Download - 1 Optimal Control of Chiller Condenser Sub-cooling, Compressor Speed, Tower Fan and Pump Speeds, and IGV Omer Qureshi, Hassan Javed & Peter Armstrong,

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Optimal Control of Chiller Condenser Sub-cooling, Compressor Speed, Tower Fan and Pump Speeds, and IGV

Omer Qureshi, Hassan Javed & Peter Armstrong, June 2013

btrc.masdar.ac.ae

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Presentation Outline

Introduction SCADA and Heat Balance Analysis Component Models Chiller System Solver Optimization Conclusion and Future Work

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Introduction

Plant under consideration-(4x2500T).

Collection and analysis SCADA

Development of sub models for Individual chiller components

Validation of model

Development of solver- to execute these sub models and predict

chiller performance.

Optimize the model to produce set of conditions for optimum

power consumption.

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District Cooling Plant

Selected District cool Plant

Capacity (4x2500T)

Shell and tube Evaporator and Condenser

Constant speed single stage centrifugal compressor

Capacity control by Pre-rotation vanes

Surge control Variable geometry diffuser

2-cell cooling tower each with variable speed fan (Fan diameter: 8m)

Variable speed chilled water pump

Constant speed condenser water pump

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Chiller Unit

1. Maintenance manual of York Chiller(Source: Tabreed)

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SCADA & Heat Balance Analysis

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Components Models—Chiller Unit

Steady-state models based on first principleInputs

Component engineering parametersSCADA Data

Simple models, less computation timeFour Component models for district cooling plant

Evaporator Model----Shell and tubeCondenser Model----Shell and tubeCentrifugal Compressor Model (Isentropic work + loss Mechanism) • Constant speed• Variable speed

Variable speed pump model

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Evaporator Model

ENGINEERING PARAMETERS

Tubes Copper

Length of shell 6.6 m

Tube Pass (water) 2

Total no. of tubes 1234

Tube Diameter 0.75" or 1.905x10-2 m

Tube thickness 0.028" or 7.11x10-4 m

Assumptions:

No pressure drop considered for refrigerant side

Thermal resistance from refrigerant side is neglected.

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Evaporator Model

Evaporation Evaporation Superheating

Evaporator

Two regions for refrigerant were modeled:EvaporationSuperheating𝞮 – NTU MethodSingle Stream HX for evaporationCrossflow HX for super heating

1st Pass 2nd Pass

𝑇𝑤 ,𝑜𝑢𝑡 ,1 𝑇𝑤 ,𝑜𝑢𝑡 ,2𝑎 𝑇𝑤 ,𝑜𝑢𝑡 ,2𝑏

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Evaporator Model

Equations utilized in Evaporator Model

h 𝑖𝑛 ,𝑒=0.023𝑅𝑒𝑒0.8𝑃𝑟

0.4 𝑘𝑤

𝐷𝑒 ,𝑖

𝑈𝐴𝑒=1

1𝐴𝑖𝑛 ,𝑒h𝑖𝑛 ,𝑒

+𝑅𝑃 ,𝑒

�̇�𝑚𝑖𝑛¿min [𝑐𝑝 ,𝑤�̇�𝑤 ,𝑒¿ ,𝐶𝑝 , 𝑟 �̇�𝑟 ]¿

𝐴𝑖𝑛 ,𝑒 ,1=𝜋 𝐷𝑒 ,𝑖𝐿𝑒(𝑁¿¿𝑒 /2)¿𝐴𝑖𝑛 ,𝑒 ,1𝑎=𝜋 𝐷𝑒 ,𝑖 𝑥𝑒𝐿𝑒(𝑁𝑒 /2)𝐴𝑖𝑛 ,𝑒 ,1𝑏=𝜋 𝐷𝑒 , 𝑖¿

𝑇𝑤 ,𝑜𝑢𝑡 ,𝑒=𝑇𝑤 ,𝑖𝑛 ,𝑒−𝑄𝑡 ,𝑒

𝑐𝑝 ,𝑤𝑚𝑤

Evaporation Evaporation Superheating

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Evaporator Model

Equations utilized in Evaporator Model

𝑇𝑤 ,𝑜𝑢𝑡 ,2𝑎=𝑇𝑤 ,𝑜𝑢𝑡 ,1−(𝑇𝑤 ,𝑜𝑢𝑡 ,1−𝑇 𝑒) (1−𝑒−𝑁𝑇𝑈𝑒 ,2 𝑎 )

