Stevenson J. Power system analysis

586

CHAPTER

ECONOMIC OPERATION OF POWER SYSTEMS

At stage 1 it is determined that the least overall cumulative cost is $361,536

from stage 6 to the initial-condition combination (and vice versa). This total cost is

own in Fig. 13.14 to derive from combination X3 of stage 2, which in turn derives

from

combination x3 of stage 3, and so on back to stage 6. The least cost path

retraced in Fig. 13.14 shows that the optimal unit commitment schedule is:

Load level,

Stage

Combin;\ t ion

units

I I 100

 \)

1.2

1400

1.2.4

1600

l. 2. 4

1800

I. 2,3,4

14()()

X.1

1. 2.4

I IO()

1,2

and the total cost to supply the daily forecast load of  ig. 13.11 amounb to

$361,536 in this example.

Example 13.9 demonstrates the great reduction in computational eort

which is possible by the dynamic programming approach. As shown by the

recorded values at the nodes of Fig. 13.14, the cumulative cost function fk)

was evaluated only 27 times, which is the sum (3 + 9 +

6 + 6

+ 3) of the

interstage transitions from stage 1 to stage 6. A brute-force enumeration

approach to the same problem would have involved a total of 2916 interstage

transitions, which is the product (3 X 9 X 6 X 6 X 3) of line segments shown in

Fig. 13.14. Indeed, given the starting and ending states as in Example 13.9, and

if there were no infeasible nodes at any of the intermeiate stages, the number

of inter stage transitions between the 15 combinations x

to X

) would increase

enormously to 15 X 152 X 152 X 152 X 15

(225)4

2.563 X 10