2.1 Dispatch strategy algorithm

Figure 3 shows the dispatch strategy flowchart used on the diesel-PV-battery model for a year which algorithm is described in detail below.


capacity. Additionally, operating and maintenance costs are high; the cost of energy (COE) is subject to changes according the national and international fuel markets. In addition, logistical challenges associated with fuel supply in remote areas can cause a significant increase in generation costs [1]. A solution for these disadvantages is the implementation of HRES which includes fossil and other energy sources. For warm and high-average daily radiation levels, photovoltaic solar energy with battery backup represents an attractive complementary source to diesel generation systems. This solution allows the reduction of generation costs and increased system

Hybrid systems have shown lower generation costs and greater reliability than dependent systems of a single source of energy [1, 2–6]. Each element of the system has to be properly sized to achieve a techno-economic profitability. Therefore, the penetration of renewable energy sources in the energy market depends mainly on

The optimization of these systems could be complex, since many variables are naturally stochastic and linked to the selected location. Examples of these variables are temperature, solar resource, and load profile of the location [8]. Moreover, the optimization technique depends on the selected objective function, which can be oriented in seeking financial gain, increasing system reliability, and reducing the

Then, it is necessary to develop a methodology for optimizing the design of HRES that allows the integration of photovoltaic and diesel generation systems, with or without energy storage, allowing to reduce energy costs and maintaining a high reliability in energy supply in off-grid areas. The methodology requires a set of input information linked to the project site, as meteorological and load profile data, and also technical and economic information of the main equipment of the HRES. Then, an optimization process is necessary to determine the best combination of diesel power, PV power, and battery bank capacity. Economic and reliability parameters that support the solution obtained is expected to be presented with the

In the last decade, several optimization techniques have been used to obtain an

The main objective of this work is to develop an optimization methodology for sizing HRES in off-grid areas of developing countries. In contrast to other works, each step of the methodology is described in detail. Also, special condition will be considered on the development of the economic and reliable model to adjust it to the reality of Colombia, for example, the national and international physical distribution cost or the incentive proposed by the Act 1715 for electrification using non-

In this methodology, the grid can be formed either from the diesel unit or from a master inverter. The diesel generation is only required when the energy produced by the photovoltaic source and the energy backup in the battery bank is lower than the demanded load. The following items summarize the key characteristics of the dispatch strategy used in this work to model PV-diesel with battery storage systems: (1) the system is considered DC-coupled (Figure 1) and (2) the load following strategy is adopted [1]. The diesel generators are only used to supply the load when

optimal solution of the sizing of HRES [7, 10–13]. The results among different approaches may vary depending on the characteristics of the model which permits to simulate the behavior of different elements of the system and also the economic

and reliability model used as base on the optimization process.

conventional energy sources in Colombia.

2. Proposed methodology

the applied sizing methodology to optimize its design [7].

reliability [2, 3].

Wind Solar Hybrid Renewable Energy System

environmental impact [9].

solution.

184

(number of batteries in parallel), Ebcell, nom (nominal capacity of one battery cell [kWh�), Vdcsist (DC voltage system [V]), Emax (maximum flow of energy to charge or discharge the battery bank [kWh]), Vdcbc (nominal voltage of each battery cell), ηbat, <sup>d</sup> (discharge efficiency of the battery), ηbat,c (charge efficiency of the battery), Crate (capacity rate), DODmax (maximum deep of discharge of the battery bank [%�), σ (self-discharge coefficient), wDG

(diesel rated power), and δmin (diesel minimum load ratio).

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

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

Non ¼ 0 (number of DG on), and δ ¼ 0 (diesel load ratio).

one time step (Ebat, max , <sup>d</sup>ð Þt [kWh]) is as follows:

the energy each hour:

Figure 3.

187

Dispatch strategy flowchart.

2.2. Initialize the following variables: Δ<sup>L</sup><sup>1</sup> ¼ 0 (difference between PV energy generated and the energy demanded by the load), t ¼ 1 (initial time instant, first hour of the year), SOCð Þ¼ 1 SOCmax (state of charge (SOC) is initialized considering that the battery is full charged), ENS ¼ 0 (energy not supplied), PFT ¼ 0 (power time failure, EW ¼ 0 (energy wasted), PDG ¼ 0 (diesel output power), FCDG ¼ 0 (consumption of the diesel generator,

3. Calculate the battery model which expresses the equations in the function of

(1) The maximum amount of energy that the battery bank can be discharged in

#### Figure 2.

Schematic diagram of the proposed methodology.

solar module in standard test conditions [Wp]), Gstc (global irradiance in standard test condition [W=m2]), α<sup>p</sup> (temperature coefficient of maximum power [%=°C]), NOCT (nominal operating cell temperature), Tstc (temperature of the cell standard test condition [°C]), T (cell's temperature), f pv (derating factor of the solar module), ηinv (efficiency of inverters), Nbp

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

Figure 3. Dispatch strategy flowchart.

