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Modeling And Control of Vapor Compression Cycle
Matt Wallace, Ryan McBride, Siam Aumi and Prashant Mhaskar
Department of Chemical Engineering
McMaster University
Hamilton, Ontario
John House and Tim Salsbury
Johnson Controls Inc.
June 24, 2011
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Introduction
Introduction: Energy Consumption Government regulations and initiatives have placed a large emphasis ($$$) on
the reduction of energy consumption and increase in energy efficiency
Distribution of Secondary Energy Usagein Canada. (Natural Resources Canada)
Heating, ventilation, and air-conditioning (HVAC) systems responsible for40-50% of total building energy consumption
15 to 20% per annum of energy consumption can be reduced by efficient andoptimal operation of buildings (NRCan)
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Introduction
Improvement Strategies
Design:
1 Building design (LEED certified buildings)
2 Retrofit replace existing equipment with more energy efficienttechnology (i.e. EnergyStar certified equipment)
Building operation and control (Controller Complexity):
Lowest - Local control of cooling device using classical control strategies
Middle - Advanced control of cooling devices
Highest - Integrated control accounting for startup/shut down ofcooling units in addition to emphasis on cost and energy efficientoperation
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Background Theory
Background
Multiple PI control strategy regulating experimental Vapor CompressionCycle (VCC) (Keir and Alleyne [2007])
Nonlinear Model Predictive Control (MPC) designs for regulation ofexperimental VCC plant/various chiller system configurations (Leducqet al. [2006], Ma et al. [2010b])
Linear-state space based MPC to regulate a chiller network (Sandipanet al. [2010])
MPC of cooling unit subject to time-weather-dependent heat loads (Maet al. [2010a], May-Ostendorp et al. [2010])
Significant benefit from MPC strategies in providing desired cooling whileminimizing energy usage
Current Work :
MPC of a detailed model of a primary unit
Interfaced with detailed building model (EnergyPlus)
Compare with classical control strategyM. Wallace (McMaster) Energy Efficient Temperature Control 4 / 21
V C i C l
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Vapor Compression Cycle
Modeling the plant-Vapor Compression Cycle (VCC)
Many air conditioning/refrigeration primary devices use a VaporCompression Cycle (VCC) to remove heat from a desired region anddissipate the heat to an alternate region
Air Cooled VCC
1 2 Evaporator- Refrigerant absorbs zone air heat
and is evaporated2 3 Compressor- Superheated vapor is compressed to
a higher P/T
3 4 Condenser
- Refrigerant rejects heat to theatmosphere and condenses to liquid
4 1 Expansion Valve- Expansion device reduces the
pressure of the refrigerant creating a
two-phase mixtureM. Wallace (McMaster) Energy Efficient Temperature Control 5 / 21
Vapor Compression C cle
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Vapor Compression Cycle
VCC Model
VCC model adapted from the Air Conditioning & Refrigeration Center(ACRC) Thermosys simulator
Dynamic Model:
Condenser
Evaporator
Compressor
Static Model:
Expansion Valve
Piping
Highly nonlinear model (13 ODEs) including lookup tables
Parameters estimated experimentally (r-134a, air medium)
Is it a perfect model of a VCC- No-but captures the essential features
Necessary to evaluate controller designs
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Interfaced System
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Interfaced System
Modeling the plant-Interfaced System
VCC model interfaced with small office building model
Small office building model developed by EnergyPlus; United StatesDepartment of Energy (US DOE) software
Weather Databased on variousyearly recordings
Single story office(511m2)
5 thermal zones
Location: Chicago, IL
(July 25th)
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Interfaced System
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Interfaced System
MATLAB-EnergyPlus Interface
MATLAB VCC connected to EnergyPlus through the Building Controls
Virtual Test Bed (BCVTB)
VCC model acts as a rooftop AC unit supplying cooling to perimeter zone 2(67m2)
