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[ "#$#%]=[space] + [for]
Lecture 4
Pr inc ip les of Model ing for Cyber-Phys ica l Systems
Instructor: Madhur Behl
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 1
modeling
buildings
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In today’s lecture..
• Heat transfer basics• Thermal gains• Single zone ‘RC’ network model
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Recall: HVAC zone control
How to model the dynamics of the zone, for better control ?
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Heat transfer 101
If a mass m1 of a substance is heated from temperature T1 to T2, the
amount of heat H which it acquires is given by:
! = #$%&(() − ($)
where 01 is the speci7ic heat of the substance
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HVAC Zone heating
Heat flowmass flow rate..
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Components of Building Heat Loss and Gain
"#$
"%&"%
"'()
"*
"$)
+, -,+. -./0/12$
• Gains• Heat flows in…
• Losses • Heat flows out…
• Sensible gain/cooling:• Change the temperature of
the interior air.• Latent gain/cooling:• Change the humidity level
of the interior air.
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Building envelop.
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Components of Building Heat Loss and Gain
"#$
"%&"%
"'()
"*
"$)
+, -,+. -./0/12$
• Heat flows through:• Walls• Windows• Doors• Roof• Floor• Internal heat gain• Lights• Occupants• Equipment
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Building envelop.
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Mechanisms of heat transfer
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Conduction – A touching story of heat transfer
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Heat Transfer: Conduction
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Heat Transfer: Conduction
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Conduction though a wall
To
Ti
W
H
L
" = $% &' − &)*
"" = &' − &)
+,
+, =*$%
Property of the material
Property of the geometry
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Recall: Generalized resistance
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Heat flow "
Temperature T
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Heat Transfer: Conduction
Through Variable Across Variable
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Composite wall
Equivalent to
R1 R2 R3
R4 R5 R6
RT
!" =1
1!% + !' + !( + 1
!) + !* + !+
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Heat Transfer: Convection
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Heat Transfer: Convection
Property of the material
Property of the geometry
Second law (of thermodynamics)
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Heat Transfer: Radiation
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Heat Transfer: Radiation
Direct Indirect
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Heat Transfer: Radiation
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Recall: Generalized Capacitance
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Heat flow "
Temperature T
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Thermal Mass
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!"#$%&'( &')) *+ &'"$%,'( -*(.&$/0&'"$%,'(
/" = 34$" (*))/6',4
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To model a single zone:
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
1. To predict…
• Zone temperature.• Zone humidity.• Electricity
consumption/demand.• Energy consumption/demand.
• Cooling load• Heating load
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To model a single zone:
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows] We could model
• HVAC equipment.• Building envelop.
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To model a single zone:
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
1. Construction:1. Material properties
2. Geometry:1. Surface Areas, 2. Surface thickness3. Volume
3. Operation:1. Internal heat gains2. HVAC cooling/heating3. Outside air4. Solar heat gain
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Single zone: Surfaces
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
1. External Walls:1. Outside surface of
external wall – Ambient temperature.
2. Inside surface of external wall – Zone temp.
2. Ceiling:1. Out surf : Ambient temp,
or floor of the zone above.
2. Special case: Plenum3. In surface: zone temp
3. Floor:1. Out surf: Ground temp, or
zone below..2. In surface: zone temp
4. Internal Walls:1. With adjacent zones.
5. Windows/Doors
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Single zone: Heat Gains
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
1. Solar Irradiance Qsol :1. External wall2. Ceiling
2. Solar radiation transmitted through windows Qsol,t:1. Absorbed by zone air, and internal
surfaces.3. Radiative internal heat gain Qrad:
1. Distributed evenly on all internal surfaces.
4. Convective heat gain Qconv:1. With adjacent zones.
5. HVAC heat gain QHVAC or Qsens6. Boundary temperatures:
1. Outside air temp.2. Other zones
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Internal heat gainsOccupants Lighting Appliances/Equipment
Radiative Convective
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All in all, its just heat transfer through the wall
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One layer slab: 3R2C
• One layer slab:
• Two interior nodes, for each surface• T1, T2
• Convection on both sides.• To, Tz
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Assumptions
• Air inside is well mixed.• One dimensional heat transfer is assumed for the walls and surfaces..• No lateral temperature
differences.