(number of batteries in parallel), Ebcell, nom (nominal capacity of one battery cell [kWh�), Vdcsist (DC voltage system [V]), Emax (maximum flow of energy to charge or discharge the battery bank [kWh]), Vdcbc (nominal voltage of each battery cell), ηbat, <sup>d</sup> (discharge efficiency of the battery), ηbat,c (charge efficiency of the battery), Crate (capacity rate), DODmax (maximum deep of discharge of the battery bank [%�), σ (self-discharge coefficient), wDG (diesel rated power), and δmin (diesel minimum load ratio).


solar module in standard test conditions [Wp]), Gstc (global irradiance in standard test condition [W=m2]), α<sup>p</sup> (temperature coefficient of maximum power [%=°C]), NOCT (nominal operating cell temperature), Tstc (temperature of the cell standard test condition [°C]), T (cell's temperature), f pv (derating factor of the solar module), ηinv (efficiency of inverters), Nbp

Figure 2.

186

Schematic diagram of the proposed methodology.

Wind Solar Hybrid Renewable Energy System

$$E\_{\text{bat}\_2 \text{ max } \mathcal{L}}(t) = \max \left[ 0, \min \left[ E\_{\text{max}}, \left( \text{SOC}(t) - \text{SOC}\_{\text{min}} \right) \right] \right] \tag{1}$$

7.2. Otherwise, diesel generation is required. Go to step 8.

(ENS) and the power time failure (PTF) are counted:

supply the load at night.

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

Go to step 10.

generation.

Go to step 9.

Go to step 9.

189

energy generated is wasted:

8. Diesel generation is necessary. Photovoltaic energy is used to charge the

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

8.1. Case 1: PLð Þt <δmin � wDG. Since the DG units cannot operate under the minimum load ratio, δmin, all DG units must be turned off (NonðÞ¼ t 0, δðÞ¼ t 0;PDGðÞ¼ t 0). The generated PV energy and the energy available in the battery bank are used to supply the load, while the energy not supplied

battery bank, and the diesel generation is used to supply the load. The energy stored in the battery bank and energy generated by the diesel unit is used to

EbatðÞ¼ t Ebat: max , <sup>d</sup> (12)

PFT ¼ PFT þ 1 (15)

EbatðÞ¼ t Ebat: max ,cð Þt (16)

⌉ (19)

(20)

SOC tð Þ¼ þ 1 SOC tð Þ� ð Þþ 1 � σ Ebatð Þ�t ηbat,c (17)

PDGðÞ¼ <sup>t</sup> min Ndg, max <sup>∗</sup> wdg , PLð Þ�<sup>t</sup> Ppv � Ebatð Þ<sup>t</sup> � <sup>η</sup>inv (18)

PDGð Þt NonðÞ�t wDG

8.2.1.1. Case 2.1.1: PLð Þ<sup>t</sup> <sup>&</sup>gt; PpvðÞ�<sup>t</sup> Ebatð Þ<sup>t</sup> � <sup>η</sup>inv � PDGð Þ<sup>t</sup> . Diesel generation is not sufficient to supply the load; the energy not supplied is accounted:

8.2.1.2. Case 2.1.2: δð Þt <δmin. If the load ratio of the DG unit is lower than the

minimum load ratio allowed, then just one DG unit (NonðÞ¼ t 1) works operating at the minimum load ratio (δðÞ¼ t δmin), and the excess of PV

ENS tðÞ¼ PLð Þ�<sup>t</sup> PpvðÞ�<sup>t</sup> Ebatð Þ<sup>t</sup> � <sup>η</sup>inv � PDGð Þ<sup>t</sup> (21)

PFT ¼ PFT þ 1 (22)

PDGð Þt wdg

NonðÞ¼ t ⌈

δðÞ¼ t

SOC tð Þ¼ þ 1 SOC tðÞ� ð Þ� 1 � σ EbatðÞ�t ηbat <sup>d</sup> (13) ENS tðÞ¼ PLð Þ�<sup>t</sup> PpvðÞþ<sup>t</sup> Ebatð Þ<sup>t</sup> � <sup>η</sup>inv (14)

8.2. Case 2: PLð Þt ≥ δmin � wDG && Ppvð Þt >0. The photovoltaic energy is used to charge the battery bank. The diesel generation supplies the load.

8.2.1. Case 2.1: Ppvð Þt ≥Ebat: max ,cð Þt . The battery bank charges at its maximum ratio, and the excess of energy is used to supply the load with the diesel

(2) The maximum amount of energy that the battery can be charged in one time step (Ebat, max ,cð Þt [kWh]) is as follows:

$$E\_{\text{bat}\_2 \text{ max } \mathcal{L}}(t) = \max \left[ \mathbf{0}, \min \left[ E\_{\text{max}} \left( \text{SOC}\_{\text{max}} - \text{SOC}(t) \right) \right] \right] \tag{2}$$

4. Calculate the hourly generated energy of the PV system (Ppvð Þt [kWh]). The PV power output for time step t is calculated using [14]:

$$P\_{pv}(t) = N\_{pv} \times P\_{pv\_{\rm{ac}}} \times \frac{G(t)}{G\_{\rm{stc}}} \times \left(1 + \frac{a\_p}{100} \times (T(t) - T\_{\rm{ac}})\right) \times f\_{pv} \tag{3}$$

5. Calculate the difference between PV energy generated and the energy demanded by the load (Δ<sup>L</sup>1ð Þt ):

$$
\Delta\_{L1}(t) = P\_L(t) - P\_{pv}(t) \times \eta\_{inv} \tag{4}
$$


$$E\_{bat}(t) = P\_{pv}(t) - \frac{P\_L(t)}{\eta\_{INV}} \tag{5}$$

$$\text{SOC}(t+1) = \text{SOC}(t) \times (1 - \sigma) + E\_{\text{bat}}(t) \times \eta\_{\text{bat}\_2c} \tag{6}$$

Go to step 10.

