Comfort as a synthesis utility function
to optimize energy for space
conditioning in buildings
AUTHORS:
Afef DENGUIR, François TROUSSET, Jacky MONTMAIN
LGI2P – Ecole des Mines d’Alès
Le projet RIDER a pour objectif de développer un système d’information
innovant fournissant les fonctions nécessaires à l’obtention d’un niveau
d’optimisation intermédiaire, situé entre les dispositifs existants au niveau d’un
bâtiment simple et ceux du gestionnaire du réseau de distribution électrique
Introduction & Problematic (1)
Total Building’ energy consumption accounts for about 40% of total energy demand
Building’s energy consumption
allocation in Europe
7%
conditioning
11%
hot water
lighting
25%
57%
other
Need of a more efficient building’s energy management
2
Introduction & Problematic (2)
A better energy management can be realized
Today
Optimizing the configuration of the conditioning units (GAT – General Air
Treatment --, Heating exchanger) w.r.t the building specificities
The optimization problem is seen as a control-command issue
Advantage
For one given building, precise optimization routines can be computed
Drawbacks
The computed optimization routines are specific to the considered building
The implementation is expensive in term of time and resources
The solution is not flexible w.r.t the system changes
Does not match the RIDER project requirements
which needs a system independent solution
3
Introduction & Problematic (3)
Our approach
To base the optimization process on the thermal comfort notion rather than
temperature which allows the conditioning units abstraction
To reason with an aggregation function
To readjust setpoints
To conceive conditioning units control rules based on qualitative recommendation
rather than precise numeric models
+ System independent solution
- Lack of precision compared to the control/command results
4
Optimization & thermal comfort
The thermal comfort is a multidimensional as well as a subjective concept
Fcomfort (Ta, Tr , Me,Va, Ci, Hy ) where
Ta : ambiant temperature (°C)
Hy : air humidity (%)
Tr : radiant temperature (°C)
Va : air velocity (m/s)
Ci : clothing index (1 clo = 0.155 m 2 .°C/W)
Me : metabolic rate (1 met = 58.2 w/m 2 )
Energy optimization formalization
min Cost (δ Ta, δ Hy , δ Tr , δ Va, δ Ci, δ Me)

 Fcomfort (Ta + δ Ta, Hy + δ Hy , Tr + δ Tr ,Va + δ Va, Ci + δ Ci, Me + δ Me) ≥ Fcomfort *
max Fcomfort (Ta + δ Ta, Hy + δ Hy , Tr + δ Tr ,Va + δ Va, Ci + δ Ci, Me + δ Me)

Cost (δ Ta, δ Hy , δ Tr , δ Va, δ Ci, δ Me) ≤ Cost *
5
Thermal comfort as statistical model
The PMV (Predicted Mean Vote) and PPD (Predicted Percentage Dissatisfied) indexes are the most
used statistical models for the thermal comfort. [Fanger, 1972] [ISO 7730, 1995]
The PMV index is based on a voting process that concerns the thermal sensation of 1300 persons.
PMV = 0,303 exp ( −0,036 M ) + 0,028 *
( M − W )



−3
 −3,05 10 * 5733 − 6,99 * ( M − W ) − pa 



 −0.42 * ( M − W ) − 58,15



−5
 −1,7 10 * M ( 5867 − pa )

4
4 

−8


 −0,0014 * M * ( 34 − ta ) − 3,96 10 f cl ( tcl + 273) − ( tr + 273)  


 − fcl hc ( tcl − ta )

