Aleksandr Rudkevich The Economics of Energy Markets

Toulouse School of Economics and IDEI, Toulouse January 29, 2010

Locational Carbon Footprint and Renewable Portfolio

Standards

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Energy conservation and renewable generating resources reduce emissions of greenhouse gases

• Is this always true?

• Does it matter where or when we reduce electricity demand?

• Does it matter where we locate renewable generation and

what its time-dependency is?

• If it matters, what should we do about this knowledge?

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How do renewable resources and demand reduction measures affect CO2 emissions in the bulk power system?

• Marginal approach:

– Similar to the theory of nodal prices (LMPs)

– LMPs are defined as a change in system-wide dispatch costs in

response to change in demand

– LMPs depend on the costs of marginal generators

– If we systematically track the change in CO2 emissions in response

to change in demand, it becomes clear these changes depend on

the marginal generators’ emissions in the same way as LMPs

depend on the marginal generators’ costs

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Marginal Carbon Intensity: Definition

• Marginal carbon intensity is the change in CO2 emissions in

the entire system for a 1 MW load increase at a given

location in a given moment in time, accounting for the re-

dispatch needed to accommodate the load change

2( )

( )system

nodenode

COMCI

Demand

5

time

time

0.6

0.4

0.9

MC

I (t

/MW

h)

coal

CC

gC

Tg

Dem

and

(MW

)

Over time MCI follows the succession of marginal unitsTechnology Heat Rate

(Btu/kWh) Fuel Price ($/MMbtu)

VO&M ($/MWh)

CO2 rate (Ton/MWh)

CO2 price ($/t)

Dispatch cost

($/MWh) Coal 9500 2.0 1.0 0.9 10 29

CCg 7000 5.0 3.0 0.4 10 42

CTg 11000 5.0 5.0 0.6 10 66

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Impact of Transmission Congestion on Locational MCI

• Shadow Carbon Intensity (SCI) of a constraint equals the reduction in total CO2 emissions in response to an infinitesimal relaxation of the constraint:

_ ,node ref bus node constr constrconstr

MCI MCI SCI

• MCI decomposition, similar to the LMP decomposition, holds

2( )

( )system

constrconstr

COSCI

Limit

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Marginal Carbon Offset of a Generator

A difference between MCI at generator’s location and its own emission rate

( ) ( ) ( )Ck k kt MCI t t

When offset is positive, generator contributes to carbon reduction, otherwise increases carbon emissions

Renewable generation has zero emission rate, it contributes to carbon reduction when MCI at its location is positive, increases carbon emissions if MCI is negative

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Examples: Mapping MCIs for the Eastern Interconnection of the US

• The following slide is based on the CRA simulation of the Eastern Interconnection using GE MAPS

• Simulation is based on 10% wind penetration scenario is SPP and MAPP with supporting transmission upgrades

• Lossless dispatch performed for the Eastern Interconnection, with reduced level of detail in representing transmission constraints outside SPP and MAPP

• MCI snapshot is shown for one off-peak hour: 10 PM, 1 November 2010

• MCI visualization is performed using PowerWorld and Transmission Atlas

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GE MAPS Simulation for 1-Nov-2010, 6-7am

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GE MAPS Simulation for 1-Nov-2010, 10-11 pm

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Preliminary observations from MCI mapping

• Locational variations in MCI are very significant and could range

from – 0.5 tCO2/MWh to 1.5 tCO2/MWh

• In relative terms, locational variability of MCI values is

comparable to the locational variability of electricity prices

• Negative MCI values are a reality which needs to be further

examined and considered

• Transmission and unit commitment limitations which make wind

resources marginal (wind curtailments) could lead to negative

MCI values in regions neighboring wind or hydro resources

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Carbon Footprint

• Defined for elements of the power system (load, generation, transmission) as element’s incremental financial responsibility in response to a small change in carbon price

• Loads:

• Generation:

• Transmission:

( ( ))[ ( )] ( )n

n nC

LMP tL t L t

P

CF

( ( ) ( ))[ ( )] n n

nC

OM t G tG t

P

CF

( ( ) ( ))[ ( )] r r

rC

SP t F tF t

P

CF

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Carbon Footprint Theorem

• Carbon footprint of each element is proportional to a relevant marginal indicator:

• Carbon footprints of all elements of the grid add up to system-wide carbon emissions:

[ ( )] ( ) ( )n n nL t MCI t L t CF

[ ( )] ( ) ( )Cn n nG t t G t CF

[ ( )] ( ) ( )r r rF t SCI t F t CF

1 1 1

( )( ) ( )

( ) ( ) ( ) ( ) ( ) ( )N N R

Cn n n n r r

n n r

TransmissionLoad Generation

System MCI t L t t G t SCI t F

CFCF CF

CF

( ) ( )System tCF

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Renewable Portfolio Standards

• RPS Policy considered as investment optimization problem solved by a notional RPS Agency: – Minimize total subsidy to renewable generators in order to achieve a

predetermined target.

