Solar Power

Technical / Solar Power

Solar Power

 

 Solar Power
 This chapter provides an introduction to the components of a standalonephotovoltaicsystem. The word standalone refers to the fact that the systemworks without any connection toan established power grid. In this chapter,we will present the basic concepts of the generation and storage of photovoltaicsolar energy. We will also provide a method for designing a functionalsolar system with limited access to information and resources.
   This chapter only discusses the use of solar energy for the direct productionof electricity (photovoltaic solar energy). Solar energy can also be used toheat fluids (thermal solar energy) which can then be used as a heat sourceor to turn a turbine to generate electricity. Thermal solar energy systems are
beyond the scope of this chapter.
Solar energy
   A photovoltaic system is based on the ability of certain materials to convertthe radiant energy of the sun into electrical energy. The total amount of solarenergy that lights a given area is known as irradiance (G) and it is measuredin watts per square meter (W/m2). The instantaneous values are normallyaveraged over a period of time, so it is common to talk about total irradiance
per hour, day or month.
   Of course, the precise amount of radiation that arrives at the surface of theEarth cannot be predicted with high precision, due to natural weather variations.Therefore it is necessary to work with statistical data based on the "solarhistory" of a particular place. This data is gathered by a weather stationover a long period and is available from a number of sources, as tables ordatabases. In most cases, it can be difficult to find detailed information abouta specific area, and you will need to work with approximate values.
   A few organizations have produced maps that include average values of dailyglobal irradiation for different regions. These values are known as peak sunhours or PSHs. You can use the PSH value for your region to simplify yourcalculations. One unit of "peak sun" corresponds to a radiation of 1000 Wattsper square meter. If we find that certain area has 4 PSH in the worst of themonths, it means that in that month we should not expect a daily irradiationbigger than 4000 W/m2 (day). The peak sun hours are an easy way to representthe worst case average of irradiation per day.
   Low resolution PSH maps are available from a number of online sources, such
information, consult a local solar energy vendor or weather station.
What about wind power?
   It is possible to use a wind generator in place of solar panels when anautonomous system is being designed for installation on a hill or mountain.To be effective, the average wind speed over the year should be at least 3 to4 meter per second, and the wind generator should be 6 meters higher thanother objects within a distance of 100 meters. A location far away from thecoast usually lacks sufficient wind energy to support a wind powered system.
   Generally speaking, photovoltaic systems are more reliable than wind generators,as sunlight is more available than consistent wind in most places. Onthe other hand, wind generators are able to charge batteries even at night, aslong as there is sufficient wind. It is of course possible to use wind in conjunctionwith solar power to help cover times when there is extended cloudcover, or when there is insufficient wind.
   For most locations, the cost of a good wind generator is not justified by themeager amount of power it will add to the overall system. This chapter willtherefore focus on the use of solar panels for generating electricity.
Photovoltaic system components
A basic photovoltaic system consists of four main components: the solarpanel, the batteries, the regulator, and the load. The panels are responsiblefor collecting the energy of the sun and generating electricity. The batterystores the electrical energy for later use. The regulator ensures that paneland battery are working together in an optimal fashion. The load refers to anydevice that requires electrical power, and is the sum of the consumption of allelectrical equipment connected to the system. It is important to rememberthat solar panels and batteries use direct current (DC).
   If the range of operational voltage of your equipment does not fit the voltagesupplied by your battery, it will also be necessary to include some type ofconverter. If the equipment that you want to power uses a different DC voltagethan the one supplied by the battery, you will need to use a DC/DC converter.If some of your equipment requires AC power, you will need to use aDC/AC converter, also known as an inverter.
   Every electrical system should also incorporate various safety devices in theevent that something goes wrong. These devices include proper wiring, circuitbreakers, surge protectors, fuses, ground rods, lighting arrestors, etc.
The solar panel
   The solar panel is composed of solar cells that collect solar radiation andtransform it into electrical energy. This part of the system is sometimes referredto as a solar module or photovoltaic generator. Solar panel arrays can bemade by connecting a set of panels in series and/or parallel in order to providethe necessary energy for a given load. The electrical current supplied by a solarpanel varies proportionally to the solar radiation. This will vary according toclimatological conditions, the hour of the day, and the time of the year.
   Several technologies are used in the manufacturing of solar cells. The mostcommon iscrystalline silicon, and can be either monocrystalline or polycrystalline.Amorphous silicon can be cheaper but is less efficient at converting solarenergy to electricity. With a reduced life expectancy and a 6 to 8% transformationefficiency, amorphous silicon is typically used for low power equipment,such as portable calculators. New solar technologies, such as silicon ribbon
and thin film photovoltaics, are currently under development. These technologiespromise higher efficiencies but are not yet widely available.
The battery
   The battery stores the energy produced by the panels that is not immediatelyconsumed by the load. This stored energy can then be used during periodsof low solar irradiation. The battery component is also sometimes calledthe accumulator. Batteries store electricity in the form of chemical energy.The most common type of batteries used in solar applications aremaintenance-free lead-acid batteries, also called recombinant or VRLA(valve regulated lead acid) batteries.
   Aside from storing energy, sealed lead-acid batteries also serve two importantfunctions:
• They are able to provide an instantaneous power superior to what the arrayof panels can generate. This instantaneous power is needed to start someappliances, such as the motor of a refrigerator or a pump.
• They determine the operating voltage of your installation.
   For a small power installation and where space constraints are important,other type of batteries (such as NiCd, NiMh, or Li-ion) can be used. Thesetypes of batteries need a specialized charger/regulator and cannot directlyreplace lead-acid batteries.
The regulator
The regulator (or more formally, the solar power charge regulator) assuresthat the battery is working in appropriate conditions. It avoids overcharging oroverdischarging the battery, both of which are very detrimental to the life ofthe battery. To ensure proper charging and discharging of the battery, the regulatormaintains knowledge of the state of charge (SoC) of the battery. TheSoC is estimated based on the actual voltage of the battery. By measuringthe battery voltage and being programmed with the type of storage technologyused by the battery, the regulator can know the precise points where thebattery would be overcharged or excessively discharged.
   The regulator can include other features that add valuable information andsecurity control to the equipment. These features include ammeters, voltmeters,measurement of ampere-hour, timers, alarms, etc. While convenient,none of these features are required for a working photovoltaic system.
The converter
The electricity provided by the panel array and battery is DC at a fixed voltage.The voltage provided might not match what is required by your load. Adirect/alternating (DC/AC) converter, also known as inverter, convertsthe DC current from your batteries into AC. This comes at the price of losingsome energy during the conversion. If necessary, you can also use convertersto obtain DC at voltage level other than what is supplied by the batteries.DC/DC converters also lose some energy during the conversion. For optimaloperation, you should design your solar-powered system to match thegenerated DC voltage to match the load.
