Optimal development of renewables: A case study in German PV

Transcription

1 Optimal development of renewables: A case study in German PV Rutger-Jan Lange University of Cambridge Cambridge,

2 Outline 1. Solar energy is an option 2. Technology learning as a random walk 3. The German policy 4. A simple model for solar learning 5. Feed-in policy as an optimal-stopping problem 6. Conclusion 2

3 Big solar April 15, 2010 How fast is fast enough? 3

4 The economics of solar energy Photovoltaic energy is still 3 to 12 times more expensive than onshore wind But in Germany, every installed panel is a profitable investment due to a generous feed-in tariff (guaranteed pay-back) Germany attracted half the world s installation, last year 4

5 Solar energy is an option The question is not: will solar energy be economical by 2020, or not? But rather: what level of feed-in tariff should you be willing to pay, at each point in time, to incentivize the market to keep exploring the option of solar energy? 5

6 Outline 1. Solar energy is an option 2. Technology learning as a random walk 3. The German policy 4. A simple model for solar learning 5. Feed-in policy as an optimal-stopping problem 6. Conclusion 6

7 How fast is fast enough? Sources: 1) National Survey Report of PV Power Applications in Germany 2008, Version 2, Lothar Wissing, Forschungszentrum Jülich, May ) Statistische Zahlen der deutschen Solarstrombranche (Photovoltaik), Bundesverband Solarwirtschaft, Nov 2009; 7

8 Moore learning The [performance of processors] has increased at a rate of roughly a factor of two per year. Certainly over the short term this rate can be expected to continue. Intel co-founder, Gordon E. Moore,

9 Learning: a random walk? Sources: 1) National Survey Report of PV Power Applications in Germany 2008, Version 2, Lothar Wissing, Forschungszentrum Jülich, May ) Statistische Zahlen der deutschen Solarstrombranche (Photovoltaik), Bundesverband Solarwirtschaft, Nov 2009; 9

10 Too cheap to meter? Our children will enjoy in their homes electrical energy too cheap to meter. Lewis Strauss, 1954, head of the US Atomic Energy Commission 10

11 Outline 1. Solar energy is an option 2. Technology learning as a random walk 3. The German policy 4. A simple model for solar learning for Germany 5. Feed-in policy as an optimal-stopping problem 6. Conclusion 11

12 Total installed capacity Source: Statistische Zahlen der deutschen Solarstrombranche (Photovoltaik), Bundesverband Solarwirtschaft, Nov 2009; 12

13 Total installed capacity 13

14 German EEG law for 2010 The tariff paid for electricity from installations generating electricity from solar radiation shall amount to cents per kilowatt-hour. The tariff paid for electricity from installations generating electricity from solar radiation which are exclusively attached to or on top of a building [...] shall amount to cents per kilowatt-hour [...]. English and German versions available on 14

15 And onwards! The annual percentage degression for tariffs [...] for electricity generated from solar radiation [...] a) shall be 10.0 percent in the year 2010 b) shall be 9.0 percent from the year 2011 onwards English and German versions available on 15

16 Lifetime value of a solar panel End-customer discounts future cash-flows at 5% p.a. when deciding lifetime value Lifetime value, per feed-in tariff, drops with 9% per year, because feed-in tariff drops Domestic prices start at 0.21/kWh and increase with 2% p.a. Industrial prices start at 0.14/kWh and increase with 2% p.a. 16

17 Will it reach the target in 2020? Estimate a GBM with µ = and σ =

18 Outline 1. Solar energy is an option 2. Technology learning as a random walk 3. The German policy 4. A simple model for solar learning 5. Feed-in policy as an optimal-stopping problem 6. Conclusion 18

19 A simple model for solar learning Start in Government announces the feed-in tariff for years to come tariff - 5 Developer of solar panels 2 The consumer decides if it is quotes new price for yr X profitable to buy & install solar panels + 4 Developer runs down the stochastic learning curve 3 If yes, total capacity grows at the maximum rate 3 If not, new deployment halts 19

20 How the consumer decides (UK): February 7,

21 Start in Pick your scenario Government announces tariff 0.42/kWh (rooftop) degression 9% p.a. tariff - New price for yr X 5 2 Consumer bases decision on Price(2009 q3) = 3,263/kWp - discounts future cash flows 5% p.a. - knows panel operates at 10% of peak production, on average + 4 Stochastic learning curve: GBM with µ = and σ = If consumer installs, then total capacity grows at rate of 15% p.a. If not, new deployment halts 21

22 What is in it for the government? The government is in it for the long run, and Eternity is very long, especially towards the end. Woody Allen 22

23 What is in it for the government? The government is in it for the long run, and Eternity is very long, especially towards the end. Woody Allen Therefore, an infinite horizon cannot lead to a sensible decision criterion 23

24 The Germans have a finite time horizon in mind 24

25 If everything goes well, what does it cost? 25

26 Total cost to completion, in

27 Fed up? January 7,

28 Outline 1. Solar energy is an option 2. Technology learning as a random walk 3. The German policy 4. A simple model for solar learning 5. Feed-in policy as an optimal-stopping problem 6. Conclusion 28

29 How the government really decides 26 March,

30 Reward upon commercialization Suppose that every cent, that solar energy is cheaper than 0.16/kWh, by 2020, leads to 40 billion of savings nationwide, after 2020 To recover the total cost of the program (~ 80 billion), the price of solar energy would have to drop to 0.02/kWh below 0.16/kWh 30

31 We now have 3 ingredients 1. Uncertainty about the final performance 2. A deterministic cost, to complete the project (this is also a decision variable, by setting the tariff) 3. An uncertain reward is received upon successful completion 31

32 Trouble ahead Beyond numerical results, very little is known about most [...] options which expire in finite time. New Palgrave Dictionary of Economics, Ross (1987) See for example Dixit & Pindyck Investment under Uncertainty 32

33 New & beautiful iterative solution of optimal policy 33

34 Assumptions made Consumer discounts future cash flows 5% p.a. Market growth grows at 15% as long as the price of solar stays below the threshold Energy prices Domestic and industrial energy prices grow by 2% p.a. German weather average solar output is 10% of peak Stochastic learning curve The process is driven by a geometric Brownian motion with µ = and σ = Time horizon the aim is that solar energy has a price of less than 0.16/kWh by 2020 Running costs Determined by the tariff (decision variable) and the yearly growth-rate Realized savings 40billion in savings are made for every cent that solar energy costs less than 0.16/kWh, by

35 German v Optimal tariff 35

36 German v Optimal tariff Year German Optimal /kWh 0.32/kWh % 8% % 8% % 7% % 7% % 7% % 6% % 6% % 6% % 6% % 6% 36

37 Outline 1. Solar energy is an option 2. Technology learning as a random walk 3. The German policy 4. A simple model for solar learning 5. Feed-in policy as an optimal-stopping problem 6. Conclusions 37

38 Conclusions This work contributes 1. To the (theoretical) literature on options with finite expirationtime, by condensing the known 4 equations for optimality into a one new equation, that can be solved by existing techniques 2. And, hopefully, to the applied literature, by showing that technology-learning problems can be viewed as optimalstopping problems After some fine-tuning And feed-back here 38