Optimal Carbon Taxes for Emissions Targets in the Electricity Sector
Daniel J. Olsen, Yury Dvorkin, Ricardo Fernández-Blanco, Miguel A. Ortega-Vazquez
11 Optimal Carbon Taxes for Emissions Targets in theElectricity Sector
Daniel J. Olsen,
Student Member, IEEE,
Yury Dvorkin,
Member, IEEE,
Ricardo Fern´andez-Blanco, andMiguel A. Ortega-Vazquez,
Senior Member, IEEE ©2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, includingreprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, orreuse of any copyrighted component of this work in other works. DOI: 10.1109/TPWRS.2018.2827333, IEEE Transactions on Power Systems.
Abstract —The most dangerous effects of anthropogenic climatechange can be mitigated by using emissions taxes or otherregulatory interventions to reduce greenhouse gas (GHG) emis-sions. This paper takes a regulatory viewpoint and describes theWeighted Sum Bisection method to determine the lowest emissiontax rate that can reduce the anticipated emissions of the powersector below a prescribed, regulatorily-defined target. This bi-level method accounts for a variety of operating conditions viastochastic programming and remains computationally tractablefor realistically large planning test systems, even when binarycommitment decisions and multi-period constraints on conven-tional generators are considered.Case studies on a modified ISO New England test systemdemonstrate that this method reliably finds the minimum taxrate that meets emissions targets. In addition, it investigatesthe relationship between system investments and the tax-settingprocess. Introducing GHG emissions taxes increases the valueproposition for investment in new cleaner generation, trans-mission, and energy efficiency; conversely, investing in thesetechnologies reduces the tax rate required to reach a givenemissions target. N OMENCLATURE
Sets and Indices A Set of representative days, indexed by a . B Set of transmission network buses, indexed by b . I Set of generating units, indexed by i . L Set of transmission lines, indexed by l . R Subset of renewable generators ( R ⊂ I ). S Set of generator power output blocks, indexed by s . T Set of time intervals, indexed by t or τ . Parameters b i,s Marginal cost of block s of generator i ($/MWh). C min i Minimum cost of generator i ($/h). C su i Start-up cost of generator i ($). d b,t,a Demand at bus b , time t , day a (MW). d ramp t,a Load ramp requirement at time t , day a (MW/h). E max Regulator’s GHG emission target (tons). E min i Minimum GHG emissions of generator i (tons/h). E su i Start-up GHG emissions of generator i (tons). f max l Capacity of transmission line l (MW). g max i Maximum power output of generator i (MW). g min i Minimum power output of generator i (MW). g max i,s Maximum power output of block s , generator i (MW). g down i Minimum down-time of generator i (h). g up i Minimum up-time of generator i (h). h i,s Marginal GHG emissions of block s , generator i (tons/MWh). m line l,b Line connection map. m line lb = 1 if line l starts at bus b , = − if line l ends in bus b , otherwise. m unit i,b Unit map. m unit i,b = 1 if generator i is located at bus b , otherwise. P CO GHG emissions tax rate ($/ton-CO e). P load Load shed penalty ($/MWh). P ren Renewable generation shed penalty ($/MWh). r down i Maximum down-ramp rate of generator i (MW/h). r up i Maximum up-ramp rate of generator i (MW/h). w down t,a Wind down-ramp requirements at time t , day a (MW/h). w up t,a Wind up-ramp requirements at time t , day a (MW/h). x l Reactance of line l ( Ω ). π a Probability of day a . Variables C gen System operator’s generation cost ($). C shed System operator’s shed cost ($). E a GHG Emissions for day a (tons). E total Total GHG emissions (tons). f l,t,a Power flow on line l , time t , day a (MW). g i,t,a Power output of generator i , time t , day a (MW). g i,s,t,a Power output of generator i , block s , time t , day a (MW). s load b,t,a Load shed at bus b , time t , day a (MWh). s ren b,t,a Renewable generation shed at bus b , time t , day a (MWh). u i,t,a Binary variable for the commitment status of genera-tor i , time t , day a . v i,t,a Binary variable for the start-up of generator i , time t ,day a . z i,t,a Binary variable for the shut-down of generator i , time t , day a . θ b,t,a Voltage phase angle of bus b , time t , day a (rad).I. I NTRODUCTION
A. Background
The risks posed by anthropogenic climate change are dire,and organized effort is required in order to mitigate andeliminate, when possible, the effects [1]. Pricing the emissionsof greenhouse gases (GHGs) is a well-established approachto internalizing these negative externalities and should resultin shifting the supply-demand equilibrium to a socially opti-mal point [2]. Since the true costs from climate change areuncertain and hard to quantify with any precision (thoughattempts have been made, as in [3]), one approach to createa price for emissions is to design policies that aim to reduce a r X i v : . [ m a t h . O C ] A p r emissions to a level that is generally accepted to avoid theworst effects. Unlike renewable portfolio standards or taxcredits for renewable energy investment or production, thisapproach is directly targeted toward reducing GHG emissions.As noted in [4], subsidies for production of renewable energycan lead to negative bids by renewable generators, which mayresult in higher costs and emissions than if they bid zero-cost.According to a 2017 study by the World Bank [5], there are47 regional, national, and sub-national carbon pricing schemesimplemented or scheduled for implementation, ranging from$1-140/tCO e and covering 15% of global