6.2. Else, the battery bank is fully charged; SOC is updated. There is excess of energy that cannot be used supplying the load or charging the battery, so energy wasted (EW) is calculated.

$$E\_{bat}(t) = E\_{bat.\,\max\,\,g}(t) \tag{7}$$

$$\text{SOC}(t+1) = \text{SOC}(t) \times (1 - \sigma) + E\_{\text{bat}}(t) \times \eta\_{\text{bat}\_2c} \tag{8}$$

$$EW(t) = P\_{pv}(t) - \frac{P\_L(t)}{\eta\_{INV}} - E\_{bat}(t) \tag{9}$$

Go to step 10.


$$E\_{bat}(t) = \frac{P\_L(t)}{\eta\_{INV}} - P\_{pv}(t) \tag{10}$$

$$\text{SOC}(t+1) = \text{SOC}(t) \times (1 - \sigma) - E\_{\text{bat}}(t) \times \eta\_{\text{bat}\_2 \text{d}} \tag{11}$$

Go to step 10.

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


$$E\_{bat}(t) = E\_{bat.\,\,max\,\,g\,\,d} \tag{12}$$

$$\text{SOC}(t+1) = \text{SOC}(t) \times (1 - \sigma) - E\_{\text{bat}}(t) \times \eta\_{\text{bat } \Delta} \tag{13}$$

$$\text{ENS}(t) = P\_L(t) - \left(P\_{pv}(t) + E\_{bat}(t)\right) \times \eta\_{inv} \tag{14}$$

$$PFT = PFT + \mathbf{1} \tag{15}$$

Go to step 10.

Ebat, max <sup>d</sup>ðÞ¼ t max 0½ � , min ½ � Emax, SOC t ð Þ ðÞ� SOCmin (1)

Ebat, max <sup>c</sup>ðÞ¼ t max 0½ � , min ½ � Emax, SOC ð Þ max � SOC tð Þ (2)

100

� ð Þ T tð Þ� Tstc 

Δ<sup>L</sup>1ðÞ¼ t PLðÞ�t PpvðÞ�t ηinv (4)

PLð Þt ηINV

SOC tð Þ¼ þ 1 SOC tð Þ� ð Þþ 1 � σ Ebatð Þ�t ηbat,c (6)

SOC tð Þ¼ þ 1 SOC tð Þ� ð Þþ 1 � σ Ebatð Þ�t ηbat,c (8)

SOC tð Þ¼ þ 1 SOC tð Þ� ð Þ� 1 � σ Ebatð Þ�t ηbat, <sup>d</sup> (11)

PLð Þt ηINV

EbatðÞ¼ t Ebat: max ,cð Þt (7)

� Ebatð Þt (9)

� Ppvð Þt (10)

� f pv (3)

(5)

(2) The maximum amount of energy that the battery can be charged in one time

4. Calculate the hourly generated energy of the PV system (Ppvð Þt [kWh]). The

� <sup>1</sup> <sup>þ</sup> <sup>α</sup><sup>p</sup>

6.1. If j j Δ<sup>L</sup>1ð Þt ≤Ebat: max ,cðÞ�t ηINV, the excess of PV energy generated (Ebatð Þt ), if any, is used to charge the battery bank, and the SOC of the battery is

6.2. Else, the battery bank is fully charged; SOC is updated. There is excess of energy that cannot be used supplying the load or charging the battery, so

EbatðÞ¼ t PpvðÞ�t

EW tðÞ¼ PpvðÞ�t

EbatðÞ¼ t

7. If Δ<sup>L</sup>1ð Þt >0, the photovoltaic source is insufficient to supply the load.

7.1. If Δ<sup>L</sup>1ð Þt <Ebat, max , <sup>d</sup>ðÞ�t ηINV, the battery bank discharge to supply the lack

PLð Þt ηINV

5. Calculate the difference between PV energy generated and the energy

PV power output for time step t is calculated using [14]:

6. If Δ<sup>L</sup>1ð Þt ≤0, then the PV source can supply the load.

G tð Þ Gstc

step (Ebat, max ,cð Þt [kWh]) is as follows:

PpvðÞ¼ t Npv � Ppvstc �

Wind Solar Hybrid Renewable Energy System

demanded by the load (Δ<sup>L</sup>1ð Þt ):

energy wasted (EW) is calculated.

of energy. SOC of the battery is updated.

updated:

Go to step 10.

Go to step 10.

Go to step 10.

