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• Moheddin U. Sumagayan

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Problem Solutions For POWER GENERATION OPERATION AND CONTROL

Allen J. Wood Bruce F. Wollenberg Gerald B. Sheblé

August 2013

Solutions to homeworks problems Chapter 5

Preface

We trust that these homework problem solutions will prove helpful in teaching a course with our text. If you find typographical errors please send us corrections via John Wiley.

Allen J. Wood Bruce f. Wollenberg Gerald B. Sheblé

Problem5.1 5.1 Problem

$/MBtu

$/ton

Problem 5.1, continued

Problem 5.1, continued

Problem 5.1, continued

Problem 5.1, continued

Problem 5.1, continued

$/ton

Problem 5.1, continued

$/ton

Problem 5.2 5.2 and 5.3

$

Problem 5.3

$

Problem 5.4

$

$

Problem 5.5

Problem 5.5, continued MATLAB Program to solve problem 5.5

Problem 5.5, continued

R/CCF

Problem 5.5, continued

Problem 5.6

Problem 5.6, continued

Problem 5.6, continued

Solution to problem 5.7 Solution was done by a Matlab program that was run for 15 intertions of a binary search on gamma. If students can give a gamma value above and below 4.6 then they should get full credit.

gamma = 4.6048 timestep = 1 Lambda =

345.19

P1 = 575.32 MW

P2 = 624.69 MW

Total Gen = 1200.01

431.48

P1 = 719.14 MW

P2 = 780.86 MW

Total Gen = 1499.99

timestep = 2 Lambda =

Gasconsumption =

59999 cuft

Total_coal_gen_cost =

$254443.63

1200

0

15000

25000

37500

50000

1500

Phydro Pcoal Pcost Fcost -126.667 1626.667 793813.3333 866826.7 INFEASIBLE hydro is below Pmin

Phydro Pcoal Pcost Fcost 123.3333 1376.667 568563.3333 734326.7 INFEASIBLE coal unit above Pmax

Phydro Pcoal Pcost Fcost 290 1210 439230 687660 INFEASIBLE coal unit above Pmax

Phydro Pcoal Pcost Fcost 498.3333 1001.667 301000.8333 676201.7

0

15000

25000

37500

Final Volume Phydro Pcoal Pcost Fcost 50000 706.6667 793.3333 188813.3333 620813.3 Cannot reach 50000 at 1500 AF/hour (max fill is to 43000)

The cost to operate the coal plant under the optimum hydro schedule (see bold arrows above) is 676201.7 The cost to operate the coal unit with the purchase of 60,000 cuft of natural gas is 254443.63, however the cost of the gas would have to be added to this to get the total cost. If the price of the 60,000 cuft of gas were greater than 421758.07 then purchasing the hydro plant would be better, otherwise not.

Load =

Phydro Pcoal Pcost 706.667 493.3333 73013

0

Phydro Pcoal Pcost 290 910 248430

Phydro Pcoal Pcost 456.667 743.3333 165763

Analysis:

Pcoal Pcost 0 1200 432000

Phydro Pcoal Pcost 81.6667 1118.333 375201

Phydro

15000

25000

37500

Starting Volume 50000

Problem 5.8 solution

Problem 5.9

Problem 5.9, continued

Problem 5.10

Problem 5.10, continued

$/

Problem 5.10, continued

Problem 5.10, continued

$

Problem 5.11

This problem requires the use of a computer. We have seen students solve it using hand held programmable calculators, personal computers, up to big mainframe campus computer center machines. Discourage anyone from trying to solve problem 5.11 by hand without a computer - we have yet to see it successfully done by hand.

Final Cost = $ 89977

Final Cost = $ 90477

Problem 5.11, continued

Problem 5.12

$/h

($)

Problem 5.12, continued ($)

($)

Problem 5.12, continued

($)

Problem 5.13

Problem 5.13, continued

Problem 5.14

$

Problem 5.14, continued