The problem of rural electrification has been traditionally handled by conventional means in a process of successive approximations. In this process, the most remote and dispersed population is attracted to larger population centers, which are then served by a mini-electrical local grid, fed by diesel gen-sets or small hydroelectric generators. As the load increases, a point is reached at which extensions of the main grid become economically viable. This process is known as pre-electrification among electric companies and has been the basic growth mechanism of the interconnected system in rural areas. Although effective from a purely technical/economic point of view, this pre-electrification process has several downsides. From the social point of view, it forces people to leave their place of origin to create larger population centers, which in turn induces the need for the central provision of other services and puts a larger stress on the environment.

The term pre-electrification is being used nowadays by some authors in reference to PV rural electrification and, in some cases such as the CEMIG example above, the operational scheme is also being transported. However, there are a number of reasons to think that using the term pre-electrification in the context of photovoltaics is not appropriate. Furthermore, transporting the concept is bound to cancel the advantages offered by photovoltaics to create a new path for rural electrification. First, from the purely technical point of view, photovoltaics offers the possibility of supplying high-quality electrical services, even to the most remote sites, without the need for relocating people or eventually having to resort to grid extensions. Because of its modular nature PV systems can grow in pace with the load. Furthermore, this vision is compatible with current trends in the electrical sector toward distributed generation systems, and is supported by the development of more efficient electrical appliances, the miniaturization of electrical technologies and the progress being made in electronic devices for system supervision and load management. There are also environmental reasons that lead to the notion that the local generation of electricity using renewable and nonpolluting energy resources is more convenient than building kilometers of electricity lines across ecologically sensitive areas. Local generation of electricity also offers the possibility for local management and, hence, for active community participation in the process of self-development.

On the other hand, there is evidence that the traditional electrification process based on the old paradigm of delivering electricity to rural people has frequently lent itself mainly to fulfill the political need to improve the electrification statistics rather than to serve the real needs of people. Thus, it is not uncommon to observe rural communities with access to the grid, where a good portion of the households are not connected, usually because of lack of money to pay for the connection fee, or because the secondary distribution network only reaches the center of the community, leaving the rest of the population unserved. Therefore, if electricity supply is to be used as a tool for development, that is understood as increased life expectancy, more knowledge and a better standard of living [56], then the present rural electrification paradigm must be urgently changed to: “increasing the access of the rural poor to electricity-based services ”. This set of services includes health, clean water, education, food preservation, entertainment and the possibility of engaging in productive activities.

Under this perspective, current PV rural electrification activities represent a landmark of the transition period into a new rural electrification scheme to substitute the old one with better results. However, the new electrification requires among other things, a new culture for electricity supply and use in rural areas, an ad hoc legal framework, new business practices within the electrical sector, innovative financial mechanisms, new and better technologies and appropriate institutional schemes. Thus, the actual value of programs and projects currently underway has to be weighted not only in terms of the number of PV users in rural areas, but also in terms of the benefits PV installations are bringing to the population. Also important to gauge the effectiveness of current PV rural electrification projects is the relevance of the lessons learned from them, which will allow the implementation of improved schemes for successful project replication.

This new paradigm for rural electrification should in turn be embedded in the broader concept of rural energy supply, which calls for a timely supply of useful energy in a variety of forms, so that people can have better opportunities to improve their own quality of life, to foster local economic development and to protect the environment.

After almost twenty years of PV applications in rural areas of the world, the problem of providing electricity-based services to about one third of the global population still remains virtually untouched. Important lessons have been learned, but a number of critical elements need to be put in place if PV is to become the main technology option for rural electrification of remote communities. Of foremost importance is the institutionalization of the process for the large scale and sustainable deployment of the technology. Much has been written about this, but few programs or projects can in fact serve as good examples of long-term sustainability.

[1] The bandgap energy or energy gap is a fundamental and unique parameter for each semiconductor material. To be a good absorber of solar energy on earth, a semiconductor should have a bandgap between about 1 and 2 eV. See figure 4.3.