The load
   The load is the equipment that consumes the power generated by your energy system. The load may include wireless communications equipment, routers,workstations, lamps, TV sets, VSAT modems, etc. Although it is not possible toprecisely calculate the exact total consumption of your equipment, it is vital tobe able to make a good estimate. In this type of system it is absolutely necessaryto use efficient and low power equipment to avoid wasting energy.
Putting it all together
   The complete photovoltaic system incorporates all of these components. Thesolar panels generate power when solar energy is available. The regulatorensures the most efficient operation of the panels and prevents damage tothe batteries. The battery bank stores collected energy for later use. Convertersand inverters adapt the stored energy to match the requirements ofyour load. Finally, the load consumes the stored energy to do work. When allof the components are in balance and are properly maintained, the systemwill support itself for years.
 We will now examine each of the individual components of the photovoltaicsystem in greater detail.
The solar panel
   An individual solar panel is made of many solar cells. The cells are electricallyconnected to provide a particular value of current and voltage. The individualcells are properly encapsulated to provide isolation and protectionfrom humidity and corrosion.
   There are different types of modules available on the market, depending onthe power demands of your application. The most common modules arecomposed of 32 or 36 solar cells of crystalline silicon. These cells are all ofequal size, wired in series, and encapsulated between glass andplastic material, using a polymer resin (EVA) as a thermal insulator. The surface area ofthe module is typically between 0.1 and 0.5 m2. Solar panels usually havetwo electrical contacts, one positive and one negative.
   Some panels also include extra contacts to allow the installation of bypassdiodes across individual cells. Bypass diodes protect the panel against aphenomenon known as “hot-spots”. A hot-spot occurs when some of the cellsare in shadow while the rest of the panel is in full sun. Rather than producingenergy, shaded cells behave as a load that dissipates energy. In this situation,shaded cells can see a significant increase in temperature (about 85 to100ºC.) Bypass diodes will prevent hot-spots on shaded cells, but reduce themaximum voltage of the panel. They should only be used when shading isunavoidable. It is a much better solution to expose the entire panel to full sunwhenever possible.
   The electrical performance of a solar module its represented by the IV characteristiccurve, which represents the current that is provided based on thevoltage generated for a certain solar radiation.
   The curve represents all the possible values of voltage-current. The curvesdepend on two main factors: the temperature and the solar radiation receivedby the cells. For a given solar cell area, the current generated is directly proportionalto solar irradiance (G), while the voltage reduces slightly with anincrease of temperature. A good regulator will try to maximize the amount ofenergy that a panel provides by tracking the point that provides maximumpower (V x I). The maximum power corresponds to the knee of the IV curve.

 

Solar Panel Parameters
The main parameters that characterize a photovoltaic panel are:
1. SHORT CIRCUIT CURRENT (ISC): the maximum current provided by thepanel when the connectors are short circuited.
2. OPEN CIRCUIT VOLTAGE (VOC): the maximum voltage that the panelprovides when the terminals are not connected to any load (an open circuit).This value is normally 22 V for panels that are going to work in 12 Vsystems, and is directly proportional to the number of cells connected inseries.
3. MAXIMUM POWER POINT (Pmax): the point where the power suppliedby the panel is at maximum, where Pmax = Imax x Vmax. The maximumpower point of a panel is measured in Watts (W) or peak Watts (Wp). It isimportant not to forget that in normal conditions the panel will not work atpeak conditions, as the voltage of operation is fixed by the load or theregulator. Typical values of Vmax and Imax should be a bit smaller than theISC and VOC
4. FILL FACTOR (FF): the relation between the maximum power that thepanel can actually provide and the product ISC . VOC. This gives you anidea of the quality of the panel because it is an indication of the type of IVcharacteristic curve. The closer FF is to 1, the more power a panel canprovide. Common values usually are between 0.7 and 0.8.
5. EFFICIENCY (h): the ratio between the maximum electrical power thatthe panel can give to the load and the power of the solar radiation (PL)incident on the panel. This is normally around 10-12%, depending on thetype of cells (monocrystalline, polycrystalline, amorphous or thin film).
Considering the definitions of point of maximum power and the fill factor wesee that:
�� h = Pmax / PL = FF . ISC . VOC / PL
   The values of ISC, VOC, IPmax and VPmax are provided by the manufacturer andrefer to standard conditions of measurement with irradiance G = 1000 W/m2,at sea-level, for a temperature of cells of Tc = 25ºC.The panel parameters values change for other conditions of irradiance and temperature.Manufacturers will sometimes include graphs or tables with values forconditions different from the standard. You should check the performance valuesat the panel temperatures that are likely to match your particular installation.Be aware that two panels can have the same Wp but very different behaviorin different operating conditions. When acquiring a panel, it is important toverify, if possible, that their parameters (at least, ISC and VOC) match the values
promised by the manufacturer.
Panel parameters for system sizing
   To calculate the number of panels required to cover a given load, you justneed to know the current and voltage at the point of maximum power: IPmaxand VPmax.
   You should always be aware that the panel is not going to perform under perfectconditions as the load or regulation system is not always going to work atthe point of maximum power of the panel. You should assume a loss of efficiencyof 5% in your calculations to compensate for this.
Interconnection of panels
    A solar panel array is a collection of solar panels that are electrically interconnectedand installed on some type of support structure. Using a solarpanel array allows you to generate greater voltage and current than is possiblewith a single solar panel. The panels are interconnected in such a waythat the voltage generated is close to (but greater than) the level of voltage ofthe batteries, and that the current generated is sufficient to feed the equipmentand to charge the batteries.
   Connecting solar panels in series increases the generated voltage. Connectingpanels in parallel increases the current. The number of panels usedshould be increased until the amount of power generated slightly exceedshe demands of your load.
   It is very important that all of the panels in your array are as identical as possible.
In an array, you should use panels of the same brand and characteristics
because any difference in their operating conditions will have a big impact on
the health and performance of your system. Even panels that have identicalperformance ratingswill usually display some variance in their characteristicsdue to manufacturing processes. The actual operating characteristics of twopanels from the same manufacturer can vary by as much as ±10%.
   Whenever possible, it is a good idea to test the real-world performance ofindividual panels to verify their operating characteristics before assemblingthem into an array.
How to choose a good panel
   One obvious metric to use when shopping for solar panels is to compare theratio of the nominal peak power (Wp) to the price. This will give you a roughidea of the cost per Watt for different panels. But there are a number of otherconsiderations to keep in mind as well.
   If you are going to install solar panels in geographical areas where soiling(from dust, sand, or grit) will likely be a problem, consider purchasing panelswith a low affinity for soil retention. These panels are made of materialsthat increase the likelihood that the panel will be automatically cleaned bywind and rain.
   Always check the mechanical construction of each panel. Verify that theglass is hardened and the aluminum frame is robust and well built. The solarcells inside the panel can last for more than 20 years, but they are very fragileand the panel must protect them from mechanical hazards. Look for themanufacturer’s quality guarantee in terms of expected power output and mechanical
construction.
