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Energy Economics 75 (2018) 261–273 Contents lists available at ScienceDirect Energy Economics journal homepage: www.elsevier.com/locate/eneco Quantifying the effects of uncertain climate and environmental policies on investments and carbon emissions: A case study of Chile Matías Bergen a , Francisco D. Muñoz b, * a Politecnico di Torino, Torino, Italy b Universidad Adolfo Ibáñez, Santiago, Chile ARTICLE INFO Article history: Received 25 January 2018 Received in revised form 13 July 2018 Accepted 13 August 2018 Available online 18 August 2018 JEL classification: N76 Q4 D80 D81 Q54 Q50 Keywords: Uncertainty Climate policies Transmission and generation planning Carbon emissions Stochastic programming Equilibrium ABSTRACT In this article we quantify the effect of uncertainty of climate and environmental policies on transmission and generation investments, as well as on CO 2 emissions in Chile. We use a two-stage stochastic plan- ning model with recourse or corrective investment options to find optimal portfolios of infrastructure both under perfect information and uncertainty. Under a series of assumptions, this model is equivalent to the equilibrium of a much more complicated bi-level market model, where a transmission planner chooses investments first and generation firms invest afterwards. We find that optimal investment strategies present important differences depending on the policy scenario. By changing our assumption of how agents will react to this uncertainty we compute bounds on the cost that this uncertainty imposes on the system, which we estimate ranges between 3.2% and 5.7% of the minimum expected system cost of $57.6B depending on whether agents will consider or not uncertainty when choosing investments. We also find that, if agents choose investments using a stochastic planning model, uncertain climate policies can result in nearly 18% more CO 2 emissions than the equilibrium levels observed under perfect information. Our results highlight the importance of credible and stable long-term regulations for investors in the electric power industry if the goal is to achieve climate and environmental targets in the most cost-effective manner and to minimize the risk of asset stranding. © 2018 Elsevier B.V. All rights reserved. 1. Introduction In 2014 the Intergovernmental Panel on Climate Change con- cluded that changes in climate due to global warming are a major threat to humans, a large number of economic activities, and most ecosystems on earth (Field et al., 2014). In response to this mes- sage, many countries and regions have enacted or are discussing the implementation of a series of environmental and economic policies that aim at reducing greenhouse gas emissions across all economic and industrial activities. In the electricity industry, these policies include carbon taxes and cap-and-trade programs (Chen and Tseng, 2011), Renewable Portfolio Standards (RPSs) (Lyon and Yin, 2010), * Corresponding author. E-mail addresses: [email protected] (M. Bergen), [email protected] (F.D. Muñoz). feed-in tariffs (Couture and Gagnon, 2010), production tax credits (Wiser et al., 2007), and energy efficiency programs (Arimura et al., 2011), among others. To date, more than 100 countries have either binding or voluntary renewable targets (REN21, 2015) and nearly 40 national jurisdictions have put a price on carbon emissions (Kossoy and Guigon, 2012). A salient feature of these policies is that they are highly uncertain, which complicates investment decisions for both power transmis- sion planners and generation firms. Part of the uncertainty of climate policies is a direct consequence of the uncertainty of multi-decadal climate forecasts and the potential effects of increasing levels of greenhouse emissions on the atmosphere (Allen et al., 2000; Murphy et al., 2004; Tol, 2003). Naturally, as prediction models improve and new information becomes available, policy makers can adjust the stringency of environmental regulations in order to mitigate the effects of climate change in the most economically efficient manner. Furthermore, the use of different methodologies can also https://doi.org/10.1016/j.eneco.2018.08.014 0140-9883/© 2018 Elsevier B.V. All rights reserved.

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  • Energy Economics 75 (2018) 261–273

    Contents lists available at ScienceDirect

    Energy Economics

    j ourna l homepage: www.e lsev ie r .com/ locate /eneco

    Quantifying the effects of uncertain climate and environmental policieson investments and carbon emissions: A case study of Chile

    Matías Bergena, Francisco D. Muñozb,*aPolitecnico di Torino, Torino, ItalybUniversidad Adolfo Ibáñez, Santiago, Chile

    A R T I C L E I N F O

    Article history:Received 25 January 2018Received in revised form 13 July 2018Accepted 13 August 2018Available online 18 August 2018

    JEL classification:N76Q4D80D81Q54Q50

    Keywords:UncertaintyClimate policiesTransmission and generation planningCarbon emissionsStochastic programmingEquilibrium

    A B S T R A C T

    In this article we quantify the effect of uncertainty of climate and environmental policies on transmissionand generation investments, as well as on CO2 emissions in Chile. We use a two-stage stochastic plan-ning model with recourse or corrective investment options to find optimal portfolios of infrastructure bothunder perfect information and uncertainty. Under a series of assumptions, this model is equivalent to theequilibrium of a much more complicated bi-level market model, where a transmission planner choosesinvestments first and generation firms invest afterwards. We find that optimal investment strategies presentimportant differences depending on the policy scenario. By changing our assumption of how agents willreact to this uncertainty we compute bounds on the cost that this uncertainty imposes on the system, whichwe estimate ranges between 3.2% and 5.7% of the minimum expected system cost of $57.6B depending onwhether agents will consider or not uncertainty when choosing investments. We also find that, if agentschoose investments using a stochastic planning model, uncertain climate policies can result in nearly 18%more CO2 emissions than the equilibrium levels observed under perfect information. Our results highlightthe importance of credible and stable long-term regulations for investors in the electric power industry ifthe goal is to achieve climate and environmental targets in the most cost-effective manner and to minimizethe risk of asset stranding.

    © 2018 Elsevier B.V. All rights reserved.

    1. Introduction

    In 2014 the Intergovernmental Panel on Climate Change con-cluded that changes in climate due to global warming are a majorthreat to humans, a large number of economic activities, and mostecosystems on earth (Field et al., 2014). In response to this mes-sage, many countries and regions have enacted or are discussing theimplementation of a series of environmental and economic policiesthat aim at reducing greenhouse gas emissions across all economicand industrial activities. In the electricity industry, these policiesinclude carbon taxes and cap-and-trade programs (Chen and Tseng,2011), Renewable Portfolio Standards (RPSs) (Lyon and Yin, 2010),

    * Corresponding author.E-mail addresses: [email protected] (M. Bergen), [email protected] (F.D. Muñoz).

    feed-in tariffs (Couture and Gagnon, 2010), production tax credits(Wiser et al., 2007), and energy efficiency programs (Arimura et al.,2011), among others. To date, more than 100 countries have eitherbinding or voluntary renewable targets (REN21, 2015) and nearly 40national jurisdictions have put a price on carbon emissions (Kossoyand Guigon, 2012).

    A salient feature of these policies is that they are highly uncertain,which complicates investment decisions for both power transmis-sion planners and generation firms. Part of the uncertainty of climatepolicies is a direct consequence of the uncertainty of multi-decadalclimate forecasts and the potential effects of increasing levels ofgreenhouse emissions on the atmosphere (Allen et al., 2000; Murphyet al., 2004; Tol, 2003). Naturally, as prediction models improveand new information becomes available, policy makers can adjustthe stringency of environmental regulations in order to mitigatethe effects of climate change in the most economically efficientmanner. Furthermore, the use of different methodologies can also

    https://doi.org/10.1016/j.eneco.2018.08.0140140-9883/© 2018 Elsevier B.V. All rights reserved.

    https://doi.org/10.1016/j.eneco.2018.08.014http://www.ScienceDirect.com/http://www.elsevier.com/locate/enecohttp://crossmark.crossref.org/dialog/?doi=10.1016/j.eneco.2018.08.014&domain=pdfmailto:[email protected]:[email protected]://doi.org/10.1016/j.eneco.2018.08.014

  • 262 M. Bergen, F.D. Muñoz / Energy Economics 75 (2018) 261–273

    have relatively large impacts on, for instance, estimates on the socialcost of carbon emissions (Tol, 2008; Ackerman and Stanton, 2012),which are ultimately used to guide environmental policies such ascarbon taxes.

