slide 1 the renewables challenge: keeping the lights on while managing variability and uncertainty...

The Renewables Challenge:Keeping the lights on while managing

variability and uncertainty

Princeton University Academic Mini-Reunion

October 2, 2015

Warren B. PowellPENSA Laboratory

Dept. of Operations Research andFinancial Engineering

http://energysystems.princeton.edu

Outline

The renewables challenge Combining wind and solar The uncertainties of energy Three energy problems

» An energy storage problem» An energy portfolio policy model» Simulating the PJM grid using SMART-ISO

Concluding remarks

Wind in the U.S.

99.9 percent from renewables!

Fossil Backup

BatteryStorage

Wind &Solar

20 GW

750 GWhr battery!

Outline

The renewables challenge Combining wind and solar The uncertainties of energy Modeling sequential decision problems under

uncertainty Three energy problems


Concluding remarks

Wind energy in PJM

Total PJM load plus actual wind (July)

53 wind farms

Wind energy in PJM

Total PJM load plus actual wind (July)

100GW

101,000 MWhr battery$50 billion!!

Wind ~ 37 percent of total load

Solar energy

Solar from all PSE&G solar farms

Solar energy

Total PJM load plus factored solar (July)

Solar ~ 15 percent of total load

Combining wind and solar

Mixture of wind and solar to meet July load

815,000 MWhr battery $989 billion!!

Combining wind and solar

Mixture of wind and solar to meet July load

100GW

260,000 MWhr battery $130 billion!!

Capacity factor analysis

Computing the “capacity factor”

Capacity

Actual

Generated windCapacity factor = 39%

Maximum capacity

Capacity factor analysis

Classical analysis of renewables» Multiply installed capacity by the capacity factor

• 1 MW solar panel• Capacity factor of .25• Translates to 0.25 MW of generation

» Now, treat the .25 MW as if it is a form of conventional generation.

» This makes it possible to scale up renewables without regard to the challenges of variability and uncertainty.

» Let’s try to do better.

Outline



Concluding remarks

Northeast Reliability Councils and Interconnects

Energy from wind

1 year

Wind power from all PJM wind farms

Jan Feb March April May June July Aug Sept Oct Nov Dec

Energy from wind

30 days

Wind from all PJM wind farms

Modeling wind

Forecast vs. actual for a single wind farm

Actual

Forecasted

Solar energy

Princeton solar array

PSE&G solar farms

Solar output over entire year (all farms)

Sept Oct Nov Dec Jan Feb March April May June July Aug

Solar from PSE&G solar farms

Solar from a single solar farm

Solar from PSE&G solar farms

Within-day sample trajectories

Brazil

Rainfall

Foz do Iguaçu (Brazil) – 2011 through 2013

2011 2012 2013

Commodity prices

The price of natural gas» Reflects global and local economies, competing global

commodities (primarily oil), policies (e.g. toward CO2), and technology (e.g. fracking).

$4 /mmBTU

$120 /mmBTU!

Locational marginal prices on the gridLMPs – Locational marginal prices

$58.47/MW


$977/MW !!!


$328/MW !

Locational marginal prices on the grid

$52/MWhr

Uncertainty

It is important to separate:» Predictable variability

• Diurnal cycles• Large weather patterns• Major human events (Super

bowl)

» Stochastic uncertainty • Temperature deviations from

forecast• Late/early arrival of a storm• Generator failures• Wind shifts

PJM load

Aggregate solar

Dealing with uncertainty

Available at energysystems.princeton.edu

Outline



Concluding remarks

Policy function approximations

Battery arbitrage – When to charge, when to discharge, given volatile LMPs

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 700.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

Grid operators require that batteries bid charge and discharge prices, an hour in advance.

We have to search for the best values for the policy parameters

DischargeCharge

Charge Discharge and .



Our policy function might be the parametric model (this is nonlinear in the parameters):

charge

charge discharge

charge

1 if

( | ) 0 if

1 if

t

t t

t

p

X S p

p

Energy in storage:

Price of electricity:


Finding the best policy» We need to maximize

» We cannot compute the expectation, so we run simulations:

DischargeCharge

0

max ( ) , ( | )T

tt t t

t

F C S X S

E

Outline



Concluding remarks

99.9 percent from renewables!

» What answer do we get if we model this problem more carefully?

SMART-Invest

Features:» Finds the optimal mix of wind, solar and storage, in the

presence of two types of fossil generation:• Slow (steam) generation, which is planned 24 hours in

advance• Fast (turbine) generation, which is planned 1 hour in advance• Real-time ramping of all fossils within ramping limits

» Simulates entire year in hourly increments, to capture all forms of variability (except subhourly)

» Minimizes investment and operating costs, possibly including SRECs and carbon tax.

