Evaluación pública de grandes proyectos: teoría y práctica Examples: Oligopolistic Electricity and General Equilibrium Mixed Complementarity Models

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1 Evaluación pública de grandes proyectos: teoría y práctica Examples: Oligopolistic Electricity and General Equilibrium Mixed Complementarity Models Renato Rodrigues 5 th July, 2013

2 Contents 1. Introduction 1. Mixed Complementarity problems 2. Application 1: Electricity sector oligopolistic model A. First step: Optimization problem B. Second step: MCP equivalent formulation and oligopolistic model C. The fun part: Case studies examples I. ETS evaluation II. Electricity demand response increase 3. Application 2: Walrasian general equilibrium models A. Introduction B. Structure and mathematical formulation C. Revisiting the Electricity demand response case study D. Conclusions: Potential and limitations 2

3 1 Introduction

4 Introduction: Class objective: Present examples of real world policy evaluations using mathematical operation research instruments. Why: Assist decision making process. Necessity for ex-ant assessments of complex policies and agents behavior Class focus: mixed complementarity problems. Lets start!!! 4

5 Nonlinear and mixed complementarity problem Special case of Variational Inequality Mixed complementarity problem: Karush Kuhn Tucker conditions: Karush Kuhn Tucker conditions provides the necessary conditions for a solution in nonlinear programming to be optimal. It is a generalization of the method of Lagrange multipliers to inequality constraints. 5

6 2 Application 1 Electricity sector oligopolistic model

7 Application 1: How to evaluate the consequences to an electricity company of different CO2 prices (or a different ETS regime)? Which are the consequences of a increase on demand response for the market prices? What a nuclear phase-out means to electricity market prices? What are the competitors behavior changes if one company changes its strategies? How much CO2 emissions are avoided by implementing a renewable subsidy? 7

8 Application 1: Instrument: Electricity operations and expansion planning simulation. First step: Simulate a single electricity company optimization problem Second step: Introduce oligopolistic competition behavior 8

9 Electricity operations and expansion planning optimization model Company objective Profit maximization Cost minimization Risk aversion Market share. Time Horizon Long vs short run decisions Technology representation Economic production function Engeneering technical constraints Level of detail data requirements and problem dimension 9

10 Electricity generation company and market problem: Demand curve Low demand Demand curve Peak hour P Fuel oil CCGT Carbon Nuclear 10

11 Electricity operations and expansion planning model (1/2): Min: Fuel cost PGEN fuel y,t,f,l,p,b η y,l,t p y,p,t,f dur l,p,b 10 6 t,f,p,b CO 2 emission costs + PGEN y,t,f,l,p,b co2 fuel_content t,f p CO2 y dur l,p,b 10 6 t,f,p,b Variable O&M equipament costs + PGEN y,t,f,l,p,boem_vom y,t dur l,p,b 10 6 t,f,p,b Renewable premiun income PGEN y,t,f,l,p,bpremium renew t,f dur l,p,b 10 6 t,f,p,b + oem_fom y,l,t labor sc + oem_fom y,l,t + oem_fom equip y,l,t 10 3 t + t overn_costs y,t idc t crf t rights CO2 CO2 y,l,t p y t,f,p,b Emission rights Fixed O&M costs cap to_be_amort y,l,t TCAP y,l,t Installed capacity amortization costs paid in the year y, l y y y` y l_t tmeityn on PINS y,l,t 11

