5.2.1 Batteries

Reliable energy storage is crucial to most stand‐alone PV systems. Without it operation of the system is confined to daylight hours when the sunlight is sufficiently strong; with it the user becomes independent of the vagaries of sunlight and can expect electricity by night and day. Many new types of storage battery have come on the market in recent years, including nickel–cadmium, nickel–metal–hydride, and lithium‐ion, but since the great majority of present stand‐alone PV systems use the more traditional lead‐acid type, we shall concentrate on it in this section.

You are probably familiar with 12 V vehicle batteries, and at first sight they might seem suitable for storing the output of a PV array. But there are important differences between the duty cycle of a standard vehicle battery and a PV storage battery. A vehicle battery’s most arduous duty is to supply large currents, typically hundreds of amps, for a very short time to the engine’s starter motor. The battery is not supposed to be substantially discharged, except on rare occasions. But a PV battery delivers smaller currents for much longer and must routinely withstand cycling, in other words going through many hundreds or even thousands of charge–discharge cycles without damage. Its duty is rather similar to that of a “leisure” battery used for running electrical appliances in caravans and boats. But the particular requirements of PV systems in terms of efficiency, reliability, and durability have led manufacturers to develop specialized deep‐cycle batteries for the PV market. It should be added that the cheapness and universal availability of standard vehicle batteries means that in practice they are often used in low‐power SHSs in developing countries, and with reasonable success due to the low current levels involved.

High‐quality lead‐acid batteries for stand‐alone PV systems must have long working lives under frequent conditions of charge and discharge. Since PV electricity is precious, especially during long cloudy periods or in winter, the batteries must also display low self‐discharge rates and high efficiency. Self‐discharge rates of around 3% per month are fairly typical. Efficiency is assessed in three ways:

• Coulombic or charge efficiency, the percentage of charge put into a battery that may be retrieved from it, typically 85% for lead‐acid.
• Voltage efficiency, reflecting the fact that the voltage when discharging is less than when charging, typically 90%.
• Energy efficiency, the product of coulombic and voltage efficiencies, typically 75%. (Unfortunately some manufacturers quote the coulombic efficiency as “battery efficiency,” which can be misleading.)

We see from these figures, and especially the one for energy efficiency, that even high‐quality lead‐acid batteries cause substantial energy losses in a stand‐alone system. Not that all the energy produced by a PV array has to go through the battery charge–discharge process: during periods of strong sunlight, the batteries may be fully charged much of the time, and the PV electricity can be passed straight to the loads.

So far we have talked about 12 V batteries. But as you are probably aware, a 12 V battery is made up of six electrochemical cells connected in series, each with a nominal voltage of 2 V. A 6 V battery contains three such cells. High‐capacity cells may also be purchased individually and connected in series. Each has positive and negative electrodes made of lead alloy, in an electrolyte of dilute sulfuric acid. Two main categories of cells (and batteries) may be identified:

• Flooded or wet, using a liquid electrolyte that must be regularly topped up with distilled water. Adequate ventilation must be provided for hydrogen given off during charging.
• Sealed or valve regulated, sealed with a gastight valve, only allowing gas to escape in the event of overpressure. In normal operation the comparatively small amounts of hydrogen and oxygen produced during charging are recombined to form water, so no topping up is required. An alternative type of sealed battery uses gel electrolyte. In general, sealed batteries require a strict charging regime, but need very little maintenance.

Batteries recommended for multiple cycling in PV systems often have special electrodes in the form of tubular plates. If not discharged with more than 30%, they typically survive several thousand charge–discharge cycles; if regularly discharged by 80%, about a thousand cycles.

The capacity of a cell or battery is normally quoted in ampere hours (Ah), which is the product of the current supplied and the time for which it flows. For example, if a fully charged 12 V battery can provide 20 A for 10 hours, its capacity is 200 A h (unfortunately many people refer to such a battery as “200 amp”). And since its voltage is 12 V, the total energy stored is 200 × 12 = 2400 W h or 2.4 kWh.

However, it is important to realize that the capacity and energy efficiency of a battery depend on the rate at which it is discharged. The faster the discharge, the lower the capacity. Therefore, when a manufacturer quotes a battery capacity as 200 A h, this refers to a particular discharge time such as 10 hours, and this should be specified. The capacity is said to be 200 A h at the 10 hour rate. In general we get the most energy from a battery by discharging it as slowly as possible. A 100 hour rate is often considered more relevant to PV applications. Battery capacity also depends significantly on temperature. The rated capacity normally applies to 20°C and reduces by about 1% for every degree drop in temperature.

We now consider how the voltage of a lead‐acid battery varies during charge and discharge. This is very important because, as we shall see in the next section, the charge controller used to regulate current flow from a PV array into a battery (or battery bank) uses voltage as a “control signal” to protect it from damage and prolong its working life. Once again we can use our 12 V battery as an example.

When a battery is put on charge at constant current, its voltage varies in the manner shown in Figure 5.3. Initially close to 12 V, it rises steadily as the state of charge (SOC) increases. In the final phase it increases more rapidly, reaching over 14 V as full charge (SOC = 100%) is approached. If the battery is of the flooded type, this last phase is accompanied by gassing in the liquid electrolyte, producing free hydrogen and oxygen. Excessive gassing can occur if charging is continued and may cause damage to the plates; it is very important to provide adequate ventilation to avoid the risk of explosion. However occasional, controlled, overcharging known as equalization charging is helpful as the gassing tends to stir up the electrolyte and prevent stratification into different levels of acid concentration. Note that overcharging must always be avoided in sealed batteries, and equalization is not relevant.

A good charging scheme, which helps keep the battery in top condition, is to provide an initial boost charge using all the available current, then, as the SOC approaches 100%, an absorption charge at constant voltage and low current; and finally a float charge to keep the battery gently topped up. Of course, in a PV system dependent on variable sunlight, with none at night, we cannot expect an optimal charging regime. We return to this point a little later.

We next consider what happens during discharge. Figure 5.4 shows typical voltage characteristics when our 12 V, 200 A h battery is discharged at constant current. The curve labeled 10 hours is for discharge at 20 A for 10 hours, which reduces the voltage from its starting value down to about 11 V, the point at which the manufacturer recommends disconnection of the load to prevent damage. Note that, at this point, the amount of charge used is 100%—the battery’s full nominal capacity. But if we discharge it at the slower rate of 2 A for 100 hours, we get the curve labeled 100 hours. The voltage holds up better, and the total available charge is substantially increased, emphasizing once again that the usable capacity of a battery depends significantly on the rate of discharge. It is also very important to note that severe overdischarge of a lead‐acid battery, or allowing it to remain at a low SOC for lengthy periods, should be avoided whenever possible. In a wet battery the main danger is sulfation, the formation of large lead sulfate crystals on the plates, leading to damage and loss of capacity.

In a practical PV system, we cannot expect charging and discharging to occur at constant current or in regular cycles of constant depth. The situation is far more complicated and depends on the availability of sunlight compared with the user’s demands for electricity. In general we may identify daily fluctuations of sunlight and demand and seasonal fluctuations. In sunny summer weather the battery bank is likely to spend more of its time close to full charge (SOC = 100%), with relatively small daily reductions due to demand; but under overcast conditions, or in the winter months, the electricity consumption pattern may lead to periods of low SOC with the risk of supply cutoff. Annual records of charge–discharge cycles in a PV system often appear somewhat random and irregular. Nevertheless, the main points outlined previously are useful guides to the performance, care, and maintenance of lead‐acid batteries, pointing to the ways in which they may be protected by suitable charge control strategies.

5.2.2 Charge Controllers

A charge controller is used to regulate the flow of current from the PV array into the battery bank and from the battery bank to the various electrical loads. It must prevent overcharging when the solar electricity supply exceeds demand and overdischarging when demand exceeds supply. Various subsidiary control and display functions, depending on the price and sophistication of the unit, are included to protect the batteries from damage and to ensure an operating regime that maximizes their performance and length of life. Batteries are an expensive part of most stand‐alone systems, especially those required to provide a highly reliable electricity supply day and night, so the relatively modest cost of a good charge controller is money well spent.

