Open access peer-reviewed chapter

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

By Oswaldo A. Arraez-Cancelliere, Nicolás Muñoz-Galeano and Jesús M. López-Lezama

Submitted: June 10th 2019Reviewed: July 26th 2019Published: September 13th 2019

DOI: 10.5772/intechopen.88830

## Abstract

In developing countries, rural electrification in areas with limited or no access to grid connection is one of the most challenging issues for governments. These areas are partially integrated with the electrical grid. This poor electricity distribution is mainly due to geographical inaccessibility, rugged terrains, lack of electrical infrastructure, and high required economic investment for installing large grid-connected power lines over long distances to provide electricity for regions with a low population. On the other hand, rapid depletion of fossil fuel resources on a global scale and progressive increase of energy demand and fuel price are other motives to reduce the reliance on fossil fuels. Hybrid renewable energy system (HRES) can be a suitable option for such remote areas. The objective of this chapter is to develop a methodology for sizing hybrid power generation systems (solar-diesel), battery-backed in non-interconnected zones, which minimizes the total cost and maximizes the reliability of supply using particle swarm optimization (PSO). The proposed methodology assists the sizing and designing process of an HRES for an off-grid area minimizing the cost of energy (COE) and maximizing the reliability of the system. Economic incentives offered by the Colombian government are considered in the model.

### Keywords

• hybrid renewable energy system (HRES)
• stand-alone systems
• off-grid areas
• particle swarm optimization (PSO)
• photovoltaic energy
• power dispatch strategy

## 1. Introduction

Due to the technological and industrial worldwide progress and the growing industry and society need of power generation for the development and increment of life quality, it is of unquestionable importance to increase sustainable access to electrical energy. In developing countries, there are still many locations without power supply.

Power generation through fossil generators offers a continuous and reliable source of energy making it a very popular option for electrification in off-grid areas. This alternative presents an initial investment cost relatively low compared to other sources of power generation. However, fossil power generators are sized to meet peak demand and have a low performance when the load is quite below to its rated 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 reliability [2, 3].

Hybrid systems have shown lower generation costs and greater reliability than dependent systems of a single source of energy [1, 2, 3, 4, 5, 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 applied sizing methodology to optimize its design [7].

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 environmental impact [9].

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 solution.

In the last decade, several optimization techniques have been used to obtain an optimal solution of the sizing of HRES [7, 10, 11, 12, 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.

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-conventional energy sources in Colombia.

## 2. Proposed methodology

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 there is insufficient power from the PV source and the battery bank. Only the minimum DG unit required operates in every time step; (3) all DG units must operate over the minimum load ratio (δmin) defined otherwise the DG unit must be turned off; (4) all DG units have the same nominal power capacity and operate at the equilibrium point at the same load ratio; (5) when diesel units are operating, the PV generation prioritizes the charge of the battery bank over the load; (6) only AC loads are considered; and (7) a maximum number of DG units are considered.

The proposed methodology is composed of the following steps: (1) a dispatch strategy algorithm, (2) calculation of economic indicators, (3) calculation of reliability indicators, (4) calculation of fiscal incentives, and (5) a PSO optimization process given an objective function which optimizes the number of components of the installation and a calculation of economic and reliability indicators for the best solution. The following subsections detail the steps of the methodology. Figure 2 shows the schematic of the proposed methodology and the optimization process.

### 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.

1. Obtain or generate inputs of the system: load profile (PL), irradiance (G), and temperature (T) for the location in a year. Load profile can be obtained through a survey considering the uncertainties on the input data (38) and (39), and also load profile can also be obtained using measurement of the electrical demand. High-quality solar resource and meteorological data can be obtained by two approaches: high-accuracy instruments installed at a meteorological station and complex solar meteorological models which are validated using high-quality ground instruments.

2. Introduce the following technical information of each element of the system and initialize variables.

2.1. According to the available location and its restrictions, introduce the following technical information: NDG,max(maximum number of DG units), wDG(rated power of the available diesel generator), δmin(minimum load ratio [%]), f0(fuel Curve intercept coefficient [l/kW]), f1(fuel curve slope coefficient [l/kW]), Npv(number of PV modules), Ppvstc(rated power of the solar module in standard test conditions [Wp]), Gstc(global irradiance in standard test condition [W/m2]), αp(temperature coefficient of maximum power [%/°C]), NOCT(nominal operating cell temperature), Tstc(temperature of the cell standard test condition [°C]), T(cell’s temperature), fpv(derating factor of the solar module), ηinv(efficiency of inverters), Nbp(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,d(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).