    A changing political landscape also leads to uncertain environ-mental policies. For instance, generation firms and transmissionplanners in the US now face large regulatory uncertainties given thegoal of the current administration to basically dismantle most of theenvironmental and climate policies enacted during the two previousadministrations (Kraft, 2017). In Europe, the UK has had a historyof inconsistent energy policies to reduce greenhouse gas emis-sions and to incentivize investments and generation from renewableenergy technologies (Newbery, 2016). Spain, a country that fostereda large amount of investments in renewables through feed-in tariffs,decided to drastically reduce the subsidies to solar PV installationsby nearly 30% in 2011 after the financial crisis, which likely affectedinvestment decisions in the Spanish electricity market (Hofman andHuisman, 2012).

    As it has been demonstrated in prior studies, an optimal portfolioof investments for one scenario of market, regulatory, and techno-logical conditions can be highly suboptimal if the future turns out tobe different to the planned one (van der Weijde and Hobbs, 2012;Munoz et al., 2014, 2015). In particular, more uncertainty increasesthe risk of stranded transmission and generation assets (Wright,2012).

    In this paper, we focus on quantifying how uncertain climate poli-cies as a consequence of changing political landscapes can affect bothtransmission and generation investments in Chile. We define a set offive different policy scenarios inspired by current regulations in Chileand on international policies and use a two-stage stochastic trans-mission and generation planning model with recourse to find optimalinvestment policies. Under the assumption of a perfectly competitivegeneration market, aligned objectives, inelastic demand, and proac-tive transmission investments that are 100% paid for by demand, thissolution is equivalent to an equilibrium on investments and opera-tions for a deregulated generation market. We employ this model toestimate bounds on the cost of uncertain climate and environmentalpolicies. The lower bound results from the assumption that all genera-tion firms and the transmission planner will develop plans consideringall scenarios explicitly, which minimizes the expected system cost ofmeeting future demand and climate policies. The upper bound resultsfrom imposing deterministic investment plans, assuming that bothgenerators and the transmission planner will act myopically, ignoringuncertainty.

    Our results indicate that, for our set of scenarios, the cost of uncer-tain climate and environmental policies for the Chilean system isbetween 3.2% ($1.8 Billion, lower bound) and 5.7% ($3.3 Billion, upperbound) of the optimal total system cost of the stochastic model.Furthermore, uncertain policies can result in nearly 18% higher CO2emissions than under perfect information if agents explicitly accountfor uncertainty in their decisions using a stochastic planning model,which could result in a high regret if more stringent emissions poli-cies are imposed in the future. Consequently, an uncertain politicallandscape can impose a rather high cost in the Chilean power sys-tem, even if all agents plan investments using sophisticated planningtools such as stochastic programming.

    The main message for regulators and planning authorities is that, ifpossible, policy uncertainties should be reduced to a minimum. Other-wise, planning with explicit consideration of uncertain policies wouldyield the lowest expected system cost. For planning authorities thatare also responsible for shaping long-term energy and environmentalpolicies, such as in Chile, this means that transmission infrastruc-ture should be selected taking into consideration that these policiescould change significantly in the near future under a different politi-cal administration or as new information becomes available. To ourbest knowledge, this is the first study that quantifies the investment

    effects and costs of uncertain climate and environmental policieson investments, costs, and carbon emissions in Chile, taking invest-ments in transmission and generation as a response to these policies.Yet, models that are similar to the one we use in this study havebeen employed before in other contexts (e.g., to quantify the valueof stochastic instead of deterministic transmission planning modelsin regions of Europe (van der Weijde and Hobbs, 2012) and the US(Munoz et al., 2014)).

    We structure the rest of the paper as follows. In Section 2 wepresent a literature review focused on previous research studies thathave quantified the effect climate change and climate change policyuncertainty on generation and transmission investment decisions. InSection 3 we present a two-stage stochastic transmission and gen-eration planning model. In Section 4 we summarize our case study.This includes a simplified representation of the Chilean power systemand our assumptions of policy scenarios. In Section 5 we present ournumerical results and analyze their implications. Finally, in Section 6we conclude and provide some policy recommendations.

    2. Literature review

    Climate change will have a large impact in the energy sector(Parkpoom et al., 2005). The rise of temperatures, changes in precip-itation, humidity variation, and the number of sunny days per yearwill affect both the consumption and production of energy (Feenstraet al., 1998). It is expected that consumption patterns of electricitywill change as average temperatures increase (Franco and Sanstad,2008; Hamlet et al., 2010). Multiples studies have shown that climatechange will lead to a decrease of hydropower production (Robinson,1997; Schaefli et al., 2007). Higher air and water surface tempera-ture, reduced river flow, and alterations in water availability will alsoaffect the efficiency of thermodynamic cycles in conventional powerplants (Mideksa and Kallbekken, 2010; Van Vliet et al., 2012). Thereis also scientific evidence that climate change will modify wind pat-terns. Since wind power is proportional to the cube of wind speed,even small changes in wind patterns could have a substantial impacton wind power resources (Pryor and Barthelmie, 2010; Breslow andSailor, 2002).

    There are also indirect impacts of climate change in the elec-tric power industry. These are a result of the uncertainty of policiesthat regulators and governments are planning to use to mitigate theeffects of climate change. Policies aimed at reducing carbon emis-sions may frequently and unexpectedly be updated for a numberof reasons, such as changes in government administration, failureto reach international and cooperative agreements, and the arrivalof new information about climate sensitivity (Pacala and Socolow,2004). While uncertainties about the unknown future of the marketarise for various reasons, unstable politics and unpredictable changesin policies are important sources of uncertainty. There are theoreticalmodels (McDonald and Siegel, 1986) and empirical evidence (Bloomet al., 2007) that show that companies might prefer to underinvest incostly innovative technologies when facing uncertain policies. Thisis an expectable behavior for rational and potentially risk-averseagents. Under uncertainty, there is an option value of waiting to seewhat policy will be implemented in the end, instead of committingto a costly investment that might become stranded if the future isnot what we planned for.

    Different studies have investigated and modeled the effects ofclimate change policy uncertainty and how decision-making in theelectricity sector is affected by such changes in policies (Fuss etal., 2009; Pacala and Socolow, 2004; Blyth et al., 2007). Fuss et al.(2009) use a real options model to quantify the effects of rising butuncertain CO2 taxes on generation investments. The authors find thatthe larger the uncertainty on future CO2 tax levels, the higher theamounts of CO2 emissions, which puts in evidence the value of cred-ible and predictable policies. In fact, they find that if policies are

  • M. Bergen, F.D. Muñoz / Energy Economics 75 (2018) 261–273 263

    updated less often, the policy itself will be more efficient in meet-ing long-term environmental goals. Fuss et al. (2008) and Blyth et al.(2007) reach similar conclusions. Fuss et al. (2012) extend the pre-vious work by considering risk aversion and portfolio effects underboth policy and fuel uncertainty. Morris et al. (2018) use a com-putable general equilibrium model of the US in a two-stage stochasticdynamic approximate program to find optimal investment decisionsunder uncertain CO2 emissions caps. They find that the optimalhedge against uncertainty is to include some non-carbon genera-tion technologies, in line with the findings of Inzunza et al. (2016)and Munoz et al. (2017b) when other sources of uncertainty (e.g.,fuel prices and the availability of hydro resources) are considered.However, none of these methods have been applied to the Chileanelectric power industry, considering both transmission and genera-tion investment levels as endogenous variables that could be affectedby uncertain policies and that could be adapted once uncertainty isrevealed.

