Integrating Variable Wind PowerUsing a Hydropower Cascade

Andrew Hamann and Gabriela HugPower Systems Laboratory, ETH Zürich

18 September 2015

5th International Workshop on Hydro Schedulingin Competitive Electricity Markets

Trondheim, Norway

1

Motivation

I Hydropower is an enormously flexible resourceI Capable of deploying stored water energy very quicklyI Fewer start-up and shut-down restrictions than thermal powerplants

I Renewable (but not necessarily environmentally friendly)I How much flexibility can hydropower provide in real-timeoperations for balancing the variability from wind power?

I How do the operations of a coordinated wind-hydro systemdiffer from those of a hydro-only system?

2

Motivation

I Hydropower is an enormously flexible resourceI Capable of deploying stored water energy very quicklyI Fewer start-up and shut-down restrictions than thermal powerplants

I Renewable (but not necessarily environmentally friendly)I How much flexibility can the Mid-Columbia hydropower systemprovide in real-time operations for balancing the variabilityfrom wind power in the Pacific Northwest?

I How do the operations of a coordinated wind-hydro systemdiffer from those of a hydro-only system?

2

Mid-Columbia System

Bonneville

TheDalles

John Day

McNary

Ice Harbor

LittleGoose

PriestRapids

LowerMonumentalWanapum

RockIsland

RockyReach

Wells

ChiefJoseph

GrandCoulee

Mica

Duncan

Libby

Noxon

HungryHorse

LowerGranite

HellsCanyon

Oxbow

Brownlee

BoiseProjects

JacksonLake

Portland

Seattle

Willa

mette

R.

AlbeniFalls

SnakeR.

Washington

Oregon

Idaho

Montana

Canada

U.S.

Co

lumbia

R.

HughKeenleyside

KootenayLake

FlatheadLakePend Oreille

Lake

Dworshak

Palisades

Snake R.

Arrow

Corps of Engineers Dams

Dams Owned by Others

Bureau of Reclamation Dams

3

Source: Army CoE

Mid-Columbia System

Name Type Head (m) MW

1 Grand Coulee Federal 100 68092 Chief Joseph Federal 53 20693 Wells Municipal 21 7744 Rocky Reach Municipal 27 13005 Rock Island Municipal 13 6296 Wanapum Municipal 23 10387 Priest Rapids Municipal 23 956

We have one year of timestamped data for this system, with atemporal resolution of five minutes

4

Wind Power in the Pacific Northwest

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Adams

Benton

Kit t i tas

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Union

Wasco

Frank l in

Gi l l iam

Walla Wal la

Whitman

Columbia

Sherman

Lewis

Pierce

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Spokane

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UV19

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UV240

UV410

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Star Point

Willow Creek

Biglow Canyon

Linden Vansycle Ridge

Condon Wind

Stateline (Nine Mile)Wheat Field

HopkinsRidge

Pebble Springs

Goodnoe Hills

Leaning Juniper I & II

North Hurlburt

Hay Canyon

Combine Hills II

Juniper Canyon IHarvest Wind

Big HornBig Horn II

Kittitas Valley

Nine Canyon I/II

Tuolumne (Windy Pt)

White Creek

Windy Flats - Dooley

Rattlesnake Road

Lower Snake River

Klondike IKlondike III Phase 2

Klondike III Phase 1Klondike II

Patu

South Hurlburt

Golden Hills I

Jordan Butte I/II

AntelopeRidge

Horseshoe Bend

Windy Flats 3

Miller Ranch

Montague I

Montague II

Lower Snake River 3

Lotus Summit Ridge

Nook Wind II & III

Harvest Wind

DesertClaim

Golden Hills Add'n

Columbia Wind

Nook Wind

WhistlingRidge

SaddleMoutain West

Heppner

Helix

Golden Hills II & III

Ella Wind III/IV

Bakeoven I/II

Gilliam County

BrushCanyon Wind

Thresher

Sand Ridge IIEast Klickitat 1-4

Caithness Shepherds Flat IIHarvest Wind

Eight Mile Canyon

Juniper Canyon II Phase 2

Juniper Canyon 2, 2A

Lower Snake River 2

Lower SnakeRiver 4

Olex

Combine Hills I (PAC)

Wild HorseExpansion

Marengo(PAC) 1 & 2

Stateline (PAC)

Wild Horse 1&2

Vantage Wind

Yakima

Pasco

Pendleton

The Dalles

Current and Proposed Wind ProjectInterconnections to BPATransmission Facilities

0 5 10 15 20Miles

.Note: Wind project locations are approximateand intended for graphic purposes only.

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Raymond

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LongBeach

South Bend

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WahkiakumWahkiakum

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Inset Area (SW Wash)

Map date: 3/9/12

Legend

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WashingtonWashington

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Portland

5

Source: BPA

Modeling: Model Predictive Control

x(k+ 1) = A · x(k) + B · u(k) for k = 0, 1, ...,K − 1

I System model is developed to predict the response of thesystem x to a sequence of control inputs u

I The system is optimized over a time-horizon k = 0, 1, ...,KI The control sequence that gives the best performance over thetime-horizon is computed

I Only the first-step of this control sequence is appliedI The reaction of the system is observed and the process isrepeated at the next time-interval

6

Modeling: Hydraulic Model

I State variables: reservoir elevation, tailrace elevationI Control variables: turbine discharge, spill, naturalinflow/sideflow

I Reservoir elevation is a linear function of inflows and outflowsI Surface area assumed to be constantI Storage is only sufficient for a few hours of operationI Run-of-river with some flexibility