In the previous section we saw how the voltage of a battery changes during charging and discharging and noted that it is used as a control signal to regulate current flow. The two paramount tasks of the charge controller are prevention of battery overcharging and excess discharging. Overcharging is avoided by disconnecting the PV input whenever the battery voltage reaches an upper set point, normally preset at 14.0 V for float charging, 14.4 V for boost charging, and 14.7 V for equalization charging of a flooded (wet) 12 V battery. Excess discharge is prevented by disconnecting the load and/or giving a warning by light or sound whenever the voltage falls to a lower set point, normally about 11 V. Between these extremes charging and discharging continue in accordance with the amount of sunlight falling on the PV array and the demands of the load.

Ideally, a charge controller continually estimates the battery SOC and uses it to regulate the current accepted from the PV array. Actually, this is more difficult than it sounds because SOC is not simply related to instantaneous battery voltage, but depends on past history. For example if a battery has been supplying load current for some time and its voltage has fallen, then on disconnection it slowly recovers, even without further charging. Conversely if it has been on charge for some time and the voltage has risen, when charging ceases, it slowly falls back to a lower level. In other words the voltage signal detected by the charge controller is not a straightforward indicator of SOC. Effective controller algorithms must take past history as well as present voltage into account in assessing SOC and select boost, float, or equalization charging accordingly.

A closely related issue is that of hysteresis. When the upper set point is reached and the PV array is disconnected to prevent overcharging, the battery voltage immediately starts to fall back, even if no load is connected. How far should it be allowed to fall before reconnection? Too much, and there will be long interruptions to charging; too little, and there will be frequent on/off oscillations. So the gap, or hysteresis, between disconnect and reconnect voltages is a compromise that must be chosen carefully. A similar situation arises at the lower set point. After disconnection at 11 V, the voltage must be allowed to recover by a reasonable amount before automatic reconnection.

Charge controllers come in many shapes and sizes. In the case of a low‐power SHS based on a single PV module and 12 V battery supplying a few low‐energy DC lights and a small TV, a simple unit to control a few amps of current at 12 V is all that is required. Figure 5.5 shows the external circuit connections for such a unit. Typically, there is a row of six terminals, one pair each for the PV, DC loads, and battery, making installation very straightforward. Note that a fuse has been included close to the positive battery terminal, generally a wise safety precaution in case of a short circuit.

Moving up the power scale, suppose we have a 1 kW_p PV array feeding a 24 V battery bank with a peak solar current of about 30 A. A suitable controller is likely to offer a number of features such as

• Choice of flooded or sealed lead‐acid batteries
• Protection against reverse polarity connection of PV modules or batteries
• Automatic selection between boost, float, and equalization charging regimes, depending on the estimated SOC of the battery bank
• Protection against battery overcharging and deep discharging, excessive load currents, and accidental short circuits
• Prevention of reverse current at night
• Display of such parameters as battery voltage and/or estimated SOC, PV, and load currents and warning of impending load disconnection

The cost of the unit will clearly depend on how many features are included, and as we move towards the top of the power range, protection and monitoring functions become ever more important and sophisticated.

How do charge controllers perform their central task and regulation of current flow into and out of a battery bank? There are three basic designs on the market: series controllers, shunt controllers, and maximum power point tracking (MPPT) controllers. Once again we will illustrate ideas and values using a 12 V system, but they apply equally to higher system voltages if voltage values are scaled up in proportion.

The main functional elements of a series controller are illustrated in Figure 5.6. It includes an electronic switch known as the low‐voltage disconnect (LVD) to prevent battery damage if the voltage falls below some critical value, normally chosen at 11 V. The diode is included to ensure that reverse current cannot flow back into the PV at night. And to the left of the figure, a second electronic switch (S), usually a MOSFET, has the vital task of overseeing the charging of the battery. When S is closed the PV current is sent to the battery; when S is open charging is interrupted. In most modern designs the required switching sequence is achieved by a subtle process known as pulse width modulation (PWM). Current is released to the battery in rapid pulses of variable width so that the average current, which determines the charging rate, is constantly adapted to take account of the battery’s SOC. This is explained in Figure 5.7. The charging rate can be varied continuously between “OFF” when the battery is fully charged and “ON” when the available solar current is all sent to the battery. In the “OFF” condition the pulse width is zero (in effect, no pulses); in the “ON” condition it is maximum (pulses contiguous). Three intermediate pulse widths are shown as examples of different charging rates (low, medium, and high). Note that the current switches between zero and I_PV the available output from the PV array. The clever part of the PWM approach is, of course, to design a control algorithm that continuously changes the pulse width in sympathy with the SOC, making the best use of the PV’s output while at the same time protecting the battery.

The operation of a shunt controller is illustrated by Figure 5.8. Here, the electronic switch S is connected across the PV array rather than in series with it, so the battery receives charge when the switch is open. Charging is interrupted when the switch is closed, short‐circuiting the PV. Most modern shunt controllers also use PWM to regulate the charging rate. Inclusion of a diode is essential in a shunt controller to prevent the battery from being short‐circuited when switch S is closed.

Supporters of the shunt concept often claim that it offers better charging efficiency than the series alternative. Switching losses (which should be small anyway) only occur when the solar current is being rejected; whereas in a series controller switching losses detract from power being sent to the battery. But there are two offsetting disadvantages. First, the shunt controller’s switch, normally a MOSFET, needs a larger heat sink and must carry the full short‐circuit current of the PV array, possibly in strong sunlight and for long periods. And second, although PV modules do not generally object to being short‐circuited, there may be a risk of hotspot formation due to a “bad” cell or severe shading (as discussed in Section 3.2.1). In practice there are far more series than shunt controllers on the market, together with a few that combine the two design approaches to produce series/shunt hybrids.

We now move to the third basic type of design—the MPPT controller. Until fairly recently its more complex electronics and higher costs made it something of a niche market product, mainly reserved for the larger stand‐alone systems. But as with many aspects of PV, technological advances coupled with volume production have reduced the cost sufficiently to make MPPT controllers attractive in a wide range of systems, even down to a few hundred peak watts. The potential advantage is clear: by working a PV array at its MPP, rather than at a voltage determined by the system’s batteries, it is possible to extract considerably more energy and improve system efficiency.

Allowing the PV array to operate at a different voltage from that of the battery bank opens up another important possibility. As we pointed out in Section 3.2.2, the rapid development of grid‐connected systems, larger PV modules, and new thin‐film technologies has tended to shift manufacture toward higher module voltages unsuited to the direct charging of batteries. Specifying an MPPT controller allows a wide choice of modules that could not be used with a more conventional series or shunt design (Figure 5.9).

The basic scheme of an MPPT charge controller is shown in Figure 5.10. The key element is a DC‐to‐DC converter that allows the PV module or array to operate at a different DC voltage from that of the battery or battery bank. Designs fall into two main categories: boost converters that raise the input voltage to a higher level and buck converters that reduce it. Buck converters are more common in PV applications, reducing the relatively high voltages of modern PV modules (or series‐connected modules) to the lower voltages of battery banks. DC‐to‐DC converters have undergone extensive development in recent years, and their ability to “transform DC” finds many applications in electronic engineering. In the case of an MPPT charge controller, the really innovative part is not the voltage change, but rather the ability to sense the MPP of the PV array as sunlight levels change, at different times of day and in variable weather. Typically this is achieved with an algorithm that performs continuous electronic tracking of the array’s MPP together with periodic sweeps along its I/V characteristic to confirm that the true MPP is being detected rather than a local power maximum. The voltage on the input side of the converter is automatically adjusted to the MPP voltage.

One further feature is required, this time on the output side of the DC‐to‐DC converter. As in more conventional charge controllers of the series or shunt type, the available output from the PV array, at its new voltage level, is presented to the batteries as a train of rapid current pulses of variable width using a PWM switch. Once again, an advanced control algorithm ensures that charging rate is continuously adapted to the estimated SOC of the batteries.

5.2.3 Inverters

We described a stand‐alone PV system for a remote farmhouse at the start of this chapter (see Figure 5.1). It includes an inverter, connected to the battery bank, for supplying AC to the various household electrical appliances. Of course, inverters are not required in systems having only DC loads, but when they are used, it is important to understand the special features required in independent, stand‐alone units. As the stand‐alone PV market develops, customers are increasingly opting for AC systems because they like the flexibility offered by a wide range of consumer electronics, household appliances, electric tools, and even washing machines. AC systems are also used by hospitals and remote telecommunications sites and for running machinery in small factories. Well over 50% of newly installed stand‐alone systems are AC.

