renewable generation- GWh-scale wind generation www.awea.org
- >1GWh of PV solar installed in 2014 www.seia.org
• Increased capacity exacerbates variability issues
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d ge
nera
tion,
GW
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Gri
d de
man
d, G
WHour ending
Data: www.ercot.com Ondeck, Edgar, Baldea, Applied Energy, 593-606, 2015
Process and Energy Systems Engineering
Demand Variability
• Grid demand desynchronized from renewables• Peak demand → fast changing, high cost
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tric
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rice
($/k
Wh)
Pow
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eman
d (G
W)
Time
Energy DemandElectricity Price
ERCOT demand and day ahead settlement point prices for June 25, 2012 from www.ercot.com
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Process and Energy Systems Engineering
The Peak Demand Problem
• Residential buildings are the primary culprits• Industry could help - how?
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Moderate Day Peak Day
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eman
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Residential
Commercial
Industrial
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Process and Energy Systems Engineering
Grid-Dependent Industries
Demand response: lower production during peak timePotential benefits for industry• Reduce production cost / generate profit from price incentives• Improve environmental performance• Improve grid operations
Soroush and Chmielewski, Comput. Chem. Eng., 51, 86-95, 2013; Paulus and Borggrefe, Applied Energy, 88, 432-441, 2011
6
Process and Energy Systems Engineering
Industrial Demand Response
• Reduce production rate (vs. nominal) during peak time• Increase production rate at off-peak hours • Excess capacity and product storage must be available
(or installed at reasonable cost)7
Process and Energy Systems Engineering
Example: DR Operation of Air Separation Unit
Production scheduled on an hourly basis to account for real-time energy pricing• Production levels• Liquid vs. gas products
Process dynamics evolve in a comparable time scale
Ierapetritou et al., Ind. Eng. Chem. Res., 41, 5262-5277, 2002; Miller et al., Ind. Eng. Chem. Res., 47, 1132-1139, 2008; Cao, Swartz, Baldea, Blouin, J. Proc. Contr., 54 (24), 6355–6361, 2015
8
Process and Energy Systems Engineering
Industrial Demand Response
• Frequent production rate (schedule) changes: process dynamics must be accounted for in production scheduling:
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Process and Energy Systems Engineering
Broader Challenge of Flexible Production
• Rapid response to market conditions: transitions occur in the same time scale as scheduled production changes
• Customizable products• Specialty chemicals, pharma, etc.
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Process and Energy Systems Engineering
Smart Manufacturing and EWO
11
“a design and operational paradigm involving the integration of measurement and actuation; environment, safety and environmental protection, regulatory control, high fidelity modeling, real-time optimization and modeling, and planning and scheduling.” (Edgar and Davis, 2009)
Process and Energy Systems Engineering
Hierarchy of Process Operation Decisions
12
Production management• Assume steady-state operation• Typically carried out off-line
Control • Account for dynamics• Online, in real-time
Different time horizons, objectives, personnel: production management and control carried out independently
Seborg et al., Wiley, 2010, Baldea and Harjunkoski, Comput. Chem. Eng., 71, 377-390, 2014, Shobrys and White, Comput. Chem. Eng, 26, 149—160, 2002
PROCESS
Regulatory control(seconds – minutes)
Multivariable and constraint control (minutes – hours)
Scheduling(hours – days)
Planning (weeks – months)
Process and Energy Systems Engineering
PROCESS
Regulatory control(seconds – minutes)
Multivariable and constraint control (minutes – hours)
Scheduling(hours – days)
Planning (weeks – months)
Hierarchy of Process Operation Decisions
13
Mezoscale interactions
Overlap in the time scales of production management and process control motivates considering the integrated problem
Seborg et al., Wiley, 2010, Baldea and Harjunkoski, Comput. Chem. Eng., 71, 377-390, 2014, Shobrys and White, Comput. Chem. Eng, 26, 149—160, 2002
Process and Energy Systems Engineering
PROCESS
Regulatory control(seconds – minutes)
Multivariable and constraint control (minutes – hours)
Scheduling(hours – days)
Planning (weeks – months)
Hierarchy of Process Operation Decisions
14
Mezoscale interactions
Goal: Mechanism for synchronizing production scheduling with the control system and accounting for the dynamic nature of transitions
Process and Energy Systems Engineering
Smart(er) Manufacturing
Scheduling- become aware of process
state/dynamics- rescheduling
ProcessSupervisory
controller
Scheduling
outputs
yinputs
u
setpoints/
targets
ysp
+
-
process state for rescheduling
schedule for predicting
Supervisory Control- become aware of future
changes in production; improved response
- dynamic models are large and cumbersome
- some details may not be necessary for scheduling
- disturbance rejection- fast/short horizon execution
needed; cannot make scheduling decisions
BUT
Baldea and Harjunkoski, Comput. Chem. Eng., 71, 377-390, 2014
15
Process and Energy Systems Engineering
', 1 , ', ,1 ' 1
τ−= =
= + +∑∑p pN N
f s ps s i s i s i i i s
i it t z z t
Slot-Based Scheduling: Conventional
16
static schedulingdemand
price
sequence zi,s
production time tps
Mixed integer program
Static:• Transition time is a pre-
-determined constant;• Agnostic to process
dynamics.
