Are Targets for Renewable Portfolio Standards Too Low? A Complementarity-Based Policy Analysis

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1 Are Targets for Renewable Portfolio Standards Too Low? A Complementarity-Based Policy Analysis Afzal S Siddiqui a Yihsu Chen b Makoto Tanaka c a Department of Statistical Science, University College London and Department of Computer and Systems Sciences, Stockholm University, address: afzalsiddiqui@uclacuk b University of California at Merced c National Graduate Institute for Policy Studies 18 June 2014

2 Table of Contents 1 Introduction 2 3 4

3 Introduction

4 Motivation Renewable Portfolio Standards: Common Market for Green Certificates (Energimyndigheten, 2012)

5 Policy Background Evolving Paradigms Vertical Integration Restructuring Generation Gen 1 Ret 1 Distribution Retailing Gen n Ret m Transmission Distribution Transmission

6 Twin Challenges Deregulation and Decarbonisation Regulated paradigm Single decision maker Single-level optimisation model for planning Post-restructuring Imperfect competition Endogenous price formation Greater focus on sustainable energy Policymaker s dilemma Comply with international treaties, eg, EU by 2020 Yet, cannot be seen to interfere with industry Delicate balance between providing incentives to guide a sustainable energy transition and blunting the market Need to understand the implications of strategic behaviour when designing markets or setting RPS targets

7 Related Work Analysis of RPS Targets in Deregulated Electricity Industries Fischer (2010) explores the impact of RPS Modest RPS targets may initially lower the equilibrium electricity price because the REC price serves as a subsidy for RE More stringent RPS targets cause NRE production to reduce Puts upward pressure on the equilibrium electricity price and provides consumers with a strong signal to reduce demand Amundsen and Bergman (2012) allow for producers to behave à la Cournot in both electricity and REC markets Tanaka and Chen (2013) develop a bi-level model: dominant firm acts as a Stackelberg leader constrained by a competitive fringe at the lower level Resulting MPEC illustrates how a dominant NRE producer can manipulate prices in both markets with adverse consequences for RE investors NRE producer lowers the REC price while increasing the electricity price

8 Complementarity 101 Playing Games Equilibrium Problem (EP) Complementarity Problem (CP) Optimisation Problem 1 Equilibrium Constraints Optimisation Problem n KKT Conditions of Problem 1 Equilibrium Constraints KKT Conditions of Problem n Optimisation Problem constrained by Optimisation Problems (OPcOP) Mathematical Program with Equilibrium Constraints (MPEC) Objective Function Objective Function Constraints Constraints Optimisation Problem 1 Optimisation Problem n KKT Conditions of Problem 1 KKT Conditions of Problem n Equilibrium Constraints Equilibrium Constraints

9 Contribution Research Objective and Findings We tackle the policymaker s problem directly by making the RPS target endogenous Analyse impact on social welfare by reflecting strategic behaviour (Cournot oligopoly) or not (perfect competition) by lower-level producers Compare different market settings: central planner (CP), perfect competition (PC), and Cournot oligopoly (CO) Show that the RPS target has the ordering: CP < CO < P C Ordering of imised welfare and emissions: CP > CO > P C Even if RPS target is set exogenously, p REC is lower for CO than for PC Single-level models pass up on the opportunity to reduce emissions further by ignoring the interplay between producers marginal revenues and costs

10 Mathematical Formulation and Analytical Insights

11 Assumptions Assumptions Policymaker s problem Set RPS target 0 α 1 at upper level Maximise SW internalising cost of emissions damage d(q n) = 1 2 Kq2 n Power sector s profit-imisation problems Power output q n and q r by NRE and RE sectors at the lower level Linear inverse demand function p(q) = A Zq Linear operating costs, ie, c n (q n ) = C n q n and c r (q r ) = C r q r Assume A > C r > C n and no capacity or transmission constraints Face RPS constraint that determines p REC Market settings: denote, ˆ, and as the optimal values for decision variables in CP, PC, and CO, respectively

12 Central Planner Single-Level Quadratic Programming Problem CP s SW imisation problem q n 0,q r 0 A (q n + q r) 1 Z (qn + qr)2 2 c n (q n ) c r (q r ) d(q n ) (1) Globally optimal solution for the problem in Eq (1) is: q n = (C r C n ) K ] [A C r Z K (Cr Cn) q r = Z ] [A C r Z K (Cr Cn) (2) (3) ᾱ = (A C r ) (4) Useful to note the function defining ᾱ: Q(α) = K (A C r) α Z (C r C n) + K (A C r) (5)