12 Electricity operations and expansion planning model (2/2): Subject to: Demand balance: demand y,l,p,b PGEN y,t,f,l,p,b + pimp y,l,p,b PPUMPED y,l,p,b own_cons PGEN y,t,f,l,p,b t,f loss y,l,p,b Hydro reservoir management level: PGEN y,t,f,l,p,b + pimp y,l,p,b + pexp y,l,p,b PPUMPED y,l,p,b t,f inflows y,l,p PGEN y,hyd_res,na,l,p,b RES y,l,p + RES y,l,p+1 b Hydro run of river production: PGEN y,hyd_ror,na,l,p,b dur l,p,b ror_inflows y,l,p Pumping efficiency: Maximum pumping capacity: PPUMPED y,l,p,b eff Pump PGEN y,pump,na,l,p,b dur l,p,b p,b PGEN y,pump,na,l,p,b dur l,p,b res_max y,l,pump p,b Fixed use proportion of combustibles in Fuel-Gas power plants: foil_on_fg PGEN y,f G,Fuel oil,l,p,b = pctg y,l PGENy,F G,f,l,p,b f Wind power production at each load block: PGEN y,wind,na,l,p,b = pgen_base_year l,p,b,wind Other special regime renewable production at each load block: PGEN y,orsr,na,l,p,b = pgen_base_year l,p,b,orsr Maximum production capacity: PGEN y,t,f,l,p,b availability y,l,t TCAP y,l,t Maximum hydro reservoir capacity: RES y,l,p res_max y,l,hyd Total installed capacity: TCAP y,l,wind cap Base year,l,wind TCAP y,l,orsr cap Base year,l,orsr TCAP y,l,t = cap y,l,t + PINS y,l,t y y y` y life_time Reserves (firm capacity reserves requirements in non-intermittent technologies): t_non_intt TCAP y,l,t non_intt_coverage max p,b demand y,l,p,b t,f 12

13 Optimization model characteristics and advantages: How to solve it. Simplex algorithm Solvers (matlab, GAMs or even excel for very small problems) Formulation: Optimization problem Equivalent mixed complementarity model Potentials of optimization problem formulation Easy and fast to solve Suitable to introduce complexities In dimension (time and technology) In variables (integer and binary variables) 13

14 Optimization model limitations: Restringing assumptions Perfect competition vs. oligopolistic market Single firm modeling Competitors decisions does not reacts to firm decisions Suppliers prices are not changed by firm decisions (small company assumption) Single objective function we only consider one objective function at time when using an optimization framework. In order to deal with company decisions influences we would need to assume a conjectural variations approach, even so this would need to be exogenously defined from our model. What if we want to evaluate different companies competing and acting together? A iterative approach could be necessary, but not all primal and dual information would be shared between the problems. The mixed complementarity formulation alternative allows us to take into account simultaneous optimization problems all together 14

15 The electricity sector oligopolistic mixed complementarity model : The idea behind it is to develop the equivalent mixed complementarity formulation of each company in the market. Market clearing and demand conditions are used to link the agents behavior all together. We formulate a large equivalent problem with all optimization equilibrium conditions (KKT conditions) we share between all agents the primal and dual information of their respective problems. A different operation from one company directly changes the behavior of their competitors that by meantime could change again the behavior of the first agent. 15

16 The electricity sector oligopolistic mixed complementarity model : Electricity generation companies Optimization company 1 Optimization company i Optimization company n MMM P s Q s P pf Q pf,s pp s. t. MMM P s Q s P pf Q pf,s pp s. t. MMM P s Q s P pf Q pf,s pp s. t. 16

17 The electricity sector oligopolistic mixed complementarity model : Electricity generation companies Optimization company 1 Optimization company i Optimization company n P = f (Q) Demand Function 17

18 MCP model characteristics and advantages: How to solve it. Path solver in GAMs or quadratic equivalent problem Formulation Non lineal mixed complementarity model (KKT complementarity slackness) Advantages Simulation of oligopolistic behavior Agents interactions Multiple markets (product, allowance, green certificates, ) 18

19 MCP model limitations: Dimensionality Memory requirements Complex and less efficient solver method Nonlinear Local optimal Integer and binary variables if introduced are much more difficult to deal 19

