Scarcity Pricing Market Design Considerations
Anthony Papavasiliou, Yves SmeersCenter for Operations Research and Econometrics
Université catholique de Louvain
CORE Energy Day
April 16, 2018
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Outline
1 ContextMotivation of Scarcity PricingHow Scarcity Pricing WorksResearch Objective
2 Building Up Towards the Benchmark Design (SCV)Energy-Only Real-Time MarketEnergy Only in Real Time and Day AheadAdding Uncertainty in Real TimeReserve Capacity
3 A Sketch of the Alternative Designs
4 Illustration on a Small Example
5 Conclusions and Perspectives
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Outline
1 ContextMotivation of Scarcity PricingHow Scarcity Pricing WorksResearch Objective
2 Building Up Towards the Benchmark Design (SCV)Energy-Only Real-Time MarketEnergy Only in Real Time and Day AheadAdding Uncertainty in Real TimeReserve Capacity
3 A Sketch of the Alternative Designs
4 Illustration on a Small Example
5 Conclusions and Perspectives
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Challenges of Renewable Energy Integration
Renewable energy integration
depresses electricity prices
requires flexibility due to (i) uncertainty, (ii) variability, (iii)non-controllable output
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Motivation for Scarcity Pricing
Scarcity pricing: adjustment to price signal of real-timeelectricity markets in order to compensate flexibleresourcesDefinition of flexibility for this talk:
Secondary reserve: reaction in a few seconds, fullresponse in 7 minutesTertiary reserve: available within 15 minutes
such as can be provided bycombined cycle gas turbinesdemand response
We will not be addressing sources of flexibility for whichscarcity pricing is not designed to compensate (e.g.seasonal renewable supply scarcity)
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The CREG Scarcity Pricing Studies
First study (2015): How would electricity prices change ifwe introduce ORDC (Hogan, 2005) in the Belgian market?Second study (2016): How does scarcity pricing dependon
Strategic reserveValue of lost loadRestoration of nuclear capacityDay-ahead (instead of month-ahead) clearing
Third study (2017): Can we take a US-inspired designand plug it in to the existing European market?
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Scarcity Pricing Adder Formula
In its simplest form, the scarcity pricing adder is computed as
(VOLL− MC(∑
g
pg)) · LOLP(R),
whereVOLL is the value of lost loadMC(
∑g pg) is the incremental cost for meeting an
additional increment in demandR is the amount of capacity that can respond within animbalance intervalLOLP : R+ → [0,1] is the loss of load probability
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Generator Example
Assume the following inputs:Day-ahead energy price: λPDA = 20 e/MWhDay-ahead reserve price: λRDA = 65 e/MWhReal-time marginal cost of marginal unit: 80.3 e/MWhReal-time reserve price: λRRT = 3.9 e/MWhReal-time energy price: λPRT = 84.2 e/MWhGenerator capacity: P+
g = 125 MW
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Forward Reserve Awarded, Not Deployed
Settlement Formula Price Quantity Cash flowtype [e/MWh] [MW] [e/h]
DA energy λPDA · pDA 20 pDA = 0 0DA reserve λRDA · rDA 65 rDA = 25 1625RT energy λPRT · (pRT − pDA) 80.3 pRT = 100 8030
Total 9655
Table: Without Adder
Settlement Formula Price Quantity Cash flowtype [e/MWh] [MW] [e/h]
DA energy λPDA · pDA 20 pDA = 0 0DA reserve λRDA · rDA 65 rDA = 25 1625RT energy λPRT · (pRT − pDA) 84.2 pRT = 100 8420RT reserve λRRT · (rRT − rDA) 3.9 rRT = 25 0
Total 10045
Table: With Adder
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Forward Reserve Awarded And Deployed
Settlement Formula Price Quantity Cash flowtype [e/MWh] [MW] [e/h]
DA energy λPDA · pDA 20 pDA = 0 0DA reserve λRDA · rDA 65 rDA = 25 1625RT energy λPRT · (pRT − pDA) 80.3 pRT = 125 10037.5
Total 11662.5
Table: Without Adder
Settlement Formula Price Quantity Cash flowtype [e/MWh] [MW] [e/h]
DA energy λPDA · pDA 20 pDA = 0 0DA reserve λRDA · rDA 65 rDA = 25 1625RT energy λPRT · (pRT − pDA) 84.2 pRT = 125 10525RT reserve λRRT · (rRT − rDA) 3.9 rRT = 0 -97.5
Total 12052.5
Table: With Adder
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Focus of this Presentation
Focus of this presentation: in order to back-propagate thescarcity signal
When should day-ahead reserve auctions be conducted?Before, during, or after the clearing of the energy market?Do we need co-optimization in real time?Do we need virtual virtual bidding?
