15th IAEE European Conference 2017 Pure or Hybrid?: Policy Options for Renewable Energy 1 Ryuta Takashima a Yuta Kamobayashi a Makoto Tanaka b Yihsu Chen c a Department of Industrial Administration, Tokyo University of Science, Chiba, Japan b National Graduate Institute for Policy Studies (GRIPS), Tokyo, Japan c Department of Technology Management, University of California SantaCruz, Santa Cruz, CA, USA 5 September 2017 1 Supported by the Grant-in-Aid for Scientific Research (B) (Grantno.15H02975) from Japan Society for the Promotion of Science
Introduction
Motivation Motivation Recently policymakers have implemented various policies for reducing greenhouse gas emissions. Concerns about global warming and climate change Policies for supporting and promoting renewable energy Feed-in tariff: FiT Feed-in premium FiT-contract for difference Renewable portfolio standards: RPS Directly impact the power prices and outputs by favoring power produced by renewables. What is the difference among those policies?
Renewable Energy Policy Renewable Energy Policy REN21 Renewables 2016 Global Status Report Many countries have implemented more than one policy. There is a need to understand their market impacts and compare to either RPS or FiT alone.
Related papers Related papers Relationship between renewable energy policy scheme and market equilibrium Fischer (2010): Effect of RPS on market equilibrium in perfect competitive markets Tanaka and Chen (2013): Allow for the market power in Stackelberg equilibrium Hibiki and Kurakawa (2013): Compare social welfare under FiT and RPS Siddiqui, Tanaka, and Chen (2016): Provide the endogenous setting of the RPS target from a policymaker s perspective. Policy mix Böhringer and Behrens (2015): Interactions between emission caps and renewable energy polies
Research Objective Research Objective Examine the efficiency of the hybrid policy consisting of RPS and FiT. Compare it to the pure policy scheme either RPS or FiT Derive optimal RPS target, and FiT price. RQ: Which policy is efficient for social welfare?
Problem Formulation
Assumption and Setting Assumption and Setting Consider two types of power producers in the electricity industry: Non-renewable: NRE Renewable: RE Setting of the market competition: Cournot except FiT scheme These two types of producers are jointly subject to a RPS requirement while only the RE producer is supported by the FiT scheme. The RE generator s profit is indirectly impacted by the power price through the FiT scheme.
Assumption and Setting (cont d) Assumption and Setting (cont d) Quadratic production cost function: NRE: c n (q n ) = 1 2 c nq 2 n RE: c r (q r ) = 1 2 c rq 2 r q n: NRE production (MWh) q r : RE production (MWh) c n < c r Electricity price: p(q n, q r ) = a b(q n + q r ) a: Intercept of the inverse demand function ($/MWh) b: Slope of inverse demand function (dollar/mwh 2 ) Damage cost of greenhouse gas emissions: Quadratic function of output: d(q n ) = 1 2 kq2 n k: Rate of increase in marginal damage cost ($/MWh 2 )
4 schemes 4 schemes Central planning (CP): Benchmark case FIT RPS A central planner simultaneously decides outputs for all power generations by maximizing the social welfare. Only the RE generator is supported by the FiT that is optimally determined by the government at the upper level. At lower level, NRE and RE generators choose the outputs subject to the RPS target determined by the government at the upper level by maximizing social welfare. Hybrid Policy (HP) NRE and RE generators decide their outputs subject to a combination of RPS and FiT with both the RPS target and the FiT price determined by the government.
