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- 1. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks The Value of Volatile Resources in Electricity Markets Sean P. Meyn Joint work with: Matias Negrete-Pincetic, Gui Wang, Anupama Kowli, Ehsan Shaﬁeeporfaard, and In-Koo Cho Coordinated Science Laboratory and the Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign, USA May 5, 2010 1 / 50
- 2. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Outline 1 Introduction 2 DAM/RTM Dynamic model 3 Multi-settlement Electricity Market 4 Who Commands the Wind? 5 Numerical Results 6 Concluding Remarks 2 / 50
- 3. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Introduction Increased deployment of renewable energy can lead to signiﬁcant environmental beneﬁts 3 / 50
- 4. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Introduction Increased deployment of renewable energy can lead to signiﬁcant environmental beneﬁts However, the characteristics of renewable resources are very diﬀerent from those of conventional resources 3 / 50
- 5. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Introduction Increased deployment of renewable energy can lead to signiﬁcant environmental beneﬁts However, the characteristics of renewable resources are very diﬀerent from those of conventional resources It is imperative to understand their characteristics to fully harness the beneﬁts of renewable resources 3 / 50
- 6. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Introduction Renewable Portfolio Standards www.dsireusa.org / February 2010 VT: (1) RE meets any increase ME: 30% x 2000 WA: 15% x 2020* New RE: 10% x 2017 MN: 25% x 2025 in retail sales x 2012; MT: 15% x 2015 (Xcel: 30% x 2020) (2) 20% RE & CHP x 2017 NH: 23.8% x 2025 OR: 25% x 2025 (large utilities)* ND: 10% x 2015 MI: 10% + 1,100 MW MA: 15% x 2020 5% - 10% x 2025 (smaller utilities) x 2015* + 1% annual increase (Class I RE) SD: 10% x 2015 WI: Varies by utility; NY: 29% x 2015 10% x 2015 goal RI: 16% x 2020 NV: 25% x 2025* CT: 23% x 2020 IA: 105 MW W O OH: 25% x 2025† CO: 20% by 2020 (IOUs) PA: 18% x 2020† 10% by 2020 (co-ops & large munis)* IL: 25% x 2025 WV: 25% x 2025*† NJ: 22.5% x 2021 CA: 33% x 2020 UT: 20% by 2025* KS: 20% x 2020 VA: 15% x 2025* MD: 20% x 2022 MO: 15% x 2021 DC DE: 20% x 2019* AZ: 15% x 2025 NC: 12.5% x 2021 (IOUs) DC: 20% x 2020 0 10% x 2018 (co-ops & munis) NM: 20% x 2020 (IOUs) 10% x 2020 (co-ops) TX: 5,880 MW x 2015 HI: 40% x 2030 State renewable portfolio standard Minimum solar or customer-sited requirement 29 states + * State renewable portfolio goal Extra credit for solar or customer-sited renewables DC have an RPS Solar water heating eligible † (6 states have goals) 6 Includes non-renewable alternative resources 4 / 50
- 7. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Wind power Wind power is currently favored over all renewables 5 / 50
- 8. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Wind power Wind power is currently favored over all renewables Its deployment presents major challenges in system operations due to its: limited control capabilities forecasting uncertainty uncertainty and intermittency 5 / 50
- 9. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Balancing Authority Load (MW) 7000 January 16-22, 2010 6000 5000 Wind generation (MW) 1000 0 Sun Mon Tues Weds Thurs Fri Sat Figure: Example of load and wind generation data 6 / 50
- 10. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Diﬀerent opinions... “The Value of Wind - why more renewable energy means lower electricity bills,” Adam Bruce, Chairman, British Wind Energy Association “Wind is a free source of fuel. When the wind blows the UK’s electricity system has access to this free source and the power generated is automatically accepted onto the system” “Wind energy means lower bills; it’s as simple as that” 7 / 50
- 11. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Diﬀerent opinions... “The Value of Wind - why more renewable energy means lower electricity bills,” Adam Bruce, Chairman, British Wind Energy Association “Wind is a free source of fuel. When the wind blows the UK’s electricity system has access to this free source and the power generated is automatically accepted onto the system” “Wind energy means lower bills; it’s as simple as that” “Wind power’s dirty secret? Its carbon footprint” “Wind power is touted as the cleanest and greenest renewable energy resource” “You’ve got a non-carbon-emitting source of energy that’s free,” said Doug Johnson of the Bonneville Power Administration “However, Todd Wynn of the Cascade Policy Institute says it’s not as clean as advocates claim. He says it’s simply because the wind is volatile and doesn’t blow all the time” 7 / 50
- 12. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Scope Goal of this work Understand how volatility impacts the value of wind generation Focus: Competitive market setting 8 / 50
