Energy Efficiency

, Volume 11, Issue 6, pp 1411–1432 | Cite as

A sensitivity analysis of a cost optimality study on the energy retrofit of a single-family reference building in Portugal

  • Sérgio Tadeu
  • António Tadeu
  • Nuno Simões
  • Márcio Gonçalves
  • Racine Prado
Original Article


Improvement of the energy efficiency of residential buildings must ensure compliance with cost optimality criteria, assuming a specific lifespan of the building. At the same time, the energy retrofit of buildings ought to preserve their intrinsic architectural and heritage value. Portuguese residential buildings constructed before 1960 did not follow any energy efficiency rules. They represent 29% of the housing stock in the country and there is a high potential for increasing their energy efficiency. However, it costs more to implement envelope energy efficiency measures through retrofitting works than to provide for them in new buildings. An evaluation based on cost optimality criteria should therefore be performed. This work evaluates the energy performance of a Portuguese reference building typical of the pre-1960 building stock for different thicknesses of thermal insulation retrofit solutions (roof, facade, and ground floor) and systems. The study describes a sensitivity analysis that took a range of climate data, intervention costs, energy prices, discount rates, and energy needs into account. An energy needs factor dealt with the occupants’ habits and the effective reduction of energy consumption compared with the estimated energy needs.


Cost optimality Energy retrofit Energy efficiency Residential buildings 




air conditioner


General Directorate for Energy and Geology


domestic hot water


Energy Certification System


electric heater


Energy Performance in Buildings Directive


energy performance certificates


expanded polystyrene


European Union


financial perspective


gas boiler


glass fiber


gas water heater


heating degree days [°C day]


heat pump


expanded cork board


expanded cork board (medium density)


Survey on Energy Consumption in the Domestic Sector


National Statistics Institute


macroeconomic perspective


mineral wool


net present value


primary energy


primary energy conversion factor


polyurethane foam


value-added tax


extruded polystyrene



linear thermal transmittance [W/m°C]

Ci, j

annual costs [€]


discount factor

Eh, k

heating energy needs [kWh/(m2 year)]

Ew, k

domestic hot water energy production [kWh/(m2 year)]

Fs, j

glazing obstruction factor associated with the orientation j

GHGi, j

carbon emission cost [€]


monthly solar energy on a south vertical surface [kWh/(m2 month)]


heat loss to elements in contact with the ground [W/°C]


heat loss to unheated spaces and to adjacent buildings [W/°C]


heat loss to the outside [W/°C]

Htr, i

overall transmission coefficient of heat transfer [W/°C]

Hve, i

overall coefficient of heat transfer from ventilation [W/°C]


initial investment costs [€]


number of systems


conversion factor between final energy and primary energy


height of ceilings [m]

Qint, i

internal solar gains [kWh/year]

Qsol, i

glazing solar gains [kWh/year]

Qtr, i

heat transfer coefficient by transmission [kWh/year]

Qve, i

heat transfer coefficient by ventilation [kWh/year]


nominal rate of renewal of indoor air in the heating season [h−1]

Vτ, j

residual value associated with each measure [€]


function of thermal inertia of the building class [W/°C]

fh, k

percentage of the energy needs for space heating [%]

fw, k

percentage of the energy needs DHW [%]


average internal thermal gain per area [W/m2]

ηH, gn

gain utilization factor




area [m2]


carbon dioxide


solar factor of the glazing


thermal resistance [(m2 °C)/W]


thermal transmittance [W/(m2 °C)]


orientation factor


global cost [€]


duration of the heating season [months]


number of measures


real discount rate [%]


thickness [m]


thermal conductivity [W/(m °C)]


calculation period [years]



vertical opaque envelope




space heating


maximum requirement


cost-optimal solution








corresponds to the each orientation


single energy source/system


domestic hot water



The first author is grateful for the financial support provided by the Ciência sem Fronteiras program and acknowledges the support of Conselho Nacional de Desenvolvimento Científico e Tecnológico through doctoral degree grant 237489/2012-0 and Fundação de Amparo à Pesquisa do Estado de São Paulo through grant PIPE—2016/00880-9 (Brazil). This research work has also been supported by the Operational Programme for Competitiveness and Internationalization (COMPETE 2020, Portugal 2020), through the European Regional Development Fund under research project POCI-01-0247-FEDER-003408 (Slimframe PV & Cork Skin).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil Engineering Construction (PCC) – Escola PolitécnicaUniversity of São PauloSão PauloBrazil
  2. 2.ITeCons - Institute for Research and Technological Development in Construction SciencesCoimbraPortugal
  3. 3.ADAI – LAETA, Department of Civil Engineering, FCTUCUniversity of CoimbraCoimbraPortugal

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