Optimal Design of Smart Grid T u n in g V a lu e s 1...

Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering

Illinois Institute of TechnologyIllinois Institute of Technology

Optimal Design of Smart Grid Optimal Design of Smart Grid

Coordinated SystemsCoordinated Systems

Donald J. Chmielewski

Department of Chemical and Biological Engineering Illinois Institute of Technology

Minimally

Baked-off

Operating

Point

Different Controller

Tuning Values

Expected

Dynamic

Operating

Regions

Steady-State

Operating

Line

Optimal Steady-State

Operating Point

Es

min (kW

T hr)

Pcm

ax (

kW

e)

0 -500 -1000 -15000

25

50

1

435 2

383 383.5 384 384.5 385 385.5387.5

388

388.5

389

389.5

390

390.5

391

391.5

T(K

)

T0(K)



ChicagoChicago

2



IIT and ChicagoIIT and Chicago

3



Presentation OutlinePresentation Outline

Review of Economic Model Predictive

Control (EMPC)

Challenges Associated with the Design of

Smart Grid Systems

ELOC and Constrained ELOC

Computationally Efficient Design of Smart

Grid Systems

4



5

AcknowledgementsAcknowledgements

Former Students:

Benjamin Omell (PhD, 2013)

David Mendoza-Serrano (PhD, 2013)

Ming-Wei Yang (PhD, 2010)

Jui-Kun Peng (PhD, 2004)

Amit Manthanwar (MS, 2003)

Current Students:

Oluwasanmi Adeodu

Jin Zhang

Funding:

National Science Foundation (CBET – 0967906)

Wanger Institute for Sustainable Engineering Research (IIT)



Review of MPCReview of MPC

iii

ik

ikikikik

ikikikik

iNif

Ni

ik

ikikikms

ss

Niikqqq

pmshq

pmsfs

tsslpmslikik

|

max

|

min

||||

||||1

|

1

|||,

1

),,(

),,(

..)(),,(min||

At time the current time, i, solve:

Then, the manipulated variable is set as: *

|iii mm

6



1

|||

)(

,),,(max

||

Ni

ik

ikikik

IP

mspmsg

ikik

Traditional vs. Economic Traditional vs. Economic MPCMPC

7

In traditional MPC the objective is regulation:

iNi

T

iNi

Ni

ik

ik

T

ikik

T

ikux

PxxRuuQxxikik

||

1

||||,

)(min||

In EMPC the objective is maximize average profit

(integral of instantaneous profit):



EconomicEconomic MPC LiteratureMPC Literature

8

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)

Building 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)

Power Scheduling: Zavala et al. (2009); Xie and Ilić (2009), Hovgaard, et al. (2011), Omell and Chmielewski (2013)



Economic Economic MPC ExampleMPC Example

A non-isothermal CSTR:

n

CA, CB, T

CA0, T0, n

KT

CekC

HTT

Vdt

dT

CekCVdt

dC

CekCCVdt

dC

A

RTE

p

r

A

RTE

BB

A

RTE

AAA

390

)(

)(

00

0

00

n

n

n

Disturbance:

Manipulation:

ss

A

ss

AA CCC 000 15.0

KT 3850

Instantaneous Profit:

BB

IP CCg n10)()(

9



EconomicEconomic MPC ExampleMPC Example

8

1385

390

),,(

..10max

|

|,0

|

||,|,||,|,0||1

1

|,, |,0|

N

ss

NiikKT

KT

TCCsCTsfs

tsC

iii

ik

ik

T

ikikBikAikikAoikikik

Ni

ik

ikBTs ikik

n

*Model converted to discrete-time using Euler’s explicit method.