MIP• Sequence zi,s ∈{0,1}• Production time ∈R+
( ), ,1 1 1
1 p p sN N Nf
scheduling i i i s storage i m s ii i sm
J z c T tT
π ω ω= = =
= − −
∑ ∑∑
1 1s fs st t s−= ∀ ≠
,1
1, sN
i ss
z i=
= ∀∑ ,1
1, pN
i si
z s=
= ∀∑
, , max ,≤ ∀p pi s i st z T i s
,1
, > T sN
pi s i s i i m
sq t iω ω δ
=
= ∀∑
Pinto and Grossmann, Comput. Chem. Eng. 18 (9), 797-816, 1994
Process and Energy Systems Engineering
,1
τ=
= + + ∀∑pN
f s ps s s i s
it t t s
Scheduling and Control: Full Dynamic Approach
17
Scheduling + Control
(Solve simultaneously)
demand
price
control action u
process output y
Embed dynamic process model in scheduling calculation
Disadvantages:• Detailed dynamics: large-
scale, computational difficulties
• Open-loop (optimal) control
MIDO:• Sequence zi,s ∈{0,1}• Production time ∈R+• u ∈ U ⊂ R+
( ), ,1 1 1
1 p p sN N Nf
scheduling i i i s storage i m s ii i sm
J z c T tT
π ω ω= = =
= − −
∑ ∑∑
1 1s fs st t s−= ∀ ≠
,1
1, sN
i ss
z i=
= ∀∑ ,1
1, pN
i si
z s=
= ∀∑( ) ( )= +x f x G x u
( )=y h x ( ) ,τ = ∑ sss i s i
izy y
,1
, > T sN
pi s i s i i m
sq t iω ω δ
=
= ∀∑
, , max ,≤ ∀p pi s i st z T i s
Process and Energy Systems Engineering
Baldea, Harjunkoski, Park, Du., AIChE J., 2015; Du, Park, Harjunkoski, Baldea. Comput. Chem. Eng., 79, 59-69, 2015
setpoints/
targets
ysp
Concept: Scale-Bridging Model
Scale-Bridging Model: • Capture closed-loop input-output dynamics• Embed in scheduling calculation
ProcessSupervisory
controller
Scheduling
outputs
yinputs
u
setpoints/
targets
ysp
+
-
process state for rescheduling
schedule for predicting
Baldea and Harjunkoski, Comput. Chem. Eng., 71, 377-390, 2014
18
Scale-Bridging Model
Scheduling
outputs
y
Process and Energy Systems Engineering 19
Scale-Bridging Model: Concept• SBM is the explicit form of the closed-loop dynamics of
process with its supervisory controller
• Low dimensional:
• Dynamics of process systems at scheduling-relevant time scales
y xn n
• Process operates in closed-loop:
• stability guarantees
• robustness to modeling error
setpoints/
targets
ysp
Scale-Bridging Model
Scheduling
outputs
y
Process and Energy Systems EngineeringSeborg, Edgar, Mellichamp, Doyle, Process Dynamics and Control (3rd Ed.), Wiley, 2011
Concept: Scale-Bridging Model
Capture closed-loop input-output dynamics• Not a trivial task for a general nonlinear
system• Historically, research has focused on stability
and speed of response, rather than the trajectory itself
ProcessSupervisory
controller
Scheduling
outputs
yinputs
u
setpoints/
targets
ysp
+
-
process state for rescheduling
schedule for predicting
Baldea and Harjunkoski, Comput. Chem. Eng., 71, 377-390, 2014
20
Process and Energy Systems Engineering
Scale-Bridging Model Approaches
Capture closed-loop input-output dynamics1. Scale bridging via input-output linearization2. Scale bridging and model predictive control (MPC)3. Scale bridging using empirical models
ProcessSupervisory
controller
Scheduling
outputs
yinputs
u
setpoints/
targets
ysp
+
-
process state for rescheduling
schedule for predicting
