Scarcity Pricing Market Design Considerations

Transcription

1 1 / 49 Scarcity Pricing Market Design Considerations Anthony Papavasiliou, Yves Smeers Center for Operations Research and Econometrics Université catholique de Louvain CORE Energy Day April 16, 2018

2 Outline 2 / 49 1 Context Motivation of Scarcity Pricing How Scarcity Pricing Works Research Objective 2 Building Up Towards the Benchmark Design (SCV) Energy-Only Real-Time Market Energy Only in Real Time and Day Ahead Adding Uncertainty in Real Time Reserve Capacity 3 A Sketch of the Alternative Designs 4 Illustration on a Small Example 5 Conclusions and Perspectives

3 Outline 3 / 49 1 Context Motivation of Scarcity Pricing How Scarcity Pricing Works Research Objective 2 Building Up Towards the Benchmark Design (SCV) Energy-Only Real-Time Market Energy Only in Real Time and Day Ahead Adding Uncertainty in Real Time Reserve Capacity 3 A Sketch of the Alternative Designs 4 Illustration on a Small Example 5 Conclusions and Perspectives

4 Challenges of Renewable Energy Integration 4 / 49 Renewable energy integration depresses electricity prices requires flexibility due to (i) uncertainty, (ii) variability, (iii) non-controllable output

5 Motivation for Scarcity Pricing 5 / 49 Scarcity pricing: adjustment to price signal of real-time electricity markets in order to compensate flexible resources Definition of flexibility for this talk: Secondary reserve: reaction in a few seconds, full response in 7 minutes Tertiary reserve: available within 15 minutes such as can be provided by combined cycle gas turbines demand response We will not be addressing sources of flexibility for which scarcity pricing is not designed to compensate (e.g. seasonal renewable supply scarcity)

6 The CREG Scarcity Pricing Studies 6 / 49 First study (2015): How would electricity prices change if we introduce ORDC (Hogan, 2005) in the Belgian market? Second study (2016): How does scarcity pricing depend on Strategic reserve Value of lost load Restoration of nuclear capacity Day-ahead (instead of month-ahead) clearing Third study (2017): Can we take a US-inspired design and plug it in to the existing European market?

7 Scarcity Pricing Adder Formula 7 / 49 In its simplest form, the scarcity pricing adder is computed as (VOLL MC( ˆ g p g )) LOLP(R), where VOLL is the value of lost load ˆ MC( g p g) is the incremental cost for meeting an additional increment in demand R is the amount of capacity that can respond within an imbalance interval LOLP : R + [0, 1] is the loss of load probability

8 Generator Example 8 / 49 Assume the following inputs: Day-ahead energy price: λpda = 20 e/mwh Day-ahead reserve price: λrda = 65 e/mwh Real-time marginal cost of marginal unit: 80.3 e/mwh Real-time reserve price: λrrt = 3.9 e/mwh Real-time energy price: λprt = 84.2 e/mwh Generator capacity: P g + = 125 MW

9 Forward Reserve Awarded, Not Deployed 9 / 49 Settlement Formula Price Quantity Cash flow type [e/mwh] [MW] [e/h] DA energy λpda pda 20 pda = 0 0 DA reserve λrda rda 65 rda = RT energy λprt (prt pda) 80.3 prt = Total 9655 Table: Without Adder Settlement Formula Price Quantity Cash flow type [e/mwh] [MW] [e/h] DA energy λpda pda 20 pda = 0 0 DA reserve λrda rda 65 rda = RT energy λprt (prt pda) 84.2 prt = RT reserve λrrt (rrt rda) 3.9 rrt = 25 0 Total Table: With Adder

10 Forward Reserve Awarded And Deployed 10 / 49 Settlement Formula Price Quantity Cash flow type [e/mwh] [MW] [e/h] DA energy λpda pda 20 pda = 0 0 DA reserve λrda rda 65 rda = RT energy λprt (prt pda) 80.3 prt = Total Table: Without Adder Settlement Formula Price Quantity Cash flow type [e/mwh] [MW] [e/h] DA energy λpda pda 20 pda = 0 0 DA reserve λrda rda 65 rda = RT energy λprt (prt pda) 84.2 prt = RT reserve λrrt (rrt rda) 3.9 rrt = Total Table: With Adder

11 Focus of this Presentation 11 / 49 Focus of this presentation: in order to back-propagate the scarcity 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?