Cooling load across evaporator inputted to EnergyPlus model as negativesensible and latent heat loads
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Control Structure Design
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Control Structure Design
Classical Control Strategy
PI controller variable pairings obtained on stand-alone VCC
Expansion valve opening-evaporator superheat temperature (TSH
) andcompressor RPM-supply air temperature (TSA)
PI controllers initialized with IMC (internal model control) values andtuned by minimizing IAE (integral of absolute error) in response todisturbances rejection
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Control Structure Design
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g
Control Structure Design
Zone dynamics slower than VCC dynamics motivating a cascade controlstructure to regulate zone conditions
Outer loop: Zone air temperature (TZone) - supply air temperature(TSA) SP
Inner loop: Either the individual PI controllers or a linear ModelPredictive Control (MPC) strategy regulating TSA and evaporatorsuperheat temperature (TSH)
PI Control
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Control Structure Design
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g
Control Structure Design
Zone dynamics slower than VCC dynamics motivating a cascade controlstructure to regulate zone conditions
Outer loop: Zone air temperature (TZone) - supply air temperature(TSA) SP
Inner loop: Either the individual PI controllers or a linear ModelPredictive Control (MPC) strategy regulating TSA and evaporatorsuperheat temperature (TSH)
MPC Control
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MPC Design
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Autoregressive Exogenous (ARX) Model IdentificationARX Model Formulation:
Input/Disturbance variable pseudo random binary sequences (PRBS) used for
MPC model identification and fitting an equation of the following form :
Yi(k) = a1Y1(k 1) + . . . aNa Y1(k Na) + b1Y2(k 1) + . . . bNbY2(kNb)
+ c1U1(k 1) + . . . cNcU1(kNc) + d1U2(k 1) + . . . dNdU2(k Nd)
+ e1Z1(k 1) + . . . eNeZ1(k Ne + f1Z2(k 1) + . . . fNfZ2(k Nf)
Figure: PRBS I/O data used to form ARX models
Note : Model not obtained via linearization, but instead through
identification experimentM. Wallace (McMaster) Energy Efficient Temperature Control 11 / 21
MPC Design
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Model Predictive Control Formulation
MPC Formulation:
Minimize - Setpoint deviation for Supply Air Temperature, compressorrpm (not deviation), compressor, valve movement
Subject to: Constraints on the inputs and Superheat, disturbance model,plant-model mismatch correction
Model: Increasing RPM increases Superheat and increases cooling
Increasing Valve opening decreases Superheat and increases cooling
Higher RPM implies higher energy usage
Lower SH results in increased energy efficiency (just a consequence ofthe above)
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MPC Design
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Model Predictive Control FormulationMPC Formulation:
minui
Nci=1
(y2,i ySP2 )TQ2(y2,i ySP2 ) + uT1 R1u1+
uT2 Rd2u2 + uT
1 Rd1u1subject to:
3.5C 1,low + 1,low y1,i 20C 1,up + 1,up
umin ui umax
umin ui umax
where yi(k) = a1y1(k 1) + . . . fNfz2(k Nf),
ySP2 = ySP
2 2 + 2,
j =yj(0)yj(0)
j j = 1, 2
(1)
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MPC Design
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Model Predictive Control Formulation (Continued)MPC Formulation (Continued):
2(k) = (y
SP
2
y2(0))2+ 2(k 1),
1,low(k) =
(3.5y1(0))
1,low+ 1,low(k 1) : y1(0) < 3.5
0 : y1(0) 3.5,
1,up(k) = (20y1(0))
1,up + 1,up(k 1) : y1(0) > 200 : y1(0) 20
Parameters Nc Q2 R1 Rd2 Rd1 2 1,low
Value 4 950 35017002 0.5 0.004 80 10
1,up 2 1,low 1,up umin umax umin umax
200 2 50 10
678.8 6
1700 15
200 1
200 1
ui =
RPMi Valvei
T
, ui = ui - ui1 y
1y
2i
= TSH TSAi, z
1z
2i
= TAmbient TReturni
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Closed-loop Preliminary Results
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Closed-loop VCC Simulation Conditions
Stand-alone VCC was regulated initially using both classical and MPC
schemes Constant air temperature and humidity values chosen corresponding to
