Problem 1: Using MATLAB, write a computer program to solve the economic dispatch problem (considering generator limits and transmission line losses) for a power system with three generating units. Use a convergence tolerance e of 0.001 MW. Your program must be based on the economic dispatch solution procedure presented in class. Please make sure that your program code is well documented. Attach a copy of your computer program. Note that you will have to use your program in order to solve Problem 2. Problem 2: Consider an electric power system with three generating units operating on economic dispatch. The fuel-cost functions of these units, as well as their corresponding feasible limits, are shown below: C(Pa) = 561 + 7.92P, +0.001562P: S/hr 150 S P S 600 (P) = 310 +7.85P, + 0.00194P), Shr 100 S P 400 (P) = 78 + 7.97P + 0.00482PShr 50 S P S 200 where P. Ps, and P. are in MW. The loss coefficients for this system are given by: 0.003 0.000 0.000 B = 0.000 0.009 0.000 x102 0.000 0.000 0.012 B. = [0.00 0.00 0.00] BO = 0.00 (a) Neglecting generation limits and transmission losses, find the economic dispatch solution (i.e., 2. P. P. P. and C) for a total power demand of 850 MW. (b) Considering generation limits and neglecting transmission losses, find the economic dispatch solution (i.e., 2. P. Por, P., and C) for a total power demand of 850 MW, if the fuel-cost function for unit 1 is modified as follows: C(P) = 459 + 6.48P + 0.00128P Shr (c) Considering generation limits and transmission losses, find the economic dispatch solution (i.e., 1, P. P. Po, and C,) for a total power demand of 850 MW. In addition, calculate the total transmission losses in the system, as well as the corresponding penalty factor of each generating unit. (d) Compare your results (manual calculations vs. MATLAB code output) for parts (a), (b), and (c). Discuss your findings