   Finally, be sure that the manufacturer provides not only the nominal peakpower of the panel (Wp) but also the variation of the power with irradiationand temperature. This is particularly important when panels are used in arrays,as variations in the operating parameters can have a big impact on thequality of power generated and the useful lifetime of the panels.
The battery
   The battery “hosts” a certain reversible chemical reaction that stores electricalenergy that can later be retrieved when needed. Electrical energy istransformed into chemical energy when the battery is being charged, and thereverse happens when the battery is discharged.
   A battery is formed by a set of elements or cells arranged in series. Leadacidbatteries consist of two submerged lead electrodes in an electrolytic solutionof water and sulfuric acid. A potential difference of about 2 volts takesplace between the electrodes, depending on the instantaneous value of thecharge state of the battery. The most common batteries in photovoltaic solarapplications have a nominal voltage of 12 or 24 volts. A 12 V battery thereforecontains 6 cells in series.
   The battery serves two important purposes in a photovoltaic system: to provideelectrical energy to the system when energy is not supplied by the arrayof solar panels, and to store excess energy generated by the panels wheneverthat energy exceeds the load. The battery experiences a cyclical processof charging and discharging, depending on the presence or absence ofsunlight. During the hours that there is sun, the array of panels produceselectrical energy. The energy that is not consumed immediately it is used tocharge the battery. During the hours of absence of sun, any demand of electricalenergy is supplied by the battery, thereby discharging it.
   These cycles of charge and discharge occur whenever the energy producedby the panels does not match the energy required to support the load. Whenthere is sufficient sun and the load is light, the batteries will charge. Obviously,the batteries will discharge at night whenever any amount of power isrequired. The batteries will also discharge when the irradiance is insufficientto cover the requirements of the load (due to the natural variation of climatologicalconditions, clouds, dust, etc.)If the battery does not store enough energy to meet the demand during periodswithout sun, the system will be exhausted and will be unavailable forconsumption. On the other hand, the oversizing the system (by adding far toomany panels and batteries) is expensive and inefficient. When designing astand-alone system we need to reach a compromise between the cost ofcomponents and the availability of power from the system. One way to dothis is to estimate the required number of days of autonomy. In the case ofa telecommunications system, the number of days of autonomy depends onits critical function within your network design. If the equipment is going toserve as repeater and is part of the backbone of your network, you will likelywant to design your photovoltaic system with an autonomy of up to 5-7 days.
On the other hand, if the solar system is responsible for a providing energy toclient equipment you can probably reduce number of days of autonomy totwo or three. In areas with low irradiance, this value may need to be increasedeven more. In any case, you will always have to find the proper balancebetween cost and reliability.
Types of batteries
   Many different battery technologies exist, and are intended for use in a varietyof different applications. The most suitable type for photovoltaic applicationsis the stationary battery, designed to have a fixed location and forscenarios where the power consumption is more or less irregular. "Stationary"batteries can accommodate deep discharge cycles, but they are not designedto produce high currents in brief periods of time.
   Stationary batteries can use an electrolyte that is alkaline (such as NickelCadmium) or acidic(such as Lead-Acid). Stationary batteries based onNickel-Cadmium are recommended for their high reliability and resistancewhenever possible. Unfortunately, they tend to be much more expensive anddifficult to obtain than sealed lead-acid batteries.
   In many cases when it is difficult to find local, good and cheap stationary batteries(importing batteries is not cheap), you will be forced to use batteriestargeted to the automobile market.
   Traction batteries are designed for vehicles and electric wheelbarrows. Theyare cheaper than stationary batteries and can serve in a photovoltaic installation,although they require very frequent maintenance. These batteriesshould never be deeply discharged, because doing so will greatly reducetheir ability to hold a charge. A truck battery should not discharged by morethan 70% of its total capacity. This means that you can only use a maximumof 30% of a lead-acid battery’s nominal capacity before it must be recharged.
   You can extend the life of a lead-acid battery by using distilled water. By usinga densimeter or hydrometer, you can measure the density of the battery’selectrolyte. A typical battery has specific gravity of 1.28. Adding distilled waterand lowering the density to 1.2 can help reduce the anode’s corrosion, at acost of reducing the overall capacity of the battery. If you adjust the density ofbattery electrolyte, you must use distilledwater, as tap water or well waterwill permanently damage the battery.
States of charge
   There are two special state of charge that can take place during the cycliccharge and discharge of the battery. They should both be avoided in order topreserve the useful life of the battery.
   Overcharge takes place when the battery arrives at the limit of its capacity. Ifenergy is applied to a battery beyond its point of maximum charge, the electrolytebegins to break down. This produces bubbles of oxygen and hydrogen, ina process is known as gasification. This results in a loss of water, oxidation onthe positive electrode, and in extreme cases, a danger of explosion.
   On the other hand, the presence of gas avoids the stratification of theacid. After several continuous cycles of charge and discharge, the acidtends to concentrate itself at the bottom of the battery thereby reducingthe effective capacity. The process of gasification agitates the electrolyteand avoids stratification.
   Again, it is necessary to find a compromise between the advantages (avoidingelectrolyte stratification) and the disadvantages (losing water and productionof hydrogen). One solution is to allow a slight overcharge condition everyso often. One typical method is to allow a voltage of 2.35 to 2.4 Volts for eachelement of the battery every few days, at 25ºC. The regulator should ensure
a periodical and controlled overcharges.
   Overdischarge
   In the same way that there is a upper limit, there is also a lower limit to a battery’sstate of charge. Discharging beyond that limit will result in deteriorationof the battery. When the effective battery supply is exhausted, the regulatorprevents any more energy from being extracted from the battery. When thevoltage of the battery reaches the minimum limit of 1.85 Volts per cell at
25°C, the regulator disconnects the load from the battery.
   If the discharge of the battery is very deep and the battery remains dischargedfor a long time, three effects take place: the formation of crystallizedsulfate on the battery plates, the loosening of the active material on the batteryplate, and plate buckling. The process of forming stable sulfate crystalsis called hard sulfation. This is particularly negative as it generates big crystalsthat do not take part in any chemical reaction and can make your batteryunusable.
Battery Parameters
The main parameters that characterize a battery are:
• Nominal Voltage, VNBat. the most common value being 12 V.
• Nominal Capacity, CNBat: the maximum amount of energy that can be extractedfrom a fully charged battery. It is expressed in Ampere-hours (Ah)or Watt-hours (Wh). The amount of energy that can be obtained from abattery depends on the time in which the extraction process takes place.Discharging a battery over a long period will yield more energy compareto discharging the same battery over a short period. The capacity of a batteryis therefore specified at different discharging times. For photovoltaicapplications, this time should be longer than 100 hours (C100).
• Maximum Depth of Discharge, DoDmax: The depth of discharge is theamount of energy extracted from a battery in a single discharge cycle, expressedas a percentage. The life expectancy of a battery depends on howdeeply it is discharged in each cycle. The manufacturer should provide graphsthat relate the number of charge-discharge cycles to the life of the battery. As ageneral rule you should avoid discharging a deep cycle battery beyond50%. Traction batteries should only be discharged by as little as 30%.
