Optimal Configuration for Design of Stand-Alone PV System

This paper presents a design for a stand-alone photovoltaic (PV) system to provide the required electricity for a single residential household in rural area in Jordan. The complete design steps for the suggested household loads are carried out. Site radiation data and the electrical load data of a typical household in the considered site are taken into account during the design steps. The reliability of the system is quantified by the loss of load probability. A computer program is developed to simulate the PV system behavior and to numerically find an optimal combination of PV array and battery bank for the design of stand-alone photovoltaic systems in terms of reliability and costs. The program calculates life cycle cost and annualized unit electrical cost. Simulations results showed that a value of loss of load probability LLP can be met by several combinations of PV array and battery storage. The method developed here uniquely determines the optimum configuration that meets the load demand with the minimum cost. The difference between the costs of these combinations is very large. The optimal unit electrical cost of 1 kWh for LLP = 0.049 is $0.293; while for LLP 0.0027 it is $0.402. The results of the study encouraged the use of the PV systems to electrify the remote sites in Jordan.


Introduction
Renewable-energy sources are becoming more and more attractive especially with the constant fluctuation in oil prices.Solar has good potential and the direct conversion technology based on solar photovoltaic has several positive attributes especially in remote areas [1][2][3][4].The Photovoltaic (PV) system is considered one of the important alternative sources in this regard.Because PV energy production is clean, freely infinitely available and of high reliability, it is a very attractive power source for many applications, especially in rural and remote areas in Mediterranean countries where they have a large quantity of solar radiation around the year.
Jordan is blessed with an abundance of solar energy.The possible amount of generating power and the scope of thermal applications using solar energy is huge.Most parts of Jordan get 300 days of sunshine per year.This makes the country a very promising place for solar energy utilization [5].The annual daily average solar irradiance (average insulation intensity on a horizontal surface) ranges between 4 -7 kWh/m 2 , which is one of the highest in the world.This corresponds to a total annual of 1400 -2300 kWh/m 2 depending upon location.
Jordan has successfully completed the plan for electrification for most of the villages through the utility grid.Due to remoteness and cost, for some parts of Jordan it is unlikely that the main grid connection will ever be established.A stand-alone PV system with storage battery will be excellent choice for such areas.
A photovoltaic (PV) cell converts sunlight into electricity.A PV or solar cell is the basic building block of a PV system.An individual PV cell is usually quite small.PV cells are connected together to form larger units called modules which can be connected to form even larger units called arrays.These arrays are connected in parallels and series to meet the required electricity demand.PV arrays produce power only when illuminated, and it is therefore standard to employ a large energy storage mechanism, most commonly a series of rechargeable batteries.To pre-2vent harmful battery over-charge and over-discharge conditions and to drive AC loads, a charge controller and a converter must be implemented.
Sizing of the PV array, inverter and battery bank for a stand-alone PV system is an important part of system design.This part requires solar radiation data for the intended geographical location of the site, load demand and manufacturing data for PV modules, inverters and batteries and their operational efficiencies.Numerous studies have been conducted to develop a sizing method which is both easy to apply and highly reliable [6].Most of these methods assume constant system load and control the variables that have an influence on the degree of reliability.Methods that are based on the concept of power supply during a number of autonomous days are typically used.These methods are simple and assure the required reliability of the PV system during autonomous days.In these methods, the storage system meets the load demand.The storage system capacity is regarded as a measure of reliability of the PV system.So the reliability is determined by the autonomous days.These methods exhibit no direct relationship between the PV array output and the storage system capacity.Also, the resultant sizing of the combination of PV array and battery bank for a solar PV system is not necessarily optimal.Method based on the study and characterization of daily energy balances is developed [7,8].More universal results are obtained when implementing these methods.Another method design of a stand-alone PV system is based on the concept of reliability of the power supply to the load, which is usually quantified by the loss of power supply probability (LPSP) [9][10][11][12][13][14][15][16][17].This concept is defined as the relationship between the energy deficit and the energy demand during the total operation time of the installation.In statistical terms, the LLP value refers to the probability that the system will be unable to meet energy demand.
Due to the random nature of the energy source, great effort must be made to optimize the design of stand-alone photovoltaic systems in terms of both energy consumption and costs.The cost of RE generation plays a major role in determining the effectiveness of the RE systems.Hernández et al. examined the development of the four main renewable energy technologies (RET) in Spain in the latest years: biomass, small hydro (SH), solar photovoltaic (solar PV) and wind [18].The study concluded that Spain is suitable in meeting the RE generation target but not efficient in costs.The task of sizing should compromise between cost and reliability.Accurate sizing ensures that demand is met and allows costs to be cut in the future.This will allow a practical use of these systems in the renewable energies market.Sizing a PV system means determining both the number and area of modules to install and the capacity or total number of ampere-hours collectable in the battery.
In this work a standard model based on daily energy balance is used to determine system size.Several design criteria are investigated.Numerical methods based on detailed simulations of PV system behavior which are performed over a specific period of time are used.The energy balance of the PV system and the state of charge of the battery are calculated daily.The simulation period is taken to be one year to have statistical significance of the value of loss of load probabilities LLP.A computer program is developed to simulate the PV system behavior and to numerically find an optimal combination of PV array and battery bank for the design of stand-alone photovoltaic systems in terms of reliability and costs.The detailed design and economical analysis of a stand-alone PV system to provide the required electrical energy for a single residential household in Jordan is presented.The considered location is Jordan University of Science and Technology, which is located in the northern part of Jordan.