The grid‐connected inverters described in Section 4.2 are not suitable for stand‐alone systems. An important difference is that whereas a grid‐connected inverter must generate AC at precisely the right frequency and phase to match the grid supply, a stand‐alone unit is not so constrained. It generates its own AC without any need to lock into a grid and is necessarily self‐commutated. Although the generated waveform must suit the various AC loads, it need not satisfy an electric utility. And whereas a grid‐connected inverter is supplied directly from a PV array and often performs MPP tracking, its stand‐alone cousin is fed from storage batteries at a more or less constant DC voltage, leaving the task of extracting energy from the PV array to a charge controller that may itself work on the MPPT principle.

Figure 5.11 shows the connections for a typical mid‐range stand‐alone system with a PV power between, say, 1 and 2 kW_p. It is similar in many ways to the much lower‐power, DC only, SHS in Figure 5.5, with an inverter added; however it is redrawn to emphasize several features of a larger, more sophisticated, system:

• The PV is an array rather than a single module.
• A battery bank replaces a single battery, giving more storage capacity.
• The charge controller has an electronic display (or a set of colored LEDs) indicating parameters such as battery voltage, SOC, PV current, and load current.
• The inverter, connected directly to the battery bank, also indicates its operating conditions.

We have not shown fuses because adequate fusing is normally included in the charge controller and inverter. Note also that many controllers supply 12 V loads; if these are not required, the system voltage may be set to a higher value such as 24 or 48 V. Some controllers offer dual voltage operation, typically 12 or 24 V, but limited to the same maximum current, so they can regulate a more powerful system, provided the higher voltage is selected. Since the inverter is connected directly to the battery bank, it should include a disconnect function if the battery voltage falls below the lower set point.

In Section 4.2 we considered ways in which the choice between various types of inverter is influenced by module connection schemes and the problem of unavoidable shading. Although similar considerations apply in principle to the stand‐alone case, in practice the situation tends to be simpler. Shading is rarely a problem because PV arrays may often be sited on open ground, with all modules facing the same direction, rather than confined to potentially awkward urban rooftops; this, together with the moderate size of most stand‐alone systems, means that a single central inverter is generally suitable.

The user of a stand‐alone inverter should look for the following technical features:

• A power rating sufficient for all loads that may be connected simultaneously
• Accurate control of output voltage and frequency, with a waveform close to sinusoidal (low harmonic distortion), making the AC supply suitable for a wide range of appliances designed to run off a conventional electricity grid
• High efficiency at low loads, and low standby power draw (possibly with automatic shutdown when all loads are turned off), to avoid unnecessary drain on batteries
• Ability to absorb or supply reactive power in the case of reactive loads
• Tolerance of short‐term overloads, particularly caused by motor start‐up

Inverter efficiency is especially important in a stand‐alone system that must obtain all its energy from precious sunlight without grid backup. Maximizing efficiency and minimizing standby consumption do not come cheap, but the resulting energy savings may allow the system designer to specify a smaller PV array and battery bank, leading to overall cost savings. Unfortunately some inverter manufacturers only quote maximum efficiency, or efficiency at full rated output, disguising unfavorable performance under low‐load conditions. Figure 5.13(a) shows two typical efficiency curves, red for an inverter incorporating a low‐frequency transformer and orange for a unit with a high‐frequency transformer. Both suffer from severely reduced efficiency when delivering less than about 10% of their rated output. With rising load the efficiency reaches a maximum over 90% and then tails off again. But there are subtle differences between the two: the unit with the low‐frequency transformer does better at low load, and vice versa (switching losses associated with HF electronics are relatively dominant at low load, whereas magnetic losses in a low‐frequency transformer are greater at high load). Such differences can be important when choosing an inverter for a particular duty.

Many stand‐alone systems, including those in solar homes, spend much of their time on low load with peaks at certain times of day. Figure 5.13(b) shows a representative daily load profile for a home running a wide range of electrical appliances for lighting, cooking, and household machines. Most of the time the inverter load is less than 20% of its rated output, with peak periods in the morning and evening. This is exactly the sort of situation where careful attention to the inverter’s low‐load efficiency and standby power requirements is likely to pay dividends.

Like other aspects of PV engineering, the stand‐alone inverter scene is advancing rapidly. AC systems are finding favor for small SHSs in developing countries, and individual PV modules with integrated inverters have entered the market. Some manufacturers offer inverters combined with charge controllers in single units; others use a modular design approach so that many inverters can be stacked together to increase power‐handling capacity. Toward the top end of the power range, there is ever‐increasing sophistication in monitoring, data logging, and intelligent power management. And some of the most powerful units are being used as central inverters for mini‐grids of 100 kW_p or more, often integrating PV with other energy sources and providing renewable electricity to remote villages and island communities.

5.4.1 Assessing the Problem

In the popular imagination, science provides firm answers to firm questions, leaving little to chance when it comes to technical decision‐making. But things are not as simple as that. For example, while almost all experts agree that global warming due to greenhouse gas emissions poses a major threat to life on Earth, there are wide‐ranging views on its exact severity and timescale because the supporting evidence is essentially statistical. Scientists and engineers are trained to understand technical uncertainty, but it often confuses the public and offers scope for vested interests to declare the whole idea erroneous or exaggerated.

In this book most of our discussion is based on “hard science,” and we have been able to describe the performance of individual system components such as PV modules, batteries, and inverters with considerable accuracy. But there are two major chapters in the PV story where chance and uncertainty play a key role. Interestingly, but perhaps unsurprisingly, they are at opposite ends of nature’s range of operations—one dealing with the miniature and the other with the large scale. The miniature, discussed in Chapter 2, concerns the quantum nature of light and the random way in which solar photons are absorbed or transmitted by solar cell materials. Although we avoided the mathematical details, you may be sure that the underlying theory is replete with probabilities! The second topic, the large‐scale one we are about to tackle, concerns system sizing—deciding how much PV power and battery storage is needed for a particular stand‐alone system, based on estimates of local insolation patterns, electricity demand, and required reliability of service. A few moments reflection will surely convince you that such estimates must always be hedged about with uncertainty. Indeed, so much so that the “sizing problem” is often considered the most difficult aspect of system design.

This is primarily a stand‐alone rather than a grid‐connected problem because independent systems lack the support of a powerful electricity grid acting as a flexible “source and sink.” A stand‐alone system, especially when powered by PV alone, cannot realistically achieve total reliability. There is inevitably a trade‐off between reliability and cost, forcing the system designer (and customer) to face some difficult choices. We can illustrate the dilemma using four stand‐alone PV scenarios with very different operational expectations:

• PV in space. Launched into space on long missions without any prospect of replacement or repair, the PV arrays on spacecraft are surely the most extreme examples of stand‐alone systems. 100% reliability is certainly the aim, probably over many years and at almost any cost, because spacecraft are entirely dependent on their PV power supplies. Fortunately, there is one simplifying factor: insolation in space, beyond the Earth’s volatile atmosphere, is highly predictable, removing one major source of design uncertainty.
• PV‐powered refrigeration. PV is increasingly used to power refrigerators for storing vaccines and medicines in remote hospitals in developing countries. Failure of the electrical supply may be life‐threatening as well as highly inconvenient and expensive, so reliability is obviously a major requirement.
• PV‐powered traffic signs. Also a “professional” application, traffic signals to warn drivers that they are speeding, or that there is an obstruction ahead, should obviously be dependable. But how dependable and over what timescale? What if the PV electricity runs out for a few days, and foggy weather makes an accident more likely? Will the highway authority’s budget stretch to units containing more PV and larger batteries?
• PV for a solar home or farmhouse. We have already illustrated a stand‐alone system for a farmhouse (see Figure 5.1). The size of the PV array and battery bank will obviously depend on the input from the wind turbine, the owner’s choice of electrical appliances, and the amount of use. There is plenty of room for flexibility and cost saving here although it may be very difficult to decide such issues at the design stage. Generally speaking, security of supply is judged less important than for the “professional” systems mentioned previously, even though to be without lights and a TV in dead of winter is not an attractive option! In a holiday home used mainly in the summer months, occasional supply failure may be quite tolerable.