20 MCP case study example 1: ETS evaluation Linares, P.; Javier Santos, F.; Ventosa, L. ; Lapiedra, L. Incorporating oligopoly, CO2 emissions trading and green certificates into a power generation expansion model, Automatica, Volume 44, Issue 6, June Evaluates the impacts of the European Emissions Trading System and of a tradable green certificate market on the operation and investments of the Spanish electricity sector. Proves the feasibility of using such models with realistic information and great data detail Models simultaneously the electricity market, the emissions market and the green certificates markets Presents the oligopolistic formulation, with competition in quantities in the short term (Conjectural variation) and in generation capacity as in a Cornout model. 20

21 MCP case study example 2: increase in electricity demand response Case study: Active household demand response potential savings in Spain Consumption variation with ADR Appliance Displacement Reduction ADR actions Washing machine 100% 40% Full shutdown Dishwasher 100% 40% ECO program Dryer 100% 20% Limitations Water heating 50% 30% stop / partial shutdown Heating - 50% Unacceptable shutdown Air_conditioner - 50% Power limitations, thermostat, time zones... Others - - Non manageable Efficiency effect Load displacement effect Original domestic demand DR domestic demand Original domestic demand DR domestic demand 21

22 MCP case study example 2: increase in electricity demand response Demand Response Simulation: Active demand response demand balance: demand y,l,p,b + IIIIIIIII_DD_LLLL y,l,p,b DDDDDDDDD_DD_LLLL y,l,p,b CCCCCCCCC_DD_LLLL y,l,p,b PGEN y,t,f,l,p,b + pimp y,l,p,b PPUMPED y,l,p,b own_cons PGEN y,t,f,l,p,b t,f t,f loss y,l,p,b PGEN y,t,f,l,p,b + pimp y,l,p,b + pexp y,l,p,b PPUMPED y,l,p,b t,f Maximum displacement: DDDDDDDDD_DD_LLLL y,l,p,b displaceable_load y,l,p,b Displacement balance: IIIIIIIII_DD_LLLL y,l,p,b dur l,p,b b = DDDDDDDDD_DD_LLLL y,l,p,b dur l,p,b b Potency conservation limit: CCCCCCCCC_DD_LLLL y,l,p,b conservable_load y,l,p,b Minimal savings requirement: DDDDDDDDD_DD_LLLL y,l,p,b ggg_ppppp y,l,p,b dur l,p,b b IIIIIIIII_DD_LLLL y,l,p,b ggg_ppppp y,l,p,b dur l,p,b b 1 min _sss dddddddddddd_llll y,l,p,b ggg_ppppp y,l,p,b dur l,p,b b 22

23 MCP case study example 2: increase in electricity demand response Results of the simulation: Benchmark DR policy Potential DR policy savings Total cost Total cost Total savings Conservation Load shifting (10 6 ) (10 6 ) (10 6 ) (10 6 ) (10 6 ) (%) (%) (%) (%) % 2.36% 1.92% 0.43% Price Quantity Emissions % % % CO2e % Acid e -3.26% -1.44% -1.88% -0.65% Final consumer savings

24 3 Application 2 Walrasian general equilibrium models

25 Computable General Equilibrium Model (CGE): Models a region, country or world economy Based on input output tables and Social accountability matrix Describes every economic flow between agents of the economy. It is composed by: Equilibrium set of variational equations (mixed complementarity formulation) that represents each economic agent behavior. Market clearing conditions. Macroeconomic closure assumptions. 25

26 CGE application examples: Main areas: Tax studies Agricultural and land use Capital and labor E3 models Bottom-up models Top-down models Cost minimization engineering models Environment General equilibrium models Great detail and computational requirements Energy Economics Macroeconomic and indirect effects evaluation Data based on technological and physical characteristics Accountability data 26

27 The electricity sector oligopolistic mixed complementarity model : Electricity generation companies Optimization company 1 Optimization company i Optimization company n P = f (Q) Demand Function 27

28 The economy-wide model (the CGE model): Foreign Sector Product Markets Importation / Exports payment Exportation / Imports payment Product Markets Expenditure Expenditure Households Goods & Services Taxes Government Goods & Services Taxes Productive Sectors Profit / Factor Income Profit / Factor Income Factor Market Foreign Savings Capital Transfers Factor Market Foreign Sector 28

