# Cooling Efficiency Algorithms: Chiller Performance and Temperature Differentials16 min read

In my previous two pieces I made recommendations for how to use environmental data collected in the data center to control temperature and airflow settings to maximize mechanical plant efficiency. I then began diving into the eco-system of that mechanical plant to explore the implications of those temperature and airflow settings, starting with cooling coil approach temperature and resultant cooling unit fan energy performance. As a dynamic eco-system, all the sub-systems in a data center interact with each other and therefore should not be envisioned or managed in isolation. Therefore, I presented an algorithm for measuring the impact of data center cooling unit approach temperature variations in terms that can be easily compared to results from other sub-systems and components, i.e., kW or annual kW/Hours. In today’s piece, I will explore variables affecting chiller performance and see how those relate to what we learned about cooling unit approach temperature.

In order to set the stage for how these various elements interact, I have developed a couple hypothetical case studies to exercise the algorithms. When I introduced this tool in the previous blog of this particular series, I wrote it as an Excel equation. In real life, as illustrated below, it is actually pretty straightforward.

If (SAT-EWT)<=4˚F, then A = 0.5” H_{2}O, if not, then

If (SAT-EWT)<=5˚F, then A = 0.45” H_{2}O, if not, then

If (SAT-EWT)<=6˚F, then A = 0.4” H_{2}O, if not, then

If (SAT-EWT)<=7˚F, then A = 0.35” H_{2}O, if not, then

If (SAT-EWT)<=8˚F, then A = 0.3” H_{2}O, if not, then

If (SAT-EWT)<=9˚F, then A = 0.28” H_{2}O, if not, then

Otherwise A = 0.25” H_{2}O

Where: SAT = Supply air temperature (from CRAH into the data center)

EWT = Entering water temperature (from chiller to CRAH coil)

X˚F = As noted from ASHRAE handbook, more precise values could come from equipment vendor

A = Pressure drop of air across CRAH coil

**Equation 1: Pressure Drop at Different Approach Temperatures**

Once we have established the pressure drop across the cooling coils, we can calculate for a value that can be dollarized with the following equation. This merely rolls up the relationship between pressure and fan energy (squared function) and our air handler fan motor baseline. Note that if there are different sizes of air handlers then this calculation should be run for each variation.

kW = (1+(A-ISPS)/TSP)^{2} (.746Hp) (AHUQ)

Where: kW = Total kW to operate CRAH fans at a specified approach temp

A = Air flow pressure drop across coils at an approach temperature

ISPS= CRAH internal static pressure specification

TSP = Total static pressure (ESP + ISP)

Hp = CRAH fan horse power rating, total of multiple fans

AHUQ= Quantity of air handlers of noted specification

**Equation 2: Fan Power as a Result of Pressure Drop**

In the original roll-out of the algorithm for cooling coils and approach temperatures, I asserted that the larger the difference was between the water temperature entering the cooling unit coils versus the air temperature entering the data center off those coils, the lower the operating cost would be for the cooling units. A couple hypothetical case study examples will illustrate that point as well as providing a baseline against which the meaningfulness of today’s chiller efficiency algorithm can be assessed. For the sake of this exercise, let us assume a one Megawatt (1MW) IT load with eight 50 ton air handlers providing us N+1 cooling redundancy. These units are delivering 23,000 CFM and their cooling capacity is based on a 22˚F ΔT between return air and supply air. I should note here the importance of good airflow management in that if bypass airflow was reducing that ΔT to 18˚F we would need nine cooling units to cool the same load with the same level of redundancy and if that ΔT were only 15˚F we would need ten CRAH units. It seems to me that buying decisions for blanking panels and grommets for sealing all variety of holes make a little more sense than purchasing and operating extra cooling units. We will operate this data center with a maximum 80˚F server inlet temperature and, unless otherwise noted, we will assume excellent airflow management exemplified by a 2˚F ΔT between supply air temperature and maximum server inlet temperature.

For this example data center, I will compare the effects of a 6˚F approach temperature to the effects of a 10˚F approach temperature. Per Equation 1 above, our resultant pressure drops will be 0.4” H_{2}O and 0.25” H_{2}O, respectively. Applying those pressure drop values to Equation 2 produces a fan power estimate for the two different scenarios below in Calculation 1.

kW_{A} = (1+(0.4”-0.3”)÷0.6”)^{2}(.746x16.2x8)

kW_{A} = (1.167^{2})(96.8)

kW_{A} = 131.8

kW_{B} = (1+(0.25-0.3”)÷0.6”)^{2}(.746x16.2x8)

kW_{B} = (0.917^{2})(96.8)

kW_{B} = 81.3

**Calculation 1: CRAH Fan Power at Two Different Pressure Drops**

Remember, my cooling unit vendor may already have all this figured out, in which case I only need to load his values into my spreadsheet. Regardless, we will still need some information from the vendor at the very least on the internal static pressure against which the CRAH fans are operating (ISP). Their technical documentation will typically give us the external static pressure (ESP) condition for which all the performance specifications apply, so I merely need to add that number to the ISP to determine the total static pressure (TSP) for the factors of Equation 2. If I am in a planning exercise for a new design, then I may want to have 8760 iterations of Calculation 1, one for each hour of environmental bin data. While that data was not a part of this particular calculation, it will be consequential to subsequent algorithms so my spreadsheet should be organized accordingly. If, on the other hand, I am using these algorithms as part of an operational management tool, then I should have as many lines as required by the granularity of my management vision. For example, if I want to ping all my environmental sensors every ten minutes, then I might want to have 52,560 lines of data per year. I will be looking at bin data in subsequent pieces of this series, but today, for the sake of showing the relationship between approach temperature and chiller efficiency, I will just annualize my initial findings. Therefore, with a 6˚F difference between coil inlet water temperature and coil exhaust air temperature, my CRAH fans are burning 1,155,000 kW/hours; whereas with a 10˚F approach temperature we are consuming 712,500 kW/hours. As predicted, our higher approach temperature nets us a savings of 440,000 kW/hours.

