Page 289 - Decision Making Applications in Modern Power Systems
P. 289
Particle swarm optimization applied Chapter | 10 249
candidate buses for renewable generation allocation. Section 10.5 showcases
the tangent-vector-based generators identification for reactive power
dispatch. Section 10.4 presents the PSO technique. Section 10.6 depicts the
overall methodology for PSO application to reactive power dispatch consid-
ering tangent-vector-based generation selection and renewable generation
penetration. Section 10.8 presents the obtained results for the IEEE 118-bus
system. At last, Section 10.9 draws the major conclusions of the chapter and
final remarks.
10.2 Voltage collapse indexes
Voltage collapse indexes are used to determine the system distance to
voltage stability problems. These factors are critical in power system
planning and operation analysis, as they can predict operational conditions
that should be avoided.
10.2.1 Tangent vector
The tangent vector indicates how the state variables (θ g , θ l , and V l ) behave
with the variation of a system parameter, such as load increase. This vector
identifies the most susceptible buses to voltage collapse for a given operating
point, thus being an effective tool for identifying critical buses and prevent-
ing the saddle-node bifurcation point [12].
2 3
Δθ g
6 Δλ 7
6 7 2 3
6 7 P g0
6 Δθ l 7
TV 5 6 7 5 J ½ 21 4 P l0 5 ð10:1Þ
6 Δλ 7
Q l0
6 7
6 7
4 ΔV l 5
Δλ
where P g0 , P l0 , and Q l0 are the active power generation, and active and
reactive power demands, respectively, λ is the increased parameter, and J is
the converged Jacobian matrix of the load flow.
10.2.2 PV curve
One of the most widely used methods for static stability analysis is based on
the PV curve behavior. The maximum point, P max , represents the maximum
loading that the system can support without voltage stability loss, as shown
in Fig. 10.1. This point corresponds to the load margin, which is defined as
the distance from an initial operating point of interest to the saddle-node
bifurcation point, that is, voltage collapse condition.