29 The economy-wide model (the CGE model): Households: MMM WWWWWWW s. t. bbbbbb cccccccccc MMM U Q H g = c H g llqh g g s. t. P g Q g H g 1 s Y H Productive Sectors: MMM PPPPPPP s. t. pppppppppp ffffffff Government: MMM PPPPPP ssssssss s. t. bbbbbb cccccccccc Integrating Equations Market Clearing: Final Goods Production Factors Y G E G = S G Y G G = P pf q pf pp + tttttt EEE G + Y TTT E G = P Q g q G g + tttttt G H g Capital Formation: IIIIIIIIIII aaa SSSSSSS rrrrrrrrrrrrr S = s H Y H + S G + S Ext S Ext = P g M Q g M g transf Ext I g = θ g P g Q I P g EX Q g EX g - MMM P s Q s P pf Q pf,s s. t. Q s pp = α VV σ 1 s a pp Q σ pp,s pp σ σ 1 Foreign Sector: IIIIIIIII ssssssssssssss IIIIIII (AAAAAAAAA AAA. ) EEEEEEE CCC MMM P D MMM P Q g Q Q g + p EX g Q EX g P D g QD g Q D g P S g Q S g p M g QM g g s. t. s. t. Q D Q D g = CET Q Q g = CES(Q S g, Q M g ) g, QEX g 29

30 The economy-wide model (the CGE model): Households: MMM WWWWWWW s. t. bbbbbb cccccccccc Government: MMM PPPPPP ssssssss s. t. bbbbbb cccccccccc Integrating Equations Market Clearing: Capital Formation: IIIIIIIIIII aaa SSSSSSS rrrrrrrrrrrrr n i= 1 supply = n i= 1 demand Productive Sectors: MMM PPPPPPP s. t. pppppppppp ffffffff n i= 1 supply = n i= 1 demand Foreign Sector: IIIIIIIII ssssssssssssss IIIIIII (AAAAAAAAA AAA. ) EEEEEEE CCC 30

31 The economy-wide model (the CGE model): Productive Sectors International Aggregations Households Government Optimization sector 1 Optimization sector j Optimization sector n Europe Rest of the World Welfare Optimization Budget Constraint n i= 1 supply = n i= 1 demand Market clearing conditions Non-lineal system of simultaneous equations Mixed Complementary Problem (MCP) 31

32 Advantages and limitations of CGE models: Advantages: Evaluates rebound effects Indirect effects evaluations Economy wide effects Limitations: Highly Non lineal (sensitivity analysis needed) Dimensionality issues in memory and time requirements follows neoclassical efficient frontier assumptions Deterministic model that disregards uncertainty 32

33 Revisiting the Demand Response Case study Case study: Active household demand response potential savings in Spain Consumption variation with ADR Appliance Displacement Reduction ADR actions Washing machine 100% 40% Full shutdown Dishwasher 100% 40% ECO program Dryer 100% 20% Limitations Water heating 50% 30% stop / partial shutdown Heating - 50% Unacceptable shutdown Air_conditioner - 50% Power limitations, thermostat, time zones... Others - - Non manageable Efficiency effect Load displacement effect Original domestic demand DR domestic demand Original domestic demand DR domestic demand 33

34 Revisiting the Demand Response Case study CGE simulation results Rebound effect of 8% on total quantities. Changes from 1.44% to 1.01% on quantity retraction for the electricity generation. Products Prices Quantities Emissions Benchm. DR Benchm. DR p.u. p.u. p.u. % CO2e p.u. % % % Acid e Electricity GEN , % % % -0.32% Electricity TD&O , % % - Manufacturing , % % % 0.01% Coal , % % % -0.67% Oil/Nuclear , % % % 0.02% Gas , % % % -0.37% Transport , % % % 0.02% Other Services , % % % 0.00% Prod. Factors Labor 1.00 Capital , % 1, % % %

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