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The purpose of this exercise is to practice basic Markov chain calculations for a discrete time, discrete state, finite state example. The Markov chain is a stochastic representation of the distribution grid where the events have the following physical meaning (ve = voltage error; f0 = voltage back to norm without intervention; s1 = first transformer switch; f1 = voltage back to norm following first switch; s2 = second transformer switch; f2 = voltage back to norm following second switch). | The purpose of this exercise is to practice basic Markov chain calculations for a discrete time, discrete state, finite state example. The Markov chain is a stochastic representation of the distribution grid where the events have the following physical meaning (ve = voltage error; f0 = voltage back to norm without intervention; s1 = first transformer switch; f1 = voltage back to norm following first switch; s2 = second transformer switch; f2 = voltage back to norm following second switch). | ||
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+ | [[File:Exercise3_MC.png|thumb|Figure 1: Markov chain model]] | ||
Step 1: Consider the Markov Chain in Figure 1. Is the Markov chain ergodic? | Step 1: Consider the Markov Chain in Figure 1. Is the Markov chain ergodic? | ||
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Step 4: Calculate the expected number of steps required to return back to norm following a voltage error. | Step 4: Calculate the expected number of steps required to return back to norm following a voltage error. | ||
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+ | Step 5: Is the voltage more likely to return back to norm before the second switch? |
Latest revision as of 22:50, 12 November 2020
The purpose of this exercise is to practice basic Markov chain calculations for a discrete time, discrete state, finite state example. The Markov chain is a stochastic representation of the distribution grid where the events have the following physical meaning (ve = voltage error; f0 = voltage back to norm without intervention; s1 = first transformer switch; f1 = voltage back to norm following first switch; s2 = second transformer switch; f2 = voltage back to norm following second switch).
Step 1: Consider the Markov Chain in Figure 1. Is the Markov chain ergodic?
Step 2: In Matlab, define the 1-step probability matrix P.
Step 3: Find the stationary distribution of this Markov chain.
Step 4: Calculate the expected number of steps required to return back to norm following a voltage error.
Step 5: Is the voltage more likely to return back to norm before the second switch?