12 Methodology Day-ahead market Real-time market Producers Random net injection Producers Virtual traders DA energy market DA reserve market Virtual traders RT energy market RT reserve market Virtual traders ORDC Consumers Consumers 12 / 49

13 The Eight Models 13 / 49 Simultaneous DA RT co-optimization Virtual energy and reserves of energy/reserve trading SCV SCP SEV SEP RCV RCP REV REP The dilemmas of the market design: Simultaneous day-ahead clearing of energy and reserve, or Reserve first (S/R)? Cooptimization of energy and reserve in real time, or Energy only (C/E)? Virtual trading, or Physical trading only (V/P)?

14 Outline 14 / 49 1 Context Motivation of Scarcity Pricing How Scarcity Pricing Works Research Objective 2 Building Up Towards the Benchmark Design (SCV) Energy-Only Real-Time Market Energy Only in Real Time and Day Ahead Adding Uncertainty in Real Time Reserve Capacity 3 A Sketch of the Alternative Designs 4 Illustration on a Small Example 5 Conclusions and Perspectives

15 Energy-Only Real-Time Market 15 / 49

16 Notation 16 / 49 Sets Generators: G Loads: L Parameters Bid quantity of generators: P + g Bid quantity of loads: D + l Bid price of generators: C g Bid price of loads: V l Decisions Production of generators: prt g Consumption of loads: drt l Dual variables Real-time energy price: λrt

17 Model 17 / 49 Just a merit-order dispatch model: max l L V l drt l g G C g prt g (λrt ) : prt g P + g, g G d l D + l, l L d l p g = g G l L p g, d l 0, g G, l L

18 Energy-Only in Real Time and Day Ahead 18 / 49

19 Additional Notation 19 / 49 Decisions Day-ahead energy production of generator: pda g Day-ahead energy consumption of load: dda l Dual variables Day-ahead energy price: λda

20 20 / 49 Model Generator profit maximization: max λda pda g + λrt (prt g pda g ) C g prt g prt g P + g prt g 0 Load profit maximization: max λda dda l + V l drt l λrt (drt l dda l ) drt l D + l drt l 0 Market equilibrium: prt g = drt l g G l L pda g = dda l g G l L

21 Remarks 21 / 49 Back-propagation: from KKT conditions of profit maximization, we have λda = λrt In fact, day-ahead and real-time parts of the model can be completely decoupled We have introduced virtual trading: agents can take positions in the day-ahead market which do not correspond to their physical characteristics

22 Adding Uncertainty in Real Time 22 / 49

23 Additional Notation 23 / 49 Sets Set of uncertain real-time outcomes (e.g. renewable supply forecast errors, demand forecast errors): Ω Parameters Real-time profit of agent: ΠRT g,ω Functions Risk-adjusted profit of random payoff: R g : R Ω R

24 Model 24 / 49 Generator profit maximization: where max λda pda g + R g (ΠRT g,ω λrt ω pda g ), Load profit maximization: where ΠRT g,ω = (λrt ω C g ) prt g,ω max λda dda l + R l (ΠRT l,ω + λda ω dda l ) Day-ahead market equilibrium: ΠRT l,ω = (V l λrt ω ) drt l,ω g G pda g = l L dda l

25 Modeling the Risk Function R 25 / 49 How do we model attitude of agent towards risk, R? Let s consider the conditional value at risk, CVaR Parameters Percent of poorest scenarios considered in evaluation of risked payoff: α g Probability of outcome ω: p ω Variables Conditional value at risk: CVaR g Value at risk: VaR g Auxiliary variable for determination of risk-adjusted real-time payoff: u g,ω Dual variables: Risk-neutral probability of agent: q g,ω

