Intermittency and the Value of Renewable Energy

Transcription

1 Intermittency and the Value of Renewable Energy Gautam Gowrisankaran Stanley Reynolds Mario Samano March 7, 2013

2 Renewable energy Electricity generation from fossil fuels is the largest single source of greenhouse gas (GhG) emissions worldwide Many observers consider solar photovoltaics (PV) a crucial part of future renewable energy production A key potential problem with renewables is intermittency: Solar facilities produce electricity intermittently, with highest production on clear, sunny days This intermittency increases the variance of energy supply This in turn adds risk to the electric system If supply does not meet demand, possibility of system outage The intermittent and cyclic nature of renewable energy is seen as among biggest hurdles to large-scale adoption

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4 Intermittency This research develops an empirical method to estimate the value of renewables accounting for intermittency A simpler approach would use levelized costs which are the present value of future average costs Levelized costs of a solar plant are total costs divided by total power, discounted over its lifetime Incremental social value of a solar plant is its environmental benefits minus extra levelized costs compared to a fossil fuel plant The levelized cost approach misses many specifics: In the short run, operators may need to schedule additional operating reserves to avoid outage In the long run, operators may need to invest in backup generation and/or storage capacity But, solar plants may produce during peak consumption periods, when output is most valuable

5 This paper Our economic approach solves for optimal changes in backup capacity, demand-side management, generation, and operating reserves Optimal decisions depend on: Variability of renewable energy source including extent to which it correlates with demand Extent to which output from the source is forecastable Costs of backup generation We use the approach to evaluate solar energy in Arizona Methods could also be used to estimate the equilibrium value of: technologies such as wind power and storage policies such as real-time pricing

6 Relation to literature The general problems posed by renewable intermittency are well understood by policymakers and academics Recent studies deal with 1 The time-varying generation profile of renewables: Borenstein (2008), Denholm and Margolis (2007), Joskow (2010), Cullen (2010) 2 Intermittency and operating reserves: GE Energy (2008), Mills and Wiser (2010), Helman et al. (2011) 3 Backup capacity investment: Hansen (2008), Hoff et al. (2008), Skea et al. (2008) We derive an assessment of the value of large-scale renewable generation that combines these insights To our knowledge, first to use weather forecast data to identify forecastable component of renewable variability; and to model reserves in an empirical economic model

7 Intermittency: a graphical example Predicted and actual load and solar output, Aug. 15, 2008 KWh of solar output MWh of load Hour Solar output TEP load Mean forecasted solar output Mean forecasted TEP load

8 Outline of model Starting point for our model is Joskow and Tirole (2007) We build on Joskow and Tirole by adding renewable energy, and demand variability and uncertainty System operator is faced with: Renewable Portfolio Standard (RPS) Retail price of electricity p Existing generators Initially, she chooses: How many fossil fuel plants to build Price for curtailment contracts Curtailment contracts allow flexible customers to be paid not to consume electricity in periods of high demand Each morning, operator sees hourly weather forecasts for next day and generator planned outages Computes hourly forecastable solar and load distributions Chooses demand curtailment and generators for production and reserves

9 Outline of model (continued) During each production hour a day after production decisions generator failure, load and solar output occur We can divide outcomes into three possibilities: 1 Realized output (including solar) is above load Operator shuts down some production to match load 2 Output is below load but output plus reserves is above load Operator uses some reserves to meet load 3 Output plus reserves falls below load System outage: loss of load for large fraction of customers Hopefully rare event! Operator balances consumer welfare loss from system outage against reserve and capacity costs

10 Limitations of our current model 1 We do not allow for oligopoly power 2 Do not model dynamic linkages from period to period Most important are probably start-up costs for generation units 3 Don t allow imports/exports outside the market 4 Model of costs of reserve operations is reduced form 5 No structural estimation

11 Demand Constant elasticity of demand up to a fixed reservation value Scale of demand is time varying and depends on weather forecast distribution, F D Fixed retail price, p

12 Demand curtailment Users agree to have their power curtailed as necessary and be paid a net per-unit price of p c p All users with valuation below p c will sign up Observing the time t forecasted state, the planner randomly selects customers to curtail Higher p c implies: More curtailment possible But, higher per unit welfare loss from curtailment Welfare Loss from Curtailment

13 Production There exists a set of current generators All generators last till year T Each generator has: a fixed production capacity constant marginal cost of operation ratio of reserve costs to operating costs probabilities of maintenance and forced outage New fossil fuel plants: The planner can choose n FF new plants All natural gas with same capacity and costs Solar production: Planner faced with a level of listed solar capacity Produced from sites dispersed in metropolitan area

