Page 40 - Mathematical Models and Algorithms for Power System Optimization

30 Chapter 2

method. Many technical treatments mentioned in Section 2.4 are used before the standard linear
mathematical programming method is employed.

2.5.1 Main Calculation Procedure

The optimization calculation procedure consists of five steps:

Step 1: Input data, to which operators may as well add some special calculation
requirements. The input data include load curve and unit parameters, such as startup and
shutdown cost, operation cost, generated output and generated energy constraints of power
plants, and output constraint of areas.
Step 2: Perform validity testing of the input data, during which operators may modify
constraint conditions to meet special calculation requirements or add some special
calculation requirements to input data.
Step 3: Form objective function, constraint function matrix, left and right hand side
constraints, upper and lower limits of variables, etc.
Step 4: Solve the problem with the standard mixed-integer programming mathematical
software, directly obtaining the mixed-integer solution.
Step 5: Output optimization calculation results.
The basic calculation flow is shown in Fig. 2.7.
The calculation of standard mixed-integer programming adopted in Step 4 is as follows:

(1) Form cost coefficient, coefficient matrix of continuous variables, coefficient matrix of
integer variables, range constraints, and variable constraints.
(2) The mixed-integer solution is directly obtained with standard MIP mathematical software.
However, this method can only be used to solve small-scale problems.

If the self-developed mixed-integer programming is adopted in Step 4 to solve the mixed-
integer programming model, calculation shall be:

(1) Relax the integer constraint.
(2) Solve with standard LP software.
(3) Round off the obtained relaxation solution and fix it at the integer value.
(4) Use standard linear programming mathematical software to obtain the mixed-integer
solution based on the fixed discrete variables.
(5) If a feasible mixed-integer solution can be obtained, then stop, otherwise return to Step 2.

2.5.2 Description of the Input Data

The input data consist of the following categories:

(1) Calculation time period card (CA), including CA identification, calculation date,
calculation day number, calculation starting time (hour), calculation ending time (hour),
print selection, and load average value deviation range (MW).