26 Modeling the Risk Function R (cont.) 26 / 49 There exists a linear programming formulation of R For example, the generator problem reads: max λda pda g + CVaR g CVaR g = VaR g 1 p ω u g,ω α g (q g,ω ) : u g,ω VaR g (ΠRT g,ω λrt ω sda g ) u g,ω 0 ω

27 Remarks 27 / 49 Two possible interpretations of profit ΠRT : Correct interpretation: λrt ω and ΠRT g,ω are parameters for day-ahead profit maximization Incorrect interpretation: λrt ω and ΠRT g,ω are variables for day-ahead profit maximization The 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 average real-time price: λda = E Qg [λrt ω ] = ω Ω q g,ω λrt ω, g G L But if there is a single risk-neutral agent with an infinitely deep pocket, then λda = E[λRT ω ] = ω Ω p ω λrt ω

28 Reserve Capacity in Real Time 28 / 49

29 Additional Notation 29 / 49 Sets ORDC segments: RL Parameters ORDC segment valuations: MBR l ORDC segment capacities: DR l ramp rate: R g Decisions Real-time demand for reserve capacity: drrt l,ω Real-time supply of reserve capacity: rrt g,ω Dual variables Real-time price for reserve capacity: λrrt

30 Model 30 / 49 Real-time co-optimization of energy and reserve for outcome ω Ω: max MBR l drrt l + V l d l C g p g l RL l L g G (λrt ) : (λrrt ) : prt g = drt l g G l L rrt g = drrt l l RL g G L prt g P g,ω, + rrt g R g, prt g+rrt g P g,ω, + g G d l D + l, rrt l R l, rrt l drt l, l L drrt l DR l, l RL prt g, rrt g 0, g G, drt l, rrt l 0, l L, drrt l 0, l RL

31 Remarks 31 / 49 Suppose that a given generator g is simultaneously offering energy (prt g > 0) and reserve (rrt g > 0) is not constrained by ramp rate (rrt g < R g ) We have the following linkage between the energy and reserve capacity price: λrt ω C g = λrrt ω This no-arbitrage relationship is the essence of scarcity pricing

32 Reserve Capacity in Day Ahead 32 / 49

33 Additional Notation 33 / 49 Decisions Day-ahead supply of reserve capacity: rda g Dual variables Day-ahead price for reserve capacity: λrda

34 34 / 49 Model Generator profit maximization: where max λda pda g + λrda rda g + R g (ΠRT g,ω λrt ω pda g λrrt ω rda g ), ΠRT g,ω = (λrt ω C g ) prt g,ω + λrrt ω rrt g,ω Load profit maximization: where max λda dda l + λrda rda l + R l (ΠRT l,ω + λrt ω dda l λrrt ω rda l ), ΠRT l,ω = (V l λrt ) drt l + λrrt rrt l,ω Day-ahead market equilibrium: g G pda g = l L dda l, g G L rda g = 0

35 Remarks 35 / 49 No need to explicitly introduce ORDC in day-ahead market: λrda = E Qg [λrrt ω ] = ω Ω q g,ω λrrt ω, g G L and λrrt is already augmented by ORDC in real-time market Should the day-ahead auction explicitly impose physical constraints? This is linked to the question of virtual trading: + Imposing explicit physical constraints may move us away from the pure financial market equilibrium - Simple examples indicate that the equilibrium solution may require unrealistic liquidity in the day-ahead market

36 To Summarize 36 / 49 We have arrived at our first target model: SCV Simultaneous day-ahead clearing of energy and reserve Co-optimization of energy and reserve in real time Virtual trading

37 Outline 37 / 49 1 Context Motivation of Scarcity Pricing How Scarcity Pricing Works Research Objective 2 Building Up Towards the Benchmark Design (SCV) Energy-Only Real-Time Market Energy Only in Real Time and Day Ahead Adding Uncertainty in Real Time Reserve Capacity 3 A Sketch of the Alternative Designs 4 Illustration on a Small Example 5 Conclusions and Perspectives

38 Moving from Virtual to Physical Trading 38 / 49 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: pda g + rda g P + g rda g R g rda g 0 However, we need a day-ahead ORDC, because otherwise there is no day-ahead reserve capacity demand in the model