14 Transmission costs 30% of solar output is produced in a distributed fashion (Arizona RPS) and does not incur transmission costs This reduces costs of solar in two ways: 1 Reduces line losses Line loss is quadratic in non-distributed generation 2 Reduces fixed costs of transmission We assume FC is proportional to maximum expected non-distributed load

15 Planner s decision The planner (system operator) makes decisions to maximize the DPV of expected total (consumer plus producer) surplus See planner s decision

16 Data We obtain data from several sources: Energy Information Administration (EIA) and EPA data on generator characteristics, and fuel and electricity prices ERCOT data from Texas for spinning reserve costs TEP/UA solar test site data Load (demand) data from the Federal Energy Regulatory Commission (FERC) Day-ahead weather forecast data from National Oceanic and Atmospheric Administration (NOAA)

17 TEP/UA solar test site

18 Summary statistics on generator marginal costs Unit type # Units Mean Size (MW) Mean MC ($/MWh) Mean NOx (lbs/mwh) Mean SO2 (lbs/mwh) Mean CO2 (lbs/mwh) Solar PV ( ) ( ) ( ) ( ) ( ) Coal (138) (4.72) 4.07 (1.10) 1.95 (1.54) 2,337 (448) Natural Gas Combined Cycle 3 62 (20.7) (0) 0.09 (0) 0.01 (0) 894 (0) Natural Gas Steam Turbine 3 89 (13.9) (0) 3.33 (0) 0.01 (0) 1,433 (0) Natural Gas Gas Turbine (18.5) (85.8) 3.58 (1.76) 0.05 (0.02) 1,964 (136) Potential New Natural Gas Combined Cycle By eqm. 60 (0) 32.0 (0) 0.09 (0) 0.01 (0) 894 (0) Note: Standard deviations in parentheses. MC figures include emissions permits. We calculate marginal cost by multiplying heat rate by fuel cost, adding emissions permit fees per unit of generation

19 Demand parameters Use demand elasticity of η = 0.1 from the literature Calculate reservation value ν to match VOLL estimates of $8,000/MWh from literature Use demand growth of g = 20% from historical load growth Use retail price of electricity p = $95.6 from EIA numbers for Tucson Estimate day-ahead forecasted load and solar via a joint regression model

20 Supply parameters Param. Interpretation Value Source d outage Mean hours fraction affected 0.98 EIA for system outage α Line loss constant Computed from TEP reported 6.5% line loss AFC T Average transmission $19.6 Borenstein and Holland fixed costs per MWh (2005), Baughman and Bottaro (1976), TEP line loss cost FC solar Solar capital cost per $4.62 EIA rated watt FC FF New gas generator capital $0.984 EIA cost per rated watt β Discount factor 0.94 T Lifetime of generators 25 (years) c s Ratio of spinning reserve cost to production cost 0.41 ERCOT auction data See details on computation of planner s problem

21 Results Levelized cost difference value of solar: Average cost of solar PV: $171/MWh Average cost of gas generation: $58 / MWh (EIA, 2011) Difference: $113 / MWh Simulation results: effects of 10, 20, 25% RPS AZ has 15% RPS by 2025; CA has 33% RPS by 2020 Simulation results: costs of variability, capacity, and geographic dispersion of sites Reoptimizing policies is very important in making renewable energy feasible Rule of thumb policy modifies base-case policies as suggested by other authors Welfare costs are over 1.4 times as high as for optimal policy; mainly due to more system outages Simulation results: RPS policies and CO 2 reductions

22 Results Table: Outcomes with different RPS levels RPS Policy 0% 10% 20% 25% Solar PV capacity (MW) ,708 2,135 Foregone gas generators (#) Reserves as % of net load 24.2% 25.7% 27.9% 28.8% Average prob. of outage 4.51e e e e-5 Curtailment price p c ($/MWh) Curtailment quantity (MWh/yr) 24,460 29,083 23,994 21,318 Prob. curtailment Jul. 12PM 13.1% 0.02% 0% 0% Prob. curtailment Jul. 6PM 13.1% 42.1% 51.2% 48.6% Production costs (mil. $/year) Reserve costs (mil. $/yr) Gas investment costs (mil. $) 1,889 1,594 1,535 1,535 Solar investment costs (mil. $) 0 3,946 7,893 9,866 Transmission FC (mil. $/yr) Transmission line loss (1000MWh/yr) 1,485 1,385 1,298 1,258 Loss surplus (mil. $/yr) Loss surplus/solar ($/MWh)

