Prices to devices, aka “let there be markets”
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Renewable energy & Electricity markets Be careful what you wish for Adam Wierman, Caltech Joint work with Sachin Adlakha, Subhonmesh Bose, Desmond Cai, John Ledyard, Steven Low, and Jayakrishnan Nair. Renewable energy is coming! MW China Americas Solar PV: Europe MW Wind: Worldwide Renewable energy is coming! …but incorporation into the grid isn’t easy Today’s grid Generation Load Key Constraint: Generation = Load (at all times) low uncertainty Today’s grid Generation Load Key Constraint: Generation = Load (at all times) controllable (via markets) low uncertainty Tomorrow’s grid Key Constraint: Generation = Load (at all times) less controllable high uncertainty low uncertainty 1) Huge price variability, leading to generators opting out of markets! 2) More conventional reserves needed, countering sustainability gains! Key Constraint: Generation = Load (at all times) less controllable high uncertainty low uncertainty What can be done? Reduce the uncertainty • Better prediction • “Aggregation” … in time (storage) … in space (distributed generation) … in generation (heterogeneous mix) Design for the uncertainty • Redesign electricity markets • Increase amount of demand response our focus at Caltech This talk: Two electricity market design challenges 1) How many markets should there be? and when should they occur? 2) The nasty economic consequences of Kirchhoff's laws stochastic networks The newsvendor problem Networked Cournot competition Forget about energy for a second… This section is really about the role of uncertainty in newsvendor problems Forget about energy for a second… This section is really about the role of uncertainty in newsvendor problems “You have to decide today how many newspapers you want to sell tomorrow…” Estimate demand, ๐ Purchase, ๐ฅ uncertainty Demand ๐ is realized ๐ > ๐ฅ ⇒ lost revenue ๐ฅ > ๐ ⇒ wasted inventory Forget about energy for a second… This section is really about the role of uncertainty in newsvendor problems “You have to decide today how many newspapers you want to sell tomorrow…” seasonal products perishable goods … compute instances energy Electricity markets markets long term int. /day ahead Utility buys power to meet demand real time time PIRP markets long term int. /day ahead real time time markets long term real time int. /day ahead 4 hr market What is the impact of long term wind contracts? As renewable penetration increases: 1) Should markets be moved closer to real-time? 2) Should markets be added? time First step: How should utilities procure electricity in the presence of renewable energy? What is the impact of long term wind contracts? As renewable penetration increases: 1) Should markets be moved closer to real-time? 2) Should markets be added? price↑ ๐๐๐ก long term ๐๐๐ int. /day ahead ๐๐๐ก real time price volatility↑ ๐๐๐ก long term ๐๐๐ก ๐ธ ๐๐๐ > ๐๐๐ก ๐๐๐ int. /day ahead ๐๐๐ ๐ธ ๐๐๐ก ๐๐๐ > ๐๐๐ ๐๐๐ก real time ๐๐๐ก price↑ wind uncertainty ↓ ๐๐๐ก ๐๐๐ long term ๐ค๐๐ก ๐๐๐ก ๐1 = ๐ค๐๐ก − ๐ค๐๐ int. /day ahead ๐ค๐๐ ๐๐๐ ๐๐๐ก real time ๐ค ๐๐๐ก ๐2 = ๐ค๐๐ − ๐ค Assumption: ๐1 and ๐2 are independent (A generalization