• Useful Capacity, CUBat: It is the real (as in usable) capacity of a battery. Itis equal to the product of the nominal capacity and the maximum DoD. Forexample, a stationary battery of nominal capacity (C100) of 120 Ah anddepth of discharge of 70% has a useful capacity of (120 x 0.7) 84 Ah.
Measuring the state of charge of the battery
    A sealed lead-acid battery of 12 V provides different voltages depending onits state of charge. When the battery is fully charged in an open circuit, theoutput voltage is about 12.8 V. The output voltage lowers quickly to 12.6 Vwhen loads are attached. As the battery is providing constant current duringoperation, the battery voltage reduces linearly from 12.6 to 11.6 V depending
on the state of charge. A sealed lead-acid batteries provides 95% of its energywithin this voltage range. If we make the broad assumption that a fullyloaded battery has a voltage of 12.6 V when "full" and 11.6 V when "empty",we can estimate that a battery has discharged 70% when it reaches a voltageof 11.9 V. These values are only a rough approximation since they depend
on the life and quality of the battery, the temperature, etc.
   According to this table, and considering that a truck battery should not bedischarged more than 20% to 30%, we can determine that the useful capacity if a truck 170 Ah truck battery is 34 Ah (20%) to 51 Ah (30%). Using thesame table, we find that we should program the regulator to prevent the batteryfrom discharging below 12.3 V.
Battery and regulator protection
   Thermomagnetic circuit breakers or one time fuses must be used to protectthe batteries and the installation from short circuit and malfunctions. Thereare two types of fuses: slow blow, and quick blow. Slow blow fuses shouldbe used with inductive or capacitive loads where a high current can occur atpower up. Slow blow fuses will allow a higher current than their rating to pass
for a short time. Quick blow fuses will immediately blow if the current flowingthrough them is higher than their rating.
   The regulator is connected to the battery and the loads, so two different kindsof protection needs to be considered. One fuse should be placed betweenthe battery and the regulator, to protect the battery from short-circuit in caseof regulator failure. A second fuse is needed to protect the regulator from excessiveload current. This second fuse is normally integrated into the regulator
itself.
   Every fuse is rated with a maximum current and a maximum usable voltage.The maximum current of the fuse should be 20% bigger than the maximumcurrent expected. Even if the batteries carry a low voltage, a short circuit canlead to a very high current which can easily reach several hundred amperes.Large currents can cause fire, damage the equipment and batteries, andpossibly cause electric shock to a human body
   If a fuse breaks, never replace a fuse with a wire or a higher rated fuse. Firstdetermine the cause of the problem, then replace the fuse with another onewhich has the same characteristics.
Temperature effects
The ambient temperature has several important effects on the characteristicsof a battery:
• The nominal capacity of a battery (that the manufacturer usually gives for25°C) increases with temperature at the rate of about 1%/°C. But if thetemperature is too high, the chemical reaction that takes place in the batteryaccelerates, which can cause the same type of oxidation that takes
places during overcharging. This will obviously reduce the life expectancyof battery. This problem can be compensated partially in car batteries byusing a low density of dissolution (a specific gravity of 1.25 when the batteryis totally charged).
• As the temperature is reduced, the useful life of the battery increases.But if the temperature is too low, you run the the risk of freezing the electrolyte.The freezing temperature depends on the density of the solution,which is also related to the state of charge of the battery. The lower the
density, the greater therisk of freezing. In areas of low temperatures, youshould avoid deeply discharging the batteries (that is, DoDmax is effectivelyreduced.)
• The temperature also changes the relation between voltage and charge. Itis preferable to use a regulator which adjusts the low voltage disconnectand reconnect parameters according to temperature. The temperaturesensor of the regulator should be fixed to the battery using tape or someother simple method.
• In hot areas it is important to keep the batteries as cool as possible. Thebatteries must be stored in a shaded area and never get direct sunlight. It’salso desirable to place the batteries on a small support to allow air to flowunder them, thus increase the cooling.
How to choose a good battery
   Choosing a good battery can be very challenging in developing regions. Highcapacity batteries are heavy, bulky and expensive to import. A 200 Ah batteryweights around 50 kg (120 pounds) and it can not be transported as handluggage. If you want long-life (as in > 5 years) and maintenance free batteriesbe ready to pay the price.A good battery should always come with its technical specifications, includingthe capacity at different discharge rates (C20, C100), operating temperature,cut-off voltage points, and requirements for chargers.The batteries must be free of cracks, liquid spillage or any sign of damage,and battery terminals should be free of corrosion. As laboratory tests arenecessary to obtain complete data about real capacity and aging, expectlots of low quality batteries (including fakes) in the local markets. A typicalprice (not including transport and import tax) is $3-4 USD per Ah for 12 Vlead-acid batteries.
Life expectancy versus number of cycles
   Batteries are the only component of a solar system that should be amortizedover a short period and regularly replaced. You can increase the useful lifetimeof a battery by reducing the depth of discharge per cycle. Even deepcycle batteries will have an increased battery life if the the number of deepdischarge (>30%) cycles is reduced.
   If you completely discharge the battery every day, you will typically need tochange it after less than one year. If you use only 1/3 of the capacity the battery,it can last more than 3 years. It can be cheaper to buy a battery with 3times the capacity than to change the battery every year.
The power charge regulator
    The power charge regulator is also known as charge controller, voltage regulator,charge-discharge controller or charge-discharge and load controller.The regulator sits between the array of panels, the batteries, and yourequipment or loads.
   Remember that the voltage of a battery, although always close to 2 V percell, varies according to its state of charge. By monitoring the voltage of thebattery, the regulator prevents overcharging or overdischarging.
   Regulators used in solar applications should be connected in series: theydisconnect the array of panels from the battery to avoid overcharging, andthey disconnect the battery from the load to avoid overdischarging. Theconnection and disconnection is done by means of switches which can beof two types: electromechanical (relays) or solid state (bipolar transistor,MOSFET). Regulators should never be connected in parallel.
   In order to protect the battery from gasification, the switch opens thecharging circuit when the voltage in the battery reaches its high voltagedisconnect (HVD) or cut-off set point. The low voltage disconnect (LVD)prevents the battery from overdischarging by disconnecting or sheddingthe load. To prevent continuous connections and disconnections the regulatorwill not connect back the loads until the battery reaches a low reconnectvoltage (LRV).
   The most modern regulators are also able to automatically disconnect the panelsduring the night to avoid discharging of the battery. They can also periodicallyovercharge the battery to improve their life, and they may use a mechanismknown as pulse width modulation (PWM) to prevent excessive gassing.
   As the peak power operating point of the array of panels will vary with temperatureand solar illumination, new regulators are capable of constantlytracking the maximum point of power of the solar array. This feature is knownas maximum power point tracking (MPPT).
