Abstract—Demand Response Resource (DRR) curtailments aregenerally triggered in response to economic signals, such as thelocational marginal prices (LMPs). However, consideration ofonly the economic signals leaves out important information aboutthe impact of the location of DRR curtailments on the system-wide carbon emissions. In this work, we use the marginal carbonintensity (MCI), the carbon emissions analogue of the LMP, todevelop a metric which may be used by the Independent SystemOperator ISO to identify nodes at which DRR curtailments havethe greatest impact on both LMP (and thereby consumer pay-ments) and system-wide carbon emissions. Through illustrativesimulations, we compare the outcome of various DRR cases andshow the usefulness of the identification metric.
I. INTRODUCTION
Concerns about climate change have driven state and federalpolicy that aims to reduce carbon emissions in the electricitysector. The electricity sector accounts for around 40% of U.S.carbon emissions [1] and a number of policies, such as CarbonCap and Trade and Renewable Portfolio Standards, havebeen proposed to achieve emissions reductions. In addition,there has been a push for increased energy efficiency andparticipation of alternative resources, such as energy storage,renewable generation and demand response resources (DRRs),to meet the supply demand balance while reducing system-wide carbon emissions.
A number of studies are dedicated to the quantification ofthe system-wide emissions impacts of the carbon emissions-reduction policies. These studies take into account the emis-sions reductions due to reduced demand, the introduction ofcarbon prices, increased use of renewable energy resources,and energy conservation on an aggregate basis [2], [3].However, in many of these studies the electricity networkis not taken into consideration in the calculation of system-wide emissions, and consequently, the impacts of resourcelocation on emissions are not evaluated. Even in those studieswhich do consider the network, the resource locational impactson emissions are not addressed. The location of DRRs andrenewable resources is crucial in the quantification of system-wide carbon emissions as congestion patterns may impact
the system-wide carbon emissions which result when suchresources are utilized. For instance, a small reduction indemand at a node for a particular system snapshot may resultin different system-wide carbon emissions levels, if congestionis present, than an equivalent reduction at another node. In thispaper, we use DRRs as an example to illustrate the significanceof the resource location on system-wide carbon emissionslevels.
DRRs are demand-side resources which provide load cur-tailments in response to signals from the system operator. Thesignals may be reliability or economically-driven. DRRs thatrespond to reliability-driven signals are known as emergencyDRRs and provide curtailments to reduce the impact of systemevents, such as the loss of a generator or transmission line.DRRs that respond to price signals are referred to simplyas DRRs and provide curtailment services in response toprice signals, such as those from the day-ahead and real-timeelectricity markets of independent system operators (ISOs) andare the majority of enrolled DRRs.
Frameworks to represent DRRs in competitive electricitymarkets and analysis of the implications of DRR utilization onthe scheduling and the pricing of electricity are available in [4]and [5]. Both analyses not only incorporate load curtailmentsduring high price periods, but also take into account theimpacts of demand recovery by the corresponding customersin the low price periods. Studies conducted [6] and [7] showthat DRRs successfully reduce the peak load demand of thesystem and yield substantial savings in the electricity costs.The topical nature of emissions reductions has resulted instudies investigating the impacts of load reduction on system-wide carbon emissions [2] and [3]. Since DRRs reduce load inpeak hours and recover a portion of it in the off-peak hours,intuitively, we expect their utilization to result in a reductionin overall emissions. However, DRR curtailments may notresult in net carbon emissions reductions due to the carbonemissions rates of the dispatched units in the curtailmentand recovery hours respectively, and level of congestion inthe network. In fact, if the DRR curtailment results in a
redispatch of generation such that units with higher carbonemissions rates are used to serve the remaining load, orDRR curtailment energy is recovered in off-peak hours whenunits with higher carbon emissions rates are marginal, thesystem-wide carbon emissions may even increase as a resultof DRR utilization. The location of the DRR in the networkdetermines how the DRR affects the marginal generators andtransmission line flows and ultimately the system-wide carbonemissions. A failure to consider resource locational impactsmay lead to over- or under-estimates of the carbon emissionsreduction potential of alternative resources, such as DRRs,when formulating policy. If carbon reduction policy is to beeffective, the locational impacts of DRR and other resourceson system-wide carbon emissions cannot be ignored.