2.2. Initialize the following variables: L1=0(difference between PV energy generated and the energy demanded by the load), t=1(initial time instant, first hour of the year), SOC1=SOCmax(state of charge (SOC) is initialized considering that the battery is full charged), ENS=0(energy not supplied), PFT=0(power time failure, EW=0(energy wasted), PDG=0(diesel output power), FCDG=0(consumption of the diesel generator, Non=0(number of DG on), and δ=0(diesel load ratio).

3. Calculate the battery model which expresses the equations in the function of the energy each hour:

(1) The maximum amount of energy that the battery bank can be discharged in one time step (Ebat,max,dt[kWh]) is as follows:

Ebat,max_dt=max0minEmaxSOCtSOCminE1

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

Ebat,max_ct=max0minEmaxSOCmaxSOCtE2

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

Ppvt=Npv×Ppvstc×GtGstc×1+αp100×TtTstc×fpvE3

5. Calculate the difference between PV energy generated and the energy demanded by the load (L1t):

L1t=PLtPpvt×ηinvE4

6. If L1t0, then the PV source can supply the load.

6.1. If L1tEbat.max,ct×ηINV, the excess of PV energy generated (Ebatt), if any, is used to charge the battery bank, and the SOCof the battery is updated:

Ebatt=PpvtPLtηINVE5
SOCt+1=SOCt×1σ+Ebatt×ηbat,cE6

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.

Ebatt=Ebat.max,ctE7
SOCt+1=SOCt×1σ+Ebatt×ηbat,cE8
EWt=PpvtPLtηINVEbattE9

Go to step 10.

7. If L1t>0, the photovoltaic source is insufficient to supply the load.

7.1. If L1t<Ebat,max,dt×ηINV, the battery bank discharge to supply the lack of energy. SOC of the battery is updated.

Ebatt=PLtηINVPpvtE10
SOCt+1=SOCt×1σEbatt×ηbat,dE11

Go to step 10.

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

8. Diesel generation is necessary. Photovoltaic energy is used to charge the 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 supply the load at night.

8.1. Case 1:PLt<δmin×wDG. Since the DG units cannot operate under the minimum load ratio, δmin, all DG units must be turned off (Nont=0, δt=0;PDGt=0). The generated PV energy and the energy available in the battery bank are used to supply the load, while the energy not supplied (ENS) and the power time failure (PTF) are counted:

Ebatt=Ebat.max,dE12
SOCt+1=SOCt×1σEbatt×ηbat_dE13
ENSt=PLtPpvt+Ebatt×ηinvE14
PFT=PFT+1E15

Go to step 10.

8.2. Case 2:PLtδmin×wDG&& Ppvt>0. The photovoltaic energy is used to charge the battery bank. The diesel generation supplies the load.

8.2.1. Case 2.1:PpvtEbat.max,ct. The battery bank charges at its maximum ratio, and the excess of energy is used to supply the load with the diesel generation.

Ebatt=Ebat.max,ctE16
SOCt+1=SOCt×1σ+Ebatt×ηbat,cE17
PDGt=min(Ndg,maxwdg,PLtPpvEbatt×ηinvE18
Nont=PDGtwdgE19
δt=PDGtNont×wDGE20

Go to step 9.

8.2.1.1. Case 2.1.1:PLt>PpvtEbatt×ηinvPDGt. Diesel generation is not sufficient to supply the load; the energy not supplied is accounted:

ENSt=PLtPpvtEbatt×ηinvPDGtE21
PFT=PFT+1E22

Go to step9.

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

PDGt=Nont×δt×wDGE23
EWt=PpvtEbattPLtPdgtηinvE24

Go to step9.

