What Investments Should We Make Now?

Transmission Investment Assessment Under Uncertainty

August 5, 2014

Benjamin F. Hobbs Director, JHU Environment, Energy, Sustainability & Health Institute

Theodore & Kay Schad Professor of Environmental Management, JHU

Richard Schuler, Cornell University Saamrat Kasina & Pearl Donohoo, JHU

Emily Fisher, LBNL

Outline

1. Method overview 2. Solving large problems

2.1 100x106 variables 2.2 Prescreening of alternatives (Pearl)

3. Analyses: 3.1 2 to 4 decision stages (Saamrat) 3.2 Champlain-Hudson Express

4. Improving models of short-run flexibility 4.1 Convex approximation of unit commitment (Saamrat) 4.2 Trading inefficiencies (Emily)

1. Multi-Stage Stochastic Transmission Planning

Stage 1: “Today’s Choices”

Investments in: • Transmission • Generation

Uncertainty

Scenarios of • $ Fuels • Load growth • Technology • Policies

• Future known with certainty in

Stage 2

• Aligned generation and

transmission objectives

- Nodal pricing + Perfect Competition

- Efficient trade

• Generation

- No unit commitment constraints/costs

Assumptions: Stage 2: “Tomorrow’s

Choices”

• Investments in trans / gen • Operations

General Formulation

“Today’s Choices”

Uncertainty “Tomorrow’s Choices”

MIN C1X1 + Σscenarios S PS * C2X2,S

A1,1 X1 < B1 {A2,1,S X1 + A2,2,SX2,S < B2,S }, ∀S

• Constraints include: -Kirchhoff’s Laws

-Generator and transmission capacity / operating restrictions

-Siting restrictions

-Emissions caps, renewable portfolio standards

Stochastic Solution

• High renewables • Generation

closer to California

• Unique stochastic lines

Stochastic 2023 Plan: WECC 3-Scenario Test Case

Outline

1. Method overview 2. Solving large problems

2.1 100x106 variables 2.2 Prescreening of alternatives (Pearl)

3. Analyses: 3.1 2 to 4 decision stages (Saamrat) 3.2 Champlain-Hudson Express

4. Improving models of short-run flexibility 4.1 Convex approximation of unit commitment (Saamrat) 4.2 Trading inefficiencies (Emily)

• Execute stochastic transmission and generation expansion planning at scale, on real-world data sets

- Stochastic models are needed, - But no commercial software available for stochastic investment

planning • Produce solutions in tractable run-times, with bounds • Develop scenario selection algorithms for execution on commodity

workstations, not just supercomputers

2.1 Goals of Decomposition Effort (F. Munoz / J.-P. Watson)

Operations Scenario 1

Investments Scenario 1

Operations Scenario 2

Investments Scenario 2

Operations Scenario N

Investments Scenario N

…

…

Subproblem 1 Subproblem 2 Subproblem 3

Progressive Hedging enforces non-anticipativity constraints

One 1st Stage investment plan for all scenarios

Progressive Hedging (Rockafellar/Wets): • Converges if problem convex, good heuristic for mixed-integer problems • Available: PySP package of Pyomo (Sandia NL) • Used to solve large stochastic Unit Commitment problems

Improvements: • Accelerate convergence through variable fixing and/or slamming , e.g.:

• Fix variable if line is needed in all scenarios • All alternatives considered only in first iterations

• New lower bounds from dual decomposition (S. Ryan, Iowa State)

In Practice: • WECC-240 and 100 scenarios: CPLEX No feasible solution after 1 day of CPU time PH 20 iterations/15 min yields 1.5% optimality gap

Decomposition by Progressive Hedging (F. Munoz/J.-P. Watson)

St. Clair Screening Model Challenge: • Expert judgment is insufficient to narrow the set • Current methods cannot consider the full set of lines

>13,900 possible transmission line

corridors

2.2 A Problem: Too Many Options

St. Clair Screening Model

The intuition: look for corridors which have any investment in any scenario.

H.P. St. Clair [1953]

All Corridors

Linear Planning Model

Integer Investments

Scenarios

Solution: St. Clair Screening Model

0

10,000

20,000

30,000

40,000

50,000

Corridors LinesPre-Screened Set Screened Set

95% Reduction 97% Reduction (629) (1,081)

Reduction in Search Space

• Combine engineering heuristic and linear optimization

• >97% reduction in investment variables

References: “Algorithmic investment screening for wide-area Transmission Network Expansion Planning.” P Donohoo, M Webster, I Perez-Arriaga. Power and Energy Society General Meeting (PES), Vancouver, Canada, 2013 “Design of Wide-Area Electric Transmission Networks under Uncertainty: Methods for Dimensionality Reduction.” P Donohoo-Vallett. Doctoral thesis. Massachusetts Institute of Technology, February 2014.