   Regulator Parameters
When selecting a regulator for your system, you should at least know theoperating voltage and the maximum current that the regulator can handle.The operating Voltage will be 12, 24, or 48 V. The maximum current must be20% bigger than the current provided by the array of panels connected to theregulator.
Other features and data of interest include:
• Specific values for LVD, LRV and HVD.
• Support for temperature compensation. The voltage that indicates the stateof charge of the battery vary with temperature. For that reason some regulatorsare able to measure the battery temperature and correct the differentcut-off and reconnection values.
• Instrumentation and gauges. The most common instruments measure thevoltage of the panels and batteries, the state of charge (SoC) or Depth of Discharge(DoD). Some regulators include special alarms to indicate that thepanels or loads have been disconnected, LVD or HVD has been reached, etc.
Converters
   The regulator provides DC power at a specific voltage. Converters and invertersare used to adjust the voltage to match the requirements of your load.
   DC/DC Converters
   DC/DC converters transform a continuous voltage to another continuousvoltage of a different value. There are two conversion methods which can beused to adapt the voltage from the batteries: linear conversion and switchingconversion.
   Linear conversion lowers the voltage from the batteries by converting excess
energy to heat. This method is very simple but is obviously inefficient.Switching conversion generally uses a magnetic component to temporarilystore the energy and transform it to another voltage. The resulting voltagecan be greater, less than, or the inverse (negative) of the input voltage.
   The efficiency of a linear regulator decreases as the difference between theinput voltage and the output voltage increases. For example, if we want toconvert from 12 V to 6 V, the linear regulator will have an efficiency of only50%. A standard switching regulator has an efficiency of at least 80%.
   DC/AC Converter or Inverter
   Inverters are used when your equipment requires AC power. Inverters chopand invert the DC current to generate a square wave that is later filtered toapproximate a sine wave and eliminate undesired harmonics. Very fewinverters actually supply a pure sine wave as output. Most models availableon the market produce what is known as "modified sine wave", as their voltageoutput is not a pure sinusoid. When it comes to efficiency, modified sinewave inverters perform better than pure sinusoidal inverters.
   Be aware that not all the equipment will accept a modified sine wave as voltageinput. Most commonly, some laser printers will not work with a modifiedsine wave inverter. Motors will work, but they may consume more power thanif they are fed with a pure sine wave. In addition, DC power supplies tend towarm up more, and audio amplifiers can emit a buzzing sound.
   Aside from the type of waveform, some important features of inverters include:
• Reliability in the presence of surges. Inverters have two power ratings:one for continuous power, and a higher rating for peak power. They arecapable of providing the peak power for a very short amount of time, aswhen starting a motor. The inverter should also be able to safely interruptitself (with a circuit breaker or fuse) in the event of a short circuit, or if therequested power is too high.
• Conversion efficiency. Inverters are most efficient when providing 50% to90% of their continuous power rating. You should select an inverter thatmost closely matches your load requirements. The manufacturer usuallyprovides the performance of the inverter at 70% of its nominal power.
• Battery charging. Many inverters also incorporate the inverse function:the possibility of charging batteries in the presence of an alternative sourceof current (grid, generator, etc). This type of inverter is known as a charger/inverter.
• Automatic fall-over. Some inverters can switch automatically betweendifferent sources of power (grid, generator, solar) depending on what isavailable.When using telecommunication equipment, it is best to avoid the use of DC/AC converters and feed them directly from a DCsource. Most communicationsequipment can accept a wide range of input voltage.
   Equipment or load
   It should be obvious that as power requirements increase, the expense of thephotovoltaic system also increases. It is therefore critical to match the size ofthe system as closely as possible to the expected load. When designing thesystem you must first make a realistic estimate of the maximum consumption.Once the installation is in place, the established maximum consumption
must be respected in order to avoid frequent power failures.
    Home Appliances
   The use of photovoltaic solar energy is not recommended for heat-exchangeapplications (electrical heating, refrigerators, toasters, etc.) Whenever possible,energy should be used sparingly using low power appliances.Here are some points to keep in mind when choosing appropriate equipmentfor use with a solar system:
• The photovoltaic solar energy is suitable for illumination. In this case, theuse of halogen light bulbs or fluorescent lamps is mandatory. Althoughthese lamps are more expensive, they have much better energy efficiencythan incandescent light bulbs. LED lamps are also a good choice as theyare very efficient and are fed with DC.
• It is possible to use photovoltaic power for appliances that require low andconstant consumption (as in a typical case, the TV). Smaller televisionsuse less power than larger televisions. Also consider that a black-and-whiteTV consumes about half the power of a color TV.
• Photovoltaic solar energy is not recommended for any application thattransforms energy into heat (thermal energy). Use solar heating or butaneas alternative.
• Conventional automatic washing machines will work, but you should avoidthe use of any washing programs that include centrifuged water heating.
• If you must use a refrigerators, it should consume as little power as possible.There are specialized refrigerators that work in DC, although their consumptioncan be quite high (around 1000 Wh/day).The estimation of total consumption is a fundamental step in sizing your solarsystem. Here is a table that gives you a general idea of the power consumptionthat you can expect from different appliances.
    Wireless telecommunications equipment
   Saving power by choosing the right gear saves a lot of money and trouble.For example , a long distance link doesn’t necessarily need a strong amplifierthat draws a lot of power. A Wi-Fi card with good receiver sensitivity and afresnel zone that is at least 60% clear will work better than an amplifier, andsave power consumption as well. A well known saying of radio amateurs applieshere, too: The best amplifier is a good antenna. Further measures toreduce power consumption include throttling the CPU speed, reducingtransmit power to the minimum value that is necessary to provide a stablelink, increasing the length of beacon intervals, and switching the system off
during times it is not needed.
   Most autonomous solar systems work at 12 or 24 volts. Preferably, a wirelessdevice that runs on DC voltage should be used, operating at the 12 Volts thatmost lead acid batteries provide. Transforming the voltage provided by thebattery to AC or using a voltage at the input of the access point different fromthe voltage of the battery will cause unnecessary energy loss. A router oraccess point that accepts 8-20 Volts DC is perfect.
   Most cheap access points have a switched mode voltage regulator insideand will work through such a voltage range without modification or becominghot (even if the device was shipped with a 5 or 12 Volt power supply).
WARNING: Operating your access point with a power supply other than theone provided by your  manufacturer will certainly void any warranty, and maycause damage to your equipment. While the following technique will typicallywork as described, remember that should you attempt it, you do so at yourown risk.
   Open your access point and look near the DC input for two relatively big capacitorsand an inductor (a ferrite toroid with copper wire wrapped around it).If they are present then the device has a switched mode input, and themaximum input voltage should be somewhat below the voltage printed on thecapacitors. Usually the rating of these capacitors is 16 or 25 volts. Be awarethat an unregulated power supply has a ripple and may feed a much highervoltage into your access point than the typical voltage printed on it may suggest.So, connecting an unregulated power supply with 24 Volts to a devicewith 25 Volt-capacitors is not a good idea. Of course, opening your devicewill void any existing warranty. Do not try to operate an access point at highervoltage if it doesn’t have a switched mode regulator. It will get hot, malfunction,or burn.
