MEMORANDUM

DATE: December 17, 2012 

SUBJECT: Establishing an Operating Limit for PM CPMS 

FROM: Steffan Johnson 

 Measurement Policy Group, SPPD 

TO: Boiler MACT Docket 

 Docket EPA-HQ-OAR-2002-0058

A. INTRODUCTION 

The EPA received many comments about the impracticality of the technique specified for 

establishing operating limits for the particulate matter (PM) continuous parameter monitoring 

systems (CPMS) in the May 2012 proposed amendments to Air Toxics Standards and New 

Source Performance Standards for Portland Cement Manufacturing. Most of the commenters 

focused on the impact on sources with very low PM emissions who, under the proposed 

amendments, may be required to conduct multiple retests due to the CPMS response to 

fluctuation of the in-stack PM characteristics. In other words, the best performing sources were 

likely to be triggering the largest number of operating limit exceedances simply because of the 

tight operating limits imposed by their low emissions measurements. A few of the commenters 

further pointed out that this is punitive on the most well-controlled sources and some offered 

“scaling” strategies for establishing the PM CPMS operating limit that they felt would alleviate 

the problem. Other commenters pointed out that under the proposed approach to establishing the 

operating limit it would be possible for a source to tie the operating limit to a test run that 

showed non-compliance with the PM emission limit. We do not wish to promulgate a regulation 

that is punitive to well-performing sources, nor do we want sources to set operating limits 

corresponding to an emissions level above the standard. Therefore, we thoroughly analyzed the 

comments and scaling strategies included to determine a more workable approach for setting the 

PM CPMS operating limit. This memorandum presents the findings of our analysis and provides 

guidance and calculations for applying this procedure in Portland cement and potentially other 

rulemakings. 

B. DISCUSSION 

The initial focus of our analysis was to more directly connect the PM CPMS operating limit to 

the determination of compliance, by requiring it to correspond to the average of three PM test 

runs rather than the single highest test run during the performance test. This would alleviate the 

potential for setting an operating limit that corresponds to an emissions result higher than the 

emission standard. 

The term “scaling” as used in this memo represents the determination of an instrument response 

slope based on the average PM CPMS output value (in milliamps) corresponding to a 3-run EPA 
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Method 5 PM performance test and the instrument output at zero PM concentration. Once the 

slope is established, a PM CPMS output theoretically equivalent to a higher PM concentration 

value may be determined, where an operating limit may be established. A significant 

complication in consideration of scaling options is that PM CPMS are not directly calibrated 

instruments, with known responses to a series of calibration test runs across a wide measurement 

range, as is a PM continuous emission monitoring system (CEMS). For PM CPMS, the only 

known relationship between the instrument signal and the in-stack PM concentration is the 

average value established during manual compliance testing using EPA Method 5. The scaling 

approach presumes a linear relationship between the instrument and PM concentration, and this 

is done for two reasons. Firstly, a linear scaling approach is simple for source operators to use in 

calculating operating limits and is therefore simpler to comply with. Secondly, where a number 

of PM instruments do have linear responses to PM concentrations, we acknowledge that this 

approach is likely to develop very accurate results. However, this presents difficulty in scaling 

measured values that lie close to the emission limit, as the linearity of the instrument response is 

not demonstrated. 

This concept is contrary to using a calibrated PM CEMS for quantitative determination of a 

compliance value but holds for qualitative determinations of in-stack PM concentrations. 

We note that a PM CPMS instrument used in this manner must have a sufficient measurement 

scale to cover not only very low PM concentrations but also values well above the actual 

emission limit, as the operating limit is a long term average and brief periods of high emissions 

must be included in such averages. 