13 Central Planner Single-Level Quadratic Programming Problem CP s SW imisation problem q n 0,q r 0 A (q n + q r) 1 Z (qn + qr)2 2 c n (q n ) c r (q r ) d(q n ) (1) Globally optimal solution for the problem in Eq (1) is: q n = (C r C n ) K ] [A C r Z K (Cr Cn) q r = Z ] [A C r Z K (Cr Cn) (2) (3) ᾱ = (A C r ) (4) Useful to note the function defining ᾱ: Q(α) = K (A C r) α Z (C r C n) + K (A C r) (5)

14 Central Planner Single-Level Quadratic Programming Problem CP s SW imisation problem q n 0,q r 0 A (q n + q r) 1 Z (qn + qr)2 2 c n (q n ) c r (q r ) d(q n ) (1) Globally optimal solution for the problem in Eq (1) is: q n = (C r C n ) K ] [A C r Z K (Cr Cn) q r = Z ] [A C r Z K (Cr Cn) (2) (3) ᾱ = (A C r ) (4) Useful to note the function defining ᾱ: Q(α) = K (A C r) α Z (C r C n) + K (A C r) (5)

15 Deregulated Power Sector with Perfect Competition Lower Level: Producers Problems and MCP q n 0 pq n c n (q n ) αp REC q n 0 q n A + Z (q n + q r ) + C n + αp REC 0 (6) q r 0 pq r c r (q r ) + (1 α)p REC q r 0 q r A + Z (q n + q r) + C r (1 α)p REC 0 (7) 0 p REC q r α (q n + q r ) 0 (8)

16 Deregulated Power Sector with Perfect Competition Lower Level: Producers Problems and MCP q n 0 pq n c n (q n ) αp REC q n 0 q n A + Z (q n + q r ) + C n + αp REC 0 (6) q r 0 pq r c r (q r ) + (1 α)p REC q r 0 q r A + Z (q n + q r) + C r (1 α)p REC 0 (7) 0 p REC q r α (q n + q r ) 0 (8)

17 Deregulated Power Sector with Perfect Competition Lower Level: Producers Problems and MCP q n 0 pq n c n (q n ) αp REC q n 0 q n A + Z (q n + q r ) + C n + αp REC 0 (6) q r 0 pq r c r (q r ) + (1 α)p REC q r 0 q r A + Z (q n + q r) + C r (1 α)p REC 0 (7) 0 p REC q r α (q n + q r ) 0 (8)

18 Deregulated Power Sector with Perfect Competition Lower-Level MCP s Interior Solutions ˆq n (α) = (1 α) [A (αc r + (1 α) C n )] Z (9) ˆq r (α) = α [A (αc r + (1 α) C n )] Z (10) ˆp REC (α) = C r C n (11) ˆp (α) = αc r + (1 α) C n (12)

19 Deregulated Power Sector with Perfect Competition Lower-Level MCP s Interior Solutions ˆq n (α) = (1 α) [A (αc r + (1 α) C n )] Z (9) ˆq r (α) = α [A (αc r + (1 α) C n )] Z (10) ˆp REC (α) = C r C n (11) ˆp (α) = αc r + (1 α) C n (12)

20 Deregulated Power Sector with Perfect Competition Lower-Level MCP s Interior Solutions ˆq n (α) = (1 α) [A (αc r + (1 α) C n )] Z (9) ˆq r (α) = α [A (αc r + (1 α) C n )] Z (10) ˆp REC (α) = C r C n (11) ˆp (α) = αc r + (1 α) C n (12)

21 Deregulated Power Sector with Perfect Competition Lower-Level MCP s Interior Solutions ˆq n (α) = (1 α) [A (αc r + (1 α) C n )] Z (9) ˆq r (α) = α [A (αc r + (1 α) C n )] Z (10) ˆp REC (α) = C r C n (11) ˆp (α) = αc r + (1 α) C n (12)

22 Deregulated Power Sector with Perfect Competition Upper Level: Policymaker s MPEC and KKT Condition {0 α 1} {q n,q r } {p REC } A (q n + q r) 1 Z (qn + qr)2 2 C n q n C r q r 1 2 Kq2 n (13) st Eqs (6) (8) α Aˆq n (α) (1 α) Z (ˆq n (α)) 2 2 (1 α) 2 Cn ˆqn (α) C r ˆq n (α) α K (ˆq n (α)) 2 (1 α) 2 (14) { ( (C n C r) Z K (1 α) 2) } + K (1 α) [A (αc r + (1 α) C n)] [A (αc r + (1 α) C n )] Z 2 = 0 (15)