Baldea and Harjunkoski, Comput. Chem. Eng., 71, 377-390, 2014
21
synopsis
Process and Energy Systems Engineering 22
Scale-Bridging via Input-Output Linearization• SBM is the explicit form of the closed-loop dynamics of
process with its supervisory controller
• Use feedback linearization to design a control law that imposes a closed-loop behavior of the type:
0
τ=
=∑ir
j spi ji
i
d yy
dt
ProcessSupervisory
controller
outputs
yinputs
u
+
-
setpoints/
targets
ysp
• Input u calculated from inverse of process model (Hirschorn, 1979)
11
( )
( )
rr
sp i fir
r g f
y y L h xu
L L h x
τ
τ=−
− −=
∑( ) ( )= +x f x g x u
( )=y h x
• Decoupled response for MIMO systems, integral action can be added to deal with disturbances and plant-model mismatch
Kravaris and Kantor, Ind. Eng. Chem. Res., 29, 2295-2310, 1990; Daoutidis and Kravaris, Chem. Eng. Sci., 49, 433—447, 1994
Process and Energy Systems Engineering
Example: Multi-Product Reactor• Exothermal reactor with coolant flow rate as control variable.• Four products (A,B,C,D), concentration depends on operating
conditions• C,D: open-loop unstable states
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Flores-Tlacuahuac and Grossmann, Ind. Eng. Chem. Res., 45, 6698–6712, 2006
Process and Energy Systems Engineering
• Integral action on 𝑦𝑦1,𝑠𝑠𝑠𝑠→ 𝑣𝑣
Scale-Bridging Model
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( )
2
2
-N y1 110 1
2 -N y210 1 2
dy 1-y= -k e ydt
ydy = +k e y - αF y -Tdt
θ
θ−f
c c
T
• Process model
• SBM: relative order 𝑟𝑟 = 2
• Impose critically damped second-order I/O behavior
• Controlled variable: 𝒚𝒚 = 𝑦𝑦1
• Manipulated variable: 𝒖𝒖 = 𝐹𝐹𝐹𝐹
Dimensionless concentration
Dimensionless temperature
22 1 1
12 2 ; 4.3β β β+ + = =d y dy y v hdt dt
Process and Energy Systems Engineering
Problem Formulation
25
• Objective function
• Cyclical production timing and sequencing:
• Demand satisfaction:
• Dynamic model discretization (Radau IIA); smoothness of u:
,1
1, pN
i si
z s=
= ∀∑ ,1
1, sN
i ss
z i=
= ∀∑
1 1s fs st t s−= ∀ ≠ s
s m st T s N≤ =
/ 1.1 , i i m iTδ ω δ≤ ≤ ,1
, ω=
= ∀∑sN
pi s i s
sq t i
, , 0, , , , ,1
+ ; ,τ=
= ∀ ∈ ∀∑
cpns
j k s k s m j m k sme
x x W x x k sn
x
0, , 0, 1, , , 1,1
+ ; 1;τ− −
=
= ∀ ∈ ∀ > ∀∑
cp
cp
ns
k s k s m n m k sme
x x W x x k sn
x
j, , 1, , 1 ; 1; ;ρ−− ≤ ∀ ∈ ∀ > ∀ ∀k s j k su u u j k su
1, , , 1, 2 ; 1;cpk s n k su u u k sρ−− ≤ ∀ ∈ ∀ > ∀u
( ), ,1 1 1
1 π ω ω= = =
= − −
∑ ∑∑
p p sN N Nf
scheduling i i i s storage i m si i sm
J c T tT
,1
τ=
= + + ∀∑pN
f s ps s s i s
it t t s , , max ,≤ ∀p p
i s i st z T i s
0,1, , 1 ;−= ∀ ∈ ∀sss i s ix z x x sx j,k, , ; 18;= ∀ ∈ ∀ > ∀ss
s i s ix z x x k sx
, , max ,ω ≤ ∀i s i sz W i s , max ,(1 ) ,ω ω≤ − − ∀i s i i sW z i s
Pinto and Grossmann, Comput. Chem. Eng., 18, 797-816, 1994; Flores-Tlacuahuac and Grossmann, IECR, 45, 6698–6712, 2006
Similar to “delta U” formulation in MPC
Process and Energy Systems Engineering
Full Dynamic Optimization
26
B DCA
Cycle time: 84.45h
Profit: $5,656
Process and Energy Systems Engineering
Schedule Based on SBM