8.2.2. Case 2.2:PpvtEbat.max,ct. All photovoltaic energy is used to charge the battery bank:

Ebatt=PpvtE25
PDGt=min(Ndg,maxwdg,PLtE26
SOCt+1=SOCt×1σ+Ebatt×ηbat,cE27
Nont=PDGtwdgE28
δt=PDGtNont×wDGE29

8.2.2.1. Case 2.2.1:PLt>PDGt.The DG is insufficient to supply the load; the energy not supplied is accounted:

ENSt=PLtPDGtE30
PFT=PFT+1E31

8.3. Case 3:(PLtδmin×wDG&& Ppvt0). At night, the battery bank and the DG units are used to supply the load.

8.3.1. Case 3.1:(PLtEbat.max,dt×ηinvδmin×wDG). Battery bank is discharged at maximum rate, and DG units generate the remaining energy necessary to supply the load.

Ebatt=Ebat.max,dtE32
PDGt=min(Ndg,maxwdg,PLtEbatt×ηinvE33
SOCt+1=SOCt×1σEbatt×ηbat,dE34
Nont=PDGtwdgE35
δt=PDGtNont×wDGE36

8.3.1.1. Case 3.1.1:(PLtPDG+Ebatt×ηinv). The diesel generationand the energy provided by the battery bank are not sufficient to supply the load; the energy not supplied is accounted.

ENSt=PLtPDGtEbatt×ηinvE37
PFT=PFT+1E38

8.3.2. Case 3.2:(PLtEbat.max,dt×ηinv<δmin×wDG). Just one DG unit works operating at the minimum load ratio (Nont=1, δt=δmin). The battery bank provides the insufficient energy to supply the load.

PDGt=Nont×δt×wDGE39
Ebatt=PLtPDGtηinvE40
SOCt+1=SOCt×1σEbatt×ηbat,dE41

9. The fuel consumption FCDGtis calculated by [15, 16]:

FCDGt=Nont×wdg×f0+PDGt×f1E42

10. Increase the time step (t=t+1). If t8760, 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

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 (CC), the annualized replacement cost (RC) and the annualized cost of maintenance (OM) [7, 17, 18, 19]. In [17], the annualized cost of the system is defined as

ACS=i=1NcCCi+RCi×CRFirR+O&Mi)E43

where Ncis the number of components; in this study there are three components (PV modules, battery banks, DG units). Subscript iis used to describe the cost of each component. The capital recovery factor (CRFirR) 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

CRFirR=ir×1+irR1+irR1E44

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

ir=inif1+ifE45

where inand ifare the nominal interest rate and expected annual inflation rate, respectively.

The capital cost for each component is described as follows:

CCpv=cpv×Npv×PpvstcE46
CCbat=cbat×Nbat×Ebcell,nomE47
CCDG=cDG×NDG×wDGE48

where cpvis 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.). cpvvaries 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 cDGin [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

RCbat=γbat×CCbat×KbatirLpvyiE49
RCDG=γDG×CCDG×KDGirLDGyiE50

where γbatand γDGare 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.). KiirLiyiis the single payment present worth [17], which is defined by

KiirLiyi=n=1yi11+irn×LiE51

where Land yare 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=RLi).

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].

O&MPV=ρpv×CCpvE52

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%.

O&Mbat=ρbat×CCbatE53

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, ρDG, and a variable cost associated to the cost of fuel, fC, in [$/gal], and the annual fuel consumption. The annual operation and maintenance cost of the diesel system can be calculated by O&MDG=ρDG×CCDG+fC×t=18760FCtE54 The cost of energy (COE) can be defined as the average cost per kWh of useful electrical energy produced by the system [21]. It can be obtained as the ratio between the annualized cost of the system and the effective load served in 1 year. The economic model assumes that the yearly effective load served is constant over the lifetime of the project. COE can be calculated as follows: COE=ACSt=18760ELtENStE55 ### 2.3 Reliability indicators The dependency on nature and unpredictability of solar resources has a great impact on energy production which leads to unreliable power supply during cloudy days. A system is reliable if it can supply the required power to the electrical load within a specific time period. The loss of power supply probability (LPSP) is the most widely used method to evaluate the reliability in hybrid system, therefore is selected, in this work, as reliability criteria. The LPSP be calculated as the ratio of power supply deficit to the electric load demand during a certain period of time (normally a year). A ratio equal to zero means all load demand, during the period of time, is served by system (53). LPSP is given by LPSP=t=18760ENStt=18760ELtE56 A method that takes into account the weight of reliability in the economic model includes a component of the cost of electricity interruptions or cost of load (Closs) [17]. The cost of electricity interruptions can be estimated in different ways, for example, looking at the customer’s willingness to pay for an expansion or at production losses at industries affected, or at the level of compensations, which makes shortages acceptable. In [17], for 2009, the cost ranges from 5 to 40 USD$/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

ACloss=Closs×t=18760ENStE57

LPSPand AClossare calculated for each possible combination considered during the sizing methodology.