[2] In 2008, with installed system costs of $US7/W or $US0.30/kW h, it was expected most of California’s 3.2% PV demand would be large, centralized power plants. By 2009, system costs fell to $US3.70/W or $US0.17/kWh due to availability of lower-cost thin film modules. Combined with land use permitting and transmission access difficulties for the large PV power plants, distributed small-scale PV looked more attractive to provide much of the 15% demand (from Garrett Hering in Photon International December 2009, 12-14.)

[3] Sun tracking increases the CF. The number of equivalent hours in a sun-facing plane (called a two-axis tracker) increases by about 40% with respect to the fixed optimally oriented module. This is discussed further in Chapters 19 and 22.

[4] There are also competing technological uses to consider. For example, Indium usage has increased substantially in recent years due to the need for transparent conductive indium tin oxide (ITO) layers in flat panel displays.

[5] This is being proven by First Solar which has been manufacturing CdTe thin film modules for 10 years, achieving the lowest manufactured price per watt since 2008 (<1.00 $US/W), becoming the world leader in PV module production in 2009.

[6] This limit applies to the individual cells in a MJ stack, but not to the stack as a whole.

[7] Nearly all of the PV cells manufactured in China are exported to other markets.

[8] Discrepancies between cumulative PV cell shipments and installations can be attributed to delays in installation after shipment. This can be significant under a fast growing PV market. According to industry analysts, on average there is a delay of two quarters between a module being shipped and its connection to the grid [132]. At the beginning of 2009, the industry had started with over 2 GWp of inventory [21].

[9] It should be noted that this comparison does not consider the relative subsidies for PV and its retail market competitors. When these are factored in, some analysts conclude that PV is very near to a market parity [19, 131]. If pollution and other external costs are included in the cost of conventional fuels, it is likely that PV is less expensive, at least over the long run [133].

[10] While China is the world’s largest solar manufacturer, it mostly sells its production to overseas markets. This section focuses on policies to stimulate domestic use of PV and, for this reason, does not include China. Future editions of the Handbook will almost certainly need to profile China’s domestic market which recently began to expand.

[11] As with many jurisdictions in the US, IOUs are only one source of electricity supply. Customers may also receive power from so-called municipal or publicly owned utilities (utilities owned and operated by a governmental jurisdiction such as a city or incorporated region), electric cooperatives (suppliers owned by their customers which often are not subject to conventional utility regulation), and special federal authorities such as the Tennessee Valley Authority and the Bonneville Power Administration. IOUs serve approximately 97 million customers, while municipal utilities, cooperatives, special federal and state authorities together serve 40 million customers. Retail power marketers serve the remaining 6 million customers of the US [123].

[12] The CPUC has regulatory authority over the IOUs serving the state, while the California Energy Commission has responsibility for long-term energy policy and planning with special responsibilities for the promotion of energy efficiency, conservation and renewable energy (see www. energy. ca. gov/commission/index. html).

[13] New Jersey has yet to build a PV project under the REPGF program.

[14] Across the US, policies regarding out-of-state SREC registration varies. At the beginning of 2010, New Jersey, and Maryland did not allow an out-of-state SREC registration, while Delaware, Ohio, Pennsylvania and the District of Columbia have accepted out-of-state SREC registrations [51].

[15] Customer support for the SREC approach may reflect the preference of solar project developers who reduce prices when SRECs are assigned to them. Because an SREC assignment for 8 years represents a predictable revenue stream, developers can sometimes find it easier to borrow needed capital from lending institutions.

[16] These rates in 2004 US dollars are equivalent to $0.66-$0.70 per kWh for building-based PV systems and $0.57 for ground-mount edPV systems (see http://www. bankofcanada. ca/en/rates/exchform. html).

[17] Due to the decline in the value of the US dollar, this rate was higher, nearly $0.74 per kWh, when valued in American currency.