It is clear from the previous examples that the designer of a stand‐alone PV system is faced with difficult decisions and choices. They can be approached in various ways. Sizing methods based on practical experience and “rules of thumb” are quite often used and may provide sensible, cost‐effective solutions without much appreciation of the background science. PV sizing software is also widely available, although there is always a danger of using inaccurate input data or failing to appreciate the underlying assumptions. At the other extreme, analytic methods that attempt to put figures (including probabilities) to the many individual factors and components in a PV system promise more accuracy and scientific insight, yet they are also highly dependent on the robustness of input data and assumptions.³ Our own approach, similar to one recommended elsewhere,⁴ is intermediate in sophistication yet sufficiently detailed to highlight the main technical issues. We will illustrate it with an example based on a holiday home in southern Germany that is mainly used in the summer months.

We start the design process by considering the range of electrical appliances required by the homeowners, the power that each appliance consumes, and the average amount of daily use. This allows us to specify the total amount of electricity required in an average day, which is basic information needed to size the PV system. The table shown in Figure 5.15 includes eight low‐energy lights and a TV (often considered priorities for homeowners) plus a number of other appliances reflecting individual needs and preferences. Note that by multiplying the power of each by its estimated average daily use, we arrive at its consumption in watt hours (W h) per day and, at the bottom of the table, the total estimated consumption for the whole system—in this case 2200 W h (2.2 kWh) per day. This is the amount of electrical energy to be supplied by the PV system and is fairly typical for an SHS that includes a good range of modern appliances (by contrast, simple SHSs in developing countries based on a single PV module and a battery often provide just 200–300 W h/day). In this case the homeowners wish to use standard AC appliances, so an inverter must be included in the system.

It is extremely important to specify the most energy‐efficient appliances available and, wherever possible, to avoid those involving heating. Electric fires for space heating must be considered taboo, PV electricity being far too precious to be used for warming human bodies! The kettle in the previous list might also be thought extravagant; a daily consumption of 200 W h is sufficient to provide about ten cups of coffee or tea, and whether its great convenience is worth, the energy cost is clearly a personal choice. The same applies to the microwave cooker (but note that it is only switched on for very short periods). A washing machine is high on many people’s list, but it must not be used to heat the water; running it once or twice a week rather than daily would be very helpful. In short, everything should be done to reduce daily usage, especially of high‐consumption units, with the aim of reducing the size and cost of the PV system. We are here confronting a reality that escapes most people living in developed economies: electricity cannot always be taken for granted and used casually but must sometimes be treated as a precious resource.

Having decided on the daily amount of electricity required, we are ready to tackle two key aspects of system design—the power of the holiday home’s PV array and the capacity of its battery bank.

5.4.2 PV Arrays and Battery Banks

In the previous section we estimated 2.2 kWh as the average daily electricity requirement for a holiday home in southern Germany, and it is now time to decide on the amount of PV and battery storage needed to meet the specification. In this section we shall often refer to arrays and battery banks, terms appropriate for medium‐size and larger systems, but our approach is also valid in principle for small systems containing a single PV module and battery.

The first task is to work out the size of the PV array: how much peak power should it have to satisfy the electricity demand? As it stands, the 2.2 kWh/day applies throughout the year whereas the amount of sunlight falling on the array is bound to be seasonal. So if we size the array to cope with the “worst” month for sunlight—usually December in the northern hemisphere—the owner is likely to be paying a lot of money for an array that is unnecessarily powerful in summer. Since this is a holiday home, it may be more sensible to restrict the 2.2 kWh daily usage to the summer months.

We will assume that the array can be sited on adjacent open ground, facing south, and inclined at a suitable tilt angle. Back in Section 3.3.2 we discussed the amount of daily solar radiation falling on south‐facing inclined PV arrays, and Figure 3.17 showed typical data in the form of monthly mean values for London and the Sahara Desert. We also introduced the concept of peak sun hours for estimating an array’s annual output. This involves compressing the total radiation (direct plus diffuse) received throughout the year into an equivalent duration of standard “bright sunshine” (1 kW/m²). The same concept may be used for daily radiation. For example, if an inclined array receives an average insolation of 3 kWh/m²/day in April, this is considered equivalent to 3 peak sun hours, so an array rated at, say, 2 kW_p is predicted to yield 3 × 2 = 6 kWh/day. Although it is an approximation that tends to be overoptimistic for arrays receiving a high proportion of diffuse radiation, it offers a very straightforward way to estimate array output in a particular location.

Figure 5.16 shows daily solar radiation levels in the same form as Figure 3.17, but using published data5 relevant to the holiday home’s location in southern Germany. Three representative values of tilt are illustrated: 33°, 48° (the latitude angle), and 63°. As expected, 33° does best over the summer months when the sun is high in the sky (an even smaller tilt would give better results at midsummer but at the expense of other times of year). A tilt of 48° gives good results around the time of the equinoxes in March and September, and 63° is marginally preferable over the winter months. We also see that radiation levels in December are only about one‐third of those in midsummer, so a PV array big enough to supply the home’s electricity in December would be three times oversized in June. Clearly, choosing an array to cope with the “worst” month of the year would be a very expensive option.

At this stage the system designer must surely discuss alternatives with the homeowners. For example, they might agree to restrict their demand for 2.2 kWh/day to the months March–September, covering the main holiday period, in exchange for a smaller PV system at lower cost. Over this 7‐month period the 33° tilt angle is a good choice. The “worst” month is now taken as March, for which the average daily radiation is 3.5 kWh/m². This figure can be used for sizing the array. The homeowners will have to make do with considerably less electricity over the winter months, unless the total is boosted by an alternative energy source, or perhaps they will agree to forgo the use of refrigerator, microwave oven, and washing machine and cut down on the drinking of coffee! Unlike the “professional” PV systems mentioned in the previous section, a “leisure” installation should offer plenty of opportunities for energy saving, trading convenience, and reliability against cost.

Using the peak sun hours concept, we may express the average daily amount of electricity available for running the home’s appliances, E_D as

(5.1)

where P_PV is the rated peak power of the PV array, S_p is the number of peak sun hours per day in the month of interest, and η is the overall system efficiency (discussed hereafter). Therefore the peak power of the array is given by

(5.2)

In the case of the holiday home, E_D = 2.2 kWh/day, S_p = 3.5 hours in March, and we will assume a system efficiency of 60% (η = 0.6), so that

(5.3)

We therefore predict that a PV array rated at just over 1 kW_p will supply the daily load requirement of 2.2 kWh during the months March–September.

The overall system efficiency η takes account of various power reductions and losses that prevent the PV array’s nominal output from getting through to the household’s AC appliances. A figure of 60% may seem disappointing, but is fairly typical of such stand‐alone systems. It is derived by multiplying together efficiencies for the various system components, expressed as numbers between 0 and 1 (e.g., an efficiency of 85% is expressed as 0.85). Although it is difficult to give exact figures the following are fairly typical:

• PV modules (0.85). Power output is less than the rated value in standard “bright sunshine” (1 kW/m²), due to such factors as raised cell operating temperatures, dust or dirt on the modules, and aging. Also, modules are not generally operated at or close to their MPP (unless a controller with MPP tracking is used).
• Battery bank (0.85). The charge retrieved from the battery bank is substantially less than that put into it (see Section 5.2.1).
• Charge controller, blocking diodes, and cables (0.92). There are small losses in all these items.
• Inverter (0.9). This is a typical figure for a high‐quality inverter, bearing in mind that it must sometimes work at low output power levels (see Section 5.2.3).

The product of all these figures is 0.6, or 60%. If MPP tracking is used and the system is DC only (no inverter), the system efficiency might approach 70%. But in practice it is hard to predict how components will behave in variable sunlight and ambient temperatures or how the system will actually be used by the homeowners as they become familiar with it, so the aforementioned figures should be treated with caution.

In view of all these uncertainties, plus the vagaries of the weather, oversizing a PV array by a reasonable amount—say, 20%—is often recommended. In the previous example 1.2 kW_p would obviously improve reliability of supply, but it is, as ever, a question of cost. An alternative is to regard PV as an essentially modular technology that can easily be upgraded. So it would be possible to install a 1 kW_p array initially and expand it later if required.

