Power density

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Rooftop and façade PVs But in Germany, the world’s leader in harnessing solar radiation for electricity, most PV cells are not massed in large solar parks but rather on the rooftops, installed by homeowners and businesses in response to feed-in tariffs guaranteeing high electricity prices for 20 years. In 2011 ground-based PV in large solar parks accounted for only 28% of Germany’s installed capacity; its largest share, 38%, was in medium-size installations (10-100 kWp) on the roofs of multifamily dwellings, schools, office, farms and small businesses; 23% of all PV were larger (>100 kWp) units on the roofs of industrial enterprises, and 10% were on the rooftops of private residences (Wirth 2013).

These rooftop PV modules come in sizes from roughly 0.5 m2 to 3 m2, most (crystalline and multicrystalline) modules have 36 cells in series, maximum power voltage of 15 V and maximum power current of 3 A. Changing irradiance affects their current and power output but voltage varies very little, facilitating battery charging. In 2012 Germany had nearly 1.1 million solar installations serving 5.2 million households, but the trend has been toward large units: in the year 2000 projects with more than 500 kWp were just over 10% of new capacity, in 2012 they accounted for nearly half of a much larger annual addition (Frauenhofer ISE 2012). The shift toward larger projects has been the principal reason for rising performance and load factors have been also rising, slowly but steadily. Average irradiance of 1,055 kWh/m2 of flat surface is boosted to about 1,200 kWh/m2 by appropriate tilting (300-400) of panels, and with performance ratio at 0.85 the effective annual radiation input is about 1,020 kWh/m2 (Wirth 2013). That implies average exploitable flux of about 116 W/m2.

With average 11% efficiency that amounts to annual electricity generation of about 112 kWh/m2 and average power density of more than 12 W/m2 of roof area covered by modules -– and all that without making any land claims. Using average PV generation full-load of nearly 970 hours (Frauenhofer ISE 2012) and the exploitable flux of 116 W/m2 confirms this density (970 x 116 = 112.5 kWh/m2). In more sunny locations power densities of rooftop PV installations will be proportionately higher. McKay (2013) lists maxima for US rooftop installations at 20.69 W/m2 for a 390-kW project in Hawaii and 17 W/m2 for an 830-kW installation in California.

Practical maximum capacity of roof-based PV is easy to calculate for a particular house or a commercial or industrial enterprise but nationwide estimates are not that easy to estimate. Many roofs are obviously poorly suited, or entirely unsuitable, for such installations due to excessive pitch (>400; on the other hand, the slope should be at least 150 for self-cleaning), suboptimal orientation and shading by surrounding buildings or trees, while the emplacement of PV modules on many other roofs is partly or fully prevented by the presence of heating, air conditioning and ventilation equipment or rooftop gardens or pools. Denholm and Margolis (2008) cite Navigant Consulting data that assume 22% availability of roof area for residential buildings in cool climates and 27% in warm/arid climates (the difference being due to reduced tree shading), while for commercial buildings the means are 60% in warm and 65% in cooler climates.

A German study based on sampling of countryside, village and suburban homes in Bavaria, assumed that 80% of the area of all sloping south-facing roofs of houses and 50% of the area of flat roofs of industrial buildings are available for PV installations (Lödl et al. 2010). This resulted in PV potential of 8.7 kWp for suburban houses with average footprint of 116 m2 and 12.5 kWp for village houses with built area of 167 m2. Based on that sample the Bavarian PV rooftop potential was put at 25.3 GWp, the nationwide total was estimated at 161 GWp, and the authors cite two other estimates of total German rooftop PV potential at 53-116 GWp and at 130 GWp. For comparison, German rooftop capacity was about nearly 18 GWp in 2011 or a third of the lowest potential estimate.

Although house sizes and residential and industrial population densities do not make any national rates readily transferable, it might be interesting to note that the German mean amounts to 75 Wp/m2 of building footprint, and so, at least in countries with similar residential/industrial patterns, that rate might be used to approximate national rooftop PV potential by using a much more readily available total of built-up area. An even more interesting recent study considered the degree to which the loss of nuclear generation in post-Fukushima Japan could be replaced by rooftop PV in Tōkyō (Stoll, Smith and Deinert 2013).