[18] The importance of policy applies more generally to renewable energy as the German case confirms. The country has employed its FiT and financing approaches to wind, solar hot water and biomass markets with similarly impressive results, making Germany the leader in newly installed capacity in all of these markets [71].

[19] In 2004, the average price in Spain was 7.24 Euro cents per kW h or 9.0 US cents, making the PV FiT equal to nearly 52 US cents for 25 years.

[20] In 2007 US dollars, these FiT rates are $0.60, $0.57 and $0.31 per kW h.

[21] In 2008 US dollars, these FiT rates are $0.63 and $0.50 per kW h, respectively.

[22] The program began as the Residential PV System Monitor Program in 1994 [81].

[23] The name of the ministry was recently changed to the Ministry of the Knowledge Economy (MKE).

[24] In 2008 US dollars, this FiT rate is equivalent to $0.68 per kW h.

[25] System price is the installed cost of a system including the PV device, balance of system (e. g. inverters, wiring, and panel array structure) and labor and other installation costs, as well as rates of return to the manufacturers and installers.

[26] This saturation rate is based on research suggesting that the integration of intermittent resource into grid supply has a technical limit roughly at this rate (e. g. [124])

[27] The BAU scenario presented here, assumes maximum level of PV share electricity supply at 25%. This level is projected to be reached in 2055.

[28] LCOE provides the means for economic evaluation and comparison of different electricity generation tech­nologies. LCOE accounts for all costs over a technology’s lifetime, including initial investment, operations and maintenance, cost of fuel, and cost of capital.

[29] 5% was obtained using 7% as a midpoint of Deutsche Bank’s financing values, adjusted for 2% inflation (i. e. [1.07/1.02 – 1] ^ 0.05).

[30] This rate does not include other federal (e. g. MACRS) and local incentives. If MACRS depreciation rules are included, PV’s LCOE in the BAU case falls to 14.5 cents per kW h. Inclusion of tax benefits is justified on the ground that all power plants and non-renewable fuels in the US have been subsidized by tax and other policy treatments. It should be noted that, typically, LCOEs for fossil fuel power plant include the MACRS tax benefit.

[31] During 2006-2008, silicon PV module prices actually increased the first time in 30 years. Then in 2009, they fell rapidly as new production capacity made it to market. For a discussion of this situation see Chapter 1, Section 1.2.3 in this Handbook.

[32]As Figure 2.16 reports, once a break-even price is reached in 2031, PV market share will grow and realize the target of 25% of total US electricity assumption in just 24 years (i. e. the rapid-growth interval of 2031-2055 in Figure 2.16).

[33] These investments are of the learning-by-doing variety.

[34] Although important differences exist between a carbon tax and a cap-and-trade strategy in terms of implemen­tation, we focus here only on the effect on retail electricity prices. For this reason, we do not distinguish between the two in our analysis.

[35] For Figure 2.19, we assumed 0.6 tons of CO2 is emitted per MW h of electricity generation, PV generation at 1,500 kW h per installed kWp, and 25 year product life. A real 5% discount rate was assumed.

[36]These numbers are based on the assumptions in footnote 29, and using the products of previously obtained numbers for carbon tax impact on break-even price and amount of additional cumulative PV installations required

to reach a break-even point (i. e., $0.64/Wp*[76 — 1.3], and $0.32/Wp*[139 — 1.3]).

[37] As with the carbon pricing and R&D scenarios, required learning investments needed to reach grid parity are assumed to be financed by rebates, incentives and other public and utility policy tools.

[38] A $25 per ton price of carbon emissions would increase the average retail electricity price in the US by about 1.5 cents per kW h, while a $50 per ton price would raise electricity prices by 3.0 cents per kW h.

[39] The 2009 Karl Boer Solar Medal was awarded to Hermann Scheer for his invention of the FiT [134].

