J. McCalley

Power System Operation, and Handling Wind Power Variability and

Uncertainty in the Grid

Outline1. Basic problems, potential solutions2. Wind power equation3. Variability4. System Control5. Comments on potential solutions

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Basic problems with wind & power balance1. Wind is a variable resource when it is

controlled to maximize its power productiona. Definition: NETLOAD.MW=LOAD.MW+LOSSES.MW-WIND.MWb. Fact: Wind increases NETLOAD.MW variability in gridc. Fact: Grid requires GEN.MW=NETLOAD.MW alwaysd. Fact: “Expensive” (based on marginal cost) gens move (ramp)

quickly, “cheap” gens don’t, some gens do not ramp at all.e. Problem: Increasing wind increases need for more and

“faster” resources to meet variability, increasing cost of wind.

2. Wind is an uncertain resourcea. Fact: Market makes day-ahead decisions for “unit

commitment” (UC) based on NETLOAD.MW forecast.b. Fact: Large forecast error requires available units compensate.c. Problem: Too many (under-forecast) or too few (over-

forecast) units may be available, increasing the cost of wind.3

Solutions to variability & uncertainty

1. We have always dealt with variability and uncertainty in the load, so no changes are needed.

2. Increase MW control capability during periods of expected high variability via control of the wind power.

3. Increase MW control capability during periods of expected high variability via more conventional generation.

4. Increase MW control capability during periods of expected high variability using demand control.

5. Increase MW control capability during periods of expected high variability using storage.

4 4

Power productionWind power equation

v1 vt v2

v

x

Swept area At of turbine blades:

The disks have larger cross sectional area from left to right because• v1 > vt > v2 and• the mass flow rate must be the same everywhere within the streamtube (conservation of mass):

ρ=air density (kg/m3)

Therefore, A 1 < At < A 2

2211

21

vAvAvA

Q Q Q

tt

t

Mass flow rate is the mass of substance which passes through a given surface per unit time.

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Power productionWind power equation

ttt

t vAt

xA

t

mQ

3. Mass flow rate at swept area:

22212

1vvmKE

1. Wind velocity:t

xv

xAm 2. Air mass flowing:

4a. Kinetic energy change:

5a. Power extracted: 222

122

21 2

1

2

1vvQvv

t

m

t

KEP t

6a. Substitute (3) into (5a):)()2/1( 22

21 vvvAP tt

4b. Force on turbine blades:

21 vvQvt

m

t

vmmaF t

5b. Power extracted:

21 vvvQFvP ttt

6b. Substitute (3) into (5b):)( 21

2 vvvAP tt

ttttt vvvvvvvvvvvvvvvvv ))(2/1()())(()2/1()()()2/1( 12212

21212122

221

7. Equate

8. Substitute (7) into (6b): ))((4

)()))(2/1(( 2122

2121

221 vvvv

AvvvvAP t

t

9. Factor out v13: )1)()(1(

4 1

22

1

231

v

v

v

vvAP t

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Power productionWind power equation

10. Define wind stream speed ratio, a:

1

2

v

va

)1)(1(4

231 aa

vAP t

11. Substitute a into power expression of (9):

12. Differentiate and find a which maximizes function:

1,3/10)1)(13(

0123122

0)1()1(24

222

231

aaaa

aaaaa

aaavA

a

P t

This ratio is fixed for a given turbine & control condition.

13. Find the maximum power by substituting a=1/3 into (11):

27

8

3

4

9

8

4)3

4)(9

11(

4

31

31

31 vAvAvA

P ttt

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Power productionWind power equation

14. Define Cp, the power (or performance) coefficient, which gives the ratio of the power extracted by the converter, P, to the power of the air stream, Pin.

)1)(1(4

231 aa

vAP t

31

211

211

21 2

1

2

1

2

10

2

1vAvvAvQv

t

m

t

KEP ttin

power extracted by the converter

power of the air stream

)1)(1(2

1

21

)1)(1(4 2

31

231

aavA

aavA

P

PC

t

t

inp

15. The maximum value of Cp occurs when its numerator is maximum, i.e., when a=1/3:

5926.027

16)3

4)(9

8(2

1

inp P

PC

The Betz Limit!

