Virtual Power Consumption and Cooling Capacity Virtual ......Cost function to estimate condenser...

Virtual Power Consumption and Cooling Capacity Virtual Sensors for

Rooftop Units

Howard Cheung, James E. Braun

R-16 Automated Fault Detection and Diagnostics

Agenda

Introduction

Methodology to develop virtual sensor

Uncertainty calculation of virtual sensors

Cost analysis

2International Refrigeration and Air Conditioning Conference at PurdueJuly 14-17, 2014

Introduction

Real-time power consumption and cooling capacity of rooftop units (RTU) monitoring is important for energy-efficient building operation

Direct measurement is costly» Hot-wire anemometer to measure air

volumetric flow rate: $1600/sensor

Use other measurement to infer the variables


Virtual sensor

Vision

Virtual sensor for cost reduction» Training virtual sensor with measurement from two types of

sensors» Skip expensive measurement such as capacity measurement


Types of sensor

Temporary Permanent

Cost High Low

Application • Installed temporarily for 2 to 3 weeks

• Removed and reused at other buildings to reduce cost

• Provide information for monitoring after the removal of permanent sensors

Example Electricity energy meter Thermocouples

Requirement

Estimate the power consumption and cooling capacity of RTUs accurately and quickly

Use both permanent and temporary sensors for training to reduce cost

Skip the cooling capacity measurement


Experimental setup

2 Field systems» Cooling capacity at 14.1kW and 17.2kW» R22 and R410A» Reciprocating and Scroll compressor» Fixed orifice

4 Laboratory systems» Cooling capacity 10.6 to 17.2kW» R22, R410A and R407C» Fixed orifice and electronic expansion valve (with 8.7K

superheat)


Experimental setup


Mass flowmeters and pressure transducers are used in the laboratory only for cooling capacity measurement

Virtual pressure sensors

Temperature (T) and status indicator (S) as permanent sensors

Electricity energy meters (W) as temporary sensors

Cooling capacity sensor

No field data on capacity for training


Compressor power consumption by energy

balance

Virtual pressure sensor

Refrigerant temperature

Semi-empiricalcompressor mass flow rate model from Jähnig

et al. (2002)

Virtual cooling capacity by energy

balance of the entire cooling

system

Condenser refrigerant mass flow rate by energy balance

Air temperature

Condenser airflow rate

As

inpu

ts

Cos

t fun

ctio

n m

inim

izat

ion

with

mea

sure

d po

wer

Power consumption sensor

Evaporator fan power consumption» Measured when only evaporator fan is operating» Use the average during the calibration period to

estimate the fan power consumption

Compressor and condenser fan power consumption» Measured together» Use the semi-empirical compressor power consumption

only» Coefficients estimated by minimizing sum of squares of

difference between measured and estimated value


Virtual sensor uncertainty

Like real sensors, uncertainty of the outputs of the virtual sensor is needed

Uncertainty of measurement quantifies the spread of the difference between » measured value» true value

Virtual sensor outputs are different: the estimated value


Virtual sensor uncertainty

Example: A compressor running at 3000W

Definition:» Uncertainty between the estimated and the true value of

the output


True 3000W

Measured from power transducer 3005W

Estimated by mathematical models with temperature and pressure measurement

2990W

Uncertainty components

Uncertainty from inputs» Propagated from inputs through the virtual sensor

mathematical model

Uncertainty from calibration data» Propagated from calibration data through the calibration

process

Uncertainty from output deviation» From the deviation between the estimated and

measured output variable


Uncertainty components

Uncertainty from covariance» Propagated from the random error of the model

Uncertainty from outputs» Virtual sensor estimates the measured value of the

variable» Need to account for the difference between the

measured and true value of the output variable


( , )true truey f x C

Result from laboratory units

Cooling capacity virtual sensor validated by laboratory data


Result from field units

Compressor and condenser fan power consumption» Calibration period: 23 days in August 2013» Validation period: 7 days in September 2013


Result from field units

Hourly energy consumption» Integrating estimated power consumption of evaporator

fan, condenser fan and compressor


Cost Analysis

Consider two scenarios:


Direct measurement Virtual sensing technology• 1 power transmitter for each unit to measure

the total power consumption• 18 thermocouples (3x3 grids) to measure the

air temperature difference across the evaporator per unit

• 2 relative humidity sensors for humidity across the evaporator per unit

• 1 airflow measurement stations with multiple hot-wire anemometers for evaporator airflow per unit

• 4 hour of technician work per unit

• 1 power transmitter for each unit during the calibration process only

• 18 thermocouples for airtemperature measurement and 5 thermocouples for refrigerant temperatures per unit

• 2 current switches to show the operating status of evaporator and compressor per unit

• Unknown technician work hour

Cost Analysis

Results under the U.S. context


($500)$0

$500$1,000$1,500$2,000$2,500$3,000

0 10 20 30 40

Cost sa

ving

per unit

Technician installation hour of virtual sensor per unit

Conclusion

Develop a method to use field data to calibrate reliable and accurate virtual sensors in packaged air conditioning units for» energy consumption» cooling capacity