𝜀2𝑏=1−𝑒𝑥𝑝 [( 1𝐶𝑟 ) (𝑁𝑇𝑈𝑒2𝑏)0.22{exp [−𝐶𝑟 (𝑁𝑇𝑈𝑒 ,2𝑏)0.78 ]−1}]𝑇𝑤 ,𝑜𝑢𝑡 ,2𝑏=𝑇𝑤 ,𝑜𝑢𝑡 , 2𝑎−𝜀2𝑏(𝑇𝑤 ,𝑜𝑢𝑡 , 2𝑎−𝑇𝑒)

𝑇𝑤 ,𝑜𝑢𝑡 ,1=𝑇𝑤 ,𝑖𝑛 ,𝑒−(𝑇𝑤 ,𝑖𝑛 ,𝑒−𝑇𝑒) (1−𝑒− 𝑁𝑇𝑈𝑒1 )

𝐿𝑒=8.947 𝑥 10−3�̇�𝑟

2−3.6279𝑥 10−1�̇�𝑟❑+7.227

Equation for regressed length:

Equation for temperatures:

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Evaporator Model

1. Maintenance manual of York Chiller(Source: Tabreed)

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Evaporator Model

1.5 2 2.5 3 3.5 41.5

2

2.5

3

3.5

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Measured Te (C)

Mod

eled

T

e (C

)

Measured Te (C) vs Modeled Te (C)

Measured Te (C)15% error line

-15% error line

RMS 0.2096 C

NRMS 0.0319

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Condenser Model

ENGINEERING PARAMETERS

Tubes CopperLength of shell 6.6 mTube Pass (water) 2Total no. of tubes 937Sub-cooling Section:Tube Diameter 0.75" or 1.905x10-2 mNo. of tubes 180Tube thickness 0.028" or 7.11x10-4 mTube Surface Area 66.78 m2 Condensation & de-superheating Section:Tube Diameter 1" or 2.54x10-2 mNo. of tubes 757Tube thickness 0.035" or 8.89x10-4 mTube Surface Area 376.44 m2

Assumptions:

No pressure drop considered for refrigerant side

Thermal resistance from refrigerant side is neglected.

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Condensation

Sub-cooling

Conden-sation

De-superheating

Condenser

Condenser Model

Three regions for refrigerant were modeled:

Sub-cooling

Condensation

De-Superheating𝞮 – NTU Method

1st Pass 2nd Pass

𝑇𝑤 ,𝑚𝑖𝑥 ,𝑐𝑇𝑤 ,𝑜𝑢𝑡 ,2𝑎 𝑇𝑤 ,𝑜𝑢𝑡 ,2𝑏

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Equations utilized in Condenser Model

1a. Sub-Cooling Section(First Pass):

Condenser Model

h 𝑖𝑛 ,𝑐 , 1𝑎=0.023𝑅𝑒𝑐 10.8𝑃𝑟❑

0.4 𝑘𝑤

𝐷𝑐 1 ,𝑖

𝑈𝐴𝑐 , 1𝑎=1

1𝐴𝑖𝑛 , 𝑐, 1𝑎h 𝑖𝑛 ,𝑐 , 1𝑎

+𝑅𝑃 , 𝑐 ,1𝑎

𝜀𝑐 ,1𝑎=1−𝑒−𝑁𝑇𝑈𝑐 ,1𝑎 (1−𝐶𝑟 ,1 𝑎 )

1−𝐶𝑟 , 1𝑎𝑒−𝑁𝑇𝑈𝑐 ,1 𝑎(1−𝐶𝑟 ,1 𝑎)

𝑇 𝑐𝑠=𝑇 𝑐 2−𝜀𝑐, 1𝑎𝐶𝑚𝑖𝑛 ,1𝑎(𝑇 𝐶 2−𝑇𝑤 ,𝑖𝑛 , 𝑐)