The remaining task is to size the battery bank. The biggest decision is how many “days” of battery storage are required. Too few, and a spell of unusually dull or wet weather may cause a serious loss of electricity supply. Too many, and the battery bank becomes unnecessarily large and expensive. Five days of usable battery storage (in the previous example, equal to 5 × 2.2 kWh = 11 kWh) is often regarded as a good compromise between reliability and cost. But of course it depends on the application; a holiday home is by no means a crucial case, and many “professional” systems demand far higher reliability to avoid risking serious inconvenience, economic penalties, or even danger to life. In such cases the amount of battery storage may have to be raised greatly, perhaps to 15 days or more. Alternatively, a reliable standby power source such as a diesel generator may be incorporated.

When the number of days of storage N has been decided, the capacity C of the battery bank can be calculated:

(5.4)

where (as before) E_D is the daily electricity requirement, D is the allowable depth of discharge of the battery bank, and η_inv is the efficiency of the inverter, assuming an AC supply is required. Note that the usable capacity of the battery bank is less than its nominal rated capacity because complete discharge must be avoided. In our example we will assume 5 days of storage, battery discharge up to 80% of nominal capacity, and inverter efficiency of 90%. Hence,

(5.5)

As with the PV array, it may be sensible to oversize the battery bank—or to treat it as modular, with the option of upgrading it later.

To summarize, the stand‐alone system for the holiday home in southern Germany should be able to supply the desired amount of electricity between March and September using a PV array rated at 1.05 kW_p with a battery bank of capacity 15.3 kWh (assessed at the 100‐hour discharge rate normal for PV systems). If the batteries are connected to give 24 V DC, which is quite common for a system of this size, then the required charge capacity is 15 300/24 = 638 A h.

This specification could be met, with a reasonable amount of oversizing, by an array of, say, eight PV modules rated at 150 W_p each (1.2 kW_p total), together with a bank of, say, eight 12 V batteries rated at 175 A h each (16.8 kWh total). The electricity yield, and hence system reliability, could be further improved at a modest cost by specifying an MPPT charge controller. The modules could be connected in series or series–parallel; the batteries as four parallel strings of two units each to give 24 V DC. The main components of the system are illustrated in Figure 5.17.

We end this section with some further remarks on reliability. First, it must be admitted that choosing a holiday home to illustrate system sizing makes life rather easy because it allows a somewhat cavalier approach toward possible supply failures. We are making use of the relative unimportance of failures in this “leisure” application and have assumed that homeowners are flexible over their use of appliances. All this changes dramatically in the case of a “professional” system with stringent load and reliability criteria, and serious thought must given to how often a failure of supply can be tolerated.

The many uncertainties of system design mean that the problem can only be discussed sensibly in terms of probabilities. A measure known as loss‐of‐load probability (LLP) is widely used. Basically, LLP denotes the probability that, at any point in time, the PV system is unable to satisfy the demand for electricity. It may also be interpreted as the proportion of total time that the system is unavailable (which should include estimated maintenance and repair outages). LLP = 0 implies that the system is 100% available; LLP = 1 that it is permanently out of action. We normally hope for and expect low LLP values, say, between 0.0001 and 0.1, but it depends very much on the importance of reliability in a particular application. The smallest values of LLP, increasingly difficult and expensive to achieve, are typically found in PV systems used on space missions or in vital telecommunication links, the largest ones in leisure applications (it is hardly a disaster if solar‐powered garden lights fail to work every evening!).

However it is much simpler to explain the LLP concept than to calculate its value for a particular system or design a new system to meet a customer’s LLP specification. The basic difficulty is that it depends on so many factors, some fairly obvious, while others obscure or random in nature. Our previous discussion makes clear, for example, that reliability is generally increased (and LLP reduced) by specifying a more powerful PV array and/or a larger battery bank—although there is, in fact, a subtle interaction between them.² Sunlight statistics plays a major role. For example, occasional lengthy periods of cloudy weather, untypical of the local climate, can result in a battery bank’s SOC being depleted to such an extent that supply cutoff is inevitable. Unfortunately rare and isolated weather events cannot be predicted from averaged meteorological data.

Yet in spite of the difficulties, various theoretical ways of incorporating LLP into stand‐alone system design have been developed in the past 25 years,² and many sophisticated computer programs for system sizing and simulation are available.⁶ Indeed, the complexity of the task more or less demands the use of computer software, even though it may be hard for the newcomer to understand its details. A straightforward quantitative approach to sizing, such as what we have introduced in this section, seems a good antidote to over‐reliance on computer software. A few simple calculations at least allow us to check that the numbers churned out by a computer program are reasonable!

5.5.1 PV in Space

For more than half a century, spacecrafts have relied on solar cells for their power supplies. In the early years of the modern PV age, solar electricity was so expensive that space exploration provided its only significant market. The costs of designing, manufacturing, and launching vehicles into space are so large that the price of cells to power them is relatively unimportant, the main criteria being technical performance and reliability in the harsh space environment. Although the total amount of PV power launched beyond the Earth’s atmosphere is tiny compared with today’s gigawatts of terrestrial installations, solar cells remain vital to modern spacecraft including those used for satellite communications, TV broadcasting, weather forecasting, and mapping—and, of course, space exploration. You may wish to follow up this brief introduction with an approachable and authoritative account given elsewhere.⁵

We may summarize the special features of the space environment that impact on the design and deployment of solar cells and arrays with a few key points:

• Radiation in space tends to damage solar cells.
• Sunlight in space, unfiltered by the Earth’s atmosphere, has a different spectrum from that received by terrestrial PV cells.
• Spacecraft, including satellites in Earth orbit, experience dramatic changes in sunlight intensity and temperature as they move in and out of shadow, causing high thermal stresses in solar cells and modules.
• PV modules and arrays need to be kept as small, neat, and light as possible to avoid adding unnecessarily to the launch payload.
• Sustained technical performance and reliability are paramount, especially on long missions.

Each of these will now be discussed in more detail.

Radiation damage to solar cells in space is a major challenge to PV designers. The risk of damage by high‐energy electrons and protons is particularly serious for satellites in mid‐Earth orbits (MEOs), defined as 2 000–12 000 km above the Earth, which pass through the Van Allen radiation belts. The neighborhood of Jupiter is also a high‐radiation environment. Special types of cover glass are effective at reducing the steady and cumulative degradation of cell performance over the lifetimes of long missions. The susceptibility of standard silicon solar cells to radiation damage was recognized in the early years of space exploration and much effort has been put into design improvements to mitigate the effects and raise cell conversion efficiencies, presently approaching 20%. Although high‐efficiency silicon cells are in widespread use, a major advance in recent years has been the development of multi‐junction III–V cells based on gallium arsenide (GaAs) and related compounds, which are much less susceptible to radiation damage and offer even better conversion efficiencies. We first described these cells in Section 2.5.1, and since they are so important to space PV, we will mention them again toward the end of this section.

In this book we have often referred to standard “strong sunlight” received by solar cells and modules at the Earth’s surface. This is defined as having an intensity of 1 kW/m² and the AM1.5 spectrum typical of sunlight after passing through the Earth’s atmosphere. Sunlight in space, unfiltered by the atmosphere, is described by the Air Mass Zero (AM0) spectrum (both spectra were illustrated in Figure 1.6). The intensity also varies according to the distance from the sun. For example, near Mercury it is almost double than near Earth, and near Jupiter only about one‐thirtieth. Clearly, solar cells and modules have to operate satisfactorily and be calibrated for use under such conditions.

Closely related to changes in light intensity are changes in operating temperatures. Whereas terrestrial solar cells and modules are normally required to work between, say, −20°C and +70°C, conditions in space can be far more demanding. Spacecraft in orbit around the planets experience extremes of temperature as they pass in and out of the sun’s illumination. Cell temperatures in low Earth orbit (LEO) may get down to −80°C in shadow, but in orbit around distant Jupiter they must work at −125°C, even when illuminated, around Mars, at up to +140°C. Sudden transits from shadow to sunlight can produce big power surges as well as exposing cells and modules to high thermal stresses.

The size and weight of space PV arrays is extremely important, as is their ability to deploy successfully on reaching zero‐gravity conditions. The smaller and neater an array, the easier it is to integrate into the spacecraft’s structure during launch; the lighter it is, the lower the payload and launch cost. For a given peak power, an array’s area is proportional to cell efficiency, favoring the most efficient cells and technologies. In the early 1970s the most powerful PV system in space was that of the Skylab 1 satellite, delivering about 16 kW_p. The International Space Station, launched in 1998 and continuously expanded and developed over the following decade, generates more than 100 kW of average power from its silicon solar cells, which are mounted in eight double arrays with a total area of over 3000 m². This is large‐scale PV, with exciting technical challenges for project teams in mechanical engineering and materials science as well as solar technology.

