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Scheduling the TVA Hydro System Using RiverWare’s Optimization

Suzanne H. Biddle, P.E.

Tennessee Valley Authority

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HL

KNOXVILLE

NASHVILLE

CHATTANOOGA

TN

KY

NC

SC

GA

AL

MS

VA

Watershed

Power Service Area

TVA region covers 40,000 sq miles

3

0

1

2

3

4

5

6

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

INC

HE

S

Rainfall Runoff

Average annual rainfall above Chattanooga is about 51 inches and runoff is about 22 inches

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TVA operates the reservoir system to meet multipurpose objectives

• Navigation

• Flood damage reduction

• Power generation

• Recreation

• Water quality

• Water supply

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Inputs

Future value of water

Hourly hydropower value

Inflow forecast

Initial conditions

Objectives

hourly generation preschedule

(current day + 2 forecast days)

9 day optimization using marginal costs for water

allocation

daily hydro

forecast

(14 days)

9 day optimization using block costs for daily generation schedule

3 day optimization using block costs for hourly generation schedule

River Scheduling issues two hydro forecasts each day

6Current Day

Observed Values

3 - 14 Days

Future Value of Water

14 - 120 Days

RiverWare 6-Hourly Forecast

14 Days

RiverWare Hourly

Preschedule

2 Days

Optimization covers short term, but also considers long term tradeoff

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ELE

VA

TIO

N (F

EE

T)

DECNOVOCTSEPAUGJULJUNMAYAPRMARFEBJAN

TOP OF GATES

RESERVED FOR FLOOD CONTROL

DESIRABLE JUNE 1 ELEVATION

TARGETED MINIMUM SUMMER LEVEL

FLOOD CONTROL

FILL PERIOD

RECREATION SEASON

DRAWDOWN PERIOD

MINIMUM OPERATIONS GUIDE

Many reservoirs follow seasonal guide curves

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These objectives are used in optimizing the hydro system

• Day 1 outflows are fixed• Ending targets are fixed for non-storage

tributaries and main river• Minimum flow requirements• Top and bottom of daily operating zone –

non-storage tribs and main river only• Minimum operations guides• Flood guides• Minimize spill• Special operations• Economic objective function

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What does “economic objective function” mean?

• All operating constraints must first be satisfied

• Then, with any remaining flexibility:• Maximize avoided operating cost +

delta (value of water in storage)

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Is water worth more this week or in future weeks?

Hourly Marginal Cost Forecast August 27, 2002

$0

$10

$20

$30

$40

$50

$60

$70

$80

Ma

rgin

al C

os

t ($

/MW

h)

Week 1 Week 6Week 5Week 4Week 3Week 2

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Block Cost Data from OPSYMAugust 27, 2002

MW

$200 & up

$100-$200

$90-$100

$80-$90

$70-$80

$60-$70

$50-$60

$40-$50

$30-$40

$25-$30

$20-$25

$15-$20

$11-$15

Less than $11

5000

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Tue TueMonSunSatFriThurWed

After water is allocated, block cost data is used to determine which hours to run

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The reservoir system is modeled as a whole for hydropower optimization