Page 27 - Mathematical Models and Algorithms for Power System Optimization

Daily Economic Dispatch Optimization With Pumped Storage Plant 17

storage plant will operate at peak and valley periods as long as possible, so as to better
shift peak load, thus improving the economic efficiency, operation security, and
stability of the overall power system.

2.2.2 Way of Processing Variables and Constraints

The basic steps to develop a mathematical model are to introduce the number of key variables
as few as possible, so as to reduce the complexity of the solution algorithm, by which to form an
expression of constraints that can reflect the physical meaning. The basic idea of developing a
mathematical model is to avoid introducing excessive variables, so as to reduce the complexity
of the solution algorithm; based upon the variables, constraints have to be analyzed from
physical meanings to mathematical expressions. However, the number of variables and
constraints shall be matched, because linear programming basically requires the number of
variables to be larger than that of its constraints.

Generation output of units is determined as the most crucial variable of the mathematical
model, which must satisfy the upper and lower limits in various time periods through an
analysis of the problem of daily multiarea economic dispatch with a pumped storage plant. By
contrast, although other outputs of power plants and areas, and power plant generating capacity
also have to satisfy their respective upper and lower limits, all of them can be indirectly derived
by summing up the generation output of all units in various time periods.

Theconstraintsforpracticaloperationthroughtheanalysisoftheproblemaredefinedasfollows:

(1) Constraints of all plants: hourly load balancing in a day, hourly output of all areas in a day,
hourly output of all plants, total generated energy of all plants in a day.
(2) Constraints of the pumped storage plant: hourly reservoir capacity, reservoir water
balancing, generation output, and pumping output. As previously mentioned, the most
crucial variable is generation output of units. As long as the identification of areas and
plants where generation units belong are given, the total output of generating units in
different areas or in various time periods can be summed up, respectively.

On the basis of taking the generation output of respective units as the key decision variable,
other constraints are processed as follows:

(1) Constraints for hourly load balancing in a day: basic expression is that hourly generation is
equal to hourly load. That is, sum up the generation output of all units in each hour, then
make the summation equal to the forecasted value of the daily load in each hour.
(2) Constraints for output of all plants in each hour: basic expression is that the sum of unit
generation daily is within the given limits. That is, sum up the total generation output of all
units of each plant in each hour, then make the summation satisfy the upper and lower
limits of the power plant.