- 13. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Scope Goal of this work Understand how volatility impacts the value of wind generation Focus: Competitive market setting Beyond mean energy... We evaluate impacts of wind resources by focussing on two parameters: penetration and volatility of wind generation. 8 / 50
- 14. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Scope Goal of this work Understand how volatility impacts the value of wind generation Focus: Competitive market setting Beyond mean energy... We evaluate impacts of wind resources by focussing on two parameters: penetration and volatility of wind generation. Vehicle Dynamic electricity market model, Multi-settlement structure Captures wind volatility Ramping constraints 8 / 50
- 15. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Day-ahead market motivations The day-ahead market (DAM) is cleared one day prior to the actual production and delivery of energy. Economic world... Forward markets for electricity which improve market eﬃciency and serve as a hedging mechanism 9 / 50
- 16. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Day-ahead market motivations The day-ahead market (DAM) is cleared one day prior to the actual production and delivery of energy. Economic world... Forward markets for electricity which improve market eﬃciency and serve as a hedging mechanism ...Physical world Facilitate the scheduling of generating units 9 / 50
- 17. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Real-time market (RTM) At close of the DAM: The ISO generates a schedule of generators to supply speciﬁc levels of power for each hour over the next 24 hour period. RTM = Balancing Market As supply and demand are not perfectly predictable, the RTM plays the role of ﬁne-tuning this resource allocation process 10 / 50
- 18. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks DAM/RTM 32000 30000 Available Resources Forecast Megawatts 28000 Day Ahead Demand Forecast 26000 Actual Demand 24000 22000 20000 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Hour Beginning Figure: March 4, 2010 CAISO forecast and real-time supply and demand 11 / 50
- 19. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks DAM/RTM Notation Total demand at time t, Dttl (t) = dda (t) + D(t), Total capacity at time t, Gttl (t) = g da (t) + G(t) Total reserve at time t, Rttl (t) = Gttl (t) − Dttl (t) = G(t) − D(t) + rda (t) DAM Reserve policy rda (t) ≡ r0 da is constant. 12 / 50
- 20. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks RTM Model RTM model of Cho & Meyn consists of the following components: Volatility Deviation in demand D is modeled as a driftless Brownian motion with instantaneous variance σ 2 . Friction Generation cannot increase instantaneously: There exists ζ ∈ (0, ∞) such that, G(t ) − G(t) ≤ζ, for all t ≥ 0, and t > t. t −t 13 / 50
- 21. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks RTM Model Write dG(t) = ζdt − dI(t), with I non-decreasing, to model the upper bound on the rate of increase in generation. 14 / 50
- 22. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks RTM Model Write dG(t) = ζdt − dI(t), with I non-decreasing, to model the upper bound on the rate of increase in generation. Reserve process regarded as a controlled stochastic system, Reserve process dR(t) = ζdt − dI(t) − dD(t) with control I. 14 / 50
- 23. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Market Analysis Market analysis assumptions: Cost The production cost is a linear function of G(t), of the form cG(t) for some constant c > 0. 15 / 50
- 24. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Market Analysis Market analysis assumptions: Cost The production cost is a linear function of G(t), of the form cG(t) for some constant c > 0. Value of power Consumer obtains v units of utility per unit of power consumed: Utility to the consumer = v min(D(t), G(t)). 15 / 50
- 25. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Market Analysis Disutility from power loss The consumer suﬀers utility loss if demand is not met: Disutility to the consumer = cbo |R(t)| whenever R(t) < 0. 16 / 50
- 26. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Market Analysis Disutility from power loss The consumer suﬀers utility loss if demand is not met: Disutility to the consumer = cbo |R(t)| whenever R(t) < 0. Perfect competition The price of power P (t) in the RTM is assumed to be exogenous (it does not depend on the decisions of the market agents). 16 / 50
- 27. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Market Analysis Disutility from power loss The consumer suﬀers utility loss if demand is not met: Disutility to the consumer = cbo |R(t)| whenever R(t) < 0. Perfect competition The price of power P (t) in the RTM is assumed to be exogenous (it does not depend on the decisions of the market agents). “price-taking assumption” 16 / 50
- 28. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Market Analysis The objectives of the consumer and the supplier are speciﬁed by the respective welfare functions, Welfare functions WS (t) := P (t)G(t) − cG(t) WD (t) := v min(D(t), G(t)) − cbo max(0, −R(t)) − P (t)G(t) 17 / 50