27
• Integrated Scheduling and Control using second-order linear SBM
• Implemented in GAMS, solved using SBB/CONOPT3
• Full order: 5.2s; SBM-based: 1.7s
Production sequence and
cycle time are very similar
Process and Energy Systems Engineering
Closed-loop Implementation of Schedule
28
B DCA Cycle time: 84.45h
Profit: $5,190
• Excellent approximation of results derived using full-order model
Process and Energy Systems Engineering
Integration of Scheduling and MPC
• I/O linearization typically limited to unconstrained square systems with stable zero dynamics
• MPC: deal with constraints, non-square systems widely accepted in industry
29
• No explicit description of input-output behavior = NO SBM?
Seborg et al.,, 3rd Ed., Wiley, 2011
Qin and Badgwell, Contr. Eng. Prac., 11, 733-764, 2003, Kolavennu, Palanki, Cockburn, Chem. Eng. Sci., 56, 2103-2110, 2001,
Process and Energy Systems Engineering
Scheduling-Oriented MPC
ProcessScheduling
Oriented Model Predictive Control
Scheduling
outputs
y
inputs
u
setpoints/
targets
ysp
+
-
• Scheduling-oriented MPC that is based on a SBM
Replace tracking objective with SBM as a hard constraint
Scale Bridging Model
Baldea, Harjunkoski, Park, Du, AIChE J., 2015
30
Process and Energy Systems Engineering
• First-order response for temperature
Case Study: Scale-Bridging Model
31
( )
2
2
-N y1 110 1
2 -N y210 1 2
dy 1-y= -k e ydt
ydy = +k e y - αF y -Tdt
θ
θ−f
c c
T
• Process model
• SBM:
• Impose second-order I/O behavior for concentraiton
• Controlled variables: 𝒚𝒚 = 𝑦𝑦1,𝑦𝑦2
• Manipulated variables: 𝒖𝒖 = 𝜃𝜃,𝐹𝐹𝐹𝐹
Dimensionless concentration
Dimensionless temperature
22 1 1
1 1 1 1, 12 2 ; 3.7spd y dy y y hdt dt
β β β+ + = =
22 2 2, 2; 3.7sp
dy y y hdt
β β+ = =
Shorter time constant
due to MIMO control
Process and Energy Systems Engineering
MPC Problem Formulation
32
Solution strategy
• Convert to NLP by discretizing process model (implicit Euler)
• Implemented in MATLAB with IPOPT
s.t. Process model equations
2252 2 1
1 , , 1 2 1 3 1, 4 2, , 2,1 2
1( ) ( ) ( )control c a c a a a a sp a aa a a
dy dTJ w F F w w y w y y dtdt dt
θ θβ− −
=
= − + − + − + − −
∑
1
2 11 1 1 1,2 y sp
dy y y ydt
β β+ + =
/c dc dt=
Constraint softening
Process and Energy Systems Engineering
Closed-loop implementation with MPC
33
• MPC tracks setpoint, imposes second-order input-output behavior
Cycle time ~81h
(compare with 84.45h
for SISO control)
Profit $5,786 (compare to $5,656)
Process and Energy Systems Engineering
Data-Driven Scale Bridging Models
Industrial Processes• MPC rarely used for transitions in practice
- Linear models- Vendor software difficult to modify
• High complexity: large scale, interactions, noise, unmeasured disturbances
• Analytical model and SBM may be very difficult to obtain
• Data driven modeling of closed-loop behavior
34
Process and Energy Systems Engineering
Data-Driven Scale Bridging Models
Industrial Processes• Increased complexity: large scale, interactions,
noise, unmeasured disturbances• Usable data sets are likely available from