I Tailrace elevation is a function of turbine discharge, spill, anddownstream forebay elevation (i.e., encroachment)

I Tailrace elevation changes more than forebay elevationI Travel time of water between plants is considered

I Tens of minutesI Constraints on turbine discharge, spill, forebay elevation,change in turbine discharge, change in spill

7

Modeling: Hydropower Generation

p(q, h) = κ · ηt(q) · ηg(q) · q · h

0 1000 2000 3000 4000 5000 6000

1015

2025

30

−200

0

200

400

600

800

1000

Turbine discharge (m3/s)Hydraulic head (m)

Gen

erat

ion

(MW

)

q1j , p1j

q2j , p2j

q3j , p3j

q4j , p4j

q5j , p5j

qminj

qmaxj

hminj

hmaxj

qjhj

pj

Figure 10: Diagram of a piecewise linear HPF

This function corresponds to the lower limit for the auxiliary variable qij , or

qi,minj (hj) ≤ qij . (18)

Ideally, for a particular turbine discharge qj , only one auxiliary variable qij will not be tight to

either its upper or lower boundary. The upper limit for qij is thus

qij ≤

⎧⎨

⎩qi,minj (hj), qi−1

j < qi,minj (hj)

qi+1,minj (hj), qi−1

j = qi,minj (hj)

. (19)

In effect, constraint (19) maintains the ordering of the piecewise linear function. This idea is one

of the standard precepts of any piecewise linearization. However, this is also the attribute that

makes piecewise linear functions difficult to integrate into linear or quadratic optimization

problems, because constraint (19) is obviously non-linear. I am thus forced to rewrite (19) as a

linear constraint

qij ≤ qi+1,minj (hj). (20)

How I adapt to this approximate constraint will be discussed in Section 5.

12

8

Modeling: Hydro Power Balance

∑Jj=1 pj(k) = phydroload(k)

Hydro Load

Wind Load

Hour0 12 24 36 48 60 72 84 96 108 120

Pow

er D

eman

ded

(GW

)

1

2

3

4

5

9

Modeling: Wind power

∑Jj=1 pj(k) + ϵ(k) = phydroload(k) + pwindload(k) − pwind(k)

I ϵ is wind curtailment if negativeI ϵ is load curtailment if positiveI pwind is wind generationI pwindload is additional wind loadI We use BPA wind generation data for pwind and BPA balancingarea load data for pwindload scaled such that...

∑Nn=1 pwindload =

∑Nn=1 pwind

10

Modeling: Objective function

minqj,sj,ϵ{∑K−1

k=0∑J

j=1

[aj · qj(k)2 + cj · sj(k)2

]+∑K−1

k=0 d · ϵ(k)2}

aj = cj =(

ηjηj+1

· Ψj+1Ψj

)2d≫ aj

I Weight turbine discharge and spill to encourage the transfer ofwater from large surface area reservoirs to small surface areareservoirs

I Choose the weight d on ϵ large to put a heavy penalty on loador wind curtailments

11

Case Study: 120 Hours in July 2012

Hydro

Wind

Curtail

System Load

Hour0 12 24 36 48 60 72 84 96 108 120

Pow

er S

uppl

ied

(GW

)

1

2

3

4

5

Load curtailment when wind generation was low and hydro hit itsupper capacity limit

12

Case Study: 120 Hours in July 2012

2000

4000

6000

Historical Hydro Hydro and Wind

Wells

2000

4000

6000 Rocky R

eachT

urbi

ne D

isch

arge

( m

3/s

)

2000

4000

6000 Rock Island

2000

4000

6000 Wanapum

Hour0 12 24 36 48 60 72 84 96 108 120

2000

4000

6000 Priest R

apids

13

Case Study: 120 Hours in July 2012

2000400060008000

Historical Hydro Hydro and Wind

Wells

2000400060008000 R

ocky ReachS

pill

(m3/s

)

2000400060008000 R

ock Island

2000400060008000 W

anapum

Hour0 12 24 36 48 60 72 84 96 108 120

2000400060008000 P

riest Rapids

14

Case Study: Statistics

I 4884 MWavg of loadI 2874 MWavg of hydro generationI 1664 MWavg of wind generationI 346 MWavg of load curtailmentI 357 MWavg of spilled waterI 5396 MW peak load and 3838 MW peak wind generationI 34% wind energy penetrationI 71% wind capacity penetration

15

Case Study: Ramping

Ramping Scorej Name Hist. Hydro H+W

1 Wells 9.3 7.8 24.32 Rocky Reach 9.4 17.0 26.63 Rock Island 6.6 5.6 31.34 Wanapum 10.9 2.9 15.55 Priest Rapids 21.6 6.0 13.9

Ramping score is proportional to the sum of the absolute change inthe turbine discharge

16

Future Work

I Apply this framework across different hydraulic conditions,system constraints, and wind/load scenarios

I What are the appropriate metrics? Ramping, unit cycling,spilled water energy, spilled wind energy, etc.?

I What should the additional load from wind look like? Should itbe normal load, hourly blocks, on-peak blocks, off-peak blocks?

I Should thermal power plants be modeled?I What does it mean when we say that we want to balance windusing hydropower? What are the best evaluation metrics?

17

Funding Acknowledgements

Electric Power Research Institute (EPRI)

Hydro Fellowship, Hydro Research Foundation (2013-2014)

Robert W. Dunlap Graduate Fellowship, Steinbrenner Institute forEnvironmental Education and Research (2013-2014)

Department of Engineering and Public Policy, Carnegie MellonUniversity

Bertucci Graduate Fellowship, Carnegie Mellon University (Spring2013)

18

Questions?

Thank you!

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