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Methodology
Consumers
Random net
injectionProducers
RT energy
market
RT reserve
market
ORDC
Real-time market
Virtual tradersVirtual traders
Consumers
Producers
DA energy
market
DA reserve
market
Day-ahead market
Virtual traders
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The Eight Models
Simultaneous DA RT co-optimization Virtualenergy and reserves of energy/reserve trading
SCV X X XSCP X XSEV X XSEP XRCV X XRCP XREV XREP
The dilemmas of the market design:
Simultaneous day-ahead clearing of energy and reserve, or Reservefirst (S/R)?
Cooptimization of energy and reserve in real time, or Energy only (C/E)?
Virtual trading, or Physical trading only (V/P)?
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Outline
1 ContextMotivation of Scarcity PricingHow Scarcity Pricing WorksResearch Objective
2 Building Up Towards the Benchmark Design (SCV)Energy-Only Real-Time MarketEnergy Only in Real Time and Day AheadAdding Uncertainty in Real TimeReserve Capacity
3 A Sketch of the Alternative Designs
4 Illustration on a Small Example
5 Conclusions and Perspectives
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Energy-Only Real-Time Market
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Notation
SetsGenerators: GLoads: L
ParametersBid quantity of generators: P+
g
Bid quantity of loads: D+l
Bid price of generators: CgBid price of loads: Vl
DecisionsProduction of generators: pRTgConsumption of loads: dRTl
Dual variablesReal-time energy price: λRT
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Model
Just a merit-order dispatch model:
max∑l∈L
Vl · dRTl −∑g∈G
Cg · pRTg
pRTg ≤ P+g ,g ∈ G
dl ≤ D+l , l ∈ L
(λRT ) :∑g∈G
pg =∑l∈L
dl
pg ,dl ≥ 0,g ∈ G, l ∈ L
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Energy-Only in Real Time and Day Ahead
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Additional Notation
DecisionsDay-ahead energy production of generator: pDAgDay-ahead energy consumption of load: dDAl
Dual variablesDay-ahead energy price: λDA
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ModelGenerator profit maximization:
maxλDA · pDAg + λRT · (pRTg − pDAg)− Cg · pRTg
pRTg ≤ P+g
pRTg ≥ 0
Load profit maximization:
max−λDA · dDAl + Vl · dRTl − λRT · (dRTl − dDAl)
dRTl ≤ D+l
dRTl ≥ 0
Market equilibrium: ∑g∈G
pRTg =∑l∈L
dRTl∑g∈G
pDAg =∑l∈L
dDAl
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Remarks
Back-propagation: from KKT conditions of profitmaximization, we have
λDA = λRT
In fact, day-ahead and real-time parts of the model can becompletely decoupledWe have introduced virtual trading: agents can takepositions in the day-ahead market which do not correspondto their physical characteristics
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Adding Uncertainty in Real Time
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Additional Notation
SetsSet of uncertain real-time outcomes (e.g. renewable supplyforecast errors, demand forecast errors): Ω
ParametersReal-time profit of agent: ΠRTg,ω
FunctionsRisk-adjusted profit of random payoff: Rg : RΩ → R
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Model
Generator profit maximization:
maxλDA · pDAg +Rg(ΠRTg,ω − λRTω · pDAg),
whereΠRTg,ω = (λRTω − Cg) · pRTg,ω
Load profit maximization:
max−λDA · dDAl +Rl(ΠRTl,ω + λDAω · dDAl)
whereΠRTl,ω = (Vl − λRTω) · dRTl,ω
Day-ahead market equilibrium:∑g∈G
pDAg =∑l∈L
dDAl
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Modeling the Risk Function R
How do we model attitude of agent towards risk, R?
Let’s consider the conditional value at risk, CVaR
ParametersPercent of poorest scenarios considered in evaluation ofrisked payoff: αgProbability of outcome ω: pω
VariablesConditional value at risk: CVaRgValue at risk: VaRgAuxiliary variable for determination of risk-adjustedreal-time payoff: ug,ω
Dual variables:Risk-neutral probability of agent: qg,ω
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Modeling the Risk Function R (cont.)