[40] + e(E-EF)/kT

[41] The wavelength of sunlight, X, is of the order of a micrometer (10 4 cm), while the lattice constant is a few

angstroms (10—8 cm). Thus, the crystal momentum is several orders of magnitude larger than the photon momentum.

[43] It is unlikely that more than one trap will be involved in a single recombination event since the traps are spatially separated.

[44] In some photovoltaic materials such as GaInN, polarization is important and Poisson’s equation becomes V ■ (sE + P) = q(p – n + N), where P is the polarization [16].

[45] A somewhat more rigorous treatment of equation 3.89 would yield a factor of 2kT/q which is ~50mV at 300K, or

[46] Solar cells usually operate at some 40-60 °C, but there is nothing theoretical against improving cooling to reach a cell temperature as close to the ambient one as desired.

[47] x, y and z are the spatial coordinates giving the position of the particle and vx, vy and vz are the coordinates of its velocity.

[48] dAx dAy

The linear unbounded operator “V-" applied to the vector Л = M Л,. Л ) is defined as V • A = —:—| +

dx dy

[49] far, for unconcentrated light, the most efficient single-junction solar cell, made of GaAs, has achieved an efficiency of 25.9% [26] of AM1.5G spectrum. This is only 21% (relative) below the highest theoretical efficiency of 32.8% for the GaAs bandgap, of 1.42 eV, for this spectrum [27]. The theoretical maximum almost corresponds to the GaAs bandgap. However, most cells are manufactured so that the radiation is also emitted towards the cell substrate located in the rear face of the cell, and little radiation, if any, turns back to the active cell. The consequence of this is that the etendue of the emitted radiation, which is n for a single face radiating to the air, is

[50] See Chapter 6.

[51] Indifferently also called silicon tetrachloride in this chapter.

[52] Berzelius, Jons, Jacob (1779-1848): Swedish physician and chemist. He is considered as one of the most important scientist who ever lived. He discovered among others the law of constant proportions which provided evidence of the atomic theory of John Dalton. Beside silicon he is credited with identifying selenium, thorium and cerium.

^ Sainte-Claire Deville, Henri (1818-1881): French chemist, one of the most influent French scientists of his time, mainly retained by history for inventing the first industrial process to aluminum (1854).

* Moissan, Henri (1852-1907): French scientist, professor at la Sorbonne (Paris), most famous for isolating fluorine for which he was awarded the Nobel prize for chemistry (1906). In 1900 he invented an arc furnace capable to reach 3500 °C opening the road to the discovery of numerous elements and compounds including silicon metal and ferroalloys.

[55] Rathenau, Walther (1867-1922): German chemist, industry leader and politician. President to the German energy group AEG, he organized war economics during World War I. Charismatic politician he was both beloved and hated. He became in 1922 the foreign affairs minister to the Weimar Republic and as such he signed the Rapallo treaty. Shortly after, he was assassinated by two nationalist activists.

^Acheson, Edward, Goodrich (1856-1931): US inventor, he worked first for Edison. He is most famous for inventing carborundum (silicon carbide SiC) and synthetic graphite as well as other abrasives and lubricants.

9 We will indifferently designate in this chapter this commercial grade of silicon either as metallurgical grade silicon or silicon metal. The former expression referred to the first historical use of this product in the alloy

[56] This term has background in the semiconductor industry, referring to its polycrystalline structure as opposed to the single crystals made from polysilicon through the Czochralski and float zone techniques.

[57] High energy consumption, over 90% of the input power is lost to the cold walls of the reactor.

• Two power supplies and preheating of the seed rods are normally required because the high – resistivity (~230 000 Q cm) seed rods require very high power supplies and high initial power

[58] For gettering, see Chapter 7.

[59] This is further explained in Chapter 6

[60] Boron back surface field. The use of boron instead of aluminum as BSF has the potential to increase cell performance, and at the same time avoids the bowing of thin cells [149]. The diffusion from a liquid source in a quartz tube is problematic because of the high temperatures needed, so that diffusion from solid sources is preferred for easier integration in the basic process. It would be very attractive to diffuse both phosphorus and boron during the same thermal step, but simultaneous optimization of the dopant profiles is not so straightforward [150].

