2.4 Fiscal incentives

Under the Colombian Renewable Energy Law, new clean energy projects will receive up to 50% tax credits, but they can only be applied during the first 5 years. In this work, when the fiscal incentives are considered, it is assumed that the company will receive the 50% of the tax credit equally distributed over the first 5 years of the project. In general, investment tax credits can be calculated as

$$i = \sum\_{j=1}^{5} i\_j = \mathbf{0.5} \tag{58}$$

systems could be complex, since many variables are naturally stochastic depending mostly on the characteristic of the solar resource and the load profile of the selected location. The objective is to minimize the total cost of the solution and maximize the

Methodology for Sizing Hybrid Battery-Backed Power Generation Systems in Off-Grid Areas

As a result of the optimization problems, the following information are obtained: (1) amount of photovoltaic modules and therefore the total photovoltaic power in kWp, (2) amount of diesel generation units and the total diesel energy power in kWp, (3) amount of battery cell required and total capacity of the energy storage system in kWh, (4) energy flow in the system showing the different states of the system according to the dispatch strategy described in this work, (5) discriminated cost of each technology in terms of initial capital required and O&M cost, (6) annualized cost of energy of the best solution, and (7) amount and cost of energy

"Santa Cruz del Islote" in Bolivar, Colombia, was used as a location for the case study. This rural community is selected to evaluate the optimization model devel-

The monthly global irradiance over the horizontal and over the plane of the array was calculated using a MATLAB routine developed in this work and then compared with results obtained from Solargis. Table 1 shows the results obtained.

> Dev [%]

Jan 183.6 182.0 0.88% 201.9 198.6 1.65% Feb 175.6 174.2 0.81% 186.9 184.3 1.41% Mar 194.3 193.0 0.68% 198.5 196.2 1.14% Apr 177.2 176.1 0.65% 175 172.9 1.17% May 166.4 165.2 0.70% 160.1 158.8 0.83% Jun 161.9 160.8 0.71% 153.6 152.6 0.65% Jul 173.2 172.0 0.69% 165.3 163.9 0.84% Aug 171.7 170.6 0.65% 167.8 166.1 1.03% Sep 160.9 159.8 0.70% 162 160.1 1.17% Oct 155.8 154.4 0.91% 162.4 159.5 1.79% Nov 149.1 147.7 0.96% 160.5 157.1 2.13% Dec 161.2 159.7 0.93% 177.8 174.1 2.09% Year 2030.9 2015.3 0.77% 2071.8 2044.1 1.34%

Global tilted irradiation [kWh/m<sup>2</sup> ] Solargis

Global tilted irradiation [kWh/m2 ] calculated

Dev [%]

reliability of the supply.

DOI: http://dx.doi.org/10.5772/intechopen.88830

not supplied and LPSP.

3. Case study

oped in this work.

Table 1.

195

Meteorological input parameters (monthly).

Global horizontal irradiation [kWh/m<sup>2</sup> ] Solargis

3.1 Meteorological inputs and load profile

Global horizontal irradiation [kWh/m<sup>2</sup> ] calculated

$$i\_1 = i\_2 = i\_3 = i\_4 = i\_5 = 0.1\tag{59}$$

In a similar way, it is assumed that the effect of depreciation is equally distributed each year, and the useful life for accelerated depreciation purposes is 5 years; then

$$d = \sum\_{j=1}^{5} d\_j = 1\tag{60}$$

$$d\_1 = d\_2 = d\_3 = d\_4 = d\_5 = 0.2 \tag{61}$$

Assuming an effective corporate tax income rate of 33% and under the previous consideration, the tax reduction factor Δ for the purpose of this work is given by

$$\Delta = \frac{\mathbf{1}}{(\mathbf{1} - t)} \times \left[ \mathbf{1} - t \times \left( \sum\_{j=1}^{T1} \frac{i\_j}{(\mathbf{1} + i\_r)^j} + \sum\_{j=1}^{T2} \frac{d\_j}{(\mathbf{1} + i\_r)^j} \right) \right] \tag{62}$$

wheret is the effective corporate tax income rate, T1 is the maximum number of years to apply the investment tax credit, T2 is the useful life of the powergenerating facility for accelerated depreciation purposes (in year) = 5, i is the investment tax credit, and d is the depreciation factor expressed as percentage of investment cost over T2 year.

Fiscal incentives granted by the Colombian Act 1715 only apply to not conventional energy source installation and its components. In this way, the incentive tax factor only applies to the capital cost of photovoltaic and battery components:

$$\begin{aligned} \text{ACC}\_{\text{adj}} &= \begin{bmatrix} \left( \text{CC}\_{pv} + \text{CC}\_{\text{bat}} \right) \times \Delta + \text{CC}\_{\text{DG}} + \text{RC}\_{\text{bat}} + \text{RC}\_{\text{DG}} \end{bmatrix} \times \text{CRF}(i\_{\text{tr}}\,\text{R}) + \text{O\&M}\_{pv} \\ &+ \text{O\&M}\_{\text{bat}} + \text{O\&M}\_{\text{DG}} \end{aligned} \tag{63}$$

#### 2.5 Objective function: optimization process

The objective of this work is sizing hybrid power generation systems (solardiesel) battery-backed, in non-interconnected zones, which minimizes the total cost of the solution and maximize the reliability of supply. To minimize the total cost of the system, the following objective function is used:

$$\text{Cost} = \frac{\text{ACS}\_{adj} + \text{AC}\_{loss}}{\sum\_{t=1}^{8760} (E\_L(t) - \text{ENS}(t))} \tag{64}$$

This work aims to develop an optimization model for sizing an energy system to supply the energy demand on an off-grid location. The optimization of these

Methodology for Sizing Hybrid Battery-Backed Power Generation Systems in Off-Grid Areas DOI: http://dx.doi.org/10.5772/intechopen.88830

systems could be complex, since many variables are naturally stochastic depending mostly on the characteristic of the solar resource and the load profile of the selected location. The objective is to minimize the total cost of the solution and maximize the reliability of the supply.

As a result of the optimization problems, the following information are obtained: (1) amount of photovoltaic modules and therefore the total photovoltaic power in kWp, (2) amount of diesel generation units and the total diesel energy power in kWp, (3) amount of battery cell required and total capacity of the energy storage system in kWh, (4) energy flow in the system showing the different states of the system according to the dispatch strategy described in this work, (5) discriminated cost of each technology in terms of initial capital required and O&M cost, (6) annualized cost of energy of the best solution, and (7) amount and cost of energy not supplied and LPSP.