Ease the Household PV System Configuration
The basic configuration of a PV stand-alone system shown in Figure 1 is considered in this study.The system consists mainly of solar panels, inverter, batteries and load.The function of the PV array is to convert the sunlight directly into DC electrical power.The inverter is used to convert the DC electrical power into AC power; to match the requirements of the common household AC appliances.
The excessive part of DC power is stored in the battery to be used when there is no sunshine.The controller monitors the electrical input from the solar panels and controls the amount going directly into the inverter and the amount for charging and discharging of the battery bank.

Prepare Site Meteorological Data
To predict the performance of a PV system in a location, it is necessary to collect the meteorological or environmental data for the site location under consideration.Copyright © 2012 SciRes.Table 1.Clear days and sunshine hours average numbers.

Electrical Demand
The household in the remote area in Jordan is assumed to be simple-not requiring large quantities of electrical energy.The electrical loads include lighting, medium size refrigerator, one microwave oven and other ordinary household electrical appliances, e.g.TV sets, hair dryers, etc.The daily electrical demand in a typical day for each device is shown in Table 2.It is assumed that this load is constant around the year.The corresponding load profile for a typical day is indicated in Figure 3.The average daily load demand EL can be calculated from Table 2 to be 13205 Wh/day.

PV System Design
Jordan is a relatively small country.The northern part of Jordan is located near 30.58˚latitude and 36.23˚longitude.Tilt angle is defined as the angle of inclination of a module measured from the horizontal.Since the considered site is located at 30.58˚ North latitude and 36.23˚east longitude, the optimal angle for solar panels is to be 30˚ degree facing south.The output of a PV array is related to the light intensity falling on the PV array, ambient temperature, cell temperature, load status and characteristics of PV modules.Since the PV array considered in this study is tilted 30˚ facing south, the hourly global radiation on a horizontal surface should be converted to that on PV modules.Chenni et al. developed a simple method to calculate global, diffuse and direct irradiance on vertical and tilted surfaces for all uniform sky conditions (clear sky and overcast sky) [19].Since the hourly global radiation on a horizontal surface is available, the total irradiance on tilted plane with any orientation can be given using Hay's sky diffusion anisotropic model [20].
where, G is total irradiance on horizontal surface (W/m 2 ), G b is direct radiation incident on horizontal surface W/m 2 ), G β is total irradiance on tilted surface (W/m 2 ), G d is diffuse incident on horizontal surface W/m 2 ), and R B the ratio of the direct radiation on the tilted plane to that on a horizontal surface and has the following form: The remaining variables and quantities are determined by:  The hourly tilted solar irradiation is calculated using the above Equations ( 1)-( 3).The average monthly tilted irradiation is shown in Figure 2.

