Quantify the Impacts of NOx Cap on Generators’ Emission Rate using Multiple Level Models
Abstract
In this paper, we applied the multiple-level model (MLM) to quantify the degree of stringency to which the US Environmental Protection Agency (EPA) NOx cap-and-trade imposes on the electricity generators. The US EPA NOx is implemented throughout the summer season from May to September every year. The design of the program is resemble to the crossover design of the case-control studies in epidemiology field. The strength of this design is that the non-summer season serves as the self-control groups where the time-invariant latent variables at generators’ level are automatically controlled. The hierarchical structure of our model includes generators at the lowest level, ownership at the second level and finally plant location at the upper level. The covariates that we control for are capacity, vintage year, output level and the fuel type at generators’ level, and price at location level. Using the MLM provides a more flexible modeling framework and allows us to decompose the residual variance which otherwise would not be explained by non-MLM approaches into variance at the various levels.
The application is to Pennsylvania – New Jersey – Maryland Interconnection market. The results show that significant variance reduction is achieved by including random-effects at three levels. Together with information about permits prices, we are able to estimate the effects of the regulatory programs on power industries in the monetary terms.
Introduction
Various studies have shown that the increases of mortality rate and other health-related endpoints are associated with the elevation levels of ozone concentration during summer time [1-5]. For example, Bell et al. [5] found that a 10-ppb increase in the previous week’s ozone was associated with a 0.52% increase in daily mortality and a 0.64% increase in cardiovascular and respiratory mortality, respectively. The formation of ozone is a complicated photochemical process, which involves the reactions of two precursors – NOx and volatile organics chemicals (VOCs) – in the presence of sunlight. The peak ozone concentration usually occurs during the early afternoon, i.e., 14:00 – 16:00, in summer time when adequate amount of biological VOCs reacts with vehicles-exhausted NOx in the morning traffic. The well-known nonlinearity in the isopleths diagram indicates whether the reduction of NOx or VOCs is an effective means to reduce ozone depends on the ratio of the two precursors [6]. This poses substantial challenges for the regulatory agencies to implement control strategies. The Mid-Atlantic region is one of the areas that are frequently in violation of ozone National Ambient Air Quality Standards (NAAQS) according to the US Environmental Protection Agency (EPA) [7]. Interestingly, unlike regulating SO2, which is led by the federal government, the establishment of ozone transportation commission (OTC) in 1997 is a joint effort by industries, environmental groups and the authorities at the state level [8]. Because the contribution of ozone precursors is mainly originated from the upwind states, notably power plants located in Ohio and Kentucky, where there is less incentive for them to reduce emissions since they are constantly in compliance with the NAAQS. The federal government seemingly should be in a great position to take the leadership.
The stewardship of the OTC led to the creation of regional cap-and-trade program for NOx in 1999 (OTC NOx Budget Program). The theoretical rationale behind the cap-and-trade programs is that the successful implementations will result in a least-cost solution for a given emission reduction target. While the geographical scope of the OTC program has evolved over time to encompass more states, the central piece of program remains intact.[1] First, the program is only enforced in the summer period from May 1st to September 30th. The program first gives out tradable permits to the affected facilities based on the historical heat input (three-year moving average) multiplied with a predetermined input emission rate.[2] One unit of tradable permit entitles the owners to emit one ton of NOx that year. Besides, the flexibility of the program allows the owners of permits freely trade them in the secondary markets; and the excess permits can be banked for future use but are subject to certain restrictions, which limit the upper bond of banking amount. Overall, the program has demonstrated great success over years.
One challenge faced by the policymakers is to know how effective the program is and to quantify the degree to which the introduced program forces the polluters to reduce their emission. Apparently, the aggregate emission cannot exceed the emission cap; but under what circumstances will a firm reduce their emission? In general, the operation of generators depends on several factors: wholesale price level, market structure, engineering constraints and etc. In particular, if marginal cost of a generator is below predicted wholesale price, the generator will be brought online given that transmission network is feasible. A generator may be operated differently if market is less competitive when demand is inelastic. Moreover, operating generators is subject to engineering constraints such as ramp rate, which limits how fast a generator can increase its output of given time. Therefore, the operating of generators is a function of where it is located, what kind of the technology it uses and what the objective the firm has.