    3. Methodology

    We quantify the effect of uncertain climate and environmentalpolicies using two different equilibrium models. One is deterministicand assumes that all market agents have access to perfect infor-mation. The other one is stochastic and assumes that all agents arerisk-neutral and make decisions trying to minimize expected systemcost (transmission planner) or maximize expected profits (gener-ation firms). We model uncertainty of climate and environmentalpolicies using a set of scenarios that affect features such as renewabletargets, carbon taxes, and demand levels. In both models transmis-sion investments are selected first by a proactive central planner thatminimizes expected system cost, then generation investment deci-sions are made by private generation firms, and finally the dispatchof generation units is made by the transmission system operatorminimizing operating costs. Under the assumption of aligned objec-tives, perfect information, risk neutrality, and perfect competition1,this equilibrium is equivalent to the solution of a two-stage stochas-tic optimization program with recourse that we describe in thissection (Munoz et al., 2017b).2

    Fig. 1 illustrates the timing of investment decisions in the two-stage stochastic planning model. The two stages are divided into threeperiods, indexed t. The first stage (t = 1) takes place before the rev-elation of the future long-term policy that will be applied, thus, alltransmission and generation investment decisions made at this stageare subject to non-anticipativity constraints. These investments thenbecome available at the beginning of period 2 (t = 2), in the sec-ond stage, after uncertainty is revealed. We assume that investorshave the option to conduct more investments in transmission andgeneration infrastructure in the second stage (i.e., recourse invest-ment decisions); however, these new investments do not becomeavailable until the beginning of period 3 (t = 3).

    1 Perfect competition is a reasonable assumption in the Chilean electricity marketbecause it relies on a cost-based mechanism for the dispatch and pricing of electric-ity. However, it has been demonstrated that in a cost-based market design can stillexercise market power through strategic investment decisions (Munoz et al., 2018)

    2 The equivalence between a central plan that minimizes expected cost and thecompetitive equilibrium on generation investments and operations when agents arerisk neutral and transmission infrastructure is fixed follows directly from Samuelson(1952). If a transmission planner selects investments minimizing expected systemcosts first, anticipating the response of generators, and transmission costs are recov-ered through a postage-stamp method and allocated 100% to an inelastic demand, thebi-level equilibrium model can be solved using a single stochastic program (Munozet al., 2017b). However, this equivalence is not valid if generators bear some trans-mission cost, demand is elastic, or the generation market is not perfectly competitive.For those cases more sophisticated models are needed (Bravo et al., 2016; Pozo et al.,2013; Sauma and Oren, 2006).

    3.1. Nomenclature

    We now introduce the nomenclature for our stochastic expansionplanning model. All currency is in US Dollars.

    Sets and indicesB Buses, indexed bL Transmission lines, indexed lG Generators, indexed kGC Subset of candidate generatorsGH Subset of hydro generators with reservoirsGR Subset of qualifying renewable generatorsH Hours, indexed hS Scenarios, indexed sT Periods, indexed t, u, and v

    ParametersCXts,l Capital cost of new transmission line [$]CYts,g Capital cost of new generation capacity [$/MW]Dts,b,h Forecasted demand [MW]EMk Carbon emissions rate [t CO2/MWh]F̄l Maximum line capacity [MW]HydroAvh Maximum annual capacity factor for hydro power plants [%]MCk Generation marginal cost [$/MWh]N Number of sampled hours in a yearNCts Noncompliance penalty with renewable target [$/MWh]ps Probability of scenario sRPSts Renewable target [%]Vt Length of period [years]VOLL Value of lost load [$/MWh]Wk,h Generation maximum hourly capacity factor [%]Ȳk Maximum resource potential [MW]Y0k Installed generation at stage t = 0 [MW]d Discount rate [1/year]Vb,k Element of node-generator incidence matrixXb,l Element of node-line incidence matrix

    Variablesf ts,l,h Power flow in transmission line [MW]gts,k,h Generation dispatch level [MW]nts Noncompliance with renewable target [MW]rts,b,h Load curtailment [MW]xts,l Transmission investment decisionyts,k Generation new build [MW]

    3.2. Model formulation

    We define the investment cost for a single scenario as the sum ofall transmission and generation investments.

    Its =∑l∈L

    CXts,lxts,l +

    ∑g∈GC

    CYts,gyts,g (1)

    The operation cost for periods t = 2, 3 and scenario s account forthe cost of operating generators and penalties for load curtailmentsplus noncompliance with renewables targets:

    Ots =8760

    N

    Vt∑v=1

    (1

    1 + d

    )v−1 ⎡⎣∑g∈G

    ∑h∈H

    MCggts,k,h +∑g∈G

    ∑h∈H

    VOLLrts,n,h + NCtsn

    ts

    ⎤⎦

    (2)

    We then formulate the objective function of the two-stagestochastic planning problem with recourse as follows:

    min I1 +∑s∈S

    ps

    [(1

    1 + d

    )V2 (I2s + O

    2s

    )+

    (1

    1 + d

    )V3O3s

    ](3)

  • 264 M. Bergen, F.D. Muñoz / Energy Economics 75 (2018) 261–273

    Fig. 1. Timing of investment decisions and operations.

    We minimize this objective subject to the following set ofconstraints:

    3.2.1. Node supply and demand balanceThis constraint accounts for local generation, demand, imports or

    exports through the transmission system, and curtailable demand ata cost of VOLL.

    ∑k∈G

    gts,k,hVb,k +∑k∈G

    f ts,l,hXb,l + rts,n,h = D

    ts,b,h ∀t ≥ 2, s, b, h (4)

    3.2.2. Generation dispatch limitsWe assume that all generators can be dispatched up to their

    nominal capacity. We capture the variability of wind, solar, and run-of-the-river hydro using hourly capacity factors from historical dataWk,h ∈ [0, 1]. For all the other technologies Wk,h = 1 ∀h.

    gts,k,h ≤ Wk,h(

    Y0k +t∑

    u=1

    yu−1s,k

    )∀t ≥ 2, s, k, h

    (5)

    3.2.3. Generation build limitsInvestments in new generation capacity are constrained by max-

    imum resource limits per area.

    ∑l∈L

    yts,k ≤ Yk ∀t ≥ 2, s, k (6)

    3.2.4. Thermal limits on existing and candidate linesWe assume that all transmission investment alternatives are par-

    allel to existing lines. Consequently, the effect of a transmissioninvestment results in an increment of the capacity of an existingline.3

    ∣∣∣f ts,l,h∣∣∣ ≤ Fl(

    1 +t∑

    u=1

    xu−1s,l

    )∀t ≥ 2, s, l, h

    (7)

    3.2.5. Maximum annual capacity factor for hydro power plants withreservoirs

    We use annual capacity factors from historical data to account forthe flexibility of hydro power plants with reservoirs.

    1N

    ∑h∈H

    gts,k,h ≤ HydroAvh(

    Y0k +t∑

    u=1

    yu−1s,k

    )∀t ≥ 2, s, k ∈ GH

    (8)

    3 For simplicity, we do not impose Kirchhoff’s Voltage Law since the Chilean trans-mission system is mostly radial. Additionally, from personal communication withprofessionals that work at the Chilean System Operator, we know that transmissionlines in meshed areas are open (when possible) if loop flows cause congestion issues.

    3.2.6. Renewable Portfolio StandardAll generation firms are required to supply a minimum fraction RPS

    of their generation from qualifying sources GR. Since the renewablepolicy allows firms to trade renewable energy certificates or to fulfillthe regulation through a noncompliance fine, under perfect compe-tition, the regulation is equivalent to a constraint on the aggregateamount of generation from qualifying renewable energy sources fromall firms (Perez et al., 2016; Munoz et al., 2017a).