emissions.The two main approaches to pricing emissions are a taxon GHG emissions ( i.e. a carbon tax) [6] and a cap-and-tradesystem [7]. A carbon tax sets a price directly with the goalof implicitly reducing emissions, while a cap-and-trade systemsets emissions reductions explicitly, implicitly creating a price.Each system has pros and cons: a cap-and-trade system can bemore precise about the level of emissions reductions achieved,but requires complex rules regarding distributing, auctioning,and trading of allowances. A carbon tax is simpler and maybe easier to implement, but impact on emissions is less certain[8], as the reactions to such a tax by the broader market ( e.g. generation and transmission investors, electricity consumers,and generation manufacturers) are difficult to model.Secondary policy considerations are similar between thetwo: entities may purchase carbon offsets to reduce net emis-sions, tariffs can maintain competitiveness with jurisdictionswithout carbon pricing, and policies can be designed tobe revenue-neutral. Such policy design considerations for acarbon tax are discussed in [9], [10]. Additionally, pricing ofcarbon in either approach can lead to carbon ‘leakage’, i.e. the increased cost of producing goods in a jurisdiction with acarbon tax can lead to a shift in production toward jurisdictionswith lower rates, or no tax at all [11].The impact of carbon taxes on the economy and the envi-ronment have been widely studied, using various tax rates: theBrookings Institute in 2012 studied a tax which would beginat $15/tCO e with an annual escalator [12], the CongressionalBudget Office in 2013 evaluated various rates between $15-29/tCO e [13], and the Energy Information Agency in 2014investigated rates of $10 & $25/tCO e [14]. However, thesestudies do not address at what rate carbon should be taxed.This paper approaches the topic from a different angle.Instead of studying the impact of a certain tax rate, we set atax rate to achieve a certain environmental impact ( e.g. pledgesfrom the Paris Agreement [15]) at minimal tax rate. Specifi-cally, we present an approach for setting the optimal carbontax for a given power system such that the resulting minimum-cost generator commitment and dispatch yields emissions thatare at or below a specified target. The consequence of a taxrate that is too low is failure to meet emissions targets, andthe consequence of a rate too high is undue economic burden.Minimizing the tax rate also has practical motivations: lowertax rates are often more politically palatable ( i.e. more likelyto be enacted, less likely to be repealed), and generally reducerates of tax evasion [16].Some carbon taxing systems are designed to ‘recycle’the revenue received, either by investing in clean generation technologies or by reducing tax rates on other sectors ofthe economy to achieve revenue ‘neutrality’. However, caremust be taken to account for the uncertainty in future carbonconsumption, especially as carbon pricing tends to reduceconsumption. B. Literature Survey
Work including emissions into generator dispatch began inthe 1970s with the concepts of minimum emissions dispatch[17], pricing of emissions to include their impact in economicdispatch [18], and varying emissions prices to investigate thetradeoffs between fuel costs and emissions [19]. However,these studies focused on local effects of NO x and SO x .The concepts of ‘pseudo fuel prices’ and algorithms forsetting them are explored in [20], and expanded in [21] toinclude periodic price adaptation in order to meet long-termfuel consumption targets as realizations differ from projec-tions. Similar algorithms are used to set weights based onemissions targets in [22] for economic dispatch problems.Several methods for coordinating long-term targets for emis-sions and short-term operations are discussed in [23], [24], butexplicit emission pricing is absent, to the best of the authors’knowledge.Explicit GHG pricing and its impact on optimal powerflow problems are discussed in [25]. [26] presents a bi-levelapproach for setting a tax rate to achieve a GHG emissionstarget with minimal tax burden, but intertemporal constraints( e.g. ramp rates, start-ups) are ignored. Without consideringthese constraints, the determined tax rate may not meet thedesired target. ‘Optimal’ tradeoffs between GHG emissionsand cost according to a Nash bargaining process are developedin [27], [28].All of the above approaches contain deficiencies when itcomes to setting a carbon tax rate with an eye on schedulingalgorithms ( i.e. unit commitment models). In short, one ormore of the following is missing:1) Intertemporal variables and constraints ( e.g. ramp ratelimitations, minimum up- and down-times).2) Explicit carbon pricing in dispatch/commitment.3) A method for setting an optimal carbon price.By contrast, in this work we propose a Weighted Sum Bi-section (WSB) method, a computationally efficient approach,to set the minimal carbon tax rate that results in a powersystem meeting emissions targets while incorporating unitcommitment, ramp rate limitations, and system flexibility andcontingency reserve requirements. C. Contributions
This work makes the following contributions:1) A bi-level planning model including unit commitmentbased on cyclic representative days, avoiding the needfor assumptions about initial conditions.2) An efficient method for determining the minimal carbontax rate which achieves emissions reductions targets.3) A demonstration of the computational efficiency ofthe proposed method and of the reciprocal relationshipbetween tax rates for emissions targets and investmentdecisions.
II. P
ROBLEM F ORMULATION
The problem is formulated as a bi-level planning problem,with the regulator’s tax rate ( P CO ) optimization in the upperlevel (1)-(2) and the system operator’s unit commitment withcarbon tax (UCCT), over a set of representative days, inthe lower level (3)-(21). The UCCT includes the dc powerflow approximation of the system power flows, penalties forshedding load and renewable generation, and reserve andramping adequacy requirements. We assume an electricitymarket based on a unit commitment in which bids representtrue fuel and tax costs. min P CO (1)subject to: E total ≤ E max (2) E total ∈ arg min (cid:110) C shed + C gen + P CO E total (3) C shed := (cid:88) a ∈ A π a (cid:88) t ∈ T (cid:88) b ∈ B (cid:16) P load s load b,t,a + (cid:88) i ∈ R P ren s ren i,t,a (cid:17) (4) C gen := (cid:88) a ∈ A π a (cid:88) t ∈ T (cid:88) i ∈ I (cid:16) C min i u i,t,a + C su i v i,t,a + (cid:88) s ∈ S b i,s g i,s,t,a (cid:17) (5) E total := (cid:88) a ∈ A π a (cid:88) i ∈ I (cid:88) t ∈ T (cid:16) E min i u i,t,a + E su i v i,t,a + (cid:88) s ∈ S h i,s g i,s,t,a (cid:17) (6)subject to: g i,t,a = g min i u i,t,a + (cid:88) s ∈ S g i,s,t,a ; ∀ i ∈ I, t ∈ T, a ∈ A (7) ≤ g i,s,t,a ≤ g max i,s u i,t,a ∀ i ∈ I, s ∈ S, t ∈ T, a ∈ A (8) v i,t,a + z i,t,a ≤ ∀ i ∈ I, t ∈ T, a ∈ A (9) v i,t,a − z i,t,a = u i,t,a − u i,t − ,a ; ∀ i ∈ I, t ∈ T, a ∈ A (10) t (cid:88) τ = t − g up i +1 v i,τ,a ≤ u i,t,a ; ∀ t ∈ T, i ∈ I, a ∈ A (11) t (cid:88) τ = t − g down i +1 z i,τ,a ≤ − u i,t,a ; ∀ t ∈ T, i ∈ I, a ∈ A (12) − r down i ≤ g i,t,a − g i,t − ,a ≤ r up i ; ∀ t ∈ T, i ∈ I, a ∈ A (13) (cid:88) i ∈ I m unit i,b g i,t,a − (cid:88) l ∈ L m line l,b f l,t,a − s ren b,t,a = d b,t,a − s load b,t,a ; ∀ b ∈ B, t ∈ T, a ∈ A (14) − f max l ≤ f l,t,a ≤ f max l ; ∀ l ∈ L, t ∈ T, a ∈ A (15) f l,t,a = 1 x l (cid:88) b ∈ B m line l,b θ b,t,a , ; ∀ l ∈ L, t ∈ T, a ∈ A (16) (cid:88) i ∈ I \ R u i,t,a ( g max i − g i,t,a ) ≥ (cid:88) b ∈ B d b,t,a + 5% (cid:88) i ∈ R g i,t,a + max i ∈ I g max i ; ∀ t ∈ T, a ∈ A (17) (cid:88) i ∈ I min (cid:0) r up i u i,t,a , ( g max i − g i,t,a ) (cid:1) ≥ w up t,a + d ramp t,a ; ∀ t ∈ T, a ∈ A (18) (cid:88) i ∈ I min (cid:0)(cid:0) r down i u i,t,a , g i,t,a − g min i (cid:1)(cid:1) ≥ w down t,a + d ramp t,a ; ∀ t ∈ T, a ∈ A (19) ≤ s load b,t,a ≤ d b,t,a ; ∀ b ∈ B, t ∈ T, a ∈ A (20) ≤ s ren b,t,a ≤ (cid:88) i ∈ R m unit i,b g i,t,a ; ∀ b ∈ B, t ∈ T, a ∈ A (cid:111) (21) The regulator’s objective is given in (1), and constrained bythe emission limit (2) and the lower-level problem (3)-(21).The system operator’s objective is given in (3)-(6). Generatorcosts curves are piecewise linear (7)-(8). Binary commitmentvariables are defined in (9)-(10) and generator minimum up-and down-times are constrained using (11)-(12). Generatorramp rate constraints are given in (13). Power balance is givenby (14). Line flow limits are given by (15)-(16). Operatingreserve requirements based on the 3+5% and N -1 policiesare ensured using (17) with flexibility requirements ensuredin (18)-(19). Load and renewable generation shedding isconstrained by physical limits in (20)-(21).For the intertemporal constraints (10)-(13), time periodsbefore the first are treated cyclically. For instance, t = 24 is substituted for t = 0 , and t = 23 for t = − . This ensuresthat end-of-day commitments are feasible and that initial con-ditions are representative, assuming that the days surroundingthe representative day are substantially similar. Consideringconstraints (17)-(19), the ideal quantity of regulation and load-following reserves is an active research topic [29], [30]; forsimplicity, we use the heuristic 3+5% rule originally proposedin [31]. This formulation assumes a perfectly competitivemarket; otherwise, the impact of the carbon tax on emissionsmay vary, as shown in [32].III. S OLUTION T ECHNIQUES
One approach to finding the optimal tax rate would be tosolve a standard unit commitment over the set of representativedays, with a constraint on total emissions, and to take themarginal value of the emissions constraint as the tax rate: min C gen + C shed (22)Equations (4)-(21) (23) E total ≤ E max : λ (24)where λ denotes the marginal value of the constraint.We call such an approach “Constrained Emission MarginalValue (CEMV)” method. However, due to the non-convexity ofthe UCCT problem (due to binary variables), this approach isliable to produce sub-optimal solutions. Varying E max will findsolutions on the Pareto frontier of the feasible cost/emissionsspace, but the resulting λ , when used as P CO in the UCCT,may find different solutions. This is because concave portionsof the Pareto frontier may not be found by the linearlyweighted UCCT formulation, since the optima only exist onthe convex hull of the Pareto frontier [33]. This undesirableoutcome is illustrated in Fig. 1 and demonstrated for the testsystem in Section V. Depending on where in the convex region E max falls, the value of λ ( i.e. the slope of the curve) wheninput as P CO into the UCCT problem may find: a) a solutionwith emissions which are greater than the target (A → A’ inthe figure), b) a solution in which emissions are lower than thetarget, but the production cost is higher than necessary (B → B’), c) the optimal cost/emissions point, but at a P CO that islarger than necessary, or d) the minimum P CO which resultsin the optimal cost/emissions point. Therefore, it should notbe assumed that the CEMV method can find (d) reliably. Generation Emissions G e n e r a ti on C o s t A A'BB' Feasibleregion
Fig. 1. The marginal values at points { A,B } , when used as tax rates, resultin the solutions at { A’,B’ } . By contrast, the WSB method finds the optimal tax rate byiteratively guessing a P CO value, solving the UCCT problem,and tuning P CO using the bisection method. Briefly, if a zeroof a continuous function is known to be in a certain interval, itcan be reliably found by repeatedly bisecting the interval andselecting the sub-interval in which the root must lie, basedon the sign of the function value at the midpoint. Since thegoal is to find the tax rate resulting in emissions at or below acertain target, the function is f ( P CO ) = E total ( P CO ) − E max ,and its zero-crossing is at the value of the optimal tax rate,where E total ( P CO ) is found for a given value of P CO bysolving the UCCT. For a given value of P CO , the UCCT canbe solved independently for each representative day, aidingcomputation. For a non-convex Pareto frontier such as ours,the values of the individual objectives as a function of theweighting factor are noncontinuous but monotonic. Therefore,the WSB method is guaranteed to find the smallest tax rateresulting in emissions at or below the target, if this target isfeasible. A very high tax rate (e.g. $1,000/ton) can be usedto estimate the maximum feasible emissions reduction and setthe upper bound of the tax range. Since precision is doubledwith each iteration, convergence is linear [34]. This approachis shown in Fig. 2. P test = ( P max + P min )/2 P min = P test Yes P max = P test NoNo YesE total ≤ E max ? P max – P min < ε ?Begin with P min =0, P max large P* = P test Solve UCCT with P test Fig. 2. Flowchart for finding optimal P CO using the Weighted Sum Bisectionmethod. IV. C
ASE S TUDY
The electrical system for this case study is a modified ISONew England (NE) test system [35]. Data from the EnergyInformation Administration (EIA) are used for fuel prices [36]and for per-MMBTu CO e emissions by fuel [37]. Thoughvariability from renewable generation can induce additionalCO emissions from thermal generators [38], this effect wasnot modeled in the case study. Five representative days arechosen using a hierarchical clustering algorithm [39] andrun at a one-hour time resolution. The load shed penalty isset at $10,000/MWh and the renewable spillage penalty is$20/MWh. Ramping requirements are set such that the systemhas the capacity to react to 1%/hour load ramps and all windfarms ramping their production ±
20% over one hour, basedon analysis of Bonneville Power Administration wind powerproduction data in [40]. This case study was implementedusing GAMS v24.0 and solved using CPLEX v12.5 with a0.1% optimality gap on an Intel Xenon 2.55 GHz processorwith at least 32 GB RAM.V. R
ESULTS
A. System Characteristics
145 150 155 160 165 170 175