The efficiency of solar cells designed for use in space is important for several interrelated reasons. For a given peak power requirement, improvements in cell efficiency reduce the area, weight, and payload costs of a PV array. As we mentioned earlier, one of the most important advances in recent years has been the commercial development of triple‐junction cells based on GaAs and related compounds, which now attain 30% efficiency under AM0 conditions, reducing array areas by over a third compared with high‐efficiency silicon. They also have better radiation resistance. Typically, a triple‐junction device consists of a “sandwich” of layers of gallium indium phosphide (GaInP), GaAs, and germanium (Ge), each carefully chosen to absorb a portion of the solar spectrum—you may like to refer back to Section 2.5.1 and Figure 2.38 for a fuller explanation. Research continues apace, with even more efficient four‐junction devices in prospect, and an increasing interest in concentrator systems to reduce the area and cost of these highly specialized cells.

It goes without saying that technical performance and reliability, sustained over long periods, are paramount in space systems. On manned missions there may be limited potential for carrying out maintenance and repair, but on long unmanned missions solar cells and arrays are quite literally on their own—surely the most extreme example of stand‐alone systems. It is hardly surprising that PV power systems in space cost hundreds of times more per peak watt than their earthbound counterparts; but without them spacecraft would, quite literally, be lost.

5.5.2 Island Electricity

Providing a small island community with an economic, convenient, and reliable electricity supply can be a major challenge. Traditionally, islanders in the developed world have installed diesel generators and depended on fuel deliveries from a mainland depot. But diesel engine maintenance is expensive—fuel costs always seem to be rising—and there is a noise and pollution problem that people who cherish their natural environment would rather avoid. Most islands have a valuable wind resource, and many have lots of sunshine and free‐running rivers or streams. Such plentiful flows of natural energy act as a strong incentive to generate renewable electricity, and when several different energy sources are available, it makes good sense to consider a hybrid system and distribute the electricity using an island mini‐grid.

Such systems are still “stand‐alone” in the sense of being unsupported by large conventional electricity grids. So are mini‐grids serving isolated communities on the mainland. Their major advantage compared with that of the individual stand‐alone systems for each user is that integration of various energy sources with different daily and seasonal peaks can provide a more consistent, reliable, and economic supply for a whole community. Although backup diesel generators are generally still needed to ensure a reliable 24‐hour service throughout the year, they can be started up for short periods only when necessary—and then run hard and at high efficiency.

The Isle of Eigg, 6 × 4 km in extent, is one of the jewels of the Inner Hebrides. Lying off the west coast of Scotland to the south of Skye, it has an equable climate, thanks to the Gulf Stream, a generous wind resource, lots of sunlight in summer, a few streams, and just under a hundred inhabitants. Like many Scottish islands, Eigg has a harsh history behind it, including the 19th‐century depopulation and more recent absentee landlords, but in 1997 funds were raised to purchase the island and set up the Isle of Eigg Heritage Trust to manage it for the inhabitants and their wonderful environment. Determined to update their electricity supply from reliance on aging diesel generators to a modern “green” alternative, they raised capital grants totaling £1.6 m for a hybrid system comprising PV, wind, and hydroelectric power, with diesel backup.⁶ Early in 2008 all 37 households and 5 businesses on Eigg were connected to the new island grid, achieving celebrity status for a state‐of‐art renewable energy system that is providing inspiration to other island communities in Scotland and around the world (Figure 5.21).

Eigg’s system, as installed in 2008, is illustrated in Figure 5.22, which summarizes the generation and consumption of electricity. A key feature is that all generators and loads are interconnected by an island‐wide AC grid. Transmission is at 11 kV for long cable runs and at 230 V for short ones (from the PV and diesel generators), with transformers inserted where necessary. Power sources that generate DC (the wind turbines and PV) feed into the grid via inverters. An advanced load management system monitors the balance between supply and demand, bringing in the diesel generators when necessary and controlling energy flow to and from the battery banks via a set of bidirectional inverter–chargers. The batteries, PV, and wind turbines are the only DC components; homes and businesses are supplied with 230 V AC. Grid frequency is set by the inverter–chargers or by the diesel generators when they are running. We now comment further on the various items:

• 10 kW_p of PV. The Hebridean islands have a better sunshine record than the mainland, where higher mountains tend to increase cloud formation and precipitation. Eigg, at latitude 57°N, has plenty of sunlight in the summer months, with up to 18 hours between sunrise and sunset in June, so PV can make a valuable contribution when wind and hydropower tend to be at their lowest. In this system the output from 60 PV modules, connected in 6 strings of 10, is converted to 230 V AC by adjacent inverters. Since the first edition of this book was published, the PV array has been upgraded from 10 to 30 kW_p, showing confidence in Eigg’s ability to generate solar electricity.
• 24 kW_p of wind energy. A group of four wind turbines, each rated at 6 kW_p, is sited at one of the island’s windiest locations. Although wind turbines are generally rated in kilowatts at a standard high wind speed, we have used kW_p units in the figure to emphasize that they rarely operate at full output—even though the months October–April are highly productive on an island subject to Atlantic storms. In fact the Eigg wind turbines make a valuable contribution throughout the year. Their DC outputs are inverted and transformed to 11 kV for transmission.
• 100 kW_p of Hydropower. The most powerful contributor to the renewable energy portfolio is a new run‐of‐river water turbine rated at 100 kW_p supplied by a substantial stream (there are also two much smaller preexisting turbines in other locations rated at 9 and 10 kW_p, not shown in the figure). However on a small island the flow of streams closely follows current rainfall and tends to be intermittent and seasonal. Hydroelectric generation on Eigg is therefore variable, much stronger in winter than summer, with an average value far lower than the nominal ratings of the turbines (Figure 5.23).
• 2 × 80 kW_p of diesel. Two new diesel generators provide backup to ensure 24‐hour service throughout the year. In an average year the renewable sources are expected to provide over 95% of total electricity demand, so the total diesel contribution is small. Typically, the generators are run hard for short periods to boost charge the battery bank on days when the renewables are unable to meet the full load demand. They generate power at 230 V AC.
• Load management. A comprehensive hybrid system of this kind, involving various energy sources and domestic and business loads, justifies a sophisticated control system. Its aims are making the most of available renewable generation, deciding between the various sources in times of surfeit, ensuring that the battery bank is neither overcharged nor over‐discharged, transmitting electricity efficiently to the various loads, and bringing in the diesel generators when necessary.
• 12 × 5 kW_p inverter–chargers. Arranged as four 3‐phase clusters, each with its own battery bank, the bidirectional inverter–chargers are at the heart of the system. When the renewable generation is insufficient to meet demand, they take energy from the batteries and invert it to augment the AC supply. When generation exceeds demand, they rectify the AC and charge the batteries. If the batteries are fully charged and excess energy is being generated, the inverters raise the frequency, and additional “opportunity” loads such as heaters in community buildings (not shown in the figure) detect the increase and switch on automatically. If there is still surplus energy, the frequency is increased further, and the various generators respond by backing off to prevent battery overcharging.
• 4 × 53 kWh battery bank. The batteries are arranged in four 48 V banks and located in the power house with the inverter–chargers and diesel generators. The banks are normally kept above 50% SOC to prolong their life. The quoted total capacity is therefore half the full nominal capacity of 424 kWh and equates to approximately 1 day’s electricity usage on the island. Additional days of storage are not needed in this case because of the diesel backup.
• Households and businesses. 37 households and 5 businesses were initially connected to the island grid and supplied at 230 V AC. Householders agreed to limit peak demand to 5 kW_p each, while businesses to 10 kW_p. All consumers are provided with an energy meter to monitor the amount of electricity being used. The islanders have adapted well to the new system and are far better informed about electricity usage and energy conservation than most people on the mainland (Figure 5.24).

Eigg’s electricity grid is an excellent example of a modern hybrid system. The PV component, being essentially modular, may be increased even further in the future to provide more summer electricity. In any case, the principles of design and implementation are of widespread relevance, even though the relative contributions from PV, wind, hydro, and diesel backup are bound to vary from one island system to another.