188


$$E\_{\text{bat}}(\mathbf{t}) = E\_{\text{bat. max}, \mathbf{c}}(\mathbf{t}) \tag{16}$$

$$\text{SOC}(t+1) = \text{SOC}(t) \times (1 - \sigma) + E\_{\text{bat}}(t) \times \eta\_{\text{bat}\_2c} \tag{17}$$

$$P\_{\rm DG}(t) = \min\left(\mathcal{N}\_{\rm dg\_{\rm g}\,\,\,\max} \* \boldsymbol{w}\_{\rm dg}, P\_L(t) - \left(P\_{pv} - E\_{\rm bat}(t)\right) \times \eta\_{inv}\right) \tag{18}$$

$$N\_{on}(t) = \lceil \frac{P\_{DG}(t)}{w\_{d\lg}} \rceil \tag{19}$$

$$\delta(t) = \frac{P\_{DG}(t)}{N\_{on}(t) \times w\_{DG}} \tag{20}$$

Go to step 9.

8.2.1.1. Case 2.1.1: PLð Þ<sup>t</sup> <sup>&</sup>gt; PpvðÞ�<sup>t</sup> Ebatð Þ<sup>t</sup> � <sup>η</sup>inv � PDGð Þ<sup>t</sup> . Diesel generation is not sufficient to supply the load; the energy not supplied is accounted:

$$\text{ENS}(\mathbf{t}) = P\_L(\mathbf{t}) - \left(P\_{pv}(\mathbf{t}) - E\_{bat}(\mathbf{t})\right) \times \eta\_{inv} - P\_{DG}(\mathbf{t}) \tag{21}$$

$$PFT = PFT + \mathbf{1} \tag{22}$$

Go to step 9.

8.2.1.2. Case 2.1.2: δð Þt <δmin. If the load ratio of the DG unit is lower than the minimum load ratio allowed, then just one DG unit (NonðÞ¼ t 1) works operating at the minimum load ratio (δðÞ¼ t δmin), and the excess of PV energy generated is wasted:

$$P\_{DG}(t) = N\_{on}(t) \times \delta(t) \times w\_{DG} \tag{23}$$

PDGðÞ¼ t NonðÞ�t δð Þ�t wDG (39)

(40)

(44)

(45)

PLðÞ�t PDGð Þt ηinv

10. Increase the time step (t ¼ t þ 1). If t≤8760, and return to step 3. Else END.

After run the previous algorithm; economic and reliability indicators should be

An economic analysis is required to determine the optimum cost and benefit ratio of HRES. These systems generally require high capital investment, even though they have low operation and maintenance (O&M) costs and less fuel costs in comparison with systems relaying only on fossil fuels. In this study, the annualized cost of the system (ACS) and the cost of energy (COE) are considered as the economic criteria to evaluate the feasibility of this hybridized system configuration. The annualized cost of the system (ACS) is the sum of the annualized capital cost (CCÞ, the annualized replacement cost (RC) and the annualized cost of maintenance (OM) [7, 17–19]. In [17], the annualized cost of the system is defined as

where Nc is the number of components; in this study there are three components (PV modules, battery banks, DG units). Subscript i is used to describe the cost of each component. The capital recovery factor (CRF ir ð Þ , R ) can be defined as a ratio used to calculate the present value of an annuity (a series of equal annual cash flows) in the function of the real interest rate (ir) and the lifetime of the project (R)

CRF ir, R ð Þ¼ ir � <sup>1</sup> <sup>þ</sup> <sup>i</sup> ð Þ<sup>r</sup> <sup>R</sup>

The real interest rate is used to convert between one-time costs and annualized costs. By defining the real discount rate, the inflation rate effect is factored out of the economic analysis. All costs, therefore, become real costs, which are in defined

> ir <sup>¼</sup> in � if 1 þ if

where in and if are the nominal interest rate and expected annual inflation rate,

in terms of constant dollars. The real interest rate is calculated by

The capital cost for each component is described as follows:

<sup>1</sup> <sup>þ</sup> <sup>i</sup> ð Þ<sup>r</sup> <sup>R</sup> � <sup>1</sup>

SOC tð Þ¼ þ 1 SOC tð Þ� ð Þ� 1 � σ Ebatð Þ�t ηbat, <sup>d</sup> (41)

FCDGðÞ¼ t NonðÞ�t wdg � f <sup>0</sup> þ PDGðÞ�t f <sup>1</sup> (42)

ð Þ� CCi þ RCi CRF ir ð Þþ , R O&MiÞ (43)

CCpv ¼ cpv � Npv � Ppvstc (46)

EbatðÞ¼ t

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

9. The fuel consumption FCDGð Þt is calculated by [15, 16]:

calculated using the following procedure.

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

ACS <sup>¼</sup> <sup>X</sup> Nc

[17]. The capital recovery factor is calculated by

i¼1

2.2 Economic indicators

respectively.

191

$$EW(t) = P\_{pv}(t) - E\_{bat}(t) - \frac{P\_L(t) - P\_{dg}(t)}{\eta\_{inv}} \tag{24}$$

Go to step 9.

