Global cost calculation

In the methodology, the main objective, the global cost, is calculated according to net-present value approach, which is a financial analysis technique where all future costs and benefits are discounted to the present to obtain a common reference for comparing competing alternatives in a long-term perspective (Fuller and Petersen, 1995).

There are numerous types of costs occur during service life of a building. In this research however, cost breakdown includes long-term energy costs due to HVAC operation, water heating and lighting energy consumption; water costs due to HVAC system water use and occupancy hot water use; ownership costs due to buying, installing, maintaining and disposing building envelope material and/or HVAC system equipment.

Moreover, if a renewable system alternative is considered, its ownership cost is also added to equipment cost category and energy cost benefits are reflected in energy category. The calculation time period is set by the designer.

All the cost elements of the equation are expressed in net-present value (NPV) and the main formula is given in equation 4.3:

𝐺𝐶 = ∑ 𝑁𝑃𝑉^𝑛_{1 𝐸𝑛𝑒𝑟𝑔𝑦}+ ∑ 𝑁𝑃𝑉^𝑛_{1 𝑊𝑎𝑡𝑒𝑟}+ ∑ 𝑁𝑃𝑉^𝑛_{1 𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙} + ∑ 𝑁𝑃𝑉^𝑛_{1 𝐸𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡} (4.3) The financial calculation are carried out from and user perspective therefore all the costs are the prices paid by the customer including VAT and charges.

Net present value of energy cost

Net present value of energy cost is a recurring annual cost that changes from year to year at a constant price escalation rate, and it is calculated for each energy source that is consumed in the building according to the algorithm illustrated in Figure 4.6:

Read energy

Figure 4.6 : NPV energy cost calculation algorithm.

The NPV cost of each energy source is calculated separately based on the annually recurring cost with an escalation rate formula given in equation 4.4:

𝑁𝑃𝑉_{𝐸𝑛𝑒𝑟𝑔𝑦} = 𝐸₀(1 + 𝑒_𝑒)

(𝑑 − 𝑒_𝑒)[1 − (1 + 𝑒_𝑒

1 + 𝑑)^𝑛] (4.4)

Where,

𝑁𝑃𝑉_{𝐸𝑛𝑒𝑟𝑔𝑦} : Net present value of energy cost for each energy source, 𝐸₀ : Annually recurring energy cost at base-date price,

𝑛 : Study period (number of years which energy consumption recurs), 𝑑 : Real discount rate,

𝑒_𝑒 : Real constant price escalation rate for energy.

Annual energy cost for each energy source is calculated as a multiplication of annual end-use energy consumption (site energy) obtained through a yearly energy balance calculation performed by EnergyPlus simulation engine and its associated energy tariff stored in the user-created database. Energy cost includes cost due to heating, ventilation air conditioning, artificial lighting, plug loads and water heating purposes.

The real discount rate, d, is used in the formula to discount future costs to the present and is calculated based on the interest rate of an alternative investment corrected with regard to the inflation rate as given in equation 4.5,

𝑑 = 1 + D

Nominal discount rate can be estimated based on market interest rate.

Similarly, the real constant price escalation rate for energy can be calculated according to the following formula:

𝑒_𝑒 = 1 + E

1 + 𝐼𝑛𝑓− 1 (4.6)

Where,

E : Nominal escalation rate, 𝐼𝑛𝑓 : Inflation rate.

Net present value of water cost

Net present value of water cost is also a recurring cost that changes from year to year at a constant price escalation rate and it is calculated for each water end-use type according to the algorithm illustrated in Figure 4.7.

Read water

Figure 4.7 : NPV water cost calculation algorithm.

The NPV cost of each end-use type is calculated based on the annually recurring cost with an escalation rate formula given in equation 4.7.

𝑁𝑃𝑉_{𝑊𝑎𝑡𝑒𝑟} = 𝑊₀(1 + 𝑒_𝑤)

(𝑑 − 𝑒_𝑤)[1 − (1 + 𝑒_𝑤

1 + 𝑑)^𝑛] (4.7)

Where,

𝑁𝑃𝑉_{𝑊𝑎𝑡𝑒𝑟} : Net present value of water cost,

𝑊₀ : Annually recurring water cost at base-date price,

𝑛 : Study period (number of years which water consumption recurs),

𝑑 : Discount rate,

𝑒_𝑤 : Constant price escalation rate for water.