PPDISO 7730 = 100 − 95 exp ( −33,53 10−3 PMV 4 − 21,79 10−2 PMV 2 )
+ Advantages
A reusable model
Capture the subjectivity and the uncertainty
related to the thermal comfort
- Drawbacks
The thermal comfort is intuitively related to a
preference model
Semantic of interactions
A non semantically explainable model
Complex to solve
The contribution of one criterion is not
explicit
6
Thermal comfort as preferential model
The preferences modeling is based on an overall utility function U which allows the definition of a weak
order relationship among alternatives.
U (Ta , Tr , M e , Va , Ci , H y ) ∈ [ 0,1]
'
'
'
'
( xTa ,..., x H y ) ≻ ( xTa
,..., x Hy
) iff U ( xTa ,..., x Hy ) ≥ U ( xTa
,..., x Hy
)
The Krantz et al. model [Krantz et al., 1971] (MAUT)
U (Ta ,..., Hy ) = g ( u Ta (Ta ),..., u Hy ( Hy ))
where
attributes are independent
and weakly separable
Aggregation function
g :[0,1] n → [0,1], g ր if
Elementary utility function
u i ( xi ) ∈ [ 0,1] , i ∈ {Ta , Tr , M e , Va , Ci , Hy }
+ Advantages
Semantically interpretable
Preferential interactions can be modeled by
fuzzy integrals
- Drawbacks
To have a generic model, statistical
techniques have to be applied in order to
identify elementary utilities.
7
Our approach of the thermal comfort modeling
Statistical
Preferential
FComfort = 100 − PPD(Ta, Tr , Me,Va, Ci, Hy )
FComfort = g (uTa (Ta),..., uCi (Ci ))
Advantages
+ Reusable
+ Captures subjectivity and uncertainty
+ Interpretable
+ Facilitates the resolution issue
Drawbacks
- Non interpretable
- Complex
- Not all preferential models are reusable
Used formalism to model the
thermal comfort with aggregation
function g
Used to identify the elementary
utilities
Choquet integral
Semantic reasons
n
n
U = Cµ (u1 , u2 ,..., un ) = ∑(u(i) − u(i−1) ).µ( A(i) ) = ∑∆µ(i ) .u(i )
i =1
0 ≤ u(1) ≤ … ≤ u( n ) ≤ 1
i =1
{
A( i ) = c( i ) ,.., c( n )
}
Interpretability
Preferential interactions
Simplex linearity
8
How identifying the aggregation operator?
Separability
.
∀xi , xi' , y N \i , y N' \i ( xi , y N \i )≻( xi' , y N \i ) ⇔ ( xi , y N' \i )≻( xi' , y N' \i )
Weakly difference independency
∀xi , yi , zi , wi υ ( xi , t N \i ) − υ ( yi , t N \i )≻ *υ ( zi , t N \i ) − υ ( wi , t N \i ) then
υ ( xi , sN \i ) − υ ( yi , sN \i )≻ *υ ( zi , sN \i ) − υ ( wi , sN \i )
Macbeth-like approach
construct the value function on attribute i by asking questions directly regarding the preference
of the DM on the set Xi (independently on the values on the other attributes)
If attributes do not check weakly difference independency…
commensurateness
We extended the Labreuche’s method [Labreuche, Eusflat 2011] to identify elementary
utilities and Choquet parameters without any commensurateness
assumption
.
9
Grabisch and Labreuche - FSS 2003
When attributes are commensurate with each other:
2 reference levels which refer respectively to an unacceptable (
Good option level ( GN ) have to be identified
ON ) option level and a
Based on the 2 identified reference levels; the elementary utility function is approximated
by an affine function for each attribute
υi ( xi ) =
U ( xi , ON / i ) − U (ON )
U (Gi , ON / i ) − U (ON )
A capacity is computed for each commensurate subset of attributes.
∀A ⊆ N , ν ( A) =
U (GA , OA ) − U (ON )
U (GN ) − U (ON )
The Choquet integral can then be defined
10
Labreuche - EUSFLAT 2011
Identifying subsets of attributes S ⊆ N that are commensurate with each other
2 reference levels which refer respectively to an unacceptable (0i) option level and a
Good option level (Gi) have to be identified. The objective is to build an option vector
where all attributes’ values have the same utility:
i* ∈ S , Oi* / υi* (Oi* ) = 0 then ∀k ∈ S / {i}, Ok / υk (Ok ) = 0
(Oi ) )
=Ok
Do it for each S and normalization
U (GA , OA ) − U (ON )
∀A ⊆ S , ν ( A) =
U (GS , ON / S ) − U (ON )
11
PPD approximation by Choquet integrals (1)
MAUT and Labreuche assumptions verification:
Separability among attributes
Monotony of elementary utility functions ∀i,
PPD(Ta,Va )
PPD Definition domain
ui ր in R
PPD(Ta, Hy )
Ta ∈ [10,30°] , Tr ∈ [10, 40°] , Hy ∈ [ 0,100% ] ,
Va ∈ [ 0,1m / s ] , Me ∈ [ 0.8, 4met ] , Ci ∈ [ 0, 2clo ]
Approximation of local zones of the PPD by a Choquet integral
12
PPD approximation by Choquet integrals (2)
Ta, Va, Hy are the only 3 thermal comfort attributes that can be controlled
We supposed that:
Ci= 0.7 Clo (pant/shirt) [ISO 7730, 1995]
Me = 1.2 Met (Average metabolic rate of administrative workers) [ISO 7730,1995]
Moreover,
Attributes Interactions with Tr are not preferential ones;
Choquet integral can not model these interactions
Construction of local tridimensional
Choquet integral for different Tr values
The thermal comfort approximation is the result of a fuzzy interpolation among the computed
integrals for a fixed Tr values.
13
Thermal comfort models
and comfort based control rules
Deduce intuitive control rules which is possible to approximate their gains.
M 3 :Ta ∈ [ 22, 28] , Hy ∈ [50,100] ,and Va ∈ [ 0.25,1 ]
[
if Hy ր then Fcomfort ց because uHy ց and δ Fcomfort = ∆µ Hy
22, 28]×[50,100]×[ 0.25,1 ]
.
du Hy
dHy
.δ Hy
14
Examples of Comfort based control rules
M 4 :Ta ∈ [ 22,27 ] , Hy ∈ [50,100] ,and Va ∈ [ 0.25,1 ]
uD ( D)
u Hy ( Hy )
1
pD = −1.34
1
0
0.25
1
uTa (Ta )
D (m/s)
1
pHy = 0.02
pTa = −0.2
0
0
50
100
∀ D ∈ [ 0.25,1] , if D ց then Fcom fort ր ,
Hy (%)
27
Ta (°C)
δ Fcom fort ≈ ∆ µ D . p D .δ D
∀ H y ∈ [50,100 ] , if H y ր then Fcom fort ր ,
∀ T a ∈ [ 22, 27 ] , if T a ց then Fcom fort ր ,
22
δ Fcom fort ≈ ∆ µ H y . p H y .δ H y
δ Fcom fort ≈ ∆ µ T a . p T a .δ T a
15
Some optimization issue using the thermal
comfort model (1)
Control: To adjust the thermal sensation of a non satisfied office occupant and maintain at
the same time the required comfort level of his neighboring offices.
Assumptions: For a same comfort level, the more Ta is small the less costly maintaining the
required comfort is.
min δ Ta (k )
Comfort (k ) = F (Ta + δ Ta (k ), Hy (k ),Tr (k ), Va + δ Va (k ), Ci, Me) = Comfort *


