1

OPTIMIZING ADVANCED POWER SYSTEM DESIGNS UNDER

UNCERTAINTY

E.S. Rubin and U.M. DiwekarCarnegie Mellon University

Pittsburgh, PA 15213

H.C. FreyNorth Carolina State University

Raleigh, NC 27695

METC COR: Kevin Williams

• Seek process designs that minimize the likelihood of:

– Performance shortfalls

– High emissions

– High cost

• Pursue R&D that offers the greatest payoff (efficiency, emissions and cost)

MINIMIZING TECHNOLOGICAL RISK

2

• Increasing complexity of advanced processes

• Multiple options for component design & selection

• Strong interactions among system components

• Significant performance and cost uncertainties

ADVANCED DESIGN AND ANALYSIS METHODS ARE NEEDED

• Process Technology Models

• Engineering Economic Models

• Advanced Software Capabilities

• Systems Analysis Framework

APPROACH

3

TECHNOLOGIES MODELED AND EVALUATED

• Integrated Gasification Combined Cycles (IGCC)

– Air and oxygen blown gasifiers

– Fixed bed and fluidized bed gasifiers

– Hot gas and cold gas cleanup systems

– Byproduct recovery options (e.g., sulfuric acid, Claus plant, direct sulfur reduction process)

– Other environmental controls (e.g., SCR)

• Pressurized Fluidized Bed Combustion (PFBC)

• Externally-Fired Combined Cycle (EFCC)

PERFORMANCE MODEL OF AGAS TURBINE PROCESS AREA

GT-SPLT1

GT-SPLT-3

AIRLEAKH

GT-TMIX1

GT-TMIX2

GT-TMIX3

GT-TMIX4

FILTERAIR

CLEANAIR

GT-EVAP

GTCOOL3

GTCOOL2

GTCOOL1

GT-SPLT2

CERHXHL QCERHX

EXH-AIRGTCOOL4

HPAIR

SATAHXIAIRLEAKC

HXALKC

SATAHXO

SATAIRH

WGT-C1 WGT-C2 WGT-C3 WGT-T1 WGT-T2 WGT-T3

SATAIRCCERHXC

QCERHXA

HXALKH

(To ModifiedCombustorFlowsheet,Figure 3.1)

(To ModifiedCombustorFlowsheet,Figure 3.1)

(To Work Calculation Flowsheet, Figure A.7)

(To Modified CombustorFlowsheet, Figure 3.1)

(1)

(3)

(5)

(7)

(12) (13) (14)

(16)

(17)

(19)

(21)

(23)

(15)

(To Modified CombustorFlowsheet, Figure 3.1)

(To Work Calculation Flowsheet, Figure A.7)

IPSTM2

SATLIQQWATINJ

Note: Boxes outlined in bold indicate newly added unit operation blocks.

WATINJI

GT-COMP3

GT-COMP1

GT-COMP2 GT-

TURB1GT-TURB2

GT-TURB3(2) (4) (6)

(18) (20) (22)

HTA

R30

HTA

R31

HTA

R20

HTA

R21

HTA

R10

HTA

R11

HPA

R30

HPA

R31

HPA

R20

HPA

R21

HPA

R10

4

NEW MODELING CAPABILITIES

Process or System

Simulation

Optimization

Synthesis

Deterministic

¦

¦

¦

Stochastic

¦

¦

¦

SIMULATION

5

CONVENTIONAL PROCESS MODELING(Deterministic Simulation)

ProcessModel

ParameterValues

ResultsResults

PARAMETER UNCERTAINTYDISTRIBUTIONS

NORMAL UNIFORM LOGNORMAL

FRACTILETRIANGULAR BETA

6

STOCHASTIC SIMULATION

StochasticModeler

SAMPLINGLOOP

ProcessModel

ParameterUncertainty

DistributionsResultsResults

SorbentSulfur

Loading

GasifierFines

Carryover

CarbonRetention inBottom Ash

EXPERT JUDGMENTS ON KEY MODEL PARAMETERS

353025201510500.0

0.1

0.2

0.3

Sorbent Sulfur Loading, wt-%20151050

0.0

0.1

0.2

0.3

Carbon Retention in Bottom Ash% of coal feed carbon

3025201510500.00

0.05

0.10

0.15

0.20

Fines Carryover, % of coal feed

7

EFCC PLANT EFFICIENCY

444342414039380.0

0.2

0.4

0.6

0.8

1.0

ProbabilisticDeterministic

Net Plant Efficiency (%, HHV basis)