There exists a linear programming formulation of R
For example, the generator problem reads:
maxλDA · pDAg + CVaRg
CVaRg = VaRg −1αg
∑ω
pω · ug,ω
(qg,ω) : ug,ω ≥ VaRg − (ΠRTg,ω − λRTω · sDAg)
ug,ω ≥ 0
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RemarksTwo possible interpretations of profit ΠRT :
Correct interpretation: λRTω and ΠRTg,ω are parametersfor day-ahead profit maximizationIncorrect interpretation: λRTω and ΠRTg,ω are variables forday-ahead profit maximizationThe two interpretations produce a different result
max(R[max]) is different from max(R)Second model can produce out-of-merit dispatch in real time
Day-ahead price can be potentially different from averagereal-time price:
λDA = EQg [λRTω] =∑ω∈Ω
qg,ω · λRTω, ∀g ∈ G ∪ L
But if there is a single risk-neutral agent with an infinitelydeep pocket, then
λDA = E[λRTω] =∑ω∈Ω
pω · λRTω
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Reserve Capacity in Real Time
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Additional Notation
SetsORDC segments: RL
ParametersORDC segment valuations: MBRlORDC segment capacities: DRlramp rate: Rg
DecisionsReal-time demand for reserve capacity: dRRTl,ωReal-time supply of reserve capacity: rRTg,ω
Dual variablesReal-time price for reserve capacity: λRRT
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Model
Real-time co-optimization of energy and reserve for outcome ω ∈ Ω:
max∑l∈RL
MBRl · dRRTl +∑l∈L
Vl · dl −∑g∈G
Cg · pg
(λRT ) :∑g∈G
pRTg =∑l∈L
dRTl
(λRRT ) :∑
g∈G∪L
rRTg =∑l∈RL
dRRTl
pRTg ≤ P+g,ω, rRTg ≤ Rg , pRTg+rRTg ≤ P+
g,ω, g ∈ G
dl ≤ D+l , rRTl ≤ Rl , rRTl ≤ dRTl , l ∈ L
dRRTl ≤ DRl , l ∈ RL
pRTg , rRTg ≥ 0, g ∈ G, dRTl , rRTl ≥ 0, l ∈ L, dRRTl ≥ 0, l ∈ RL
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Remarks
Suppose that a given generator gis simultaneously offering energy (pRTg > 0) and reserve(rRTg > 0)is not constrained by ramp rate (rRTg < Rg)
We have the following linkage between the energy and reservecapacity price:
λRTω − Cg = λRRTω
This no-arbitrage relationship is the essence of scarcity pricing
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Reserve Capacity in Day Ahead
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Additional Notation
DecisionsDay-ahead supply of reserve capacity: rDAg
Dual variablesDay-ahead price for reserve capacity: λRDA
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ModelGenerator profit maximization:
maxλDA · pDAg + λRDA · rDAg +
Rg(ΠRTg,ω − λRTω · pDAg − λRRTω · rDAg),
where
ΠRTg,ω = (λRTω − Cg) · pRTg,ω + λRRTω · rRTg,ω
Load profit maximization:
max−λDA · dDAl + λRDA · rDAl +
Rl(ΠRTl,ω + λRTω · dDAl − λRRTω · rDAl),
where
ΠRTl,ω = (Vl − λRT ) · dRTl + λRRT · rRTl,ω
Day-ahead market equilibrium:∑g∈G
pDAg =∑l∈L
dDAl ,∑
g∈G∪L
rDAg = 0
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Remarks
No need to explicitly introduce ORDC in day-ahead market:
λRDA = EQg [λRRTω] =∑ω∈Ω
qg,ω · λRRTω,∀g ∈ G ∪ L
and λRRT is already augmented by ORDC in real-timemarketShould the day-ahead auction explicitly impose physicalconstraints? This is linked to the question of virtual trading:
+ Imposing explicit physical constraints may move us awayfrom the pure financial market equilibrium
- Simple examples indicate that the equilibrium solution mayrequire unrealistic liquidity in the day-ahead market
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To Summarize
We have arrived at our first target model: SCVSimultaneous day-ahead clearing of energy and reserveCo-optimization of energy and reserve in real timeVirtual trading
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Outline
1 ContextMotivation of Scarcity PricingHow Scarcity Pricing WorksResearch Objective
2 Building Up Towards the Benchmark Design (SCV)Energy-Only Real-Time MarketEnergy Only in Real Time and Day AheadAdding Uncertainty in Real TimeReserve Capacity
3 A Sketch of the Alternative Designs
4 Illustration on a Small Example
5 Conclusions and Perspectives
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Moving from Virtual to Physical Trading
It is easy to replace virtual trading (V) with physical trading (P),by introducing physical constraints in the day-ahead model
For example, for generators:
pDAg + rDAg ≤ P+g
rDAg ≤ Rg
rDAg ≥ 0
However, we need a day-ahead ORDC, because otherwisethere is no day-ahead reserve capacity demand in the model
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Moving from Real-Time Co-optimization to Energy-OnlyTrading
It is similarly easy to switch from real-time co-optimization ofenergy and reserve to energy-only trading by switchingbetween co-optimization and merit order dispatch in realtime