312

1vACPCP tPinp

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Power productionCp vs. λ and θ

Tip-speed ratio:11 v

R

v

u u: tangential velocity of blade tip

ω: rotational velocity of blade

R: rotor radiusv1: wind speed

Pitch: θ

GE SLE 1.5 MW 9

Power productionWind Power Equation

31),(

2

1vACPCP tPinp

So power extracted depends on 1.Design factors:

• Swept area, At 2.Environmental factors:

• Air density, ρ (~1.225kg/m3 at sea level)• Wind speed v3

3. Control factors affecting performance coefficient CP: • Tip speed ratio through the rotor speed ω• Pitch θ 10

Power productionCp vs. λ and θ

Tip-speed ratio:11 v

R

v

u u: tangential velocity of blade tip

ω: rotational velocity of blade

R: rotor radiusv1: wind speed

GE SLE 1.5 MW

Important concept #1:The control strategy of all US turbines today is to operate turbine at point of maximum energy extraction, as indicated by the locus of points on the black solid line in the figure.

Important concept #2:• This strategy maximizes the energy produced by a given wind turbine.• Any other strategy “spills” wind !!!

Important concept #3:• Cut-in speed>0 because blades need minimum torque to rotate.• Generator should not exceed rated power• Cut-out speed protects turbine in high winds

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Power productionUsable speed range

Cut-in speed (6.7 mph) Cut-out speed (55 mph)

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Wind Power Temporal & Spatial Variability

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JULY2006JANUARY2006

Notice the temporal variability:• lots of cycling between blue and red;• January has a lot more high-wind power (red) than July;

Notice the spatial variability• “waves” of wind power move through the entire Eastern Interconnection;• red occurs more in the Midwest than in the East

Blue~VERY LOW POWER; Red~VERY HIGH POWER

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Time frame 1: Transient control

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Time frame 1: Transient control

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Source: FERC Office of Electric Reliability available at: www.ferc.gov/EventCalendar/Files/20100923101022-Complete%20list%20of%20all%20slides.pdf

1-20 seconds

Time frames 2 & 3: Regulation and Load following

-100

-80

-60

-40

-20

0

20

40

60

80

100

07:00 07:20 07:40 08:00 08:20 08:40 09:00 09:20 09:40 10:00

RE

GU

LA

TIO

N I

N M

EG

AW

AT

TS

Regulation

=

+

Load Following Regulation

Source: Steve Enyeart, “Large Wind Integration Challenges for Operations / System Reliability,” presentation by Bonneville Power Administration, Feb 12, 2008, available athttp://cialab.ee.washington.edu/nwess/2008/presentations/stephen.ppt.

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16

4 seconds to 3 minutesEvery 5 minutes

Analogy for supply-demand-frequency relationship

1717

Inflow SupplyOutflow DemandWater leve lFrequency

How Does Power System Handle Variability

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Turbine-Gen 1Turbine-Gen 2Turbine-Gen …Turbine-Gen N

∆f∆Ptie

ACE=∆Ptie -10B∆f

Primary control controls output in response to transient frequency deviations

Secondary control provides regulation

B is BA’s frequency bias in MW/0.1Hz.B is negative.

How Does Power System Handle Variability

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ACE= ΔPtie – BΔf = ΔPtie +| B|Δf

ΔPtie=Ptie,act-Ptie,sch

Δf=fact-60

If ΔPtie=0, Δf =0, then ACE=0, and generation does not change;If ΔPtie>0 which means the actual export exceeds the scheduled export, then this component would make ACE more positive therefore tending to reduce generation;If Δf>0 which means the actual frequency exceeds the scheduled frequency of 60 Hz, then this component would make ACE more positive therefore tending to reduce generation.

