Page 33 - Mathematical Models and Algorithms for Power System Optimization

Daily Economic Dispatch Optimization With Pumped Storage Plant 23

P imin X i tðÞ P imax (2.13)

(8) Generated output constraint of the pumped storage plant in each time period (continuous
variable constraints with the total number of 24D)

(2.14)
P pg min P pg t ðÞ P pg max

(9) Pumping output of the pumped storage plant in each time period (integer variable
constraints with the total number of 24D)
1. Initial expression

0 P pp t ðÞ P pp max
2. Final expression

0 Y p tðÞ Y p max
(2.15)
Y p max ¼ P pp max =P pp unt
where Y p (t) is an integer variable.

2.3.3 Basic Structure of the Constraint Matrix

To have a certain understanding of the structure of the mathematical model and better
comprehend its complexity, the structure of the constraint matrix in this mathematical model is
specified and shown in Table 2.3.

2.4 Preprocessing of the Optimization Calculation

The daily economic operation planning problem can be solved by two solution procedures: one
is a standard mixed-integer mathematical programming method, and the other is a linear
mathematical programming method in which integer variables are relaxed first then rounded.
The relaxed problem can be solved repeatedly by the standard linear mathematical
programming method to obtain an integer solution or by random optimization method. Many
technical treatments are used before a standard linear mathematical programming method is
employed.

After having finished the conversion of practical problems into mathematical models, it does
not mean that the correct results can be obtained by simply applying the existing solution
methods or by developing new algorithms. It is necessary to preprocess the data before carrying
out a series of calculations and to consider whether some special computational demands
can be satisfied by setting data without needs to modify the mathematical model. Because
the pumped storage plant cannot operate by both pumping and generating at the same time, the
pumping variable (integer variable) and generating variable (continuous variable) are set in