Emissions (000 tons) P r odu c ti on c o s t ( $ M ) $1$5$10$50$100$1000 (load shed)$1000 (no load shed) True ParetoUCCT Solutions(no load shed)UCCT Solutions(with load shed) Fig. 3. The cost/emissions Pareto frontier. The line is points found byconstraining emissions, the crosses are points found by varying P CO . Fig. 3 shows the Pareto frontier of the trade-off betweenemissions and production costs ( i.e. fuel and shed costs). Thefull Pareto frontier is sampled at 100 equally-spaced points byconstraining emissions and varying E max , and the convex hullof the cost/emissions space is sampled by using the UCCT andvarying P CO , with and without load-shedding. Load sheddingis only economically justified under very high tax rates andresults in very high costs, so load-shedding solutions areomitted in all following figures for the sake of clarity. Thoughthe Pareto frontier may at first glance appear convex, there aremany small concave regions. This can be seen by plotting themarginal value at the sample points, as shown in Fig. 4; sincethe marginal values do not increase monotonically, the frontiermust be non-convex [41]. B. Determining a Tax Rate to Meet Policy Goals
If the CEMV method were used to set a tax rate, there isno guarantee that the solution to the UCCT problem wouldmeet the desired emissions reduction. This is illustrated inFig. 5, which uses the same set of sample points as Figs.
Desired emissions reduction (relative to zero-tax solution) M a r g i n a l v a l u e o f e m i ss i on s ( $ /t on ) marginalszero marginal Fig. 4. Marginal value found at 100 sample points on the Pareto frontier. P CO derived from the CEMVmethod do not reliably meet their desired emissions reductionswhen used in the UCCT. By comparison, the WSB method isguaranteed to meet or exceed the emissions reduction target.Convergence of the WSB method to its final values is shownin Fig. 6 for a target emissions reduction of 15%. The WSBmethod, given an emissions target, reliably converges to anoptimal tax rate within ¢ from an initial range of $0-$100/tonin 14 iterations of the UCCT problem. Though the tax ratewhich is converged upon may not be the true optimum, itcan be shown that the solution exceeds the true optimum byno more than a specified tolerance, and this tolerance can behalved with each additional iteration of the UCCT problem. Bycomparison, naively finding the tax rate by solving for eachpossible rate in ¢ increments would require 10,000 solves.The wider the range of potential solutions, and the greater thedesired accuracy, the more efficiently the WSB performs.
0% 5% 10% 15%
Desired emissions reduction (relative to zero-tax solution) R e s u lti ng e m i ss i on s r e du c ti on (r e l a ti v e t o ze r o - t a x s o l u ti on ) Target missedCEMV methodWSB method1:1 line
Fig. 5. Comparison of results using the CEMV method and the WSB method.
The importance of including binary variables is illustratedin Fig. 7. For this figure, the UCCT formulation is transformedinto a transmission-constrained economic dispatch (TCED)problem by ignoring intertemporal constraints (10)-(13) andsetting g min i , C min i , E min i = 0 for all generators. By using theWSB method to find the required tax rate for a given desiredemissions reduction for the TCED problem, and inputting thatresulting tax rate into the UCCT problem, it can be seenthat the realized emissions reductions fail to meet the targets.Factors which can contribute to this outcome include: therequirement to burn fuel to synchronize generators on start-up,and the requirement to commit additional generators to preparefor large ramps in net load, which occur more commonlyand with greater magnitude with the introduction of large Iteration number R e l a ti v e v a l u e Target reduction: 15% emissionscost1 3 5 7 9 11 13 15
Iteration number T a x r a t e ( $ /t on ) penalty Fig. 6. Convergence of WSB method to final value. quantities of renewables.
0% 5% 10% 15% 20%
Desired emissions reduction (relative to zero-tax solution) R e s u lti ng e m i ss i on s r e du c ti on (r e l a ti v e t o ze r o - t a x s o l u ti on ) Target missedWSB using TCEDWSB using UCCT1:1 line
Fig. 7. Comparison of WSB results when ignoring binary variables and in-tertemportal constraints (TCED problem) vs. including them (UCCT method).