Obviously we want our approach temperature to be as high as possible, right? Well, not so fast. First, just to keep things simple for the start of this series, my calculations are based on our CRAH fans operating at capacity. In reality, since we are operating at N+1 on our cooling units, we may be only running these eight CRAH fans at 87.5%, which means my fan affinity law energy use would only be 70% of the rated horse power value (.875^{3}). While such a reduction theoretically affects both scenarios resulting in no change to the relative difference between the two sets of annual energy use, the base number would be significantly lower. Thus meaning that the gross difference of 440,000 kW/Hours of energy use will be lower in reality – significantly lower after we factor in some of the additional variables in later pieces of this series. For the time being, I would add just one additional caveat: depending on your equipment, approach temperature manipulation may be a better planning design tool than an operational management tool. While we were able to do some approach temperature manipulations in the CPI data center lab by varying water flow volume, in some cases coil size is going to be your most significant variable. Practically speaking, coil size changes are going to be more feasible on a blueprint than on an installed cooling unit.

As I am all-to-fond of saying, these data centers are living, breathing eco-systems with an intricate web of inter-relationships between all the various elements. The mechanical elements as I am discussing in this seven-part series, as well as the IT and networking elements as I have discussed previously. As for this discussion, one of the balancing factors to CRAH approach temperature is chiller plant efficiency. There are a variety of variables affecting chiller efficiency and I will eventually be covering the most important ones as we move through this series, but today I will limit myself to chiller leaving water temperature. In simple terms, the higher the leaving water temperature the lower the cost of operating chillers. Based on an example line graph from the ASHRAE manual, ** Best Practices for Datacom Facility Energy Efficiency**, I am going to use 2.4% per degree as the effect on kW per ton for operating a centrifugal chiller in Equation 3 below. I have heard and read everything from 1% to 4% so there are a couple different ways to make this calculation a little more precise. The ASHRAE chart (Figure 3.5a, Sample Chiller Efficiency as a Function of Leaving Chilled-Water Temperature, units of kW/ton with all other parameters held essentially constant) indicates a higher percentage difference at lower temperatures and a lower percentage difference at higher temperatures, which makes sense with a more or less diagonal slope: 2.4% equated to a median value on that chart. The equation could be more granular by breaking it into smaller sub-groups. Even better, the chiller vendor may have the data already in an Excel format that could be easily integrated into these inter-dependent algorithms.

CP = (1-(LWT-45).024) (BPxCT)

Where: CP = Chiller plant power

LWT= Chiller leaving water temperature ˚F

BP = Base power (kW per ton @ 45˚F LWT)

CT = Chiller tons

**Equation 3: Chiller Plant Energy as a Result of Leaving Water Temperature**

The first part of Equation 3 merely calculates the percent change in energy use based on the difference between the leaving water temperature and some baseline. I picked 45˚F as my baseline as that has historically been a pretty standard operating point for chilled water loop temperature and most vendors specify performance for 7˚C, which is close enough for me. The second part of the equation is merely establishing the baseline from which the variation is being calculated. As noted above, the .024 efficiency factor per degree change in LWT can be fine-tuned by the user.

Calculation 2 shows the comparison of the same two scenarios I explored in the review of differences in CRAH approach temperatures. The impact here is that the lower approach temperature allows us to deliver a higher supply temperature and the algorithms give us the ability to assess the trade-offs between the two competing principles.

CP_{A} = (1-(68-45).024(.9 X 800)

CP_{A} = 1-(23 X .024) X 720

CP_{A} = .448 X 720

CP_{A} = 322.6 kW

CP_{B} = (1-(64-45).024(.9 X 800)

CP_{B} = 1-(19 X .024) X 720

CP_{B} = .544 X 720

CP_{B} = 392.8 kW

**Calculation 2: Example Chiller Energy at Different LWT**

With a 6˚F approach temperature, I am able to cool the data center with 68˚F chilled water; whereas with a 10˚F approach temperature, I am cooling the data center with 64˚F chilled water. As with the coil pressure drop calculation, if I am planning a new data center I will have 8760 lines of this equation to correspond to my bin data, which will become important on subsequent algorithms. On the other hand, if these algorithms are being built for operational management, then the level of temporal granularity is a management decision. For my purposes here to just make a first pass rough assessment between the competing values for coil pressure drop versus chiller efficiency, I annualize these results to 2,861,000 kW/hours to operate the chiller with 6˚F CRAH coil approach temperature and 3,441,000 kW/hours with a 10˚F approach temperature, resulting in a 580,000 kW/hour savings with the higher LWT resulting from the lower approach temperature.

The higher approach temperature netted a 440,000 kW/hour savings versus the lower approach temperature for this sample 1MW data center case study. Whereas, the lower approach temperature netted a 580,000 kW hour savings from baseline, or 140,000 kW/hours less than the benefits of operating with a higher approach temperature across CRAH cooling coils. Contrary to what may appear most obvious here, the conclusion is not necessarily that I want to minimize my CRAH coil approach temperature. We are only through part three of seven parts, plus we have not adequately explored the economies that come with running partial load redundancy on CRAHs and chillers. Thus the conclusion so far is merely that everything is not always what it seems and, most importantly, we are three-sevenths of the way toward having an Excel tool for either planning or managing a data center space.

#### Ian Seaton

Data Center Consultant

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