# T

Figure 4.37 Boost Converter Circuit

The output voltage V2 is:

The dimensioning of L and C1 with = -i ■ Vj ■ (l - Vt / V2)• Ts / L is possible:

V 11

Other DC-DC converters

Besides buck and boost converters, some other types of DC-DC converter exist. The output voltage of the buck-boost converter of Figure 4.38 is:

The flyback converter shown in Figure 4.39 uses a transformer instead of the inductance. The output voltage can be calculated in the same way as for the

Generator -O

Generator -O

Figure 4.39 Flyback Converter Circuit

buck-boost converter, except that the transformation ratio r must be considered. This is defined by the ratio of the number of turns in the winding on either side of the transformer. Hence, the output voltage becomes:

For high power applications a push-pull converter is used that needs more than one switch. If capacitors replace the inductances, a converter using the charge pump principle can be realized.

### MPP tracker

The above-described voltage converters can maintain different voltages at the solar generator and at the load. If the solar generator voltage is set to a fixed value with a chosen duty cycle (see Figure 4.33), the energy yield is much higher than with a simple resistive load. On the other hand, the optimal operating voltage varies depending on irradiance and temperature. Therefore, a variation in the duty cycle of the DC-DC converter changes the solar generator voltage and thus can improve the energy yield.

Fluctuations in temperature û have the highest influence on the optimal solar generator voltage. A temperature sensor attached to the back of a solar module can measure its temperature. With the temperature coefficient of the open circuit voltage (e.g. aVOC = -3-10"3/°C to -540-3/°C for silicon solar cells) the duty cycle for a buck converter can be estimated with the MPP voltage VMPP at a reference temperature and the known output voltage V2:

If the duty cycle additionally is adapted to the solar irradiance, the solar generator can be operated at the maximum power point in most cases. If the DC-DC converter operates the solar generator at its MPP, the converter is called an MPP tracker.

There are several methods for implementing MPP tracker control that will be described in the following section:

Sensor-controlled regulator: As described above, the MPP voltage is calculated as a function of the temperature and irradiance sensor input.

Control using a reference cell: The characteristics, i.e. open circuit voltage VOC and short circuit current ISC, of a solar cell mounted near the solar generator is recorded. These measurements allow the estimation of the MPP voltage VMPP. Using the equation of the simple equivalent circuit, the MPP current IMPP becomes:

exp f vM

The derivative of the power with respect to the voltage is equal to zero at the power maximum:

Inserting IMPP into this equation and solving it for the MPP voltage VMPP results in:

nt'Vj

Numerical or approximation methods can be used to solve this equation. The MPP voltage can be obtained from the open circuit voltage. A more precise estimate can be made using the two-diode model:

Oscillating search control (hill climbing): Voltage and current are measured at the converter input or output and the power is calculated and stored.

Figure 4.40 shows the principle of this system. Small changes in the duty cycle cause a voltage change. The power is then estimated again. If the power increases, the duty cycle is changed again in the same direction. Otherwise, the duty cycle is changed in the opposite direction. For constant output voltages, the search for the maximum output current is sufficient. In this case, the power itself need not to be estimated.

Zero transit method: Generator voltage and current are measured and multiplied. A derivative unit estimates the derivative dP/dV. The generator voltage is increased or decreased depending whether the derivative is positive or negative.

Figure 4.40 Structure of MPP Trackers

Control with differential changes: Voltage and current are measured and their differential change estimated. With

i.e. the electronics must balance both quantities.

Control with characteristics method: This method also measures voltage and current. Starting with the open circuit voltage VA are changed alternately in the following manner:

VOC, voltage and current

After a few steps, this method obtains two operating points, one to the left and one to the right of the MPP; the controller oscillates between these points.

Various MPP trackers have difficulty in finding the optimal operating point when the solar generator is partially shaded, in rapidly changing conditions or for non-standard modules. Shading occurring over prolonged periods of time can cause high losses; therefore, a good MPP tracker should also provide good results for irregular operating conditions, in which multiple local maxima can occur in the I-V characteristic (see Figure 4.28, p146). When an unusually low generator power indicates a shading situation, the MPP tracker must scan through the whole voltage range to find the maximum for the optimal power output.