5.5.3 PV Water Pumping

Infectious diseases caused by tainted drinking water and primitive sewage disposal are largely unknown to those of us who live in the developed world. We tend to take the benefits of pure water for granted. But who should we thank for this blessing? It has been said that the civil engineers of the 19th century did more to improve public health than all the doctors and surgeons put together, by designing and building the infrastructure for modern water supplies.

The situation can be very different elsewhere. In rural areas of some of the poorest countries in the world, millions of people, especially women, spend hours each day fetching and carrying water, sometimes from polluted streams or pools. Yet new village wells can transform lives and health and, if equipped with automatic pumps, eliminate the daily grind of water collection (Figure 5.25).

Water pumping is one of the most successful applications of stand‐alone PV in developing countries. By the year 2000 over 20 000 PV‐powered systems were in use worldwide and the pace of installation continues. Of course, small water pumps can be worked by hand, larger ones by windmills or diesel engines. But the PV alternative, in addition to its cleanliness, reliability, and long life, often proves economic for medium‐sized systems. Water pumping is also used for crop irrigation and stock watering.²

A typical scheme for village water supply is illustrated in Figure 5.26. A submersible pump/motor, protected by installation underground, raises water to a storage tank whenever sunlight falling on the PV array is sufficiently strong. From there it is fed by gravity to one or more taps. In previous sections we have often discussed the need for battery storage in stand‐alone systems. But one major feature of water pumping is that the water tank replaces batteries as the energy store, using PV electricity directly to increase the potential energy of the raised water.

Although the scheme is simple in principle, a number of technical choices must be made:

• Type of pump. Of the many types of pump on the market, centrifugal designs are widely used to raise water against pumping heads up to about 25 m (the height difference between the water table and tank’s input pipe). Multistage versions can cope with higher heads. A centrifugal pump has an impeller that throws water against its outer casing at high speed, the kinetic energy then being converted to a pressure head by an expanding output pipe. Centrifugal pumps are compact, robust, and well suited to PV applications, but they are not normally self‐priming and must therefore be kept submerged. This makes them suitable for pump/motors positioned below the water table. Alternative displacement or volumetric pumps including various self‐priming types are more suitable for lower flow rates from very deep wells or boreholes.
• Type of motor. DC motors are generally more efficient than AC ones, but more expensive. AC motors are very rugged and need little or no maintenance so are suitable for submersion at the bottom of a well, but inverters are needed to convert PV electricity to AC, adding to the capital cost. Among DC motors the permanent magnet type is often preferred; but all conventional designs use carbon brushes that must be periodically adjusted or replaced, making submersion awkward. Modern brushless DC motors overcome this difficulty, at a cost.
• Matching the motor and PV array. Ideally, the PV array should be operated close to its MPP in all sunlight conditions. Unfortunately the resistive load offered by most motors does not allow this to happen, so an MPP tracking controller based on a DC‐to‐DC converter may be inserted to improve matching and increase efficiency.

From the PV perspective the most important task is to size the array to pump the desired amount of water. A well‐known hydraulic equation is a good starting point. The hydraulic energy E_h required to raise 1 m³ of water against a head of H_w meters is given by

(5.6)

where ρ is the density of water (1000 kg/m³) and g is the acceleration due to gravity (9.81 m/s²). In this case H_w is the height of the holding tank’s input pipe above the water table.

In this book we have generally used the kilowatt hour (kWh) as our unit of energy. We note that 1 joule is equivalent to 1 W s, or 1/3.6 × 10⁶ kWh. Therefore if we wish to raise a volume V_w cubic meters of water per day, the required hydraulic energy is

(5.7)

For example, suppose that a village population of 300 needs an average of 50 l of water per person per day—a total of 15 000 l or 15 m³/day—and that the tank’s inlet pipe is 20 m above the water table. The hydraulic energy required is

(5.8)

We can now estimate the size of the PV array using the peak sun hours concept first mentioned in Section 3.3.2. Basically, this involves compressing the total daily radiation received by the array into an equivalent number of hours of standard “bright sunshine” (1 kW/m²). The peak power of the array is then approximately given by

(5.9)

where S_p is the number of peak sun hours for the particular location and η is the overall system efficiency. The peak sun hours are normally chosen for the “worst” month to ensure continuity of supply throughout the year. The system efficiency must take account of electrical losses in the motor and cabling, hydraulic and friction losses in the pump and pipework, and mismatch between the motor and the PV that prevents the array from working at its MPP. An average efficiency of about 40% is fairly typical for a centrifugal pump and, together with other losses, gives a typical system efficiency of around 25% (0.25). So, as an example, if the location has an insolation equivalent to 3 peak sun hours per day in the “worst” month, then the PV array needs a peak power:

(5.10)

Although peak powers up to a few kilowatts are fairly typical of systems supplying water to individual villages in sunshine countries, considerably larger PV arrays are sometimes installed to serve larger communities—for example, a cluster of villages obtaining water from a single source that is distributed by hand or pipe. A good example is the Ouarzazate scheme in Morocco, consisting of more than 20 autonomous stand‐alone systems supplying a total population in excess of 10 000 people. One of the smaller PV systems in this scheme has already been shown in Figure 5.2; a much larger one, incorporating a substantial roof‐mounted PV array, is shown in Figure 5.28—an impressive example of PV water pumping in action.

5.5.4 Solar‐Enabled Water Desalination

In addition to pumping water from the ground, electricity from PV can be used for sustainable production of potable water from sea water. Producing fresh water via water desalination is essential for arid, water‐scarce regions, but expensive and energy intensive. The cost of energy can account for half the total cost of producing water, and the use of fossil fuels to power the desalination plants causes emissions of CO₂ and other hazardous pollutants.

Availability of clean, potable water is challenging for almost 25% of the world’s population, and it is projected that by 2030, 47% of the global population will face water scarcity. Solar energy could be an alternative energy source for water desalination technologies, but it is not widely used as there are not yet many concepts and system designs that can handle the deterministic and stochastic variability of renewable energy resources. However, the decline in the price of PV is catalyzing developments in membrane‐based and thermal desalination systems that require a lot of energy and are typically needed in regions of high solar insolation.

The long‐term sustainability of the desalination infrastructure in arid and sunny countries requires a transition to more energy‐efficient desalination technologies and gradual displacement of fossil fuels with renewable energy (Figure 5.29).

PV‐powered reverse osmosis (RO) is currently the least expensive RE desalination option in many areas.⁷ The wholesale cost of electricity from PV is currently in the range of 4–8 US cents/kWh in areas of high irradiation. This is lower than the cost of subsidized grid electricity from fossil fuels in several sunny and arid regions, and solar electricity can help reduce the full cost of producing fresh water from seawater in these areas. PV electricity is cost competitive in many high insolation regions based on direct costs (levelized cost of electricity (LCOE)) and is a lot cheaper than fossil fuel electricity taking proper account of resource (fuel and water) depletion and environmental impacts.

Solar energy can be integrated into desalination plants, but for the transition to happen, the current fossil fuel subsidies should be phased out or given equally to the solar industry. Perhaps the most important enabling factor will be the empowerment of government agencies to take holistic, comparative views of energy costs and act on them.

5.5.5 Solar‐Powered Boats

Boats powered by sunlight represent one of the most successful and attractive applications of PV in the field of sustainable transport. Less well‐known to the public than the solar car races that have achieved international fame in Australia and the United States, solar boating has recently made headlines with a growing number of international events and a circumnavigation of the globe. Unlike road vehicles, boats do not have to climb hills or travel at high speed, and they require surprisingly little power for propulsion in calm conditions. This makes solar‐powered boating on lakes, rivers, and canals relatively inexpensive and opens up a new market for PV in an important leisure industry.

The low‐power levels needed to propel boats at modest speeds in calm water can be nicely illustrated with a historical example. Two hundred years ago Britain was in the middle of a canal‐building frenzy. The heavy materials of the early industrial revolution, including coal and iron, needed to be transported over considerable distances for which the road network was totally inadequate. So the English narrow canals, with locks just over 2 m wide and 22 m long, were carved through the countryside by gangs of “navvies” (derived from the word navigation) using picks, shovels, wheelbarrows, and human muscle power. This extraordinary feat of civil engineering revolutionized inland transport and allowed cargos up to about 30 tonnes to be carried in individual barges, the so‐called narrowboats that just squeezed into the locks. And how did the boats move in those early days? They were towed, often two at a time, by a single horse! Admittedly at slow speed, typically 2–3 km/h, but it was a vast improvement on existing methods of transport by land.