### 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=j=15ij=0.5E58
i1=i2=i3=i4=i5=0.1E59

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=j=15dj=1E60
d1=d2=d3=d4=d5=0.2E61

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

=11t×1t×j=1T1ij1+irj+j=1T2dj1+irjE62

wheretis the effective corporate tax income rate, T1is the maximum number of years to apply the investment tax credit, T2is the useful life of the power-generating facility for accelerated depreciation purposes (in year) = 5, iis the investment tax credit, and dis the depreciation factor expressed as percentage of investment cost over T2year.

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:

### 2.5 Objective function: optimization process

The objective of this work is sizing hybrid power generation systems (solar-diesel) 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:

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 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.

## 3. Case study

“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 developed in this work.

### 3.1 Meteorological inputs and load profile

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. The difference can be accounted to the simplicity of the transposition model used in our MATLAB routine; nevertheless the results are good enough for the purpose of this work.

Jan183.6182.0−0.88%201.9198.6−1.65%
Feb175.6174.2−0.81%186.9184.3−1.41%
Mar194.3193.0−0.68%198.5196.2−1.14%
Apr177.2176.1−0.65%175172.9−1.17%
May166.4165.2−0.70%160.1158.8−0.83%
Jun161.9160.8−0.71%153.6152.6−0.65%
Jul173.2172.0−0.69%165.3163.9−0.84%
Aug171.7170.6−0.65%167.8166.1−1.03%
Sep160.9159.8−0.70%162160.1−1.17%
Oct155.8154.4−0.91%162.4159.5−1.79%
Nov149.1147.7−0.96%160.5157.1−2.13%
Dec161.2159.7−0.93%177.8174.1−2.09%
Year2030.92015.3−0.77%2071.82044.1−1.34%

### Table 1.

Meteorological input parameters (monthly).

The load profile data was obtained from the National Monitoring Center (CNM) of the IPSE [22]. Table 2 shows the input data used to generate the daily load profile curve. Figure 4 shows the daily load profile for a week generated by a MATLAB routine developed in this work.

HourPower [%]Uncertainty factor [%]HourPower [%]Uncertainty factor [%]
hαpowerαunchαpowerαunc
07.7810120.9610
17.6810132.8810
27.4010145.6710
37.2010155.8610
46.3410163.7510
51.1510171.5410
60.000180.9610
70.000196.2410
80.000208.6510
90.000218.6510
100.000228.6510
110.3810238.2610
Yearly average daily energy demand [kWh], EAV,day520.5

### Table 2.

Daily load profile for “Santa Cruz del Islote” July 2018.

### 3.2 Technical inputs

This subsection describes the technical inputs required by the photovoltaic, diesel, and battery model employed in the optimization model developed in this work.

#### 3.2.1 Photovoltaic module technical data

A monocrystalline PV module of 300 Wp, reference JKM300M-60, from the company JINKO SOLAR, is used. Table 3 shows the technical characteristics of the PV module selected. The cost per Wp installed presented in Table 3 includes other costs not related to the price of the PV modules as the cost of charge controller, the PV inverters, and the mounting structure. Also this price includes indirect cost associated to the PV installation as engineering study costs, logistic costs, and certification costs. The cost per Wp presented is taken as reference and is provided by experts consulted in companies of energy sector.

SymbolDescriptionValue
PpvstcMaximum power [Wp]300
VmppMaximum power voltage [V]32.6
ImppMaximum power current [A]9.21
VocOpen-circuit voltage [V]40.1
IscShort-circuit current [A]9.72
ηpvModule efficiency (%)18.33
αPPower temperature coefficient [%/°C]−0.39
αVVoc temperature coefficient [%/°C]−0.29
αIIsc temperature coefficient [%/°C]0.05
NOCTNOCT [°C]45
cPVCost per Wp installed [USD/Wp]2
ρPVFixed OM factor as ratio of the PV CC0.01
fPVPhotovoltaic derating factor0.85
ηINVInverter efficiency0.9

### Table 3.

PV module technical inputs.