• Dielectric passivation. A number of techniques for rear passivation based on deposition of dielectric layers (silicon oxide, nitride and carbide, or aluminum oxide) have proven their

[61] Angular distribution of light. Due to the movement of the Sun and the diffuse components of the radiation, light does not fall perpendicular to the module, as is the case when measurements are done and the nominal efficiency is determined.

[62] Irradiance level. For a constant cell temperature, the efficiency of the module decreases with diminished irradiance levels. For irradiances near one sun, this is primarily due to the logarithmic

[63] Spectral content of light. For the same power content, different spectra produce different cell photocurrents according to the spectral response. And the solar spectrum varies with Sun’s position, weather and pollution, etc. and never exactly matches the AM 1.5 standard.

[64] Changing scale. The current boom in the markets enables and fosters technological and processing improvements.

• Laboratory-industry gap. There is a mature technology at the laboratory that has led to impres­sive performance levels, on one hand, and a reliable, fast, 30-year-old industrial process producing modest efficiency, on the other one: closing this gap is the key to a lower $/Wp figure of merit.

• Novel silicon materials. Market growth and the threat of silicon shortage stimulates new mate­rials and very thin substrates that demand new technological solutions.

[65] Material lattice-matched at room temperature is lattice-mismatched at growth temperature. This is due to a difference in the thermal expansion coefficients between GaxIn1-xP and GaAs (see Table 8.4). For kinetic reasons, it is probably more important that the layers be lattice-matched at growth temperature. A layer that is lattice-matched at a growth temperature of 625 °C will

exhibit a lattice mismatch of A0 ———- 200arcsec at room temperature [48], or alternatively, a

layer that is lattice-matched at room temperature, would exhibit a A0 = 200 arcsec at 625 °C. Because it is easier to introduce misfit dislocations at high temperatures, it is probably better to grow the layer lattice-matched at the growth temperature. Hence, a ±50 arcsec tolerance at growth temperature would yield a room-temperature tolerance of -250 < A0 < -150 arcsec.

[66] Lattice constant close to that of GaInP;

• Eg much larger than that of the emitter;

[67] Diffusion coefficients are thermally activated. So, in general, dopants and junctions are less mobile and more stable at lower growth temperatures.

• As noted by Tobin et al. [115], the diffusion coefficient of As in Ge at 700 °C is higher than that of Ga, but the solid solubility of Ga is larger than that of As.

• For three-junction GaInP/GaAs/Ge devices with a reasonably good-quality Ge subcell, the only Ge-device parameter that is of consequence is the VOC, because the Jsc of the Ge subcell is potentially much greater than that of the GaInP (or GaAs) subcell so it is not the current-limiting junction.

• One of the highest VOCs of a Ge solar cell reported to date is 0.239V [112]. This VOC is a sensitive function of process conditions and is most sensitive to the quality of the III-V/Ge interface and its fabrication.

[68] As this chapter goes to press, 41.6% has been achieved.

[69] As this chapter goes to press, an efficiency of 42.3% has been reported for a 3-junction cell with a GaInAs junction grown on the back of the wafer.

[70] It must be remembered that, ideally, for each air-glass interface that the light crosses, the power is reduced to 96%, the reflections on the aluminum are reduced by 85% and with silver by 92%.

[71] L2 F2

Cell size (cm") = — = -— (10.19)

Cg 2Cg

[72] We assume familiarity with the concept of a photon energy hv and of an optical absorption coefficient a; see Chapter 3, Section 3.2 in this volume.

[73] The very different optical properties of c-Si and a-Si reflect the completely different nature of their electronic states. In solid-state physics textbooks, one learns about the “selection rules” that greatly reduce optical absorption in c-Si, which is an “indirect bandgap” semiconductor. Such selections rules do not apply in a-Si. Additionally, the “bandgap” of a-Si is considerably larger than for c-Si.

