What Investments Should We Make Now? Transmission ......What Investments Should We Make Now?...
Transcript of What Investments Should We Make Now? Transmission ......What Investments Should We Make Now?...
![Page 1: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/1.jpg)
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
![Page 2: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/2.jpg)
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)
![Page 3: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/3.jpg)
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
![Page 4: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/4.jpg)
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
![Page 5: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/5.jpg)
Stochastic Solution
• High renewables • Generation
closer to California
• Unique stochastic lines
Stochastic 2023 Plan: WECC 3-Scenario Test Case
![Page 6: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/6.jpg)
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)
![Page 7: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/7.jpg)
• 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)
![Page 8: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/8.jpg)
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)
![Page 9: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/9.jpg)
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
![Page 10: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/10.jpg)
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
![Page 11: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/11.jpg)
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
![Page 12: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/12.jpg)
• 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
![Page 13: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/13.jpg)
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)
![Page 14: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/14.jpg)
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?
![Page 15: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/15.jpg)
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)
![Page 16: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/16.jpg)
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!)
![Page 17: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/17.jpg)
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
![Page 18: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/18.jpg)
Next: Analysis with Cornell Team of Champlain-Hudson Power Express
3.2
• Structure decision tree
with key uncertainties
• SuperOPF to populate tree with outcomes
![Page 19: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/19.jpg)
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)
![Page 20: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/20.jpg)
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?
![Page 21: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/21.jpg)
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
![Page 22: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/22.jpg)
Time to solve (s)
![Page 23: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/23.jpg)
Price Duration Curves
-10
10
30
50
70
90
0 50 100 150
Pric
e (€
/MW
h)
hours
UCTRUCLDC
![Page 24: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/24.jpg)
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
![Page 25: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/25.jpg)
• Reality: flow between control areas ≠ prediction by “least cost” models (E. Fisher, LBNL, FERC TransAtlantic InfraDay, Nov. 2013)
Assumption of “Efficient Trade”
4.2
![Page 26: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/26.jpg)
26
Comparing E.I. flows: Actual 2010 vs. MRN-NEEM
(draft results)
![Page 27: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/27.jpg)
27
Comparison of flow direction between regions – draft results
![Page 28: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/28.jpg)
• 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”
![Page 29: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/29.jpg)
• 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
![Page 30: What Investments Should We Make Now? Transmission ......What Investments Should We Make Now? Transmission Investment Assessment Under Uncertainty August 5, 2014 Benjamin F. Hobbs Director,](https://reader033.fdocuments.us/reader033/viewer/2022060520/604e9a036a47006973053db9/html5/thumbnails/30.jpg)
Questions?