Please ONLY solve problem 1. i posted some lecture notes below the problem hope
ID: 3349566 • Letter: P
Question
Please ONLY solve problem 1. i posted some lecture notes below the problem hope it is helpful. Please do all parts A,B and C.
1. Consider a system with 2 generators that are supplying a total load of 350 MW. You may neglect generator active power limits. Assume that the incremental cost curve of each generator is given by 21 0.007 Pgl +4.1 2 0.007 Pg2 +4.1 S/MWh S/MWh Total system losses in this network can be calculated using the equation PL 0.001 (Pe 50)2 MW a. (2 points) Find the penalty factor of each generator (L1 and L2) (5 points) Write the economic dispatch rule for this system, considering system losses. b. (3 points) Use MatLab to solve the system of equations in part (b) to determine the optimal dispatch of each generator (ie. Pgl and Pg2) AND the system . c. HINT: for this system lies in the interval [5.5, 6.01.Explanation / Answer
Economic dispatch rule for the system with losses-
L1 1 = L22 (Increament cost of both systems are equal)
L1 = 1/1-(dPL/dPg1) = 1/1-0 = 1
L2 = 1/1-(dPL/dPg2) = 1/1-(0.002(Pg2- 50))
Pg1 + Pg2 = 350 MW
1 * (0.007Pg1 + 4.1) = 1/1-(0.002(Pg2-50)) * (0.007Pg2 + 4.1)
(1-0.002Pg2+0.1)*(0.007(350-Pg2)+4.1) = 0.007Pg2 + 4.1
(1.1-0.002Pg2) * (2.45-0.007Pg2+4.1)= 0.007Pg2 + 4.1
(1.1-0.002Pg2)* (6.55-0.007Pg2) = 0.007Pg2 + 4.1
7.205-0.0077Pg2-0.0131Pg2 = 0.007Pg2 + 4.1
3.105= 0.0278Pg2
Pg2= 111.7 MW
Pg1 = (350-111.7) = 238.3 MW