[74] It is worth noting that the adjoining p-type and n-type layers do not form a p-n junction diode, but rather a simple ohmic contact. We discuss the interesting physics underlying this fact in Section 12.5.3.

[75] Figure 12.9 is based on the function Eg = 1.62 + 1.3h — 0.7x that we obtained by fitting to experimental results reported by Hama, et al. [55] and Middya, et al. [58].

[76] In this chapter, we discuss only “two-terminal” multijunction cells in which the same electrical current flows through the series-connected cells. See Chapter 8 for further discussion of two-, three- and four-terminal multi­junction cell operation.

[77] One can consider this as a neutralization process.

[78] More recent triple junction devices from USO have large cell currents (8.8/9.2/8.8 mA/cm2) and integrated total currents of >26 mA/cm2.

[79] The first continuous roll-to-roll solar cell deposition process was for the Cu2S cell on Cu foil as demonstrated in the early 1980s at the Institute of Energy Conversion at University of Delaware (see US Patent 4,318,938 issued March 9, 1982).

[80] Light-induced degradation must be better understood. Approaches for reducing or controlling the degradation need to be further developed. At this moment, there are many engineering compromises in the device design, such as the use of thin г-layers to limit the degradation. If the materials can be made more stable under light, these compromises can be relaxed and the device can be made with much higher efficiency.

[81] As the gross defects associated with light soaking are minimized, the next performance limitation to be addressed is improving the drift mobility of holes.

[82] We need to improve a-SiGe so that narrower-bandgap materials can be incorporated into cells and more of the infrared region of the solar spectrum can be exploited.

[83] Faster deposition processes need to be developed that (at least) preserve the conversion efficien­cies achieved by present processes. This is critical for low-cost and high-throughput manufac­turing. In addition, these high-rate processes must also achieve high gas utilization.

[84] Nanocrystalline Si-based solar cells need to be fully explored as narrow-bandgap component cells in tandem or triple-junction cells as an alternative to a-SiGe. But much faster deposition processes, >20 A/s, will be required. Methods for improving the open-circuit voltage to >0.60 V needs to be better understood.

[85] Transparent conductors are needed with better light trapping and better templating for nc-Si growth. Optical performance includes less internal parasitic absorption and texture that allows high Jsc without sacrificing VOC due to shunting. Resistance to plasma damage for high power H-diluted nc-Si deposition is valuable. Plasmonic back reflectors are promising.

[86] – 18 16 – 14 12 – 10 8 6

4 –



Handbook of Photovoltaic Science and Engineering, Second Edition Edited by Antonio Luque and Steven Hegedus © 2011 John Wiley & Sons, Ltd. ISBN: 978-0-470-72169-8

[88] No ASTM standard currently exists for rating flat-plate PV systems, though a proposed standard was submitted in the fall of 2009 by A. Kimber in the paper Improved Test Method to Verify the Power Rating of a Photovoltaic (PV) Project.

[89] PVUSA was a CEC-sponsored PV research and demonstration project headquartered in Davis, CA that ran from 1988-2000. PVUSA Test Conditions are defined as 1000 W/m2 plane of array irradiance (850 W/m2 direct normal irradiance for concentrators), 20°C air temperature, and 1 m/s wind speed at 10 meters above grade.

[90] Davis’s climate matches that of Sacramento, 30 km east.

[91] PVSYST v4.37, University of Geneva, Switzerland.

[92] Security clearances to allow for access to the system.

• Storage for spare parts and tools.