�̇�𝑟 𝑐𝑝 ,𝑟

𝑇𝑤 ,𝑜𝑢𝑡 ,1𝑎=𝑇𝑤 , 𝑖𝑛 ,𝑐+�̇�𝑟 𝑐𝑝 ,𝑟 (𝑇 𝐶 2−𝑇 𝑆𝐶)�̇�𝑤 ,𝑐𝑥1 ,𝑎𝑐𝑝 ,𝑤

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1b. Condensation Section (First Pass):

Mixing Section:

Condenser Model

h 𝑖𝑛 ,𝑐 , 1𝑏=0.023𝑅𝑒𝑐 1𝑏0.8𝑃𝑟❑

0.4 𝑘𝑤𝐷𝑐 2 , 𝑖

𝑈𝐴𝑐 , 1𝑏=1

1𝐴𝑖𝑛 , 𝑐 ,1𝑏h𝑖𝑛 ,𝑐 ,1𝑏

+𝑅𝑃 , 𝑐 ,1𝑏

𝑁𝑇𝑈 𝑐 ,1𝑏=𝑈𝐴𝑐 ,1𝑏

�̇�𝑚𝑖𝑛,𝑤

𝑇𝑤 ,𝑜𝑢𝑡 ,1𝑏=𝑇𝑤 ,𝑖𝑛 ,𝑐+𝑥𝑐𝑎�̇�𝑟 (𝐻𝐶2−𝐻𝐶 3)

�̇�𝑤 ,𝑐(1−𝑥¿¿1𝑎)𝑐𝑝 ,𝑤 ¿

𝑇𝑤 ,𝑚𝑖𝑥 ,𝑐=�̇�𝑤 ,𝑐𝑥1 ,𝑎𝑇𝑤 ,𝑜𝑢𝑡1 ,𝑎−�̇�𝑤 ,𝑐

(1−𝑥¿¿1𝑎)𝑇𝑤 ,𝑜𝑢𝑡 1𝑏

�̇�𝑤 ,𝑐

¿

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2a. Condensation Section (Second Pass):

2b. De-superheating Section (Second Pass):

Condenser Model

h 𝑖𝑛 ,𝑐 , 2𝑎=0.023𝑅𝑒𝑐 2𝑎0.8𝑃𝑟❑

0.4 𝑘𝑤

𝐷𝑐 2 ,𝑖

𝑈𝐴𝑐 , 2𝑎=1

1𝐴𝑖𝑛 , 𝑐 ,2𝑎h𝑖𝑛 , 𝑐 ,2𝑎

+𝑅𝑃 ,𝑐 , 2𝑎𝑁𝑇𝑈 𝑐 ,2𝑎=

𝑈𝐴𝑐 , 2𝑎

�̇�𝑚𝑖𝑛,𝑤

𝑇𝑤 ,𝑜𝑢𝑡 ,2𝑎=𝑇𝑤 ,𝑚𝑖𝑥 ,𝑐+𝑥𝑐𝑏�̇�𝑟𝑐𝑝 ,𝑟 (𝐻𝐶 2−𝐻𝐶 3)

�̇�𝑤 ,𝑐𝑐𝑝 ,𝑤

𝑇𝑤 ,𝑜𝑢𝑡 ,2𝑏=𝑇𝑤 ,𝑜𝑢𝑡 2𝑎+�̇�𝑟𝑐𝑝 , 𝑟 , 2𝑏(𝑇 𝐶1−𝑇 𝐶 2)

�̇�𝑤 ,𝑐𝑐𝑝 ,𝑤

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Condenser Model

22 24 26 28 30 32 3422

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26

28

30

32

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Measured Tc (C)

Modele

d

Tc (

C)

Measured Tc (C) vs Modeled Tc (C)

Measured Tc (C)2.5% error line

-2.5% error line

RMS 0.0949 C

NRMS 0.0225

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Condenser Model

20 25 30 3520

25

30

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Measured Tw.out (C)

Mod

eled

T

w,o

ut (

C)

Measured Tw,out (C) vs Modeled Tw,out (C)

Measured Tw,out (C)5% error line

-5% error line

RMS 0.6481 C

NRMS 0.1471

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Compressor Model

Integral and mathematically most complex part of chillerConstant and variable speed compressor modelNon-Dimensional loss model based on Aungier(2000)