In the evolving landscape of carbon emissions reductionpolicy, there is a clear need for tools and methods to assessnot only the aggregate carbon emissions impacts of DRRs,but also the locational carbon emissions impacts in orderto formulate policy which will have the intended impacton carbon emissions reductions. We quantify the impactsof DRR curtailments in a transmission-constrained networkand develop a metric, which captures the location-dependent,carbon-emissions impacts of DRRs, to select nodes at whichDRR curtailments may produce the greatest value in terms ofsavings in consumer payments and system-wide carbon emis-sions reductions. This metric translates the value of carbonemissions impacts into monetary terms and may be used todevelop incentives for DRRs to provide curtailments wherethey are most effective from both carbon-emissions reductionand consumer payment reduction perspectives. We apply theproposed metric to the IEEE 118-bus test system over a threemonth period to demonstrate the mechanics of the proposedmetric.
The remainder of the paper consists of four additionalsections. In section II, we explain the concepts used toexpress DRR locational emissions impacts and demonstratetheir analogy with the concept of locational marginal pricing.In section III, we describe the simulation methodology andexplain the proposed metric for selecting nodes with highcurtailment value. In section IV, we present an illustrativeexample of the implementation of the proposed metric anddiscuss the salient aspects of the proposed metric. In sectionV, we provide concluding remarks and give the directions forfuture research.
II. LMP AND MCI CONCEPTS
The locational pricing model that makes use of nodal pricesin electricity markets is widely used by many ISOs for short-term congestion management. Such prices are the outcomes ofthe day-ahead markets (DAMs) that the ISO clears based onthe sellers’ offers and the buyers’ bids. The DAM’s clearingmechanism objective is to maximize the social surplus orminimize cost in the case of inelastic demand. The marketclearing explicitly considers transmission network constraintsand so the market outcomes in terms of the locational marginalprices (LMPs) reflect the impacts of congestion in the grid.
The LMP at a node is the sensitivity of the objective functionof the DAM clearing mechanism with respect to an injec-tion/withdrawal at that node. The LMPs may differ at eachlocation in the presence of transmission congestion, sincetransmission congestion restricts energy flows from low-costgeneration from meeting the loads. When congestion arises,higher electricity prices emerge in several nodes and the socialsurplus is decreased. DRRs respond to the high LMPs andcurtail load, which will relieve congestion. However, if theelectricity price is the only signal for DRR curtailments, totalsystem-wide carbon emissions may increase as a result of thecurtailments. In many electricity systems, the base loaded unitsare more carbon-intensive than the peak-hour units. As a result,DRRs, which recover curtailed energy in the off-peak hours,use those more carbon intensive units to recover energy andthe net effect of the curtailment is an increase the total system-wide carbon emissions. Therefore, if emissions impacts havevalue (i.e., there is a price for carbon), it is important that theISO is able to identify nodes at which DRRs have the dualimpact of relieving congestion and reducing emissions. Wedefine the curtailment value of a DRR to be it’s impact onboth relieving congestion, and therefore reducing LMPs, anddecreasing system-wide carbon emissions. To identify suchnodes, we use the concept of marginal nodal carbon intensity(MCI), which was introduced in [8], that specifically addressesthe locational impacts of carbon emissions within the operationof a power system. The MCI of a specified node, which ismeasured in tonnesCO2/MWh is defined as the decreasein carbon emissions in the electrical network in response to a1MW decrease in demand at the specified node. We use theMCI to support the need for a more detailed consideration oflocational effects in emission reduction policies and resourceutilization.