10



EconomicEconomic MPC SimulationMPC Simulation

11

383.5 384 384.5 385388

388.5

389

389.5

390

T0 (K)

T (

K)

0 5 10 15

0.8

1

1.2

1.4

time (minutes)

CA

0 (

km

ole

/m3)

0 5 10 15388

388.5

389

389.5

390

390.5

time (minutes)

T (

K)

0 5 10 15383

383.5

384

384.5

385

385.5

time (minutes)

T0 (

K)




A non-isothermal CSTR:

12

n

CA, CB, T

CA0, T0, n




A non-isothermal CSTR with preheater:

Instantaneous Profit:

4.05)303(005.010 0 nn TCB

13

n

CA, CB, T

CA0, T0, n

Tf = 303K

Q

Manipulation: KTK 385303 0

)303(005.010),( 00

)( TCTCg BB

IP n




14

0 5 10 15

0.8

1

1.2

1.4

time (minutes)

CA

0 (

km

ole

/m3)

0 5 10 15

386

388

390

time (minutes)

T (

K)

0 5 10 15383

383.5

384

384.5

385

385.5

time (minutes)

T0 (

K)

0 5 10 15300

320

340

360

380

time (minutes)

T (

K)

0 5 10 15300

320

340

360

380

time (minutes)

T0 (

K)




15

0 5 10 15

0.8

1

1.2

1.4

time (minutes)

CA

0 (

km

ole

/m3)

0 5 10 150.4

0.6

0.8

1

time (minutes)

CA

(k

mo

le/m

3)

0 5 10 150

0.2

0.4

0.6

0.8

time (minutes)

CB

(k

mole

/m3)

0 0.5 10

0.5

1

CB

(kmole/m3)

CA

(k

mole

/m3)

)303(005.010

),(

0

0

)(

TC

TCg

B

B

IP

n




16

0 5 10 15

0.8

1

1.2

1.4

time (minutes)

CA

0 (

km

ole

/m3)

0 5 10 15388

388.5

389

389.5

390

390.5

time (minutes)

T (

K)

0 5 10 15383

383.5

384

384.5

385

385.5

time (minutes)

T0 (

K)

0 5 10 150.4

0.5

0.6

0.7

0.8

time (minutes)

CA

(k

mo

le/m

3)

0 5 10 15

0.4

0.5

0.6

0.7

time (minutes)

CB

(k

mole

/m3)

Change horizon

from N = 8 to N = 10



4) If N=10 and objective ,


then UNSTABLESTABLE

Stability of EStability of EMPCMPC


then STABLESTABLE

17

)303(005.010 0 TCBn

BC10n


then UNSTABLEUNSTABLE

)303(005.010 0 TCBn3) If N=10 and objective ,

then STABLESTABLE

)303(025.010 0 TCBn

)303(025.010 0 TCBn5) If N=25 and objective ,

then STABLESTABLE



Why the Instability?Why the Instability?

18

n

CA, CB, T

CA0, T0, n

Tf = 303K

Q

Answer: Myopic Behavior

• EMPC tries to lower costs by lowering To

• In the short run T, CB and Profit will remain high

• In the long run T, CB and Profit will drop-off

• If N is small, then EMPC will not know about the drop-off

• Short term gains lead to long term losses

)303(025.010 0 TCBn




Review of EMPC

Challenges Associated with the Design

of Smart Grid Systems



Grid Systems

19



Generators with Dispatch Consumer Demand Transmission

Renewable Sources

Energy Storage

Smart Homes

Commercial Buildings

Smart Manufacturing

Smart Grid OpportunitiesSmart Grid Opportunities



Motivation for Smart Grid CoordinationMotivation for Smart Grid Coordination

21

Design systems to exploit these time-varying electricity prices.

Applications range from: Building HVAC, Electric Vehicle Charging, Distributed Generation and Storage, Industrial Demand Response

170 171 172 173 174 175 176 177 178 179 180

0

50

100

150

Day of the Year

Ele

ctr

icit

y P

ric

e

($/M

Wh

r)

Historic electricity prices (Chicago, 2008), [PJM, 2013]



Building HVAC ExampleBuilding HVAC Example

22

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Houston, TX (July, 2012)

Solid – Outside Temperature Dotted – Electricity Price



Building HVAC ExampleBuilding HVAC Example

23

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

TES

Thermal

Energy Storage

Heat to

Chiller

23 24 25 26

200

300

400

500

600

Chiller Cooling Load (Qc)

Time (days)

Hea

t F

low

(K

We)