Assumptions

• Gear efficiency is taken as 90%

• Velocity profile is assumed as constant, along the hub and tip

• The kinetic energy of refrigerant entering the diffuser is completely converted to useful energy

• Diffuser and IGV losses are not modeled

• Water flow rate for motor cooling is taken as constant

• Complex engineering parameters in impeller geometry

Centrifugal Compressor Specification

Refrigerant R134A

Rating (Btuh) 2500

Rating (kW input) 1817

Rating discharge pressure (psig) 162

Rating suction pressure psig) 34

Rating suction temperature (F) 33/34

Impeller diameter (outlet diameter) m 0.7

Impeller hub diameter (inlet diameter) 0.3

Impeller Blade Angle (degree) 45/50

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Constant Speed Model

Variable speed Model

Compressor Model-Inputs and Outputs

Input Output

Mass flow rate of refrigerantInlet and outlet pressure of compressorInlet and outlet blade and velocity angles of impeller Impeller Inlet and outlet engineering parameters and dimensionsGear efficiency

Compressor Power Compressor RPMPressure at impeller exitTemperature at compressor outletPressure drop due to Impeller losses

Input Output

IGV PositionsConstant RPMInlet and outlet pressure of compressorInlet and outlet blade and velocity angles of impeller Impeller Inlet and outlet engineering parameters and dimensionsGear efficiency

Compressor Power Pressure at impeller exitTemperature at compressor outletPressure drop due to Impeller losses

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Validation Constant Speed Compressor Model

0 200 400 600 800 1000 1200 14000

200

400

600

800

1000

1200

1400

1600

No. of Observations

Cop

mre

ssor

Pow

er (

KW

)

Actual Power(kW)Model Power(kW)Loss Power(kW)Model Comp Power(kW)

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Validation Constant Speed Compressor Model

400 600 800 1000 1200 1400 1600400

600

800

1000

1200

1400

1600

Measured Power(kW)

Mod

el P

ower

(kW

)

Measured Power(kW) vs Model Power(kW)

Measured Power(kW)10% Error line

-10% Error lineRMS 108.34 KW

NRMS 0.1553

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Variable Speed Compressor Model

𝐼𝑠𝑒𝑛𝑡𝑟𝑜𝑝𝑖𝑐 𝑊𝑜𝑟𝑘 = 𝑤𝑖𝑠𝑒𝑛 = − 1 𝑃1𝜌1 ൬𝑃3𝑃1൰

−1ൗ�− 1 𝜂𝑔𝑒𝑎𝑟൘

𝑀𝑎𝑠𝑠 𝐹𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑓𝑟𝑖𝑔𝑒𝑟𝑎𝑛𝑡= 𝑚ሶ= 𝜙2𝐴2𝑈2𝜌2

RPM is calculated in an iterative process by satisfying the following equation

𝑟𝑒𝑠𝑢𝑙𝑡 = 𝑚ሶ𝑠𝑐𝑎𝑑𝑎 − 𝑚ሶ𝑐𝑎𝑙

Total Work

𝑊𝑎𝑐𝑡 = 𝑊𝑐𝑜𝑚𝑝 + 𝑊𝑙𝑜𝑠𝑠

𝑊𝑙𝑜𝑠𝑠 = ∆𝑃𝑡𝑟𝑉𝑟

Total Relative Pressure Drop (Due to Losses)

∆𝑃𝑡𝑟 = 𝑓𝑐(𝑃𝑡𝑟1 − 𝑃𝑠1) ഥ𝑖𝑖

Loss Model Calculations

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Variable Speed Compressor Model-Benefits/comparison

Variable Speed Compressor (KW)Measured Compressor Power (KW)

Com

pres

sor P

ower

(KW

)

No. of Observations

Operation Conditions:1. mr (kg/s)2. Pout/Pin

Power (KW) 1504.702IGV Position 44.2

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Impeller Loss Model

𝐼𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒 𝐿𝑜𝑠𝑠= 1− 𝑉𝑚1𝑊1 sinሺ𝑚1ሻ൨2 + 𝑡𝑏1𝑍2𝑟𝑚1 sinሺ𝑚1ሻ൨