[93] A survey of long-term system degradation literature shows repeated references to the 0.5-2% range. PowerLight (now SunPower) reports – 0.5% based on field measurements. The PVUSA project observed 1% degradation as typical for flat-plate crystalline silicon PV systems. Others, such as NREL, the Southwest Technology Development Institute and Ben-Gurion University, Israel, have reported 1% degradation rates at past NREL performance and reliability workshops. David King of Sandia reports module degradation of 0.5-2% for 1991 to 1998 modules. Virtually all manufacturers’ warrantees allow for 1% degradation, in most cases starting from the low end of their nameplate power tolerance. Kristopher Davis and H. Moaveni conducted a 4-year study of two systems and found a 1.2%/year degradation for the c-Si system and a 2.1%/year degradation for the a-Si system.

[94] The American Society of Heating, Refrigeration, and Air Conditioning Engineers (ASHRAE) periodically pub­lishes its Handbook of Fundamentals, with statistically based guidelines for design high and low temperatures for hundreds of US locations. This document is for sale, but a free resource on the internet is www. weather. com, which lists average and record high and low temperatures worldwide.

[95] Hourly power demand profile.

• Monthly utility bill.

[96] The PV Resources website at http://www. pvresources. com/en/software. php has a lengthy list of both comprehen­sive and specialty software.

[97] The National Renewable Energy Laboratory (NREL) publishes the National Solar Radiation Data Base where annual radiation for several orientations is available for 239 US locations.

[98] This yield is based on the product of the reference yield Yr of 5.5 sun hours/day x 365 days/yr x 0.7 PR ^ 1, 400kWh/kWP. The typical 0.7 performance ratio, PR, means 30% of the potential sunlight energy is lost in the conversion to ac electricity. About one-third of the 30% loss is attributable to temperature, one-third to inverter losses, and the remaining third due to the combined effects of wire resistance, mismatch, soiling, and similar small losses.

[99] According to NEC Table 310.15(B)(2)(a)

[100] According to 2008 NEC Table 310.16.

[101] According to 2008 NEC section 250.122 for grounding and Table 9 for conduit sizing.

[102] Low maintenance requirements •

• High availability worldwide •

• High power availability •

• Easy estimation of state of charge •

and state of health

[103] This section is based on Chapters 2.1, 2.2 and 2.3 from the book of D. Berndt Maintenance-free Bbatteries [3] which can be highly recommended for a deeper insight into applied battery technology.

[104] Note: the wording used herein is characteristic for classical electrochemical secondary accumulators with solid active masses and a liquid electrolyte. In fact, batteries with solid electrolytes and liquid active masses exist as well. Examples are redox-flow batteries (see Section 20.5.1) or the NaS batteries (liquid Na and S as active masses, solid oxide ceramic as electrolyte).

[105] Occasionally, the equilibrium voltage is called the open-circuit voltage. However, strictly speaking this term only means a voltage without external current flow, and may concern a mixed potential as well. On account of secondary reactions, the rest potential in batteries are usually mixed potentials, but this is not strictly observed in practical languages.

[106] Activity described the effective concentration. Thermodynamic rules are derived for dilute solutions. The activity is equivalent to the concentration in very dilute solutions, but the activity can be different at higher concentrations as interactions among the ions in the solution need to be taken into account.

[107] The standard hydrogen electrode means a hydrogen electrode immersed in acidic solution with H+ ion activity of 1 mole/dm3 and H2 pressure of 1 atm. The specification of the electrolyte concentration is required because the potential of the hydrogen electrode depends on the H+ ion concentration and is shifted by —0.0592 V when the H+ concentration is reduced by one decade. The potential of the standard hydrogen electrode at 25 °C is synonymous with the zero point of the potential scale. The temperature coefficient of the standard hydrogen electrode is +0.871 mV/K.

[108] It is worth noting that the current density caused by the current flow through the electrode during a charge or discharge of a lead-acid battery (approximately loh discharge or charge) is of the order io—5-io—6 A/cm2 for the Pb electrode (assumptions: capacity of the lead electrode 3.865 g/Ah, inner surface of Pb active material o.5 m2/g and discharge current o. l A/Ah). This gives a feeling for the very high activity in equilibrium conditions.