Electricity Storage

### Types of batteries

Consumers are hardly ever connected directly to a solar generator. In reality, photovoltaic systems are more complex. In the absence of any kind of storage,

 Lead-acid NiCd NiMH NaS Positive electrode PbO2 NiOOH NiOOH S Negative electrode PbO Cd metals Na Electrolyte h2so4+h2o koh+h2o koh+h2o ß-Al2O3 Energy density (Wh/l) 10-100 80-140 100-160 150-160 Energy density (Wh/kg) 25-35 30-50 50-80 100 Cell voltage (V) 2 1.2 1.2 2.1 Charge/discharge cycles 500-1500 1500-3000 about 1000 about 1500 Operating temperature (°C) 0-55 -20 to 55 -20 to 45 290-350 Self-discharge rate (%/month) 5-15 20-30 20-50 0 Wh efficiency 70-85% 60-70% 60-85% 80-95%

there would be periods without any power for a solely photovoltaic-powered system, which clearly is not desirable.

Storage systems can be classified into short-term storage for a few hours or days to cover periods of bad weather and long-term storage over several months to compensate for seasonal variations in the solar irradiation in summer and winter. Since long-term storage is extremely expensive, the photovoltaic generator is usually oversized so that it also can provide sufficient energy in wintertime. Another solution is hybridization with wind or diesel generators.

Secondary electrochemical elements are mainly used for storage over short-and medium-term periods; they are usually called batteries. For economic reasons, the lead-acid battery dominates the current market. When higher energy densities are needed due to weight considerations, for example, in laptop computers, other batteries such as nickel-cadmium (NiCd) or nickel-metal hydride (NiMH) are used. Other batteries such as sodium-sulphur (NaS) have been tested for use in electrical (battery-powered) vehicles but are no longer being developed. Table 4.7 summarizes the data for various types of rechargeable battery.

Today, the most common battery for electricity storage is the rechargeable lead-acid battery. The main reason is cost. The car industry, especially, prefers lead-acid batteries. So-called solar batteries have a slightly modified structure compared with car batteries and achieve longer lifetimes. However, the principle structure of the solar battery is similar to the car battery. It has two electrodes. In the charged state, the positive electrode consists of lead dioxide (PbO2) and the negative electrode of pure lead (Pb). A membrane embedded in a plastic box separates the two electrodes. Diluted sulphuric acid (H2SO4) fills the empty space between the two electrodes. A fully charged lead-acid battery has an acid density of about 1.24 kg/litre at a temperature of 25°C, and this

Figure 4.41 Charging and Discharging a Lead-Acid Battery

density changes with the temperature and charge state. An acid density meter or a voltmeter can indicate the charge state of a battery. Since the nominal voltage of one lead-acid battery cell is 2 V, six cells are connected in series to get the common operating voltage of 12 V. The number of cells can be adapted for other voltage levels.

Figure 4.41 illustrates the chemical reactions inside the lead-acid battery; they are represented by the following equations:

Negative electrode: Pb+ SO^" < ^tlT >PbS0*+ 2e~

Positive electrode: Pb03 + S0;~ + 4H+ + 2e < >PbS04+2H,0

Net reaction: Pb02+ Pb+2 H2SO, < >2PbS04+2H,0 (4.94)

When discharging a lead-acid battery, the electrode material and the electrolyte react to form lead sulphate (PbSO4). This reaction releases electrons that can be used as electrical energy by the consumer. Electrical energy must be fed into the battery for charging. The PbSO4 at the electrodes transform to Pb and PbO2 again. The charging process needs more energy than is set free during discharging. The charge efficiency is the ratio of the discharge over the charge. For the charge efficiency, a distinction is made between the Ah efficiency nAh and the Wh efficiency nWh The Ah efficiency is calculated on the basis of integrated currents; the Wh efficiency considers currents and voltages during the discharge and charge periods needed to regain the same charge level as follows:

The Wh efficiency is always lower than the Ah efficiency because the battery voltage during charging is higher than during discharging. The Ah efficiency of a lead-acid battery is between 80 and 90 per cent depending on the battery type; the Wh efficiency is about 10 per cent lower.

Battery self-discharge, which causes additional losses, reduces the system efficiency. The self-discharge rate increases with the temperature and is about 0.3 per cent per day or 10 per cent per month at temperatures of 25°C. However, some battery types provide lower self-discharge rates.

The usable capacity of a battery depends on the discharge current, as shown in Figure 4.42. The capacity decreases with higher discharge currents and the end of discharge voltage is reached earlier.