We introduce the following notation to formulate the MCIs.We consider a power system with the set of (N + 1) nodesN = {0 , 1, . . . , N}, with the slack bus at node 0 , and the setof L lines L = {` 1, . . . , `L}. We assume the network to belossless. We denote the diagonal branch susceptance matrixby B d ∈ RL×L and the reduced branch-to-node incidencematrix for the subset of nodes N /{0} by A ∈ RL×N .The corresponding nodal susceptance matrix is B ∈ RN×N .For the simplicity of the discussion, we assume the networkcontains no phase shifting devices. The injection shift factors(ISFs) matrix is denoted by Ψ = B dAB
−1. The injectionshift factor ψn` is a linear approximation of the first ordersensitivities of the active power flow on line ` with respectto an injection or withdrawal at node n [9]. The LMPsat the nodes, denoted by the vector λ, and the marginalgenerators are outcomes of the DAM clearing mechanism[10]. The marginal generators are those whose output are notat their physical limits and may change their output at anoptimal redispatch in response to a small variation of a systemparameter. We denote by L̃ the set of lines that are congested,i.e., whose line flow constraint is binding. Let us assume thatthe number of congested lines is K − 1, then the numberof marginal generators is K [11]. The MCI κn at node n is
defined as
κn = r̃ T[1T
Ψ̃
]−1 [1ψn
], (1)
where r̃ is the vector of carbon emission rates for the marginalgenerators with dimension K×1, 1 is a K-dimensional vectorof ones, Ψ̃ with dimension K−1×K the reduced ISF matrixconsisting of the elements of Ψ which contain the impact onthe congested lines with respect to injections/withdrawals atnodes where marginal generators exist and ψ
nthe vector with
dimension K − 1× 1 the column of Ψ that shows the impacton the congested lines of an injection/withdrawal at node n.We denote by κ the N + 1-dimensional vector of MCIs.
If the system has no congestion, i.e., zero line flows areat their maximum limits, then there exists only one marginalgenerator. As a result, each bus has the same LMP, equal to theoffer of the marginal generator, as well as the same MCI, equalto the carbon intensity of the marginal generator. However,when congestion arises there exist at least two marginalgenerators. As a result, each node may have a unique LMP andMCI. It is interesting to note that even with congestion, theMCIs may still be the same at all nodes. This situation arises ifthe marginal generators have the same carbon intensity sincewe have assumed a lossless system and the conservation ofenergy must hold.
The MCIs are used to identify the nodes where DRRcurtailments results in the greatest emission impacts. However,this may lead to non-economically efficient results, i.e., theconsumer payments could be further decreased by selectingDRRs based on LMPs. Our proposed solution is to use ametric, which we define as the Net Nodal Curtailment Value(NCV), that combines the LMPs and MCIs to determine thenodes at which DRRs have the greatest curtailment value.In order to combine the LMPs and the MCIs to developthe NCV, they must have the same units. We may translatethe MCIs to dollars by multiplying each node’s MCI withthe per-unit carbon price, γ. The range of γ is selected tobe representative of expected future carbon prices [12]. Theresult of the translation of the MCI into monetary termsrepresents the nodal social value (or cost), for a particularcarbon emission price (in $/tonneCO2), of a 1MW loadreduction (or increase). Mathematically, we denote the NCVby the N + 1-dimensional vector function
ν(λ,κ) = f(λ) + g(κ) . (2)
In the next section, we define the functions f and g, toformulate the NCV.
III. METHODOLOGY
To assess the locational impacts of DRRs on system-widecarbon emissions and develop a metric for selecting nodes atwhich DRR curtailment will be likely to produce carbon emis-sions reductions, we consider a test system over a specific timeperiod. The system is assumed to operate an hourly electricitymarket with locational marginal pricing which clears daily forall twenty-four hours of the following day, similar to that of a
number of ISOs. Each generator is assumed to submit hourlyblock offers consisting of a quantity (in MW ) and a price.The generators are assigned carbon intensities, the carbonemissions per MWh of generation (in tonnesCO2/MWh),which is assumed to be constant for each generator across theiroperating range, based on their input fuel and technology. Thedemand in each hour is assumed to be inelastic.
