ECE 558 - Spring 2021

Power System Reliability

Project 3 - Due 23 Feb 2021

1. A system has a continuous load of 80 MW. Find the expected load loss and the expected number of hours that any curtailment will exist if the generation is composed of
   1. five 20 MW hydro-generating units each with an unavailability of 0.5%
   2. nine 10 MW thermal units each with an unavailability of 1.5%
2. The following transformer systems are to be compared:
   1. 3 transformers each rated at 100% of full load,
   2. 3 transformers each rated at 90% of full load,
   3. 3 transformers each rated at 50% of full load,
   4. 4 transformers each rated at 33.33% of full load,
   Compare the adequacy of these systems in terms of the expected percent load curtailed and the expected hours of load curtailment, if the transformer unavailability is 0.01.
3. Using the "coin_toss.m" MATLAB function, find an initial seed for the pseudo-random number sequence, i.e., in version 7.14.0.739 (R2012a)
   
   s = RandStream.create('mt19937ar','seed',mySeed);
   RandStream.setGlobalStream(s); % sets initial seed
   
   or in 7.8.0.347 (R2009a)
   
   s = RandStream.create('mt19937ar','seed',mySeed);
   RandStream.setDefaultStream(s); % sets initial seed
   
   or in an older version without RandStream
   
   rand('state',mySeed); % sets initial state
   
   where you supply the integer parameter "mySeed" and then run coin_toss(10), such that the coin_toss function gives an average value greater than 2/3 at the end of 10 trials. What number did you supply for the intial state? What were the results for the ten trials?
4. Modify the "coin_toss.m" MATLAB function to simulate two coin tosses in each trial (say, toss1 and toss2). Store the Heads (1) and Tails (0) values in a 2 x ntrials "results" array. Tell MATLAB to allocate the array before the "for" loop as follows:
   
   results = zeros(2,ntrials);
   
   Then, modify the storage statement as follows:
   
   results(:,i) = [coin1_outcome; coin2_outcome];
   
   If one Head appears, then the player wins $1. If two Heads appear, then the player wins $2. If no Heads appear, then the player loses $5. Store the payoff in a 1 x ntrials array called payoff. Compute an average payoff after each trial by summing all payoffs and dividing by ntrials. Plot the average payoff vs. ntrials.
   1. Submit your MATLAB code as an appendix (it should start a new page) within your electronic SafeAssignment file via Blackboard.
   2. Submit your average payoff plot vs. 100 trials.
   3. Does your average payoff plot settle? To what value? Is this what you expected? Why or why not?

Main Campus students must submit their assignments on paper at the beginning of the lecture. In addition, both Internet students and Main Campus students must submit an electronic copy via SafeAssignment on the ECE 558 Blackboard site BEFORE the beginning of class. SafeAssign does not allow multiple files, so you'll need to find a way to submit a single file, e.g., scanned images (PNG or JPEG) of handwritten work can be inserted in a Word Document. MATLAB code, if any, must appear in an appendix so that we can copy and paste your code into an M-file to test it. MATLAB code must not be scanned. It must be included as formatted text. See the "Blackboard SafeAssign" link on the course home page for details on allowed file types. Please make sure your file is less than 1 MB in size!