To compare different rechargeable battery types, the capacity is often reported in combination with the discharge duration. C100 means that this capacity is usable when the discharge current is chosen so that the battery

Figure 4.42 Usable Capacity Related to C100 = 100 A h of a Lead-Acid Battery as a Function of the Discharge Current and Temperature
 State of charge (SOC) 100% 75% 50% 25% 0% Voltage in V 12.7 12.4 12.2 12.0 11.9 Acid density in kg/l 1.265 1.225 1.190 1.115 1.120

reaches the end of discharge voltage after 100 hours. A rechargeable battery with a capacity of C100 = 100 A h has a nominal discharge current of i100 = C100/100 hours = 1 A. If the battery is discharged in 10 hours with a current of 8 A, the capacity C10 is reduced to less than 80 per cent of C100. The usable capacity decreases to about 50 per cent at a temperature of 0°C and a discharge time of 5 hours. The lifetime of the battery, i.e. the number of cycles achievable, decreases with increasing temperature and discharge depth. The recommended maximum depth of discharge is normally about 80 per cent, whereas depths of discharge of more than 50 per cent (filling level below 50 per cent) should be avoided if possible.

Table 4.8 shows the open circuit voltage and acid density of a 12-V lead-acid battery. The nominal acid density for 100% charge varies between 1.22 kg/litre and 1.28 kg/litre depending on battery design and operational area. Higher acid densities improve the operating behaviour at low temperatures, whereas lower acid densities reduce corrosion. The given voltages are only valid for open circuit operation, i.e. the battery has not been charged or discharged recently. A temperature compensation of -25 mV/°C can be expected. When charging or discharging the battery, the voltage is above or below the open circuit voltage. The voltage difference compared with the open circuit voltage depends on the current. Figure 4.43 shows the voltage over the discharge time. Starting at the open circuit voltage of 12.7 V for a fully charged battery, the voltage falls depending on the discharge current. If the initial charge is lower, the voltage drop is higher.

The battery's state of health also influences the voltage slightly. The voltage is also an indicator of the state of charge (SOC) of a rechargeable battery (see Table 4.9).

The rechargeable battery should be protected against deep discharge or overcharging. If the battery is totally empty, crystalline lead sulphate is created. This type of lead sulphate is difficult to reconvert and some material will remain in the crystalline form. This damages the battery permanently. Therefore, deep discharge should be avoided in any case. This can be achieved in most cases by switching off the load at about 30 per cent of the remaining capacity. At common operating conditions, this is equivalent to a battery voltage of about 11.4 V. Lower voltages for ending discharge can be chosen for higher discharge currents above I10. In addition, if the battery is not used for a long time, damage as a result of deep self-discharge is possible. The battery should be recharged from time to time to minimize the risk of damage.

Figure 4.43 Battery Voltage as a Function of Discharge Time and Discharge Current

If the lead-acid battery is continuously charged, it starts to produce gas at a voltage of 14.4 V; the electrolysis decomposes the water within the electrolyte into hydrogen and oxygen and these gases escape from the battery. Therefore, the battery must be refilled with water from time to time. Continuous strong gassing can damage a battery. To protect the battery, charging should be stopped at voltages between 13.8 V and 14.4 V. However, it is advisable to charge lead-acid batteries until they begin gassing from time to time to mix the electrolyte thoroughly.

The batteries should be placed in a dry room at moderate temperatures. Battery gassing can produce explosive oxyhydrogen, so good ventilation of battery rooms is essential.

An equivalent circuit that describes battery behaviour is essential for exact simulations. However, an equivalent circuit that describes the battery perfectly is difficult to find, because many parameters such as temperature, current, state of charge (SOC) or state of health influence the operation. A standing joke is that a perfect model for a rechargeable battery is a black bucket with hole. However, several battery models have been developed over recent decades. One of these models, the Gretsch equivalent circuit, is described here as an example (Gretsch, 1978).

Table 4.9 State of Charge Estimation for a 12-V Lead-Acid Battery Based on Measured Operating Voltages

Voltage range (V)

State of charge (SOC)

11.4

Stop charging, battery is full Normal voltage range during charging without load Normal voltage range during charging with load Normal voltage range during discharging Disconnect load, start charging

Source: Gretsch, 1978

Figure 4.44 Gretsch Equivalent Circuit of a Lead-Acid Battery

Figure 4.44 shows the equivalent circuit for one cell of a lead-acid battery. Most of the resistances of the equivalent circuit depend on temperature state of charge SOC and the battery current I. The equation

considers these influences. R0 is a constant base resistance that is modified by the three factors r depending on the operating conditions.