#### 3.2.2 Diesel genset technical data

The input data required by the diesel generation model is presented in Table 4. This information is collected from expert opinions on companies in the energy sector. This information must be validated each time the optimization model is used since it can vary depending on the studied case.

Diesel input data
SymbolDescriptionValue
NDG,maxMaximum number of DG unit5
LDGLifecycle [years]10
ρDGFixed OM value as percentage of the diesel initial investment [%]0.1
fCFuel cost [USD/l]0.8

### Table 4.

Diesel model technical inputs.

Table 5 shows a database of diesel generation units with the cost per kW and the fuel curve parameters. This table was built using information supplied by the Colombian Regulation Commission of Energy and Gas (CREG—Comisión de Regulación de Energía y Gas) in [23]. The cost per kW presented in Table 5 includes the direct and indirect costs related to the installation of a Diesel plant in non-interconnected zones.

DG power [kW]Cost per kW installed [USD/kW]Derate factors of the initial capital cost invested [%]1/2 load 1 hour in litersFull-load 1 hour in litersf0 [L/kWh]f1 [L/kWh]
102724.0931.831.42.60.0200.240
201697.2632.433.46.050.0370.265
251540.1231.633.66.40.0320.224
301934.4423.006.810.960.0880.277
401654.0923.718.6915.120.0560.321
501434.9225.129.82516.630.0600.272
601343.7525.2610.9618.140.0630.239
701788.8318.1311.4319.770.0440.238
801686.0818.5611.921.40.0300.237
1001723.4017.2412.8523.060.0260.204
1251587.1117.9218.934.40.0270.248
1501572.6317.5522.341.20.0220.252
2001373.7319.3229.1154.430.0190.253

### Table 5.

Diesel genset unit database.

#### 3.2.3 Battery bank technical data

In this chapter book, vented lead-acid battery banks only are considered. This kind of battery cells are often selected for large energy storage banks due the low cost, low maintenance, and high cycle stability. Table 6 shows the input data required by the battery bank. The battery bank charge and discharge efficiency and the self-discharge ratio is taken from [24]. The maximum depth of discharge is set in 0.5 since the battery bank can accomplish 3000 cycles during its life service according the datasheet. Other values as maintenance cost,ρbat, and the fraction of reposition cost, δbat, are set according to the recommendation of experts in the energy sector.

Battery bank input data
SymbolDescriptionValue
VdcbcBattery voltage [V]2
VdcsistDC system voltage [V]48
CrateCapacity rate [h]5
ηbat_cCharge efficiency0.9
ηbat_dDischarge efficiency1
σSelf-discharge rate0.000083
LbatLifecycle [years]10
δbatFactor of the initial capital cost invested for the battery bank0.7
ρbatFixed OM factor as ratio of the battery bank initial investment0.02
DODmaxMaximum depth of discharge0.5

### Table 6.

Battery bank technical inputs.

The main characteristics and price of the battery cells of the reference used in this work are presented in Table 7. The information was obtained from inquiries to local companies.

Battery cell capacity [Ah] at C10Battery cell capacity [kWh] at C10Battery cell voltage [V]# of cycles at 50% DODPrice per unit [USD] (€)Price per kWh [USD/kWh] (€)
2800.5623000114.00203.57
3500.723000135.00192.86
4200.8423000153.00182.14
5201.0423000161.00154.81
6201.2423000186.00150.00
7301.4623000210.00143.84
9101.8223000234.00128.57
10702.1423000303.00141.59
12202.4423000330.00135.25
13702.7423000361.00131.75
15203.0423000389.00127.96
16703.3423000426.00127.54
18203.6423000460.00126.37
21704.3423000538.00123.96
25405.0823000664.00130.71
29005.823000744.00128.28
32506.523000834.00128.31
36107.2223000906.00125.48
39807.9623000981.00123.24
43408.68230001056.00121.66
47009.4230001097.00116.70

### Table 7.

Battery cell database.

#### 3.2.4 System inputs

The system input parameters are shown in Table 8. The cost of energy lost is assumed in 0.2 USD/kWh. This value depends on the necessities and characteristics of the users of the select location. The interest rate considered in this work is 8.08% taken in [25].