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One layer slab: 3R2CWhy are resistors, capacitors, and temperature elements floating and not grounded in this diagram ?
Its convenient
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One layer slab: 3R2C
Heat flux, W/m2
e.g. solar irradiance
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3R2C – A closer look
Convection Convection Convection
Conduction
Conduction
Thermal Mass
Thermal Mass
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Announcements• Install EnergyPlus before the next lecture on Thursday, September 20.• https://energyplus.net/• Whole building energy simulator
• Optional:• Create an account at https://usonialabs.com/
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Assignment 2 is out
• Thermal RC modeling for a single zone.
• Due in 1 week: Tuesday, Sep 25 at 2:00pm
• No programming parts
• If you are submitting an electronic copy on collab:
• Upload a single PDF file only.
• Use the following filename format: <FirstName_LastName_UVA-ID>.pdf
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Zone temperature dynamics
"#$%
"&'()
*+
*+ ,-.,/ = ℎ2 34 − 36 + "#$% + "&'()
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Zone temperature dynamics
!" #$%#& = ℎ) *+ − *- + 0123 + 04567
States:
Inputs:
*8, *+ , *"
*: , ;<=>?@A), 0123, 04567
Parameters (unknown)
ℎ, B, ), !, !"
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State-Space dynamics
!" #$%#& = ℎ) *+ − *- + 0123 + 04567
*8*+*"
=
−ℎ)! − 1
:!1:! 0
1:!
−ℎ)! − 1
:!ℎ):!
0 ℎ)!"
−ℎ)!"
*8*+*"
+
ℎ)!
1! 0 0
0 0 0 00 0 1
!"1!"
*<=>?@ABC)012304567
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State-Space dynamics
"#"$"%
=
−ℎ)* − 1
,*1,* 0
1,*
−ℎ)* − 1
,*ℎ),*
0 ℎ)*%
−ℎ)*%
"#"$"%
+
ℎ)*
1* 0 0
0 0 0 00 0 1
*%1*%
"/0123456)789:7;<=>
? = )? + @A
Which variables are changing with time?
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 46
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"#(%)"'(%)"((%)
=
−ℎ,- − 1
/-1/- 0
1/-
−ℎ,- − 1
/-ℎ,/-
0 ℎ,-(
−ℎ,-(
"#(%)"'(%)"((%)
+
ℎ,-
1- 0 0
0 0 0 00 0 1
-(1-(
"2(%)3456789(%),:;<=(%):>?@A(%)
State-Space dynamics
B(%) = ,B(%) + CD(%)
Is this system LTI ?
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 47
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Output equation
!(#) = &'(#) + )*(#)
+,(#) = 0 0 1+/ #+0 #+, #
+ [ 0 ]
+3(#)456789:(#);=>?@(#)=ABCD(#)
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 48
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To model a single zone:
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
Great!, I know how to model an external wall.(external because, the outside boundary was
ambient temperature)
But what about
Floor, Ceiling,
Windows,Other ‘internal’ walls
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 49
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To model a single zone:
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 50
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1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
External Wall : Convenient notations
!"#$%&"'(%& )&*(*'+$"& =1ℎ/ =
10"#$%&"'(%& "#$12"'(#$
!'3&)4+5 )&*(*'+$"& =1
0'3&)4+5 "#$12"'(#$
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 51
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1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
External Wall : Convenient notations
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 52
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Ceilings – from a modeling perspective
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
“ We are walls too”
- Ceilings (since forever)
“..so are we..”
- Floors
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 53
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1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
Ceilings (..floors..internal walls..) -
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 54
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Windows (little to no thermal mass – only thermal resistance)
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 55
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Plenums – from a modeling perspective
Tp
Tz
1/Up
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 56
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RC modeling methodology
1. All exterior walls are combined into a single exterior wall.a. External boundary condition: Outside air temperature, Incident solar irradiation.
2. Windows/doors (without thermal mass) – Resistive element.
3. Ground and ceiling with appropriate boundary conditions.a. Another zone, ground temperature, outside temperature, plenum.
