Metropolitan’s SWP Supply Forecasting and Optimal

Scheduling

CWEMF Annual MeetingFebruary 27, 2007

Peter LouieMetropolitan Water District of So. California

Objectives

• Improve short-term water management decision-making and scheduling for MWD

• Allow varying levels of risk to be considered in decision-making

• Utilize optimization to mimic water supply, water quality, and cost preferences

MWD Water OperationsRegional water supply to 6 counties

26 Member Agencies Supply 18 million people Supply 1.5 billion gallons of water/day 1,072 miles of pipelines, tunnels, & canals 5 treatment plants 17 reservoirs 16 hydroelectric power plants 45 major control structures 5 pumping plants on the CRA

SWP entitlement: 1.9 MAF (2006) CRA entitlement: 652 TAF

Dry-YearDry-Year PortfolioPortfolioDry-YearDry-Year PortfolioPortfolio

San Joaquin Valleytransfers

Sacramento Valley transfers& DWR Drought Bank

Surface ReservoirsSurface Reservoirs Multi-Year ProgramsMulti-Year Programs (Ground water)(Ground water)

Single-Year OptionsSingle-Year Options (Transfers)(Transfers)

Lake PerrisLake Perris

Skinner ReservoirSkinner Reservoir

Diamond Valley LakeDiamond Valley LakeLake MathewsLake Mathews

Castaic LakeCastaic Lake

San Luis ReservoirSan Luis Reservoir

Kern Delta W.D.Kern Delta W.D.

Semitropic W.S.D.Semitropic W.S.D.

Hayfield BasinHayfield Basin

Coachella Valley W.D.

Coachella Valley W.D.

Imperial I.D.Imperial I.D.

Palo Verde I.D.

Palo Verde I.D.

Arizona BankingArizona Banking

Arvin-Edison W.S.D.Arvin-Edison W.S.D.

San Bernardino Valley M.W.D.San Bernardino Valley M.W.D.

Mojave W.A.Mojave W.A.

2005 2006

Dec Jan MayFeb Mar Apr Nov Dec

EWANegotiations

SWP initialAllocation

SBVMWDTransfersNotification

Kern DeltaNotificationFor Put only

Decision to take SBVMWDTransfers

Final Kern DeltaNotificationPut/Take

Arvin EdisonNotificationPut/Take

TurnbackPool B

SemitropicNotification

Put

DWCVCallback

Notification

SemitropicNotification

Take

SWPFinal

Allocaton

DWCVDeliveries

Set Carryover

Limits

WSDM Action Timeline

SWP ForecastsWQ, WS

Delta Ops

Aqd./Res. Model

TransfersNorth of Delta

Transfers South of Delta

CRA ForecastsWQ, WSMWD

Dist. System Model

Availability of quantity,timing and wq characteristics

Availability of quantity,timing and wq characteristics

Allocation and storage conditionswq characteristics

Allocation and storage conditionswq characteristics

Res. ops/ wq targets for treatment plants/consumptive use/seasonal storage

WQCP/ESA/EWA/b2 and otherDelta regulations and requirements

Tracking wq

System Models IntegrationAnd Optimization Schema

OptimizationProcedure

LP/DP approach to determinethe desirable combination of SWP/CRA/EWA/Transfers/MWD storage ops in meetingboth the ws/wq objectives.

Hydrologic Forecasts (DWR Flood Management, CNRFC)

System State (CDEC, USGS, IEP)

Demand Forecasts (Contractors, Env, Reg)

Allocation Forecasting Tool

(CALSIM-CAM)

Scheduling Optimization Tool

(SISAGUA)

Priorities

MWD-Specific Network

MWD Delivery Point Demands

Non-CALSIM-CAM Supplies

Con

trol

ler/I

nter

face

Too

l (V

BA

) (D

ata

acqu

isit

ion

and

tran

sfer

, con

trol

seq

uenc

e of

sim

ulat

ion,

con

trol

it

erat

ion

and

clos

ure,

use

r in

ferf

ace

)

SWP allocation, forecasts of availability of supplies, storage, system conditions

MWD preferred delivery request schedule

Data acquisition/ transfer

Data acquisition/ transfer

Data acquisition/ transfer

Overall Analytical Approach

SWP Allocation Forecasting Tool

Source Data

CAM Input

Runtime Control/ Data Setup

• Period of greatest uncertainty: October – January• Critical information

– Risk of spill of carryover storage – Initial allocation – Positional Analysis provides broad sampling of

possible hydrologic conditions– Monte-Carlo simulation with uniform sampling of

historic hydrology• Climate indicators may indicate skewness from the

uniform sampling– Reshaping of Position Analysis inputs – As forecast becomes available, CAM stand-alone

may be used in conjunction with PA-CAM

Projections under Poor/No Forecast

• Improving forecasts: February – May• Critical information

– Delivery reliability– Storage conditions

• P25, P50, P75, P90, P99 forecasts provide traces of possible hydrologic conditions