   Equipment based on traditional Intel x86 CPUs are power hungry in comparisonwith RISC-based architectures as ARM or MIPS. One of the boards withlowest power consumptions is the Soekris platform that uses an AMDElanSC520 processor. Another alternative to AMD (ElanSC or GeodeSC1100) is the use of equipment with MIPS processors. MIPS processorshave a better performance than an AMD Geode at the price of consumingbetween 20-30% of more energy.
   The popular Linksys WRT54G runs at any voltage between 5 and 20 voltsDC and draws about 6 Watts, but it has an Ethernet switch onboard. Havinga switch is of course nice and handy - but it draws extra power. Linksys alsooffers a Wi-Fi access point called WAP54G that draws only 3 Watts and canrun OpenWRT and Freifunk firmware. The 4G Systems Accesscube drawsabout 6 Watts when equipped with a single WiFi interface. If 802.11b is sufficient,mini-PCI cards with the Orinoco chipset perform very well while drawinga minimum amount of power.
   The amount of power required by wireless equipment depends not only onthe architecture but on the number of network interfaces, radios, type ofmemory/storage and traffic. As a general rule, a wireless board of low consumptionconsumes 2 to 3 W, and a 200 mW radio card consumes as muchas 3 W. High power cards (such as the 400 mW Ubiquity) consume around 6W. A repeating station with two radios can range between 8 and 10 W.
   Although the standard IEEE 802.11 incorporates a power saving mode (PS)mechanism, its benefit is not as good as you might hope. The main mechanismfor energy saving is to allow stations to periodically put their wirelesscards to "sleep" by means of a timing circuit. When the wireless card wakesup it verifies if a beacon exists, indicating pending traffic. The energy saving
therefore only takes place in the client side, as the access point alwaysneeds to remain awake to send beacons and store traffic for the clients.Power saving mode may be incompatible between implementations fromdifferent manufacturers, which can cause unstable wireless connections. It isnearly always best to leave power saving mode disabled on all equipment, asthe difficulties created will likely outweigh the meager amount of savedpower.
    Selecting the voltage
   Most low power stand-alone systems use 12 V battery power as that is themost common operational voltage in sealed lead-acid batteries. When designinga wireless communication system you need to take into considerationthe most efficient voltage of operation of your equipment. While the inputvoltage can accept a wide range of values, you need to ensure that the overallpower consumption of the system is minimal.
    Wiring
   An important component of the installation is the wiring, as proper wiringwill ensure efficient energy transfer. Some good practices that you shouldconsider include:
• Use a screw to fasten the cable to the battery terminal. Loose connectionswill waste power.
• Spread Vaseline or mineral jelly on the battery terminals. Corroded connectionhave an increased resistance, resulting in loss.
• For low currents (<10 A) consider the use of Faston or Anderson powerpoleconnectors. For bigger currents, use metallic ring lugs.
   Wire size is normally given in American Wire Gauge (AWG). During your calculationsyou will need to convert between AWG and mm2 to estimate cableresistance. For example, an AWG #6 cable has a diameter of 4.11 mm andcan handle up to 55 A. A conversion chart, including an estimate of resistanceand current carrying capacity, is available in Appendix D. Keep in
mind that the current carrying capacity can also vary depending on the typeof insulation and application. When in doubt, consult the manufacturer formore information.
    Orientation of the panels
   Most of the energy coming from the sun arrives in straight line. The solarmodule will capture more energy if it is “facing” the sun, perpendicular to thestraight line between the position of the installation and the sun. Of course,the sun’s position is constantly changing relative to the earth, so we need tofind an optimal position for our panels. The orientation of the panels is determinedby two angles, the azimuth a and the inclination or elevation ß.The azimuth is the angle that measures the deviation with respect to thesouth in the northern hemisphere, and with respect to the north in the southernhemisphere. The inclination is the angle formed by the surface of the
module and the horizontal plane.
    Azimuth
   You should have the module turned towards the terrestrial equator (facingsouth in the northern hemisphere, and north in the southern) so that duringthe day the panel catches the greatest possible amount of radiation (a = 0).It is very important that no part of the panels are ever under shade!. Studythe elements that surround the panel array (trees, buildings, walls, otherpanels, etc.) to be sure that they will not cast a shadow on the panels at anytime of the day or year. It is acceptable to turn the panels ±20º towards theeast or the west if needed (a = ±20º).
    Inclination
   Once you have fixed the azimuth, the parameter that is key in our calculationsis the inclination of the panel, which we will express as the angle beta(ß). The maximum height that the sun reaches every day will vary, with themaximum on the day of the summer solstice and the minimum on the wintersolstice. Ideally, the panels should track this variation, but this is usually notpossible for cost reasons.
   In installations with telecommunications equipment it is normal to install thepanels at a fixed inclination. In most telecommunications scenarios the energydemands of the system are constant throughout the year. Providing for sufficientpower during the "worst month" will work well for the rest of the year.
 The value of ß should maximize the ratio between the offer and the demand
of energy.
• For installations with consistent (or nearly consistent) consumption throughoutthe year, it is preferable to optimize the installation to capture the maximumradiation during "the winter" months. You should use the absolute valueof the latitude of the place (angle F) increased by 10° (ß = |��F��| + 10 °).
• For installations with less consumptions during winter, the value of the latitudeof the place can be used as the solar panel inclination. This way thesystem is optimized for the months of spring and autumn (ß = |��F��|).
• For installations that are only used during summer, you should use the absolutevalue of the latitude of the place (angle F) decreased by 10° (ß = |��F��| - 10°).The inclination of the panel should never be less than 15° to avoid the accumulationof dust and/or humidity on the panel. In areas where snow and iceoccur, it is very important to protect the panels and to incline them an angleof 65° or greater.
   If there is a considerable increase in consumption during the summer, you mightconsiderarranging for two fixed inclinations, one position for the months ofsummer and another for the months of winter. This would require special supportstructures and a regular schedule for changing the position of the panels.
    How to size your photovoltaic system
   When choosing equipment to meet your power needs, you will need to determinethe following, at a minimum:
• The number and type of solar panels required to capture enough solar energyto support your load.
• The minimum capacity of the battery. The battery will need to store enoughenergy to provide power at night and through days with little sun, and willdetermine your number of days of autonomy.
• The characteristics of all other components (the regulator, wiring, etc.)needed to support the amount of power generated and stored.
   System sizing calculations are important, because unless the system componentsare balanced, energy (and ultimately, money) is wasted. For example,if we install more solar panels to produce more energy, the batteriesshould have enough capacity to store the additional energy produced. If thebank of batteries is too small and the load is not using the energy as it isgenerated, then energy must be thrown away. A regulator of a smaller amperagethan needed, or one single cable that is too small, can be a cause offailure (or even fire) and render the installation unusable.