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Moving from Simultaneous Day-Ahead Clearing toReserve First
Qualitatively, we want to capture the difference between thefollowing:
Simultaneous auctioning: system operator co-optimizes,taking into account all the relevant inter-dependencies ofpower production and reserve capacitySequential auctioning: agents determine opportunity costson the basis of possibly inaccurate forecasts of the systemstate for the following day
We formulate the problem as a multistage stochasticequilibrium by nesting risk functions (Philpott, 2016)
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Sequence of Events
Decide
DA reserve
State of the
system in the
following day
Decide
DA energyRT dispatch
Revelation of
RT imbalance
Type of day: assessment of the TSO for what quantity of operating reservewill be required for the following day
In line with current effort of ELIA to transition towards dynamic reserve sizingand procurement in the day ahead (De Vos, 2018)
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Populating the Tree with Data
Denote a given node as (t , ω), where t is stage and ω isoutcome
No specific random vector is revealed in stage 2, instead thesystem state:
Node (2, 1): Low-risk dayNode (2, 2): Medium-risk dayNode (2, 3): High-risk day
In stage 3, renewable supply P+wind is revealed:
Node (3, 1): 111 MW; node (3, 2): 101 MWNode (3, 3): 156 MW; node (3, 4): 56 MWNode (3, 5): 206 MW; node (3, 6): 6 MW
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Outline
1 ContextMotivation of Scarcity PricingHow Scarcity Pricing WorksResearch Objective
2 Building Up Towards the Benchmark Design (SCV)Energy-Only Real-Time MarketEnergy Only in Real Time and Day AheadAdding Uncertainty in Real TimeReserve Capacity
3 A Sketch of the Alternative Designs
4 Illustration on a Small Example
5 Conclusions and Perspectives
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Numerical Illustration
Consider the following market bids:Blast furnace: 323 MW @ 38.13 e/MWhRenewable: 106 MW @ 35.71 e/MWhGas-oil: 5 MW @ 85 e/MWhLVN: 212 MW @ 315 e/MWhDemand: 100 MW (inelastic)
Percent of worst-case scenarios considered in CVaR:Blast furnace: α = 20%
Renewable: α = 30%
Gas-oil: α = 50%
LVN: α = 70%
Demand: α = 90%
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Summary Statistics
Consider the scenario tree of the previous section with equaltransition probabilities at every stage
λDA λRDA λRTS1 λRTS2 λRRTS1 λRRTS2 WelfareSCV 47.9 11.1 35.7 63.1 0 25 1,001,800SCP 55.3 18.2 35.7 63.1 0 25 1,005,260SEV 37.1 0 35.7 38.1 NA NA 996,369SEP 37.4 0.4 35.7 38.1 NA NA 996,556RCV 47.9 12.8 35.7 63.1 0 25 1,001,950RCP 50.6 25.0 35.7 63.1 0 25 1,007,120REV 37.1 0 35.7 38.1 NA NA 996,329REP 37.4 0.3 35.7 38.1 NA NA 996,452
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Outline
1 ContextMotivation of Scarcity PricingHow Scarcity Pricing WorksResearch Objective
2 Building Up Towards the Benchmark Design (SCV)Energy-Only Real-Time MarketEnergy Only in Real Time and Day AheadAdding Uncertainty in Real TimeReserve Capacity
3 A Sketch of the Alternative Designs
4 Illustration on a Small Example
5 Conclusions and Perspectives
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Conclusions
S/R C/E V/P Preliminary observationsSCV X X X Theoretical first-best, large (long and
short) positions in DA reserve marketSCP X X Mitigates DA reserve exposure with
minor effect on DA-RT price convergenceSEV X X Not reasonable: degenerates to energy-
only market without reserve marketSEP X Weak DA reserve capacity signal, not the
result of back-propagation of RT priceRCV X X Inflation of DA reserve price due to
uncertainty regarding TSO reserve needsRCP X Highest DA reserve priceREV X Same weakness as SEVREP Same attributes as SEP
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Perspectives
Multiple periodsMultiple reserve types
Differentiate secondary and tertiaryDifferentiate upward and downward
Unit commitment (per work of De Maere and Smeers)Additional features: pumped hydro, imports/exportsPractical questions:
width of ORDCeffects of switch every 4 hours on volatility of RT price
Computational challenges: regularized decomposition ofequilibrium models seems promising
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Thank You for Your Attention
For more information:[email protected]
http://uclengiechair.be/
https://perso.uclouvain.be/anthony.papavasiliou/public_html/
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