8.2.2. Case 2.2: Ppvð Þt ≤Ebat: max ,cð Þt . All photovoltaic energy is used to charge the battery bank:

$$E\_{bat}(t) = P\_{pv}(t) \tag{25}$$

$$P\_{DG}(t) = \min\left(\mathcal{N}\_{\text{dg}\_2 \ max} \ast w\_{\text{dg}}, P\_L(t)\right) \tag{26}$$

$$\text{SOC}(t+1) = \text{SOC}(t) \times (1 - \sigma) + E\_{\text{bat}}(t) \times \eta\_{\text{bat}\_2c} \tag{27}$$

$$N\_{on}(t) = \begin{bmatrix} \frac{P\_{DG}(t)}{\omega\_{dg}} \end{bmatrix} \tag{28}$$

$$\delta(t) = \frac{P\_{DG}(t)}{N\_{on}(t) \times w\_{DG}} \tag{29}$$

8.2.2.1. Case 2.2.1: PLð Þt >PDGð Þt : The DG is insufficient to supply the load; the energy not supplied is accounted:

$$\text{ENS}(t) = P\_L(t) - P\_{DG}(t) \tag{30}$$

$$PFT = PFT + \mathbf{1} \tag{31}$$


$$E\_{\text{bat}}(t) = E\_{\text{bat. max}\_{\text{J}}d}(t) \tag{32}$$

$$P\_{\rm DG}(t) = \min \left( N\_{\rm dg\_{\rm g} \,\,\max} \ast w\_{\rm dg}, P\_L(t) - E\_{\rm bat}(t) \times \eta\_{\rm inv} \tag{33} \right)$$

$$\text{SOC}(t+1) = \text{SOC}(t) \times (1 - \sigma) - E\_{\text{bat}}(t) \times \eta\_{\text{bat},d} \tag{34}$$

$$N\_{on}(t) = \lceil \frac{P\_{DG}(t)}{w\_{dg}} \rceil \tag{35}$$

$$\delta(t) = \frac{P\_{DG}(t)}{N\_{on}(t) \times w\_{DG}} \tag{36}$$

8.3.1.1. Case 3.1.1: (PLð Þt ≥PDG þ Ebatð Þ�t ηinv). The diesel generation and the energy provided by the battery bank are not sufficient to supply the load; the energy not supplied is accounted.

$$\text{ENS}(t) = P\_L(t) - P\_{DG}(t) - E\_{bat}(t) \times \eta\_{inv} \tag{37}$$

$$PFT = PFT + \mathbf{1} \tag{38}$$

8.3.2. Case 3.2: (PLðÞ�t Ebat: max , <sup>d</sup>ðÞ�t ηinv <δmin � wDG). Just one DG unit works operating at the minimum load ratio (NonðÞ¼ t 1, δðÞ¼ t δmin). The battery bank provides the insufficient energy to supply the load.

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

$$P\_{DG}(t) = N\_{on}(t) \times \delta(t) \times w\_{DG} \tag{39}$$

$$E\_{bat}(t) = \frac{P\_L(t) - P\_{DG}(t)}{\eta\_{inv}} \tag{40}$$

$$\text{SOC}(t+1) = \text{SOC}(t) \times (1 - \sigma) - E\_{\text{bat}}(t) \times \eta\_{\text{bat}\_{\text{b}}d} \tag{41}$$

9. The fuel consumption FCDGð Þt is calculated by [15, 16]:

$$FC\_{DG}(t) = N\_{on}(t) \times w\_{dg} \times f\_0 + P\_{DG}(t) \times f\_1 \tag{42}$$

10. Increase the time step (t ¼ t þ 1). If t≤8760, and return to step 3. Else END.

After run the previous algorithm; economic and reliability indicators should be calculated using the following procedure.

### 2.2 Economic indicators

PDGðÞ¼ t NonðÞ�t δð Þ�t wDG (23)

PLðÞ�t Pdg ð Þt ηinv

EbatðÞ¼ t Ppvð Þt (25)

⌉ (28)

PDGðÞ¼ <sup>t</sup> min Ndg, max <sup>∗</sup> wdg , PLð Þ<sup>t</sup> (26)

ENS tðÞ¼ PLðÞ�t PDGð Þt (30) PFT ¼ PFT þ 1 (31)

EbatðÞ¼ t Ebat: max , <sup>d</sup>ð Þt (32)

(33)

⌉ (35)

SOC tð Þ¼ þ 1 SOC tð Þ� ð Þþ 1 � σ Ebatð Þ�t ηbat,c (27)

PDGð Þt wdg

PDGð Þt NonðÞ�t wDG

8.2.2.1. Case 2.2.1: PLð Þt >PDGð Þt : The DG is insufficient to supply the load; the

8.3. Case 3: (PLð Þt ≥δmin � wDG && Ppvð Þt ≤0 ). At night, the battery bank and

discharged at maximum rate, and DG units generate the remaining energy

SOC tð Þ¼ þ 1 SOC tð Þ� ð Þ� 1 � σ Ebatð Þ�t ηbat, <sup>d</sup> (34)

ENS tðÞ¼ PLðÞ�t PDGðÞ�t EbatðÞ�t ηinv (37)