Table 4.10 describes the different elements of the equivalent circuit. Gretsch has found the parameters L = 1-10 ^H, RI0 = 50 mQ, Rp = 1.4 Q, CP = 1 ,uF, RG0 = 765 mQ, VG = 2.4 V, RS = 5-10 kW, RDC0 = 25 mQ,

 Symbol Component Chemical-physical description L Inductance Filamentary current separation across plates ri Transient internal resistance Metallic and ionic conductance rp Polarization resistance Re-orientation losses of dissociation product cp Polarization capacity Displacement current without chemical conversion rg Gassing resistance Inhibition of water decomposition Gassing voltage Start of water decomposition rs Self-discharge resistance Minor reaction, soiling rdc Discharge conversion Inhibition of forming PbSO4 resistance RCC Charge conversion resistance Inhibition of dissolving PbSO4 rdd Discharge diffusion resistance Acid concentration gradient rcd Charge diffusion resistance Acid concentration gradient CW Work capacity Direct convertible acid volume in pores Cr Rest capacity Acid volume between plates, convertible

mass mass

RCC0 = 140 mQ, RDD0 = 40 mQ, RCD0 = 40 mQ, CA = 20-50 F, CR = 20 kF. However, these parameters can vary a lot between different battery types.

Much simpler models are used for most simulations. The Gretsch equivalent circuit can be simplified by ignoring CP, Rp and L and unifying RDC and RCC as well as RDD and RCD. For long-term considerations, the capacitance CA can be ignored as well.

Charge balancing offers another simple method to describe rechargeable battery behaviour. Here, a limited number of features is sufficient. If the battery is full, further charging is not possible; an empty battery cannot be discharged any further. The charge efficiency must be considered when charging and discharging a battery. Finally, self-discharge losses must be considered. Most simulation programs use simple charge balancing methods to get fast and adequate results.

### Other rechargeable batteries

Other more expensive rechargeable battery types such as NiCd or NiMH are used in addition to the lead-acid battery. They have the advantages of higher energy density, fast charging capability and longer lifetime.

• higher cycle number

• larger temperature range

• possibility of higher charge and discharge currents

• fewer problems with deep discharge.

On the other hand, NiCd batteries have the disadvantages of higher costs and the so-called memory effect. If charging of a NiCd battery is stopped before the full capacity is reached, the capacity decreases. Repeated full charging and discharging partly counteracts the capacity reduction; however, the memory effect is one of the most important problems for this type of battery.

Materials used in the production of NiCd batteries are the metals nickel and cadmium. The electrolyte is diluted potash lye with a density of between 1.24 kg/litre and 1.34 kg/litre. The chemical reactions in NiCd batteries are:

Negative electrode: Cti+20H" c >Cd(OH)2 + 2e" (4.98)

Positive electrode: 2NiO(OH) +2H,0+2e" < >2Ni(OH),+20H"

Net reaction: 2NiO(OH) + Cd+ 2 H,0< ^'¡f )2 Ni(OH)2 + Cd(OH)2

The nominal voltage of a NiCd cell of 1.2 V is lower than that of a lead-acid battery cell. NiCd batteries are mainly used as household batteries as well as for laptops or electric cars.

One major disadvantage of NiCd batteries is the use of environmentally problematic materials. It surely cannot be avoided that constituent materials of disposed batteries are released into the environment after the end of the battery's useful life. Cadmium accumulates in the food chain, and in human bodies, because it is excreted only partially. High cadmium contamination can cause organ damage or cancer.

Nickel-metal hydride (NiMH) batteries are much less environmentally problematic. Applicable metals are nickel, titanium, vanadium, zirconium or chrome alloys. However, small amounts of toxic materials are also used for these batteries. The electrolyte is diluted potash lye, the same as for NiCd batteries. Besides good environmental compatibility, NiMH batteries have further advantages compared to NiCd batteries such as higher energy density and the absence of the memory effect. Disadvantages are the smaller temperature range and the high self-discharge rate (about 1 per cent per day). Since the cell voltage of 1.2 V is the same as for NiCd batteries, NiMH batteries can easily replace NiCd batteries.

The chemical reactions in NiMH batteries are:

Positive electrode: Ni00H+H,0+e" +OH (4.102)

Estimation of the state of charge for NiCd and NiMH batteries is more complicated compared with lead-acid batteries. The temperature influence is greater and the voltage of a fully charged NiCd or NiMH battery even decreases a little.