» Able to directly specify the cost of fossil generation (anticipating dramatic reduction in fossils).

» Properly accounts for the marginal cost of each unit of investment.

8760

,1

min ( ) ( , ( | ))Invi

inv inv opr opr invt t t tx i I

t

C x C S X S x

SMART-Invest

The investment problem:

Investment cost in wind, solarand storage.

Capital investment cost inwind, solar and storage

( )oprtX S is the operating policy.

Operating costs of fossil generators,energy losses from storage, misc. operating costs of renewables.

Wind

Solar

SMART-Invest

Stage 1:Investment

Hour 1 Hour 2 Hour 3 Hr 8758 Hr 8759 Hr 8760…

Wind CapacitySolar Capacity

Battery CapacityFossil Capacity

Wind

Solar

Find search direction

Update investments

SMART-Invest

Operational planning

» Meet demand while minimizing operating costs» Observe day-ahead notification requirements for

generators» Includes reserve constraints to manage uncertainty» Meet aggregate ramping constraints (but does not

schedule individual generators)

24 hour notification of steam

1 hour notification of gas

Real-time storage and ramping decisions (in hourly increments)

36 hour planning horizon using forecasts of wind and solar

SMART-Invest

Operational planning model

» Model plans using rolling 36 hour horizon» Steam plants are locked in 24 hours in advance» Gas turbines are decided 1 hour in advance

Slow fossil running units1 24 36

1 24 36Slow fossil running units







…

…

…1 2 3 4 5 8760

1 year

Lock in steam generation decisions 24 hours in advanceThe tentative plan is discarded

SMART-Invest

Lookahead model with adjustment» Objective function

» Reserve constraint:

» Other constraints:• Ramping• Capacity constraints• Conservation of flow in storage• ….

Tunable policy parameter

Robust policies

Policy search – Optimizing reserve parameter

Low carbon tax, increased usage of slow fossil, requires higher reserve margin ~19 percent

High carbon tax, shift from slow to fast fossil, requires minimal reserve margin ~1 pct

The value of storage

The marginal value of storage» On the margin, value of storage can be expensive!

Ene

rgy

in s

tora

ge

Time

This investment in batteries is only used a small fraction of the time.

Policy studies

Renewables as a function of cost of fossil fuels

Solar

Wind

$/MWhr cost of fossil fuels

100

80

60

40

20

0Perc

ent f

rom

ren

ewab

le Total renewables

0 20 50 60 70 80 90 100 150 300 400 500 1000 3000

» Study assumes unconstrained access to wind at lowest cost (this is not available in the eastern U.S.)

» Note the reluctance to introduce solar…

» … and even greater reluctance to use storage.

Battery

Policy studies

Sensitivity to CO2 tax.

Slow fossil Fast fossil

Nuclear

Wind

Solar

“Other” fast fossil

Outline



Concluding remarks

© 2010 Warren B. Powell Slide 59

Lecture outline

Simulating the PJM grid with SMART-ISO

The PJM planning process Model validation Modeling wind Integrating offshore wind

The timing of decisions

Day-ahead planning (slow – predominantly steam)

Intermediate-term planning (fast – gas turbines)

Real-time planning (economic dispatch)


The day-ahead unit commitment problemMidnight

Noon

Midnight Midnight Midnight

Noon Noon Noon


Intermediate-term unit commitment problem

1:15 pm 1:45 pm

1:30

2:15 pm

1:00 pm 2:00 pm 3:00 pm

2:30 pm


Intermediate-term unit commitment problem

Turbine 3

Turbine 22

Turbine 1

Notification time

1:15 pm

1:30

2:00 pm 3:00 pm

Ramping, but no on/off decisions.

Commitment

decisions


Real-time economic dispatch problem

1pm 2pm

1:05 1:10 1:15 1:20 1:25 1:30


Real-time economic dispatch problem

1pm 2pm

1:05 1:10 1:15 1:20 1:25 1:30

Run economic dispatch to perform 5 minute ramping

Run AC power flow model


Lecture outline



SMART-ISO: Calibration

Historical generation mix during 22-28 Jul 2010

Nuclear

Steam

Comb. cycle+gasPumped hydro

SMART-ISO: Calibration

Simulated generation mix during 22-28 Jul 2010

Steam

Nuclear

Comb. cycle+gasPumped hydro

Actual vs. simulated LMPs

January April

July October


Lecture outline



Energy from wind

30 days

Wind power from all PJM wind farms

Energy from wind

Illustration of forecasted wind power and actual» The forecast (black line) is deterministic (at time t, when the forecast

was made). The actuals are stochastic.

