ELEC 5194 Fall 2021 Power Systems Operation & Control Department of Electrical Engineering University of Colorado Denver Homework Assignment 2 Due October XXXXXXXXXXvia Canvas Consider the power...

I want also the matlab file include in this file. i just want the code the writing part, i can take care of it


ELEC 5194 Fall 2021 Power Systems Operation & Control Department of Electrical Engineering University of Colorado Denver Homework Assignment 2 Due October 17 2021 via Canvas Consider the power system described in pages 269/270 in the textbook, in particular the tables entitled “generator data” and “generation cost function data”. These tables provide, respectively, generation limits and generators cost function coefficients (power entered in MWs giving cost in $/h). The cost coefficient represent quadratic cost functions of the form C(P ) = aP 2 + bP + c. In order to make the generation costs more realistic, multiply all cost coefficients (a, b and c) × 3. 1) Economic dispatch through QP: Solve the economic dispatch using Matlab’s quadprog command for a total demand of PD = 250 MW. (1.1) Report the total generation cost, the dispatch for each power plant, their marginal costs, and the shadow price for the power balance constraint. (1.2) Verify numerically that the KKT conditions hold. (1.3) Discuss the relationship between generators marginal cost, total cost and shadow prices. You may use numbers to complement your discussion. (1.4) Change the total demand to PD = 450 MW and repeat (1.1) through (1.3). 2) Economic dispatch through LP: Transform the quadratic cost functions to piecewise linear functions considering two segments, splitting the power range in half. Solve the economic dispatch using Matlab’s linprog command for a total demand of PD = 250 MW. (2.1) Report the total generation cost, the dispatch for each power plant, their marginal costs, and the shadow price for the power balance constraint. (2.2) What is the penalty cost for the power system if the ISO were to use LP instead of QP to solve the economic dispatch problem? 3) Environmental dispatch through QP: Recently, there has been concern that optimum economic dis- patch is not environmentally friendly. The principles of economic dispatch can fairly easily be extended to handle this problem. Consider all three power plants burn coal with a heat content of 11,500 Btu/lb, which costs $42/st. The combustion process in each unit results in 11.75% of the coal by weight going up the stack as fly ash. Units 1, 2 and 3 have precipitators installed that remove, respectively, 95%, 90%, and 92% of the fly ash. Formulate the environmental dispatch (cost function to be minimized is the fly ash going out into the air in lb/h) and solve it using Matlab’s quadprog command for a total demand of PD = 250 MW. (3.1) Report the dispatch for each power plant. What does the cost function represent in this case? (3.2) Compute the economic cost (in $/h) for both the environmental and the economic dispatches and the environmental cost (in lb/h) for both dispatches. Discuss penalty costs for the two different dispatches. You have to submit one .zip file with the following: a) A pdf file with your report b) A file called quetion1.m that generates results for question 1 c) A file called quetion2.m that generates results for question 2 d) A file called quetion3.m that generates results for question 3 Hint : The economic dispatch for (1.1) is Pg = [51.081 105.77 93.153] T in (MW). 1 Document5