δ Ta (k ) ≥ 0
∀k ' ≠ k , Comfort (k ') ≥ consigne(k ')
A new setpoint can than be computed
{
}
Arg min (Ta, Hy , Tr ,Va , Ci , Me) ∈ S k / F (Ta + δ Ta , Hy, Tr ,Va + δ Va, Ci, Me) = Comfort *
Ta
Where :
*
*
S k corresponds to areas that provide the comfort level Comfort *
16
Some optimization issue using the thermal
comfort model (2)
0.02
P1
0.01
0.02
P2
0.01
0.3
1
0.833
0.1
0.3
uD ( D)
P3
0.01
0.01
0
0.25
0.375
1
D (m/s)
0.04
P1 occupant is
unsatisfied
Comfort(1) = 70%
Tr(1)=25 C, Hy(1)=50%
Ta(1)=22.1 C, D(1)=1m/s
Confort*(1) = 85%
ր
ց
Comfort*(1) = 85%
Tr(1)=25 C, Hy(1)=50%
Ta(1)=21.7 C, D(1)=0.375m/s
Comfort by 15%
Cost by 9.83%
The cost is proportional to the product TA * D
17
Some optimization issue using the thermal
comfort model (3)
Adaptation: To consider office’s orientation (north, south) and their sunlight exposure
during the day. We note Tr (k )[t ] the radiant temperature in the time of the office k .
Assumptions: The more an office adaptation is small, the less costly maintaining the
required comfort is.
min ∑ α k . δ Ta (k ) ,α k = ∑
α
k
k '∈voi sin age kk '

∀k , Comfort (k ) = F (Ta + δ Ta (k ), Hy (k ), Tr (k )[t ],Va + δ Va(k ), Ci, Me) ≥ consigne(k )
Where : α kk ' is the exchanging heat ratio between offices k and k’.
It consists on minimizing the total offices temperature variations among 2
different sunlight exposures without including specific building details.
Anticipation: corresponds to seasons changes ( Tr (k )[t ] ) and the occupation rate variation
( Me (k )[t ] ). For instance, it consists on decreasing the comfort setpoint comfort* when there
is no one in the building.
18
Some optimization issue using the thermal
comfort model (4)
3

min
α k . δ Tak ,
∑

k =1

∀k = 1..3, C = F (Ta + δ Ta , Hy , Tr [t ], D + δ D , Ci, Me) ≥ C *

k
k
k
k
k
k
k
k
*
 C1 = 50% 
 α1 = 0.63 




tq,  α 2 = 0.43  et  C2* = 90% 
 α = 0.46 
 C * = 80% 
 3

 3

Tr1(°C)
25
23
21
8
14
17.5
20
t(h)
Tr2(°C)
25
22
20
8
14
17.5
20
t(h)
 Ta = 18.6478 
 Ta = 26.1836 
 Ta = 21.479 
P1  1
, P2  2
, P3  3



D2 = 1
 D1 = 0.375 [8,14 h]

[8,14 h]
 D3 = 0.375 [8,14 h]
Tr3(°C)
24
 Ta = 21.3648 
 Ta = 17.8199 
 Ta = 26.4775 
P1  1
, P2  2
, P3  3