Other rechargeable battery types such as sodium-sulphur (NaS) batteries promise advantages of higher energy densities; however, problems with high operating temperatures and dangerous materials such as sodium have not yet been resolved fully. Because only prototypes of these batteries exist, they are not discussed in detail.

### Battery systems

The simplest battery system consists only of a photovoltaic generator, a battery and a load. Since the internal resistance of the photovoltaic generator is very small, the battery discharges through the photovoltaic generator if the solar irradiance is low. A blocking diode between the photovoltaic generator and the battery, as shown in Figure 4.45, can avoid these reverse currents from the battery to the photovoltaic generator; however, this diode causes permanent losses:

Therefore, diodes with low forward voltages such as Schottky diodes (VD ~ 0.55 V) are often used. Cables cause further losses; a connection cable with cross-section A, specific resistance p and cable lengths l1 and l2 for the cables from the photovoltaic generator to the battery and back, respectively, causes the following losses:

^L.inble - ^PV ' (V„ + ^Cl) — ^PV ' i^ci + ^Cî) — ^PV ' , ' + )

A copper cable (pCu = 0.0175 Q mm2/m) with cable lengths (l1 = l2 = 10 m), a cross-section of A = 1.5 mm2 and a current IPV = 6 A causes cable losses 8.4 W. Assuming a photovoltaic generator power of 100 W, these of P

L,cable cable losses plus the blocking diode losses of 3.3 W are considerable at 12 per cent of the power generated. To minimize losses, cables should be as short as possible and the cable cross-section appropriately large. For a 12-V battery system, a voltage drop of 3 per cent, or 0.35 V, is acceptable in the cables from the photovoltaic generator to the battery and 7 per cent, or 0.85 V, from the battery to the load. For the above example, the cable cross-section must therefore be 6 mm2.

For systems with higher power, the losses can be reduced if some batteries are connected in series. This increases the battery voltage VBat and decreases the current flow and thus the losses.

The photovoltaic generator has the voltage:

The diode voltage VD is nearly constant, the cable voltage drop VC1 and VC2 are proportional to the photovoltaic current IPV. The battery voltage VBat depends on the charge current and state of charge. Hence, the voltage at the photovoltaic generator increases slightly with rising currents and increasing

Figure 4.45 Simple Photovoltaic System with Battery Storage
Figure 4.46 Operating Points of a Solar Module Connected to Battery Storage with a Blocking Diode and 0.1 Q Cable Resistance without Load

irradiances, and it varies with the battery state of charge. If a photovoltaic generator is connected directly to a battery, a good operating point is achieved for a wide irradiance range (see Figure 4.46). Therefore, DC-DC converters and MPP trackers are very rarely used in battery systems. In some cases, the power consumption of the additionally required electronics is higher than the possible energy gain. Only for inhomogenously irradiated solar generators do MPP trackers have some advantages.

Rechargeable batteries in simple battery systems with the photovoltaic generator and load directly connected to the battery are not protected against deep discharge or overcharging. Such a simple system should be chosen only if negative operating conditions for the battery can be avoided with certainty; otherwise, the battery can be damaged very quickly.

Therefore, most battery systems use a charge controller (see Figures 4.47 and 4.48). Charge-controller lead-acid battery systems usually work on the basis of voltage control. The charge controller measures the battery voltage VBat. If it falls below the deep discharge voltage (11.4 V for a 12-V lead-acid battery), the switch S2 disconnects the load from the battery. When the battery is charged again, i.e. the battery voltage rises above an upper threshold, the switch reconnects the load. If the battery voltage rises above the end of charge voltage (about 14.4 V for a 12-V lead-acid battery), the switch S1 stops charging. The series charge controller (see Figure 4.47) and the parallel or shunt charge controller are two principal charge controller types (see Figure 4.48).

Power semiconductors such as power field-effect transistors (power MOSFETs) are normally used as switches. Continuous forward losses at the switch S1 are a disadvantage of the series charge controller. The forward resistance of good MOSFETS is less than 0.1 Q; nevertheless, for a current of 6 A, the field-effect transistor BUZ 11 with a forward resistance of 0.04 Q

Figure 4.47 Photovoltaic Battery System with Series Charge Controller

still causes losses of 1.44 W. If the photovoltaic generator voltage is monitored in addition to the battery voltage, the blocking diode can be omitted and the forward losses reduced. In this case, the charge controller must open the switch S1 if the solar generator voltage falls below the battery voltage.