The study used data from 34 years of solar irradiance for the Tōkyō metropolitan area (averaging 154 W/m2); a satellite-based analysis of the area available for rooftop greening in the city (flat and free of obstruction), a total of 50.69 km2, and assumed that it would be available for PV panels; and an adjusted total of 10.03 km2 for sloped house roofs. Suitable rooftop area of Tōkyō’s 23 wards was thus put at 64.28 km2 and the total was 204.05 km2 for Kantō, the region surrounding the city that is supplied by the Tōkyō Electric Power Corporation (TEPCO) whose total service area is 297.45 km2: that area could support 43.1 GWp of PV capacity and when its generation would be coupled with the region’s existing pumped storage of 7.28 GW the combined system could provide 4.8 GW 91% of the time.

A further step toward land-less solar electricity generation is the installation of PV walls: thin film PV cells made of copper indium gallium diselenide can be laminated directly into walls (and, obviously, into roofing materials) and as their efficiency rises to rival the silicon-based cells it will become more appealing to embed them into south-facing walls of new buildings. Tall buildings will offer the greatest opportunities but they will also experience significant reductions of insolation due to shading and wall PV installations will have suboptimal angles of irradiation. These realities are well illustrated by a study of a pioneering PV wall installation, a completely integrated curtain wall façade that spans 12 floors of the lower part of the Solaire Building in New York built in 2004 (Perez et al. 2012).

The PV array of monocrystalline silicon cells covers 153.5 m2, it has a peak capacity of 11.3 kW, and it faces the Hudson River waterfront and hence its azimuth is 2750. That is 950 west of south, hardly an optimal orientation whose only advantage is largely unobstructed exposure except for shading by a few trees. The building’s wall receives 766 kWh/m2, the unshaded rate would be 822 kWh/m2, horizontal area in the same location would get 1,430 kWh/m2 and the tilted south-facing surface would receive 1,615 kWh/m2, that is 2.1 times as much as the actual wall installation whose annual electricity generation was only 5,560 kWh/year (635 W), resulting in power density of just 4.1 W/m2.

Concentrating solar power CSP stations use tracking (computer-controlled) parabolic mirrors (heliostats) to reflect and concentrate radiation on a central receiver placed on a high tower; the concentrated radiation is then used to heat transfer fluid (molten salt whose temperatures reach up to 6500C) which then heats steam to power a turbogenerator. This technique has three obvious advantages when compared to PV plants: it can achieve higher conversion efficiencies; it can be used in a dual arrangement with fossil fuel or wood used to generate steam during the nights of during periods of higher demand; and a part of the peak heat flux can be stored in order to generate electricity at night or during periods of low irradiation, with molten salts as the best storage medium (Azcárraga 2013). Despite these advantages typical power densities of CPS are not superior to those of PV generation.

Solar One, the pioneering solar tower project designed by the US Department of Energy and located east of Barstow in California, generated electricity between 1982 and 1986 (CSP World 2012). Its field of 1,818 tracking heliostats covered 72,650 m2. The project was reopened in 1995 as Solar Two with added heliostats and with the use of molten salt eat storage to smooth the fluctuating irradiation; it generated 17.5 GWh/year (that is an average rate of 2 MW) from the total area of 82,750 m2 of heliostats (USDOE 1998). Average power density of about 24 W/m2. Only four years later it was shut down and in 2009 the tower was demolished and all heliostats were removed.

Europe’s first commercial solar tower project, Spain’s PS (Planta Solar) 10, completed by Abengoa Solar in Sanlúcar la Mayor in 2007, is rated at 11 MWp and it generates 24.3 GWh/year, that is 87.5 TJ/year at a rate of 2.77 MW (Abengoa Solar 2013). At 25% its capacity factor is fairly high, its heliostats occupy 74,880 m2 (624 x 120 m2), and the entire site is about 65ha. This translates to power density of about 37 W/m2 of heliostats, and to a bit more than 4 W/m2 for the plant’s total area, a rate very similar to PV plants. PS20 (in operation since 2009) is rated at 20 MWp, it generates 48.6 GWh/year (175 TJ/year at the mean rate of 5.55 MW) and it has a slightly higher capacity factor of nearly 28%. With mirrors covering 150,600 m2 the project’s heliostat power density is 36.85 W/m2, almost identical to that of PS10, but at 6 W/m2 the rate for the entire site (about 90 ha) is nearly 50% higher.