Develop uncertainty calculation process

Estimate potential cost saving


Future work

Develop self-training algorithm with uncertainty calculation to determine the amount of data needed automatically


Correction

Eqn. (7)» Incorrect

» Correct


1

,1 , ,1,cov ,

,

) ] ] )( ([ [ ) (T Tcal cal calest es

cal

est estt de

p est est pest ev

st

f f f ff fy yC C C CC C

yest ,cov udev ( fx

)T ([ fxcal ,1

fxcal ,n

]T [ fxcal ,1

fxcal ,n

] )1( fx

)

Acknowledgement

Energy Efficient Hub of the Department of Energy» Project sponsor

Hugh Henderson» Sensor installation

Andrew Hjortland» Data management


Reference

Jähnig, D. I., Reindl, D. T., Klein, S. A., 2000, A semi-empirical method for representing domestic refrigerator/freezer compressor calorimeter test data, ASHRAE Trans., 106: p. 112 - 130


Appendix

Semi-empirical mass flow rate model

Refrigerant mass flow rate from energy balance on condenser


mr ,comp ,est ,1 r ,comp,in(C1 C2((Pr ,comp ,out

Pr ,comp ,in

)(1/k ) 1)

mr ,comp ,est ,2 a ,cond ,in(Ta,cond ,in )cp,a,cond ,inC5(Ta,cond ,out Ta,cond ,in )

hr ,cond ,in(Tr ,cond ,in , Pr ,cond ,in ) hr ,cond ,out (Tr ,cond ,out , Pr ,cond ,out )

Appendix

Compressor power consumption from energy balance

Cost function to estimate condenser airflow


, , ,1, , , ,2, , ,12 21

, , ,1,

( ) ( )r comp est i r comp est i comp est compi

r comp est i comp

Jm m W W

m W

Wcomp,est ,1 mr ,comp ,1(hr ,comp ,out (Tr ,comp ,out , Pr ,comp ,out ) hr ,comp ,in(Tr ,comp ,in , Pr ,comp ,in ))

C3(Tr ,comp ,out Ta ,cond ,out )C4 (Tr ,comp,in Ta ,cond ,out )

Appendix

Cooling capacity virtual sensor


, , , , , , , , 5 , , , ,( ) ( )evap est a cond in a cond in p a cond in a cond out a cond in

comp cond

T c C TQ

W W

T

Appendix

Average evaporator power consumption calculation

Result


Wevap ,est 1n i

Wevap ,i

System

Estimated power [kW]

Relative uncertainty of the power transmitter

Relative uncertainty of the virtual sensor

Coefficient of variation

Number of data points

1 0.78 2.31% 4.34% 1.83% 58

2 0.95 1.76% 3.85% 1.71% 63

Appendix

Compressor and condenser fan power consumption model

Objective function


6 7 8 , , 9 10 , ,( ) ( )r comp in r comp outC exp C C exp PC P C

Wcomp,est ,2 Wcond ,est 1

(C1 C2((Pr ,comp,out

Pr ,comp ,in

)(1/k ) 1) kk 1

Pr ,comp,in((Pr ,comp ,out

Pr ,comp ,in

)(11

k)1)

J2 i((C1 C2 ((

Pr ,comp,out ,i

Pr ,comp ,in,i

)(1/ki ) 1)ki

ki 1Pr ,comp,in,i((

Pr ,comp ,out ,i

Pr ,comp,in,i

)(1 1

ki)1)

Wcomp,i Wcond ,i

i )2

Appendix

General regression model» Ideal model

» Model in use


ytrue f ( x,Ctrue )

yest f ( x,Cest )

Cest g( ycal ,1,..., ycal ,n , xcal ,1,...,

xcal ,n )

Appendix

Uncertainty from inputs

Uncertainty from calibration data


yest ,input i ( f ( x,

Cest )

xi

xi )2

yest ,cal i j (k ( f ( x,

Cest )

Cest ,k

Cest ,k

xcal ,i

)xcal ,i, j )2 i(k (

f ( x,Cest )

Cest ,k

Cest ,k

ycal ,i

)ycal )2

Appendix

Uncertainty from output deviation

Uncertainty from covariance


yest ,dev t0.95,n p1

i ( f ( xcal ,i ,Cest ) ycal ,i )

2

n p 1

1

,1 , ,1,cov ,

,

) ] ] )( ([ [ ) (T Tcal cal calest es

cal

est estt de

p est est pest ev

st

f f f ff fy yC C C CC C

Appendix

Uncertainty from outputs

Overall uncertainty


,est output caly y or ,,

,

1 cal iest output

cal i

yy

n y

2 2 2 2 2, , , , ,est est input est cal est dev est cov est outputy y y y y y

Appendix

Cost of sensors (under the U.S. context)» Power transmitters: $500/sensor» T-type thermocouples: $50/sensor» Relative humidity sensor: $240/sensor» Hot-wire anemometers for airflow: $1600/station» Current switch as status indicator: $50/sensor» Technician salary: $70/hour


Virtual Power Consumption and Cooling Capacity Virtual ......Cost function to estimate condenser...

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