2

𝐷𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑙𝑜𝑠𝑠= 0.81− 𝑊1𝑇ℎ𝑊1 ൨2 − 𝐼𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒 𝐿𝑜𝑠𝑠

𝑆𝑘𝑖𝑛 𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝐿𝑜𝑠𝑠= 4𝑐𝑓ቆ𝑊ഥ𝑊1ቇ2 𝐿𝐵𝐷𝐻

𝐵𝑙𝑎𝑑𝑒 𝐿𝑜𝑎𝑑𝑖𝑛𝑔 𝐿𝑜𝑠𝑠= (∆𝑊 𝑊1)Τ 224

𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛 𝐿𝑜𝑠𝑠= ቈሺ − 1ሻ𝑉𝑚2𝑊1 2

𝐶𝑙𝑒𝑎𝑟𝑎𝑛𝑐𝑒 𝐺𝑎𝑝 𝐿𝑜𝑠𝑠= 2𝑚ሶ𝐶𝐿∆𝑃𝐶𝐿𝑚 ሶ1𝑊12

𝐻𝑢𝑏− 𝑆ℎ𝑟𝑜𝑢𝑑 𝐿𝑜𝑠𝑠= (ത𝑚𝑏ത𝑊ഥ 𝑊1)Τ 26

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Variable Speed Compressor Model-losses profile

20 25 30 35 40 45 500

20

40

60

80

100

120

Refrigerant Mass Flow (kg/s)

Pre

ssu

re D

rop

(kP

a)

Clearance gap loss (kPa)Diffusion loss (kPa)Hub-shroud Loss (kPa)Incident loss (kPa)Skin friction loss (kPa)Blade Loading Loss (kPa)Expansion Loss (kPa)

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Effectiveness NTU Method

Cooling Tower Model

𝐻𝑒𝑎𝑡 𝑅𝑒𝑗𝑒𝑐𝑡𝑒𝑑= 𝑄𝑟𝑒𝑗𝑒𝑐𝑡𝑒𝑑 = 𝑚𝑤ሶ∗𝑐𝑝𝑤 ∗ሺ𝑇𝑐𝑤𝑠− 𝑇𝑐𝑤𝑟ሻ 𝐶𝑜𝑜𝑙𝑖𝑛𝑔 𝑇𝑜𝑤𝑒𝑟 𝑅𝑒𝑡𝑢𝑟𝑛 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒= 𝑇𝑐𝑤𝑠− 𝑄𝑟𝑒𝑗𝑒𝑐𝑡𝑒𝑑𝑚𝑤ሶ∗𝑐𝑝𝑤

𝑄𝑟𝑒𝑗𝑒𝑐𝑡𝑒𝑑 = ∗𝐶ሶ𝑚𝑖𝑛 ∗ሺ𝑇𝑐𝑤𝑠− 𝑇𝑤𝑏ሻ = 1− 𝑒−𝑁𝑇𝑈(1−)1− 𝑒−𝑁𝑇𝑈(1−)

𝑁𝑇𝑈= 𝑚_𝑤ሶ𝑚_𝑎ሶ 𝑀𝑒𝑀

𝑀𝑒𝑀= 𝐾 ∗𝑎∗𝑉𝑚_𝑤ሶ

𝑀𝑎𝑠𝑠 𝐹𝑙𝑜𝑤 𝑜𝑓 𝐴𝑖𝑟= 𝑚_𝑎ሶ = 𝑉𝑚𝑎𝑥ሶ ∗𝜌𝑎 ∗𝑓

Regression Coefficient

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Assumptions, Specifications and Input/ Output Variables

Cooling Tower Model

Assumptions

• Air exiting the tower is saturated with water

vapor and is only characterized by its

enthalpy

• Reduction of water flow rate by evaporation is

neglected in the energy balance.

• Mass flow rate is calculated by considering

linear proportionality of mass flow rate of air

and motor speed.