of the martingale model of forecast evolution) price↑ wind uncertainty ↓ ๐๐๐ก ๐๐๐ long term ๐ค๐๐ก ๐๐๐ก int. /day ahead ๐ค๐๐ ๐๐๐ Key Constraint: Generation = Load ๐๐๐ก + ๐๐๐ + ๐๐๐ก + ๐ค ≥ ๐ (we ignore network constraints for now) ๐๐๐ก real time ๐ค ๐๐๐ก Utility goal: min ๐ธ[๐๐๐ก ๐๐๐ก + ๐๐๐ ๐๐๐ + ๐๐๐ก ๐๐๐ก ] Subject to causality constraints price↑ wind uncertainty ↓ ๐๐๐ก long term ๐ค๐๐ก ๐๐๐ก ๐๐๐ int. /day ahead ๐ค๐๐ ๐๐๐ ๐๐๐ก real time ๐ค ๐๐๐ก Utility goal: min ๐ธ[๐๐๐ก ๐๐๐ก + ๐๐๐ ๐๐๐ + ๐๐๐ก ๐๐๐ก ] Subject to causality constraints Variant of the newsvendor problem [Arrow et. al. ’51], [Silver et. al. ’98], [Khouja ’99], [Porteus ’02], [Wang et. al. ’12]. ๐๐๐ก long term ๐ค๐๐ก ๐๐๐ก ๐๐๐ int. /day ahead ๐ค๐๐ ๐๐๐ ๐๐๐ก real time ๐ค ๐๐๐ก Theorem: The optimal procurement strategy is characterized by reserve levels ๐๐๐ก and ๐๐๐ such that where and ๐๐๐ก uniquely solves Scaling regime ๐ผ:baseline, e.g., average output of a wind farm ๐พ: scale, e.g., number of wind farms ๐:aggregation, e.g., degree of correlation between wind farms long term ๐ค๐๐ก ๐1 = ๐ค๐๐ก − ๐ค๐๐ ๐๐๐ ๐ธ = ๐ธ๐ถ ๐บ๐ ๐ธ = ๐ธ๐ฝ ๐บ๐ int. /day ahead ๐ค๐๐ real time ๐ค ๐2 = ๐ค๐๐ − ๐ค ๐บ๐ ๐ธ = ๐ธ๐ฝ ๐บ๐ Scaling regime ๐ผ:baseline, e.g., average output of a wind farm ๐พ: scale, e.g., number of wind farms ๐:aggregation, e.g., degree of correlation between wind farms Theorem: ๐ธ Procurement = ๐ − ๐ผ๐พ + ๐ฟ๐พ ๐ Procurement with zero uncertainty Extra procurement due to uncertainty Scaling regime ๐ผ:baseline, e.g., average output of a wind farm ๐พ: scale, e.g., number of wind farms ๐:aggregation, e.g., degree of correlation between wind farms Theorem: ๐ธ Procurement = ๐ − ๐ผ๐พ + ๐ฟ๐พ ๐ Depends on markets & predictions - prices - forecasts Depends on wind aggregation - ๐=1/2 (independent) - ๐=1 (correlated) Scaling regime ๐ผ:baseline, e.g., average output of a wind farm ๐พ: scale, e.g., number of wind farms ๐:aggregation, e.g., degree of correlation between wind farms Theorem: ๐ธ Procurement = ๐ − ๐ผ๐พ + ๐ฟ๐พ ๐ This form holds more generally than the model studied here: -- more than three markets: [Bitar et al., 2012] -- when prices are endogenous: [Cai & Wierman, 2014] -- when small-scale storage is included: [Hayden, Nair, & Wierman, Working paper] Electricity markets markets long term real time int. /day ahead What is the impact of long term wind contracts? As renewable penetration increases: 1) Should markets be moved closer to real-time? 2) Should markets be added? No! time Electricity markets markets long term int. /day ahead real time 4 hr ahead market? What is the impact of long term wind contracts? As renewable penetration increases: 1) Should markets be moved closer to real-time? 2) Should markets be added? time long term real time v/s long term int. What happens to ๐ธ[Cost] if a market is added? ๐ธ Cost ↓ What happens to ๐ธ[Procurement] if a market is added? ๐ธ Procurement ↓ ๐๐ ↑ real time ๐2 ~ Gaussian long term ๐๐๐ก = 6 int. /day ahead 6 < ๐๐๐ < 10 real time ๐๐๐ก = 10 ๐ธ[Procurement] 2 markets 3 markets are always better! 3 markets 6 6.5 7 7.5 ๐๐๐ 8 When does this happen? 