23 Deregulated Power Sector with Perfect Competition Upper Level: Policymaker s MPEC and KKT Condition {0 α 1} {q n,q r } {p REC } A (q n + q r) 1 Z (qn + qr)2 2 C n q n C r q r 1 2 Kq2 n (13) st Eqs (6) (8) α Aˆq n (α) (1 α) Z (ˆq n (α)) 2 2 (1 α) 2 Cn ˆqn (α) C r ˆq n (α) α K (ˆq n (α)) 2 (1 α) 2 (14) { ( (C n C r) Z K (1 α) 2) } + K (1 α) [A (αc r + (1 α) C n)] [A (αc r + (1 α) C n )] Z 2 = 0 (15)

24 Deregulated Power Sector with Perfect Competition Upper Level: Policymaker s MPEC and KKT Condition {0 α 1} {q n,q r } {p REC } A (q n + q r) 1 Z (qn + qr)2 2 C n q n C r q r 1 2 Kq2 n (13) st Eqs (6) (8) α Aˆq n (α) (1 α) Z (ˆq n (α)) 2 2 (1 α) 2 Cn ˆqn (α) C r ˆq n (α) α K (ˆq n (α)) 2 (1 α) 2 (14) { ( (C n C r) Z K (1 α) 2) } + K (1 α) [A (αc r + (1 α) C n)] [A (αc r + (1 α) C n )] Z 2 = 0 (15)

25 Deregulated Power Sector with Perfect Competition Characteristics of RPS Target under PC 5 4 Q functions with respect to α CP PC CO 3 2 Q(α) α

26 Deregulated Power Sector with Cournot Oligopoly Lower Level: Producers Problems and MCP q n 0 p (q n + q r ) q n c n (q n ) αp REC q n 0 q n A + Z (q n + q r ) + Zq n + C n + αp REC 0 (16) q r 0 pq r c r (q r ) + (1 α)p REC q r 0 q r A + Z (q n + q r ) + C r (1 α)p REC 0 (17) Eq (8)

27 Deregulated Power Sector with Cournot Oligopoly Lower Level: Producers Problems and MCP q n 0 p (q n + q r ) q n c n (q n ) αp REC q n 0 q n A + Z (q n + q r ) + Zq n + C n + αp REC 0 (16) q r 0 pq r c r (q r ) + (1 α)p REC q r 0 q r A + Z (q n + q r ) + C r (1 α)p REC 0 (17) Eq (8)

28 Deregulated Power Sector with Cournot Oligopoly Lower Level: Producers Problems and MCP q n 0 p (q n + q r ) q n c n (q n ) αp REC q n 0 q n A + Z (q n + q r ) + Zq n + C n + αp REC 0 (16) q r 0 pq r c r (q r ) + (1 α)p REC q r 0 q r A + Z (q n + q r ) + C r (1 α)p REC 0 (17) Eq (8)

29 Deregulated Power Sector with Cournot Oligopoly Lower-Level MCP s Interior Solutions q n (α) = (1 α) [A (αcr + (1 α) Cn)] ZF (α) (18) q r (α) = α [A (αc r + (1 α) C n )] ZF (α) (19) p REC (α) = (C r C n ) (1 α) (A C r ) F (α) (20) p (α) = A (1 α)2 + αc r + (1 α) C n F (α) where F (α) = α 2 2α α [0, 1] (21)

30 Deregulated Power Sector with Cournot Oligopoly Lower-Level MCP s Interior Solutions q n (α) = (1 α) [A (αcr + (1 α) Cn)] ZF (α) (18) q r (α) = α [A (αc r + (1 α) C n )] ZF (α) (19) p REC (α) = (C r C n ) (1 α) (A C r ) F (α) (20) p (α) = A (1 α)2 + αc r + (1 α) C n F (α) where F (α) = α 2 2α α [0, 1] (21)

31 Deregulated Power Sector with Cournot Oligopoly Lower-Level MCP s Interior Solutions q n (α) = (1 α) [A (αcr + (1 α) Cn)] ZF (α) (18) q r (α) = α [A (αc r + (1 α) C n )] ZF (α) (19) p REC (α) = (C r C n ) (1 α) (A C r ) F (α) (20) p (α) = A (1 α)2 + αc r + (1 α) C n F (α) where F (α) = α 2 2α α [0, 1] (21)