process operation history
• Multi-product transitions resemble system identification experiments
35
Process and Energy Systems Engineering
Case Study: DR of Air Separation Unit
36
Separate components of air via cryogenic distillation: high purity (>99%) Refrigeration via thermal expansion and energy recovery Large energy consumers: 19.4 TWh in US in 2010 Store energy as liquefied molecules: potential to shift grid load
Johansson, MSc thesis, KTH/UT Austin, 2015
Process and Energy Systems Engineering
Interaction with Electric Grid
37
Optimal process operation: Overproduce, store liquid
nitrogen off-peak Reduce production and gasify
stored product at peak periods
Challenges: Scheduled production changes
occur over time frames much shorter than the longest time constant of the process
Must ensure that sequence of production rate targets is feasible (product quality and process operation constraints)
ERCOT prices, September 2013
Process and Energy Systems Engineering
Product Quality Constraints (QCs):- Product purity (99.8%)- Production flowrate (20 mol/s)
Process Constraints (PCs):- Prevent tray flooding in the
column- Liquid level in the reboiler
does not deplete- All streams in the first zone of the PHX are in the gas phase- All streams exiting the second zone of the PHX are in the liquid phase- The temperature driving force in the reboiler/condenser is above the
lower limit
Product and Process Constraints
38
Process and Energy Systems Engineering
ASU Production Scheduling
39
Static formulation
𝐉𝐉 = �𝟎𝟎
𝑻𝑻𝒑𝒑 𝒕𝒕 𝑾𝑾 𝒕𝒕 𝒅𝒅𝒕𝒕min
s.t.
𝒚𝒚𝒔𝒔𝒑𝒑 (t)
Production quality and demand constraints
Rate of change constraints
Steady-state correlation between power consumption
and production rate
Inventory model
Process and Energy Systems Engineering
Implementing the Schedule: System Dynamics
40
Production rate changes are
NOT instantaneous
Schedule computed using
STATIC formulation :
Potentially severe quality violations
Pattison, Touretzky, Johansson, Harjunkoski, Baldea, IECR, submitted
Process and Energy Systems Engineering
ASU Scheduling Under (Dynamic) Constraints
41
Full-order dynamic model (P1)
𝐉𝐉 = �𝟎𝟎
𝑻𝑻𝒑𝒑 𝒕𝒕 𝑾𝑾 𝒕𝒕 𝒅𝒅𝒕𝒕min
s.t.
𝒚𝒚𝒔𝒔𝒑𝒑 (t)
Production quality and demand constraints
Inventory constraints
Full-order process model (DAE System with
6094 eqns, 430 state variables)
Process operating constraints
Inventory model
Static formulation
𝐉𝐉 = �𝟎𝟎
𝑻𝑻𝒑𝒑 𝒕𝒕 𝑾𝑾 𝒕𝒕 𝒅𝒅𝒕𝒕min
s.t.
𝒚𝒚𝒔𝒔𝒑𝒑 (t)
Production quality and demand constraints
Rate of change constraints
Steady-state correlation between power consumption
and production rate
Inventory model
Process and Energy Systems Engineering
ASU Scheduling Under (Dynamic) Constraints
42
Full-order dynamic model (P1)
𝐉𝐉 = �𝟎𝟎
𝑻𝑻𝒑𝒑 𝒕𝒕 𝑾𝑾 𝒕𝒕 𝒅𝒅𝒕𝒕min
s.t.
𝒚𝒚𝒔𝒔𝒑𝒑 (t)
Production quality and demand constraints
Inventory constraints
Full-order process model (DAE System with
6094 eqns, 430 state variables)
Process operating constraints
Inventory model
Scheduling-oriented low-order dynamic model (P2)
𝐉𝐉 = �𝟎𝟎
𝑻𝑻𝒑𝒑 𝒕𝒕 𝑾𝑾 𝒕𝒕 𝒅𝒅𝒕𝒕min
s.t.
