Page 38 - Mathematical Models and Algorithms for Power System Optimization

28 Chapter 2

the power plant should be shut down; for the situation in Fig. 2.6B, the lower limit of
the specified range should be reduced, or some standby units of the power plant should
be put into operation.
(2) The generated energy constraint specified for all power plants shall also be compatible
with the sum of generated output of all units of the plant, namely, it should have an
intersection with the sum of output of all units of the plant in all periods so that the
specified range is reasonable. An unreasonable range may be modified according to the
modification method for power plant output constraint previously mentioned.
(3) The generated output constraint specified for all areas shall also be compatible with the
sum of the output of all units of the plant in the area, namely, it should have an intersection
with the sum of the output of all units in the area in any period so that the specified ranges
are reasonable. An unreasonable range may be modified according to the modification
method for power plant output constraint previously mentioned.

2.4.3 Forming the Virtual Cost Function for a Pumped Storage Plant

During optimization, the cost coefficient of a pumped storage plant is normally assumed as zero
to gain the peak shift ability of the pumped storage plant. The virtual cost coefficient introduced
can make the pumped storage plant pump as much water as possible during valley load duration
and to generate power as much as possible during peak load duration.
All virtual cost coefficients for a pumped storage plant are negative and proportional to the
fluctuations of the load curve, by which a pumped storage plant can reduce the difference
between load curve and average load during the optimization procedure, so that the economy
and safety of the whole power system can be improved. The details are given as follows:
(1) Calculate average load P avg :

24D
1 X
P avg ¼ PL tðÞ
24D
i¼1
(2) Calculate differences ΔP L , between load and average load P avg :

ΔP L tðÞ ¼ P L tðÞ P avg

(3) Calculate deviation [P amin ,P amax ]:

P amin , P amax ¼ P avg ΔP L , P avg + ΔP L
(4) Set the duration when load<P amin as the duration of pumping for the pumped storage
plant, set the duration when load>P amin as the duration of generation, and set the duration
of [P amin , P amax ] as the duration of stop. If ΔP L ¼0, the pumped storage plant never stops.
(5) Calculate virtual cost coefficient C pr (t) as follows; take the cost coefficient for pump state:

C pr tðÞ ¼ PL t P avg 0ð Þ, t ¼ 1 24D