8.5 9 9.5 10 Theorem: If ๐๐2 ๐ฅ is increasing for ๐ฅ < 0, decreasing for ๐ฅ > 0, and satisfies: ๐ ๐๐2 (๐ฅ)/๐น๐2 ๐ฅ is decreasing for ๐ฅ ≤ 0 ๐ ๐๐′2 (๐ฅ)/๐๐2 ๐ฅ is decreasing for ๐ฅ ≤ 0 then the expected procurement is lower with 3 markets than with 2 markets. Satisfied by the Gaussian distribution ๐2 ~ Weibull ๐ธ[Procurement] long term ๐๐๐ก = 6 int. /day ahead 6 < ๐๐๐ < 10 3 markets can be worse! 2 markets 3 markets 6 6.5 7 real time ๐๐๐ก = 10 7.5 When does this happen? ๐๐๐ 8 8.5 9 9.5 10 Estimation errors are heavy-tailed (specifically, long-tailed) Theorem: If ๐2 satisfies the condition: lim ๐๐2 (๐ฅ)/๐น๐2 ๐ฅ =0 , ๐ฅ→−∞ then there exist prices such that the expected procurement is higher with 3 markets than with 2 markets. markets long term int. /day ahead real time time 4 hr market What is the impact of long term wind contracts? As renewable penetration increases: 1) Should markets be moved closer to real-time? No! 2) Should markets be added? It depends, Gaussian or heavy-tailed? PIRP markets long term int. /day ahead real time time What is the impact of long term wind contracts? How should wind be incorporated into the markets? This talk: Two electricity market design challenges 1) How many markets should there be? and when should they occur? 2) The nasty economic consequences of Kirchhoff's laws The newsvendor problem Networked Cournot competition Forget about energy for a second… This section is really about intermediaries & competition in networked markets Forget about energy for a second… This section is really about intermediaries & competition in networked markets Rarely is competition in a single, well defined market… firms typically compete across a variety of markets Firms Markets Forget about energy for a second… This section is really about intermediaries & competition in networked markets Rarely is competition in a single, well defined market… firms typically compete across a variety of markets Examples: gas, airlines, construction, … , energy Gas pipelines in the US Key Constraint: Generation = Load (at all times) L L G G G L G G Key Constraint: Generation = Load (at all times) controllable (via markets) L cost L G G G quantity L G G Market run by the Independent System Operator (ISO) Determines the quantity to procure and price to charge each generator in order to meet the load s.t. network constraints. cost A toy example ๐บ1 capacity = 1 quantity cost Load = 6 ๐บ2 quantity ๐บ1 2 capacity = 1 3 1 ๐บ2 Load = 6 ๐บ1 capacity = 1 3 3 1 1 ๐บ2 2 2 Load = 6 But what if ๐ฎ๐ is strategic? 3 ๐บ1 capacity = 1 2 cost 1 ๐บ2 quantity Load = 6 Kirchhoff's laws create a hidden monopoly! Kirchoff’s laws can have nasty market consequences… Kirchoff’s laws can have nasty market consequences… Kirchoff’s laws can have nasty market consequences… How can “market power” be identified and quantified? Can markets be designed to mitigate market power? cost Networked Cournot competition L G G G quantity L G G Market run by the Independent System Operator (ISO) Determines the quantity to procure and price to charge each generator in order to meet the load s.t. network constraints. Networked Cournot competition Generators Bid: quantity ๐๐ Quadratic Costs: ๐ ๐๐ = ๐๐ ๐๐2 Profit: ๐๐ ๐๐ − ๐๐ ๐๐2 Load Linear demand function ๐๐ ๐๐ = ๐๐ − ๐๐ ๐๐ Market maker / Intermediary (ISO) Determines