• RPS policy can be implemented in parallel to carbon regulation (e.g. cap-and-trade or carbon tax)

• Traditional RPS policy: target is set terms of total generation by renewable resources

• Carbon Controlling RPS policy: target is set in terms of total carbon emissions in the electrical grid

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RPS as an Investment Problem

• RPS Agency provides subsidy to renewable resource developers

• At each location there is an offer curve Z(R) – required subsidy from RPS agency to build R MW of installed capacity of renewable generation

• The RPS Agency can either optimize RPS target given total investment level of investment or minimize investments required to achieve set target

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RPS Theorem

• Traditional RPS– Prefers locations with the lowest

ratios of

– - capacity factor of renewable resource

– Optimal solution yields an RPS price [$/MWh]

– Subsidy is paid to funded renewable generators based on the following formula

• Carbon controlling RPS– Prefers locations with the lowest

ratios of

– - generation weighted average marginal carbon offset of renewable resource

– Optimal solution yields an RPS price [$/tCO2]

– Subsidy is paid to funded renewable generators based on the following formula

( )krenk

Z R

renk

( ) ( )RSubsidy t P G t

( )kCk

Z R

Ck

( ) ( ) ( )CC kSubsidy t P G t t

[ ]( )k CG t P CF

RPCP

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RPS Example

Zone AOnPeak Hours: 4160Fuel on the Margin = CoalMarg. Carbon Intensity = 1.08 T/MWhCoal Price = $2/MMbtuMarket Heat Rate = 12,000Wind Capacity Factor = 20%

OffPeak Hours: 4600Fuel on the Margin = Nat. GasMarg. Carbon Intensity = 0.4 T/MWh Gas Price = $5/MMbtuMarket Heat Rate = 7,000Wind Capacity Factor = 40%

Zone BOnPeak Hours: 4160Fuel on the Margin = Nat. GasMarg. Carbon Intensity = 0.51 T/MWhGas Price = $5/MMbtuMarket Heat Rate = 9,000Wind Capacity Factor = 20%

OffPeak Hours: 4600Fuel on the Margin = Nat. Gas

Marg. Carbon Intensity = 0.4 T/MWhGas Price = $5/MMbtuMarket Heat Rate = 7,000Wind Capacity Factor = 40%

ConstrainedOnPeak

Not constrainedOffPeak

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RPS Example Results

Zone A Zone B Total Zone A Zone B TotalBudget Constraint ($K)Required subsidy in $/MWh of renewable energy $27.98 $25.85 $25.85 $27.98 $25.85 $27.98Required subsidy in $/T of carbon offset $45.74 $59.34 $59.34 $45.74 $59.34 $45.74Subsidized wind capacity (MW) - 145 145 134 - 134 Renewable energy generated (GWh) - 387 387 357 - 357 CO2 Emissions Offset (000 T) - 169 169 219 - 219 RPS Price ($/MWh) $25.85 $27.98RPS Price ($/T of CO2) $59.34 $45.74

Traditional RPS Carbon Controlling RPS

$10,000 $10,000

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Conclusions

• Marginal Carbon Intensity in power systems varies significantly over time and in the presence of transmission congestion – by location

• System-wide carbon emissions could be decomposed among individual loads, generating units and system constraints. This decomposition is based on marginal properties – marginal carbon intensity for loads, marginal carbon offsets for generators and shadow carbon intensities for binding constraints

• The RPS approach presently implemented in the US and in other countries should not be considered efficient as long as ultimate goal of the RPS policy is the reduction of greenhouse gases.

• An alternative approach based on the subsidy rule compensating renewable generation for the negative carbon footprint they provide achieves the optimal strategy in targeting carbon emissions through RPS.

• This alternative design would require a precise calculation of locational marginal carbon intensity which could be provided by system operators responsible for the operations of regional electrical grids and a design of renewable cost allocation rules by regulatory agencies

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Aleksandr Rudkevich

arudkevich@crai.com

Charles River Associates

John Hancock Tower

200 Clarendon Street, T-33

Boston, MA 02116

(617) 425-6446