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Goal intervals in dynamic multicriteria problems

Goal intervals in dynamic multicriteria problems . The case of MOHO. Juha Mäntysaari. 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

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Goal intervals in dynamic multicriteria problems

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  1. Goal intervals in dynamic multicriteria problems The case of MOHO Juha Mäntysaari

  2. 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

  3. 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

  4. Tout T q d Q Dynamics of the house Q(t)=Q(t-1)+Dtq(t-1)-d(t-1) where d(t) = aDt(T(t) - Tout(t)) Q(t) = T(t)/C, (b = 1/C) Þ T(t) = T(t-1) +bDtq(t-1) -abDt(T(t-1) - Tout(t-1)) Units: [Q] = kWh, [a] = kW/°C, [C] = kWh/°C

  5. Example houses House 2 House 1

  6. Tout p a, b Tmin£T£ Tmax 0 £ q £ qmax d Tref Q Information summary

  7. Goal models 1. Hard constraint (pipe is hard) 2. Soft constraints (pipe is soft)“Interval goal programming” 3. Hard constraint with a goal inside(pipe with a goal)

  8. Hard constraints

  9. Soft constraints

  10. Hard constraints with a goal

  11. Goal models (summary) 1. Hard constraints 2. Soft constraints 3. Hard constraints with a goal

  12. MultiObjective Household heating Optimization (MOHO)

  13. 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 e-constraints method (upper bound must be active in order to succeed)

  14. Example: House 2 (1/4) Minimized heating costs:

  15. Example: House 2 (2/4) Decreased costs by 5 %

  16. Example: House 2 (3/4) Decreased again by 5 %

  17. Example: House 2 (4/4) And again by 5 %

  18. 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

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