We utilize the generators of the test system and an ISO-based offer and generator profile to create generator offersand carbon intensities which approximate the offer curve andgeneration mix of an ISO. We assume the offer curve changesmonthly but is fixed within each month. We also use ISOload data over the same period as the offers and scale theload data to the generation level of the test system minusa reserve margin. For the market simulation, we use thenetwork assumptions given in section II, employ the DC powerflow and clear the market as a linear program including thetransmission network constraints and with the minimizationof cost as the objective. Using forecasts for the networktopology, load, and offer data, we obtain a forecast of themarket outcomes, that we use to calculate the NCVs.
In the market simulation, DRRs are assumed to submit offersto provide curtailment and bid for energy recovery in hourswhere they do not provide curtailments. For DRR curtailments,we consider the day a twenty-four hour period from midnightto midnight. We assume DRRs will recover at most the totalenergy curtailed over a day in the day in that it providedthe curtailment. An in-depth explanation electricity marketformulation including DRRs is found in [13].
To accurately represent the current market status of DRRsin our simulations, we incorporate the requirements of therecently issued FERC Order No. 745 into the DRR dispatch.The FERC order mandates DRRs be paid the LMP when itexceeds a predefined, system-wide threshold price. We assumeall DRRs offer curtailment service at the threshold price (i.e.,they would like to be paid if they are obligated to provide acurtailment), and thus all DRRs at a node are cleared if theLMP exceeds the threshold price and DRRs recover curtailedenergy when the LMP falls below the threshold price.
The threshold price is determined by the ISO on a monthlybasis from a regression based on the electricity supply curveand historical fuel price data. For an in-depth description ofthe threshold price calculation methodology see [14]–[16].
In order to calculate NCV and identify nodes where DRRswill have a high curtailment value, we categorize the hoursof the simulation period into peak and off-peak. We definethe peak hours of a period to be all hours in which the LMPexceeds the threshold price. The number of peak hours neednot be the same for each node. Off-peak hours are defined tobe all hours on days which had at least one peak hour but inwhich the threshold is not exceeded. We only consider off-peak hours on days with at least one peak hour because ofour assumption that DRRs recover energy on the same day itwas curtailed.
As stated in section II, we consider the NCV as the metricto identify nodes at which DRRs have the greatest curtailment
value. The NCV is based on the peak and off-peak LMP andMCI. We define µλ and µκ to be the vectors of the mean of theLMP and MCI, respectively, and σλ and σκ to be the vectorsof the standard deviation of the LMP and MCI, respectively.We denote peak values by the superscript p and off-peak valuesby the superscript o. We may then define the components ofthe NCV introduced in (2)
where γ is the system-wide per-unit carbon price, ρ is aparameter representing risk aversion, which results in moreconservative estimates of the node performance metric as it isincreased, ξp and ξo weight the metric at each node by thenumber of expected peak and off-peak hours, respectively, ina given period and diag(ξp) (diag(ξo)) is an N +1×N +1diagonal matrix of the node weights for the peak (off-peak)hours. The vector function f represents the expected netimpact on the consumer payments of a DRR curtailment ateach node. The vector function g represents the expectednet carbon-emissions impact value of a DRR curtailment ateach node (which is zero when there is no carbon price).In the following section, we apply the NCV to illustrateits application in the identification of nodes at which DRRcurtailments provide the greatest curtailment value and wediscuss the nature of the results.
