Creating Performance Curves for VRF System

8/22/2019 Creating Performance Curves for VRF System

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4.2.3 Creating Performance Curves for VRF System

In order to simulate the performance of AC System Energy plus need the performance

curves of the system. The performance of a VRF AC system is based on multiple

performance characteristics.

The cooling model inputs for a VRF AC system are:

Rated Total Cooling Capacity 5.2 kW

Rated Cooling COP 3.25

Minimum Outdoor Temperature inCooling Mode

-5 OC

Maximum Outdoor Temperature inCooling Mode

46 OC

Cooling Capacity Ratio ModifierFunction of Low Temperature Curve

NameDaikinCAPFTLow

Cooling Capacity Ratio BoundaryCurve Name

VRFBoundary

Cooling Capacity Ratio ModifierFunction of High Temperature Curve

NameDaikinCAPFTHi

Cooling Energy Input Ratio ModifierFunction of Low TemperatureCurveName

DaikinEIRFTLow

Cooling Energy Input Ratio BoundaryCurve Name

VRFBoundary

Cooling Energy Input Ratio ModifierFunction of High TemperatureCurveName

DakinEIRFTHi

Cooling Energy Input Ratio ModifierFunction of Low Part-Load RatioCurveName

CoolingPLR

Cooling Part-Load FractionCorrelation Curve Name

PLRFraction


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Full-load performance data defines the variations of capacity and power when outdoor

or indoor conditions changes. Part-load performance identifies how the capacity and

power change when variable compressor changes speed.

Table 9Capacity Table of Inverter based VRF AC

AFR 16.8

BF 0.29

INDOOREWB C 14 16 18 19 22 24

EDB C 20 22 25 27 30 32

OUTDOORTEMPERATURE

(CDB)

20

TC 5.33 5.57 5.81 5.93 6.29 6.53

SHC 3.84 3.77 3.93 4.13 3.97 3.86

PI 1.23 1.23 1.24 1.25 1.26 1.26

25

TC 5.09 5.32 5.56 5.68 6.04 6.28

SHC 3.71 3.65 3.82 4.02 3.88 3.78

PI 1.35 1.35 1.36 1.36 1.37 1.38

30

TC 4.84 5.08 5.32 5.44 5.8 6.04

SHC 3.59 3.54 3.71 3.92 3.79 3.69

PI 1.46 1.47 1.48 1.48 1.49 1.5

32

TC 4.75 4.99 5.23 5.35 5.7 5.94

SHC 3.54 3.49 3.67 3.87 3.75 3.66

PI 1.51 1.52 1.53 1.53 1.54 1.55

35

TC 4.6 4.84 5.08 5.2 5.56 5.8

SHC 3.47 3.42 3.6 3.81 3.7 3.61

PI 1.58 1.59 1.6 1.6 1.61 1.62

40

TC 4.36 4.6 4.84 4.96 5.32 5.56SHC 3.35 3.31 3.5 3.71 3.61 3.53

PI 1.7 1.71 1.71 1.72 1.73 1.74


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Table 9 shows typical information provided by manufacturer of the system which is

used in this study, using tabular representations. From this information, full-load

capacity and power performance curves can be developed.

The data here is presented as an absolute value Tabular data with rated condition

highlighted, as shown in Table 9 (i.e., 5.2 kW rated total capacity, 3.81 rated Sensible

Heat capacity and 1.6 kW rated power).

4.2.3.1 Cooling Performance Curves

The operating capacity of the VRF system is calculated based on the rated cooling

capacity and the actual operating conditions. The operating conditions describing

cooling performance are outdoor dry-bulb (DB) temperature entering the condenser

and average indoor wet-bulb (IWB) temperature entering the active zone terminal

units. The first step in defining cooling performance is plotting the manufacturers

data from Table 9 to represent the relation of cooling capacity with Indoor WBT and

outdoor DBT.

Figure 21 Cooling Capacity Ratio as a Function of Outdoor Drybulb and Indoor WetbulbTemperature

It is evident from the plotted manufacturers data in Figure 21 that the system

performance behavior changes at 30 0C.

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30

20 25 30 32 35 40

CoolingCapacityRat

io

Outdoor Drybulb Temperature

14

16

18

19

22

24

Indoor

Wetbulb


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We can therefore conclude that the boundary curve equation for our system can be

defined as =30 and the corresponding energy Plus class object definition is

shown in theFigure 22.

Figure 22Input values of Boundary curve object

. A typical cooling capacity curve equation is given below

= +, +,+() +() ++,()

Where:

CAPFT= heat pump Cooling Capacity Ratio Modifier

TWB,i= wet-bulb temperature of the air entering the cooling coil.

a f = equation coefficients for Cooling Capacity Ratio Modifier

TC= Temperature of the air entering the condenser

The equation for the simulation model is generated by following algorithm defined

below.