Cum

ulat

ive

Prob

abili

ty

UNCERTAINTY IN TOTAL COSTOF LURGI-BASED IGCC PLANT

Cum

ulat

ive

Prob

abili

ty

1201008060400.0

0.2

0.4

0.6

0.8

1.0

DeterministicProbabilistic

Levelized Cost of Electricity, Constant 1989 Mills/kWh

Based on Experts LG-1 and ZF-1

8

VALUE OF ADDITIONAL RESEARCH

1201101009080706050400.0

0.2

0.4

0.6

0.8

1.0

Base Case UncertaintiesReduced Uncertainties inSelected Performanceand Cost Parameters

Levelized Cost of Electricity, Constant 1989 Mills/kWh

Input Uncertainty Assumptions

Cum

ulat

ive

Prob

abili

ty

EXTERNALLY-FIRED COMBINED CYCLE

Electricity

Coal

Slag

Air

SteamTurbine

Gas Turbine

Slag Screen

Compressor

Gas TurbineExhaust

CombustorFlue Gas

Steam

CombustorCombustor

CerHxCerHx

HRSGHRSG

FilterFilter

CondenserCondenserAsh

ExhaustGas

Shaft

Generator

ID FanStabilizedSludge

LimestoneMakeup Water

FabricFilter

FabricFilter FGDFGD

Generator

9

UNCERTAINTY IN PLANT EFFICIENCYFOR LURGI-BASED IGCC SYSTEM

Cum

ulat

ive

Prob

abili

ty

4038363432300.0

0.2

0.4

0.6

0.8

1.0

DeterministicProbabilistic

Net Plant Thermal Efficiency, percent (HHV basis)

Based on Experts LG-1 and ZF-1

SIMPLIFIED SCHEMATIC OF ASECOND GENERATION PFBC PLANT

Air fromGas

Turbine

Condenser

Water to PFBC &Heat Exchanger

SteamTurbine

Steam

Steam

Ash

ToppingCombustor

Clean HotCoal Gas

Hot GasCleanup

Hot GasCleanup

HotFlueGas

Char

Char

HotCoalGasGasifier/

Carbonizer

Limestoneor Dolomite

Coal

Ash

HotFlueGas

Air

GasTurbine

HeatExchanger

PFBCPressurizedFluidized-

BedCombustor

10

SECOND GENERATION PFBC SYSTEMTOTAL CAPITAL COST

Cum

ulat

ive

Prob

abili

ty

Total Capital Requirement ($1994/kW)1000 1100 1200 1300 1400 1500

0.0

0.2

0.4

0.6

0.8

1.0

524 MW net

DeterministicProbabilistic

SECOND GENERATION PFBC SYSTEMTOTAL CAPITAL COST

Cum

ulat

ive

Prob

abili

ty

Total Capital Requirement ($1994/kW)1000 1100 1200 1300 1400 1500

DOE (1989)Probabilistic

0.0

0.2

0.4

0.6

0.8

1.0

524 MW net

11

OPTIMIZATION

• Is there a better choice of parameter values for this process to improve its performance? To lower its cost?

• What levels of performance and cost can we expect from an optimized design?

• How do uncertainties in process performance and cost variables affect the optimal design?

• What design choices will minimize the risk of a performance shortfall? Or the risk of a cost overrun?