   Never forget that the ability of the photovoltaic energy to produce and storeelectrical energy is limited. Accidentally leaving on a light bulb during theday can easily drain your reserves before nighttime, at which point no additionalpower will be available. The availability of "fuel" for photovoltaic systems(i.e. solar radiation) can be difficult to predict. In fact, it is never possible
to be absolutely sure that a standalone system is going to be able toprovide the necessary energy at any particular moment. Solar systems aredesigned for a certain consumption, and if the user exceeds the plannedlimits the provision of energy will fail.
   The design method that we propose consists of considering the energy requirements,and based on them to calculate a system that works for themaximum amount of time so it is as reliable as possible. Of course, if morepanels and batteries are installed, more energy will be able to be collectedand stored. This increase of reliability will also have an increase in cost.
   In some photovoltaic installations (such as the provision of energy for telecommunicationsequipment on a network backbone) the reliability factor ismore important that the cost. In a client installation, low cost is likely going tobe a the most important factor. Finding a balance between cost and reliabilityis not a easy task, but whatever your situation, you should be able to determine
what it is expected from your design choices, and at what price.
   The method we will use for sizing the system is known as the method ofthe worst month. We simply calculate the dimensions of the standalonesystem so it will work in the month in which the demand for energy isgreatest with respect to the available solar energy. It is the worst month of
the year, as this month with have the largest ratio of demanded energy toavailable energy.
   Using this method, reliability is taken into consideration by fixing the maximumnumber of days that the system can work without receiving solar radiation(that is, when all consumption is made solely at the expense of the energystored in the battery.) This is known as the maximum number of daysof autonomy (N), and can be thought of as the number of consecutivecloudy days when the panels do not collect any significant amount of energy.
   When choosing N, it is necessary to know the climatology of the place, as wellas the economic and social relevance of the installation. Will it be used to illuminatehouses, a hospital, a factory, for a radio link, or for some other application?Remember that as N increases, so does the investment in equipmentand maintenance. It is also important to evaluate all possible logistical costs ofequipment replacement. It is not the same to change a discharged battery froman installation in the middle of a city versus one at the top a telecommunicationtower that is several hours or days of walking distance.
   Fixing the value of N it is not an easy task as there are many factors involved,and many of them cannot be evaluated easily. Your experience willplay an important role in this part of the system sizing. One commonly usedvalue for critical telecommunications equipment is N = 5, whereas for lowcost client equipment it is possible to reduce the autonomy to N = 3.
   In Appendix E, we have included several tables that will facilitate the collectionof required data for sizing the system. The rest of this chapter will explainin detail what information you need to collect or estimate and how to use themethod of the "worst month".
   Data to collect
• Latitude of the installation. Remember to use a positive sign in thenorthern hemisphere and negative in the south.
• Solar radiation data. For the method of the "worst month" it is enough toknow just twelve values, one for every month. The twelve numbers are themonthly average values of daily global irradiation on horizontal plane(Gdm(0), in kWh/m2 per day). The monthly value is the sum of the values ofglobal irradiation for every day of the month, divided by the number of days
of the month.
    If you have the data in Joules (J), you can apply the following conversion:
       1 J = 2.78 �� 10-7 kWh
   The irradiation data Gdm(0) of many places of the world is gathered in tablesand databases. You should check for this information from a weather stationclose to your implementation site, but do not be surprised if you cannot findthe data in electronic format. It is a good idea to ask companies that installphotovoltaic systems in the region, as their experience can be of great value.
   Do not confuse "sun hours" with the number of "peak sun hours". The numberof peak sun hours has nothing to do with the number of hours without clouds,but refers to the amount of daily irradiation. A day of 5 hours of sun withoutclouds does not necessary have those hours when the sun is at its zenith.
   A peak sun hour is a normalized value of solar radiation of 1000 W/m2 at 25C. So when we refer to 5 peak sun hours, this implies a daily solar radiationof 5000 W/m2.
    Electrical characteristics of system components
   The electrical characteristics of the components of your system should beprovided by the manufacturer. It is advisable to make your our own measurementsto check for any deviation from the nominal values. Unfortunately,deviation from promised values can be large and should be expected.
   These are the minimum values that you need to gather before starting your
system sizing:
    Panels
   You need to know the voltage VPmax and the current IPmax at the point of
maximum power in standard conditions.
    Batteries
   Nominal capacity (for 100 hours discharge) CNBat , operational voltage VNBat ,and either the maximum depth of discharge DoDmax or useful capacity CUBat .You also need to know the type of battery that you plan to use, whethersealed lead-acid, gel, AGM, modified traction etc. The type of battery is importantwhen deciding the cut-off points in the regulator.
    Regulator
   You need to know the nominal voltage VNReg, and the maximum current thatcan operate ImaxReg.
   DC/AC Converter/Inverter
  If you are going to use a converter, you need to know the nominal voltage VNConv,instantaneous power PIConv and performance at 70% of maximum load H70.
    Equipment or load
   It is necessary to know the nominal voltage VNC and the nominal power ofoperation PC for every piece of equipment powered by the system.In order to know the total energy that our installation is going to consume, itis also very important to consider the average time each load will be used. Isit constant? Or will it be used daily, weekly, monthly or annually? Considerany changes in the usage that might impact the amount of energy needed(seasonal usage, training or school periods, etc.)
    Other variables
   Aside from the electrical characteristics of the components and load, it isnecessary to decide on two more pieces of information before being able tosize a photovoltaic system. These two decisions are the required number ofdays of autonomy and the operational voltage of the system.
    N, number of days of autonomy
   You need to decide on a value for N that will balance meteorological conditionswith the type of installation and overall costs. It is impossible to give aconcrete value of N that is valid for every installation, but the next table givessome recommended values. Take these values as a rough approximation,and consult with an experienced designer to reach a final decision.
    VN, nominal voltage of the installation
   The components of your system need to be chosen to operate at a nominalvoltage VN. This voltage is usually 12 or 24 Volts for small systems, and if thetotal power of consumption surpasses 3 kW, the voltage will be 48 V. Theselection of VN is not arbitrary, and depends on the availability of equipment.
• If the equipment allows it, try to fix the nominal voltage to 12 or 24 V. Manywireless communications boards accept a wide range of input voltage andcan be used without aconverter.
• If you need to power several types of equipment that work at differentnominal voltages, calculate the voltage that minimizes the overall powerconsumption including the losses for power conversion in DC/DC and DC/AC converters.
    Procedure of calculation
   There are three main steps that need to be followed to calculate the propersize of a system:
1. Calculate the available solar energy (the offer). Based on statisticaldata of solar radiation, and the orientation and the optimal inclination ofthe solar panels, we calculate the solar energy available. The estimationof solar energy available is done in monthly intervals, reducing the statisticaldata to 12 values. This estimation is a good compromise betweenprecision and simplicity.