the quantity to procure and price to charge each generator in order to meet the load s.t. network constraints. ISO behavior is typically regulated Often forced to maximize one of : 1) Social welfare: Consumers’ utility – generation costs 2) Residual social welfare: Consumers’ utility – generator profits 3) Consumer surplus: Consumers’ utility – consumer payments Market maker / Intermediary (ISO) Determines the quantity to procure and price to charge each generator in order to meet the load s.t. network constraints. Choose “rebalancing quantities” ๐๐ to Maximize ๐ ๐, ๐ ๐ . ๐ก. ๐ ๐๐ = 0 −๐ ≤ ๐ป๐ ≤ ๐ Shift factor matrix (Kirchhoff’s Laws) line constraints Market maker / Intermediary (ISO) Determines the quantity to procure and price to charge each generator in order to meet the load s.t. network constraints. Networked Cournot competition [Barquin & Vasquez 2005, 2008], [Iklic 2009], [Neuhoff et at, 2005], [Yao, Oren, Adler, 2005, 2007] … Generators Bid: quantity ๐๐ Quadratic Costs: ๐ ๐๐ = ๐๐ ๐๐2 Profit: ๐๐ ๐๐ − ๐๐ ๐๐2 Load Linear demand function ๐๐ ๐๐ = ๐๐ − ๐๐ ๐๐ Existence? Market maker / Intermediary (ISO) Choose “rebalancing quantities” ๐๐ to Maximize ๐ ๐, ๐ s. t. ๐ ๐๐ = 0 & −๐ ≤ ๐ป๐ ≤ ๐ Theorem A generalized Nash equilibrium always exists when the ISO maximizes social welfare or residual social welfare. However, a generalized Nash equilibrium may not exist if the ISO maximizes consumer surplus. very susceptible to market power manipulations A toy example: “Path 15” A toy example: “Path 15” quadratic cost ๐1 = ๐2 ๐บ1 linear demand ๐1 = ๐2 ๐1 > ๐2 ๐ฟ1 ๐ ∈ [−๐พ, ๐พ] ๐บ2 ๐ฟ2 quadratic cost ๐1 = ๐2 linear demand ๐1 = ๐2 ๐1 > ๐2 A toy example: “Path 15” ๐บ1 residual social welfare social welfare quadratic cost linear demand ๐1 = ๐2 ๐1 > ๐2 ๐บ2 Profit ๐1 = ๐2 ๐บ1 ๐พ ๐ฟ1 EvenLine without line constraints the 2-node network expansion has very different impact is notdepending equivalent aggregated market! ontotheanmarket objective ๐ ∈ [−๐พ, ๐พ] ๐บ2 ๐ฟ2 quadratic cost ๐1 = ๐2 linear demand ๐1 = ๐2 ๐1 > ๐2 A toy example: “Path 15” quadratic cost ๐1 = ๐2 ๐บ1 linear demand ๐1 = ๐2 ๐1 > ๐2 ๐ฟ1 Theorem A generalized Nash equilibria exist for all three objectives, but the equilibria differ considerably: - For social welfare, ๐ ∗ < 0. - For residual social welfare, ๐ ∗ = 0. - For consumer surplus, ๐ ∗ > 0. EvenLine without line constraints the 2-node network expansion has very different impact is notdepending equivalent aggregated market! ontotheanmarket objective ๐ ∈ (−∞, ∞) ๐บ2 ๐ฟ2 quadratic cost ๐1 = ๐2 linear demand ๐1 = ๐2 ๐1 > ๐2 How can “market power” be identified and quantified? Can markets be designed to mitigate market power? What is the “right” market objective? This talk: Two electricity market design challenges 1) How many markets should there be? and when should they occur? 