1) Sorting the manufacturers' data in the tabular form of CAPFT, Indoor Wet

Bulb, and Outdoor Dry Bulb.

2) Prepare the data and compute the values for (WB2), (DB2) and (WB*DB)

3) The equation is generated using a regression analysis tool called Eureqa

Formulize developed by Nutonian which is a scientific data mining software

package that searches for mathematical patterns hidden in a data set.


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Since the cooling capacity of the system cannot be defined by single curve, two

different equations have been generated for high and low outdoor dry bulb

temperature

(i)Cooling Capacity Ratio Modifier Function of LowTemperatures

Select the data from Table 9 that represent the cooling capacity ratio at low outdoor

temperatures (i.e., data to the left of and including the boundary curve inFigure 21)

and organize the indoor and outdoor temperatures according to the fundamental form

of the CAPFT equation. The tabular data given by the manufacturer is in the form

capacity(kW), in order to obtain the capacity curves the data must be converted to a

cooling capacity ratio term (i.e., the data must be normalized).

Table 10Regression Analysis for Creating Cooling Performance curve

CAPFT IWB IWB^2 DB DB^2 IWB*DB Predicted

CAPFT

1.025 14 196 20 400 280 1.02517

0.978846 14 196 25 625 350 0.977386

0.930769 14 196 30 900 420 0.930878

1.071154 16 256 20 400 320 1.07123

1.023077 16 256 25 625 400 1.02345

0.976923 16 256 30 900 480 0.976942

1.117308 18 324 20 400 360 1.1173

1.069231 18 324 25 625 450 1.06951

1.023077 18 324 30 900 540 1.02301

1.140385 19 361 20 400 380 1.14033

1.092308 19 361 25 625 475 1.09255

1.046154 19 361 30 900 570 1.04604

1.209615 22 484 20 400 440 1.20942

1.161538 22 484 25 625 550 1.161641.115385 22 484 30 900 660 1.11513

1.255769 24 576 20 400 480 1.25549

1.207692 24 576 25 625 600 1.2077

1.161538 24 576 30 900 720 1.1612


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To do so we use the rated conditions as the reference point and Divide all capacity

data by the Rated Total Cooling Capacity to yield cooling capacity ratio. Table below

shows a typical spreadsheet layout of this data.

= 0.906616945+0.02303191162 +2.552047779

( 2) 0.01070512808

Table 11 Statistical data of Generated Cooling Performance Equation

R^2 Goodness of Fit 0.999

Correlation Coefficient 0.999

Maximum Error 0.001

Mean Squared Error 1.64E-07

Mean Absolute Error 2.44 E-04

(ii)Cooling Capacity Ratio Modifier Function of HighTemperatures

Similar analysis is done to create Cooling Capacity Ratio Modifier Function of High

Temperatures and following equation is obtained

=0.885+ 0.0231 IWB 0.009425 DB



Maximum Error 0.001


Mean Absolute Error 0.000272

4.2.3.2 Cooling Energy Input Ratio Modifier

The method used to create performance curve coefficients for cooling energy input

ratio modifier function of temperatures is identical to the method used for cooling

capacity ratio. Table 12 below shows the power input ratio data extracted from

capacity tables provide by manufacturer. This data is normalized to the rated power

input in order to create the performance curves.


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Table 12 Input Power Ratio Normalized to Rated Power

IWB 14 16 18 19 22 24

ODB Power ratio

20 0.768750 0.76875 0.775 0.78125 0.7875 0.7875

25 0.843750 0.84375 0.85 0.85 0.85625 0.8625

30 0.912500 0.91875 0.925 0.925 0.93125 0.9375

32 0.943750 0.95 0.95625 0.95625 0.9625 0.96875

35 0.987500 0.99375 1 1 1.00625 1.0125

40 1.062500 1.06875 1.06875 1.075 1.08125 1.0875

Figure 23 Manufacturer's Data of Cooling Energy Input Ratio

0.76

0.86

0.96

1.06

20 25 30 32 35 40

PowerInputRatio

Outdoor Dry Bulb Temperature

14

16

18

19

22

24

IWB


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It is evident from the cooling energy input data plotFigure 23 that performance of the

system changes at the outdoor temperature of 30 OC Therefore same boundary curve

from cooling capacity curve is used The following equations are obtained from the

analysis of manufacturers performance data.

=0.4802+0.01317 +5.854 +3.169



Maximum Error 0.003891


Mean Absolute Error 0.001406

= = 0.4355+ 0.01484 + 0.002364



Maximum Error 0.003136


Creating Performance Curves for VRF System

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