condensation conditions
Air Parameter ValueTamb (
oC) 28
Treturn (o
C) 26RH (%) 87
TSA SP trajectory values corresponded to a range of possible operatingconditions for interfaced VCC
Feasible and infeasible TSA SP values used; infeasible values possible assudden fluctuations in zone air conditions could make a feasible SPinfeasible
Once stand-alone VCC was regulated, both control structures were
implemented on the interfaced systemM. Wallace (McMaster) Energy Efficient Temperature Control 15 / 21
Closed-loop Preliminary Results
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Closed-loop performance criteria
TSA tracking of prescribed SP value; quantified using IAE
VCC energy demand quantified as the sum of instantaneous compressorpower (inst) over the test period
instant = mk(hout
hin)k(2)
Total Energy = t
tendi=1
instant,i
(3)
Maintain TZone at a SP of 24oC; ensure comfort standards (loosely
based on ASHRAE) satisfied
Results in a meaningful TSA SP sent to the primary unit controller
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Closed-loop Preliminary Results
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Simulation Results: Stand-alone VCC Input/OutputProfiles
MPC exploits trade-off between TSA SP tracking and high RPM values; High
cooling loads correspond to operating at high VO values, resulting in low TSHM. Wallace (McMaster) Energy Efficient Temperature Control 17 / 21
Closed-loop Preliminary Results
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Simulation Results: Stand-alone VCC Measures
Control Structure PI(TSH SP= 10oC) MPC
TSA IAE ( so
C) 35.32 9.41TSA Cumulative Settling Time (seconds) 6120 8400
Cumulative Energy (kJ) 10017 9217
Large discrepancy in TSA IAE caused by tracking ability of infeasible TSA SP
PI strategy maintained TSH at its SP reducing ability of PI strategy tominimize TSA SP deviation
PI strategy using a TSH SP= 20oC was examined and had similar SP
tracking performance as MPC, but used more energy
Control Structure PI(TSH SP= 10oC) PI(TSH SP= 20
oC)TSA IAE ( s
oC) 35.32 10.40TSA Cumulative Settling Time (seconds) 6120 5520
Cumulative Energy (kJ) 10017 11915
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Closed-loop Preliminary Results
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Simulation Results: Interfaced VCC Input/Output Profiles
MPC again exploits trade-off existing in the system in addition to achieving
off-set free trackingM. Wallace (McMaster) Energy Efficient Temperature Control 19 / 21
Closed-loop Preliminary Results
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Simulation Results: Interfaced Measures
Control Structure PI(TSH SP= 10oC) MPC
Cumulative Energy (kJ) 5080 4284TSA IAE ( soC) 2907 881
Zone Temperature Responses
TZone maintained within comfort standards for entire test period using
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Conclusions
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Conclusions/Future Work MPC uses less energy (reduction by 16 % relative to PI) to provide
better supply air tracking (a 70 % improvement compared with PI)
Achieved through using the multi-variable nature of the problem andconstraint handling abilities of MPC
MPC allows the SH to drop low (when possible), resulting in betterenergy efficiency, and higher when necessary to provide the desiredcooling
Evaluate using MPC as a RTO layer, with adaptive PIs with decouplersworking at the lower level
Data-based model for use within MPC
Acknowledgment
Financial support from NSERC (CRD) and JCI is gratefullyacknowledged
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Conclusions
M Keir and A Alleyne Feedback structures for vapor compression cycle
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energy and demand optimization of multi-zone buildings. 2010 AIChEConference, 2010a.
Y. Ma, F. Borrelli, B. Hencey, B. Coffey, S. Bengea, and P. Haves. Model
predictive control for the operation of building cooling systems. 2010American Control Conference, 2010b.
P. May-Ostendorp, G. P. Henze, C. D. Corbin, B. Rajagopalan, andC. Felsmann. Model-predictive control of mixed-mode buildings with ruleextraction. Building and Environment, pages 110, 2010.
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