BA

REST OF THE INTERCONNECTION

P3P1

P2

Ptie=P1+P2+P3

Power Balance Control Levels

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Control level

Name Time frame

Control objectives Function

1 Primary control, governor

1-20 seconds

Power balance and transient frequency

Transient control

2 Secondary control, AGC

4 secs-3 mins

Power balance and steady-state frequency

Regulation

3 Real-time market

Every 5 mins

Power balance and economic-dispatch

Load following and reserve provision

4 Day-ahead market

Every day, 24 hrs at a time

Power balance and economic-unit commitment

Unit commitment and reserve provision

Why Does Variability Matter?

NERC penalties for poor-performance Consequences of increased frequency variblty:

Some loads may lose performance (induction motors) Relays can operate to trip loads (UFLS), and gen (V/Hz) Lifetime reduction of turbine blades Frequency dip may increase for given loss of generation Areas without wind may regulate for windy areas

Consequences of increased ACE variability (more frequent MW corrections):

Increased inadvertent flows Increase control action of generators

Regulation moves gen “down the stack” cycling!21

Power Balance Control Levels

22

kkk LFLLR Load regulation component

Load following component

Load

12

......

12

1 11

T

LLLLLL

TLF TkTkkTkTk

Tk

Tkiik

Δt=2 min, 28 min rolling average, so T=7.

15

...... 7667 kkkkk

kLLLLL

LF

Regulation component varies about the mean and tends to go up as much as it goes down and is therefore normal with 0 mean.

Power Balance Control Levels

23

n

ixix x

n 1

22 )(1

Consider two random variables, X and Y.

If Z=X+Y, then

222yxz

Hourly Load Variability and Load-Wind Variability When Wind Penetration is 10%

0

500

1000

1500

2000

2500

3000

3500

4000

-800

-700

-600

-500

-400

-300

-200

-100

0 100

200

300

400

500

600

700

800

Load and Load-Wind Hourly Variability (MW)

Fre

qen

cy

Load Hourly Variability Load-Wind Hourly Variability

Characterizing Netload Variability∆T HISTOGRAMMeasure each ∆T variation for 1 yr (∆T=1min, 5min, 1 hr)Identify “variability bins” in MWCount # of intervals in each variability binPlot # against variability binCompute standard deviation σ.

Regulation

Load following

Ref: Growing Wind; Final Report of the NYISO 2010 Wind Generation Study, Sep 2010.www.nyiso.com/public/webdocs/newsroom/press_releases/2010/GROWING_WIND_-

_Final_Report_of_the_NYISO_2010_Wind_Generation_Study.pdf

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Loads:2011: 12600 MW2013: 12900 MW2018: 13700 MW

Solutions to variability & uncertainty1. Do nothing: fossil-plants provide reg & LF (and die ).2. Increase control of the wind generation

a. Provide wind with primary control• Reg down (4%/sec), but spills wind following the control • Reg up, but spills wind continuously

b. Limit wind generation ramp rates• Limit of increasing ramp is easy to do• Limit of decreasing ramp is harder, but good forecasting

can warn of impending decrease and plant can begin decreasing in advance

3. Increase non-wind MW ramping capability during periods of expected high variability using one or more of the below:a. Conventional generation b. Load controlc. Storaged. Expand control areas

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%/min $/mbtu $/kw LCOE,$/mwhr

Coal 1-5 2.27 2450 64

Nuclear 1-5 0.70 3820 73

NGCC 5-10 5.05 984 80

CT 20 5.05 685 95

Diesel 40 13.8125

How to decide?First, frequency control for over-frequency conditions, which requires generation reduction, can be effectively handled by pitching the blades and thus reducing the power output of the machine. Although this action “spills” wind, it is effective in providing the necessary frequency control. Second, frequency control for under-frequency conditions requires some “headroom” so that the wind turbine can increase its power output. This means that it must be operating below its maximum power production capability on a continuous basis. This also implies a “spilling” of wind.Question: Should we “spill” wind in order to provide frequency control, in contrast to using all wind energy and relying on some other means to provide the frequency control? Answer: Need to compare system economics between increased production costs from spilled wind, and increased investment, maint, & production costs from using storage & conventional gen.

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