𝒚𝒚𝒔𝒔𝒑𝒑 (t)
Production quality and demand constraints
Inventory constraints
Low-order dynamic process model
Reduced set of process operating constraints
Inventory model
Static formulation
𝐉𝐉 = �𝟎𝟎
𝑻𝑻𝒑𝒑 𝒕𝒕 𝑾𝑾 𝒕𝒕 𝒅𝒅𝒕𝒕min
s.t.
𝒚𝒚𝒔𝒔𝒑𝒑 (t)
Production quality and demand constraints
Rate of change constraints
Steady-state correlation between power consumption
and production rate
Inventory model
Process and Energy Systems Engineering
Scheduling-Oriented Low-Order Dynamic Models
43
SBMsProduction targets (desired product quality, flow rate)
Process operating constraints
Production output (quality, quantity)
In an industrial process
Must select judiciously the variables to model
Process and Energy Systems Engineering
Proposition (Pattison et al.)
“In a complex process with multiple operating constraints related to the process performance, efficiency, and safety, the constraints relevant to the scheduling calculation […] closely approach or reach their bounds during steady state operation and/or during transitions between operating points.”
• SBM: capture response of process variables involved in this subset of constraints
Pattison, Touretzky, Johansson, Harjunkoski, Baldea, IECR, submitted
44
Process and Energy Systems Engineering
Model Identification
45
Training data: implementation of static scheduling result• Similar to historic data
collected during process operations
• Eight scheduling-relevant states (out of >400)
Identification challenges (Hammerstein-Wiener models):
• Multiple time scale response• High nonlinearity
Constraint
violations
Process and Energy Systems Engineering
Scheduling Results
46
Full-order dynamic model (P1)
𝐉𝐉 = �𝟎𝟎
𝑻𝑻𝒑𝒑 𝒕𝒕 𝑾𝑾 𝒕𝒕 𝒅𝒅𝒕𝒕min
s.t.
𝒚𝒚𝒔𝒔𝒑𝒑 (t)
Production quality and demand constraints
Inventory constraints
Full-order process model (DAE System with
6094 eqns, 430 state variables)
Process operating constraints
Inventory model
Scheduling-oriented low-order dynamic model (P2)
𝐉𝐉 = �𝟎𝟎
𝑻𝑻𝒑𝒑 𝒕𝒕 𝑾𝑾 𝒕𝒕 𝒅𝒅𝒕𝒕min
s.t.
𝒚𝒚𝒔𝒔𝒑𝒑 (t)
Production quality and demand constraints
Inventory constraints
Low-order dynamic process model:
51 differential variables
Reduced set of process operating constraints
Inventory model
Static formulation
𝐉𝐉 = �𝟎𝟎
𝑻𝑻𝒑𝒑 𝒕𝒕 𝑾𝑾 𝒕𝒕 𝒅𝒅𝒕𝒕min
s.t.
𝒚𝒚𝒔𝒔𝒑𝒑 (t)
Production quality and demand constraints
Rate of change constraints
Steady-state correlation between power consumption
and production rate
Inventory model
Process and Energy Systems Engineering
Production Target
47
• Static formulation predictably yields most aggressive schedule• Embedding dynamics has a smoothing effect
Pattison, Touretzky, Johansson, Harjunkoski, Baldea, IECR, submitted
Process and Energy Systems Engineering
Production Target
48
• Production rate scheduled to increase at off-peak timesPattison, Touretzky, Johansson, Harjunkoski, Baldea, IECR, in prep.