Inputs Outputs

• Wet-bulb temperature• Cooling tower supply water temperature• Dry-bulb temperature • Mass flow rate of water• Cooling tower fan/motor speed

• Cooling tower return water temperature• Merkel’s Number

Cooling Tower Specifications

Rating (RT) 5000

Rating flow rate (GPM) 15300

Rating ambient wet bulb (F) 86

Rating ambient dry bulb (F) 122

Rating entering condenser water

temperature (F)

105

Fan diameter and speed (m, RPM) 8/152.6

Air flow rate (CFM) 776383

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Cooling Tower Model

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Pump Model

Mainly there are two mode of operation for these pumps:

Constant flow pump

Variable flow pump with a variable speed drive

To model a variable pump power following relationship is used:

Where,PMP = pump motor power at rated condition, kWC1, C2, C3 and C4 are pump performance coefficients

Also,PLRi = pump part load ratio defined as follows:

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Pump Model

Validation Graph

+ 5%Error Line

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Solver Description

Qt,e

Tw,in,e

Tw,in,c

Ve

Vc

dTsh,e

35

Optimization

Optimization performed with two configurations:

Chiller Water Flow Optimization

Chiller Water Flow And Condenser Water Flow Optimization

Objective Function:

Minimize total power consumption i.e. compressor power and pump(s)

power combined.

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Optimization

Chiller Water Flow Optimization:

Vc Vc Vc VcQe 10000 KW Qe 8000 KW Qe 6000 KW Qe 4000 KW

Power Total (KW)

Ve (m3/s)

COPPower

Total (KW)Ve

(m3/s)COP

Power Total (KW)

Ve (m3/s)

COPPower

Total (KW)Ve

(m3/s)COP

2791.90 0.1419 3.58 1768.81 0.1419 4.52 1102.50 0.1419 5.44 649.15 0.1419 6.162494.66 0.1774 4.01 1617.53 0.1774 4.95 1032.45 0.1774 5.81 626.16 0.1774 6.392325.43 0.2129 4.30 1535.14 0.2129 5.21 997.69 0.2129 6.01 622.12 0.2129 6.432226.70 0.2484 4.49 1492.30 0.2484 5.36 988.83 0.2484 6.07 633.21 0.2484 6.322171.34 0.2839 4.61 1476.36 0.2839 5.42 998.06 0.2839 6.01 657.75 0.2839 6.082145.79 0.3194 4.66 1483.94 0.3194 5.39 1023.13 0.3194 5.86 695.26 0.3194 5.752149.01 0.3548 4.65 1512.07 0.3548 5.29 1065.53 0.3548 5.63 746.65 0.3548 5.362177.04 0.3903 4.59 1559.59 0.3903 5.13 1122.92 0.3903 5.34 811.97 0.3903 4.932227.85 0.4258 4.49 1623.07 0.4258 4.93 1197.94 0.4258 5.01 892.40 0.4258 4.482300.43 0.4613 4.35 1708.17 0.4613 4.68 1288.91 0.4613 4.66 988.98 0.4613 4.042389.48 0.4968 4.19 1809.82 0.4968 4.42 1397.89 0.4968 4.29 1103.05 0.4968 3.63

Tw,in,c = 25 C and Tw,in,e = 14 C0.4795 m3/s 0.4795 m3/s 0.4795 m3/s0.4795 m3/s

37

Optimization

Chiller Water Flow And Condenser Water Flow Optimization:

Qe = 10,000 kWVe,opt = 0.349 m3/sVc,opt = 0.408 m3/s

Tw,in,e = 14 C; Tw,in,c = 25 C

Vc (m3 /s)

Vc (m 3/s)

Tota

l Pow

er (K

W)

38

Optimization




Vc (m3 /s)

Vc (m 3/s)

Tota

l Pow

er (K

W)

39

Optimization




Vc (m3 /s)

Vc (m 3/s)

Tota

l Pow

er (K

W)

40

Optimization




Vc (m3 /s)

Vc (m 3/s)

Tota

l Pow

er (K

W)

41

Optimization



42

Optimization


43

Conclusions

Variable Speed compressor provide savings of 30-40%

Variable speed pump for water circulation play an imperative role in

reducing overall power consumption of chiller plant.

Modeling of chiller components can be performed with limited

engineering information from manufactures.

44

Future Work

More rigorous compressor loss model

Transient model for the condenser and evaporator

Cooling tower Model

Variable Speed condenser pump

Investigate the effect of pressure drop and resistance from

refrigerant side

45

Q&A

45