C. Handling Uncertainty
Since this formulation requires estimating the distribution ofrepresentative days in a future year, there is some uncertaintyin the actual realization. The variance in annual realizedemissions, based on this sampling probability, is given by(25). If policy-makers desire to achieve emissions reductionswith a specified level of certainty, tax rates can be set suchthat the likelihood of achieving such reduction happens withthe desired probability using (26) due to the Central LimitTheorem [42].Var [ E total ] = σ E = 365 (cid:88) a ∈ A π a ( E a − E total ) (25)Prob [ E total ≤ E max ] = Φ (cid:18) E max − E total σ E total (cid:19) (26)where Φ( · ) is the cumulative distribution function of thestandard normal distribution.The choice of increasing or decreasing the tax rate in theWSB method is then based on whether this likelihood meetsthe desired level of certainty. Fig. 8 illustrates the uncertaintyrange around the expected cost and emissions, and Fig. 9illustrates the tax rate required to achieve a desired emissions −1 Tax rate ($/ton) A nnu a l P r odu c ti on c o s t ( $ M ) E m i ss i on s ( m illi on t on s ) cost emissions Fig. 8. Fuel cost and emissions as a function of tax rate, incorporating weatheruncertainty. Bands represent 95% certainty range.
Desired emissions reduction (relative to zero-tax solution) R e qu i r e d p e n a lt y v a l u e ( $ /t on )
99% certainty95% certainty90% certainty50% certainty
Fig. 9. Tax rate required to achieve emissions reductions, based on weatheruncertainty. reduction for various values of certainty. As shown, the re-quired tax rate to meet a given emissions target increases withthe level of certainty required, and some emissions reductionstargets which are achievable on average are not able to be metwith much certainty, no matter the tax rate.A similar process can be used in order to handle the uncer-tainty of fuel prices. Currently in the United States, abundantshale gas makes gas-fired power plants more competitive, butthese low prices may not persist. If there is a desire to set atax rate to be robust to fluctuations in the price of natural gas,the tax-setting process can be run using the highest gas pricethat can be reasonably expected.
D. Sensitivity Analyses
Sensitivity analyses to changes in the system’s wind pen-etration, coal plant retirement, gas prices, and gas supplylimitations on UCCT solutions are shown in Figs. 10(a)-(d), respectively, and the impact on the tax rates required toachieve desired emissions reductions are shown in Figs. 11(a)-(d). Additional scenarios are also run for specific emissionsreductions targets and shown in Fig. 12: • Wind Penetration : Wind penetration, initially at 8% oftotal energy, is increased by 10, 20, or 50%. • Coal Retirement : Coal generation is retired, either oneor two highest-cost generators (15% or 30% of the coal-generating capacity), consistent with estimates in [43]. • New Gas Generator : One new 250 MW gas generator isadded at the bus with highest average locational marginalprice (LMP), bus 8, increasing the gas capacity by 2.4%. • Gas Price : The price of natural gas generation is in-creased by either 50 or 100%. • Gas Limit : For each day, gas generators are limited inthe amount of energy that they can supply, at either 30or 35% of daily total energy. This is intended to simulateregional gas shortages such as those experienced in NewEngland [44] and Southern California [45] in 2014. • Load Increase/Decrease : The demand for electricity ateach hour is scaled up or down by 2%. • Transmission Capacity : The capacity of all transmissioncorridors is increased by 20%.Several of these scenarios have similar effects: increasesin wind penetration, gas generation capacity, or transmissioncapacity, or decreases in load. For all of these scenarios, thezero-tax solutions have lower costs and emissions than thebase case, a given emissions target can be met with a lowertax rate, and the maximum emissions reduction is increased.These effects can be seen in Figs. 10(a) and 11(a) for the windpenetration case and in Fig 12 for the other cases.Other scenarios have differing effects. For the coal plantretirement case, the zero-tax solution has lower emissionsthan the base case but is more expensive, since the retiredcoal generation is replaced by more-expensive gas generation.However, despite the higher zero-tax cost, a desired emissionsreduction can be met with a lower tax rate, as shown in Figs.10(b) and 11(b), and some targets can be met at a lower totalcost. For example, a 15% GHG reduction target in the basecase requires a tax rate of $23/ton and a total cost of increaseof 71%, but the same target can be met with a $17/ton taxrate and 56% cost increase in the 30% coal retirement case,as shown in Fig. 12. For the gas price increase cases, the zero-tax solution is both more expensive and higher-emitting thanthe base case, and a desired emissions reduction requires ahigher tax rate, but the range of possible emissions reductionsis not