It is also important to understand the differing instrument responses to varying PM 

concentrations, as may be found by examining the cross section of technologies employed by 

various instrument manufacturers. PM CPMS instrument output generally conforms to one of 

two basic patterns, linear non linear (exponential). Data showing these two correlations are 

displayed below: 
3 

The above graphic shows a PM CEMS calibration trial using PS 11 and illustrates a linear 

relationship between PM CPMS instrument response and in stack PM concentration. While 

several data points are required to establish this relationship, we note that if linearity is assumed 

with such an instrument, PM CPMS instrument output at any PM concentration may be closely 

predicted based on the known location of zero and another non-zero data point. 
4 

This graphic, again using data from a PS 11 certification of a PM CEMS instrument, illustrates 

an exponential or non-linear relationship between PM CPMS instrument response and in stack 

PM concentration. In this example it is problematic to assume a linear relationship and try to 

predict the PM CPMS instrument response at any other point when only given a zero and single 

non-zero data point. Several data points are needed to establish the curve and relate the 

instrument signal to actual PM concentrations in the stack. 

Both linear and exponential relationships are acceptable when correlating PM CEMS with PS 

11; as the number of data points required (15) is sufficient to characterize the instrument 

response curve. With a PM CPMS installation, we do not have the luxury of data with which to 

establish such relationships. It is important to note that not only is it difficult to accurately 

calculate a PM concentration value from just two data points (1 at zero and 1 non zero) by 

assuming a linear relationship, but it is also not possible to determine the curve and thereby 

calculate an accurate estimate. Instruments with either exponential or non-linear types of signal 

output correlation provide sufficient sensitivity to gauge small PM concentration changes in the 

stack; they just have different ways of presenting what they detect. As we do not know what 

instrumentation will be employed at any given facility we recognize that we must be sufficiently 

conservative in our approach of leveraging a single, non zero data point to demonstrate 

compliance with an operating limit. 

We reviewed the scaling alternatives provided by commenters as well as several other 
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alternatives developed internally, in an attempt to find a workable solution to avoid triggering the 

most operating limit exceedances on the cleanest sources. We were looking for an approach to 

“scaling” that leveraged an inverse relationship between PM concentration and the operating 

limit whereby a source with very low PM concentrations would be provided greater operational 

flexibility than a source with higher PM concentrations and those closest to the PM emission 

limit would be provided the least amount of flexibility with respect to the operating limit. This 

approach was undertaken in an attempt to provide the greatest operational flexibility to the 

cleanest sources. We were also aware of potential issues with non linear instrument responses 

and wanted to investigate options that would provide this flexibility without putting the emission 

limit at risk in our effort to try and make the operating limit more flexible for clean sources. 

With scaling, we are concerned primarily about uncertainty in values that lie above and 

below the instrument response noted during the performance test. Note the above illustration 

(p. 3) displaying a non linear instrument response. Errors made in calculating values higher 

than the measured emissions value, where we assume a linear relationship, are always going 

to underestimate the actual PM concentration when such a calculation is conducted. 

Likewise, calculated values below the measured emissions value on the same graph would be 

overestimated. While the far right portion of the graph represents a great deal of risk in 

estimating an emission value, errors due to the non linear relationship are mitigated when we 

focus on the left half of the graph; an area where the relationship of signal to PM 

concentration is much closer to a linear relationship. We recognize that non linear 

instruments provide increased uncertainty in estimating PM concentrations above the 

performance test data point and in our best professional judgement have determined that the 

75 percent scaling cap is appropriate for protecting the emission standard in this regard. 

The options considered were: 

1. Establish a linear scale, determine the emission limit on that scale, and allow sources to 

operate below the emission limit on a 30-day rolling average (as suggested by 

Commenter 0261 from the Portland cement rule Response to Comment Document); 

2. Establish a linear scale and set the source operating limit at a point where that scale 

intersects with the PM CPMS average plus some percentage (x) of the “unused” emission 

limit where x is equal to the percent of the emission limit not consumed by source 

emissions as established by a compliance test (an in house EPA suggested approach); 

3. Establish a linear scale and set the source operating limit at a point equal to the average 

PM CPMS value measured during the compliance test plus one-half of the remaining 

scale up to the emission limit (an in house EPA suggested approach); 

4. Establish a linear scale and set the source operating limit at a point equal to the average 

PM CPMS value measured during the compliance test plus one-third of the remaining 

scale up to the emission limit (an in house EPA suggested approach); 

5. Use Option 3, but also roll back the operating limit a distance equivalent to one standard 

deviation of the three PM CPMS average values recorded during the three performance 

tests(as suggested by Commenter 0261 from the Portland cement rule Response to 

Comment Document); and 
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6. Establish a linear scale and set the source operating limit at 75 percent of the emission 

limit if a source showed compliance below that level, and set the operating limit at the 

average PM CPMS values for sources demonstrating compliance above that limit (an in 

house EPA suggested approach). 