The world’s largest CSP project is Ivanpah Solar Electric Generating System (SEGS) in the Mojave Desert in San Bernardino county in California, a site with an exceptionally high annual irradiation of 2,717 kWh/m2 (310 W/m2). The project is owned by NRG Energy, Google, and BrightSource Energy, the latter being the designer of the three adjacent plants. Construction began in 2010 and the full operation is expected in 2014; the three fields will have the total of 173,500 heliostats covering 260 ha (the entire project area is 1,400 ha) serving three 138-m tall towers; the project’s total gross installed capacity is 392 MWp and expected annual generation is 1.079 TWh, that is an average rate of 123.2 MW (BrightSource 2013).

These specifications prorate to power densities of 47.4 W/m2 for the heliostat area and 8.8 W/m2 for the entire project area. The first rate is substantially higher than the power densities of the best currently operating PV facilities. Unlike in the case of PV generation where there is a high expectation of further conversion efficiency gains no stunning improvements are foreseen for CSP efficiencies and this makes it safe to conclude that optimally located solar concentrating plants will generate electricity with power densities of 40-50 W/m2 of their large heliostat fields and with rates no higher than 10 W/m2 of their entire site area.

There is yet another choice to concentrate solar power, not by focusing sunlight onto a single point as in CSP plants but by deploying large numbers of Fresnel lenses to concentrate sunlight (raising its intensity by 2-3 OM) onto individual mulitjunction PV cells. Best efficiencies of these expensive cells are now in excess of 40% and Fthenakis and Kim (2013) prepared an LCA of such a system, Amonix 7700 high-concentration PV in Phoenix, AZ. This massive tracking unit has area of 267 m2 and its installed peak capacity of 53 kW was expected to rise to 62 kW with the improvement in the optical bath and better lens tuning. These specifications translate to power density of 231.2 W/m2, an order of magnitude higher than for non-concentrating PV installations.

Potential gains and limits Increased power densities will come with further gradual improvements of PV conversion efficiencies. New of such gains come regularly: in summer 2013 the record was held by Sharp’s concentrator triple-junction compound solar cell using Fresnel lenses to concentrate radiation onto a layered cell made from, from the top, InGaP, GaAs and InGaAs on Si substrate) at 44.4% (Sharp 2013). But these are the most expensive PV cells and advances in large-scale electricity generation will come from cheaper modules. Given the history of continuing efficiency gains of PV generation it is only a matter of time when the best annual power densities of PV conversions in large stations will commonly surpass 10 W/m2 and it is not unrealistic to think that in 20-30 years solar plants in the sunniest locations will routinely approach, and surpass, not just 20 but even 30 W/m2.

Significant power density gains would be realized with solar energy generation in three dimensions. Bernardi et al. (2012) explored such possibilities by modeling and building experimental three-dimensional PV structures (3DPV) that combine absorbers and reflectors in the absence of sun tracking. Their three choices -– an open cube, an open parallelepiped tice as tall as the cube, and a tower using slanted panels –- could generate power densities that were 2-20 times higher per base area than for stationary flat PV panels, that is maximum rates in excess of 100 W/m2. In comparison, the gain for a flat panel with dual-axis tracking would be only 30-80%. Of course, this increased density required a larges cell area (by a factor of 1.5-4 compared to flat panels) but this drawback is more than compensated by other advantages of the 3D designs: compared to flat stationary panels they can double the hours of peak power generation, and they can greatly reduce seasonal, latitudinal and weather variations. In combination with inexpensive thin PV films they could open new possibilities for large-scale PV generation.