- 29. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Market Analysis The consumer and supplier each optimize the discounted mean-welfare Discounted mean-welfare expressions For given initial values of generation and demand g = G(0), d = D(0), the respective discounted rewards are denoted KS (g, d) := E e−γt WS (t) dt , KD (g, d) := E e−γt WD (t) dt , γ > 0 is the discount rate. 18 / 50
- 30. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Market Analysis The social planner’s problem is deﬁned as the maximization of the total discounted mean welfare, Social planner’s objective K(g, d) = E e−γt WS (t) + WD (t) dt . 19 / 50
- 31. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Market Analysis The optimal reserve process is a reﬂected Brownian motion (RBM) on the half-line (−∞, r∗ ], with ¯ Reserve threshold 1 cbo + v r∗ = ¯ log . θ+ c where θ+ is the positive solution to the quadratic equation 2 σ θ − ζθ − γ = 0 1 2 2 20 / 50
- 32. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Market Analysis The equilibrium price functional is a piecewise constant function of the equilibrium reserve process, Equilibrium price functional pe (re ) = (v + cbo )I{re < 0} The sum cbo + v is in fact the maximum price the consumer is willing to pay, often called the choke-up price. 21 / 50
- 33. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks A little bit of technical details... On substituting the price into the respective welfare functions: Expected welfare values E[WS (t)] = (v + cbo ) E[D(t)I{Re (t) ≤ 0}] ∗ + E[Re (t)I{Re (t) ≤ 0}] − cE[Re (t)] E[WD (t)] = −(v + cbo )E[D(t)I{Re (t) ≤ 0}] ∗ where R = Re is the equilibrium reserve process. 22 / 50
- 34. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks How does this look?... Prices Reserves Normalized demand v + cbo r∗ 0 Figure: Model price dynamics 23 / 50
- 35. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Familiar, right? Illinois, July 1998 California, July 2000 Spinning reserve prices PX prices $/MWh 5000 Purchase Price $/MWh 70 250 Previous week 60 4000 200 50 3000 150 40 2000 30 100 20 1000 50 10 0 0 Mon Tues Weds Thurs Fri Weds Thurs Fri Sat Sun Mon Tues Weds Ontario, November 2005 APX Power NL, April 23, 2007 Forecast Demand Demand in MW Last Updated 11:00 AM Predispatch 1975.11 Dispatch 19683.5 Current Week Volume Current Week Price 21000 7000 400 Prev. Week Volume Prev. Week Price 18000 6000 300 Price (Euro/MWh) 5000 Volume (MWh) 15000 4000 Hourly Ontario Energy Price $/MWh Last Updated 11:00 AM Predispatch 72.79 Dispatch 90.82 200 2000 Forecast Prices 3000 1500 2000 100 1000 500 1000 0 3 6 9 12 15 18 21 3 6 9 12 15 18 21 3 6 9 12 15 18 21 Time 0 0 Tues Weds Thurs Tues Wed Thus Fri Sat Sun Mon Figure: Real-world price dynamics 24 / 50
- 36. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Coupling DAM/RTM Multi-settlement market model: A coupling of the DAM and RTM. Consumers’ welfare in the multi-settlement market WD (t) := v min(Dttl (t), Gttl (t)) − cbo max(0, −R(t)) ttl − P e (t)G(t) − pda (t)g da (t) 25 / 50
- 37. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks DAM/RTM Consumer’s welfare Principle of optimality =⇒ Formulae for total discounted mean welfare, Consumers’ mean welfare in the multi-settlement market KD = KD (r) + γ −1 (r − G(0))(pe (r) − pda ) ttl ∗ ∞ + (v − p(t))dda (t) e−γt dt . 0 in which KD (r) corresponds to the RTM welfare. ∗ 26 / 50
- 38. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Coupling DAM/RTM Total supplier welfare: Through similar and simpler arguments, Suppliers’ welfare in the multi-settlement market WS (t) = WS (t) + pda (t) − cda g da (t) ttl (1) 27 / 50
- 39. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks DAM/RTM Supplier’s Welfare Principle of optimality =⇒ Formulae for total discounted mean welfare, Supplier’s mean welfare in the multi-settlement market KS = KS (r) + γ −1 (r − G(0))(pda − cda ) ttl ∗ ∞ + p(t) − cda dda (t) e−γt dt . 0 in which KS (r) corresponds to the RTM welfare. ∗ 28 / 50
- 40. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Integrating Wind... Figure: Who Commands the Wind? 29 / 50
- 41. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Extending the dynamic model Goal Extend the DA/RT market model to diﬀerentiate power generated by wind and by conventional generation units 30 / 50
- 42. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Extending the dynamic model Goal Extend the DA/RT market model to diﬀerentiate power generated by wind and by conventional generation units Assumption All the wind power available is injected into the system 30 / 50
- 43. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Extending the dynamic model Goal Extend the DA/RT market model to diﬀerentiate power generated by wind and by conventional generation units Assumption All the wind power available is injected into the system Key issue Conventional generators serve residual demand. 30 / 50