Recap of St. Clair Screening Model

Outline

1. Method overview 2. Solving large problems

2.1 100x106 variables 2.2 Prescreening of alternatives (Pearl)

3. Analyses: 3.1 Deterministic to 3 uncertain stages (Saamrat) 3.2 Champlain-Hudson Express

4. Improving models of short-run flexibility 4.1 Convex approximation of unit commitment (Saamrat) 4.2 Trading inefficiencies (Emily)

3.1 Possible biases in stochastic multi-stage optimization

• Three stage model: might it avoid those biases?

2014 2024 2034 2044

• Two uncertain stages bias which way?

• One uncertain stageunderbuild in stage 1 (because uncertainty eliminated)?

• Deterministicoverbuild in stage 1?

Simple example - CO2 price uncertainty

Aggr

essiv

e N

on-a

ggre

ssiv

e

*Carbon price (p) ranges from $37/t to $86/t (WECC-2013 transmission scenarios)

Best 2014 lines change as you consider more stages of uncertainty & decisions

Optimal 3 stage: Consider all

(2024, 2034, 2044) uncertainties

Optimal line not built

Suboptimal line built

1 Stage: Consider only

2024 uncertainty

2 Stage: Consider 2024,

2034 uncertainties

Deterministic: Ignore all

uncertainty. Assume no CO2 price

(Preliminary Results!)

Value of considering more uncertainties = improvement in expected costs

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2

$ B

VSSu = Cost with 1st-stage investments imposed minus Optimal Cost

• The timing and cost of the

uncertainties matter

• Showed how to optimize generation & transmission investment over multiple uncertain stages

• Showed the value of stochastic solutions and how they can differ from deterministic solutions

2% of E(PV) of Generation investment cost 23% of E(PV) of Transmission investment cost

vs Deterministic

vs 1 stage

vs 2 stage

Next: Analysis with Cornell Team of Champlain-Hudson Power Express

3.2

• Structure decision tree

with key uncertainties

• SuperOPF to populate tree with outcomes

Outline

1. Method overview 2. Solving large problems

2.1 100x106 variables 2.2 Prescreening of alternatives (Pearl)

3. Analyses: 3.1 2 to 4 decision stages (Saamrat) 3.2 Champlain-Hudson Express

4. Improving models of short-run flexibility 4.1 Convex approximation of unit commitment (Saamrat) 4.2 Trading inefficiencies (Emily)

4.1 Challenge: A more accurate depiction of generator operating constraints: Start-up & Min-Load

• Load-duration curve (LDC) / merit-order dispatch: Does it distort impact of new transmission on short-run flexibility?

• Task: Incorporate convexified (“tight relaxed”) Unit Commitment models (TRUC) in planning models • Relax 0-1 commitment/start-up variables

= portion of capacity of particular type committed • Energy, spin, rampability all limited by portion committed

• Here: How well do LDC & TRUC approximate: • Costs? • Prices?

• How do those approximation errors depend upon: • system size? • generation mix?

Total Cost = f(System size)

10500

11000

11500

12000

12500

13000

13500

14000

1x 2x 3x 4x

KEur

o/w

eek

UCTRUCLDC

• Case study: 11 (“1x”) to 44 (“4x”) generators, 168 hours • No transmission

Time to solve (s)

Price Duration Curves

-10

10

30

50

70

90

0 50 100 150

Pric

e (€

/MW

h)

hours

UCTRUCLDC

Errors in prices, start-up costs

1300

1350

1400

1450

1500

UC TRUC

k€/w

eek

Start-up costs (1x)

Price errors

02468

10

1x 2x 3x 4x

RMSE

(€/M

Wh)

TRUCLDC

• Reality: flow between control areas ≠ prediction by “least cost” models (E. Fisher, LBNL, FERC TransAtlantic InfraDay, Nov. 2013)

Assumption of “Efficient Trade”

4.2

26

Comparing E.I. flows: Actual 2010 vs. MRN-NEEM

(draft results)

27

Comparison of flow direction between regions – draft results

• Reality: flow between control areas ≠ prediction by “least cost” models

Benefits of new transmission actually >> or << than anticipated?

Might: • justify inefficient lines • fail to justify efficient lines

• Want a more flexible system? Enlarged markets/efficient trade might be better than new lines (J. Bushnell, UC Davis, “The Real Balkanization of the Grid” Blog, Nov. 3. 2014)

First intelligently use what you got? Market enlargement & transmission additions together

best?

Assumption of “Efficient Trade”

• Theory of market barriers: how can they be represented, & how do they affect trade and value of transmission? (CERTS) risk: sins of commission/omission

• For realistic contexts, what is: value of transmission

vs value of market enlargement

Similar in magnitude? (van der Weijde & Hobbs, JRE, 2011)

Research Questions

Questions?