Another advantage of PV systems is due to their relatively high safety. Fthenakis and Kim (2011) used USEPA’s Risk Management Program accident records (that embrace all of the US chemical storage and processing) as they studied material and energy flows in four commercial PV designs, those of monocrystalline silicon, multicrystalline silicon, ribbon silicon, and cadmium telluride. Their results how that the PV cycle is much safer than conventional energy sources both in terms of statistically expected and possible maximum consequences. At the same time, German-like mass installation of both rooftop PV units and large multi-MW projects is not a precept readily applicable to all kinds of environments and to all levels of economic development. Germany is not an obvious choice for the world’s largest installed PV capacity as average irradiance over large parts of southern Spain and Italy is nearly twice as high, but the country’s combination of many distinct advantages is not to replicated anywhere else anytime soon.

Germany has modern electrical grid and distribution system, diverse manufacturing capabilities and technical prowess that made it fairly easy to ramp up the production of modules (later undercut to a large extent by chap, subsidized, imports from China) and that has facilitates production and installation of the needed infrastructure of distributed PV generation (panel frames, wiring, inverters, meters, and now increasingly also storage batteries). Germany’s rainy climate provides natural cleansing of modules exposed to the deposition of dust and organic debris. Traditionally fairly highly electricity prices have made even early PV relatively more competitive than in countries with inexpensive electricity, and a large segment of German population prefers to adopt, and is willing to pay for, ‘’green’’ practices. And, of course, generous feed-in tariffs with prices guaranteed for two decades have offered a sure way to make profit for anybody who has the initial capital investment.

This combination explains why the pace of rooftop PV advances has been much slower even in countries where only a few German advantages are missing: the US is not as ‘’green’’ and Americans have always paid much less for their electricity but a large part of the country has irradiance twice as high as Germany, and the country’s HV grid, electricity distribution, manufacturing potential and technical skills are not inferior in comparison, But thanks to high feed-in tariffs in 2012 Germany had in per capita terms 16 times as much PV capacity as did the US (Fraunhofer ISE 2012). And replicating Germany’s PV achievements would be outright impossible in countries with dodgy grids and unreliable electricity distribution (including a large share of illegal hook-ups).

And it would be a challenge in nations with insufficient manufacturing base and with shortage of technical skills needed to deploy PV infrastructure for millions of units; in climates where seasonally heavy deposition not only coats the modules in dust but where wind-driven sand pits module surfaces; in societies where subsidized energy prices created unrealistic expectations about the cost of future supply and where the abundance of domestic energy resources does not create such urgency as does Germany’s high dependence on fossil fuel imports; and in economies where only very few people could afford the initial investment in rooftop PV units, even when assuming that house roofs were accessible and free for installation: in many densely populated cities of the Middle East and Asia they are not.

And systems considerations dictate that major future shares of PV generation (depending on specifics that may mean anything above as little as 5% and as much as 15%; in 2012 Germany derived 4% of its electricity from PV) will be possible only with greatly expanded storage, a strategy that is now pursued both by Germany and California. In Germany the program (started in May 2013) is limited to small PV system of up to 30 kW and it offers a subsidy of up to 30% for the price of storage systems tied to new or existing PV units. In California’s three major utilities will have to buy 1.325 GW of storage capacity by the year 2020 (California Public Utilities Commission 2013).

Wind and wind-generated electricity

As only a tiny fraction of solar energy reaching the Earth goes into energizing the global atmospheric circulation the aggregate power of wind is orders of magnitude smaller than that of the planetary irradiance but some of its recent estimates concluded that it is still many times larger than the global TPES. Archer and Jacobson (2005) assessed the global wind power potential at 72 TW (compared to the 2012 TPES, including all biomass fuels, of nearly 17 TW) even when exploiting only 13% of the Earth’s windiest regions. Lu, McElroy and Kiviluoma 2009), assuming a larger area and more powerful turbines, put the total land-based potential nearly 75% higher at 125 TW. Later Jacobson and Archer (2010) implied that more than 170 PW of wind power is available for extraction in the atmospheric boundary layer region.