 

After a review of these six options we noted the following: 

Option 1 placed a great deal of confidence in the presumption that the instrument 

response to in-stack PM concentrations are linear beyond the average value determined 

during the performance test. This approach presumes PM CEMS capabilities from an 

uncalibrated instrument and ignores potential errors from non linear instruments. 

Option 2 provided for a great deal of flexibility for the lowest emitting sources but also 

resulted in operating limits for these sources that were significantly higher than some 

sources with higher PM concentrations. This approach also ignored potential errors 

introduced by non linear instrument response. 

Options 3 and 4 provided for flexibility at low concentrations, but also provided 

flexibility even very close to the PM limit which did not seem appropriately protective of 

the emission standard when a non linear instrument may be in use. For example, this 

approach would “bump up” operating limits that were set where the compliance 

demonstration showed the source operating any small amount below the emissions 

standard. We do not feel it is appropriate to measure PM emissions of .0698 lb/ton 

clinker and adjust the operating limit upward to further crowd the emission limit of 0.07 

lb/ton clinker. 

Option 5 addressed the issue noted with Options 3 and 4, but added a level of complexity 

that seemed to confuse rather than simplify the process. Subtracting one standard 

deviation moves toward being more protective of the emission standard, but is focused at 

addressing test variability and not instrument linearity. 

Option 6 provided flexibility for low emitting and well-operated sources, and was 

determined to be a reasonable compromise of flexibility and protection of the emission 

standard. Seventy-five percent of the emission limit is an already-established threshold in 

the Standards of Performance for New Stationary Sources and Emission Guidelines for 

Existing Sources: Commercial and Industrial Solid Waste Incineration Unit (76 FR 

15757) to determine the frequency of subsequent compliance testing. In that rule, owners 

or operators of sources were able to reduce their performance test frequency when 

emissions were equivalent with or below 75 percent of the limits. Otherwise, 

performance testing was to occur at the normal frequency prescribed in the rule. We 

believe this threshold can be used in conjunction within a PM CPMS scaling factor, as 

results above 75 percent of the equivalent emissions limit would be ineligible for scaling 

factor use and could lead to increased performance testing, while results equivalent with 

or below 75 percent of the equivalent emissions limit would be eligible for scaling factor 
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use and provide greater operational flexibility for sources demonstrating compliance at 

lower emission rates. 

Here is an overview of what scaling looks like considering linear and non-linear signals: 

This example shows a linear signal output (blue line) and two corresponding non linear 

signals, one showing decreasing PM concentrations with increased milliamp output 

(green line) and the other showing rapidly increasing PM concentrations as milliamp 

signal increases (red line). Toward the left side of the graph are two vertical lines, the 

left most represents 75 percent of the emission limit, with the vertical line slightly right of 

that representing the emission limit. We are primarily interested in what is happening to 

the left of this emission limit line, though not entirely. 

Of primary interest is just how a scaling approach that assumes a linear instrument 

response compares both to the emission limit and to predicted PM concentrations from 

the instrument. 

Below is a close up of the region of primary interest: 
8 

In this image you see the linear instrument response (straight blue line) through the middle of 

the graph. Each line is marked with the same data points, indicating theoretical 

concentrations of PM in the flue gas. Data points on the x axis start at zero (represented by 4 

milliamps on the instrument) then 0.025, 0.04, 0.0525, 0.06, 0.07, and 0.08. In the Portland 

cement rule, these values represent lb/ton clinker; and you will note the y-axis scale 

represents the instrument signal output in milliamps. With each instrument slope we have 

drawn an assumed linearity line from zero through a theoretical emission test result, in this 

instance that is 0.04. A scaling approach would follow this line to its intersection with 

75percent of the emission limit and establish the corresponding milliamp output as the 

operating limit for that source. 

