Lifetime extension of the high voltage asynchronous machine in relation to the voltage endurance test

Abstract

The study aims to achieve a simple, reliable, and significant lifetime extension of the high-voltage asynchronous machine in relation to the voltage endurance test. To achieve this goal, the focus was on achieving longer-lasting and more stable insulation of the stator package of an asynchronous machine. Longer-lasting and more stable insulation of a stator is achieved by reinforcing the weak points on its prefabricated multiturn coils. These reinforcements were performed with standard insulating materials that are used for the production of the prefabricated multiturn coils (because there is no data regarding the long-term behavior of new materials that show some better properties in laboratories, but only during short-term tests). With such reinforced weak spots based on prefabricated models, they were made by the classical procedure with the use of standardized tools. To track the effects of the improvement of the insulation characteristics of a stator, an algorithm was developed based on the law of increasing probability and the determination of lifetime curves to the voltage endurance test. The lifetime curves were determined by the method of increasing voltage with the transformation of the obtained results to the corresponding results by the constant voltage method. The applied algorithm that was formed for this study, had been verified with statistical reliability of 95%. The combined measurement uncertainty of the measurement procedure was about 5%.

Appendix Determination of the lifetime curves of an insulation system

The random variable "the breakdown time" was obtained by the constant voltage procedure in the following steps: 1—50 identical voltages were woven in parallel into identical linings; 2–All parallel connected samples are brought under the same voltage value U_d1; 3—The breakdown of one sample was ascertained by measuring the capacity of the parallel connection, 4—At the moment of breakdown, the breakdown time was recorded (random variable "the breakdown time"), 5—The breakdown sample was replaced by ours (marked) due to the constancy of the capacitive load; 6—After the breakdown of all 50 initial capacitors, a statistical pattern of the random variable "the breakdown time" was formed. The entire constant voltage measurement procedure was completely automated [16].

The empirical distribution of the statistical distribution breakdown time (Fig. 

Fig. 11

Determination of the distribution functions of the breakdown time: a Lifetime characteristics; b derivative functions of the breakdown voltage; c schematic diagram

11a) was obtained based on the updated analysis. It is emphasized and physically explained that the obtained random variables are best described by the Weibull distribution (the Weibull distribution fits the random variables obtained by the constant voltage experiment):

$$ F(t_{d} ;u_{d1} ) = 1 - \exp \left[ { - \left( {\frac{{t_{d} }}{{t_{d63} (u_{d1} )}}} \right)^{{\delta_{t} }} } \right] $$

(1)

The lifetime characteristic, which is another name for the breakdown voltage/breakdown time diagram, is constructed using arbitrarily selected quantiles of the specified distribution. Experience has shown that the diagram forms a line on a double exponential scale, Fig. 11b. In the case when confidence intervals are known for the given quintiles, they will be transferred to the lifetime characteristics. For each quantile p of the breakdown time, the lifetime characteristic is described as:

$$ u_{{{\text{dp}}}} = k_{{{\text{dp}}}} t_{{{\text{dp}}}}^{ - 1/r} $$

(2)

where the k_dp constant is determined by the geometry of the structure, while r is the exponent of the lifetime which depends exclusively on the insulating material. Deviation from the shape of the lifetime line indicates that the aging mechanism of the insulating material is changing.

By adopting the Weibull distribution, analogous to Eq. (1), and for the random variable breakdown voltage U_d with a fixed breakdown time t_d1, it follows that for the same breakdown probability $F(t_{d} ;u_{d1} ) = F(u_{d} ;t_{d1} ):$

$$ F(u_{d} ;t_{d1} ) = 1 - \exp \left[ { - \left( {\frac{{u_{d} }}{{u_{d63} (t_{d1} )}}} \right)^{{\delta_{u} }} } \right] $$

(3)

$$ u_{d63} (t_{d1} )\left[ {t_{d1} } \right]^{{\delta_{t} /\delta_{u} }} = u_{d1} \left[ {t_{d63} (u_{d1} )} \right]^{{\delta_{t} /\delta_{u} }} $$

(4a)

Based on Eq. (2) (law of lifetime), assuming that the exponent r is identical for all quantiles, a relation is obtained for the same dependence and the value:

$$ u_{d63} (t_{d1} )\left[ {t_{d1} } \right]^{1/r} = k_{d63} $$

(4b)

Based on Eqs. (4a) and (4b), a relation is obtained between Weibull exponents for breakdown time δ_t, breakdown voltage δ_u, and lifetime exponent r:

$$ r = \frac{{\delta_{{\text{u}}} }}{{\delta_{{\text{t}}} }} $$

(5)

It should be emphasized that the given relationship is correct only if both variables U_d and T_d belong to the Weibull distribution, Fig. 1c, which has been repeatedly emphasized and physically explained. It should be emphasized that Eq. (5) and the mathematical model can only be used if r applies equally to all quantiles.