Qc

Qr

23 24 25 26

2000

4000

6000

Time (days)

Hea

t F

low

(K

We)

Heat to Chiller Heat from Room

Thermal Energy Storage



HVAC Equipment Sizing Problem HVAC Equipment Sizing Problem

24

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

TES

Thermal

Energy Storage

Heat to

Chiller

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

TES

Thermal Energy Storage

Heat to

Chiller

23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr

23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr

23 24 25 26

2000

4000

6000

Time (days)

Hea

t F

low

(K

We)


23 24 25 26

2000

4000

6000

Time (days)

Hea

t F

low

(K

We)




Outside

Environment

(T3)

...

Windows

...

Walls

To T3T21T12T11T11To To

...

Outside

Environment

(T3)

Room

Room

Room

Room

Room

Room

5 State Building Example 5 State Building Example

25

1

|,|,|,

minNi

ik

ikcikeP

PCikc

opo

scooo

VC

QQTTAKTTAKT

0

2122111111 )()(

111

121112111111

)()(

xC

TTKTTKT

p

o

111

12111212

)(2

xC

TTKT

p

222

21212132221

)()(

xC

TTKTTKT

p

o

ss QE



EMPC Simulation EMPC Simulation

26

Solid – EMPC with TES

Dotted – EMPC without TES



EMPC Simulation with Smaller Storage EMPC Simulation with Smaller Storage

27

Solid – EMPC with TES

Dotted – EMPC without TES



Smart Grid Equipment Design ProblemSmart Grid Equipment Design Problem

28

Design problem is a Stochastic Program

CapCostOpCostPV fSizeEquip

min

N

k

kEqipSizeOpVar

OpVarInstOpCostN

OpCostk 1

0)(

1min

If no energy storage, then two-stage problem

If energy storage is allow, then a multistage problem



Simulation Period: 28 days Operating Cost (no TES): $759 Operating Cost Reduction with 1.5MWhr: 31.4% Simulation Time: 1.4 hrs EMPC Horizon Size: 24 hrs Operating Cost Reduction with 1.5MWhr: 13.8% Simulation Time: 6.7 sec EMPC Horizon Size: 3 hr

Possible Solution MethodPossible Solution Method

29



Inventory CreepInventory Creep

30

Simulation Period: 28 days Operating Cost (no TES): $759 Operating Cost Reduction with 1.5MWhr: 31.4% Simulation Time: 1.4 hrs EMPC Horizon Size: 24 hrs Operating Cost Reduction with 1.5MWhr: 13.8% Simulation Time: 6.7 sec EMPC Horizon Size: 3 hr

Solid – EMPC with 24hr horizon

Dotted – EMPC with 3hr horizon



Use of Surrogate Controllers Use of Surrogate Controllers

31

ELOC Constrained ELOC




Review of EMPC


Smart Grid Systems



Grid Systems

32



Economic Linear Optimal Control (ELOC)Economic Linear Optimal Control (ELOC)

Steady-State

Operating

Line

Steady-State

Operating

Line


Operating Point

Expected

Dynamic

Operating

Region

Steady-State

Operating

Line


Operating Point

Minimally

Baked-off

Operating

Point

Expected

Dynamic

Operating

Regions

Steady-State

Operating

Line


Operating Point

33


Tuning Values

Expected

Dynamic

Operating

Regions

Steady-State

Operating

Line


Operating Point

Minimally

Baked-off

Operating

Point


Tuning Values

Expected

Dynamic

Operating

Regions

Steady-State

Operating

Line


Operating Point

iELOCi xLu



Economic Linear Optimal Control Economic Linear Optimal Control

34

min

,

max

,

cos.

,,,,,

)()(

)()(

),,(),,,(..