The Model
CP CP The CP selects generation of either type in order to maximise SW by solving the following QP: max q n 0,q r 0 KKTconditions: qn+q r 0 p(q )dq c n (q n ) c r (q r ) d n (q n ) 0 q n a + b (q n + q r ) + c n q n + kq n 0 0 q r a + b (q n + q r ) + c r q r 0 Optimal interior solutions: qn ac r = b (c n + c r + k) + c r (c n + k) q r = a (c n + k) b (c n + c r + k) + c r (c n + k) p ac r (c n + k) = b (c n + c r + k) + c r (c n + k) Output ratio of electricity from renewable sources: α = cn + k c n + c r + k
FIT: Lower-level FIT: Lower-level Profit maximisation: KKTconditions: max q n 0 max q r 0 p (q n + q r ) c n (q n ) p F IT q r p F IT q r c r (q r) 0 q n a + 2b (q n + q r) + c nq n 0 0 q r p F IT + c r q r 0 Optimal interior solutions: ˆq n = ac r 2bp F IT c r (2b + c n ) pf IT ˆq r = c r ˆp = ac r (b + c n ) bc n p F IT c r (2b + c n )
FIT: Upper-level FIT: Upper-level Social welfare maximisation: max {p F IT >p} {q n,q r} qn+q r 0 p(q )dq c n (q n ) c r (q r ) d n (q n ) s.t 0 q n a + 2b (q n + q r) + c nq n 0 0 q r p F IT + c r q r 0 KKTcondition: ac n c r (2b + c bc ( n acr + c n p F IT ) n) c 2 r (2b + c n) 2 + (c n + k) 2b ( ac r 2bp F IT ) c 2 r (2b + c n) 2 Optimal interior solutions: ˆp ˆp F IT = ac r(3bc n +2bk+c 2 n) c r(2b+c n) 2 +4b 2 (c n+k)+bc 2 n pf IT c r = 0 (p F IT < ˆp) (p F IT ˆp)
PRS: Lower-level RPS: Lower-level Profit maximisation: max pq n c n (q n) αp REC q n q n 0 max q r 0 pq r c r (q r) + (1 α) p REC q r KKTconditions: 0 q n a + b (q n + q r ) + bq n + c n q n + αp REC 0 0 q r a + b (q n + q r ) + bq r + c r q r (1 α) p REC 0 Market clearing condition for REC: 0 p REC q r α(q n + q r ) 0 Optimal interior solutions: a (1 α) q n = (2b + c n + c r) α 2 2 (b + c n) α + (2b + c n) aα q r = (2b + c n + c r) α 2 2 (b + c n) α + (2b + c n) p REC a [(2b + c n + c r) α (b + c n)] = (2b + c n + c r ) α 2 2 (b + c n ) α + (2b + c n ) p = a [ (2b + c n + c r ) α 2 2 (b + c n ) α + (b + c n ) ] (2b + c n + c r ) α 2 2 (b + c n ) α + (2b + c n )
RPS: Upper-level Social welfare maximisation: RPS: Upper-level max {0 α 1} {qn,q r } {p REC } qn +q r p(q )dq c n (q n ) c r (q r ) d n (q n ) 0 s.t 0 q n a + b (q n + q r ) + bq n + c n q n + αp REC 0 KKTcondition: 0 q r a + b (q n + q r ) + bq r + c r q r (1 α) p REC 0 0 p REC q r α(q n + q r) 0 1 F (α) 3 [ (4b + cn + c r k) (2b + c n + c r) α 3 3 (2b + c n k) (2b + c n + c r ) α 2 + ( 8b 2 + 3c 2 n 4bk 3kc n + 10bc n + 4bc r + c nc r 2kc r ) α ( 2b 2 + 4bc n + c 2 n kc n )] = 0 F (α) = (2b + c n + c r ) α 2 2 (b + c n ) α + (2b + c n )
HP: Lower-level Profit maximisation: max qn 0 max qr 0 KKTconditions: HP: Lower-level p (q n + qr ) cn (qn) p F IT qr (αqn qr ) p REC pf IT qr cr (qr ) + (1 α) p REC qr 0 qn a + 2b (qn + qr ) + cnqn + αp REC 0 0 qr p F IT + cr qr (1 α) p REC 0 Market clearing condition for REC: Optimal interior solutions: 0 p REC 2qr α(qn + qr ) 0 [( (2 α) p F IT ) ] a α + a qn = (cn + cr ) α 2 + (4b + 3cn) α + 2 (2b + cn) [( α p F IT ) ] a α + a qr = (cn + cr ) α 2 + (4b + 3cn) α + 2 (2b + cn) ( ṗ REC cnp F IT ) + acr α 2 (2b + cn) p F IT = (cn + cr ) α 2 + (4b + 3cn) α + 2 (2b + cn) [a (cn + cr )] α 2 [ a (2b + 3cn) + 2bp F IT ] α + 2a (b + cn) ṗ = (cn + cr ) α 2 + (4b + 3cn) α + 2 (2b + cn)