PFT ¼ PFT þ 1 (38)

PDGð Þt wdg

PDGð Þt NonðÞ�t wDG

8.3.1.1. Case 3.1.1: (PLð Þt ≥PDG þ Ebatð Þ�t ηinv). The diesel generation and the energy provided by the battery bank are not sufficient to supply the

8.3.2. Case 3.2: (PLðÞ�t Ebat: max , <sup>d</sup>ðÞ�t ηinv <δmin � wDG). Just one DG unit

battery bank provides the insufficient energy to supply the load.

works operating at the minimum load ratio (NonðÞ¼ t 1, δðÞ¼ t δmin). The

8.3.1. Case 3.1: (PLðÞ�t Ebat: max , <sup>d</sup>ðÞ�t ηinv ≥ δmin � wDG). Battery bank is

PDGðÞ¼ t min Ndg, max ∗ wdg , PLð Þ�t EbatðÞ�t ηinv

NonðÞ¼ t ⌈

δðÞ¼ t

load; the energy not supplied is accounted.

(24)

(29)

(36)

EW tðÞ¼ PpvðÞ�t Ebatð Þ�t

8.2.2. Case 2.2: Ppvð Þt ≤Ebat: max ,cð Þt . All photovoltaic energy is used to charge

NonðÞ¼ t ⌈

δðÞ¼ t

energy not supplied is accounted:

the DG units are used to supply the load.

necessary to supply the load.

190

Go to step 9.

the battery bank:

Wind Solar Hybrid Renewable Energy System

An economic analysis is required to determine the optimum cost and benefit ratio of HRES. These systems generally require high capital investment, even though they have low operation and maintenance (O&M) costs and less fuel costs in comparison with systems relaying only on fossil fuels. In this study, the annualized cost of the system (ACS) and the cost of energy (COE) are considered as the economic criteria to evaluate the feasibility of this hybridized system configuration.

The annualized cost of the system (ACS) is the sum of the annualized capital cost (CCÞ, the annualized replacement cost (RC) and the annualized cost of maintenance (OM) [7, 17–19]. In [17], the annualized cost of the system is defined as

$$\text{ACC} = \sum\_{i=1}^{N\_c} (\text{CC}\_i + \text{RC}\_i) \times \text{CRF}(i\_r, \text{R}) + \text{O\&M}\_i \tag{43}$$

where Nc is the number of components; in this study there are three components (PV modules, battery banks, DG units). Subscript i is used to describe the cost of each component. The capital recovery factor (CRF ir ð Þ , R ) can be defined as a ratio used to calculate the present value of an annuity (a series of equal annual cash flows) in the function of the real interest rate (ir) and the lifetime of the project (R) [17]. The capital recovery factor is calculated by

$$CRF(ir, R) = \frac{i\_r \times (\mathbf{1} + i\_r)^R}{\left(\mathbf{1} + i\_r\right)^R - \mathbf{1}} \tag{44}$$

The real interest rate is used to convert between one-time costs and annualized costs. By defining the real discount rate, the inflation rate effect is factored out of the economic analysis. All costs, therefore, become real costs, which are in defined in terms of constant dollars. The real interest rate is calculated by

$$i\_r = \frac{i\_n - i\_f}{1 + i\_f} \tag{45}$$

where in and if are the nominal interest rate and expected annual inflation rate, respectively.

The capital cost for each component is described as follows:

$$\text{CC}\_{p^{v}} = \mathfrak{c}\_{p^{v}} \times \text{N}\_{p^{v}} \times P\_{p^{v\_{\text{st}}}} \tag{46}$$

$$\text{CC}\_{bat} = \text{c}\_{bat} \times \text{N}\_{bat} \times E\_{bcell\_9 \text{ }nom} \tag{47}$$

$$\text{CC}\_{DG} = \mathfrak{c}\_{DG} \times \text{N}\_{DG} \times \mathfrak{w}\_{DG} \tag{48}$$

ρDG, and a variable cost associated to the cost of fuel, f <sup>C</sup>, in [\$/gal], and the annual fuel consumption. The annual operation and maintenance cost of the diesel system

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

The cost of energy (COE) can be defined as the average cost per kWh of useful

The dependency on nature and unpredictability of solar resources has a great impact on energy production which leads to unreliable power supply during cloudy days. A system is reliable if it can supply the required power to the electrical load

The loss of power supply probability (LPSP) is the most widely used method to

P<sup>8760</sup>

P<sup>8760</sup> <sup>t</sup>¼<sup>1</sup> ELð Þ<sup>t</sup>

A method that takes into account the weight of reliability in the economic model includes a component of the cost of electricity interruptions or cost of load (Closs) [17]. The cost of electricity interruptions can be estimated in different ways, for example, looking at the customer's willingness to pay for an expansion or at production losses at industries affected, or at the level of compensations, which makes shortages acceptable. In [17], for 2009, the cost ranges from 5 to 40 USD\$/kWh for

The cost of electricity lost for non-interconnected zone can vary with respect the reference cost and could be difficult to estimate, as depends on the willingness of users to pay for a more robust system. The cost of electricity not supply (Closs) in [USD/kWh] is an input parameter in the economic model. The annualized cost of

> 8760 X t¼1

LPSP and ACloss are calculated for each possible combination considered during

ENS tð Þ (57)

<sup>t</sup>¼<sup>1</sup> ENS tð Þ

evaluate the reliability in hybrid system, therefore is selected, in this work, as reliability criteria. The LPSP be calculated as the ratio of power supply deficit to the electric load demand during a certain period of time (normally a year). A ratio equal to zero means all load demand, during the period of time, is served by system (53).

