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Employment of PSO algorithm to improve the neural network technique for radial distribution system state estimation


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Figure 1:

General scheme of state estimation (Husham and Ahmed, 2018).
General scheme of state estimation (Husham and Ahmed, 2018).

Figure 2:

Flow chart for the placement of PMUs for network observability.
Flow chart for the placement of PMUs for network observability.

Figure 3:

Reactive power compensation principle (Husham and Ahmed, 2018).
Reactive power compensation principle (Husham and Ahmed, 2018).

Figure 4:

Voltage bus magnitude (actual, estimated PMU, estimated PSO–NN) of IEEE 9-bus RDS.
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.
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.
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.
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.
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.
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.
Voltage bus magnitude (actual, estimated PMU, estimated PSO–NN) of IEEE 69-bus RDS.

Figure 11:

Voltage bus angle (actual, estimated PMU, estimated PSO–NN) of IEEE 69-bus RDS.
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.
Regression plots of IEEE 69-bus: (A) bus voltage magnitudes; and (B) angle bus voltage values.

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
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