IV. NUMERICAL RESULTS
We illustrate the application of the proposed metric on amodified IEEE 118-bus test system, which has 186 lines.The load buses, where we may have DRR, are 99 out of118 buses. The test system is modified such that the supplycurve reflects that of an ISO and so the line limits are suchthat there is a sufficient level of congestion to illustrate thelocational emissions impacts which are the focus of this work.In particular the line limits vary between 1982 and 2374MW . The test system has 54 generators and we assumethat 50% are steam turbine coal units, 33% combined-cycle(CC) natural gas (NG) units and 17% combustion turbine(CT) NG units. The carbon intensities assumed for each unittype as well as the generation mix are shown in Table I. The
TABLE I: IEEE 118-bus system generation mix and carbonintensities
generation carbon intensity proportion oftechnology (tonnesCO2/MWh) system capacity (%)
coal 0.9 50CC NG 0.4 33CT NG 0.6 17
load and generator offer data are obtained from New EnglandIndependent System Operator (NEISO) for the months of Juneto August 2010 [17]. The generation capacity is scaled to thetest system capacity of 9966 MW and a 5% reserve margin
is applied resulting in a peak load of 9468 MW . We presentthe results here that are representative of the extensive testsof the proposed methodology we have carried out on varioussystems. In these studies, we demonstrate the mechanics ofcalculating the NCVs and discuss how we make use of thephysical grid characteristics and the insights we gain from thesolution. To make the discussion of the numerical results moremanageable, we choose only one DRR node in each case.
We assume we have perfect forecast information for theload, offers and network topology and clear the DAMs in orderto calculate the vector of NCVs, ν. We modify the parametersof system-wide per-unit carbon price, γ, and risk aversion, ρ,and calculate the NCVs. We choose the node with the highestNCV for each case and present the results in Table IV. For
ρ = 0, i.e., without consideration of the variability of the LMPsand MCIs, the node with the largest NCV is the node with thelargest weighted difference between average peak and off-peakLMPs and MCIs given a system-wide per-unit carbon price. As
0 20 40 60 80 100 118−5
0
5
10
15
20
node number
$/M
Wh
γ = 50
γ = 20
γ = 5
γ = 0
Fig. 1: NCVs of nodes for various carbon prices γ and riskaversion ρ = 0.
is depicted in Fig. 1, the resulting NCVs show that node 60 hasthe highest curtailment value for carbon prices ranging from 0to 50. The µλ,p60 is 71.72 and µλ,o60 is 39.94, whose differenceindicates the savings from off-peak vs peak consumption in thepresence of DRR curtailments. As for the MCIs, we have µκ,p60
is 0.4131 and µκ,o60 is 0.7502, which indicates a net increasein emissions as a result of peak curtailments and off-peakrecovery. We weight the peak and off-peak LMP and MCIvalues by the coefficients ξp60 = 0.4121 and ξo60 = 0.2726that show the expected proportions of the period of time thatwe have curtailments and recovery to better approximate theactual impacts of DRRs curtailments at node 60 on consumerpayments and system-wide emissions. Since the weighted
average peak MCI is less than the weighted average off-peakMCI we expect a net increase in emissions from curtailmentsat node 60. However, the comparison of the weighted averagegives equal importance to each hour and doesn’t capture thedisproportionate impacts of curtailments (recovery) in thosehours in which the MCI is significantly greater (less than)than the mean. Fig. 2 depicts a week where the MCI in somepeak hours is clearly greater (≈ 0.6) than the period mean(0.4131). Fig. 2 also shows that the MCI in the off-peak hoursis significantly less (≈ 0.4) than the period mean (0.7502). Ifa large proportion of the curtailments for the period take placein such weeks, the expected impacts of DRR curtailment at thenode will prove to be conservative. According to our metric,
1 24 48 72 96 120 144 1680
100
200
300
hour (h)
$ /
MW
h
1 24 48 72 96 120 144 1680.2
0.4
0.6
0.8
hour (h)
ton
nes
CO
2 /
MW
h
MCI at node 60
LMP at node 60
Fig. 2: LMP and MCI for a week at node 60.
we select node 60 to have a 1MW DRR, denoted by the caseD60. The results of the simulation, reported in Table IV, showa carbon emissions reduction of 330.50 ktonnesCO2 and aconsumer payment reduction of $1, 131. The carbon emissionsreduction indicates that the component of the NCV quantifyingemissions reductions provided a conservative estimate.
