Vozhakov Roman Mathematical model of residual resource evaluation of the power transformer when working in conditions other than nominal

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Vozhakov Roman

Igor Sikorsky Kyiv polytechnic institute, Ukraine

Mathematical model of residual resource evaluation of the power transformer when working in conditions other than nominal

In the energy sector as in any branch of industry an equipment in some reasons works in conditions other than those for which it was calculated and under which it is guaranteed to work a predetermined amount of time.

There is the question, eventually arisen before the responsible for equipment operation personal, whether it worked it’s resource and how long can still working in the given conditions.

In the work [1] the formula for calculation of electrical equipment residual resource during the working out time R₀ was derived

, (1)

where - spent electrical equipment resource in operation conditions other than nominal in p.u.(assigned to the nominal lifetime, specified in the passport) –"working out" time in p.u.; – duration of equipment operation in j-th abnormal regime; N_TH, N_E, N_М, N_CH – amount of thermal, electrical, mechanical and chemical factors, that that affect the resource of electrical equipment; , , , – meanings of thermal, electrical, mechanical and chemical factors in j-th abnormal regime; , , , – normalized change of factor, that reduces the resource in е times; moreover .

The residual resource in further operation conditions other than nominal is determined based on formula (1) by substitution and , where – residual resource in conditions of further equipment operating in nominal conditions. In the result:

. (2)

Formula (1) was derived from the suppose that every increase of х_і factor under nominal value х_0і to ∆хі actual spent electrical equipment resource increases in n times, and while decreasing - reduced in n times. That formula can be written: ,

or in per-units:

Then we can propose, that electrical equipment residual resource will be worked out in n times faster while increasing of хі factor by an ∆хі amount and in n times slower – while decreasing, and it will be rightful formula:

,

where – residual resource under condition, that equipment will be operated in nominal conditions; where – actual residual resource, if хі factor does not equal to its nominal value.

Or in p.u.:

Then, according to the calculations, similar to the calculations [1] for actual spent resource:

, (3)

where – residual resource under condition of further operation in nominal conditions ( ); – planned duration of j-th abnormal regime in further operation of electrical equipment.

In [1] is given an calculations example of spent and residual resource for transformer TD-80000/220 with a normative resource of 25 years, which is hypothetically worked for 20 years with the following parameters of daily load: 16 hours – 78 MVA – θ_cool = 17 °С, 7,5 hours – 72 MVA – θ_cool = -13 °С, 0,5 hours – 85 MVA – θ_cool = 22 °С. According to the formulas, based on (1) and (2), it was found, that the spent resource is 10.025 years, residual resource when working in nominal parameters is 14.975 years, and if transformer continue working in the same conditions, then residual resource will be equal to 29.95 years. And if you calculate the residual resource based on formula (3), then residual resource of transformer in further working in the same conditions, is evaluated at 45.4 years, that is 1.5 times more than in calculations based on formula (2).

References

1. Назарычев А.Н. Методы и математические модели комплексной оценки технического состояния электрооборудования / А.Н. Назарычев, Д.А. Андреев.– Иваново: Иван. гос. энерг. ун-т, 2005.–224 с.