affected, as shown in Figs. 10(c) and 11(c). For thecase where there are limitations on the energy supplied by gasgenerators, the effect is highly dependent on the limit valuesand emissions targets, as shown in Figs. 10(d) and 11(d). Whengas generators are limited to providing no more than 35% oftotal energy, there is minimal impact for emissions reductionsless than 10%, but past this point there is limited ability toreduce emissions, and reductions require a higher tax rate. At alimit of 30%, the zero-tax solution is 7.6% more expensive andemits 7.6% more GHGs when compared to the base case, andonly a very modest reduction in emissions (1.5%) is possible.This illustrates the impact that gas system constraints can haveon emission reductions goals.The impact of relaxing the system flexibility constraints(18)-(19) is also investigated. For this system, the greatestimpact is seen at lower tax rates, where relaxing the rampingcapability requirement results in slightly higher emissions atslightly lower production cost, as shown in Fig. 13(a). Atzero tax rate, emissions are 0.4% higher and production costis 0.1% lower as compared to the base case. The impacton the tax rate required for a given emission reduction issimilar, as shown in Fig. 13(b): greater impact at low emis-sions reductions targets, with differences diminishing at moreaggressive emissions reductions targets. The converse is true
80% 90% 100%
Emissions(relative to base case, zero-tax)(a) P r odu c ti on c o s t (r e l a ti v e t o b a s e ca s e , ze r o - t a x ) Wind Penetration Sensitivity base+10%+20%+50% 85% 90% 95% 100%
Emissions(relative to base case, zero-tax)(b) P r odu c ti on c o s t (r e l a ti v e t o b a s e ca s e , ze r o - t a x ) Coal Plant Retirement
Emissions(relative to base case, zero-tax)(c) P r odu c ti on c o s t (r e l a ti v e t o b a s e ca s e , ze r o - t a x ) Gas Price Sensitivity +100%+50%base 90% 100%
Emissions(relative to base case, zero-tax)(d) P r odu c ti on c o s t (r e l a ti v e t o b a s e ca s e , ze r o - t a x ) Gas Supply Limit
Fig. 10. Sensitivities of Pareto frontier to (a) wind penetration, (b) coal plant retirement, (c) natural gas price, and (d) gas supply limit.
0% 5% 10% 15% 20% 25%
Desired emissions reduction(relative to base case, zero tax)(a) R e qu i r e d p e n a lt y v a l u e ( $ /t on ) Wind Penetration Sensitivity base+10%+20%+50% 0% 5% 10% 15% 20%
Desired emissions reduction(relative to base case, zero tax)(b) R e qu i r e d p e n a lt y v a l u e ( $ /t on ) Coal Plant Retirement base15%30% 0% 5% 10% 15% 20%
Desired emissions reduction(relative to base case, zero tax)(c) R e qu i r e d p e n a lt y v a l u e ( $ /t on ) Gas Price Sensitivity +100%+50%base 0% 5% 10% 15% 20%
Desired emissions reduction(relative to base case, zero tax)(d) R e qu i r e d p e n a lt y v a l u e ( $ /t on ) Gas Supply Limit
Fig. 11. Sensitivities of required tax rate to (a) wind penetration, (b) coal plant retirement, (c) natural gas price, and (d) gas supply limit. B a s e C o a l c a p . - % N e w g a s g e n . G a s p r i c e + % G a s l i m i t % L o a d + % L o a d - % W i n d + % T r a n s . + % Scenario(a) T o t a l c o s t (r e l a ti v e t o b a s e ca s e , ze r o - t a x ) no increase5% reduction10% reduction15% reductioninfeasible B a s e C o a l c a p . - % N e w g a s g e n . G a s p r i c e + % G a s l i m i t % L o a d + % L o a d - % W i n d + % T r a n s . + % Scenario(b) $0$10$20$30$40$50$60$70$80 T a x r a t e ( $ /t on ) no increase5% reduction10% reduction15% reductioninfeasible Fig. 12. Results of selected scenarios for specified emission reduction targets, (a) total cost, (b) required tax rate. when observing the impact on profit by generation technology:low tax rates have minimal impact, while higher tax rateshave more significant impacts. At tax rates of $0-10/ton, theaverage impact on profit is within 1.5% for all generationtechnologies, while for tax rates of $10-100/ton, relaxing theflexibility constraints results in profits on average 102% higherfor coal generators, and 5-6% lower for all other generationtechnologies.
E. Impact on Investment Decisions
As can be seen in Fig. 14(a), larger emissions reduction tar-gets lead to higher average LMPs, which translates to a better value proposition for investing in new non-coal generation (asshown in Fig. 14(b), the carbon tax reduces profit by coalgenerators). For example, at a target emissions reduction of5%, the profit for wind generators is 17% higher as comparedto the zero-tax solution; at a target of 10%, the profit is 33%higher. In the New Gas Generator scenario, the new generatormakes 12% more profit at an emissions reduction target of10%; at a target reduction of 5%, no tax is required.Along with higher LMPs, emission reduction targets alsoresult in increased congestion surplus, improving the valueproposition for investments in new transmission. At a targetGHG reduction of 5%, the congestion surplus is increasedby 9.5%; at a 10% target the surplus is increased by 16.1%.
