Question

Power economic schedule, economic dispatch question

Problem 02) The system to be studied consists of two units as described as follows. Assume that the fuel inputs in MBtu per hour for units 1 and 2, which are both on-line, are given by H = 8P+0.024P2 + 80 H, = 6P, +0.04P + 120 Where, H = fuel input to unitn in MBtu per hour (millions of Btu per hour) (n = 1,2) Pr = unit output in megawatts (n = 1,2) The minimum loading of each unit is 20 MW and that the maximum loading is 100 MW and the cost of fuel is $1.5/MBtu. These two units plans to supply a daily load cycle for 24-hours as follows: Time period (time band) 1-6 6-18 18-24 Load (MW) 50 150 50 a. What is the economic schedule for the period of 24-h (1-6, 6-18, 18-24) for both units based on the daily load cycle? Would it be more economical to keep both units in service for this 24-h period or to remove one of the units from service? b. Fill the following table. Calculates the power generation dispatch of each generation units. Load (MW) Pi P2 Total cost Time period 1-6 6-18 18-24 150 50

Answer 1

from the given data H, = 8P, +0.024 PM +80 -->0 Hy = 6P2+ 0.048XX+120 > 0 minimum load of P = 20 MW Maximum load of each unit = 100 mW. cost of fuel is =$15/MB tu. Time period i Load(MED) 1-6 + Pi=50 6-18 50 150 50 O - 18-24 Pitb2 = 150 Pitta - SD + The incremental production costs of both the units are di = 8+0.048P, $mw br. dH2 = 6+ 0.08 P2 $mw hr. ap2 Now for of the units Economic operation dhi dHz ap, apo

8 + 0.048P = 6+ 0.08 P2 0.048P,-0.08P2 = -2 Pit P2 = 50 -> ☺ ① giver value. from &o P = 15.625 mwl But Pimin = 2040 P2 = 34. 375 m ) Pemax = 100mw So in this case P. is off state. . B is. On State for Economic view, Calculations: Now cost of generalioni = H, the (Cose Pi= 15.625 H,= 8x153625 +-0.024x15628+80 = 210.05 P2 = 34.375 + H, = 6X34.375 +0.04X34.375°+120 = 373-5|| Hi+H2 564.36 Case & Pizo le for Economic vierd. P2 = 50 J Hy = 50x6 + 0.04xsor +20 - 320$t. 520 million Bte per hor. case is not perfeved Crompare to case 2).

> 0 0.048P, -0.08P2 =-2 Pites = 150 g P2 = 71.875 6 both ) the limits are exist Pruun & pray. .: H= 8X78.125 +0.024 x 76.125"+80 = $51.48 He = 6*71.975 +0.04x71.878 +120 = 75729 Hit-H, - 1609:37 Hith, = 1609.37 million Buper hr. The duration of 1 1. Told cost = (1-6) hr P, = off , P2=ON. Generating units. ( for Economic (6-18) hr Pi=ON ,P2=ON - Schedule CIF --24) hr P, = 0ft , P2= ON - of daily cycle Total cost = [620 x filter + (69.39)12 +60X6)•s = (25,552.44)*1:5 - 38,328.66 %.

time peated Load (MW) PI P2 total cost olo 4680 $ 6-18 150 / 78.125 711835-19312.448 46508 18-12