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Publication# 35 years of photovoltaics: Analysis of the TISO-10-kW solar plant, lessons learnt in safety and performance-Part 1

Abstract

The TISO-10-kW solar plant, connected to the grid in 1982, is the oldest installation of this kind in Europe. Its history is well documented, and the full set of modules has been tested indoors at regular intervals over the years. After 35 years of operation, we observe an increase in the degradation rates and that the distributions of modules' performances are drastically changing compared with previous years. Two groups of modules can be observed: (a) group 1: 21.5% of the modules show a very modest degradation, described by a Gaussian distribution with mean yearly power degradation of only -0.2%/y. (b) Group 2: 72.9% of the modules form a negatively skewed distribution with a long tail described by mode (-0.54%/y), median (-0.62%/y), and mean (-0.69%/y) values. In earlier years, decreases in performances could strongly be correlated to losses in fill factor (FF). After 35 years, the situation changes and, for a subset of modules, losses in the current (Isc) are superimposed to losses in FF. The reasons for this will become clearer in part 2, where we will present results of a detailed visual inspection on the whole set of modules and will focus on safety aspect too. We conclude that, after 35 years of operation in a temperate climate, approximately 60% (similar to 70% if considering a +/- 3% measurement uncertainty) of the modules would still satisfy a warranty criteria that module manufacturers are presently considering to apply to the technology of tomorrow: 35 years of operation with a performance threshold set at 80% of the initial value.

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In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module generalizes also the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers. Like a vector space, a module is an additive abelian group, and scalar multiplication is distributive over the operation of addition between elements of the ring or module and is compatible with the ring multiplication.

Projective module

In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules. Various equivalent characterizations of these modules appear below. Every free module is a projective module, but the converse fails to hold over some rings, such as Dedekind rings that are not principal ideal domains.

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Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.

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