    ∑k∈GR

    ∑h∈H

    gts,k,h + nts ≥ RPSts

    ∑k∈G

    ∑h∈H

    gts,k,h ∀t ≥ 2, s (9)

    3.2.7. Non-divisibility of transmission alternativesIn line with Munoz et al. (2013), we assume that all transmission

    investment decisions are discrete.

    xts,l ∈ {0, 1} ∀t ≥ 2, s, l (10)

    3.2.8. Non-negativity of decision variablesWe assume that all generation investments can be made in small

    increments.

    gts,k,h, yts,k, n

    ts, r

    ts,b,h ≥ 0 ∀t ≥ 2, s, b, k, h

    (11)4. Case study

    Our case study is a network reduction of the Chilean powersystem. We considered the two largest power systems in the coun-try that currently operate in a single synchronized grid known asthe National Electric System (SEN) operated by the national systemoperator: The Northern Interconnected System (SING) and the Cen-tral Interconnected System (SIC). The model consists of 28 buses,36 transmission elements, and 351 aggregated generators with aninstalled capacity of 22.74 GW. We model investment decisions atthe beginning of years 2030 and 2040 (period 1, V1 = 10), assum-ing a ten-year delay between the investment decision and projectcompletion.4 Market operations are modeled for 2040 (repeated for10 years, period 2, V2 = 10) and for 2050 (repeated for 30 years,period 3, V3 = 30).

    4.1. Data assumptions

    We use the latest demand projection by the Chilean Ministry ofEnergy for 2050 as a baseline to construct our demand projectionsfor 2040 and 2050 (ME, 2015). For renewable resource potentialsper region we use estimates from a study commissioned by the

    4 Note that this is a strong assumption, because some generation technologies,including wind and solar, can be developed in relatively short periods of time (1–2 years). This means that in the stochastic model and in the regret analysis weoverestimate the cost of adapting transmission and generation infrastructure to real-ized scenario in the second stage. Our model could be modified to account for differentlead times by, for instance, assuming that investment choices for technologies withshort lead times are second-stage variables (i.e., they are always made under perfectinformation). Incorporating this feature is, however, beyond the scope of this paper.

  • M. Bergen, F.D. Muñoz / Energy Economics 75 (2018) 261–273 265

    Table 2Investment and (average) operation costs, installed capacity, and resource potential for all generation technologies. The symbol – denotes unrestricted investments.

    Technology Investment cost Operation cost Installed capacity Resource potential

    [MMUSD/MW ] [USD/MWh] [MW] [MW]

    Biogas 3.4 15.7 53 1000Biomass 3.4 7.2 423 1000Coal 3.2 52.9 5140 –Diesel 0.6 190 3215 –Natural gas 0.8 90 4658 –Hydro 3.4 0 3402 4521Hydro RoR 3.4 0 2802 4293Mini hydro 3.2 0 423.2 3958Solar 0.9 0 1396 ∞Wind 1.6 0 1229 37,477

    Table 1Fuel prices per type.

    Coal Diesel Natural gas Fuel oil nro. 6

    [US$/ton] [US$/m3] [US$/MMBtu] [US$/m3]

    Price 120 630 12.5 443

    Chilean Department of Energy in 2014 (Santana et al., 2014). Weimpose no limit on resource potentials for investments in solar gen-eration since these are orders of magnitude larger that the ones forother resources. We use estimates of investment costs determinedby the National Energy Commission (CNE, 2015) and the EnergyInformation Administration (EIA, 2013), considering engineering andinspection expenses, equipment purchase and construction costs,financial expenses and general expenses (see Table 2). The operatingcosts of existing power plants were estimated using the heat rate ofeach unit reported in SING (2016) and SIC (2016). For new plants theestimation was made based on the reported heat rates provided byEIA (2013). Our projections of fuel prices are the ones used in CNE(2015) (Table 1).5

    As in Munoz et al. (2017a), we model renewable resource variabil-ity using hourly profiles from historical and modeled data. We use 3representative solar profiles, one for the northern region, one for thecentral region, and one for the southern region. Hourly generationprofiles for these locations were generated using the Chilean SolarEnergy Explorer (ES, 2015). Wind profiles were taken from Munoz etal. (2017a), who used 4 representative wind profiles to represent thevariability of wind generators, 1 for the SING and 3 for the SIC sys-tem, all of them generated from EE (2015). Tables A.7 and A.8 in theAppendix show the annual capacity factors and standard deviationsof the solar and wind profiles that we used in this study. We limitthe annual generation of large-scale hydro power plants with reser-voirs using annual capacity factors for year 2013 (SIC, 2016).6 Thehourly availability of run-of-river (RoR) and mini hydro power plantsis modeled using historical data for 2013 (SING, 2016; SIC, 2016).Tables A.9 and A.10 in the Appendix summarize the main statisticalproperties of all hydro resources.

    We use a sample of 300 h from the full set of time-dependentdata. To ensure that the sample preserves the original statistical

    5 Throughout the paper, MM denotes million and B denotes billion.6 We chose 2013 as a reference year for hydro generation because it is one of the

    driest years of the last decade (2006–2016) (Systep, 2017). We prefer using dry insteadof average hydro conditions because the latter might introduce a downward bias intotal system costs and estimates of the regret of planning for the wrong scenario dueto an overstatement of the system’s flexibility. However, for a more detailed planningstudy we recommend explicit consideration of uncertain hydro conditions through aset of scenarios based on both historical and forecasted data, as in Inzunza et al. (2016)and Ramirez-Sagner and Munoz (2017).

    properties (i.e., means, standard deviations, and correlations), wesampled 10,000 sets of 300 h and selected the sample that closelymatched the original properties of full dataset of 8760 h (van derWeijde and Hobbs, 2012; Munoz and Mills, 2015).

    We allow for transmission reinforcements to all existing corridorsin the case study. The cost and characteristics of the alternatives aretaken from CMI (2015) and shown in Table A.11 in the Appendix.Finally, based on the new Chilean transmission law (BCN, 2016), weassume that all transmission costs will be paid for by final consumersthrough a postage-stamp method. This means that generators willnot bear any transmission charges, regardless of their location in thetransmission grid.

    4.2. Scenarios

    In line with Bayesian decision theory, we model uncertainty usinga set of scenarios with subjective probabilities that can be elicitedfrom experts (Winkler, 1968; Cooke et al., 1991). Under this paradigm,there are no right or wrong scenarios or probabilities, because theseare only subjective views of the future. Our approach is in line with thespirit of planning approaches used in the Western Electricity Coor-dinating Council, the Midcontinent ISO, and the California ISO in theUS (Munoz et al., 2015). Scenario planning—sometimes used in com-bination with stochastic optimization—is a widely-used approachemployed in many other areas outside of the electric power industryas well (Huss, 1988; Duinker and Greig, 2007).

    We develop five scenarios that capture the effect of differentenvironmental and climate change policies in the electricity mar-ket in Chile based on different policies that are either enacted orthat have been discussed as potential options for the future.7 Thesepolicies are rather broad and can materialize directly as environmen-tal regulations (e.g., renewable targets or CO2 targets) or indirectly,through other factors in the model (e.g., reduced demand levelsdue to energy efficiency programs or lower natural prices due toincreasing collaboration with neighboring countries). We now pro-vide a brief description of each scenario. Table 3 summarizes howeach scenario affects different input parameters in the planningmodel. Just for illustration purposes we assume that all five scenarioshave the same probability. However, there are formal approaches to

    7 As in the study Munoz et al. (2017b) for the US Western Electricity CoordinatingCouncil, we use scenarios based on policy objectives that have been actually discussedin practice by regulators in Chile. Of course, one could imagine more extreme scenariosand assess their effect on transmission and generation investment decisions. Forinstance, Scenario 2 (70% RPS without large hydro) could be replaced by a 90%renewables target by 2050 without hydro. However, to date, such renewable targethas not been proposed by the regulator in Chile (not even as an indicative plan) and,in our opinion, its consideration as a scenario in our study would not be crediblebased on current available information.

