Question

Flicker in an electrical power system. An assessment of the quality of the electrical power system in Turkey was the topic of an article published in Electrical Engineering (March 2013). One measure of quality is the degree to which voltage fluctuations cause light flicker in the system. The perception of light flicker (x) when the system is set at 380 kV was measured periodically (over 10-minute intervals). For transformers supplying heavy industry plants, the light flicker distribution was found to follow (approximately) a normal distribution, with m = 2.2% and s = .5%. If the perception of light flicker exceeds 3%, the transformer is shut down, and the system is reset. How likely can a transformer supplying a heavy industry plant be shut down due to light flicker?

Short answer

The chance of electric flicker is 0.0548,which is high. Therefore, it is likely for a transformer supplying a heavy industry plant to be shut down due to light flicker.

Step-by-step solution

Given information

For transformers supplying heavy industry plants, the light flicker distribution has a normal distribution with a meanof 2.2% and a standard deviationof 0.5%.

 Computing the probability

Here, $X~N\left(2.2,0.5\right)$

Let,

$\begin{array}{rcl}P\left(X>3\right)& =& 1-P\left(\frac{X-2.2}{0.5}>\frac{3-2.2}{0.5}\right)\\ & =& P\left(z>1.6\right)\\ & =& 1-P\left(z<1.6\right)\\ & & \end{array}$

Therefore, from the z-score table,

$\begin{array}{rcl}P\left(X>3\right)& =& 1-0.9452\\ & =& 0.0548\\ & & \end{array}$

Let 0.05 be the significance level. 0.0548 is greater than 0.05. The chance of electric flicker is 0.0548, which is high. Therefore, it is likely for a transformer supplying a heavy industry plant to be shut down due to light flicker.