Parameterizing the variability

and uncertainty of wind and

solar in CEMs 

Bethany Frew 

EIA Electric Capacity Expansion Modelling Workshop 

Washington, D. C.

July 11, 2016 
2

1. Capacity Value (CV): a metric of the firm-power 

equivalent for a given installation

2. Curtailed Energy: generated power that exceeds 

load must be curtailed

3. Forecasting Error Reserve Requirement: additional 

operating reserves induced by uncertainty in supply 

from a generator

The big 3 variability and uncertainty parameters
3

1. Capacity Value (CV): a metric of the firm-power 

equivalent for a given installation

2. Curtailed Energy: generated power that exceeds 

load must be curtailed

3. Forecasting Error Reserve Requirement: additional 

operating reserves induced by uncertainty in supply 

from a generator

The big 3 variability and uncertainty parameters
4

• We care about Effective Load Carrying Capability (ELCC) in 

highest Loss of Load Probability (LOLP) hours

• See Hasche et al. (2011) for inter-annual variability

Modeling CV in CEMs – ideal treatment

Load − VG
5

• ELCC estimations

o Approximate the relationship between capacity 

additions and LOLP 

o e.g., Z-method (Dragoon and Dvortsov 2006), Garver’s

method (Garver 1966), and Garver’s method extended to 

multistate generators (D’Annunzio and Santoso 2008)

• Capacity factor proxy

o Applied to “high risk” hours (e.g., Milligan and Parsons 1999 

for wind, Madaeni et al. 2013 for solar)

o Applied to top load hours in load duration curve (LDC)

– RPM and future ReEDS (Hale et al. 2016)

Modeling CV in CEMs – simplifications 
6

RPM and future ReEDS LDC approach: CV

Hour

LDC

NLDC

Demand (MW)

NLDC(δ)

Capacity value 

of existing VG

Marginal 

capacity value 

of new VG

100 hrs
7

1. Capacity Value (CV): a metric of the firm-power 

equivalent for a given installation

2. Curtailed Energy: generated power that exceeds 

load must be curtailed

3. Forecasting Error Reserve Requirement: additional 

operating reserves induced by uncertainty in supply 

from a generator

The big 3 variability and uncertainty parameters
8

Modeling curtailment (surplus) in CEMs – ideal

Curtailed VG

Mingen
9

• Implicit integration cost function

o e.g., WITCH

• Step-wise marginal curtailment function

o e.g., MESSAGE

• Statistical parameterization

o e.g., current ReEDS

• LDC approach

o REMIND-D (Ueckerdt et al. 2015)

o RPM (Hale et al. 2016)

• Simplified 8760 dispatch

o Future ReEDS

Modeling curtailment – simplifications 
10

• Curtailment based on interplay of NLDC and mingen

RPM LDC approach: curtailments

Hour

LDC

NLDC

Demand (MW)

NLDC(δ)

mingen curtailment

incremental 

curtailment for 

new VG

mingen (δ)

incremental 

curtailment for 

new thermal 

capacity
11

Future ReEDS curtailment and storage via dispatcher

Initial mingen

Final mingen

Curtailment reduction from storage

Curtailment reduction from 

thermal unit shutdown

Final curtailment

Netload

Approximated 

netload

Initial curtailment
12

• Improving the representation of VG variability and 

uncertainty in CEMs is increasingly important as VG 

penetration levels grow

• There are different ways to model CV and 

curtailment, with varying computational and data 

requirements

• RPM and ReEDS are working toward 8760 exogenous 

methods

Summary
13

ReEDS team

David Bielen

Ph.D. Economics

Duke University

Jonathan Ho

M.S. Engineering Science 

Johns Hopkins University

Nate Blair

M.S./M.B.A.

University of Wisconsin, Madison

Venkat Krishnan

Ph.D. Electrical Engineering

Iowa State University

Stuart Cohen

Ph.D. Mechanical Engineering

University of Texas, Austin

Trieu Mai

Ph.D. Theoretical Physics

University of California, Santa Cruz

Wesley Cole

Ph.D. Chemical Engineering

University of Texas, Austin

Benjamin Sigrin

M.S. Energy & Earth Resources, M.P. Aff

University of Texas, Austin

Kelly Eurek 

M.S. Engineering & Technology Management 

Colorado School of Mines

Daniel Steinberg

M.E.Sc. Environmental Economics & Energy 

Analysis

Yale School of Forestry & Environmental Studies

Bethany Frew

Ph.D. Civil & Environmental Engineering

Stanford University

Thanks also: James Richards, Brady Stoll, Elaine Hale, 

Paul Denholm

Funding provided by: DOE Office of Energy Efficiency and 

Renewable Energy, Solar Energy Technologies Office, and 

Energy Policy and Systems Analysis 
14

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References and additional sources