[109] The standard hydrogen electrode is a platinum electrode rinsed with hydrogen gas in 1 N electrolyte. Its potential is defined as 0 V.

[110] Diesel gen-sets are currently the most common solution for an additional controllable generator. Other solutions like thermoelectric, thermophotovoltaic or fuel cell generators have been developed in many places and might be alternatives in the near future.

[111] The charging and discharging currents are small compared with the standard 10-h discharging current /10 (at least for system Classes 1 and 2).

• For long periods, sometimes weeks or even months, the batteries do not reach a fully charged state (SOC = 100%).

[112] Tubular-plate electrodes are not very common in North America. Traditionally, tubular-plate batteries are more popular in Europe for cycling applications like, for example, fork-lift trucks.

[113] Hybrid vehicles have a conventional motor, but with less power than in traditional cars. Acceleration is supported by electric motors powered by the batteries. The batteries are charged during regenerative breaking and from the

[114] Figure 20.17 is based on a detailed battery model including modelling of the vertical acid-density distribution. The model was verified by measurements in a battery. The model and verification are described in [19]. Therefore, the state of charge and the acid density above the electrode displayed in Figure 20.18 are calculated by the model. The calculations are based on detailed measurements of the battery current, voltage and temperature in the system.

[115] As stated in Section, on charging, a complete discharge of the battery to 100% DOD twice a year is of benefit to the battery. This is not in contradiction to a limited DOD during normal operation. The defined discharge is done within a short time and is followed directly by complete recharging of the battery. In normal operation, discharge times and duration in deep states of charge can be very long and the next full charging may occur only weeks or month later.

[116] Alkaline electrolysers.

• Polymer electrolyte membrane (PEM) electrolysers.

[117] N m3 is the typical dimension for a gas amount. It is a gas in a volume of 1 m3 at a pressure of 1 bar and a temperature of 0 °C.

[118] The battery causes a considerable part of the initial investment costs.

[119] Indirect MPP trackers

This type of MPP tracker estimates the MPP voltage by means of simple assumptions and


Some examples from practice include the following:

– The operating voltage of the solar generator can be adjusted seasonally. Higher MPP voltages can be expected in winter due to lower cell temperatures and vice versa.

– The operating voltage can be adjusted according to the module temperature.

– The operating voltage can be derived from the instantaneous open-circuit voltage by multiplica­tion with a constant factor, for example, 0.8 for crystalline silicon solar cells. The open-circuit voltage is measured periodically (e. g. every two seconds) by disconnecting the load for a few milliseconds.

[120] Supervision of the grid voltage (passive single phase or three phase systems);

• Supervision of the grid frequency (passive systems);

• shifting of the inverter’s output frequency (active system)

• supervision of the grid impedance (active systems).

[121] There are 8760 hours per year, and the sun shines exactly half of the year in any location, hence there are 4380 hours of sunshine per year.

[122] Optimally oriented, a = 0, and optimally tilted, в = eopt Equation (22.51), a = 0 ^ gi = gis

Equation (22.50), в = eopt ^ Geffdy(eopt) = 0.9314Gdy(eopt) = 3517 Wh/m2

Note that the total losses due to the optical effects of the angle of incidence (^7%) are larger

than pure normal transmittance losses (^3%)

[124] Designed by Simone Giostra and ARUP for Greenpix.

[125] Archis, February 1998.

[126] Gridula is not a common word outside architectural vocabulary. It means the grid that is used for the design that is a (sometimes hidden) part of the building.

[127] This overview just gives an impression and is not a total overview of all available systems. Also product specifications and brand names may be changed. A good digital overview is yearly updated by the German magazine Photon.

[128] Personal communication from Jaap Hoornstra, Solar Energy Department of ECN.

[129] See Chapter 12.

[130] “Plug and play” refers to very simple wiring and components that fit together like a computer and can easily be replaced.

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