Of note is the illustration of how close these lines are to the “true linear” when we make use 

of them on the low end of the instrument scale. The further toward the left from the emission 

limit line we move our scaling mark the tighter these lines become to “true linear”. 

For the instrument represented by the green line its signal is digressing from linear but in a 

direction that will trigger re-testing via scaling more frequently than its red-line counterpart. 

A source using this instrument with test emissions of 0.04 will hit the 75 percent operating 

limit at approximately 0.05. For the instrument represented by the green line we see that its 

signal is digressing from linear in the opposite direction; PM emissions per milliamp are 

increasing more rapidly. An instrument with a non linear output such as this is the reason we 

need to be cautious in our approach. In the illustration above, a source using this instrument 

with performance test PM emissions of 0.04 will trigger the 75 percent operating limit retest 

requirement when actual stack emissions are greater than 75 percent of the emissions limit. 
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In the example above, this signal will trigger a retest when the average source emissions are 

at about 0.0625, or 89 percent of the emission limit. 

When we review these examples we must also recognize that there are other parameters in 

stack emissions that fluctuate and will have an impact on the instrument output. Light 

scattering PM CPMS are known to vary their instrument response with respect to 

characteristics of the PM itself. 

In light of such non linear instrument outputs, and the potential for varying signal based on 

PM characteristics, we cannot allow scaling to approach 100% of the emission limit. 

Furthermore, we feel it prudent to allow room beyond the scaling for an instrument to vary in 

its response, beyond any signal linearity issue. 

While the example above displays very marked divergence from linearity on both sides, we 

recognize that we do not have sufficient data to characterize the universe of PM CPMS 

technology and thus, must exercise cautious judgement in this regard. As such, it is our best 

technological and engineering judgement that scaling of PM CPMS signals is appropriate to 

75 percent of the emission limit, and no further. While we might work to justify being even 

more conservative, we also recognize that the affected sources must have already 

demonstrated compliance well under the emissions standard to qualify for scaling using this 

approach. 

One outcome of this assessment is that we find this approach to be an appropriate technique to 

establish operating limits for parametric monitors where the monitor is measuring the pollutant 

of interest qualitatively. This approach is not appropriate where a parametric monitor (i.e., pH 

meter, pressure monitor or thermocouple) represents an operating condition of a control device 

(i.e., pH, pressure drop, combustion temperature) rather than an actual qualitative measurement 

of the pollutant of interest. 

A second outcome of this assessment is its versatility across production-based standards (e.g., the 

Portland cement rule’s PM/ton-clinker limit and the MATS rule’s PM/MWh limit). One need 

only ensure that the appropriate units are used when developing equations and conducting 

calculations. 

A third outcome is that we find with the Portland cement source category, which includes many 

sources with emission levels at or near the method detection levels (MDLs) for PM, 

measurement imprecision is a significant factor that should be ameliorated to the extent possible 

when establishing an operating limit. Measurement imprecision is typically highest for values 

measured below or near a method’s detection level and decreases as values increase above the 

method detection level. When establishing such a curve based on a single compliance test series, 

we recognize longer Method 5 test times and/or duplicate Method 5I tests as a best practice; 

better data will result in a better operating limit. With this in mind, we recommend source 

operators and testers to consider extended test times and the use of Method 5I, as appropriate, to 

adequately quantify in-stack PM concentration and more accurately establish a PM CPMS output 

relationship to the compliance test results. 
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C. DETERMINING AN OPERATING LIMIT BOTH FLEXIBLE AND PROTECTIVE 

After a review of a number of PM CPMS signal scaling approaches, we arrived at the sixth 

option above, which is a hybrid approach to allowing scaling of the PM CPMS measurements 

upward to a point. We find it reasonable to allow flexibility to sources who have demonstrated 

compliance below 75 percent of the emission limit while holding sources whose compliance test 

results were closer to the emission limit to an operating limit with less flexibility and tied directly 

to their PM compliance demonstration. 

To establish an operating limit using a PM CPMS a source must conduct a Method 5 or Method 

5I performance test – consisting of at least 3 runs – annually and establish the relationship 

between the average milliamp output from the PM CPMS and the average of the PM test runs. 

