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S ystemsAnalysis LaboratoryHelsinki University of Technology

Goal intervals in dynamic multicriteria problems

The case of MOHO

Juha Mäntysaari

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Decision problem of space heating consumers

• Under time varying electricity tariff space heating consumers can save in heating costs by– Storing heat in to the house during low tariff hours

– Trading living comfort to costs savings

• A dynamic decision problem

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Space heating problem

• Space heating consumers try to– MIN “Heating costs”

– MAX “Living comfort”

subject to • Dynamic price of the electricity

• Dynamics of house

• Other (physical) constraints

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Dynamics of the house

Q(t)=Q(t-1)+tq(t-1)-d(t-1)

where

d(t) = t(T(t) - Tout(t))

Q(t) = T(t)/C, ( = 1/C)

T(t) = T(t-1) +tq(t-1) -tT(t-1) - Tout(t-1))

Units: [Q] = kWh, [] = kW/C, [C] = kWh/C

T

Q

Tout

q d

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Example houses

House 1 House 2

Type of the house Doublefamily house singlefamily house

Building material lekatermi with a brick cover wood

Floor area [m2] 170 139

Number of floors 2 1

Heating equipment ceiling and floor heating, radiators ceiling and floor heating

[kWh/C] 0.170 0.077

[C/kWh] 0.038 0.380

Heating power [kW] 9.0 8.7

House 1 House 2

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Information summary

Q

dTref

q qmax

Tout p

TminTTmax

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Goal models1. Hard constraint (pipe is hard)

3. Hard constraint with a goal inside(pipe with a goal)

2. Soft constraints (pipe is soft)“Interval goal programming”

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Hard constraints

Min p q

s e T T

i ii

N

i i

q

0

1

0

. . ,

,

maxT iDynamics of house, i

T T

q q i

imin

0 N

i imax

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Soft constraints

Min p q s s

s e T T s

T T s

i i i i i ii

N

i i i

i i i

q s s, ,

min

max

. . ,

,

,

0

1

0

0

0

i

iDynamics of house, i

T T

q q i

0 N

i imax

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Hard constraints with a goal

Min p q s s

s e T T s s

T T

i i i i i ii

N

i iref

i i

i i

q s s, ,

max

. . ,

,

,

0

1

0

0

i

T iDynamics of house, i

T T

q q i

imin

0 N

i imax

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Goal models (summary)

3. Hard constraints with a goal

1. Hard constraints

2. Soft constraints

Min p q

s e T T

i ii

N

i i

q

0

1

0

. . ,

,

maxT iDynamics of house, i

T T

q q i

imin

0 N

i imax

Min p q s s

s e T T s

T T s

i i i i i ii

N

i i i

i i i

q s s, ,

min

max

. . ,

,

,

0

1

0

0

0

i

iDynamics of house, i

T T

q q i

0 N

i imax

Min p q s s

s e T T s s

T T

i i i i i ii

N

i iref

i i

i i

q s s, ,

max

. . ,

,

,

0

1

0

0

i

T iDynamics of house, i

T T

q q i

imin

0 N

i imax

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S ystemsAnalysis LaboratoryHelsinki University of Technology

MultiObjective Household heating Optimization (MOHO)

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Idea of MOHO• Minimize heating costs using hard lower and

upper bounds for indoor temperature– The case of hard constraints

• Ask: “How many percents would you like to decrease the heating costs from the current level?”

• Solve again trying to achieve the desired decrease in cost by relaxing the indoor temperature upper bound– The -constraints method (upper bound must

be active in order to succeed)

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Example: House 2 (1/4)

Minimized heating costs:

17.0

18.0

19.0

20.0

21.0

22.0

23.0

24.0

25.0

26.0

27.0

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Tem

per

atu

re [

°C]

Min

Max

Temperature

Indoor temperature for House 5CLICK HERE TO RETURN

OptimalCost Energy

FIM / day kWh / dayDaytime 20.63 37.2Nighttime 4.85 24.7Total 25.48 62.0

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Example: House 2 (2/4)

Decreased costs by 5 %

17.0

18.0

19.0

20.0

21.0

22.0

23.0

24.0

25.0

26.0

27.0

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Tem

per

atu

re [

°C]

Min

Max

Temperature

Indoor temperature for House 5CLICK HERE TO RETURN

OptimalCost Energy

FIM / day kWh / dayDaytime 18.58 33.5Nighttime 5.63 28.7Total 24.21 62.3

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Example: House 2 (3/4)

Decreased again by 5 %

17.0

18.0

19.0

20.0

21.0

22.0

23.0

24.0

25.0

26.0

27.0

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Tem

per

atu

re [

°C]

Min

Max

Temperature

Indoor temperature for House 5CLICK HERE TO RETURN

OptimalCost Energy

FIM / day kWh / dayDaytime 16.54 29.9Nighttime 6.45 32.9Total 23.00 62.8

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Example: House 2 (4/4)

And again by 5 %

17.0

18.0

19.0

20.0

21.0

22.0

23.0

24.0

25.0

26.0

27.0

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Tem

per

atu

re [

°C]

Min

Max

Temperature

Indoor temperature for House 5CLICK HERE TO RETURN

OptimalCost Energy

FIM / day kWh / dayDaytime 14.52 26.2Nighttime 7.33 37.4Total 21.85 63.6

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Summary

• Model and parameters of the house identified• Depending on the definition of the “living

comfort” different multicriteria models can be used

• Benefits of the simplified approach:– Only bounds of the indoor temperature asked

– Comparison and tradeoff only with heating costs