Page 28 - Mathematical Models and Algorithms for Power System Optimization

18 Chapter 2

(3) Constraints for total generated energy of all plants in a day: basic expression is that daily
total generated energy of plants is within the given limits. That is, sum up the total
generation output of all units in all power plants within the total time period (one day), then
make the sum satisfy the upper and lower limits of the power plant generating capacity.
(4) Constraints for output of all areas in each hour: basic expression is that area generation is
within the given limits. That is, sum up the total generation output of all units in all power
plants of all areas in each time period, then make the sum satisfy the upper and lower
output limits of the area.
(5) Constraints for reservoir capacity of pumped storage plant in each hour: basic expression
is that hourly reservoir capacity is within the given limits. To satisfy the starting and
ending capacity of each day, the pumped storage plant must satisfy the reservoir capacity
constraint in each hour in operation. On the basis of transforming water balancing into
power balancing for the pumped storage plant, first, obtain the former by summing up
the generation output of all units of the pumped storage plant in each time period,
then obtain the later by adding up the pumping output of all units of the pumped storage
plant in each time period. Finally, obtain the difference between the former and the latter,
which have to satisfy the upper and lower limits of the reservoir capacity of the pumped
storage plant in the time period. Based on operational requirements, the output of a
pumped storage plant in each hour must be one of 0, 165, 330, 495, 660, 825, 990, 1155,
and 1320MW.
(6) Constraints for daily reservoir water balancing of the pumped storage plant: basic
expression is that hourly reservoir water is within the given limits. With reference to the
method of processing reservoir capacity, first, obtain the total generation output of all units
of the pumped storage plant in the total time period (one day), then obtain the total
pumping output of all units of the pumped storage plant in the total time period (one day),
and finally calculate the difference between total generation output and total pumping
output, which have to satisfy the daily reservoir water quantity difference of the pumped
storage plant in one day.

Based on the actual situation in the provincial power grid, in terms of calculation scale, the
number of areas is 6, the number of power plants is 30, the number of units is 100, and the
number of time periods is 24D (D¼1, 2, 4, i.e., D¼1 for one point in 1h, D¼2 for one point in
0.5h, or D¼3 for one point in 20min, to describe load). Correspondingly, the number of
constraints shall be less than 3000, and the number of continuous variables shall be 2400–7200.
The pumping condition of pumped storage units is transformed into an integer variable. The
corresponding number of discrete variables shall be 24–72.

Due to the large calculation scale with many discrete variables, it is difficult to choose a
calculation method for the studied problem. After the following special processing, the number
of integer variables may be greatly reduced from 24–72 to 9–27. The detailed processing
method is introduced as follows: