Download Modeling competitive equilibrium prices for energy and balancing

Modeling competitive equilibrium prices in
exchange-based electricity markets
The case of non-convex preferences
André Ortner, Daniel Huppmann, Christoph Graf
5th International PhD-Day of the AAEE Student Chapter
Czech Technical University
Prague, 8th November 2016
DI André Ortner
Energy Economics Group
T: +43 1 58801 370367
[email protected]
Introduction
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Research questions
 What are competitive prices for balancing reserves in exchangebased electricity markets?
• Such prices should consider arbitrage effects / interlinkages with other market segments
• Prices should constitute market equilibria
• Explicitly consider non-convex preferences and indivisibilities of market players
 How can we derive such prices from bottom-up electricity market
models?
• Hypothesis: Optimal dual variables of market clearing conditions from “fixed-binary” MIP
models are not suitable for this task
 How do common model approaches differ with regard to
• Deviation in prices
• Deviation in dispatch and unit-commitment
• Resulting compensation payments
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Background
 In economic analysis of markets it is often justified to neglect
non-convex preferences of supply and demand (Starr, 1969)
• For a sufficiently large market the impact of non-convexities on prices is small
• In such case the standard neoclassical market model can be applied and equilibrium
prices can be derived from the dual variables of a linear program
 In capacity reserve auctions this assumption is often not valid
• Still mostly national capacity auctions within Europe
• Small number of participants to compete for a exogenously given amount of capacity
demand (typically ~5% of peak load)
• More strict flexibility requirements for reserves require an adequate representation of
technical capabilities of power units
 Oligopolistic structure in reserve auctions require benchmarks
for competitive prices
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Applied modeling approaches
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The social planner approach (SP)
Maximize welfare
Demand for electricity
Market clearing and
reserve requirements
Maximum consumption
Demand for pos. reserves
Demand for neg. reserves
Upper limit on output
Technical constraints
on output level
Lower limit on output
Upper limit on reserve provision
Lower limit on reserve provision
Mapping on/off states
Intertemporal
constraints
Maximum on-time
Maximum off-time
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The binary equilibrium approach (BE)
 Adapted approach by Huppmann/Siddiqui 2015:
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The binary equilibrium approach (BE)
 The binary decision problem of each generator
1
2
3
4
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The binary equilibrium approach (BE)
1 Quantities in case of spot market and reserve capacity auction
Generator optimization
problem
Fix
KKT conditions in case
of capacity reserve
provision
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The binary equilibrium approach (BE)
 The binary decision problem of each generator
1
2
3
4
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The binary equilibrium approach (BE)
2 Quantities when generator solely operates on spot market
Generator optimization
problem
KKT conditions
in two cases
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The binary equilibrium approach (BE)
 Binary variables additionally have a linking function
Actual generation variables are linked to variables in corresponding KKT conditions
In case of no reserve provision the linkage goes further
Also reserve variables are linked
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The binary equilibrium approach (BE)
 The binary decision problem of each generator
1
2
3
4
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The binary equilibrium approach (BE)
 Incentive-compatibility conditions
3 Compare profits to determine optimal commitment decision (
)
4 Compare profits of tree paths to determine optimal decision on
Additional function of binary
variables: On/Off switches
of correct variables
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Illustrative example
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Data
 Demand Side
• Characterization of residual load
of Germany in 2012
• Time series have been scaled in
order to fit to a smaller set of
generators
• Days have been selected to
represent a range of extreme and
average days
• Demand for reserves is
exogenous and ~ 5% of peak load
 Generation Side
• Ten representative plants
• Most important nonconvexities implemented
• Form of supply curve
imitates the actual average
supply curve
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Results
 Comparison of resulting spot prices of three modeling
approaches for different days
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Results
 Comparison of resulting reserve prices of three modeling
approaches for different days
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Results
 Generation deviations of each generator between the SP and
the BE model relative to total consumption for different days
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Results
 Required compensation payments for different days
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Conclusions and further research
 The proposed model approach allowed the formulation of a
mixed-integer linear problem formulation
 The framework allows to integrate non-convexities and to derive
commodity prices that constitute a competitive quasi-equilibrium
 Optimal dual prices of Social Planner model are quiet good
proxies and generation deviations are mostly below 10 percent of
load
 Not possible to eliminate all required compensation payments
 Small model size might overestimate the impact of nonconvexities in reality
 Model upscaling and the integration of quantity constraints and
combinatorial bids
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References
 Starr, Ross M. "Quasi-Equilibria in Markets with Non-Convex Preferences."
Econometrica 37, no. 1 (1969): 25-38.
 Scarf, H.E., 1994. The Allocation of Resources in the Presence of Indivisibilities,
Journal of Economic Perspectives 8, 111-128.
 Huppmann, D., Siddiqui, S., 2015. An exact solution method for binary
equilibrium problems with compensation and the power market uplift problem.
DIW Discussion Paper 1475.
 Hogan, W.W., Ring, B.J., 2003. On minimum-uplift pricing for electricity markets.
Electricity Policy Group.
 Gribik, P.R., Hogan, W.W., Pope, S.L., 2007. Market-Clearing Electricity Prices
and Energy Uplift Working Paper.
 O'Neill, R.P., Sotkiewicz, P.M., Hobbs, B.F., Rothkopf, M.H., Stewart Jr, W.R.,
2005. Efficient market-clearing prices in markets with non-convexities. European
Journal of Operational Research 164, 269-285.
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Background (1/2)
 Different market designs and pricing mechanisms have evolved
after liberalization
 In Pool-based markets large-scale mixed-integer optimization
models are solved by ISOs
• Participants submit cost structure and production capabilities of each unit
• Commodity prices and side-payments are derived from the optimal solution of
these models
 Exchange-based markets apply linear pricing schedules
• Power exchanges receive bidding curves from buyers and sellers of electricity and run a
large-scale MPEC model (+ price & quantity constraints)
• Common practice is to avoid additional compensation payments
 How to model prices in exchange-based markets without having
bidding curves?
• Marginal prices from MIP models do not suffice to ensure market equilibrium
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Terminology
 We define a competitive market equilibrium as a set of
commodity prices and allocations such that
• The prices and allocations are an optimal solution to the individual optimization problem
of each market player
• For each commodity the number of bought units is equal to the number of sold units
 In general, it is not possible to find equilibria in non-convex
markets with strict linear pricing schemes (Scarf, 1944)
• To make that possible, it is allowed to have in-the-money orders with a non-convex
component that are entirely rejected
• Also only fractions of offered capacity can be accepted by the exchange
• Out-of-money orders cannot occur in existing market clearing algorithms
 A competitive quasi-equilibrium is a set of prices, allocations
and individual compensation payments such that
• The prices and allocations are an optimal solution to the individual optimization problem
of each market player including compensation payments
• The sum over all compensation payments is minimal
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