## 1 Introduction  
The power transformer is a key component of the Electric Transmission and Distribution (T&D) system. Its integrity assessment is very complex but essential to avoid irreversible damages with consequent heavy impacts on maintenance costs and on T&D network services, due to outages. Among causes which can lead to a transformer failure (_i.e._, hot spots, partial discharges), the accelerated degradation of its solid insulating system, _i.e._, oil impregnated cellulosic insulation materials, strongly depends on the operating condition of the transformer [1, 2]. Actually, sometimes the degradation of its dielectric parts begins much earlier than the designed end-of-life of the transformer (foreseen as 30 years), due to an accelerated thermal aging of both the insulating oil and the paper, but while the regeneration of a degraded insulating oil is possible by appropriate treatments or even by its replacement with a new compatible oil [3], the refurbishment of degraded paper requires invasive and costly operations that must be necessarily performed by the manufacturer, because it can involve the total replacement of transformer windings. For this reason it is well established [4, 5] that the end of useful life of a transformer is mainly determined by thermal deterioration of papers and that a careful monitoring of parameters linked to this process is of fundamental importance for utilities to check the \"health\" of the in-service transformers. One of the main components of the insulation paper (_i.e._, Kraft paper) is cellulose, which consists of a long linear chain of \(\beta\)-D glucose molecules [5, 6]. As the paper ages, its mechanical strength changes significantly because of degradation (depolymerization) of the cellulose chains; in a domino effect, the decrease of mechanical strength also reduces the ability of the transformer to withstand short circuit stress, confirming that these two properties are not mutually disjoint but are in synergy. For this reason, the mechanical strength of the paper is considered an important diagnostic parameter in transformers and its reduction down to 50% is assumed as an indication of the end-of-life of a transformer [4]. The mechanical performance of the cellulose is defined by the degree of polymerization (DP) of the paper, which corresponds to the average number of glucosidic (\(\beta\)-D glucose) units in a single chain of cellulose [4, 6]. During the aging of paper, the DP parameter decreases from values of 1000 \(\div\) 1200 (new paper) to 150 \(\div\) 100 (degraded and fragile paper). The viscometric test, according to the IEC 60450 [7], provides a reliable and direct measure of the DP value but actually this method is not practical, because it requires a sample of paper from the transformer insulation system, which is impossible to access during regular operation. The indirect measure of the insulating paper decomposition products dissolved in oil, such as carbon dioxide and carbon monoxide (CO\({}_{2}\) and CO) [8, 9], methanol [4, 10], furfural (furan-2-carbaldehyde, 2-FAL) and related furans is generally preferred. While CO and CO\({}_{2}\) can be generated by decomposition of the oil during long term oxidation too, methanol, furfural and furans are only formed by the processes of thermal degradation of the cellulose [4, 8, 11]. Their concentration in transformer oil is strictly correlated to the degree of polymerization of the paper [4, 8, 9], as for instance in the case of Kraft insulating paper. Although methanol has been widely demonstrated to be very promising as a marker of ageing [4, 10, 11], currently the 2-FAL concentration is used worldwide as one of the main indicators to estimate the ageing of the paper in a transformer [4, 8]. As the presence of furan compounds in oil is not related to the degradation of the oil itself, they can be used as chemical markers in transformer insulating oil to assess the overall DP with a high degree of confidence [8, 12].