To answer the aforementioned question turns out to be a daunting task, in part, because there are many ways an industry can response to the policy changes. In the short run, firms can modify their production factors such as labors, materials or the production processes; in the long run, it can engage in the research for advanced control technologies. In addition, the market structure and the nature of regulatory regime also have significant influence on it. For example, a monopoly under cost-of-service pricing scheme has little incentive to improve its performance since the incurred costs can be fully passed through on consumers [10][11]. Therefore, a full analysis requires considering the factors that affect generators’ operations at the market’s, the ownership’s and the generators’ level.
In compared with structural analysis, we take an empirical approach and model the resulting changes of generators’ performance as a consequence of the interplay of various factors at the different levels. The report is organized as following. In the section two, we will introduce the analytical framework of multi-level models. This includes defining the dependent variables and the covariates at each level. The data sources that we use for this analysis will be briefly discussed in the third section. We present our preliminary results in the section four, and enclose this report with a discussion. [TAL1]
Analytical Framework
To simplify the analysis, we consider covariates at the three levels[3] including a generator’s location or regional market, type of the ownership and the generation technology, which are indicated by l, f and g, respectively. Following the convention, the alphabetical letters are used for donating variables while the Greek variables are used for presenting coefficients. The capital letters indicate the time-invariant variables. The input NOx emission rates are assumed to have a normal distribution with mean and variance . We begin with the simplest multi-level model in which the only source of random effects is from the intercepts related to a generator’s location, type of the ownership and the generation technology. (The fixed-effect model can be obtained by ignoring the random-effect coefficients: , and .)
(1)
(2)
(3)
(4)
(5)
(6)
The dependent variable is the hourly input NOx emission rate in lbs/mmBTU of g-type generator owned by the f-type of ownership located at the location l during hour t. The nonlinear relationship between heat rate and output level is well known by power engineers. This is in particular the case for the peaking units such as combined-cycle and combustion turbines. However, it is unclear whether the nonlinearity is apparently for the relationship between the emission rate and output. As a beginning point, the model is analyzed with the linearity assumption[4]. To illustrate it, in Figure 1 we plot the NOx emission rate vs. output level of two generators, representing steam and combined-cycled technology. The first plot shows that steam unit’s input emission rate is scattered between 0.1 and 0.4 lbs/mmBTU, while in the second plot, the emission rate of combined-cycled unit is centered around 0.1 lbs/mmBTU. In both cases, there is no apparently nonlinearity existed. The distribution of the input NOx emission rate and output is displayed in Figures 2-3. A rather bi-mode distribution is shown in the steam unit and a single mode is with the combined-cycled unit. The possible explanation is the ramping-up process for steam unit has different effects on NOx emission rate. Figure 3 indicates that a significant amount of time steam unit is online at its capacity, while combined-cycled is operating only half of the time. The variable is an indicator variable, in which its value is equal to 1 when t is under ozone period, and 0, otherwise. The variable is the power price in $/MWh at the location l during t period; the variable indicates the output level in MW by the generators located at l with f-type of ownership using g-type technology in the period ; the variable donates the rated capacity in MW of the generator located at l with f-type ownership using g-type technology; the variable is the vintage year of the generator located at l with f-type of ownership using g-type technology. The variable is an indicator with value equals to 1 for utility and 0 otherwise. The location variables are also indicator variables that are used to represent the ten distinct locations in the network. Finally, the variable is the error term and we assume it follows the AR(1) process (equation (3)). The random-effect coefficients (, and ) which are used to capture the variation of the latent variables are assumed to have normal distributions with mean 0 and variance , and , respectively. The coefficient is of our interest and it summaries the extra reduction in hourly NOx emission rate (if negative) in the logarithm scale.
Data Sources
There are two primary data sources supporting this analysis. The generation characteristics are obtained from Energy Information Administration (EIA). This includes an inventory of generating units and their NOx input emission rate, vintage year, generation capacity, generation technology and type of ownership. The information is then cross-validated with the information from the EPA’s Emissions and Generation Resource Integrated Database (eGRID)[5]. The data retrieved from the US EPA Continuous Emission Monitoring system (CEMS) provides the hourly measurements of NOx emission rate and generating output level. Of the total 265 emission sources listed in the CEMS in 2003 for Pennsylvania – New Jersey – Maryland (PJM) Interconnection, we identified 134 generating units, which have one year worth data. (Some emission sources are industrial boilers or oil refineries, which are not considered in the analysis.) The set of generating units accounts for 43% of total generation capacity but more than 70% of fossil-fueled capacity.