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    Table 3Summary of scenarios. The symbol * denotes a renewable target that does not considerhydro power plants larger than 20 MW as qualifying renewable technologies.

    S1 S2 S3 S4 S5

    Probability 1/5 1/5 1/5 1/5 1/5

    Renewable targets2040 30% 30%* – 30% –2050 70% 70%* – 70% –

    Carbon taxUS$/tCO22040 – – 8.75 – –2050 – – 16.25 – –

    Demand changes w.r.t. baseline2040 – – – −15.0% –2050 – – – −25.0% –

    Cost of generation with NGUS$/MWh2040 90 90 90 90 402050 90 90 90 90 40

    elicit probabilities based on expert judgment that could be used inreal-world studies (Clemen and Winkler, 1999; O’Hagan et al., 2006).

    • Scenario 1- 70% RPS to 2050 with hydro generation: This sce-nario is inspired by the 2050 Energy Roadmap of the Chileangovernment which proposes a renewable policy that requiresthat at least 70% of all the electricity should come from renew-able sources by 2050, considering all hydro generation as aqualifying renewable resource to meet the target (ME, 2015).

    • Scenario 2 - 70% RPS to 2050 without large hydro: This sce-nario is a variant of Scenario 1. It assumes that the 70% targetof renewables by 2050 will be actually much more stringentand that all hydro power plants with an installed capacity of20 MW or more will not be considered as eligible technologiesto meet the policy (Munoz et al., 2017a).

    • Scenario 3 - Carbon tax: In this scenario, the assumption isthat government regulation will be focused on CO2 emissionsreductions instead of on promoting a renewable target. We setCO2 taxes based on scaled projections of Synapse (2015), suchthat the value of the CO2 tax for 2017 matches the current CO2tax in Chile (5 USD/t CO2).

    • Scenario 4 - Higher energy efficiency: In this scenario weassume that government policies will be focused on energyefficiency standards that will ultimately reduce the demand forelectricity. In this scenario, the baseline demand was adjustedaccording to a national target for energy efficiency (PRIEN,2010). This results in 15% and 25% reductions of demand by2040 and 2050, respectively.

    • Scenario 5 - Conventional generation: In this scenario weassume that there will be no environmental or climate changepolicies in place. Instead, we assume that the government willreach agreements with neighboring countries (e.g., Bolivia orArgentina) in order to facilitate the imports of natural gas toChile through pipelines. This will result in much lower naturalgas prices in the country than in the other 4 scenarios, wherewe assume that natural gas will be still imported in a liquifiedform from very distant locations.

    We assume that in any scenario it is possible to curtail demand ata cost of VOLL = 500 US$/MWh. Similarly, we assume that any non-compliance with renewable targets is priced at NC = 35 US$/MWh,

    which is slightly lower than the noncompliance fine enacted in thecurrent renewable target in Chile (Munoz et al., 2017a).8

    5. Results

    The model outlined in Section 3.2 is a mixed-integer linear pro-gram that was formulated in AIMMS version 4.25 (64-bit) and solvedusing CPLEX 12.6.3 in a computer with an Intel Core i5-2450 M [email protected] 2.50 GHz with 6GB of RAM. The size of the stochastic optimiza-tion model is 3.2 million variables (555 integer) and 3.4 millionconstraints. We solved all optimization problems to a 0.5% optimalitygap,9 solution times ranged from 10 to 90 min.

    5.1. Market equilibrium under perfect foresight of climate andenvironmental policies

    In this section we present results assuming that both the trans-mission planner and all generation firms have access to perfectinformation regarding future environmental and climate changepolicies. We find this equilibrium by solving the planning problemfrom Section 3.2 for each of the five scenarios separately, assigning aprobability ps∗ = 1 to each scenario s∗ in question and removing allconstraints from other scenarios s �= s∗.

    Fig. 2 shows optimal investments in generation per technologyand year for the five different scenarios. We observe that equilibriuminvestments in generation are heavily dependent on the environ-mental and climate change policies that could be implemented inthe future. The exceptions are first-stage investments in mini hydro,which remain constant across scenarios at the maximum resourcepotential of 3958 MW. Similarly, investments in conventional gener-ation are nearly constant across scenarios and comparatively smallwith respect to the capacity additions of other technologies, suchas hydro, solar, and wind. We recognize that this result could bean artifact of our assumptions since we are not considering short-term generation constraints (e.g., ramping limits) that could triggernew investments in flexible generation technologies, such as com-bustion turbines, under high penetrations of renewables (Palmintierand Webster, 2011). However, the Chilean power system has largeshares of flexible generation from hydro units with storage capabili-ties (Munoz et al., 2017a). Furthermore, energy storage units, whichare not explicitly accounted for in our models,10 are more likelyto become competitive investment alternatives in the near future(Schmidt et al., 2017). As documented in Denholm and Hand (2011)

    8 Note that increasing the value of the noncompliance fine NC or the cost of unsup-plied demand VOLL could bias our results upwards. This is because, under uncertainty,it is possible that the optimal first-stage investment plans for one scenario mightbe infeasible when tested against a different scenario, in which case some fractionof demand will go unsupplied and some fraction of the renewable target will beunfulfilled. Although we allow for second-stage, corrective, investment decisions thatwould reduce or eliminate curtailed demand and noncompliance with renewable tar-gets in the long-term, we assume a 10-year delay between investments that limitsthe effect of these corrective decisions. Consequently, assuming higher values of NC orVOLL will bias our estimates of the economic regret faced by society upwards, withoutchanging optimal first-stage investment decisions.

    9 As pointed out by a referee, our choice of this optimality gap could potentiallybias our conclusions. However, we performed a sensitivity analysis on the optimalitygap in the stochastic two-stage planning problem. Decreasing the gap from 0.5% to0.001% neither changed optimal investment solutions nor total system costs, it onlyimproved the LP bound. In Munoz and Watson (2015) and Munoz et al. (2016) wereached similar conclusions. We expect this result to carry over the deterministicmodels because they are all particular cases of the stochastic problem.10 Although we do not explicitly consider energy storage devices in our model, as

    in Go et al. (2016), we do model hydro units with reservoirs using maximum annualcapacity factors. This modeling assumption allows large hydro units to freely allocatethe annual water resources available for the generation of electricity throughout theyear. Under perfect competition, the optimal operation of large hydro units with reser-voirs resemble the optimal use of energy storage devices, but without the ability towithdraw energy from periods when solar or wind resources are abundant.

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    Fig. 2. Generation investments in 2030 and in 2040 under perfect information for each possible scenario.

    and Hirth (2016), these resources can be used to accommodate alarge fraction of the variability and unpredictability of wind or solargeneration and reduce the need for additional investments in flex-ible gas or diesel units. Under these circumstances, we believe thatimpact of these short-term constraints in our long-term projectionsfor policy analysis is rather small, but we do recognize that theyshould probably be considered for medium-term studies or in powersystems with inflexible generation units using approaches such asthe ones proposed by Flores-Quiroz et al. (2016).