The parallel charge controller is the most commonly used type of charge controller. If the battery is fully charged, the charge controller short-circuits the solar generator across switch S1. The solar generator voltage falls to the voltage drop across the switch (<1 V). The blocking diode avoids reverse currents from the battery across the switch. If the generator is in the regular mode of operation, the short circuit does not cause any problems; however, if the solar generator is partially shaded and thus not irradiated homogenously, the short circuit conditions can strain the shaded cells very significantly.

Individual battery cells of large battery systems can be severely strained due to small differences between the cells. These cells age faster, and if one cell fails, other cells will be affected. Therefore, battery management systems that not only monitor the voltage of the whole battery unit but also the voltage of single cells should be used for large battery systems for optimal battery protection.

Besides these relatively simple battery systems with a photovoltaic generator, a battery, charge controller and a load, more complex systems exist.

Figure 4.48 Photovoltaic Battery System with Parallel Charge Controller
 Lower calorific value (LCV) Upper calorific value (UCV) Density 3.GG kWh/mn3 33.33 kWh/kg 3.55 kWh/mn3 39.41 kWh/kg G.G9 kg/m3 (gaseous) 7G.9 kg/m3 (liquid, -252°C)

Note: 1 mn3 = 1 nominal cubic metre, equal to 0.09 kg of hydrogen gas

Note: 1 mn3 = 1 nominal cubic metre, equal to 0.09 kg of hydrogen gas

Battery backup systems can be connected to the grid with a photovoltaic inverter. Photovoltaic generators can be combined with a wind generator or diesel generator to create a hybrid system. This can reduce energy costs and increase system availability; however, operating complex systems needs a complex energy management system. If an AC load should be operated, an inverter must be integrated into the system; inverters for photovoltaic systems are described below.

Hydrogen storage and fuel cells

A promising option for future storage of large amounts of energy is hydrogen (H2) storage (see energetic data in Table 4.11).

Electrolysis processes can produce hydrogen by using electricity as the driving force. In alkaline electrolysis, water is split into hydrogen and oxygen using two electrodes in a dilute alkaline electrolyte (see Figure 4.49). The following equations describe the reactions:

Alkaline electrolysis currently achieves efficiencies of 85 per cent. Besides alkaline electrolysis, other methods for generating hydrogen from water exist (e.g. membrane electrolysis or high-temperature vapour electrolysis). A smaller

Figure 4.49 Principle of Hydrogen Electrolysis with Alkaline Electrolyte

Anode

not converted Ho h2

2 e" Electrolyte

Cathode

not converted Oo

Figure 4.50 Principle of the Fuel Cell with Acid Electrolyte amount of electric energy is sufficient to keep the process running at temperatures above 700°C; prototypes of pressurized electrolysers have already reached efficiencies of 90 per cent.

Gas and steam turbine power plants or fuel cells can generate electricity from hydrogen. However, fuel cells are the most promising option to date. A fuel cell with an acid electrolyte reverses the electrolysis by regenerating water (H2O) from oxygen O2 and hydrogen H2 (see Figure 4.50); electrical energy is a result of this reaction. The anode collects electrons that are released. The hydrogen ions H+ diffuse through the electrolyte to be collected at the cathode. There they coalesce with the oxygen ions and electrons from outside to form water molecules.

The equations of the reactions in the fuel cell are:

To increase the voltage, several cells are connected in series into stacks (Figure 4.51).

The efficiency of an ideal fuel cell is 94.5 per cent. Today, efficiencies of up to 80 per cent can be achieved. Fuel cells are divided into low-temperature, mid-temperature and high-temperature cells. In addition to the electricity generated, the heat from mid- and high-temperature fuel cells, such as the phosphoric acid fuel cell (PAFC), the molten carbonate fuel cell (MCFC) and the solid oxide fuel cell (SOFC), can be used. This increases the total efficiency.

The total efficiency ntot of hydrogen storage is the sum of the electrical efficiency nel and the thermal efficiency n^:

Figure 4.51 Photograph of a Fuel Cell Stack Prototype

The electrical efficiency

is obtained from the electrolysis efficiency nEly, transport losses fTr, storage losses fSt and the electrical efficiency of the fuel cell nFC el. The electrical efficiency nel of further-improved systems could be about 50 per cent. Assuming a thermal efficiency nth of 20 per cent provides a total efficiency ntot of 70 per cent.

Owing to the relatively poor electrical efficiency of the hydrogen storage chain, the direct use of electricity is preferred, even if the electricity must be transported over very large distances.