The PJM is spatially comprised with the ten zones/nodes: METED, PPL, BGE, PEPCO, JCPL, DPL, PECO, PSEG, AECO, and PENELEC. The difference in nodal power prices reflects the network topology and the locations of the generation capacity. In general, the power prices during the ozone period are roughly 30% to 40% higher than that during non-ozone period. This indicates fewer peaking units are operated during non-ozone period; and this could be problematic for our analysis because only a smaller portion of the generating units operating frequently in both periods. To account for this, we selected two types of generators: steam turbines and combined-cycle generators. The steam-turbine units are baseload units, which are operated through out the year; and combined-cycle generators are intermediate units, which are operated more frequently than other non-steam units. This left us a total of 88 generating units. Due to the large dataset, we decided to select the hour of 14:00 as the sample of our daily measurement and further sampled a subset of dataset as our sample.[6] This reduces our sample size to a manageable scale. The other approaches such as taking daily average will lead to the substantial loss of information and statistical relevance. The final dataset is in a relative large scale with roughly 603 observations for each of 28 variables.
Results
Table 1 provides the summary statistics of our database grouped by location, technology, fuel and ownership. The dataset accounts for a total of 24,000 MW of generating capacity, of which 23,227 MW (96.7%) is owned by non-utilities and 768 MW (3.3%) is owned by utilities.[7] Moreover, a total of 85 generating units are steam-turbine units and their capacity accounts for 92.6% of the total capacity. The number of units fueled by coal, oil and gas is 55, 18 and 36, respectively. The capacity of them is 64%, 16% and 20% for three fuel sources, respectively.
We conducted the MLM analysis using both STATA(8) and SAS (v8) statistical packages. The initial data cleaning and examination was done in SAS, which handled large datasets more efficiently. In addition, Proc Mixed with random statement was attempted to illuminate the MLM structures of the specified relationship (Equation (2)). However, due to limited proficiency with the software, we could only specify generators as the grouping variable (i.e., data within each generator is correlated assuming AR(1)) but not able to include higher level indicators (e.g., location, ownership, and technology). [TAL2] We resolved to include these indicators as level-2 covariates in the regression model and presented the SAS results in Table 2.
Table 3 summarized our modeling results using STATA. The fixed- and random-effects models give not compatible coefficient estimations for fixed effects. For instance, the coefficient of load estimated by fixed – and random-effects models is -.0000344 and .0001144, respectively. The inconsistency could be due to different modeling specification. In general, we pay with variance explained by the model (larger SE’s) to gain generalizability in random effects models.[TAL3]
The coefficient of ozone is the most policy relevant. Based on random-effects model, it suggests that in average, the implement of NOx results in a reduction of 0.105316 lb/mmBTU in hourly NOx emission rate. If we assume the heat rate is 10000 BUT/kWh, the estimated incurred cost is roughly 1.05316 $/MWh. For a coal unit with capacity equal to 1 MW and a capacity factor of 0.8, the annual cost becomes 7,381 $/year. Given its 95% CI, the estimated cost will be between 9461.1 and 5300 $/year.
Discussion
We presented an application of using MLM to quantify the policy impacts on energy industries. To solving models using STATA is subject to curse of dimension. As number of observation and variables increases, the integration procedure embedded in the package becomes extremely slow. For instance, it takes more than three hours to finish the run for our simplest dataset. However, our sample procedure should provide unbiased estimation of coefficients since the sample scheme is independent from other factors.
The comparison between fixed – and random-effects clearly shows that the estimations from fixed-effects models could sometimes be misleading. This can be attributed to the fact that fixed-effects model fail to take into accounts the underlying hierarchical nature of the problems. The results also show that the latent variables effectively explain a significant amount of variance, which is not explained in the fixed-effect model.