Annual water cost is calculated as a multiplication of annual water consumption obtained through building simulation and its associated water tariff. In the methodology the water cost especially focuses on water use due to HVAC system operation.

Net present value ownership of material, HVAC and renewable system equipment cost

The net-present value ownership cost of different energy efficiency measures (independent and dependent building material, HVAC or renewable system equipment) is calculated according to the algorithm illustrated in Figure 4.8.

The financial information about each material/equipment is stored in a user-created database; therefore at each optimization run, the data is read from the database and transferred to the objective function equations.

Read capital cost

Figure 4.8 : NPV material/equipment ownership cost calculation algorithm.

The algorithm is based on the NPV of initial, maintenance, replacement and scrap cost for the material/equipment life, as given in equation 4.8.

𝑁𝑃𝑉𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙/𝐸𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡 = 𝐼 + 𝑅𝑒𝑝 + 𝑀 − 𝑆 (4.8)

Where,

𝐼 : Present-value investment cost,

𝑅𝑒𝑝 : Present-value capital replacement cost, 𝑀 : Present-value maintenance cost, 𝑆 : Present-value scrap cost.

The investment costs include costs for purchasing and installing building envelope material and/or system equipment. The investment takes place in the present

therefore the net present value of the investment cost is equal to the sum of the investment costs, for each material or equipment as given in equation 4.9.

𝐼𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙/𝐸𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡= ∑ 𝐼_𝑘

𝑘

𝑗=1

(4.9)

Replacement costs occur due to shorter lives of building components than the building and hence they are required to be replaced during the building service life.

The replacement cost of a component can be considered as an extra expense equal to the initial investment cost for the component occurring when the service life of the component ends. The present value of replacement cost, which occurs at irregular or non-annual intervals, is calculated according to the formula given in equation 4.10.

𝑅𝑒𝑝𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙/𝑒𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡 = 𝑅₀ 1

(1 + 𝑑)^𝑡 (4.10)

Where,

𝑅𝑒𝑝𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙/𝑒𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡 : Present-value of replacement cost occur at year t,

𝑅₀ : Replacement cost at base-date price,

𝑑 : Real discount rate,

𝑡 : Future cash occurs at the end of year t (service life).

The building components need regular maintenance in order to remain functional during its life span and it is a recurring cost element of the GC. The equation 4.11 below is used to calculate the present-value of annual routine maintenance costs.

𝑀𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙/𝐸𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡 = 𝑀₀×(1 + 𝑑)^𝑛− 1

𝑑(1 + 𝑑)^𝑛 (4.11)

𝑀𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙/𝐸𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡 : Present-value of replacement cost occur at year t, 𝑀₀ : Annually recurring uniform maintenance cost,

𝑛 : Study period (number of years which maintenance recurs),

𝑑 : Discount rate.

Scrap cost is a one-time amount cost that occurs once at end of products service life and can include scrap value and removal cost. In this study, however, the removal cost is neglected. The base-date value of scrap cost is estimated as a user-defined percentage of the purchase price. The equation to calculate scrap value is as given below:

𝑆𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙/𝐸𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡 = 𝑆₀ 1

(1 + 𝑑)^𝑡 (4.12)

Where:

𝑆𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙/𝐸𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡 : Present-value of scrap cost occur at year t, 𝑆₀ : Salvage cost at base-date price,

𝑑 : Discount rate,

𝑡 : Future cash occurs at the end of year t (service life).

In the current study, the NPV ownership cost is calculated through two different approaches:

The change in cost due to change in the value of discrete variable with stepwise definition is calculated based on the multiplication of unit value of the variable with its current value. For example, adding insulation to a wall is calculated as the amount of insulation (m³) times unit value of the insulation (TL/m³).

On the other hand, the change in cost due to change in the value of a standard discrete variable is calculated based on the actual price of the component. For instance, while selecting a boiler, all the cost information of the equipment at that instance is directly obtained from the equipment database. By doing so, optimization algorithm can individually evaluate the economic performance of each component in the database.