    Solar and wind investments seem to be the two generation tech-nologies that are most sensitive to the environmental and climatechange policies that could be implemented in the future. Optimalinvestments in solar generation are consistently above 3000 MW forall scenarios in the first stage (2030) and they can be as high as nearly9000 MW for Scenario 2. Optimal wind investments also reach sur-prisingly high levels under Scenario 2 in the second stage, nearly11,000 MW. This result does not come as a surprise since in Sce-nario 2 we assume that the regulator will enact a 70% RPS and largehydropower will not be considered an eligible resource to meet therenewable target, in line with the analysis of Munoz et al. (2017a).Yet, under the scenarios that provide the least favorable investmentconditions for renewables (i.e., scenarios 4 and 5), optimal windinvestments are equal to zero.

    As expected, investments in generation under Scenario 4 arelower than under any of the other four scenarios. This occurs becausedemand projections are lower than under the other scenarios dueto policies that incentivize energy efficiency. Additionally, Scenario4 does not include renewable targets or a carbon tax, which meansthat the economic incentives for investments in solar and wind gen-eration are much weaker than under scenarios 1, 2, and 3. This sameargument applies for the relatively low levels of investments in windand solar generation under Scenario 5.

    Just as generation investments, optimal transmission reinforce-ments are also dependent on the scenario of environmental andclimate change policy that will actually occur in the future. Table 4shows optimal investments per line number, stage, and scenariounder perfect foresight. While all optimal investment plans sharesome common features, e.g. lines 8, 10, and 37, they all have somedecisions that make them distinct. For example, optimal investmentsin transmission lines for scenarios 1 and 5 have overlapping decisionsfor all transmission corridors, except for line 6, which is not builtunder Scenario 5. Note that this is consistent with generation invest-ments in equilibrium for these two scenarios (Fig. 2), since both arevery similar.

    We also observe that the most transmission-intensive investmentplan is for Scenario 2, where most of the developments in wind andsolar generation take place. This result comes as no surprise since

    most of the best sites for the development of new wind farms andsolar power plants in Chile are far from the main load centers.11

    Consequently, taking advantage of the best wind and solar resourcesin the country will require important upgrades to the existing trans-mission grid if large cities such as Santiago remain as the main loadcenters. However, an increase in mining operations in the northernregion or a potential interconnection with the Peruvian power systemcould potentially change load patterns and transmission require-ments to accommodate the investments in generation described inFig. 2.

    The scenario analysis presented in this section illustrates theimpact of different environmental and climate change policies onoptimal transmission and generation investment decisions underperfect information. Yet, these government policies can be uncertainand decision makers must commit to transmission and generationinvestment decisions without having access to perfect information.

    5.2. Market equilibrium under uncertain climate and environmentalpolicies

    In this section we present results assuming that any of the five sce-narios of future environmental and climate change policies can occurwith equal probability. We assume that the transmission planner andgeneration firms deal with uncertainty in two possible manners. Onealternative is that they will act myopically, disregarding uncertainty,and will choose first-stage investment decisions assuming that onlyone of the five scenarios is more likely to occur. However, againsttheir beliefs, any of the five scenarios can materialize in the secondstage with equal probability. Abusing notation, we find these equilib-ria by imposing the optimal first-stage transmission and generationinvestment plans xs∗ and ys∗ , respectively, under perfect informa-tion for each scenario s∗ from the previous section in the stochasticplanning model described in Section 3.2. Second-stage investmentvariables are free, which means that the imposed infrastructure inthe first-stage can be adapted to any of the five possible scenarios.The other alternative is that the transmission planner and all gener-ation firms will explicitly account for uncertainty in their planningstrategy. We find this solution by solving the stochastic planningmodel that minimizes expected system costs considering all five pos-sible scenarios simultaneously. The outcome is a single first-stagetransmission and generation investment plan and five second-stagerecourse strategies, one for each scenario.

    Fig. 3 shows the optimal first-stage investment decisions in gen-eration per technology for each of the deterministic or myopic plans

    11 This is also the case in the U.S. (Munoz et al., 2014).

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    Table 4Optimal first- and second-stage transmission investments per scenario under perfect information.

    First stage Second stage

    Line no. 6 8 10 15 17 24 25 37 7 13 14 15 17 24 25 31 32

    Scenario 1 1 1 1 1 1 1 1 1Scenario 2 1 1 1 1 1 1 1 1 1 1 1Scenario 3 1 1 1 1 1 1 1 1 1Scenario 4 1 1 1 1 1 1Scenario 5 1 1 1 1 1 1 1

    and the stochastic solution. We observe that if all generators are riskneutral and share the same view regarding possible future scenar-ios, generation investments in equilibrium will differ from all thedeterministic plans. This is a well-known result in the literature ofstochastic programming since, in general, an optimal decision underuncertainty is always suboptimal in retrospect (Wallace, 2000).Interestingly, in this case the stochastic solution is contained withinthe space defined by the deterministic plans, at least in aggregateterms per technology. This means that, for instance, the transmissionplanner could expect generation firms to select investment levelsthat are somewhat close to the mean or expected levels observedin the deterministic analysis (Fig. 2). This first-stage strategy allowsgenerators to adapt their portfolios to any of the five possible sce-narios with more investments in the second stage. However, thisadaptation in the second stage is rather imperfect compared tothe plans under perfect information because investments cannot bereversed.

    Let’s try to understand the main drivers behind the stochastic solu-tion considering two extreme alternatives as first-stage investmentstrategies. One simple option would be to plan generation for Sce-nario 4 (low demand because of efficiency measures and no carbonor renewable policies) in the first stage since it requires the lowestinvestment levels out of all five scenarios. Under uncertainty, tryingnot to commit too much capacity in the first stage and delay costlyinvestments might seem like a reasonable plan. Yet, having too lit-tle wind and solar generating capacity becomes very costly if any ofthe scenarios with renewable targets or carbon taxes develop in thesecond stage because new generation capacity cannot be developedinstantaneously. An alternative in the other extreme is to plan fora seemingly stringent outcome, such as Scenario 2 (high renewabletarget, excluding large hydro). Under this plan, any of the 5 possibleoutcomes would be feasible. However, this strategy is also subopti-mal in a stochastic sense because it involves adding wind and solarcapacity in excess of what would be needed in any outcome otherthan Scenario 2. The optimal stochastic strategy strikes a balanceamong the cost of committing too much capacity in the first stage,the cost of operating the system with a suboptimal generating port-folio from year 2030 to 2040, and the cost of adapting the systemwith new investments to the realized scenario in the second stage.

    Fig. 3. Comparison of first-stage generation investments under perfect informationand under uncertainty.

    While the stochastic solution in this case seems to be a combinationof the optimal plans under perfect information, there is empiricalevidence that constructing a stochastic solution based on a convexcombination of deterministic plans is a poor heuristic in more generalsettings (Wallace, 2000; Munoz et al., 2014).

    Fig. 4 shows first-stage transmission investment decisions forall deterministic plans and for the stochastic solution in a map ofthe network reduction. Unlike aggregate generation investments pertechnology, the optimal transmission investment plan under uncer-tain climate change and environmental policies is not containedwithin the space defined by all first-stage deterministic solutions. Wedo observe that if a line is optimal under all deterministic plans, thenthat line is part of the stochastic solution, i.e. lines 8, 10, and 37. How-ever, line 16 (see arrow in Fig. 4) is optimal in a stochastic sense butis not included as part of any deterministic solution, which highlightsthe importance of uncertainty on planning decisions. This result wasalso highlighted inMunoz et al. (2014), where the authors find thatthe optimal stochastic transmission investment plan includes trans-mission lines that are not selected under perfect information. Theselines are the ones that impart flexibility to the stochastic solution.

    5.3. Economic analysis

    In Sections 5.1 and 5.2 we showed how different planningassumptions, i.e. perfect or imperfect foresight about climate changeand environmental policies, affect equilibrium investments on trans-mission and generation assets. Here we provide bounds on the costthat uncertainty and different planning assumptions impose on thesystem.