Design Criteria
To design a stand-alone PV system for the considered household, the size of the PV array and battery bank capacity should be determined.Two design criteria are used: average daily solar radiation and average lowest month.The ability of the resulting sizes from these two criteria to meet the daily demand is investigated.The size of the PV array used in this study can be calculated by the following equation [21]: where, G in is solar energy input per day on PV panels, TCF is the temperature correction factor, η PV is PV efficiency, η out is battery efficiency (η B ) × inverter efficiency (η Inv ).
As for the sizing of the battery, the storage capacity of the battery can be calculated according to the following relation [22,23]: where, N c is number of autonomous days (the largest number of continuous cloudy days of the site).DOD is maximum permissible depth of discharge of the battery.The selected modules are PS-P 60 mono-crystalline silicon (see [24]), with the following specifications at standard test conditions (i.e., 1000 W/m 2 and 25˚C): -Max Power = 250 W; -Max Current = 8.17 Amps; -Max Voltage = 29.4Volts; -Nominal Output Voltage 24 Volts; -PV Efficiency η PV = 14%.For the first design criteria based on average daily solar radiation, the average daily solar energy input over the year (G av ) on a south facing surface tilted at an angle equal to 30˚ is calculated from Figure 2 to be about 5.475 kWh/m 2 •day.If the cell temperature is assumed to reach 45˚C in the field, then the temperature correction factor (TCF) will be 0.9 as indicated in [21].Assuming battery efficiency η B = 0.85 and inverter efficiency η Inv = 0.94, then η out = 0.85 * 0.94.Thus, using Equation ( 4), the PV area is 25.4 m 2 , if the largest number of continuous cloudy days Nc in the selected site is about 3 days.Thus, for a maximum depth of discharge for the battery DOD of 0.8, the storage capacity according to Equation ( 5) is 61.975 kWh.For the second design criteria based on the average lowest month of solar irradiation, Figure 2 shows that the lowest irradiation corresponds to Dec. with tilted average equal to 3.4 kWh/m 2• day.The design will be based on this value G min .According to equation (4), the PV area is 40.9 m 2 .The required storage capacity for five autonomous days is 61.975 kWh.
In order to determine the ability of the resulting sizes from these two criteria to meet the daily demand, the daily amount of charge remaining in the batteries is calculated.The batteries supply the required electricity when there is no direct electricity PV production.The batteries recharge during the daylight if extra energy is available.Figure 4 shows the daily amount of charge remaining in the batteries for four months in row starting in Oct. On October first, the batteries are assumed to be fully charged.The amount of energy in fully charged batteries is 61.975 kWh.For PV area = 25.4 m 2 , the battery completely discharged on Dec. 6 and this failure continued for the next two months.On the other hand, when PV area = 40.9m 2 , the stand-alone PV system meet the required load without any failure.However, if there is a charge controller set to prevent discharging the batteries at 20%, then there will be power out for five nights.production completely charge the batteries during Oct.However, during November, there is not enough PV production to completely charge the batteries during the daytime.The amount of battery charge kept decreasing during November all the way until it is completely discharged on the beginning of December.It took the system over two months to completely recharge the batteries.
As for PV area = 40.9m 2 , the PV production during day is able to completely recharge the batteries until the beginning of December.The amount of energy stored in the batteries stays relatively large except for few days at the beginning of January.After that is increased rapidly.

Design of the Battery Charge Controller
The primary function of a charge controller in a standalone PV system is to maintain the battery at highest possible state of charge while protecting it from overcharge by the array and from over discharge by the loads.Wu et al. developed a new fast charging method that is applied to micro-grid photovoltaic systems to eliminate batteries undercharge or overcharge due to random changes of solar radiation [25].Some PV systems can be effectively designed without the use of charge control.In the present study, a charge control is required due to the fact that the load is unpredictable.Another reason for the charge control is that the battery storage is optimized resulting in undersized system, a charge control is need to prevent the severe discharge resulting in short life of the battery.The algorithm or control strategy of a battery charge controller determines the effectiveness of battery charging and PV array utilization, the ability of the system to meet the load demands and extend the lifetime of a battery.When the irradiation is high (typically during summer), energy generated by the PV array often exceeds the electrical load demand.To prevent battery damage resulting from overcharge, a charge controller is used to protect the battery.A charge controller should prevent overcharge of a battery regardless of the system sizing/design and seasonal changes in the load profile, operating temperatures and solar irradiation.It has to be capable of carrying the short circuit current of the PV array.Thus, in this case, it can be chosen to handle 73.4A and to maintain the DC bus voltage to about 36 V.