Figure 1. Input NOx emission rate vs. output level (ST: steam and CC: combined cycle)
[TAL4]
Figure 2. Histograms of input NOx emission rate (ST: steam and CC: combined cycle)
Figure 3. Distribution of Output (ST: steam and CC: combined cycle)
Table 1. Generator characteristics (n=134), EPA emission data of PJM Region, 2003
Characteristics / Total (n=134) / Study (n=88)Frequency
/%
/Frequency
/%
LocationMETED / 6 / 4.48 / 5 / 5.68
PPL / 14 / 10.45 / 10 / 11.36
BGE / 12 / 8.96 / 11 / 12.50
PEPCO / 15 / 11.19 / 8 / 9.09
JCPL / 17 / 12.69 / 9 / 10.23
DPL / 14 / 10.45 / 11 / 12.50
PECO / 10 / 7.46 / 5 / 5.68
PSEG / 29 / 21.64 / 18 / 20.45
AECO / 10 / 7.46 / 6 / 6.82
PENELEC / 7 / 5.22 / 5 / 5.68
Technology
ST / 85 / 63.43 / 67 / 76.14
CC / 24 / 17.91 / 21 / 23.86
CT / 5 / 3.73
GT / 20 / 14.93
Fuel type
Coal / 55 / 41.04 / 44 / 50.00
Oil / 25 / 18.66 / 13 / 14.77
Gas / 54 / 40.30 / 31 / 35.23
Utility
Yes / 123 / 91.79 / 81 / 92.05
No / 11 / 8.21 / 7 / 7.95
Table 2. SAS Proc Mixed output of the specified model (Equation (2)) with random intercept and assuming autoregression correlation between observations
Covariance Parameter Estimates
Cov Parm Subject Estimate
Variance gid 0.01339
AR(1) gid 0
Residual 0.01269
Solution for Fixed Effects
Standard
Effect LOCATION Estimate Error DF t Value Pr > |t|
Intercept 10.0557 3.0227 72 3.33 0.0014
price -0.00003 0.000037 17E3 -0.76 0.4483
load 0.000257 0.000012 17E3 21.06 <.0001
ozone1 0.09787 0.001873 17E3 52.25 <.0001
CAPACITY 0.000020 0.000082 17E3 0.24 0.8071
nyear -0.00503 0.001520 17E3 -3.31 0.0009
oil1 0.05929 0.04415 17E3 1.34 0.1793
gas1 0.1422 0.04728 17E3 3.01 0.0026
tech_st1 -0.00923 0.07644 17E3 -0.12 0.9039
utility1 -0.1369 0.1275 17E3 -1.07 0.2831
LOCATION 1 -0.04764 0.07928 17E3 -0.60 0.5479
LOCATION 2 -0.04778 0.06505 17E3 -0.73 0.4626
LOCATION 3 0.1073 0.06891 17E3 1.56 0.1194
LOCATION 4 0.001963 0.07368 17E3 0.03 0.9787
LOCATION 5 0.006692 0.08095 17E3 0.08 0.9341
LOCATION 6 0.01065 0.07138 17E3 0.15 0.8814
LOCATION 7 -0.2078 0.08098 17E3 -2.57 0.0103
LOCATION 8 0.04526 0.06989 17E3 0.65 0.5173
LOCATION 9 -0.02575 0.1434 17E3 -0.18 0.8575
LOCATION 10 0 . . . .
The Mixed Procedure
Type 3 Tests of Fixed Effects
Num Den
Effect DF DF F Value Pr > F
price 1 17E3 0.57 0.4483
load 1 17E3 443.70 <.0001
ozone1 1 17E3 2730.54 <.0001
CAPACITY 1 17E3 0.06 0.8071
nyear 1 17E3 10.93 0.0009
oil1 1 17E3 1.80 0.1793
gas1 1 17E3 9.04 0.0026
tech_st1 1 17E3 0.01 0.9039
utility1 1 17E3 1.15 0.2831
LOCATION 9 17E3 3.23 0.0006
Table 2. STATA output of fixed-effects model and random-intercept model
. *** fixed effect*
Source | SS df MS Number of obs = 325
------+------F( 18, 306) = 16.42
Model | 8.03624335 18 .446457964 Prob > F = 0.0000
Residual | 8.32022108 306 .027190265 R-squared = 0.4913
------+------Adj R-squared = 0.4614
Total | 16.3564644 324 .050482915 Root MSE = .16489
------
nox | Coef. Std. Err. t P>|t| [95% Conf. Interval]