• CAM stand-alone study provides delivery and storage estimates

• Longer term assessed with CAM-PA simulations

Projections with Available Forecast

SWP Allocation Forecasting Tool

Source Data

CAM Input

Runtime Control/ Data Setup

0

500

1000

1500

2000

2500

3000

3500

4000

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

S4_DEC Oroville EOM Storage

0

100

200

300

400

500

600

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

D6_DEC SWP Contractor Deliveries

Precipitation Indices

Precipitation or Climate

Indices

Official B-120 Forecast

Historical Inflow Traces Ranked Inflow Distribution

+

+

=

=

Updated Inflow Distribution

Method for developing revised inflow distributions

Proposed Monte Carlo simulation method

Dynamic Programming Schematics For Optimizing Water Quality/Water Supply/CostsProblem Formulation: Optimization Objectives and System Constraints Specifications

Objectives: Minimizing the water quality indices from prescribed targets (As, Br, Cr, Cr+6, NO3, TDS, DOC,TOC, SO4, U, V); this could be a linear combination of all the indices or minimizing each in turn.

Minimizing operating costs (energy consumption, disruption penalties, etc.)

Maximizing supply reliability (probability in meeting the quantities requested)

Constraints: Resources availabilitySystem fill and withdrawal capacitiesOperational requirements (system ramping up and down )Water supply and quality requirementsBudgetary limitationSystem ops requirements

Time step =1Quantity & Quality required

Dynamic Programming Schematics For Optimizing Water Quality/Water Supply/CostsThrough Water Transfers and Exchanges and System Re-ops

Source1(Semitropic)

100%

90%

80%

70%

0%

10%

Source1(Semitropic)

100%

90%

80%

70%

0%

10%

Source2(Arvin Edison)

100%

90%

80%

70%

0%

10%

Source2(Arvin Edison)

100%

90%

80%

70%

0%

10%

SourceN(SC Reservoir

Re-Ops)

100%

90%

80%

70%

0%

10%

SourceN(SC Reservoir

Re-Ops)

100%

90%

80%

70%

0%

10%

Time step =iQuantity & Quality required

Source1(Semitropic)

100%

90%

80%

70%

0%

10%

Source2(Arvin Edison)

100%

90%

80%

70%

0%

10%

SourceN(SC Reservoir

Re-Ops)

100%

90%

80%

70%

0%

10%

Source1(Semitropic)

100%

90%

80%

70%

0%

10%

Source1(Semitropic)

100%

90%

80%

70%

0%

10%

Source2(Arvin Edison)

100%

90%

80%

70%

0%

10%

Source2(Arvin Edison)

100%

90%

80%

70%

0%

10%

SourceN(SC Reservoir

Re-Ops)

100%

90%

80%

70%

0%

10%

SourceN(SC Reservoir

Re-Ops)

100%

90%

80%

70%

0%

10%

Time step =T

Sourcej Sourcej

Dec

isio

n k

Z1(i,j,x)= minimum deviation of WQI from target attainable from source j, j+1,N at time step i with xdollars available to implement the decision dj.

= min f(WQIj, Z1(i,j+1,x-Costdjdj

Where dj would yield the minimum WQI up to the j source from the backward sense. A subsystem model f()* would be used, given the dj, to determine the best WQI can be attained. Among the best WQIs from djs, the minimum would be selected.

Boundary and starting conditions:Z1(i,j,x)= for x<=0 j=1 to N ; i= 1 to TZ1(i,N+1,x)= 0 for x>=0

*The subsystem model(s) could be simulation models or optimization models themselves dependingon the systems involved.

Srf Wtr_In

-800,000

-600,000

-400,000

-200,000

0

200,000

400,000

600,000

800,000

1975 1976 1977 1978 1979

Time Period

Put/T

ake

(AF)

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

900,000

Acc

ount

Bal

ance

(AF)

Put/Take Account MaxAccount Min Account TrackingPut Capacity Take Capacity

2 3 4 5 1

Pu

tT

ake

Grd Wtr_Out

-500,000

-400,000

-300,000

-200,000

-100,000

0

100,000

200,000

300,000

400,000

1975 1976 1977 1978 1979

Time Period

Put/T

ake

(AF)

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1,600,000

1,800,000

Acco

unt B

alan

ce (A

F)

Put/Take Account MaxAccount Min Account TrackingPut Capacity Take Capacity

2 3 4 5 1

Tak

eP

ut

Summary

• Forecast-Optimization approach shows promise for improving MWD water management

• Consideration of uncertainty allows MWD decision-makers/operators to assess internal risk

• Optimization approaches are actively being used in SWP and MWD systems

• Future work will consider continuously-updated adjustments to forecasts

• Prototype for MWD’s SWP-side supplies may be expanded