2. Estimate the required electrical energy (the demand). Record thepower consumption characteristics of the equipment chosen as well asestimated usage. Then calculate the electrical energy required on amonthly basis. You should consider the expected fluctuations of usagedue to the variations between winter and summer, the rainy period / dryseason, school / vacation periods, etc. The result will be 12 values ofenergy demand, one for each month of the year.
3. Calculate the ideal system size (the result). With the data from the“worst month”, when the relation between the solar demanded energyand the energy available is greatest, we calculate:
• The current that the array of panels needs to provide, which willdetermine the minimum number of panels.
• The necessary energy storage capacity to cover the minimumnumber of days of autonomy, which will determine the requirednumber of batteries.
• The required electrical characteristics of the regulator.
• The length and the necessary sections of cables for the electricalconnections.
    Required current in the worst month
   For each month you need to calculate the value of Im, which is the maximumdaily current that an array of panels operating at nominal voltage of VN needsto provide, in a day with a irradiation of Gdm for month "m", for panels with aninclination of ß degrees..
   The Im(WORST MONTH) will be the largest value of Im, and the system sizingis based on the data of that worth month. The calculations of Gdm(ß) for a certainplace can be made based on Gdm(0) using computer software such asPVSYST (http://www.pvsyst.com/) or PVSOL (http://www.solardesign.co.uk/).
   Due to losses in the regulator and batteries, and due to the fact that the panelsdo not always work at the point of maximum power, the required currentImMAX is calculated as:
ImMAX = 1.21 Im (WORST MONTH)
   Once you have determined the worst month, the value of ImMAX, and the totalenergy that you require ETOTAL(WORST MONTH) you can proceed to the finalcalculations. ETOTAL is the sum of all DC and AC loads, in Watts. To calculateETOTAL see Appendix E.
    Number of panels
   By combining solar panels in series and parallel, we can obtain the desiredvoltage and current. When panels are connected in series, the total voltage isequal to the sum of the individual voltages of each module, while the currentremains unchanged. When connecting panels in parallel, the currents aresummed together while the voltage remains unchanged. It is veryimportant,to use panels of nearly identical characteristics when building an array.
   You should try to acquire panels with VPmax a bit bigger than the nominal voltageof the system (12, 24 or 48 V). Remember that you need to provide afew volts more than the nominal voltage of the battery in order to charge it. Ifit is not possible to find a single panel that satisfies your requirements, youneed to connect several panels in series to reach your desired voltage. Thenumber of panels in series Nps is equal to the nominal voltage of the systemdivided by the voltage of a single panel, rounded up to the nearest integer.
          Nps = VN / VPmax
   In order to calculate the number of panels in parallel (Npp), you need to dividethe ImMAX by the current of a single panel at the point of maximum powerIpmax, rounded up to the nearest integer.
          Npp = ImMAX / IPmax
    Capacity of the battery or accumulator
   The battery determines the overall voltage of the system and needs to haveenough capacity to provide energy to the load when there is not enoughsolar radiation.
   To estimate the capacity of our battery, we first calculate the required energycapacity of our system (necessary capacity, CNEC). The necessary capacitydepends on the energy available during the "worst month" and the desirednumber of days of autonomy (N).
      CNEC (Ah)= ETOTAL(WORST MONTH)(Wh) / VN(V) x N
   The nominal capacity of the battery CNOM needs to be bigger than the CNEC aswe cannot fully discharge a battery. To calculate the size of the battery we needto consider the maximum depth of discharge (DoD) that the battery allows:
     CNOM(Ah) = CNEC(Ah) / DoDMAX
   In order to calculate the number of batteries in series (Nbs), we divide thenominal voltage of our installation (VN) by the nominal voltage of a singlebattery (VNBat):
     Nbs = VN / VNBat
    Regulator
   One important warning: always use regulators in series, never in parallel. Ifyour regulator does not support the current required by your system, you willneed to buy a new regulator with a larger working current.For security reasons, a regulator needs to be able to operate with a currentImaxReg at least 20% greater than the maximum intensity that is provided bythe array of panels:
    ImaxReg = 1.2 Npp IPMax
    DC/AC Inverter
   The total energy needed for the AC equipment is calculated including all thelosses that are introduced by the DC/AC converter or inverter. When choosingan inverter, keep in mind that the performance of the inverter varies accordingto the amount of requested power. An inverter has better performancecharacteristics when operating close to its rated power. Using a 1500
Watt inverter to power a 25 Watt load is extremely inefficient. In order toavoid this wasted energy, it is important to consider not the peak power of allyour equipment, but the peak power of the equipment that is expected to operatesimultaneously.
    Cables
   Once you know the numbers of panels and batteries, and type of regulatorsand inverters that you want to use, it is necessary to calculate the length andthe thickness of the cables needed to connect the components together.
   The length depends on the location of your the installation. You should try tominimize the length of the cables between the regulator, panels, and batteries.Using short cables will minimize lost power and cable costs.
   The thickness is chosen is based on the length of the cable and the maximumcurrent it must carry. The goal is to minimize voltage drops. In order tocalculate the thickness S of the cable it is necessary to know:
• The maximum current IMC that is going to circulate in the cable. In the case ofthe panel-battery subsystem, it is ImMAX calculated for every month. In thebattery-load subsystem it depends on the way that the loads are connected.
• The voltage drop (Va-Vb) that we consider acceptable in the cable. The voltage drop that results of adding all possible individual drops is expressedas a percent of the nominal voltage of the installation. Typicalmaximum values are:
     Typical acceptable voltage drops in cables
   The section of the cable is determined by Ohm’s Law:
                  S(mm2) = r(��mm2/m)L(m) ImMAX(A)/ (Va-Vb)(V)
where S is the section, r is resistivity (intrinsic property of the material: forcopper, 0.01286 ��mm2/m), and L the length.
    S is chosen taking into consideration the cables available in the market. Youshould choose the immediately superior section to the one that is obtainedfrom the formula. For security reasons that are some minimum values, for thecable that connects panels and battery, this is a minimum of 6 mm2. For theother sections, that minimum is 4 mm2.
    Cost of a solar installation
   While solar energy itself is free, the equipment needed to turn it into usefulelectric energy is not. You not only need to buy equipment to transform thesolar energy in electricity and store it for use, but you must also replaceand maintain various components of the system. The problem ofequipmentreplacement is often overlooked, and a solar system is implemented without
a proper maintenance plan.
   In order to calculate the real cost of your installation, we include an illustrativeexample. The first thing to do it is to calculate the initial investment costs.
   The calculation of our investment cost is relatively easy once the systemhas been dimensioned. You just need to add the price for each pieceequipment and the labor cost to install and wire the equipments together.For simplicity, we do not include the costs of transport and installation but
you should not overlook them.
   To figure out how much a system will really cost to operate we must estimatehow long each part will last and how often you must replace it. In accountingterminology this is known as amortization. Our new table will look like this:
 

 

As you see, once the first investment has been done, an annual cost of$262.50 is expected. The annual cost is an estimation of the required capitalper year to replace the system components once they reach the end oftheir useful life.