System inputs parameters
SymbolDescriptionValue
RTime of the project [years]20
irReal interest rate [%]8.08
clossCost of energy loss [USD/kWh]0.2
ΔFiscal incentive factor0.9038

### Table 8.

System input parameters.

Fiscal incentive factor is calculated applying an effective corporate tax income rate of 33%. The resulting incentive factor is 0.938.

The parameters for the PSO algorithm and the boundaries for each decision variable are shown in Table 9.

PSO input parameters
SymbolDescriptionValue
NPVlLower bound number of PV modules0
wDGlLower bound nominal power of diesel0
NBplLower bound number of battery cell in parallel0
Ebcell,nomlLower bound nominal capacity of battery cell [kWh]0
NPVuUpper bound number of PV modules20,000
wDGuUpper bound nominal power of diesel unit in [kW]200
NBpuUpper bound number of battery cell in parallel10
Ebcell,nomuUpper bound nominal capacity of battery cell [kWh]9.40
MaxitMaximum number of iterations50
nPopPopulation size200
wInertia coefficient1
wmaxInertia coefficient max0.9
wminInertia coefficient min0.5
c1Personal acceleration coefficient2.5
c2Social acceleration coefficient1.5

### Table 9.

PSO input parameters.

## 4. Results of the case study

Table 10 summarized the obtained results after applying the proposed sizing methodology. The best cost achieved was 0.2090 USD/kWh being the lowest obtained. The optimization results deliver no only the design (number of components) but also economic and reliability indicators.

ComponentDesignUnitIndicatorValueUnit
Npv13UnitsCCpv7800.00USD
Ppvstc3.9[kWp]CCDG48257.99USD
wDG25[kW]CCbat3864.00USD
NDG2UnitsO&Mpv78.00USD/year
PDG50[kW]O&MDGf4825.80USD/year
Nbp1UnitsO&MDGv26884.74USD/year
Nbs24UnitsO&MDG31710.54USD/year
Nbat24UnitsO&Mbat77.28USD/year
Ebcell,nom1.04[kWh]RCDG7019.48USD
Ebat,n24.96[kWh]RCbat1243.60USD
FC38406.77[l]
LPSP1.25%
ACloss475.03USD/year
LPVG0.00%
Cost0.21USD/kWh

### Table 10.

Results of the case study.

## 5. Conclusions

In this work, an optimization methodology was developed and described in detail to help sizing HRSE integrated by photovoltaic and diesel generation with energy storage.

The main features of the sizing methodology developed were as follows: (a) it allows the simulation of hybrid renewable systems and the evaluation of its economic and reliability integrated by diesel and photovoltaic generation with energy storage, (b) the dispatch strategy developed prioritize the use of renewable energy among other energy sources, and (c) fiscal incentives granted by the Act 1715 of 2014 in Colombia were considered on the calculation of the cost of energy using the fiscal incentive factor.

The reliability of the system was included in the objective function of the PSO algorithm through the annual cost of the energy not supplied. Also a fiscal incentive factor was used to include the financial benefits granted by the Act 1715 of 2014 in Colombia to non-conventional renewable source of energy. The results were obtained after simulating the energy flow of the system for 1 year with 1-hour resolution.

Dispatch strategy was described in detail, prioritizing the use of renewable resource over diesel generation to supply the load. Also diesel generation cannot be used to charge the battery bank. This condition was based on the fact that, in off-grid areas, the complications associated to supply the fuel and the maintenance of DG units are commonly underestimated.

It is expected that this work will help the process of designing HRES in non-interconnected areas, thus contributing to the development of these locations and improving the life quality of the population living on these places.

## Acknowledgments

The authors gratefully acknowledge the financial support provided by the Colombia Scientific Program within the framework called “Ecosistema Científico” (Contract No. FP44842-218-2018).

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© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Oswaldo A. Arraez-Cancelliere, Nicolás Muñoz-Galeano and Jesús M. López-Lezama (September 13th 2019). Methodology for Sizing Hybrid Battery-Backed Power Generation Systems in Off-Grid Areas, Wind Solar Hybrid Renewable Energy System, Kenneth Eloghene Okedu, Ahmed Tahour and Abdel Ghani Aissaou, IntechOpen, DOI: 10.5772/intechopen.88830. Available from:

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