Though in the case reported above, the variability of theMCI resulted in a reduction in system-wide carbon emissions,this may not always occur. In order to prevent overestimationof the emissions reductions DRR curtailments may achieve,we consider several increasing values of the risk aversionparameter, ρ. We show in Fig. 3, the standard deviations,σκ,o for all load nodes. We note that σκ,o60 has a large valuecompared to the other nodes. If we increase the value of ρ, weidentify nodes whose values of LMPs and MCIs have smallvariability over the test period and are more likely to resultin the expected emissions outcomes. By giving lesser weightto nodes with higher LMP and MCI variability, we may notachieve emissions impacts as great as in the case where ρ = 0.However, we are more confident that the resulting reductionsin consumer payments and system-wide carbon emissions willconform to our expectations and that we are less likely tooverestimate the reductions. We show in Fig. 4 and Fig. 5,the resulting NCVs for values of ρ = 1.6 and ρ = 2.2. Forρ = 1.6, we see node 60 no longer has the greatest NCV dueto the greater variability of the LMP and MCI compared tothose of other nodes. In this case, the node with the highestNCV is node 45. As we further increase the value of ρ we
0 20 40 60 80 100 1180
0.02
0.04
0.06
0.08
0.1
node number
ton
nes
CO
2 /
MW
h
Fig. 3: Standard deviation σκ,o for all load nodes.
0 20 40 60 80 100 118−25
−20
−15
−10
−5
0
5
node number
$/M
Wh
γ = 50
γ = 20
γ = 5
γ = 0
Fig. 4: NCVs of nodes for various carbon prices γ and riskaversion ρ = 1.6.
0 20 40 60 80 100 118−40
−30
−20
−10
0
node number
$/M
Wh
γ = 50
γ = 20
γ = 5
γ = 0
Fig. 5: NCVs of nodes for various carbon prices γ and riskaversion ρ = 2.2.
assign even greater value to low variability and those nodeswith high variability, such as 45 and 60, have lower NCV. Aswe see in Fig. 5, when the risk aversion parameter, ρ = 2.2,node 8 has the highest NCV. This result is consistent withnode 8’s average off-peak MCI variability shown in Fig. 3.The identified nodes with the highest NCV for various valuesof ρ and γ are reported in Table II.
We now report the results of the simulations for DRR
cases D45 and D8, as given in Table III. The results of
these simulation cases are given in Table IV. In case D45 theresulting emissions reductions are 327.70 ktonnesCO2 andthe consumer payments reductions are $1, 130. Because thevalue of ρ is relatively small, we see similar results to that ofcase D60. However, when we increase the value of ρ to 2.2 weobserve a significant decrease in the system-wide emissionsreductions. Since node 60 had variability which increasedthe emissions reductions achieved as described above, we ex-pected the conservative choice of node 8 would result in lowersystem-wide carbon emissions reductions. The advantage ofincreasing the value of ρ and selecting node 8 is the greatercertainty of the emissions reduction achieved.
TABLE IV: consumer payments and carbon emissions reduc-tions
The simulations also demonstrate the location of the DRRhas a significant impact on the system-wide emissions reduc-tions. The emissions reductions achieved in case D8 are 84%of those achieved in case D60 due to congestion effects drivenby the network topology.
V. CONCLUDING REMARKS
In this paper, we have used the example of DRRs to demon-strate the importance of resource location on the system-widecarbon emissions reductions that may be achieved through theimplementation of alternative resources. We use the LMP andthe analogous emissions concept, the MCI, to quantify thecurtailment value and formulate a metric, the NCV, whichidentifies nodes that have the greatest impact on both consumerpayment and carbon emissions reductions. Such a metric maybe used in the design of effective carbon emissions reductionspolicy.
In the future, this work may be extended to simulatethe impacts of a more diverse generation mix, additionalpollutants, and the impacts of other resources, such as energystorage devices.
ACKNOWLEDGMENT
The authors would like to thank their adviser, Prof. GeorgeGross, for his guidance and input in their research endeavors.
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