4. Internal walls for adjacent zones, and/or partitions.
5. Inputs:a. Heat gains to the zone temperature,
b. Solar irradiance, c. All boundary temperatures
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 57
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1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
Gray box modeling: “RC-Networks”
Every surface is a ‘RC’ branch in the network
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 58
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1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
Every surface is a ‘RC’ branch in the network
Branch heat balance equations [3R2C]
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 59
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1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
Every surface is a ‘RC’ branch in the network
Zone heat balance equation
External Wall Ceiling
Internal Wall
Floor
Windows Heat Gains/Losses
Zone AirThermalmass
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 60
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1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
Gray box modeling: “RC-Networks”
All the heat balance equationsBraches + zone temperature
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 61
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1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
Gray box modeling: “RC-Networks”
States : All nodes of the network except boundary nodes
Inputs: All boundary conditions and heat gains.
Parameters: The resistances/conductances and capacitances
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 62
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1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
Gray box modeling: “RC-Networks”
Inputs:1. Disturbances : Non-manipulated variables2. Control: Manipulated variables
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 63
Pro(gramming) Tip ! : Convention to order control inputs at the end of the input vector
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A closer look at the heating/cooling input
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 64
Assuming return air temperature is the same as zone air temperature.
Mass flow rate Supply air temperature
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Zone heat balance equation
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 65
+ #$%& '&,)*+ (-$%& − -/)
Inputs: All boundary conditions and heat gains.
#$%&, -$%&
1 = 31 + 45
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Zone heat balance equation
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 66
+ #$%& '&,)*+ (-$%& − -/)
Model has become non-linear (bi-linear) !
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Modeling complexity depends on the purpose
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 67
Lets say you had to model this one zone on the second level of the building
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Modeling choices
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 68
1. Does every internal wall require its own RC branch ?
2. What about windows which maybe the same material but face different directions ?
3. Do doors have thermal mass ?4. How do you compute the total internal
heat gain at any time ?
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Recall: Single zone: Heat Gains
1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
1. Solar Irradiance Qsol :
2. Solar radiation transmitted
through windows Qsol,t:
3. Radiative internal heat gain Qrad:
4. Convective heat gain Qconv:
5. HVAC heat gain QHVAC or Qsens
6. Boundary temperatures:
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 69
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Heat gain from occupants
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Heat gain from occupants
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Single zone: Heat flows
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 72
Ambient airtemperature
Solarirradiance Zone Air
!"
Envelopegains
Interior Structure
Furnishings
ConvectiveConvective
Radiative
Radiative
Convective
Radiative
Cooling load
Internalgains
Solar gains
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Modeling choices
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 73
1. Does every internal wall require its own RC branch ?
2. What about windows which maybe the same material bur face different directions ?
3. Do doors have thermal mass ?4. How do you compute the total internal
heat gain at any time ?5. How are wall temperatures and
incident solar irradiance measured ?
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Measuring solar irradiance.
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 74
Designed to measure the solar radiation flux density (W/m2)
Pyranometer
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Alternate representation
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Alternate representation
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Energy CPS modeling assignments
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 79
4 perimeter zones1 interior zone
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Module 1 modeling assignments
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 80
• Assignment 2:• Create the RC model structure.
• Assignment 3:• Nominal values of model parameters.• Model structure in Matlab• Training data set.
• Assignment 4:• Parameter tuning in Matlab.• Model validation.
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1/Ugw
1/Ugi
1/Ugo
Cgo
Cgi
Tgo
Tg
Tgi
Tz
Q.rad,e
1/Uei1/Uew1/Ueo
Ceo Cei
Ta
Teo Tei
Q.sol,e
Q.solt/2
1/Uci
1/Ucw
1/UcoCci
Cci
Ta
Q.sol,c
Q.rad,c
Ta
Q.conv + Q.
sens
1/Uii 1/Uiw 1/Uio
Cii Cio
Tci
Tco
1/Uwin Tii Tio
Q.solt/2
Q.rad,g
[ExternalWalls]
Ti
[Ceiling]
[Floor]
[InternalWalls]
[Windows]
How to find the values of the parameters ?
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 83
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Next lecture:
• Intro to whole building simulation.•White-box vs Grey-box• EnergyPlus tutorial and demo• working with IDF files
Principles of Modeling for CPS – Fall 2018 Madhur Behl [email protected] 84