),(min

jjjzjjjz

T

uxxuxz

T

w

T

xx

zz

ztop

Lqms

qqqq

LDDLDD

GGBLABLA

mshqpmsfsts

qg

zx

Global Solutions can be efficiently determined using GBD



35

383 383.5 384 384.5 385 385.5387.5

388

388.5

389

389.5

390

390.5

391

391.5

T(K

)

T0(K)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

CB

(km

ol/

m3)

CA

(kmol/m3)

CSTR CSTR ExampleExample

383 383.5 384 384.5 385 385.5387.5

388

388.5

389

389.5

390

390.5

391

391.5

T(K

)

T0(K)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

CB

(km

ol/

m3)

CA

(kmol/m3)

383 383.5 384 384.5 385 385.5387.5

388

388.5

389

389.5

390

390.5

391

391.5

T(K

)

T0(K)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

CB

(km

ol/

m3)

CA

(kmol/m3)

Statistical constraints are clearly enforced.

What about point-wise-in-time constraints?

Constrained ELOC



iii

ikikik

iNi

T

iNi

Ni

ik

ik

T

ikik

T

ikux

xx

BuAxx

tsPxxRuuQxxikik

|

|||1

||

1

||||,

..)(min||

36

iLQRi xLu

Predictive Form of ELOC Predictive Form of ELOC

iii

ikikik

iNiELOC

T

iNi

Ni

ik

ikELOC

T

ikikELOC

T

ikux

xx

BuAxx

tsxPxuRuxQxikik

|

|||1

||

1

||||,

..)(min||

iELOCi xLu

* see Chmielewski & Manthanwar (2004) for details

Linear Quadratic RegulatorLinear Quadratic Regulator



Predictive Form of ELOC Predictive Form of ELOC ConstrainedConstrained ELOCELOC

37

max

|

min

|||

zzz

uDxDz

ik

ikuikxik

383 383.5 384 384.5 385 385.5387.5

388

388.5

389

389.5

390

390.5

391

391.5

T(K

)

T0(K)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

CB

(km

ol/

m3)

CA

(kmol/m3)

iii

ikikik

iNiELOC

T

iNi

Ni

ik

ikELOC

T

ikikELOC

T

ikux

xx

BuAxx

tsxPxuRuxQxikik

|

|||1

||

1

||||,

..)(min||



Constrained ELOCConstrained ELOC

38

383 383.5 384 384.5 385 385.5387.5

388

388.5

389

389.5

390

390.5

391

391.5

T(K

)

T0(K)

383 383.5 384 384.5 385 385.5387.5

388

388.5

389

389.5

390

390.5

391

391.5

T(K

)

T0(K)

383 384 385 385.5387.5

388.5

389.5

390.5

391.5

Rea

cto

r T

em

pera

ture T

(K

)

Manipulated Variable Tin

(K)



Constrained ELOCConstrained ELOC

39

0 5 10 15

384

384.5

385

T0(K

)

EMPC

Constrained ELOC

0 5 10 15388.5

389

389.5

390

390.5

T(K

)



Constrained ELOC and Horizon SizeConstrained ELOC and Horizon Size

40

0 2 4 6 8 10 12 14

384

384.5

385

T0(K

)

EMPC

Constrained ELOC N=1

Constrained ELOC N=10



Constrained ELOCConstrained ELOC and Nonlinear Plantsand Nonlinear Plants

iiiikikik

iNiELOC

T

iNi

Ni

ik

ikELOC

T

ikikELOC

T

ikux

xxBuAxx

tsxPxuRuxQxikik

||||1

||

1

||||,

..)(min||

41

max

|

min

|||

zzz

uDxDz

ik

ikuikxik

max

|

min

|||

||||1

),(

),(

zzz

uxhz

xxuxfx

ik

ikikik

iiiikikik



ELOC in Building HVACELOC in Building HVAC

42



Constrained ELOC in Building HVACConstrained ELOC in Building HVAC

43



Horizon Size Insensitivity Horizon Size Insensitivity

44



Computational EfficiencyComputational Efficiency

45




Review of EMPC


Smart Grid Systems


Computationally Efficient Design of

Smart Grid Systems

46



Where Are We?Where Are We?