Design of the Inverter
The selected inverter must be able to handle the maximum expected power of AC loads.The rated power of the inverter Prat, inv taken to be 20% higher than the rated power of the total AC loads that presented in Table 2. Thus the rated power of the required inverter will be 1800 W. the specification of the required inverter will be 1800 W, 36 VDC, and 50 Hz.

Sizing of the Battery
The life of battery is a function of maximum depth of discharge DOD.The maximum depth of discharge for the battery is taken to be 0.8.The sizing method for barratry storage is based on the concept of power supply during a number of autonomous days; during these days the load demand is met solely by the storage system.If the largest number of continuous cloudy days (number of autonomous days) is NC, then the minimum required amperehours of the battery Ah totB is calculated by: If the selected battery is lead acid with nominal voltage = 12 Volts and rated capacity = 220 Amp-hrs, then the number of Batteries in Parallel NB p is calculated by: Ah Ah rated capacity 220 Three batteries are needed to meet the system nominal voltage.Finally, the total number of batteries s is NM P × NM S batteries.

Sizing of PV Modules
The numbers of PV modules are determined by the following expressions: where PV peak power is calculated by where PSI is the maximum radiation intensity taken to be 1000 W/m 2 , and the peak power of the selected module is 250 W. The number of modules in parallel NM p and series are calculated by: Ah , ,

Sizing Optimization
As mentioned previously, the method presented here is quit simple and quick, but the resulting sizing of the combination of PV array and battery bank for a solar PV system is not necessarily optimal.It is the objective of this section to find a sizing combination that minimizes the cost while maintaining desired values of reliability.The reliability of power supply of system is expressed in terms of the loss of load probability (LLP), defined as the power failure time Tf divided by the estimated period of time T, i.e.LLP = Tf/T.For the given LLP value of the whole year, many configurations can meet this reliability demand of power supply.In this study, a program for calculating the LLP values and the total cost of different configurations is developed.In the program, a PV area and number of autonomous days are provided to the program.The program calculates the daily PV output for the whole year according to the following equation and compares it with the daily demand E L .A charge controller is simulated that prevents the both overcharge and the undercharge of batteries bank.The amount charge stored in batteries is calculated daily.A power failure is indicated if the amount of charge reaches the lower limits, which is specified here to be 20% of the storage capacity given by Equation (5).The program counts these times and calculate LLP for the given combination.The program calculates the total number of PV modules (parallels and series) required according to Equations ( 10) and (11).
The program has calculated the whole year's LLP values of different configurations with PV area changing from 30 m 2 to 50 m 2 and number of autonomous days changing from 1 to 7. The trade-off curves between the numbers of PV modules and number of batteries for several LLPs are shown in Figure 5. Figure 5 shows only parts of calculation results.
The objective function of the optimization problem is the life cycle cost (LCC) of stand-alone PV system.The LCC of any system consists of the total costs of owning and operating it over its lifetime, expressed in today's money.The costs of a stand-alone PV system include acquisition costs, operating costs, maintenance costs, and replacement costs.The LCC of the PV system includes the sum of all the present worth's (PWs) of the costs of the PV modules, storage batteries, battery charger, and inverter, the cost of the installation, and the maintenance and operation cost (M&O) of the system.The details of the used cost data for all items are shown in Table 3.These data was obtained from the manufacturer of PV system [26].
The lifetime N of all the items is considered to be 20 years, except that of the battery which is considered to be 5 years.Thus, an extra three groups have to be purchased, after 5 years, 10 years, and 15 years.Assuming an inflation rate i of 3% and an interest rate d of 10%.
The program calculates the LLC for any combinations according to the following equations: PV array cost C PV is given by: where PV peak power is calculated by Equation ( 9) Initial cost of batteries is given by: where Ah tot is the required ampere-hour of the batteries calculated from Equation ( 6) The charger cost is given by:  The LCC of the system is calculated by summing all the above cost, I'e The installation cost is taken to be 10% of the PV cost.As for the current value of the maintenance cost C MPW is calculated by [25]: Table 4 list sample of the calculation results output from the program developed.For a given value of LLP there is an optimum configuration that has the lowest cost.For example, for LLP = 0.0027, the cost of the combination that meet this requirement ranges from $22,267 to 26,177.However, the optimum combination is number of batteries = 10 and PV modules = 20.Another example for LLP = 0.033, the cost of the system The maintenance cost per year (M/yr) is assumed 2% of the PV cost.
The present value of the n th extra group of batteries C BnPW purchased after N years is calculated by: For LLP = 0, the stand-alone system works without any power failure.The optimal cost for such system is $23,239, which is combined of 11 batteries and 20 PV modules.However, for LLP = 0.049, which means there are 18 nights without power in the whole year.The optimal cost for such system is $16,212.Knowing this difference can help the designer decided to install another auxiliary hybrid system or not.
It is sometimes useful to calculate the LCC of a system on an annual basis.The annualized LCC (ALCC) of the PV system in terms of the present day dollars can be calculated by: Unit electrical cost of 1 kWh is ALCC 365 L E .
Table 5 summarizes the optimal configurations and the corresponding unit cost of electricity.The calculated current unit cost of PV systems depends on the LLP values.There values range between 0.419 S/kWh and 0.293 $/kWh.Although this price is very high compared to the current unit cost of electricity in Jordan (0.114 $/kWh), it is predicted that this price will drop significantly in the future due to decrease in the initial cost of the PV modules.At the same time, if the future unit cost of electricity in Jordan increases due to the rapid increase in the conventional fuel prices, therefore PV energy generation will be promising in the future house electrification due to its expected future lower unit electricity cost, efficiency increase, and clean energy generation compared to the conventional utility grid.

