Page 31 - Mathematical Models and Algorithms for Power System Optimization

Daily Economic Dispatch Optimization With Pumped Storage Plant 21

X min X Y max (2.4)

Y min Y Y max (2.5)
where Eq. (2.1) is a linear objective function, Eq. (2.2) is an equality constraint, Eq. (2.3) is an
inequality constraint, Eq. (2.4) is a continuous variable constraint, and Eq. (2.5) is a constraint
with integer variables. Problem P is a standard mixed-integer programming model, which can
be solved with a standard mixed-integer programming method. If integer constraint Eq. (2.5) is
relaxed, then the model can also be solved with a standard linear programming method, so that
an approximate optimal solution can be efficiently obtained.
Daily multiarea economic dispatch optimization with a pumped storage plant is designed to
minimize total fuel cost of a system under certain constraints, so as to make full use of the peak
regulating ability of the pumped storage plant. The calculation cycle of the daily dispatch
schedule with a pumped storage plant is 24D (D¼1, 2, 4, when D¼1, time interval¼60min,
D¼2, time interval¼30 min, D¼4, time interval¼15min) periods, where both objective
function and constraint functions are linear functions, and the variables are divided into
continuous and integer ones, so the following programming model can be formed:
Problem PZ:

Linear objective function

" #
N T
X X
min C i tðÞX i tðÞ + F i Y i (2.6)
i¼1 t¼1
Constraint equations:

(1) Load balance constraint in each time period (equality constraint with the total number of
24D, D¼1, 2, 4)

N
X
X i tðÞ + P pg tðÞ 165Y pp tðÞ ¼ PL tðÞ, t ¼ 1,…,24D (2.7)
i¼1
(2) Generated output constraint of each plant in each time period (inequality constraints with
the total number of N PLANT 24D)
X
SI j X i tðÞ SA j , j ¼ 1,…,N PLANT ; t ¼ 1,…,24D (2.8)
i2NP
(3) Generated energy constraint of the power plant in each time period (inequality constraints
with the total number of N PLANT )

24D
X X
SIT j X i tðÞ SAT j , j ¼ 1,…,N PLANT (2.9)
i2NP t¼1