Such extremely high totals were in line with the arguments by Roberts et al. (2007) who claimed that power that could be extracted from planetary jet streams is between one and two orders of magnitude greater than that extractable by equally-sized ground-based wind turbines, and proposed that a tethered rotocraft (a variety of gyroplane) be used to extract this enormous flux reaching horizontal power densities up to 20 kW/m2, compared to less than 500 W/m2 for a large modern ground-based turbine (the derivation of this rate follows shortly). Miller, Gans and Kleidon (2011) exposed the fallacy of these high estimates by pointing out that all of them have neglected energy conservation, and proceeded to derive a realistic estimate first by tracing the fundamental to-down process of energy transfer.

About 25% of the incoming solar radiation (45 PW) goes into differential solar heating that creates pressure differences (Lorenz 1976); about 2% of that total (900 TW) is the maximum available for wind power extraction and of that half is dissipated in the atmospheric boundary layer (Peixoto and Oort 1992) and 25% of the remainder (112 TW) is dissipated over land of which no more than 60% (68 TW) could be extracted over all non-glaciated land. Miller, Gans and Kleidon (2011) then proceeded to refine this estimate by a simple momentum model with reanalysis wind data and by climate model simulations. Their conclusion: the maximum wind power that could be extracted from the atmospheric boundary layer over all non-glaciated land –- and that is limited by the rate of its generation in the climate system -– is, depending on the estimation approach, as low as 18 TW and no higher than 68 TW.

The lower estimate would prorate to 0.15 W/m2 of ice-free land, the higher one to 0.57 W/m2, both being merely theoretical maxima of extractable kinetic energy. Obviously, in practice only a very small share of the Earth’s wind energy that could be captured will be eventually converted to electricity by commercially viable turbines: it is a safe bet that tethered rotocrafts will not be delivering electricity on TWh scale anytime soon, and that the vast continental regions with very low wind speed and with seasonal doldrums will not see installation of extensive wind farms. Hoogwijk, de Vries and W. Turkenburg (2004) used annual wind speed data from the UK’s Climate Research Unit put the economic potential (cut-off costs at about $1/kWh) at 96 PWh/year (10.96 TW)

The best assessed new total comes from a study that combined reanalysis wind speed data with assumptions about updated wind turbine performance, land suitability factors and average costs, including those of requisite long-distance transmission (Zhou et al. 2012). Its central assumptions result in the total global economic (at less than 9 cents/kWh) wind generation potential of approximately 119.5 PWh a year, or 13.6 TW. Sensitivity analyses show that the estimates depend particularly on assumed wind speed (ranging from −70% to +450%), land suitability (from −55% to +25%), turbine density (from −60% to +80%), and cost and financing options (from −20% to +200%). The central estimate of 13.6 TW would prorate to just 0.11 W/m2 of ice-free land.

That mean is, obviously, depressed due to large continental areas with low wind speeds, particularly during extended high-pressure spells in the northern hemisphere, and power densities for windy coastal and inland regions will be at least an order of magnitude higher. Still, wind’s considerable vertical power densities (Kapitsa’s Umov-Poynting vector, explained in the second chapter of this book) translate into relatively low (horizontal) power densities of electricity generation even at the windiest sites. I will illustrate this progression of values by using actual data for one of the largest machines on the market, Vestas model V90 with the rated power of 3 MW (Vestas 2013).

The turbine’s cut-in wind speed is 3.5 m/s, cut-out speed is 25 m/s and the rated wind speed (v) is 15 m/s. With the rotor diameter of 90 m the three blades sweep (with the nominal revolution of 16.1 rpm) an area (A) of 6,362 m2. These ratings (and air density ρ=1.2 kg/m3) set the maximum power (P) of this Vestas turbine at 12.88 MW:

Maximum power of Vestas wind turbine
P = ½ρAv3

= ½ x 1.2 kg/m3 x 6,362 m2 x (15 m/s)3

= 12,883,050 W
Betz limit (0.59) takes that down to maximum achievable rating of 7.6 MW and the actual rated power of 3 MW means that the machine has a fairly high correction factor (0.39, due to performance losses in mechanical energy conversions) and that the Umov-Poynting vector (vertical energy flux) of its electricity generation is 471.5 W/m2 of the area swept by its blades.

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