Page 26 - Mathematical Models and Algorithms for Power System Optimization

16 Chapter 2

2.2.1 Way of Processing Objective Function

As previously mentioned, the problem of the daily multiarea economic dispatch with pumped
storage plant is to minimize total fuel costs under the condition of satisfying all security
operations, using the specific peak regulation capacity of the pumped storage plant as
rationally as possible. Minimizing total fuel costs means that, on the premise of assuring
system security, as few generating units as possible of the thermal power plant shall be put
into operation, whereas as many generating units as possible of the hydropower plants and
pumped storage plant shall be put into operation. Because the problem will be formulated as a
minimization problem of a linear programming, where the total cost is equal to the sum of
c i *x i , the basic idea of setting a cost coefficient is to make the decision variables x i contribute
to the total cost as minimally as possible within the feasible solutions; the details are
explained as follows:

(1) Setting of cost coefficient for units of thermal power plant: the practical startup and
shutdown cost coefficients of thermal units in the different periods are directly used (i.e., c i
is set as the positive value), by which the decision variables x i of thermal units will make
the total cost as minimally as possible within the feasible solutions (the output of thermal
units will certainly be as small as possible).
(2) Setting of cost coefficient for units of hydropower plant: the startup and shutdown cost
coefficients of hydro units in different time periods are basically ignored (i.e., c i is set as
zero for the generating costs of hydro units), by which the decision variable x i of the hydro
units will not have any impact on the total cost within the feasible solutions (the output of
hydro units will certainly be as large as possible).
(3) Setting of cost coefficient of units of pumped storage plant: with the objective to make the
pumped storage plant pump more water at the valley load and to generate more electricity
at the peak load, so as to smooth the equivalent load curve after the optimization
calculation, the concept of virtual pumped storage cost coefficient is introduced, which is
calculated through the following steps:
1. Calculate the average load of the given load curve.
2. Calculate the difference sequence between the given load curve and the average load.
3. Take the negative value of the difference sequence as the cost coefficient of the
pumped storage plant under pumping conditions.
4. Take the minus of the positive value of the difference sequence as the cost coefficient
(c i is a negative value for pumped storage plant under the specific generating
conditions).
Because the virtual cost coefficient of the pumped storage plant is a negative value
(less than zero), which could automatically reduce the value of the objective function
when solving the linear programming, the larger peak-valley load difference, the less
the objective function value. Therefore, within the feasible solutions, the pumped