Figure 1:
General scheme of state estimation (Husham and Ahmed, 2018).
Figure 2:
Flow chart for the placement of PMUs for network observability.
Figure 3:
Reactive power compensation principle (Husham and Ahmed, 2018).
Figure 4:
Voltage bus magnitude (actual, estimated PMU, estimated PSO–NN) of IEEE 9-bus RDS.
Figure 5:
Voltage bus angle (actual, estimated PMU, estimated PSO–NN) of IEEE 9-bus RDS.
Figure 6:
Regression plots of IEEE 9 bus: (A) bus voltage magnitudes; and (B) angle bus voltage values.
Figure 7:
Voltage bus magnitude (actual, estimated PMU, estimated PSO–NN) of IEEE 33-bus RDS.
Figure 8:
Voltage bus angle (actual, estimated PMU, estimated PSO–NN) of IEEE 33-bus RDS.
Figure 9:
Regression plots of IEEE 34 bus: (A) bus voltage magnitudes; and (B) angle bus voltage values.
Figure 10:
Voltage bus magnitude (actual, estimated PMU, estimated PSO–NN) of IEEE 69-bus RDS.
Table 1.
MSE for voltage magnitudes and angle values in each test.
| VB | δ | |
|---|---|---|
| Test | MSE | MSE |
| IEEE 9 | 6e−08 | 4e−07 |
| IEEE 33 | 2.5e−07 | 4e−07 |
| IEEE 69 | 1.43e−10 | 5.5e−09 |
Figure 11:
Voltage bus angle (actual, estimated PMU, estimated PSO–NN) of IEEE 69-bus RDS.
Figure 12:
Regression plots of IEEE 69-bus: (A) bus voltage magnitudes; and (B) angle bus voltage values.