- 44. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Extending the dynamic model Goal Extend the DA/RT market model to diﬀerentiate power generated by wind and by conventional generation units Assumption All the wind power available is injected into the system Key issue Conventional generators serve residual demand. Volatility of the residual demand will result in higher reserves in the dynamic market equilibrium 30 / 50
- 45. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Emerging issues Not only mean energy The details depend on both volatility of wind and its proportion of the overall generation What about now? If the penetration of wind resources is low, then the increase in load volatility will be negligible, and hence there will be negligible impact on the market outcomes 31 / 50
- 46. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Emerging issues Not only mean energy The details depend on both volatility of wind and its proportion of the overall generation What about now? If the penetration of wind resources is low, then the increase in load volatility will be negligible, and hence there will be negligible impact on the market outcomes What about in 2020? Potential negative market outcomes are possible with a combination of high wind generation penetration and high volatility of wind 31 / 50
- 47. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Who Commands the Wind? Approach To quantify the impact of volatility we obtain expressions for the total welfare in two market models, diﬀerentiated by who commands the wind generating units 32 / 50
- 48. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Who Commands the Wind? Approach To quantify the impact of volatility we obtain expressions for the total welfare in two market models, diﬀerentiated by who commands the wind generating units Main ﬁnding Volatility can have tremendous impact on the market outcomes 32 / 50
- 49. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Who Commands the Wind? Approach To quantify the impact of volatility we obtain expressions for the total welfare in two market models, diﬀerentiated by who commands the wind generating units Main ﬁnding Volatility can have tremendous impact on the market outcomes Asymmetric and surprising result The supplier can achieve signiﬁcant gains, even when the consumer commands the wind 32 / 50
- 50. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Consumers command the wind Wind generating units are commanded by the demand side: Consumers’ and suppliers’ welfare expressions WD,W (t) = v min(Dttl (t), Gttl (t) + Gttl (t)) ttl W − cbo max(0, −R(t)) − P (t)G(t) − p(t)g da (t) WS,W (t) = P (t) − crt G(t) + p(t) − cda g da (t) ttl 33 / 50
- 51. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Consumers command the wind Welfare expressions: DAM/RTM decomposition WD,W (t) = WD,W (t) ttl rt + vdda (t) − p(t)(dda (t) − gW (t)) da + (P (t) − p(t))r0 + vGW (t) da WS,W (t) = WS,W (t) + p(t) − cda g da (t) ttl rt WD,W (t), WS,W (t): Welfare obtained in the RTM rt rt with residual demand Dnet (t). 34 / 50
- 52. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Suppliers command the wind The other alternative is to consider wind as part of the supply side, Consumers’ welfare WD,W (t) = v min(Dttl (t), Gttl (t) + Gttl (t)) ttl W − cbo max(0, −R(t)) − P (t)(G(t) + GW (t)) − p(t)(g da (t) + gW (t)) da = WD,W (t) rt + (v − p(t))dda + (P (t) − p(t))r0 da + (v − P (t))GW (t) 35 / 50
- 53. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Suppliers command the wind Suppliers’ welfare WS,W (t) = P (t) − crt G(t) + P (t)GW (t) ttl + p(t) − cda g da (t) + p(t)gW (t) da = WS,W (t) rt + p(t) − cda g da (t) + P (t)GW (t) + p(t)gW (t) da The welfare gain p(t)gW (t) is now taken by the suppliers da 36 / 50
- 54. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Numerical Results: Setting the stage I Parameters used in all of our experiments: Parameters [$/MWh] Cost of blackout and value of consumption: cbo = 200, 000 v = 50 Cost and prices of generation: crt = 30, and cda = 0.75 ∗ crt , pda = 0.85 ∗ crt Discount factor: γ = 1/12 (12 hour time horizon). 37 / 50
- 55. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Numerical Results: Setting the stage II Parameters (physical) Ramp limit: ζ = 200 MW/min ¯ Mean demand: D = 50, 000 MW Standard deviation: σ = 500 MW. 38 / 50
- 56. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Numerical Results: Setting the stage III Penetration and volatility Coeﬃcient of variation to capture the relative volatility of wind: σw cv = E[Gttl (t)] W Percentage of wind penetration: ¯ k = 100 ∗ E[Gttl (t)]/D W . 39 / 50
- 57. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Numerical Results: Volatility Impacts 3 x 10 140 120 Optimal Reserve Level k = 20 100 k = 15 80 60 k = 10 40 20 k=5 0 k=0 0 0.1 0.2 0.3 0.4 cv Figure: Optimal reserves depend on penetration and coeﬃcient of variation. 40 / 50
- 58. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Numerical Results: Volatility Impacts 6 x 10 18 Total Welfare ζ = 200 16 ζ= 500 14 12 ζ = 0. 1 10 0 200 400 600 800 1000 σ Figure: Social planner’s welfare. 41 / 50