Sources with performance tests that show their average PM emissions rate at or below 75 percent 

of the standard have the flexibility to establish a correlation curve for their CPMS. This 

correlation curve is based on two data points: the output of the PM CMPS during the 

performance tests and the corresponding PM emissions rates, and the PM CPMS instrument 

value during a period of no PM emissions. 

The scale used to determine the operating limit value at 75 percent of the emission limit is 

developed using two pieces of information: the PM CPMS output at zero and the average PM 

CPMS response during the performance test. To simplify the process, we specify a commonly 

used instrumental output, 4 - 20 milliamps, as the basis for all PM CPMS measurements. To 

establish the low end of the scale we require an accurate value that represents how the instrument 

reads zero PM concentration. Theoretically, the zero PM concentration would be represented by 

a value near 4 milliamps, but not necessarily 4.0, so we leverage the steps presented in 

performance specification (PS) 11, section 8.6 (5) to direct the source owner/operator in 

establishing a zero value that is specific to their PM CPMS, preferably in its installed location. 

With the PM CPMS output value that represents zero, and the PM CPMS average values 

recorded during the compliance test, the scale is delineated in units of the emission standard over 

the instrument output, e.g., for the Portland cement rule, these units would be in terms of lb PM 

per ton clinker PER milliamp. One could determine this value for the Portland cement rule using 

the following formula: 

  X z

Y

 

1

1 R

Where: 

R = the relative lb/ton-clinker per milliamp for a PM CPMS, 

Y1 = the three run average lb/ton-clinker PM concentration from a compliance test, 

X1 = the three run average milliamp output from the PM CPMS, and 

z = the milliamp equivalent of a PM CPMS instrument at zero. 

Note: Because of the 4 - 20 milliamp scale we need to subtract the value representing 

zero from the average milliamp output so that we may determine the relationship between 

PM concentration and the actual milliamp response above zero. The value representing 
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zero is factored back in once this relationship is established (see equation below). 

Once the level of PM concentration relating to a milliamp of signal output from the PM CPMS is 

established, we may determine where on a slope of milliamp output signals the PM concentration 

representing 75 percent of the emission limit intersects. This represents the operating limit and is 

determined by the formula: 

ሻܮሺ0.75൅ ݖൌܧ

ܴ

Where, continuing with our use of the Portland cement rule as an example: 

E = the operating limit for the PM CPMS, in milliamps. 

L = the source emission limit expressed in lb/ton clinker, 

z = the instrument zero in milliamps, determined from (1)(i), and 

R = the relative lb/ton-clinker per milliamp for the PM CPMS, from above. 

Note: With other rulemaking applications the units above that are Portland cement specific 

(lb/ton-clinker) would need to be replaced with appropriate units of production (i.e. lb/Gw Hr, 

lb/Mmbtu, etc.) depending on the units of compliance determination with the rule. 

While this process results in a good deal of flexibility for sources well below 75 percent of the 

emission limit, we recognize the importance of being protective of the emission limit. Not all PM 

CPMS instruments are expected to have a linear output in regards to milliamp signal versus PM 

concentration, we recommend that sources demonstrating compliance at or above 75 percent of 

emission limit be held to an operating limit representing their average PM CPMS output during 

the performance testing. 

It is important to note that emission testing is a snapshot and not an indicator of long term 

emission profiles at a source; so we recognize that the relationship established between PM 

CPMS output and in-stack PM concentration may be predicated on data that is subject to other 

operational and seasonable variability which may present operational challenges to maintaining 

operations within the established operating limit. Therefore we see the need to provide an 

allowance for a source to conduct another compliance test and reset this relationship to the most 

current data set if the source is unable to meet its operating limit. Sources who show compliance 

in the range just below, to anywhere above, the 75 percent level are most likely to find 

themselves facing this mode of operation (i.e., more frequent retesting to reset the operating 

limit). Finally, it bears repeating that we believe allowing a PM CPMS scaling function in 

excess of 75 percent of the emission limit is not an appropriate approach for compliance 

assurance through long term operating limit averaging.