47

EMPC

Provides economically optimized performance

Need for large horizons makes it slow


Both are good surrogates for EMPC

Both are computationally fast

Objective: Use ELOC to enable computational tractability of Equipment Design problem



Use of Surrogate Controllers Use of Surrogate Controllers

48

ELOC Constrained ELOC



Possible Search SchemePossible Search Scheme

49

Global Search with ELOC

minimize NPV

over here-and-now variables and ELOC parameters

Statistical Constraint Enforcement

Constrained ELOC

Simulations

Point-wise-in-time

Constraint Enforcement

Gradient Search

minimize NPV

over here-and-now variables

Gradient Search with Constrained ELOCProvide:

here-and-now values

Return: minimum

average operating costs



Economic Linear Optimal Control Economic Linear Optimal Control ELOC Based DesignELOC Based Design

50

min

,

max

,

cos.

,,,,,

)()(

)()(

),,(),,,(..

),(min

jjjzjjjz

T

uxxuxz

T

w

T

xx

zz

ztop

Lqms

qqqq

LDDLDD

GGBLABLA

mshqpmsfsts

qg

zx

),(),(min minmax

cos.cos.

,

,,,,,,

minmax

jjtcapztop

qq

Lqms

qqgqg

jj

zx

Global Solutions can be determined efficiently using GBD



HVAC Equipment Sizing Problem HVAC Equipment Sizing Problem

51

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

TES

Thermal

Energy Storage

Heat to

Chiller



ELOC Based DesignELOC Based Design

52



Proposed Search SchemeProposed Search Scheme

53

Global Search with ELOC

minimize NPV

over here-and-now variables and ELOC parameters

Statistical Constraint Enforcement

Constrained ELOC

Simulations

Point-wise-in-time

Constraint Enforcement

Gradient Search

minimize NPV

over here-and-now variables

Gradient Search with Constrained ELOCProvide:

here-and-now values

Return: minimum

average operating costs



Es

min (kW

T hr)

Pcm

ax (

kW

e)

0 -500 -1000 -15000

25

50

Es

min (kW

T hr)

Pcm

ax (

kW

e)

0 -500 -1000 -15000

25

50

1

435

2

Gradient Search with Constrained ELOCGradient Search with Constrained ELOC

54



ConstrainedConstrained ELOCELOC

55

max

|

min

|||

zzz

uDxDz

ik

ikuikxik

iii

ikikik

iNiELOC

T

iNi

Ni

ik

ikELOC

T

ikikELOC

T

ikux

xx

BuAxx

ts

xPxuRuxQxikik

|

|||1

||

1

||||,

..

)(min||

szzsz ik max

|

min

scxPxuRuxQx siNiELOC

T

iNi

Ni

ik

ikELOC

T

ikikELOC

T

ikux ikik

||

1

||||,

)(min||

ConstrainedConstrained ELOC with Soft ConstraintsELOC with Soft Constraints



Penalty for Infeasible OperationPenalty for Infeasible Operation

56



Conclusions Conclusions

57

EMPC

Provides economically optimized performance

Need for large horizons makes it slow


Both are good surrogates for EMPC

Both are computationally fast

Equipment Design for Smart Grid Systems

ELOC enables computational tractability

Penalty method developed to address infeasibilities



58

Design of Design of DispatchableDispatchable Energy StorageEnergy Storage

max

110 SS EE

max

220 SS EE

max*000,100$ Sjj ECapCost

ELOC Solution:

MWhrEE SS 239max

2

max

1



59

ELOC Operating RegionELOC Operating Region with ELOC Optimal Storage Sizing with ELOC Optimal Storage Sizing

0 50 100 150 200 250 300 350200

300

400

500

600

Gas Turbine PG1

(MW)

Co

al

Pla

nt

PG

6(M

W)

0 50 100 150 2000

20

40

60

80

100

Power Flow P23

(MW)

Pow

er F

low

P2

1(M

W)

250 300 350 400 450 500 550 600

-100

-80

-60

-40

-20

0

Power Flow P62

(MW)

Pow

er F

low

P4

2(M

W)

-300 -250 -200 -150-50

0

50

100

Power Flow P46

(MW)

Po

wer F

low

P4

1(M

W)

Optimal Design of Smart Grid T u n in g V a lu e s 1...

Documents

Transcript of Optimal Design of Smart Grid T u n in g V a lu e s 1...