This is our forecast of the wind power at time t’, made at time t.

'ttf

This is the actual energy from wind, showingthe deviations from forecast.

Energy from wind

Two types of uncertainty arise in forecasting:» At time t, we have forecasts for different times into the

future:

• The forecast is an imperfect estimate of the actual load at time t’:

» As new information arrives, the forecasts themselves change from time t to t+1:

'ttf

1, ' , ' 1, 'f

t t t t t tf f This change in the forecast is “stochastic” at time t.

' , ' 'L

t t t tL f The actual load at time t’ is “stochastic” at time t.

Forecasting wind

Rolling 24-hour forecast of PJM wind farms

Actual

Hour of day1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Meg

awat

ts

Onshore & offshore wind farms

We were given access to data on the wind power generated by onshore wind farms within PJM

Proposal: Use onshore data to calibrate a stochastic model of forecasting errors. Then use this model to create a simulated “actual” for offshore.

Distribution of forecast errors» Uses adjusted spatial correlations to improve fit.

Simulating onshore wind

Observed

Simulated

Error in forecasted wind speed

Simulating onshore wind Cumulative histogram of the # of consecutive time intervals the

observed/simulated time series is above the forecasted one (chosen farm only):

Time actual is above forecast

ObservedSimulated

Simulating onshore wind Cumulative histogram of the # of consecutive time intervals the

observed/simulated time series is below the forecasted one (chosen farm only):

Time actual is below forecast

ObservedSimulated

Wind forecast samples80

70

60

50

40

30

20

10

0

Simulating offshore wind

Offshore wind – Buildout level 5

Forecasted wind


Lecture outline



SMART-ISO: Offshore wind study

Mid-Atlantic Offshore Wind Integration and Transmission Study (U. Delaware & partners, funded by DOE)

29 offshore sub-blocks in 5 build-out scenarios:» 1: 8 GW» 2: 28 GW» 3: 40 GW» 4: 55 GW» 5: 78 GW

Modeling wind

» Steadier than onshore? Where???

GW

Modeling wind

The power from wind:

» The cubic relationship means small changes in speed translate to large changes in power.

31

2P B Av

Wind speed (in m/sec)v

3Area of rotor blades in mA

3Density of air ( 1.225kg/m )

Power coefficient

fraction of wind converted to mechanical energy

.593 (the Betz limit)

B

Unit commitment under uncertainty

Actual wind

Hour ahead

forecast

How forecasting uncertainty causes outages.


Less steamUniform increase in gas


Outage probabilities over 21 scenarios for January, April and October:

Per

cent

of

sam

ples

ther

e is

an

outa

ge

Bas

e P

JM r

eser

veO

ptim

ized

res

erve

sP

erfe

ct in

form

atio

n


Outage probabilities over 21 scenarios for July

Per

cent

of

sam

ples

ther

e is

an

outa

ge


Ramping reserves, July, 2010

Perfect forecast

Imperfect forecast

16 14 12 10 8

6

4

2

0

1 2 3 4 5

Buildout levels

Ram

ping

res

erve

s (G

W)


Observations» The requirement of reserves at 20 percent of capacity is only for

July, and we believe this over-estimates the reserves needed.» Other months require reserves at 10 percent of capacity, which is

still substantial, considering that renewables generate energy at roughly 20 percent of capacity.• 10 percent reserves means that 100 MW of wind generation

requires 10 MW of spinning reserve.• 100 MW of generating capacity translates to around 25 MW of

power (on average). So 25 MW of power requires 10 MW of spinning reserve from a fossil plant.

» This is for an “as is” network – we are using existing generation technologies and existing planning procedures.

» A richer portfolio including demand response, battery storage and more sophisticated planning should help.

Outline



Concluding remarks

The challenge of renewables

What did we learn?» Wind and solar are variable, and uncertain, with very

different characteristics.» Back-of-the-envelope analysis (e.g. capacity factor

analysis) completely ignores the challenges of dealing with variability and uncertainty.

» It is important to design effective policies for dealing with variability, forecasts, and uncertainty.

» Reserves to handle uncertainty can be significant, and are easily overlooked.

» Renewables are a powerful alternative to reduce our CO2 footprint, but they need to be planned properly to avoid unexpected costs.

slide 1 the renewables challenge: keeping the lights on while managing variability and uncertainty...

Documents

wind farmswind energy

actual wind

solarmixture of wind

pjm wind farmsjan

single solar farm solar

interconnects energy

pjm grid

pjmtotal pjm load