Page 134 - Mathematical Models and Algorithms for Power System Optimization

Load Optimization for Power Network 125

5.3 Formulation of Load Optimization Problem

The problem of minimizing LC can be described as follows: the objective function is to
minimize the total curtailed load at load points; the optimal solution is the curtailed load and
generation output at each bus.

The problem of maximizing LSC can be described as follows: the objective function is to
maximize the load that network can supply; the optimal solution is the load and generation
output at each bus.
The LCO can be explained by a LP mathematics optimization problem:
minimize the total values of LCs; the optimal solution is the curtailment quantities
at all load buses. So, based on the standard form of mathematics
optimization, the variables, objective function, and constraint conditions are
given as follows.

This chapter gives the expressions of variables, objective function, and constraints,
respectively, in the standard form of mathematical programming.

5.3.1 Notations

Table 5.1 shows mathematical notations.

Table 5.1 Mathematical notations

Notations Descriptions
N The set of nodes in the grid, and the number of nodes is N. N : the set of nodes except slack
0
node; N D : the set of load nodes; N G : the set of generation nodes except slack node; there may
be some intersections between N D and N G. .
The set of branches in grid, and the number of nodes is b.
N B
W The weighted column vector of load nodes (specified); W i : the weight of load node i.
0
The column vector of curtailed load nodes; P Ci : the LC of node i; P Cs : the LC of slack node s; P C :
P C

0
the column vector of curtailed load nodes except slack node, P C ¼ P C .
P Cs
The column vector of nodes (specified current active power), P Li ; P Ls : the current active power
P L
0
of node i or slack node s; P L : the column vector of nodes for current active power but the slack

0
node, and P L ¼ P L .
P Ls
The column vector of nodes for active power output; P Gl : active output of bus i; P Gs : active
P G
0
output at slack bus s; P G : the active power output of node for active power output except the

0
slack node, and P G ¼ P G .
P Gs
The upper or lower limit column vector of generation nodes (specified active power output),
P G P G
P Gi P Gi : the upper or lower limit of node i for active power.
Continued