The distributed control approach using local linear control was validated for two test feeders that were based on the IEEE 13 node and IEEE 37 node radial distribution test feeders. Each feeder was equipped with three PV sources along the feeder. Each PV inverter was equipped with a local linear PV controller.
5.4.1. Results for 13-node radial distribution test feeder
The modified IEEE 13 node distribution test system is described in detail in Section 4.4 and a single line diagram can be seen in Figure 14. The test feeder used for analysis in this section had three PV generators, instead of two, connected at nodes 634, 675, and 680. The voltage fluctuations for phase A with and without the local reactive and PV sources installed at nodes 634, 675, and 680 shown in Figure 16. The voltage fluctuations are significantly reduced with the distributed local reactive power control, which is indicated by the Figure 16. The PV systems installed at nodes 634, 675, and 680 each have a rated 1600 kW real power output. The generation profiles for a 30-minute study period are shown in Figure 17. The generation profiles are derived from the one- second global irradiance record collected at National Renewable Energy Laboratory (NREL) Solar Measurement Grid in Oahu, HI [71]. The data used for this study was collected on July 20, 2010. The specific locations used for the measurements were DH3, AP1, and AP6 on the NREL measurement grid. The locations are displayed on the map in [71].
Figure 16: Phase A voltage fluctuations for the 13-node radial distribution test feeder with PV sources installed at nodes 634, 675, and 680.
Figure 17: PV generation profiles for 1600 kW systems installed at nodes 634, 675, and 680.
The voltage fluctuations are further analyzed in Table 5.1. The first column of Table 5.1 describes the type of voltage fluctuation measured. The second and third columns display the fluctuations measured for the installed PV systems with and without the control. In the first column, PU denotes per unit, MSEV denotes mean squared
0 200 400 600 800 1000 1200 1400 1600 1800 112 113 114 115 116 117 118 119 120 121 122 123 Time (s) V ol ta ge ( V )
Node 634 without control Node 634 voltage with local control Node 671 without control Node 671 voltage with local control Node 675 without control Node 675 voltage with local control
0 200 400 600 800 1000 1200 1400 1600 1800 200 400 600 800 1000 1200 1400 1600 O u tput pow er ( k W ) Time (s) PV at 632 PV at 675 PV at 680 86
voltage error from average voltage value, MaxΔV denotes the maximum local peak to peak voltage variation at node 675, and MaxVe denotes the maximum global voltage error.
The maximum global voltage error is defined as the maximum difference between the actual voltages and the average voltage values.
Table 5.1: Voltage fluctuations with and without distributed reactive power control of PV inverters installed at nodes 634, 675, and 680.
Measurement With Q control Without Q control
PU MSEV at node 675 6.05×10-7 1.93×10-4
PU MaxΔV at node 675 2.94×10-3 4.75×10-2
PU global MSEV 5.80×10-7 5.84×10-5
PU global MaxVe 6.23×10-3 3.37×10-2
The results recorded in Table 5.1 indicate that the local reactive power control reduced the local MSE measured at 675 by 99.7%. The local voltage variations were reduced by 93.8% from 5.70V to 0.35 V on a 120 V base voltage. Global MSE for voltages was reduced by 99.0% and global voltage variation by 81.5% from 4.00V to 0.75V on a 120 V base voltage. The results show that the MSE of voltages were reduced by approximately two orders of magnitudes both locally and globally. The reductions in the maximum local voltage variations at node 675 and the maximum global voltage deviations were also significant. The studies performed for the 13-node test feeder demonstrated that the distributed control approach is effective for reducing voltage fluctuations caused by intermittency of PV generations.
5.4.2. Results for 37-node radial distribution test feeder
The presented local control approach was also applied to the 37-node radial distribution test feeder, which is already described in section 4.5. The single line diagram for the test system is shown in Figure 15. The 37-node test feeder used for analysis in this section had three PV generators, instead of two, connected at nodes 727, 732, and 736. The voltage fluctuations for phase A with and without the local reactive with PV sources installed at nodes 727, 732, and 736 are shown in Figure 18. The voltage fluctuations are also significantly reduced for the 37-node test feeder with the distributed local reactive power control. The PV systems installed at nodes 727, 732, and 736 have a rated 1600 kW real power output each. The generation profiles for a different 30-minute study period are shown in Figure 19. Similar to the 13-node test feeder the generation profiles are derived from the one-second global irradiance recorded collected at NREL solar Measurement Grid at Oahu, HI [71].
Figure 18: Voltage at node 741 of the 37-node test feeder with 1600 kW PV systems installed at nodes727, 732, and 736.
0 200 400 600 800 1000 1200 1400 1600 1800 112 113 114 115 116 117 118 119 120 Time (s) V ol ta ge ( V )
With local control Without local control
Figure 19: PV generation profiles for 1600 kW systems installed at nodes727, 732, and 736.
Table 5.2: Voltage fluctuations with and without distributed reactive power control of PV inverters installed at nodes 727, 732, and 736.
Measurement With Q control Without Q control
PU MSEV at node 741 1.18×10-6 2.43×10-4
PU MaxΔV at node 741 2.84×10-3 5.33×10-2
PU global MSEV 1.30×10-6 7.90×10-5
PU global MaxVe 6.16×10-3 3.59×10-2
The voltage fluctuations are further analyzed in Table 5.2. The columns and rows of Table 5.2 are described the same way as in Table 5.1. The results indicate that the local reactive power control reduced the local MSE measured at 741 by 99.5%. The local voltage variations were reduced by 94.7% from 6.40V to 0.34 V on a 120 V base voltage. Global MSE for voltages was reduced by 98.2% and global voltage variation by 82.3%
0 200 400 600 800 1000 1200 1400 1600 1800 0 200 400 600 800 1000 1200 1400 1600 O u tput pow er ( k W ) Time (s) PV at 727 PV at 732 PV at 736 89
from 4.30V to 0.74V on a 120 V base voltage. The results show that the MSE of voltages were reduced by approximately two orders of magnitudes both locally and globally. The reductions in the maximum local voltage variations at node 675 and the maximum global voltage deviations were also significant. The studies performed for the 13-node test feeder demonstrated that the distributed control approach is effective for reducing voltage fluctuations caused by intermittency of PV generations.