SOME QUESTIONS ADDRESSED BYOPTIMIZATION CAPABILITIES

12

DETERMINISTIC OPTIMIZATION

Optimizer

OPTIMIZATIONLOOP

ProcessModel

Objective Function,Constraints, and

Initial ValuesResultsResults

STOCHASTIC OPTIMIZATION

StochasticModeler

OPTIMIZATIONLOOP

Optimizer

SAMPLINGLOOP

ProcessModel

ParameterUncertainty

Distributions

ProbabilisticObjective Function

and ConstraintsResultsResults

13

STOCHASTIC PROGRAMMING

StochasticModeler

SAMPLINGLOOP

Optimizer

OPTIMIZATIONLOOPProcessModel

Objective Function,Constraints, and

Initial Values

ParameterUncertainty

DistributionsResultsResults

• Hot gas cleanup systems for sulfur and particles

– Zinc ferrite/titanate sorbents

– Ceramic filters & cyclones

• NOx controls still under development

– Advanced staged combustion

– Selective catalytic reduction

ENVIRONMENTAL CONTROL OFADVANCED IGCC SYSTEMS

14

• 650 MW IGCC system

• Air-blown moving bed gasifier

• Illinois No. 6 coal

• 80% capacity factor

• Zinc ferrite and SCR units

ILLUSTRATIVE CASE STUDY

IGCC SYSTEM WITH HOT GAS CLEANUP

CoalHandling

Gasification,Particulate &Ash Removal,Fines Recycle

GasTurbines

BoilerFeedwaterTreatment

SteamTurbine

SteamCycle

& SCR

SteamCycle

& SCR

ZincFerriteProcess

ZincFerriteProcess

SulfuricAcid PlantSulfuric

Acid Plant

SulfuricAcid

Rawwater

Coal Coal

CleanSyngas

Exhaust Gas

Gasifier Steam

Boiler Feedwater

Exhaust Gas

Shift & Regen.Steam

Cyclone

RawSyngas

Cyclone

Blowdown

Return Water

CoolingWater

Makeup

CoolingWaterBlowdown

Air

NetElectricityOutput

InternalElectricLoads

Ash Gasifier Air

AirTailgas

Off-GasCaptured Fines

15

• Zinc Ferrite Desulfurization System

– Absorption cycle time

– Vessel length-to-diameter ratio

• Selective Catalytic Reduction System

– Required NOx removal efficiency

– Catalyst replacement interval

KEY PROCESS DESIGN PARAMETERS

UNCERTAINTIES MODELED

• Performance parameters:

– Gasification area

– Zinc ferrite system

– Gas turbine area

– SCR unit

• Cost parameters:

– Direct capital costs

– Indirect capital costs

– Fixed O&M costs

– Variable O&M costs

– Financial factors

• Screening studies to identify 20 key parameters

16

MINIMIZE TOTAL COST SUBJECT TONOx EMISSION CONSTRAINT

(mill

s/kW

h)M

inim

um E

xpec

ted

Cos

t

0.2 0.3 0.4 0.5 0.6

Expected NOx Emissions (lbs/106 Btu)

58.058.258.458.6

58.859.059.259.4

BaselineDesign

MINIMIZE TOTAL COST SUBJECT TONOx EMISSION CONSTRAINT

(mill

s/kW

h)M

inim

um E

xpec

ted

Cos

t

0.2 0.3 0.4 0.5 0.6

Expected NOx Emissions (lbs/106 Btu)

BaselineDesign

51.451.5

51.651.751.851.9

52.052.152.2

17

EFFECT OF UNCERTAINTIESON OPTIMAL DESIGN COST

Cum

ulat

ive

Prob

abili

ty

Optimum Cost of Electricity (mills/kWh)40 60 80 100 120 140 160 180

Objective Function :Minimize Cost of Electricity

Constraints :NOx ≤ 0.6 lbs/106 BtuSOx ≤ 0.06 lbs/106 Btu

0.0

0.2

0.4

0.6

0.8

1.0

EFFECT OF UNCERTAINTIESON OPTIMAL DESIGN COST

Cum

ulat

ive

Prob

abili

ty

Optimum Cost of Electricity (mills/kWh)40 60 80 100 120 140 160 180

Objective Function :Minimize Cost of Electricity

Constraints :NOx ≤ 0.6 lbs/106 BtuSOx ≤ 0.06 lbs/106 Btu

0.0

0.2

0.4

0.6

0.8

1.0

18

MINIMIZE NOx SUBJECTTO A COST CONSTRAINT

Cum

ulat

ive

Prob

abili

ty

NOx Emissions for Optimal Design (lbs/106 Btu)

0 0.2 0.4 0.6 0.8

Objective Function :Minimize NOx Emissions

Constraints :COE ≤ 60 mills/kWhSOx ≤ 0.06 lbs/106 Btu

0.0

0.2

0.4

0.6

0.8

1.0

MINIMIZE NOx SUBJECTTO A COST CONSTRAINT

Cum

ulat

ive

Prob

abili

ty

NOx Emissions for Optimal Design (lbs/106 Btu)

0 0.2 0.4 0.6 0.8

Objective Function :Minimize NOx Emissions

Constraints :COE ≤ 60 mills/kWhSOx ≤ 0.06 lbs/106 Btu

0.0

0.2

0.4

0.6

0.8

1.0

19

SYNTHESIS

• How should the flowsheet be configured to achieve performance goals at lowest cost?