This example suggests that a single “horsepower” (HP), nowadays taken as equivalent to 746 W, is enough to shift many tonnes of boat at modest but useful speeds. And if careful attention is paid to design by making hull, motor, and propeller as efficient as possible, we now know that one or two HP can propel a modern leisure craft with several passengers at realistic speeds—say, up to 10 km/h (6.4 mph) in calm water. The quest for efficiency mirrors that of solar car design with its emphasis on streamlined bodywork and high‐performance motors, transmission, and tyres. But in the case of boats, the power levels, and therefore costs, tend to be much lower.

Electric boats are a novelty to many people. For the last 100 years, most motorboats have used petrol or diesel engines for propulsion, helping to deplete the Earth’s valuable fossil fuels, making a lot of noise, and polluting the waterways. But it was not always so. In the period from the 1880s up to the start of the First World War in 1914, there were plenty of battery‐powered electric boats on the lakes and rivers of Europe, including some that could carry over 50 passengers. The river Thames in England boasted a scheduled passenger service, with electric charging stations along the bank. However the advent of internal combustion engines proved nearly fatal, and by 1930 electric boating was in severe decline. Half a century later it began to emerge again, largely due to increasing environmental awareness, and today represents a small, but flourishing sector of the leisure boating industry. The essential components—batteries, control circuits, electric motors, and propellers—are constantly being developed and refined, giving wonderfully silent cruising with minimal disturbance to wildlife and riverbank.

Solar electric boats are even more of a novelty. We are not talking about the many boats that use a PV panel or two to power their electronic equipment and cabin lights, but true electric boats that use PV for propulsion. These exciting craft literally “cruise on sunlight.” Today there are many examples on the inland waterways of Europe, North America, and Australia, and the number rises year by year. The combination of a virtually silent, nonpolluting electric drive and solar energy is extremely attractive.

As already noted, quite a lot can be achieved with a propulsive power of 1 HP, equivalent to 746 W. In fact, the range 200 W to 3 kW covers most modern electric leisure boats at normal cruising speed, and there are a few larger craft, including passenger ferries, that require considerably more. We are referring to the mechanical power needed to propel the boat forward; more electrical power is required because of combined motor and propeller losses, typically amounting to 40%.

We now describe three recent boats with different design criteria, specifications, and passenger accommodation. The first, 6.2 m catamaran Solar Flair III, cruises on inland waterways in England. Designed as an experimental boat to test various combinations of PV modules, motors, and propellers, she also appears at boat shows and rallies, helping to promote PV and solar boating and convince the public of its viability, even in the British climate. She carries six 75 W_p monocrystalline silicon PV modules in front of a small cabin, plus two more behind (not visible in the photo), giving a total of 600 W_p to charge batteries that power an electric outboard motor. A smaller additional motor, mounted below the front module, acts as a bow thruster to aid sharp turning on narrow canals and rivers. The main motor takes about 450 W of input power to attain a cruising speed of 8 km/h in calm conditions. Average summer sunshine produces enough PV electricity to move Solar Flair III about 32 km (20 miles) per day at this speed. The design aims at technical performance and a streamlined appearance rather than passenger accommodation (Figure 5.30).

Our second example, the 6.7 m (22 ft) pontoon boat Loon, has been designed and developed in Ontario, Canada, as a spacious canal and river cruiser able to accommodate up to eight passengers in comfort (Figure 5.31). Raising the 1 kW_p of PV modules on a canopy greatly increases passenger space and gives protection against rain—and maybe also the sun! The input motor power to achieve 8 km/h is about 1 kW, and PV provides enough electricity, in the Canadian summer months, to travel an average of about 24 km (15 miles) per day at this speed. On long cruises the boat’s batteries may be fully recharged by plugging into shore power electricity. The same company is currently also offering a twin‐engined solar boat, the Osprey, capable of taking 30 passengers.

The third example, known under the project name PlanetSolar, is the largest solar‐powered boat in the world (Figure 5.32). Built in Germany after extensive model testing in wind tunnels and water tanks, it is registered in Switzerland and completed the first solar circumnavigation of the globe with a crew of six in May 2012. During the voyage it broke two other records: the fastest crossing of the Atlantic Ocean by a solar boat, and the greatest distance ever covered by a solar electric vehicle. The 31 m craft is covered by 537 m² of solar panels rated at 93 kW, fitted with 8.5 tons of lithium‐ion batteries, and driven by electric motors in the twin hulls. The craft is entirely solar driven, absolutely no diesel engine!

The hull’s fine lines allow it to reach speeds of up to 14 knots (26 km/h). PlanetSolar was given a rapturous reception at many international ports during its 584‐day circumnavigation, which ended, as it had begun, in Monte Carlo. Registered in Switzerland, it has recently been used as a floating marine research laboratory by Geneva University.

The catamaran or pontoon form of hull is clearly very popular for solar‐powered boats, with sleek twin floats providing a good stable platform for PV, especially when raised on a canopy. However there is nothing to stop designers from using conventional monohulls; the main criterion is an efficient low‐drag hull that creates minimal wash and uses the precious PV energy to best advantage.

Finally, we consider the question, “What exactly makes a boat solar powered?” Exaggerated claims are sometimes made; it is easy to stick a PV module or two on a boat and claim that it is powered by the sun. But it does PV no good to overstate its performance and capabilities, leading to disappointment and skepticism. One answer is to use a simple measure known as the solar boat index (SBI) to quantify performance and allow sensible comparison of a wide variety of leisure boats used on lakes, rivers, and canals.⁸

The SBI is based on the peak sun hours concept introduced in Section 3.3.2. We have also used it to size PV arrays for water pumping in Section 5.5.3. It involves compressing the daily radiation received by an array into an equivalent number of hours of standard “bright sunshine” (1 kW/m²). In this case the most relevant radiation data is that for a horizontal surface (most PV modules on boats are mounted horizontally) during the summer months of the boating season. An array rated at peak power P_PV watts and receiving an average S_p peak sun hours per day is expected to yield about S_p P_PV watt hours per day. If the boat needs an input motor power P_M watts to cruise at a standard speed (normally taken as 8 km/h) in calm conditions, then the SBI is defined as

(5.11)

where η is a system efficiency that accounts for the PV generally operating away from its MPP, and for battery storage losses. Using typical figures of 80% (0.8) for the PV and 75% (0.75) for the batteries, the system efficiency η = 0.8 × 0.75 = 0.6. If we now assume S_p = 5 (typical daily peak sun hours for midsummer in western Europe), Equation (5.11) becomes

(5.12)

This is easy to remember and is in fact used in the United Kingdom to quantify the performance of solar‐powered boats.

SBI has a simple interpretation. It represents the approximate number of hours per day, in average summer weather, that a boat can travel at standard speed on its PV electricity. For example, if a boat’s SBI is unity, this means it can travel about 1 hour a day, or 7 hours a week at 8 km/h, to give a range of 56 km. Most inland leisure boats are weekend boats, for which this amount of cruising is fairly typical. Therefore it seems reasonable to describe leisure boats with SBI values of 1.0 or above as “solar powered” in the west European and similar climates; otherwise they are “solar assisted.” Although the SBI is only approximate, it does provide a simple quantitative measure of a boat’s cruising range on sunlight and allows the solar performance of different boats to be compared. The SBIs for our first two examples are as follows:

Clearly, these values need sensible interpretation because the patterns of use of the two boats are different and so are the solar climates in which they operate. What we can say is that, if they met together on a European lake, their SBIs should give a good indication of relative solar performance.

Worldwide, there are a number of competitions for solar‐powered boats that act as good catalysts for new ideas and designs, encouraging young people to get involved. A good example is the Dutch Solar Challenge,⁹ held biannually on canals and lakes in the Netherlands. Such events do an excellent job of bringing to public attention the exciting future of solar‐powered boats with their silence, lack of pollution, and minimal environmental impact.

5.5.6 Far and Wide

The applications described in previous sections represent a broad range of technical, economic, and social objectives. Yet the scope and geographical spread of stand‐alone PV systems stretch much wider. We end this chapter with a few more photographs and captions to illustrate some of PVs past and present successes and help stir the imagination for its future potential.

On Land and Sea

In Heat and Cold

For Education and Information