    We first compute the expected cost savings that could result fromhaving access to perfect information regarding future climate changeand environmental policies. The second column in Table 5 showsthe total costs under perfect information (CPIs) for the five possiblescenarios, which is by definition the lowest possible cost in each case.On the other hand, if climate change and environmental policies areuncertain, the minimum expect cost results from the implementa-tion of the stochastic solution. In this case, the expected cost of thestochastic solution is ECSS = $57, 607MM. Based on this information,we can compute a lower bound LB on the cost of uncertain climatechange and environmental policies in the Chilean power system. Thislower bound is equal to the Expected Value of Perfect Information(EVPI) and corresponds to the maximum willingness to pay for a per-fect forecast, given that all market participants are making decisionsusing a stochastic planning model. We compute the LB as follows:

    LB = EVPI = ECSS −∑s∈S

    psCPIs = $1826MM (12)

    In this case, if all market participants make decisions explic-itly considering uncertainty and foresee the same possible scenar-ios, then uncertain climate change and environmental regulationsimpose a cost of at least $1826MM, which is nearly 3.2% of the ECSS.

    We also compute an upper bound UB on the cost imposed by pol-icy uncertainty by assuming that agents will not necessarily foreseeall possible scenarios. In fact, they might just plan for one of them,

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    Fig. 4. Comparison of first-stage transmission investments under perfect information and under uncertainty. Green lines are existing transmission backbones, red lines indicatenew investments in transmission lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

    myopically. Columns 3–8 in Table 5 show results from a regret anal-ysis for all myopic investment plans and the stochastic solution. Notethat if, for instance, agents plan their first-stage decisions for Sce-nario 1 but Scenario 2 occurs, there is a regret of $3614MM withrespect to the optimal system cost for Scenario 2 ($67,452MM). How-ever, if all agents plan their first-stage decisions for Scenario 1 andthis scenario of climate change and environmental policy actuallyoccurs, the regret is zero. The last column on the right shows theexpected regret ERs for each deterministic or myopic plan, assum-ing that any of the five scenarios can occur with equal probability.

    We compute UB as the expected value across all scenarios of theexpected regret for each myopic investment plan as follows:

    UB =∑s∈S

    psERs = $3255MM (13)

    In this case, the UB represents nearly 5.7% of the ECSS. However, thisupper bound is only in expectation since under specific conditions theregret can be much higher. For instance, if agents plan for Scenario

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    Table 5Regret matrix and costs under perfect information for all 5 deterministic solutions and the stochastic plan. Abusing notation, ERs denotes the expected regret for a first-stageinvestment plan s.

    First-stage investment plan from Cost under perfect info. [$MM] Regret analysis [$MM]

    Realized scenario ERs

    S1 S2 S3 S4 S5 [$MM]

    Scenario 1 58,069 0 3614 43 9220 283 2632Scenario 2 67,452 3035 0 3578 6766 2958 3267Scenario 3 59,710 90 7219 0 9626 553 3498Scenario 4 38,366 4380 8423 6034 0 2601 4288Scenario 5 55,307 284 3675 465 8518 0 2588Stochastic – 1666 1587 2657 2332 889 1826

    3 but Scenario 4 develops, the regret can be as high as $9626MM or16.7% of the ECSS. These results highlight the economic implicationsof uncertain climate change and environmental policies in the Chileanpower system and, ultimately, on society.12

    5.4. Impact of policy uncertainty on CO2 emissions

    Although not all of the climate change or environmental policiesconsidered in the five possible scenarios aim at reducing CO2 emis-sions, it is interesting to analyze if uncertainty has an impact on CO2emissions with respect to the equilibrium under perfect informa-tion. Table 6 shows the percentage difference of total CO2 emissionswith respect to the optimal solution under perfect foresight forthe five myopic plans (i.e., deterministic) and for the stochasticsolution.

    As expected, realized emissions for all myopic plans dependstrongly on the scenario that market agents planned for in the firststage. For example, if agents plan for Scenario 3 (Carbon tax) but anyof the other four scenarios actually occur in the second stage, real-ized CO2 emissions will be always lower than the socially-optimallevels for the scenario in question. Yet, if agents plan for Scenario 4(Higher energy efficiency) there is always a positive “regret” in termsof CO2 emissions with respect to the socially-optimal levels for eachof the other four possible scenarios in the second stage. Therefore,the difference in expected CO2 emissions for the five myopic first-stage plans with respect to the equilibria under perfect informationcan be either positive or negative. Interestingly, the expected differ-ence in CO2 emissions over the five expected myopic plans is nearlyzero.13 This means that, in expectation, there is almost no “regret”in terms of CO2 emissions for the myopic plans with respect to thesocially-optimal levels for the equilibria under perfect information.But this is obviously not true if we choose one specific first-stage plansince, for instance, emissions can be 36.5% higher than under perfectinformation if all agents plan myopically for Scenario 4.

    Results for the stochastic solution are also ambiguous on a perscenario basis (i.e., CO2 emissions are always higher than the socially-optimal levels, except for Scenario 4), but in expectation they are 18%higher than the optimal levels for the five equilibria under perfectforesight. In particular, the regret in terms of CO2 emissions for the

    12 As suggested by a referee, we performed a sensitivity analysis on the impactof considering Scenario 5 as part of the scenario set. Removing this scenario andsetting the probabilities of the remaining four scenarios to 1/4 increases the LB by13%, the UB by 19%, and the ECSS by 0.06% with respect to the solutions consideringfive scenarios.13 These are expected emissions assuming that all agents will plan for only one

    scenario in the first-stage, randomly, but any of the five scenarios can occur in thesecond stage.

    stochastic equilibrium is always below the maximum difference inemissions with respect to the socially-optimal levels for all scenar-ios (e.g., under the stochastic equilibrium, in Scenario 2 the regret inCO2 emissions is 47.4%, which is lower than the regret that resultsfrom planning for Scenario 4, 70.4%). This is because reducing CO2emissions beyond the optimal level for a particular scenario of cli-mate policies is costly, which means that under uncertainty it isoptimal to make some but not all of the investments that would beoptimal for a specific policy under perfect information. Our result isin line with the findings of Fuss et al. (2009), where the authors con-clude that increasing the uncertainty of future CO2 taxes increasesemissions.

    6. Conclusions

    Several countries around the world have already enacted or areconsidering implementing climate change or environmental policiesto reduce greenhouse emissions, particularly in the electric powerindustry. Unfortunately, changing political agendas and uncertainestimates of the social costs of CO2 emissions and other pollutantsmake investment planning in new transmission and generationinfrastructure very difficult, mainly because these are long-livedassets.

    In this paper we use a two-stage stochastic transmission andgeneration planning model with recourse to quantify the possibleeconomic implications of uncertain climate change and environmen-tal policies in the Chilean power system. Under perfect competitionand perfect information, this model is equivalent to the marketequilibrium that results from a transmission planner that acts asa Stackelberg leader and competitive generation firms that investand operate afterwards. Based on publicly available information andgovernment reports we develop five hypothetical scenarios of cli-mate change and environmental policies. These include stringentrenewable targets that exclude large hydropower as an eligible tech-nology, taxes on carbon emissions, energy efficiency programs, andthe absence of these policies paired with an emphasis on new agree-ments with neighboring countries that would allow generation firmsin Chile to have access to cheaper natural gas. These scenariosare inspired by policies that have been enacted or that have beendiscussed as potential options for the future.

    Using a deterministic variant of the planning model we first findthe optimal investment plans for each scenario, assuming that allagents have access to a perfect foresight. As expected, the opti-mal transmission and generation infrastructure is rather sensitive tothe different possible scenarios of climate change or environmen-tal policies. For instance, we observe differences of up to 15 GWof total wind investment among scenarios, which also affect trans-mission reinforcements since most of the best wind resources arerelatively far from the main load centers. This result suggest that

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    Table 6Percentage difference in CO2 emissions with respect to optimal solution under perfect foresight for the five first-stage myopic plans and the stochastic solution.