LPSP ¼

ACloss ¼ Closs �

industrial users and 2–12 USD\$/kWh for domestic users.

energy not supplied can be calculated as

the sizing methodology.

193

8760 X t¼1

<sup>t</sup>¼<sup>1</sup> ð Þ ELðÞ�<sup>t</sup> ENS tð Þ (55)

FC tð Þ (54)

(56)

O&MDG ¼ ρDG � CCDG þ f <sup>C</sup> �

electrical energy produced by the system [21]. It can be obtained as the ratio between the annualized cost of the system and the effective load served in 1 year. The economic model assumes that the yearly effective load served is constant over

> COE <sup>¼</sup> ACS P<sup>8760</sup>

the lifetime of the project. COE can be calculated as follows:

can be calculated by

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

2.3 Reliability indicators

within a specific time period.

LPSP is given by

where cpv is the cost per Watt peak installed of photovoltaic power in [USD/ Wp]; this cost includes the cost of the module, the electronic power equipment required (charge controller and inverter), and the installation cost (engineering, transportation, balance of system equipment as cable, mounting rack, electrical protection, etc.). cpv varies according to the project location and site conditions; it can range from 3 to 10 USD/Wp. The cost per unit of the battery system, cbat, in [USD/Wh], includes the average cost of the battery cell and the installation cost of the battery system. The parameter cDG in [USD/kW] is the cost per unit of diesel generation installed and also includes the cost of the diesel generator unit and the associated installation costs.

The replacement cost is calculated for each element. The replacement cost of the photovoltaic system is assumed null, as the photovoltaic modules have a life cycle superior to the lifetime of the project and it is assumed in this model that the charge controllers and inverters do not need replacement during the lifetime of the project. The replacement cost of the battery system and the DG unit can be calculated as

$$RC\_{bat} = \gamma\_{bat} \times \text{CC}\_{bat} \times K\_{bat} \left( i\_r, L\_{pv}, \mathcal{y}\_i \right) \tag{49}$$

$$RC\_{DG} = \gamma\_{DG} \times CC\_{DG} \times K\_{DG} \left( i\_r, L\_{DG}, \mathcal{y}\_i \right) \tag{50}$$

where γbat and γDG are derate factors of the initial capital cost invested for the battery system and the diesel genset, respectively, as some cost necessary during the installation are no longer needed during the replacement (civil works, battery rack, electrical protections, fuel tank, etc.). Ki ir, Li, yi � � is the single payment present worth [17], which is defined by

$$K\_i(i\_r, L\_i, \boldsymbol{\chi}\_i) = \sum\_{n=1}^{\mathcal{I}\_i} \frac{1}{(1 + i\_r)^{n \times L\_i}} \tag{51}$$

where L and y are the useful lifetime and the number of replacements of the component during the lifetime of the project, respectively. The number of replacements of each component is a function of useful lifetime of the component and the lifetime of the project (yi <sup>¼</sup> ⌊<sup>R</sup> Li⌋).

The fixed mount PV systems do not have moving parts, so operating and maintenance costs consist of regular cleaning and monitoring of performance, the annual operation, and maintenance cost can be estimated as a percentage of the PV system total investment, ρpv, usually between 1 and 2% [20].

$$\text{O\\$}\text{\&M}\_{PV} = \rho\_{pv} \times \text{CC}\_{pv} \tag{52}$$

In a similar way, the annual operation and maintenance cost for the battery system can be calculated as percentage of the total investment cost of the battery system. This cost can vary according to the technology of the battery bank. For example, the cost of operation and maintenance for vented lead-acid batteries is higher than maintenance-free sealed lead-acid batteries or Li-ion batteries. The percentage of the total investment cost, ρbat, can vary between 1 and 3%.

$$\text{O\\$}\text{\&M}\_{\text{bat}} = \rho\_{\text{bat}} \times \text{CC}\_{\text{bat}} \tag{53}$$

The operation and maintenance cost for the diesel system components is divided in two values: a fixed cost, expressed as a percentage of the diesel initial investment, Methodology for Sizing Hybrid Battery-Backed Power Generation Systems in Off-Grid Areas DOI: http://dx.doi.org/10.5772/intechopen.88830

ρDG, and a variable cost associated to the cost of fuel, f <sup>C</sup>, in [\$/gal], and the annual fuel consumption. The annual operation and maintenance cost of the diesel system can be calculated by

$$\text{O8\&M}\_{\text{DG}} = \rho\_{\text{DG}} \times \text{CC}\_{\text{DG}} + f\_{\text{C}} \times \sum\_{t=1}^{\text{8760}} FC(t) \tag{54}$$