• What are the feasible flowsheet options to meet specified goals and constraints? Which options are not feasible?

• What are the cost savings (or performance gains) from moving to a more optimal design?

SOME QUESTIONS ADDRESSED BY PROCESS SYNTHESIS CAPABILITIES

20

PROCESS SYNTHESIS

MILPMaster

Optimizer

Process Model

SYNTHESISLOOP

OPTIMIZATIONLOOP

SelectedFlowsheetTopology

SuperstructureAlternatives

Start

ResultsResults

PROCESS SYNTHESIS CASE STUDY

Objective: Choose desulfurization system that minimizestotal cost of air-blown KRW with HGCU

Constraint: SO2 emissions < 0.015 lb/million Btu(Illinois No. 6 coal)

Options: – In-bed sulfur removal only ? (sulfation ash waste)

– Zinc ferrite removal only ?(sulfuric acid byproduct)

– Combined in-bed + zinc ferrite ?(recycle + sulfation ash waste)

21

OPTIMAL CONFIGURATION

CalciumSorbent

Sorbent

GasifierAir

Ash and SpentLimestone

SulfationAsh

Coal

Cyclone

Regenerator OffGas w/SO2

RegeneratorAir

Diluent andRegeneration Steam

QuenchWater

GasifierSteam

SyngasLimestone

or DolomiteHandling

Limestoneor Dolomite

Handling

SulfationSulfation

In-beddesulfur-

ization

In-beddesulfur-

ization

Fixed-bedZinc Ferrite

Process

Fixed-bedZinc Ferrite

Process

GasificationGasification

OPTIMIZATION RESULTS FOR THESULFUR REMOVAL ALTERNATIVES

TechnologicalAlternatives

Modeled

Modelfor Ca/S

Ratio

DesulfurizationEfficiency

(fraction in bed)

AbsorptionCycle Time

(hours)

MaximumLength/Dia.

(ratio)

Levelized Costof Electricity(mills/kWh)

In-bed plusGas StreamDesulfurization

Linear 0.89 150.5 2.29 53.8Nonlinear 0.81 84.5 4.00 52.1

Gas StreamDesulfurizationOnly

Linear 0.15 30 2.00 62.3Nonlinear 0.15 30 2.00 62.3

In-bedDesulfurizationOnly

Linear InfeasibleNonlinear Infeasible

22

SYNTHESIS OF IGCC SYSTEMQuench

WaterIllinois No. 5Illinois No. 6W. Ky. No. 9

E. Ky. ElkhornPittsburgh No. 8Utah Blind Can.

GasifierGasifier

Steam

CalciumSorbent

Air

Oxygen

In-BedDesulfurization

In-BedDesulfurization

CycloneCycloneFixed-Bed

Zinc FerriteProcess

Fixed-BedZinc Ferrite

Process

Reg. AirSteam

SulfationSulfation Sulfation Ash

Syngas(to Turbines)Ash and Spent

Limestone

?

?

?

?

• Large number of configurations: 10.2 million

• 99% of the configurations are infeasible

• Large functional discontinuities(not amenable to MINLP synthesis)

• Only 0.02% of feasible solutions are optimal

• Annealing technique takes 1/1000 of the time required for exhaustive search

SIMULATED ANNEALING APPLIED TOA BRAYTON CYCLE POWER PLANT

23

CONCLUSIONS

• New modeling capabilities for process design and optimization under uncertainty

• Applicable to large-scale advanced energy systems

• Important for:

– Process design– Risk analysis– Cost estimation– R&D management

– Technology evaluation– Environmental compliance– Marketing studies– Strategic planning