 D1 = 0.375 [14,17 h30]
 D2 = 0.25 [14,17 h30]
 D3 = 0.1875 [14,17 h30]
22
20
8
14
17.5
20
t(h)
 Ta = 17.6491
 Ta = 25.9316 
 Ta = 23.7941
P1  1
, P2  2
, P3  3



 D1 = 0.1875 [17 h30, 20 h]
 D2 = 0.239 [17 h 30, 20 h]
 D3 = 0.2168 [17 h30, 20 h]
19
Some optimization issue using the thermal
comfort model (5)
Without considering Tr variations
TotalCost (12h) = 24 446 unit
When considering Tr variations
TotalCost (12h) = 21778 unit
Monitoring Tr
Decreasing the cost by 10.9%
20
Notre approche: Vue globale
RIDER Enhancement Services
Context data
Aggregated performance based reasoning
Set-points
User friendly interface
Hybrid model based thermal process enhancement
Historical data
Quantitative
model
Command
Qualitative
model
Improved
command
Database
Thermal kits
measurements
21
Modèle hybride pour l’amélioration thermique
Objectif
Assurer une conduite adaptative (par rapport
aux connaissances disponibles) et efficiente du
processus thermique afin de réaliser les
consignes personnalisées.
Modèle qualitatif: Implémente des stratégies et règles d’amélioration
Modélisation
Actions
Représentation événementielle
de la loi de commande
ua (t )
 t0 
 
c(a) =  ∆y 
 ∆p 
 
Facteurs d’influence (calculés sous des hypothèses)
Appris sur un modèle mathématique simplifié
Performances
Critères d’évaluation des signaux de sortie
Setpoint
Tr (t)
TCTA (t )
≈Coût
t0
Composante
du confort
t flex
trép
Déjà appris du modèle du confort
 comfortr 


perf r =  Coûtr 
 Flexibility 

r 
t*
Flexibilité
22
Modèle hybride pour l’amélioration thermique
Objectif
Assurer une conduite adaptative (par rapport
aux connaissances disponibles) et efficiente du
processus thermique afin de réaliser les
consignes personnalisées.
Solveur
Modèle qualitatif: Implémente des stratégies et règles d’amélioration
Règles
d’influences
Chercher une amélioration sur la commande
Commande
Chercher une
amélioration sur ∆y
oui
∃
non
Chercher une
amélioration sur ∆p
oui
∃
non
Heuristique: Priorité aux paramètres qui
ont le plus grand rapport gain/risque
Cherche une
amélioration sur t0
Commande
améliorée
Amélioration du modèle qualitatif
Amélioration multi-pièces: définition des agrégations sur les recommandations.
23
Modèle hybride pour l’amélioration thermique
Objectif
Assurer une conduite adaptative (par rapport
aux connaissances disponibles) et efficiente du
processus thermique afin de réaliser les
consignes personnalisées.
Connaissance
Modèle quantitatif: Gère la connaissance sur un bâtiment
Cas
Evénement modélisant un changement
d’états du processus thermique
Représentation
de la connaissance
∀s ∈ CASE , s = (Tes , Tinit s , Tend s )
LB : CASE → CMD
CASE
CMD
24
Modèle hybride pour l’amélioration thermique
Objectif
Assurer une conduite adaptative (par rapport
aux connaissances disponibles) et efficiente du
processus thermique afin de réaliser les
consignes personnalisées.
Gestion
Modèle quantitatif: Gère la connaissance sur un bâtiment
Consignes
Données
du contexte
Données
de l’historiques
Chercher les cas
les plus proches
Apprentissage de la commande
Commandes les
plus proches
Evaluer et choisir la commande
la plus performante
Commande
Base des données
Amélioration du modèle quantitatif
Introduction d’une stratégie de pénalisation des échecs d’amélioration
Implémentation d’une fonction de normalisation des données,
Plus de densité sur les données d’apprentissage.
Maitrise de la variabilité de la température extérieur.
25
Modèle hybride pour l’amélioration thermique
Objectif
Assurer une conduite adaptative (par rapport
aux connaissances disponibles) et efficiente du
processus thermique afin de réaliser les
consignes personnalisées.
Exemple d’amélioration: amélioration sur une pièce
Jour 0
Gain en coût
∆ Confort*
>5%
Jour 1
Jour 2
Jour 3
Jour 4
Jour 5
14.53%
2.51%
4.81%
3.72%
0.59%
<0.5%
Quelques résultats: amélioration
sur une pièce : gains en coût entre 7,25% et 31,01%.
sur plusieurs pièces : gains en coût entre 12.30% et 24.10%.
26
Conclusion & Perspective
Reasoning with an aggregation function modifies (shifts) the energy
management thinking strategy. It is used to:
recommend less costly setpoints for space conditioning.
identify qualitative rules for the thermal comfort regulation.
The way to reach the computed setpoints can also be optimized. For this
we intend to use qualitative model in order to provide controlling
recommendation to the energy manager.
27