HP: Upper-level Social welfare maximisation: HP: Upper-level max {p F IT >p, 0 α 1} {q n,q r } {p REC } qn +q r p(q )dq c n (q n) c r (q r) d n (q n) 0 s.t 0 q n a + 2b (q n + q r ) + c n q n + αp REC 0 0 q r p F IT + c r q r (1 α) p REC 0 0 p REC 2q r α(q n + q r) 0 KKTconditions: α [2aF (α) G (α) H (α)] F (α) 2 = 0 2a [F (α) G (α) + F (α) G (α)] 1 2 G (α) [G (α) H (α) + 2G (α) H (α)] F (α) 2 2 [ 2aF (α) 1 2 G (α) H (α)] F (α) G (α) F (α) 3 = 0 F (α) = (c n + c r) α 2 (4b + 3c n) α + 2 (2b + c n) G (α) = ( p F IT a ) α + a H (α) = 4b + (c n + k) (2 α) 2 + c rα 2
Numerical Analysis
Parameters Parameters Intercept of the inverse demand function a 100 Slope of inverse demand function b 0.01 NRE production c n 0.025 RE production c r 0.25 Rate of increase in marginal damage cost k [0, 0.1]
Equilibrium Electricity Price Equilibrium Electricity Price 95 ] h W / M [$ e ric P ity c tric le E 90 85 80 75 70 CP FIT RPS HP 65 0 0.02 0.04 0.06 0.08 0.1 The electricity price for FIT is smaller than those for other policies. K Incentive of increases in the productions due to the fixed price NRE sells those in the market
Equilibrium REC and FIT Prices Equilibrium REC and FIT Prices 160 230 140 RPS 210 FIT ] 120 h W 100 / M [$ e 80 ric p 60 C E R 40 HP 190 ] h W170 / M 150 [$ e 130 ric p 110 IT F 90 HP 20 70 0 50 0 0.02 0.04 0.06 0.08 0.1 K REC price: HP < PRS The demand for REC decreases due to FIT. FiT price: HP < PRS 0 0.02 0.04 0.06 0.08 0.1 FiT price decreases and becomes the same as the electricity price. Mitigate the increases in FiT price due to RPS scheme K
Optimal RPS Target and Output Ratio for Renewable Source Optimal RPS Target and Output Ratio for Renewable Source 0.9 y r g e 0.8 n E 0.7 le b a0.6 w e n0.5 e R r0.4 fo t io 0.3 a R t0.2 u t p u0.1 O 0 CP FIT RPS HP HP > RPS > FIT 0 0.02 0.04 0.06 0.08 0.1 Effect of the REC market and FiT FiT scheme K NRE needs to produce and sell relatively large electricity in order to buy RE s electricity through FiT.
Social Welfare Social Welfare 0.16 ) 0.14 6 0 1 ( re lfa e W l c ia o S 0.12 0.1 0.08 0.06 CP FIT RPS HP 0.04 0 0.02 0.04 0.06 0.08 0.1 Order of the maximised social welfare: HP > RPS > FIT Large producer surplus and small damage cost K
Conclusions
Summary and Future Work Summary and Future Work Efficiency of the hybrid policies, i.e., RPS and FiT Compare it to the single policy scheme (either RPS or FiT) Maximized social welfare for the hybrid policy is greater than those for single policies, e.g., RPS or FiT The ratio of renewable energy output to the non-renewables is greater than that under the single policy. Directions for future research Verify findings analytically Extend the model to introduce uncertainty of the demand Allow for investment decisions and capacity choice for renewable energy