Page 25 - Mathematical Models and Algorithms for Power System Optimization

Daily Economic Dispatch Optimization With Pumped Storage Plant 15

standard mixed-integer programming mathematical model. In the model, both objective
function and constraint function are linear, and there are two kinds of variables: continuous
variables (output of hydropower and thermal power units) and integer variables (output of
pumped storage units), each with a large calculation scale. The model in this chapter can
effectively optimize the operation of the pumped storage unit, achieve the purpose of peak load
shifting, and provide great reference to the intelligent operation of a power grid with energy
storage devices.

Section 2.2 specifically presents the basic ideas of optimization modeling for reference.
Section 2.3 proposes the optimization mathematical model for daily economic dispatch of a
pumped storage plant. Section 2.4 introduces the preprocessing work required before the
optimization calculation. Section 2.5 introduces the optimization algorithm and processes.
Section 2.6 first uses a small-scale example to verify the proposed optimization model and
algorithm, then presents and analyzes the detailed results of a large-scale practical system.

2.2 Basic Ideas of Developing an Optimization Model

A daily multiarea economic dispatch making use of the capacity of a pumped storage plant
should satisfy all related constraint conditions so as to ensure that the total power generated in
each hour by different power plants in the multiarea system can satisfy the total load of the
system (in each hour), and make the best use of the pumped storage plant’s capacity. The
practical problem should be firstly described in a familiar mathematical language before it is
transformed into a mathematical problem.

The daily multiarea economic dispatch with a pumped storage plant is expressed in
mathematical language as follows: to satisfy the daily load demand (24h) of the whole system,
the objective is to minimize the total generating cost of all generating units, while subjecting to
satisfy all kinds of constraints, such as hourly load balancing, hourly output schedule of each
area, hourly output of power plant and daily power energy schedule, hourly output limit of each
unit, and hourly limits of generated output and water quantity for the pumped storage plant, as
well as limits of initial water quantity and final water quantity for the pumped storage plant.

In general, based on practical operation conditions, the seemingly complicated practical
problem shall be transformed into a standard mixed-integer programming mathematical model,
in which both objective function and constraint function are linear ones. The objective function
is unit piecewise linear cost function. There are two kinds of variables: continuous ones and
integer ones. All variables of generating unit outputs are continuous ones.

The concrete ideas and processing methods about how to develop a mathematical model by
converting the physical problem into brief mathematical expressions (objective function and
constraints) are given as follows, as well as the method how to transform the pumping variables
of the pumped storage plant into integer variables.