**6. Calculation Models**

### *6.1. Model Developed to Calculate the Evolution of the Vehicle Fleet and its Energy Consumption*

The evolution of the vehicle fleet and the energy consumption by fuel type in the BLS is estimated from the following equations:

$$\text{Stock}\_{tfn} = \sum \text{Stock}\_{tfn-1} + V\_{tfn} \* S\_{tfn} + I\_{tfn} \* S\_{tfn} \tag{1}$$

where: *Stocktfn*−1: Remaining vehicle fleet of type *t*, using fuel *f* in year *n* − 1; *Vtfn*: Sales of vehicle type *t*, using fuel *f* in year *n*; *Itfn*: Number of imported used vehicles type *t*, using fuel *f* in year *n*.

*Stfn*: Survival percentage of vehicles type *t*, using fuel *f* in year *n*; *Sitz f n*: Survival percentage of imported used vehicles type *t* and model year z, using fuel *f* in year *n*.

$$AllStock\_n = \sum Stock\_{tfn} \tag{2}$$

*AllStockn* = Total number of vehicles in year *n*.

$$E\_t = \sum \text{Stock}\_{tfn} \* K\_{tfn} \* L\_{tfn} \tag{3}$$

where: *Et*: Energy consumption in year *n* by vehicle type *t*; *Stocktfn*: Vehicle fleet of type *t*, using fuel *f* in year *n*; *Ktfn*: Average fuel economy per kilometer travelled for vehicle type *t*, using fuel *f* by year *n*; *Ltfn*: Average annual distance travelled in kilometers by vehicle type *t*, using fuel *f* by year *n*.

### *6.2. Cost-Benefit Assessment and Mitigation Costs*

The following calculation model was used to obtain the cost-benefit and mitigation cost based on [73]:

$$CB\_{LCS-BUS} = IC\_{LCS-BUS} + OMC\_{LCS-BUS} + EC\_{LCS-BUS} \tag{4}$$

where: *ICLCS*−*BLS*: Overall incremental investment costs for all alternative measures in the LCS in present value; *OMCLCS*−*BLS*: Overall incremental costs of operation and maintenance for all alternative measures in the LCS scenario in present value; *ECLCS*−*BLS*: Overall avoided costs of energy for all alternative measures in the LCS in present value.

With:

$$IC\_{LCS-BLS} = \sum\_{i=1}^{M} \sum\_{n=1}^{P} \frac{IC\_{LCS-BLS\_{ni}}}{(1+r)^n} \tag{5}$$

where: *ICLCS*−*BLSni* : Annual incremental investment costs in relation to the implementation of the mitigation measure *i* for any year *n* in the period *P*; *n*: Year, *n* = 1, ... , *P*; *i*: Mitigating measure, *i* = 1, ... , *M*; *r*: Discount rate (10%); *P*: Analyzed period (25 years); *M*: Number of mitigation measures in LCS (21 measures).

$$\text{OMC}\_{\text{LCS-BLS}} = \sum\_{i=1}^{M} \sum\_{n=1}^{P} \frac{\text{OMC}\_{\text{LCS}-\text{BLS}\_{ni}}}{(1+r)^{n}} \tag{6}$$

where: *OMCLCS*−*BLSni* : Incremental costs of operation and maintenance for mitigating measure *i* in year *n*:

$$EC\_{LCS-BLS} = \sum\_{i=1}^{M} \sum\_{n=1}^{P} \frac{EC\_{LCS-BLS\_{ni}}}{(1+r)^n} \tag{7}$$

where: *ECLCS*−*BLSni* : Annual cumulative incremental costs of operation and maintenance (O&M) for the mitigating measure *i* accumulated in the year *n* in the period *P*:

$$\text{MCC}\_{\text{LCS-BLS}\_i} = \frac{T\mathbf{C}\_{\text{LCS}-\text{BLS}\_i}}{\mathbf{G}\mathbf{H}\mathbf{G}\_{\text{LCS}-\text{BLS}\_i}} \tag{8}$$

where: *TCLCS*−*BLSi* : Total incremental costs for the mitigating measure *i* in the LCS in present value; *GHGLCS*−*BLSi* : Total avoided GHG emissions for mitigating measure *i* in the BLS.

With:

$$TC\_{LCS-BLS\_i} = \sum\_{n=1}^{P} \left( \frac{IC\_{LCS-BLS\_{ni}}}{1+r^n} + \frac{OMC\_{LCS-BLS\_{ni}}}{1+r^n} + \frac{EC\_{LCS-BLS\_{ni}}}{1+r^n} \right) \tag{9}$$

$$\text{GHG}\_{\text{LCS}-\text{BLS}\_i} = \sum\_{f} \left( \text{ES}\_{\text{LCS}-\text{BLS}\_{fi}} \ast \text{EF}\_f \right) \tag{10}$$

where: *ESLCS*−*BLS fi*: Total avoided energy from energy carriers f (gasoline, diesel, fuel oil, NG, LPG, kerosene and electricity), use of which generates emissions in the implementation of measure i during the considered period; *EFf* : Carbon Dioxide Emission Factor from fuel *f*.