- 59. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Numerical Results: Consumers command the wind 6 6 x 10 x 10 15 k = 20 Consumer Welfare Supplier Welfare k = 15 5 k=0 k = 10 10 k=5 4 k=5 5 k = 10 3 k=0 k = 15 0 k = 20 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 cv Figure: Consumer and supplier welfare when consumer owns wind for diﬀerent coeﬃcient of variation cv and cda < pda < crt . 42 / 50
- 60. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Facing wind volatility The results of this paper invite many questions: C1 The impact of demand management and storage on the market 43 / 50
- 61. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Facing wind volatility The results of this paper invite many questions: C1 The impact of demand management and storage on the market C2 The impact of supply management and storage on the market. e.g., modern wind turbines allow pitch angle control. 43 / 50
- 62. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Facing wind volatility C3 Mechanisms to reduce consumers and suppliers exposure to supply-side volatility. 44 / 50
- 63. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Facing wind volatility C3 Mechanisms to reduce consumers and suppliers exposure to supply-side volatility. C4 How to create policies to protect participants on both sides of the market, while creating incentives for R&D on renewable energy? 44 / 50
- 64. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks The main messages... It is not so easy... The main message of this paper is that consumer welfare may fall dramatically as more and more wind generation is dispatched A beautiful world... This is true even under the most ideal circumstances: 45 / 50
- 65. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks The main messages... It is not so easy... The main message of this paper is that consumer welfare may fall dramatically as more and more wind generation is dispatched A beautiful world... This is true even under the most ideal circumstances: consumers own all wind generation resources and price manipulation is excluded 45 / 50
- 66. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks The main messages... It is not so easy... The main message of this paper is that consumer welfare may fall dramatically as more and more wind generation is dispatched A beautiful world... This is true even under the most ideal circumstances: consumers own all wind generation resources and price manipulation is excluded No “ENRON games” – no “market power” 45 / 50
- 67. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Concluding remarks Volatility and mean energy are key parameters for new energy sources. Our results show that resource volatility can have tremendous impacts on the market outcomes Currently adopted wind integration schemes can be harmful for consumers with larger wind penetration Suppliers can achieve signiﬁcant gains even when the consumer commands the wind 46 / 50
- 68. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Concluding remarks Who faces the uncertainty and risk associated to volatile resources is a big challenge from an economic viewpoint Under certain conditions consumers are better oﬀ not dispatching wind 47 / 50
- 69. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Concluding remarks Who faces the uncertainty and risk associated to volatile resources is a big challenge from an economic viewpoint Under certain conditions consumers are better oﬀ not dispatching wind Storage and demand management emerge as solutions for a smooth integration of wind power 47 / 50
- 70. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Concluding remarks Market analysis requires dynamic rather than snapshot models Greater wind penetration will require redesigns of both power system operations and electricity markets 48 / 50
- 71. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Thanks! Figure: Celebrating with Dutch Babies after ﬁnishing part of this work 49 / 50
- 72. Introduction DAM/RTM Dynamic model Multi-settlement Electricity Market Who Commands the Wind? Numerical Results Concluding Remarks Bibliography S. Meyn, M. Negrete-Pincetic, G. Wang, A. Kowli, and E. Shaﬁeepoorfard. The value of volatile resources in electricity markets. In Proc. of the 49th Conf. on Dec. and Control, pages 4921–4926, Atlanta, GA, 2010. I.-K. Cho and S. P. Meyn. Eﬃciency and marginal cost pricing in dynamic competitive markets. To appear in J. Theo. Economics, 2006. M. Chen, I.-K. Cho, and S. Meyn. Reliability by design in a distributed power transmission network. Automatica, 42:1267–1281, August 2006. I.-K. Cho and S. P. Meyn. A dynamic newsboy model for optimal reserve management in electricity markets. Submitted for publication, SIAM J. Control and Optimization., 2009. D. J. C. MacKay. Sustainable energy : without the hot air. UIT, Cambridge, England, 2009. L. M. Wein. Dynamic scheduling of a multiclass make-to-stock queue. Operations Res., 40:724–735, 1992. 50 / 50

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