Modeling competitive equilibrium prices in exchange-based electricity markets

Transcription

1 Modeling competitive equilibrium prices in exchange-based electricity markets The case of non-convex preferences André Ortner, Daniel Huppmann, Christoph Graf 5 th International PhD-Day of the AAEE Student Chapter Czech Technical University Prague, 8 th November 2016 DI André Ortner Energy Economics Group T: ortner@eeg.tuwien.ac.at

2 Introduction 2

3 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 3

4 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 4

5 Applied modeling approaches 5

6 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 Technical constraints on output level Upper limit on output 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 6

7 The binary equilibrium approach (BE) Adapted approach by Huppmann/Siddiqui 2015: 7

8 The binary equilibrium approach (BE) The binary decision problem of each generator

9 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 9

10 The binary equilibrium approach (BE) The binary decision problem of each generator

11 The binary equilibrium approach (BE) 2 Quantities when generator solely operates on spot market Generator optimization problem KKT conditions in two cases 11

12 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 12

13 The binary equilibrium approach (BE) The binary decision problem of each generator

14 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 14

15 Illustrative example 15

16 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 16

17 Results Comparison of resulting spot prices of three modeling approaches for different days 17

18 Results Comparison of resulting reserve prices of three modeling approaches for different days 18

19 Results Generation deviations of each generator between the SP and the BE model relative to total consumption for different days 19

20 Results Required compensation payments for different days 20

21 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 21

22 References Starr, Ross M. "Quasi-Equilibria in Markets with Non-Convex Preferences." Econometrica 37, no. 1 (1969): Scarf, H.E., The Allocation of Resources in the Presence of Indivisibilities, Journal of Economic Perspectives 8, Huppmann, D., Siddiqui, S., An exact solution method for binary equilibrium problems with compensation and the power market uplift problem. DIW Discussion Paper Hogan, W.W., Ring, B.J., On minimum-uplift pricing for electricity markets. Electricity Policy Group. Gribik, P.R., Hogan, W.W., Pope, S.L., 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., Efficient market-clearing prices in markets with non-convexities. European Journal of Operational Research 164,

23 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 23

24 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 24