2) The nasty economic consequences of Kirchhoff's laws The newsvendor problem Networked Cournot competition Many other rich, challenging stochastic networks problems… Renewable Energy & Electricity Markets Be careful what you wish for Adam Wierman, Caltech Joint work with Sachin Adlakha, Subhonmesh Bose, Desmond Cai, John Ledyard, Steven Low, and Jayakrishnan Nair. ๏ง Subhonmesh Bose, Desmond Cai, Steven Low and Adam Wierman. “The role of a market maker in networked Cournot competition.” Under submission. ๏ง Chenye Wu, Subhonmesh Bose, Adam Wierman and Hamed Mohsenian-Rad. “A unifying approach for assessing market power in deregulated electricity markets.” Proceedings of IEEE PES General Meeting, 2013. ``Best Paper on System Operations and Market Economics'' award recipient. ๏ง Jayakrishnan Nair, Sachin Adlakha and Adam Wierman. “Energy procurement strategies in the presence of intermittent sources.” Proceedings of ACM Sigmetrics, 2014. ๏ง Desmond Cai and Adam Wierman. “Inefficiency in Forward Markets with Supply Friction.” Proceedings of IEEE CDC, 2013. This talk: 3 electricity market design challenges 1) How many markets should there be? and when should they occur? 2) The nasty economic consequences of Kirchhoff's laws 3) Who should have control: the engineer or the economist? the newsvendor problem networked Cournot competition shadow pricing vs. VCG Tomorrow’s grid Key Constraint: Generation = Load (at all times) less controllable high uncertainty low uncertainty Grid needs huge growth in Demand Response News articles The big debate for demand response: The economist vs. The engineer Prices to devices, a.k.a. “let there be markets” Send nodal price signals to consumers and let consumer devices respond [ADD REFS TO DEMOS, ETC] The big debate for demand response: The economist vs. The engineer Prices to devices, a.k.a. “let there be markets” Send nodal price signals to consumers and let consumer devices respond + Prices can be designed so that, at equilibrium, social optimality is achieved - Consumer response is uncertain - Markets do not equilibrate instantaneously, and convergence is likely unstable [ADD CITATIONS] The big debate for demand response: The economist vs. The engineer Direct control, a.k.a. “Hand over the keys” Give the utility control over consumer devices [ADD REFS TO DEMOS, ETC] The big debate for demand response: The economist vs. The engineer Direct control, a.k.a. “Hand over the keys” Give the utility control over consumer devices + Response is fast and guaranteed - Computational demands on utility are extreme - Utility does not know customer preferences, so control is not socially optimal The big debate for demand response: The economist vs. The engineer How can we combine these perspectives? “Mechanisms for control” Idea: price control policies rather than consumption A toy example: “Path 15” Social objective: ๐1 generators w/ quadratic cost ๐1 consumers with utility ๐ข G max ๐ก s. t. L ๐๐ ๐ข๐,๐ก ๐๐,๐ก − ๐ ๐๐ ๐๐,๐ก (๐๐,๐ก ) ๐ ๐ ๐๐ ๐ข๐,๐ก ๐๐,๐ก = ๐ ๐๐ ๐๐,๐ก (๐๐,๐ก ) −๐พ ≤ ๐1 ๐1,๐ก − ๐1 ๐1,๐ก ≤ ๐พ ๐ ∈ [−๐พ, ๐พ] G ๐2 generators w/ quadratic cost L ๐1 consumers with utility ๐ข “Mechanism for control” ′ 1. Consumers report ๐ข๐,๐ก 2. Utility computes allocation and prices Social objective: max ๐๐ ๐ข๐,๐ก ๐๐,๐ก − ๐ก s. t. ๐ ๐ ๐๐ ๐ข๐,๐ก ๐๐ ๐๐,๐ก (๐๐,๐ก ) ๐ ๐๐,๐ก = ๐ ๐๐ ๐๐,๐ก (๐๐,๐ก ) −๐พ ≤ ๐1 ๐1,๐ก − ๐1 ๐1,๐ก ≤ ๐พ The challenges: 1. Communication: Can the consumers describe their utilities? 2. Incentives: Will the consumer be truthful? 3. Computation: Can the utility compute the prices efficiently?