    First-stage investment plan from Realized scenario Difference in expected emissions

    S1 S2 S3 S4 S5

    Scenario 1 0.0% −37.8% 3.9% −27.7% −13.7% −14.2%Scenario 2 5.2% 0.0% 32.0% −20.8% −1.7% 4.5%Scenario 3 −7.1% −39.8% 0.0% −39.7% −19.0% −19.6%Scenario 4 49.5% 24.0% 70.7% 0.0% 24.4% 36.5%Scenario 5 3.5% −33.6% 10.5% −4.3% 0.0% −5.5%Stochastic 22.4% 4.4% 47.4% −4.5% 14.0% 18.0%

    policy uncertainty can result in a high risk of stranded assets if agentsplan for the wrong scenario.

    We also find that the economic implications of uncertain regula-tory conditions are significant. A lower bound on the cost of policyuncertainty is, in expectation, equal to the value of perfect informa-tion if all agents make investment decisions explicitly consideringuncertainty (i.e., they plan using a stochastic model). An upper boundon the cost of policy uncertainty is, in expectation, equal to the regretthat results from myopic plans that completely disregard uncertaintywith respect to the optimal system costs under perfect foresight.We find that the expected cost of uncertain policies ranges between$1.8B and $3.3B, which represent 3.2% and 5.7% of the expectedcost of the stochastic solution, respectively. To put these numbers incontext, electricity revenues in Chile in 2016 from spot prices wereapproximately $4B,14 which means that policy uncertainty can cost,in expectation, between 45% to 83% of a full year’s worth of rev-enues. While this might seem like a high number, recall that in ourmodel this economic loss is a discounted expectation over 40 yearsof system operation.

    We can think of two policy implications of these results. The firstone is that the planning process of infrastructure that is centrally-managed in deregulated electricity markets, such as transmissionlines, should account for regulatory uncertainty. This means that aregulator, which we assume plans for transmission assets and setspolicy objectives, should not only hedge against market uncertainties(e.g., technology costs) but also against uncertainties that are rootedin a continually evolving regulatory environment. A second impli-cation is that a certain, but potentially suboptimal, environmentalor climate change policy might yield more efficient results (e.g., interms of CO2 emissions or system costs) than a broad set of uncertainmeasures. This is a direct consequence of the effects of uncertaintyon investors’ decisions.

    Naturally, our conclusions are not general and could be affectedby our assumptions. For instance, we assume that all agents in themarket are risk neutral, which means that they make investmentdecisions based on the expected profits they will make from the salesof power (generators) or the expected system costs that will resultfrom some transmission upgrade (transmission planner). However,in practice, it is more likely that investors will put more weighton a subset of the worst possible scenarios for their objectives (i.e.,left tail of profits or right tail of costs). To account for risk aversionone could also use an optimization-based planning tool under theassumption that there is a complete financial market (Munoz et al.,2017b). Interestingly, Munoz et al. (2017b) find that the effect ofrisk aversion at an aggregate level in a large power system (i.e., theWestern Electricity Coordinating Council in the U.S.) is rather small,

    14 This estimate is for the two main interconnected systems, the SIC and SING. For2016 the aggregate annual sales of electricity were 67 GWh and the average spotprice was 61$/MWh (CE, 2016).

    but there might be significant regional impacts. Conducting an anal-ysis of the effect of risk aversion in our results is beyond the scope ofthis study, we leave it as a subject of future research.

    Acknowledgments

    The research in this article was supported by FONDE-CYT #11150029, CONICYT/FONDAP/15110019 (SERC-CHILE), andCONICYT-Basal Project FB0008. We thank the editor and twoanonymous reviewers for their constructive comments, which helpedus to improve earlier versions of this manuscript.

    Appendix A. Case study

    A.1. Time-dependent data

    Table A.7Representative wind profiles (Munoz et al., 2017a).

    Profile System Region Mean capacity factor Standard deviation

    Tachamma SING II 0.45 0.37Canela SIC IV 0.26 0.3Llay-Llay SIC IV 0.08 0.16Tolpán SIC IX 0.39 0.38

    Table A.8Representative solar profiles (Munoz et al., 2017a).

    Profile System Region Mean capacity factor Standard deviation

    Antofagasta SING/SIC II 0.21 0.28Santiago SIC RM 0.15 0.25Concepción SIC VIII 0.16 0.25

    Table A.9Hydro availability per year for each dam central[MWh/year] (SIC, 2016).

    Generation central [GWh/year]

    Canutillar 910Cipreses 332Colbún 1713El Toro 1263Machicura 376Pangue 1554Pehuenche 2128Ralco 2170Rapel 523

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    Table A.10Representative RoR hydro profiles (Munoz et al., 2017a).

    Region Generation central System Mean capacity factor Standard deviation

    I Alto Hospicio SING 0.13 0.23III Río Huasco SIC 0.10 0.10IV Los molles SIC 0.13 0.23V Chacabuquito SIC 0.58 0.24V Juncalito SIC 0.21 0.34V Hornitos SIC 0.37 0.28VI La Higuera SIC 0.49 0.30VI Mayarauco SIC 0.60 0.25VII San Clemente SIC 0.28 0.29VII Loma Alta SIC 0.46 0.26VIII Angostura SIC 0.43 0.13VIII Rucúe SIC 0.47 0.18VIII Quelleco SIC 0.47 0.18VIII El Diuto SIC 0.74 0.34IX El Canelo SIC 0.56 0.17IX Allipén SIC 0.75 0.36X Dongo SIC 0.69 0.23XIII Alfalfal SIC 0.46 0.26XIII Puntilla SIC 0.75 0.13XIII Guayacán SIC 0.79 0.22XIV Rucatayo SIC 0.76 0.22XIV Reca SIC 0.67 0.30

    A.2. Transmission data

    Table A.11Line capacity and investment cost (CMI, 2015).

    Line Line capacity Investment cost

    [MW] [MM US$]

    1 394.8 1.542 394.8 2.213 394.8 0.514 365.8 1.755 218 1.196 365.8 4.077 266.8 3.328 586 4.849 772 4.1610 491 3.6411 586 3.7212 879 1.2413 777 7.8914 3777 22.0215 3394 35.9116 446 8.5217 3446 55.3118 3000 0.6219 446 1.5620 2000 3.3821 310 3.2222 3600 4.4923 3600 6.1324 1800 8.1925 3000 0.8526 3600 5.7827 1500 1.6828 800 1.3929 3464 19.3530 944 3.4931 3532 17.6432 910 1.1033 265.2 5.4734 5000 1.1535 7500 26.5736 1500 86.88

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    Quantifying the effects of uncertain climate and environmental policies on investments and carbon emissions: A case study of Chile1. Introduction2. Literature review3. Methodology3.1. Nomenclature3.2. Model formulation3.2.1. Node supply and demand balance3.2.2. Generation dispatch limits3.2.3. Generation build limits3.2.4. Thermal limits on existing and candidate lines3.2.5. Maximum annual capacity factor for hydro power plants with reservoirs3.2.6. Renewable Portfolio Standard3.2.7. Non-divisibility of transmission alternatives3.2.8. Non-negativity of decision variables

    4. Case study4.1. Data assumptions4.2. Scenarios

    5. Results5.1. Market equilibrium under perfect foresight of climate and environmental policies5.2. Market equilibrium under uncertain climate and environmental policies5.3. Economic analysis5.4. Impact of policy uncertainty on CO2 emissions

    6. ConclusionsAcknowledgmentsReferences