23 Results Levelized cost difference value of solar: Average cost of solar PV: $171/MWh Average cost of gas generation: $58 / MWh (EIA, 2011) Difference: $113 / MWh Simulation results: effects of 10, 20, 25% RPS AZ has 15% RPS by 2025; CA has 33% RPS by 2020 Simulation results: costs of variability, capacity, and geographic dispersion of sites Reoptimizing policies is very important in making renewable energy feasible Rule of thumb policy modifies base-case policies as suggested by other authors Welfare costs are over 1.4 times as high as for optimal policy; mainly due to more system outages Simulation results: RPS policies and CO 2 reductions

24 Results Table: Costs Associated with 20% RPS RPS policy Foregone new gas generators Loss in surplus per MWh solar Feasible solar 6 $125.6 Solar cost drop from $4.62 to $2/W 6 $28.2 No unforecastable variance 7 $121.6 One single solar site 5 $131.1 Fully dispatchable 26 $74.4 No interruptible power contracts 4 $127.7 Rule of thumb policy 4 $170.8

25 Results Levelized cost difference value of solar: Average cost of solar PV: $171/MWh Average cost of gas generation: $58 / MWh (EIA, 2011) Difference: $113 / MWh Simulation results: effects of 10, 20, 25% RPS AZ has 15% RPS by 2025; CA has 33% RPS by 2020 Simulation results: costs of variability, capacity, and geographic dispersion of sites Reoptimizing policies is very important in making renewable energy feasible Rule of thumb policy modifies base-case policies as suggested by other authors Welfare costs are over 1.4 times as high as for optimal policy; mainly due to more system outages Simulation results: RPS policies and CO 2 reductions

26 Results Current solar costs are $4.62 / W Many analysts believe that costs will soon drop to $2 / W U.S. government recently set social cost of carbon values 20% RPS eliminates 2.3 million tons of CO 2 at $186/ton Table: Break-even solar capital costs with CO 2 benefits RPS Policy 10% 15% 20% 25% Benefit per ton of CO 2 reduction $ $ $ $

27 Conclusions We analyze the value of renewable energy with a three-part approach that accounts for intermittency 1 Theoretical model based on Joskow and Tirole (2007) 2 Process to estimate and calibrate parameters using publicly-available data 3 Computational approach to compute impact of RPS and other policies Costs of unforecastable intermittency are less than most utilities and forecasters believe to be true Optimizing approach is important Costs of solar per MWh produced increasing in RPS level Our methods can be used to understand relative costs of other policies Battery storage, electric cars, time-of-day pricing, etc.

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29 Curtailment level z: 0 z D min [ p η p η c where D min is the minimum demand for a given F D Welfare Loss from Curtailment: WLC(z, p c ) = ] η(p1 η p 1 η c )z (η 1)(p η p η c ) Return

30 Define actual production costs as PC(D, x) Example, two generators, capacity 1, c 2 > c 1, D = 1.6: PC(1.6, (1, 1)) = c c c 2 c s Without loss of generality, order the 5-minute solar draws within a period as S 1 t... S 12 t Individual generator output { x j (onj t ) = kj, with prob (1 Pj Fail )onj t 0, otherwise System outage probability [ J+n SOP(z, on, w, n FF, n solar FF ) = Prob j=1 x j (on j ) < D(w)p η ] z + LL(D(w)p η z d solar n solar S 1 (w)) n solar S 1 (w) Return

31 Let B(Q) be gross consumer benefit B(Q) = VOLL Q Let m j denote 0 1 maintenance status Planner s hourly optimization problem: W (w, m n FF, n solar, p c ) = max z,on { E [ (1 d outage SOP(z, on, w, n FF, n solar )) ( B(D(w) p η ) WLC(z, p c ) ) 1 Y ( ) ]} Y y=1 PC p η D(w) z + LL( ) n solar S y (w), x(on) w such that m j = 1 = on j = 0 Expand LL( ) as LL( p η D(w) z d solar n solar S y (w)) Return

32 Annual expected welfare: V (n FF, n solar, p c ) = N E[W t (w t, m t ) n FF, n solar, p c ] Expected total surplus: TS(n FF, n solar, p c ) = 1 βt 1 β V (nff, n solar, p c ) FC FF k FF n FF FC solar n solar TFC(n solar ) Transmission fixed cost TFC(n solar ) = AFC T max w {E[D(w)p η 1 Y Y y=1 d solar n solar S y (w)]} The planner chooses n FF and p c to maximize TS Return

33 Computation of planner s problem We make some relatively small simplifying assumptions: Planner will schedule plants in ascending order of MC Planner will only curtail demand if all plants operating OR MC of last plant > dwlc(z)/dz Planner s problem involves simulation of very small probability events We integrate over six dimensions: Number of coal plants down for maintenance and failure (2) Number of gas plants down for maintenance and failure (2) All hours in 2008, which gives w t Variation in demand and solar output given w t For each point in these six dimensions, we randomly select which generators are down Return