39 Moving from Real-Time Co-optimization to Energy-Only Trading 39 / 49 It is similarly easy to switch from real-time co-optimization of energy and reserve to energy-only trading by switching between co-optimization and merit order dispatch in real time

40 Moving from Simultaneous Day-Ahead Clearing to Reserve First 40 / 49 Qualitatively, we want to capture the difference between the following: Simultaneous auctioning: system operator co-optimizes, taking into account all the relevant inter-dependencies of power production and reserve capacity Sequential auctioning: agents determine opportunity costs on the basis of possibly inaccurate forecasts of the system state for the following day We formulate the problem as a multistage stochastic equilibrium by nesting risk functions (Philpott, 2016)

41 Sequence of Events Decide DA energy RT dispatch Decide DA reserve State of the system in the following day Revelation of RT imbalance Type of day: assessment of the TSO for what quantity of operating reserve will be required for the following day In line with current effort of ELIA to transition towards dynamic reserve sizing and procurement in the day ahead (De Vos, 2018) 41 / 49

42 Populating the Tree with Data 42 / 49 Denote a given node as (t, ω), where t is stage and ω is outcome No specific random vector is revealed in stage 2, instead the system state: Node (2, 1): Low-risk day Node (2, 2): Medium-risk day Node (2, 3): High-risk day In stage 3, renewable supply P + wind is revealed: Node (3, 1): 111 MW; node (3, 2): 101 MW Node (3, 3): 156 MW; node (3, 4): 56 MW Node (3, 5): 206 MW; node (3, 6): 6 MW

43 Outline 43 / 49 1 Context Motivation of Scarcity Pricing How Scarcity Pricing Works Research Objective 2 Building Up Towards the Benchmark Design (SCV) Energy-Only Real-Time Market Energy Only in Real Time and Day Ahead Adding Uncertainty in Real Time Reserve Capacity 3 A Sketch of the Alternative Designs 4 Illustration on a Small Example 5 Conclusions and Perspectives

44 Numerical Illustration 44 / 49 Consider the following market bids: Blast furnace: e/mwh Renewable: e/mwh Gas-oil: 5 85 e/mwh LVN: e/mwh Demand: 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%

45 Summary Statistics 45 / 49 Consider the scenario tree of the previous section with equal transition probabilities at every stage λda λrda λrt S1 λrt S2 λrrt S1 λrrt S2 Welfare SCV ,001,800 SCP ,005,260 SEV NA NA 996,369 SEP NA NA 996,556 RCV ,001,950 RCP ,007,120 REV NA NA 996,329 REP NA NA 996,452

46 Outline 46 / 49 1 Context Motivation of Scarcity Pricing How Scarcity Pricing Works Research Objective 2 Building Up Towards the Benchmark Design (SCV) Energy-Only Real-Time Market Energy Only in Real Time and Day Ahead Adding Uncertainty in Real Time Reserve Capacity 3 A Sketch of the Alternative Designs 4 Illustration on a Small Example 5 Conclusions and Perspectives

47 Conclusions 47 / 49 S/R C/E V/P Preliminary observations SCV Theoretical first-best, large (long and short) positions in DA reserve market SCP Mitigates DA reserve exposure with minor effect on DA-RT price convergence SEV Not reasonable: degenerates to energyonly market without reserve market SEP Weak DA reserve capacity signal, not the result of back-propagation of RT price RCV Inflation of DA reserve price due to uncertainty regarding TSO reserve needs RCP Highest DA reserve price REV Same weakness as SEV REP Same attributes as SEP

48 Perspectives 48 / 49 Multiple periods Multiple reserve types Differentiate secondary and tertiary Differentiate upward and downward Unit commitment (per work of De Maere and Smeers) Additional features: pumped hydro, imports/exports Practical questions: width of ORDC effects of switch every 4 hours on volatility of RT price Computational challenges: regularized decomposition of equilibrium models seems promising

49 Thank You for Your Attention 49 / 49 For more information: anthony.papavasiliou@uclouvain.be