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A Hierarchical Framework for Long-Term PowerPlanning Models
Tang & Ferris
René Glogg
Dasun Perera
Martin Repoux
Quanjiang Yu
Zinal Winter School 2017
Outline
• Context of the problem
• Energy-economic model
• Solving methods
• Numerical example
19.01.2017 Winter School on Optimization 2017, Zinal 2
Context of the problem
• Where energy systems meet optimization• Distributed generation is getting popular
• Renewable energy integration• Flexible demand and generation• Real time pricing• Virtual power plants
• Number of parties involved• Power generation companies• Distributors + transmission• Regulators• Consumers
• Long term planning, system designing and operation is challenging
3
Optimization
19.01.2017 Winter School on Optimization 2017, Zinal
Scott & Michael (LANL Tech. Report, 2013)
Context of the problemAuthors Journal Year Method 1 2 3 4 5 6
Jayasekara et-al Ap. En. 2013 Bi: MINLP+LP √ x √ x x x
Movraj et-at Ap. En. 2016 Bi: MINLP+BB √ 1/2 √ x x x
Maroufmashat et-al
Egy 2015 MILP √ √ √ x x x
Rad & Moravej Egy 2017 BB x √ √ √ √ √
Bages & Elsayed EPSR 2017 BB x √ √ √ √ x
Tang & Ferris IEEE T POWER SYST
2015 MOPEC ++ √ √ √ √ ++
4
1. Node dispatch2. OPF3. System sizing problem4. Transmission planning A: Line
sizing5. Transmission Planning B: System
sizing/locating 6. Transmission Planning C:
ConnectivitySha & AIELLO (Energies, 2016)Scott & Michael (LANL Tech. Report, 2013)
19.01.2017 Winter School on Optimization 2017, Zinal
Context of the problem
5
Regional transmission organizations
(RTO)
Firm
Independent system operators
(ISO)
Scott & Michael (LANL Tech. Report, 2013)
Nash Equilibrium
19.01.2017 Winter School on Optimization 2017, Zinal
Model: Hierarchical framework
RTO
ISO Firm
Line capacity Prices - LMP
Generator Size
Real powerUnit commitment
19.01.2017 Winter School on Optimization 2017, Zinal 6
UPPER LEVEL:expansion
LOWER LEVEL: market = supply and demand
Expansion Model
• Minimization over expansion on specific transmission lines
• Uses information from the lower hierarchy, specifically what the LMP is and whether a generator is dispatched or not
19.01.2017 Winter School on Optimization 2017, Zinal 7
Optimal power flow model
• Solved by the ISO to manage grid operations and provide LMP
• Modeled by short term competitive behavior of firms
• Minimize cost of unit commitment
• Solved to equilibrium with the firm models, where each firm has the option to improve efficiency of existing generators or of retiring them
• Provides LMPs and unit commitments to upper hierarchy
19.01.2017 Winter School on Optimization 2017, Zinal 9
Generator Upgrades
The cost of generating units of energy is given by:
The paper models the impact of an investment by a diminishing rewards function , therefore:
New generator capacity or introduction may be accommodated by an additional hierarchy, but due to complexity it is preferable to use additional dispatch variables and constraints.
19.01.2017 Winter School on Optimization 2017, Zinal 11
Solution method: principle
RTO
ISO Firms
Line capacity Prices - LMP
Generator Size
Real powerUnit commitment
UPPER LEVEL: expansion
Derivative-free optimization
REQUIRES prices 𝒑𝒋𝝎
LOWER LEVEL: market
Multiple Optimization Problems
GIVES prices 𝒑𝒋𝝎
19.01.2017 Winter School on Optimization 2017, Zinal 12
Lower level: MOPEC
19.01.2017 Winter School on Optimization 2017, Zinal 13
KKT conditions of 𝑚𝑖𝑛𝑢,𝑔,𝑧,𝜃 σ𝑗∈𝐺 𝑢𝑗𝜔𝐶𝑗 𝑔𝑗
𝜔 , 𝑦𝑗 ∀𝜔 ∈ Ω
KKT conditions of 𝑚𝑖𝑛𝑦 σ𝜔∈Ω𝜋𝜔 σ𝑗∈𝐺𝑓(𝑢𝑗
𝜔𝐶𝑗 𝑔𝑗𝜔 , 𝑦𝑗 +Φ(𝑦𝑗)) ∀𝑓 ∈ 𝐹
+
=
CP
KKT conditions cannot be written due to binary variables 𝑢
Approximation for generator costs
𝑢𝑗𝜔𝐶𝑗 𝑔𝑗
𝜔, 𝑦𝑗 ሚ𝐶𝑗(𝑔𝑗𝜔, 𝑦𝑗)
19.01.2017 Winter School on Optimization 2017, Zinal 14
Solution method: MCP*
• Smooth and continuous model – KKT conditions can be derived
• Non-convexity of objective functions
Obtain good starting points for equilibrium
Convergence test
Solving the equilibrium
19.01.2017 Winter School on Optimization 2017, Zinal 15
2nd Solution method: RMCP
OBSERVATION: MCP does not change generators chosen in dispatch
Variables 𝑢 fixed inside each loop
Convexity of the objectives functions
Convergence test
Solving the equilibrium
19.01.2017 Winter School on Optimization 2017, Zinal 16
Results and observations
• Solved using PATH
• Same solutions with the two procedures
• RMCP converges faster
• Uniqueness issues Need to break symmetry
19.01.2017 Winter School on Optimization 2017, Zinal 17
Numerical Example
Graphical depiction of 14-bus example.
19.01.2017 Winter School on Optimization 2017, Zinal 18
Transmission ExpansionNash equilibrium gives us the dual variables at the upper hierarchy.jp
19.01.2017 Winter School on Optimization 2017, Zinal 20
Transmission Expansion Model(RTO)
Penalty function
Budgeted Transmission Expansion
• When increasing line limits, x , allow for a generator to be dropped from the active dispatch set in order to reduce operational cost.
• The remaining generators in the active set are forced to pick up the slack by increasing their production, which leads to an overall increase in the marginal cost.
• This has a direct impact on consumer cost because the LMP values, , correspond of the marginal cost.
• When the line expansion variable is sufficiently increased, it is possible for the LMP prices to either increase or decrease.
19.01.2017 Winter School on Optimization 2017, Zinal 22
jp
jp
Conclusion
• Framework which takes into account RTO, ISO and firms interactions
• Energy modelling issues• Generator expansion
• RTO objective function
• AC vs. DC power flow equations
• Uncertainties
• Only 2 horizons: scaling of the problem and interactions?
19.01.2017 Winter School on Optimization 2017, Zinal 23