The cost of energy (COE) can be defined as the average cost per kWh of useful electrical energy produced by the system [21]. It can be obtained as the ratio between the annualized cost of the system and the effective load served in 1 year. The economic model assumes that the yearly effective load served is constant over the lifetime of the project. COE can be calculated as follows:

$$COE = \frac{ACS}{\sum\_{t=1}^{8760} (E\_L(t) - ENS(t))} \tag{55}$$

### 2.3 Reliability indicators

CCbat ¼ cbat � Nbat � Ebcell, nom (47) CCDG ¼ cDG � NDG � wDG (48)

� � (49)

� � (50)

� � is the single payment present

<sup>1</sup> <sup>þ</sup> <sup>i</sup> ð Þ<sup>r</sup> <sup>n</sup>�Li (51)

where cpv is the cost per Watt peak installed of photovoltaic power in [USD/ Wp]; this cost includes the cost of the module, the electronic power equipment required (charge controller and inverter), and the installation cost (engineering, transportation, balance of system equipment as cable, mounting rack, electrical protection, etc.). cpv varies according to the project location and site conditions; it can range from 3 to 10 USD/Wp. The cost per unit of the battery system, cbat, in [USD/Wh], includes the average cost of the battery cell and the installation cost of the battery system. The parameter cDG in [USD/kW] is the cost per unit of diesel generation installed and also includes the cost of the diesel generator unit and the

The replacement cost is calculated for each element. The replacement cost of the photovoltaic system is assumed null, as the photovoltaic modules have a life cycle superior to the lifetime of the project and it is assumed in this model that the charge controllers and inverters do not need replacement during the lifetime of the project. The replacement cost of the battery system and the DG unit can be calculated as

RCbat ¼ γbat � CCbat � Kbat ir, Lpv, yi

RCDG ¼ γDG � CCDG � KDG ir, LDG, yi

where γbat and γDG are derate factors of the initial capital cost invested for the battery system and the diesel genset, respectively, as some cost necessary during the installation are no longer needed during the replacement (civil works, battery rack,

yi

1

O&MPV ¼ ρpv � CCpv (52)

O&Mbat ¼ ρbat � CCbat (53)

n¼1

The fixed mount PV systems do not have moving parts, so operating and maintenance costs consist of regular cleaning and monitoring of performance, the annual operation, and maintenance cost can be estimated as a percentage of the PV system

In a similar way, the annual operation and maintenance cost for the battery system can be calculated as percentage of the total investment cost of the battery system. This cost can vary according to the technology of the battery bank. For example, the cost of operation and maintenance for vented lead-acid batteries is higher than maintenance-free sealed lead-acid batteries or Li-ion batteries. The percentage of the total investment cost, ρbat, can vary between 1 and 3%.

The operation and maintenance cost for the diesel system components is divided in two values: a fixed cost, expressed as a percentage of the diesel initial investment,

where L and y are the useful lifetime and the number of replacements of the component during the lifetime of the project, respectively. The number of replacements of each component is a function of useful lifetime of the component and the

associated installation costs.

Wind Solar Hybrid Renewable Energy System

electrical protections, fuel tank, etc.). Ki ir, Li, yi

Ki ir, Li, yi

Li⌋).

total investment, ρpv, usually between 1 and 2% [20].

� � <sup>¼</sup> <sup>X</sup>

worth [17], which is defined by

lifetime of the project (yi <sup>¼</sup> ⌊<sup>R</sup>

192

The dependency on nature and unpredictability of solar resources has a great impact on energy production which leads to unreliable power supply during cloudy days. A system is reliable if it can supply the required power to the electrical load within a specific time period.

The loss of power supply probability (LPSP) is the most widely used method to evaluate the reliability in hybrid system, therefore is selected, in this work, as reliability criteria. The LPSP be calculated as the ratio of power supply deficit to the electric load demand during a certain period of time (normally a year). A ratio equal to zero means all load demand, during the period of time, is served by system (53). LPSP is given by

$$LPSP = \frac{\sum\_{t=1}^{8760} ENS(t)}{\sum\_{t=1}^{8760} E\_L(t)}\tag{56}$$

A method that takes into account the weight of reliability in the economic model includes a component of the cost of electricity interruptions or cost of load (Closs) [17]. The cost of electricity interruptions can be estimated in different ways, for example, looking at the customer's willingness to pay for an expansion or at production losses at industries affected, or at the level of compensations, which makes shortages acceptable. In [17], for 2009, the cost ranges from 5 to 40 USD\$/kWh for industrial users and 2–12 USD\$/kWh for domestic users.

The cost of electricity lost for non-interconnected zone can vary with respect the reference cost and could be difficult to estimate, as depends on the willingness of users to pay for a more robust system. The cost of electricity not supply (Closs) in [USD/kWh] is an input parameter in the economic model. The annualized cost of energy not supplied can be calculated as

$$\text{AC}\_{\text{loss}} = \text{C}\_{\text{loss}} \times \sum\_{t=1}^{8760} \text{ENS}(t) \tag{57}$$

LPSP and ACloss are calculated for each possible combination considered during the sizing methodology.
