Page 133 - Mathematical Models and Algorithms for Power System Optimization

124 Chapter 5

5.2 Basic Ideas of Load Optimization Modeling

5.2.1 Way of Processing the Objective Function

P
(1) The objective function is to minimize (min C i P Ci ) after N 1, in which different
i2N D
weight C i is assigned to each bus load P Ci due to different load properties. Based on load
reliability requirements, cost coefficient is set as 1 (precutting), 0, or +1 (postcutting), by
which the bus LC P Ci will be minimized during the optimization calculation, and the
reliability requirements are automatically met.
P
(2) The objective function is maximized (max C i P Li ) under the given network structure
i2N D
conditions where load is supplied. The different weight C i is assigned to each bus load P Li
duetodifferentloadproperties.Basedonloadreliabilityrequirements,costcoefficientisset
as +1 (preoperating), 0, or 1 (postoperating), by which the bus load will be maximized
duringtheoptimizationcalculationwiththereliabilityrequirementsautomaticallysatisfied.

5.2.2 Way of Processing the Variable Settings and Constraints

The load optimization model is an optimal model based on the DC power flow method. The
optimization model of minimizing total curtailed load and the model of maximizing LSC are
the supplement and improvement to the static security analysis. On the basis of existing
network structure, bus load is optimized by way of setting variables described as follows:

(1) Idea of setting variables for minimizing total curtailed load: set bus output as P G ; set
variable of bus LC as P C whose upper limit is bus load P L ; P L in the bus power balance
expression is divided into two parts, P L P C, of which P C is taken as the variable of
objective function minimization.
(2) Idea of setting variables for maximizing LSC: set bus load variable as P L ; P L in the bus
power balance expression is directly taken as the variable of objective function
maximization.
Although the variables in the two models are different, the forms of constraints in the two
models are basically the same: equality constraints are power balance constraints of the
DC power flow (grid power balance, bus power balance, and branch power balance);
inequality constraints include network branch power constraint, generation bus output
constraint, and load bus capacity constraint.
(3) Except for different variables, equality constraints in the two models have basically the
same forms, including:
1. Power balance constraint (DC power flow): grid power balance, bus power balance,
and branch power balance.
2. Inequality constraint: network branch power constraint.
3. Variable constraint: generation bus output constraint, load bus capacity (or LC)
constraint, and voltage power angle variable constraint.