# THE SECOND-LAW APPROACH

Thermodynamics heavily dwells on a variety of phenomena which in­volve the generation of useful work (electricity for our purpose); in particular, "the maximum work that can be extracted from a given system in a given state by a process which brings it into equili­brium with its environment". That maximum work is termed the avall- ibitv or exerav. The lower heating value of fossil fuel comes out ti be quite close to 100% exergy (AIP, 1970; Krenz, 1984) (therefore wi use the symbol Wir» for it). We can see that the power-engineering approach closely relates to the exergy (second-law) concept. If we use a coefficient k, such that for a particular fossil-fired power plant

^OUt — kWln,

then the power-engineering and the exergy approaches become usefull correlated. In fact, к is the power-plant conversion efficiency. Fo instance, for a modern, large Rankine cycle plant, к may be assigne the value of 0.37, and for an advanced combined-cycle power-plant, к = 0.5. The values of к have been increasing throughout the years, and they may still grow, as new materials are developed to allow higher temperatures, pressures, etc., in power cycles.

The case of к = 1 is a limiting (thermodynamic) condition, useful only as a reference. It represents the hypothetical attainment of the full value of exergy. Analyzing our sample solar hybrid plant vs. an ideal power cycle with к = 1 as a reference ("exergy analy-

sis”), gives :

Exergy gained = Wout – Vxr, = <64.47 – 84.244) x 106,

= -19.77 x 10* kWh(e)

This expresses a loss of exergy, which, per unit exergy output, is 19.77/64.47 = 0.307. As a corollary: the entropy increase per kWh(e) exergy output is 0.307 kWh(e)/T. mbi«nt.

The conventional fossil-fired power plant is even more dissipative: for the 337. conversion plant, the exergy loss per unit exergy output is 1 – 0.33 = 0.67. For the 505C conversion plant, it will be 1-0.50 = 0.50. Thus, the solar hybrid plant is less dissipative and entails a smaller increase of entropy as compared to the conventional fossil-fired plant. Exergy analysis thus serves as a basic yardstick for assessing overall systems’ efficiency, including also the quantitative solar contribution for hybrid systems.

A note should be added with regard to the thermodynamic reference states. Both the hybrid and the strictly-fossil reference plants have the same environmental and other usual thermodynamic condi­tions. Deviations can be calculated. Concerning the exergy analysis involving solar irradiation, the treatment of the solar plant depicted here is made in comparison to an adjacent site with similar insolation but without any utilization of solar energy, the latter being immediately degraded to the "dead state"; i. e., it is fully turned into entropy upon its impingement on the ground. In other words, in comparison to the adjacent bare field site, taken as a reference, the solar plant produces or, rather, preserves a part of the solar exergy. This is the thermodynamic perspective of the concept of "renewable" which characterizes solar energy.

CONCLUSIONS

The second-law (exergy) approach, particularly when adjusted by the conversion coefficient k, is practically identical to the power­engineering approach and is very useful for analyzing solar hybrid power plants. It provides justifiable rules for deriving the speci­fic solar contribution and solar efficiency of a solar hybrid power plant, and a generalized scale for energetic assessments and compa­risons. The conversion coefficient к is dominated by the size of the plant and by local, economic and current conditions. The first-law approach is less desirable, in particular when the working fluid temperature as obtained from the solar technology is substantially lower than that of advanced, strictly fossil-fired cycles. Meaning­ful ranking of solar power plants and comparing technologies can thus be facilitated.

REFERENCES

1. AIP Conference Proceedings, (1970). Efficient Use of Energy. Academic Press, New York.

2. Krenz, J. H., (1984). Energy Conversion and Utilization. 2nd

ed. , Allyn and Bacon, Boston, pp. 170-172.



Г = 37.6 (2)

hs I

HW

where I and I are the integrated intensities of the stretching and wagging bands, defined by equation (1), respectively.

 This section describes stationary measurements only during battery charging.

 From the measured I-V curve, obtain N measured V, J points (Vm, Jm) by digitizing the curve between the Isc and Voc points. For a nominal PV module, Im values should be found in about IV increments starting at

 At least one manufacturer (Advance) advertises the fact that their ballasts operate on dc.

 NOAA local climatological data monthly summaries..

 All methods used normalized chi-square, e, as fitting criterion.

 = (PI + P2Tc)-G (5) , and VT = k-Tc/q (g)

where Iph is the photogenerated current, I is the module current, Io is the saturation current, V is the module voltage, П is the diode quality factor, к is the Boltzmann’s constant, Tc is the cell temperature, G is the global irradiance and Rsh is the equivalent shunt resistance. By applying the routine Amoeba, using starting values based on the numerical analysis of , we obtain the values of the parameters. The results are to be published.

Another, especially important, factor is the degradation of the amorphous-silicon panels. We have noticed that during the first 9 months of operation of the first photovoltaic array, the panel efficiency has ctegraded approximately 4% a month. This empirical value has been incorporated into the hybrid system simulation program while the degradation phenomenon is currently studied in order to establish a parametric model.