32 Deregulated Power Sector with Cournot Oligopoly Lower-Level MCP s Interior Solutions q n (α) = (1 α) [A (αcr + (1 α) Cn)] ZF (α) (18) q r (α) = α [A (αc r + (1 α) C n )] ZF (α) (19) p REC (α) = (C r C n ) (1 α) (A C r ) F (α) (20) p (α) = A (1 α)2 + αc r + (1 α) C n F (α) where F (α) = α 2 2α α [0, 1] (21)

33 Deregulated Power Sector with Cournot Oligopoly Upper Level: Policymaker s MPEC and KKT Condition {0 α 1} {q n,q r } {p REC } A (q n + q r) 1 Z (qn + qr)2 2 C n q n C r q r 1 2 Kq2 n (22) st Eqs (8), (16) (17) α Aqn (α) (1 α) Z (q n (α)) 2 2 (1 α) 2 C nqn (α) C rqn (α) α K (q n (α)) 2 (1 α) 2 (23) [A (αc r + (1 α) C {[ n)] Z 2 F (α) 3 Z (2F (α) 1) K (1 α) 2] (C n C r) F (α) + [A (αc r + (1 α) C n )] [F (α) (K 2Z) (1 α) [ +2 (1 α) Z (2F (α) 1) K (1 α) 2]]} = 0 (24)

34 Deregulated Power Sector with Cournot Oligopoly Upper Level: Policymaker s MPEC and KKT Condition {0 α 1} {q n,q r } {p REC } A (q n + q r) 1 Z (qn + qr)2 2 C n q n C r q r 1 2 Kq2 n (22) st Eqs (8), (16) (17) α Aqn (α) (1 α) Z (q n (α)) 2 2 (1 α) 2 C nqn (α) C rqn (α) α K (q n (α)) 2 (1 α) 2 (23) [A (αc r + (1 α) C {[ n)] Z 2 F (α) 3 Z (2F (α) 1) K (1 α) 2] (C n C r) F (α) + [A (αc r + (1 α) C n )] [F (α) (K 2Z) (1 α) [ +2 (1 α) Z (2F (α) 1) K (1 α) 2]]} = 0 (24)

35 Deregulated Power Sector with Cournot Oligopoly Upper Level: Policymaker s MPEC and KKT Condition {0 α 1} {q n,q r } {p REC } A (q n + q r) 1 Z (qn + qr)2 2 C n q n C r q r 1 2 Kq2 n (22) st Eqs (8), (16) (17) α Aqn (α) (1 α) Z (q n (α)) 2 2 (1 α) 2 C nqn (α) C rqn (α) α K (q n (α)) 2 (1 α) 2 (23) [A (αc r + (1 α) C {[ n)] Z 2 F (α) 3 Z (2F (α) 1) K (1 α) 2] (C n C r) F (α) + [A (αc r + (1 α) C n )] [F (α) (K 2Z) (1 α) [ +2 (1 α) Z (2F (α) 1) K (1 α) 2]]} = 0 (24)

36 Deregulated Power Sector with Cournot Oligopoly Characteristics of RPS Target under CO 5 4 Q functions with respect to α CP PC CO 3 2 Q(α) α Proposition ᾱ < α < ˆα

37 Deregulated Power Sector with Cournot Oligopoly Comparison of Equilibrium Prices Level curves of the SW and locus of optimal solutions for lower level with various α q r q n Proposition p (α) > ˆp (α) and p REC (α) < ˆp REC (α)

39 Optimal RPS Target A = 100, Z = 001, K [001, 010], C n = 20, C r = α CP PC CO K

40 Equilibrium Power Price p CP PC CO K

41 Equilibrium REC Price p REC PC CO K

42 Optimal NRE Output CP PC CO q n K

43 Optimal RE Output q r CP PC CO K

44 Equilibrium Damage from Emissions 9 x CP PC CO EX K

45 Maximised Social Welfare 16 x CP PC CO SW K

47 Summary Complementarity approach to compare CP, PC, and CO settings in analysing transition to a more sustainable energy system via implementation of RPS CP matches the most efficient resource with demand but has the highest emissions as overall consumption is unaffected after RE is marginal PC: higher RPS target is used to entice RE output without needing consumption to be reduced so drastically CO: similar incentives as PC, but RPS target needs to be scaled back in order to subvert NRE sector s desire to exert market power Somewhat counterintuitively, lowest (highest) imised SW and emissions under PC (CP) For the same RPS target, higher (lower) power (REC) price in CO setting vis-à-vis PC Future work: stochastic model, representation of transmission network, energy storage

Pure or Hybrid?: Policy Options for Renewable Energy 1

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