Conclusion
An electrification study for a single residential house in a remote isolated site of Jordan is carried out using a stand-alone PV system.The complete design steps and the life cycle cost analysis of the PV system is presented.
A method based on calculating the yearly loss of load probability LLP has been presented for a PV sizing.A computer program that simulates the stand-alone PV system daily behavior is developed.According to local hourly measured meteorological data, load demand, the characteristic and price of the components and reliability requirement on power supply, the optimum configuration which meets the load demand with the minimum cost can be uniquely determined by the program.The unit electrical cost for electrifying a remote isolated house using PV systems is calculated.The results of study indicates that using the optimal configuration for electrifying remote areas in Jordan is beneficial and suitable for long-term investments, especially if the initial prices of the PV systems are decreased and their efficiencies are increased.Therefore, in remote sites that are too far from the Jordanian power grid, it is encouraged to install PV systems to generate electricity.

Figure 2 .
Figure 2. Monthly average daily global radiation (total irradiance) on a horizontal surface and on a 30 o tilted plane at the considered site.

Figure 3 .
Figure 3.The load profile of the household.
For PV area = 25.4 m 2 , the amount of extra PV

Figure 4 .
Figure 4. Daily amount of charge remaining in the batteries.

Figure 5 .
Figure 5. Trade off curves between the numbers of batteries and PV modules for the different LLP values.

The monthly average daily solar radiation data incident on a horizontal surface at the considered site is shown in Fig- ure 2. It is clear from Figure 2 that solar energy incident in the considered site is very high especially during the summer months, where it exceeds 7 kWh/m 2 /day on hori- zontal. Table 1 lists the average number of clear days for
each month and the average number of shining hours for each month.It is clear from Table1that even in winter, Jordan enjoys more than twenty days of sunshine per month.The total number of sunshine days in Jordan exceeds 300 annually.

Table 2 . The Household Load Data.
where, θ theta is incidence angle of light rays (deg), θ z is Zenith angle (deg), β is the Tilt angle of plane to gorund (deg), δ is declination of the sun (deg), ϕ is latitude,  is azimuth angle of inclidned plane (deg),  s is solar azimuth angle (deg),  is hours angle (deg).

Table 1 ,
to be 6 hours and the system nominal voltage is taken to be 36 volt.The losses and safety factor is assumed to be 1.2.The total number of modules NM tot is