Process and Energy Systems Engineering
Production Rates
49
• Reduced-order model closely resembles the results derived using full-order model
Pattison, Touretzky, Johansson, Harjunkoski, Baldea, IECR, submitted
Process and Energy Systems Engineering
Inventory Levels
50
• Synchronized with energy prices (rise off-peak, deplete at peak time)
•H
oldu
p (k
mol
)
Process and Energy Systems Engineering
Product Quality (Impurity Levels)
51
• Reduced-order model closely resembles the results derived using full-order model
Pattison, Touretzky, Johansson, Harjunkoski, Baldea, IECR, submitted
Impu
rity
in N
2 st
ream
, ppm
Process and Energy Systems Engineering
Economics and Computational Statistics
52
*gPROMS ProcessBuilder 1.0, Intel Core i7 @3.40GHz, 16GB RAM, Windows 7 x64
Problem Variables Operating cost ($) CPU time (h)
Constant production rate
- 22,187 -
P1 (full-order model)
430 differential5,764 algebraic
21,520 (-3.0%) 97*
P2 (SBM) 51 differential 21,584 (-2.7%) 1.2*
• Exploiting energy price variability (vs. operating at constant production rate): significant savings
• Must account for dynamics to ensure quality and process constraints are met
• Scheduling-oriented low-order data-driven model: order-of-magnitude improvement in computation time – real time implementation possible
Process and Energy Systems Engineering
Process Constraints
53
• Condenser temperature gradient: ensure driving force for column operation
Pattison, Touretzky, Johansson, Harjunkoski, Baldea, IECR, submitted
Process and Energy Systems Engineering
Process Constraints
54
• Reboiler holdup: ensure internal refrigeration is not depleted
Pattison, Touretzky, Johansson, Harjunkoski, Baldea, IECR, submitted
=
Process and Energy Systems Engineering
Conclusions and Perspective
• Integrated scheduling and control- Required when frequency of scheduling decisions
overlaps with dynamic modes of the plant- Scale-bridging model: Low-order schedule-relevant
model of closed-loop dynamics- Closed-loop implementation: stability, robustness- Computational efficiency, scalability: SBM size
unlikely to increase significantly for large plants, real-time calculations
• Smarter operations- Chemical and petrochemical processes- Electric grid- Other players (e.g., buildings)
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Process and Energy Systems Engineering
Quo Vadis, Integrated Scheduling and Control?
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• Feedback: moving horizon implementation- Define rescheduling triggers (cf. Touretzky et al.,
AIChE Annual Meeting, AIChE J., in prep). - Define state observation/estimation strategy, “integral
action”- Extension to batch processes
• Applications: - Interaction of industrial energy users with the grid:
optimal plan operation from the user perspective != optimal operation from the grid perspective
- Cooperative approaches
Process and Energy Systems Engineering
Selected Publications
57
• M. Baldea, J. Du, J. Park, I. Harjunkoski, Integrated Production Scheduling and Model Predictive Control of Continuous Processes, AIChE J., 61(12), 4179–4190, 2015 http://dx.doi.org/10.1002/aic.14951
• J. Du, J. Park, I. Harjunkoski, M. Baldea, A Time Scale Bridging Approach for Integrating Production Scheduling and Process Control, Comput. Chem. Eng., 79, 59-69, 2015 http://dx.doi.org/10.1016/j.compchemeng.2015.04.026
• M. Baldea, I. Harjunkoski, Integrated Production Scheduling and Process Control: A Systematic Review, Comput. Chem. Eng., 71, 377-390, 2014, http://dx.doi.org/10.1016/j.compchemeng.2014.09.002
• C.R. Touretzky, M. Baldea, A Hierarchical Scheduling and Control Strategy for Thermal Energy Storage Systems, Energy and Buildings, 110, 94-107, 2015 http://dx.doi.org/10.1016/j.enbuild.2015.09.049
• R.C. Pattison+, C.R. Touretzky+, T. Johansson, M. Baldea, I. Harjunkoski, Optimal Process Operations in Fast-Changing Energy Markets: Framework for Scheduling with Low-Order Dynamic Models and an Air Separation Application, Ind. Eng. Chem. Res., submitted
•
Process and Energy Systems Engineering 58
Acknowledgements
• Dr. Juan Du, Cara R. Touretzky, Richard C. Pattison, Ted Johansson, Jungup Park
• Drs. Iiro Harjunkoski, Alf Isaksson, Michael Lundh and Per-Erik Modén
• ABB Corporate Research, NSF CAREER Award 1454433, NSF CBET-1512379, DOE DE-EE0005763, NSF I/UCRC IIP-1134849, Moncrief Grand Challenges Award, EPA STAR Fellowship (CRT), Engineering Doctoral Fellowship (RCP), KTH support (TJ)