80% 90% 100%
Emissions(relative to base case, zero-tax)(a) P r odu c ti on c o s t (r e l a ti v e t o b a s e ca s e , ze r o - t a x ) baseno ramp req. 0% 5% 10% 15% 20% Desired emissions reduction(relative to base case, zero tax)(b) R e qu i r e d p e n a lt y v a l u e ( $ /t on ) baseno ramp req. Fig. 13. Impact of relaxing system ramp requirement constraint on (a)cost/emissions Pareto frontier, and (b) tax rate required to achieve emissionsreductions.
0% 2% 4% 6% 8% 10% 12% 14%
Desired emissions reduction (relative to base case, zero tax)(a) A v e r a g e L M P ( $ / M W h ) b1b2 b3b4 b5b6 b7b80% 2% 4% 6% 8% 10% 12% 14% Desired emissions reduction (relative to base case, zero tax)(b) -50%0%50%100%150% P r o f it (r e l a ti v e t o b a s e ca s e , ze r o t a x ) coaloilgas windnuclear Fig. 14. (a) Average LMPs for buses b1-b8 as a function of desired emissionsreduction, and (b) Profit by fuel as a function of desired emissions reduction.
Congestion surplus as a share of total cost remains relativelyconstant, however: 20.6% in the zero-tax case, 20.4% in the5% target case, and 19.6% in the 10% target case.In addition to higher average LMPs, there is also anincrease in the variability of LMPs, which improves the valueproposition for grid-scale energy storage devices, consistentwith findings in [46]. At a 5% emissions reduction target,the average LMP for each bus is 35-60% higher (average of46%), while the standard deviation of LMPs for each bus is101-113% higher. However, while investments in wind andgas generation tend to reduce emissions (and therefore the taxrate required to meet emissions targets), the impact of energystorage is much less clear [47].
F. Coal Generators and Market Share
As would be expected, as the desired emissions reductionand the tax rate required to achieve this reduction bothincrease, the share of energy which is provided by coal andthe profit made by coal generators both decrease, as canbe seen in Figs. 14(b) and 15. These reduced profits maylead to earlier coal generation retirement and reductions incoal mining employment [48]. However, strategic investmentsin new wind generation and transmission network expansion −2 −1 Tax rate ($/ton) E n e r gy s h a r e ( % ) gascoaloil windnuclear Fig. 15. Energy by fuel as a function of tax rate.TABLE IC
OAL PROFIT DEPENDENCE ON INVESTMENTS , 5%
REDUCTION TARGET , GIVEN INCREASES IN WIND PENETRATION OR TRANSMISSION CAPACITY
Scenario Additional CoalProfit ($) Additional WindProfit ($) % Increase(coal/wind)+10% Wind 24,212 77,336 31.3%+20% Wind 62,170 140,276 44.3%+10% Trans. 22,835 N/A N/A+20% Trans. 131,112 N/A N/A both allow emissions targets to be met with a lower taxrate compared to the base case, and increase the profit ofcoal-powered generators, as shown in Table I. Additionally,emissions taxes which are set based on emissions targetsincrease the incentive for owners of coal-powered generationto invest in renewable generation, since the increased profitsfor coal generators caused by a lower tax rate provides an‘extra’ revenue stream.VI. C
ONCLUSION
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Daniel Olsen (S’14) received the B.Sc. degreein mechanical engineering and electric power en-gineering from Rensselaer Polytechnic Institute in2010. He is currently pursuing the Ph.D. degree inelectrical engineering at the University of Wash-ington. Previously, he was a Research Associatewith Lawrence Berkeley National Laboratory. Hisresearch interests include planning and policies forpower system emissions, multiple-energy systems,and distributed flexibility resources. Yury Dvorkin (S’11-M’16) received his Ph.D. degree from the University ofWashington, Seattle, WA, USA, in 2016. Dvorkin is currently an AssistantProfessor in the Department of Electrical and Computer Engineering atNew York University, New York, NY, USA. Dvorkin was awarded the2016 Scientific Achievement Award by Clean Energy Institute (Universityof Washington) for his doctoral dissertation “Operations and Planning inSustainable Power Systems”. His research interests include power systemoperations, planning, and economics.
Ricardo Fern´andez-Blanco (S’10-M’15) receivedthe Ingeniero Industrial degree and the Ph.D. degreein electrical engineering from the Universidad deCastilla-La Mancha, Ciudad Real, Spain, in 2009and 2014, respectively. He is currently a PostdoctoralResearcher at the University of M´alaga, Spain. Healso was a Postdoctoral Researcher at the Univer-sity of Washington, Seattle, WA, USA. He wasworking as a Scientific/Technical Project Officer inthe Knowledge for the Energy Union Unit at theDG JRC (Joint Research Center) of the EuropeanCommission, Petten, The Netherlands. His research interests include thefields of operations and economics of power systems, smart grids, bilevelprogramming, hydrothermal coordination, electricity markets, and the water-energy nexus.