Page 49 - Energize May 2022

TECHNICAL

nodes. They define a mathematical weighted measurement to is a three-phase unbalanced system. There are several single-
indicate whether a particular node has a significant contribution and two-phase branches. Because the energy storage systems
to the system voltages on average, when an energy storage device should be installed at three-phase buses, and because the
is installed at that location. Newton-Raphson method is suitable for balanced systems, all the
single- and two-phase branches are pruned, and an equivalent
Candidate bus selection three-phase balancing modification is applied. The comparison
The flow chart of the proposed methodology is depicted in of bus voltages (three-phase) per unit between original and
Figure 2. The steady state planning methodology calculates the balanced systems is shown in Table 1. The error is negligible, so
indexes once the Newton-Raphson method converges to meet the approximation is acceptable.
the requirements of the power flow. A change in the loading As in determining the placement of energy storage devices in
condition is applied at a selected node in the system and the the microgrid, the voltage sensitivity indexes are used to indicate
indexes are recalculated. After following this procedure for the best candidates of nodes, where the regulating of active and
various loading conditions, the voltage sensitivity indexes for each reactive power has a significant impact on the system voltage
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node are obtained. magnitudes. Therefore, Indexes II and IV draw more attention
Figure 3 shows curves of four indexes with respect to different and are enlarged to show details in Figures 4 and 5. Four locations
loading conditions for the four selected buses, after applying are selected as candidates: bus 828, bus 862, bus 848, and
the proposed method to the microgrid. At first glance, the four bus 858, namely as locations I – VI, respectively. The last three
curves look identical, but when zoomed-in they are different. The candidates are selected because they are the top three sensitive
explanation and analyses of the curves, as well as the selected buses in the microgrid, indicated by Indexes II and IV in Figure 3.
zoomed-in pictures, will be discussed further. Before that, it is Bus 828 is at a medium level of sensitivity selected as a candidate
important to mention that the microgrid studied in the paper to be compared. It is also the original location for energy storage
studied in [7-9].
7-9

Bus no. Original (p.u.) Average (p.u.) Error (%)
800 1.05 1.05 0
802 1.0481 1.0481 0
806 1.047 1.047 0
808 1.0253 1.0253 0
812 0.999 0.9994 0.04004
814 0.9787 0.9794 0.07152
850 0.9786 0.9794 0.08175
816 0.9784 0.9788 0.04088
824 0.9696 0.9696 0
828 0.9687 0.9691 0.04129
830 0.9517 0.9517 0
854 0.9512 0.9513 0.01051
852 0.9211 0.9215 0.04343
Figure 2: Diagram of the process used to calculate the indexes
832 0.9211 0.9215 0.04343
888 0.9035 0.9032 0.03193
890 0.883 0.8838 0.09801
858 0.9188 0.9189 0.01088
834 0.9116 0.9116 0
842 0.9158 0.9159 0.01092
844 0.9155 0.9156 0.01092
846 0.9156 0.9157 0.01092
848 0.9157 0.9158 0.01092
860 0.9154 0.9155 0.01092
836 0.9152 0.9153 0.01093
862 0.9153 0.9154 0.01093
840 0.9151 0.9152 0.01093
Summation of errors (%) 0.60106
Figure 3: Curves of four indexes for the microgrid with respect to different Table 1: Comparison of three-phase bus voltages between the original and
loading conditions balanced systems

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