Figure 6.8 – Voltages on the circuit when the DG with 0.92 leading is inserted.
4 12 14 16
0.95 1.00 1.05
PCC
Voltage (pu)
2 6 8 10
Before the DG After the DG
Source: the author.
of the voltage limits of the network.
For both leading PF values, at point 8, the voltage level remained about 1% above the reference value of 1 pu, and even the other points had an increase in the voltage level to a value above 1 pu but did not reach or exceed the maximum limit of 1.05 pu established by regulation, in this scenario, the maximum ∆V = 0.06. As for the lagging PF, the voltage levels remained below the reference of 1 pu, and on PCCs 6, 7 and 8 even below the minimum limit value of 0.95 pu. As the power was determined from scenario #1 under unitary PF, it can be stated that even with lower PFs in leading, when analyzing just a single PCC, the voltage level does not exceed the standards. This can be corroborated because the maximum power for each point of the studied grid can be given from Equation (4.3).
However, even with several DGs, almost 30% of the PCCs with a maximum power current source to regulate V∗=1 pu, the values stayed between 0.95 and 1.05 pu, within the standard limits. Thus, it is possible to assume that considering the present regulation, in which the DG should operate with power factor (PF)=1, that the proposed strategy with maximum power for regulating each PCC to V∗=1 pu, can be used to evaluate the maximum DG penetration.
6.1 RESULTS UNDER IMPEDANCE AND LOAD VARIATIONS BASED ON MONTE
Chapter 6. Results 44
0.92 1.02 1.04
PCC 2
0.94 0.96 0.98
0.90 1.00
4 6 8 10 12 14 16
Voltage (pu) Voltage (pu)
0.97 0.972 0.974 0.976 0.978 0.98 0.982 0.984
16 14 14.2 14.4 14.6 14.8 15 15.2 15.4 15.6 15.8
PCC
Figure 6.9 – Voltage variation under line impedance changing using the Monte Carlo method.
variation, random values of load and line impedance were generated within the range stipulated for each scenario. Thus, the large amount of random values generated makes it closer to obtaining an estimate of the real values of variation of each situation. These tests were made using the "rand" function in Matlab ®.
1. a variation of±10% was considered for the line parameters, as temperature changes;
2. a variation of± 100 % was considered, as the load varies according to the demand;
3. a variation in both,±10% on the line parameters and±100 % on the load impedance parameters simultaneously.
The limit of 100% for the load was chosen based on the fact that the load varies depending on the consumers’ demand, going from almost no load (0%) to a high load (100%). The variation of the line impedance parameters between the nodes is small due
only to the losses caused by temperature variations, so the limit of 10 % was chosen.
The voltage variation that was simulated with the grid impedance is shown in Figures 6.9, 6.10 and 6.11 using the Monte Carlo method as mentioned before. The three cases were considered and it is possible to observe the higher variation on the PCCs of the second branch.
The highlight in PCC 8 and PCC 16 shows that the variation is greater for the most sensitive points, due to the high equivalent impedance of these PCCs.
Although the impedance influences the sensitivity, the variation of load and line parameters does not change (see lines 12 to 16 on Figures 6.12, 6.13, 6.14, the PCCs that are more sensitive to the insertion of DG. It is possible to note the change in the sensitivity values, but it does not imply a change in the order of the PCCs’ sensitivity.
2 4 6 8 10 12 14 16 PCC
1.04 1.02 1.00 0.98 0.96 0.94 0.92 0.90 Voltage (pu)
Figure 6.10 – Voltage variation under load changing using the Monte Carlo method.
2 4 6 8 10 12 14 16
PCC 0.90
0.92 0.94 0.96 0.98 1.00 1.02 1.04
Voltage (pu)
Figure 6.11 – Voltage variation under grid parameters changing (line and load impedance) using the Monte Carlo method.
For the case with a load variation, the PCCs 9, 4, 13 and 8 changed the order of sensitivity compared to the other impedance variations and when the impedance is constant, according to the values shown in Figure 6.14. However, as there are 4 PCCs and a small variation in values, it does not influence the use of the index to indicate the most sensitive points.
For the scenario with variation of 10 % in the line parameters and 100 % in the load simultaneously, there was a change in the sensitivity levels of PCCs 7, 9, 10 and 11 (Figure 6.15) but compared with Figure 6.14, with only the load variation, there was a change in the sensitivity level of PCC 11 indicating that the line impedance variation does not have as much influence on the sensitivity of most grid’s PCCs as the load variation.
Chapter 6. Results 46
Figure 6.12 – Constant impedance.
1
11 10
12 16
15
13 2
14 39
4 6 5
8
7 L R Eg
PCC Z Z Z
1 0.0676 0.1617 0.1415 2 0.0787 0.1617 0.1415
3 0.0970 0.1617 0.1415 4 0.1062 0.1617 0.1415 5 0.1296 0.1617 0.1415 6 0.1390 0.1617 0.1415 7 0.1666 0.1617 0.1415 8 0.2095 0.1617 0.1415 9 0.1040 0.1617 0.1415 10 0.1125 0.1617 0.1415 11 0.1439 0.1617 0.1415 12 0.2266 0.1617 0.1415 13 0.2000 0.1617 0.1415 14 0.2514 0.1617 0.1415 15 0.2601 0.1617 0.1415 16 0.2944 0.1617 0.1415 Label:
Low sensibility level: Z < Z and Z < Z Medium sensibility level: Z > Z High sensibility level: Z > Z
~
~
~
Source: the author.
Figure 6.13 – Line impedance variation.
1
11 10
12 16
15
13 2
14 39
4 6 5
8
7 L R Eg
PCC Z Z Z
1 0.0676 0.1634 0.1422 2 0.0795 0.1634 0.1422
3 0.0952 0.1634 0.1422 4 0.1039 0.1634 0.1422 5 0.1292 0.1634 0.1422 6 0.1372 0.1634 0.1472 7 0.1616 0.1634 0.1472 8 0.2068 0.1634 0.1472 9 0.1044 0.1634 0.1472 10 0.1104 0.1634 0.1472 11 0.1472 0.1634 0.1472 12 0.2235 0.1634 0.1472 13 0.2139 0.1634 0.1472 14 0.2645 0.1634 0.1472 15 0.2662 0.1634 0.1472 16 0.3040 0.1634 0.1472 Label:
Low sensibility level: Z < Z and Z < Z Medium sensibility level: Z > Z High sensibility level: Z > Z
~
~
~
Source: the author.
Figure 6.14 – Load variation.
1
11 10
12 16
15
13 2
14 39
4 6 5
8
7 L R Eg
PCC Z Z Z
1 0.0676 0.1617 0.1415 2 0.0787 0.1617 0.1415
3 0.0970 0.1617 0.1415 4 0.1062 0.1617 0.1415 5 0.1296 0.1617 0.1415 6 0.1390 0.1617 0.1415 7 0.1666 0.1617 0.1415 8 0.2095 0.1617 0.1415 9 0.1040 0.1617 0.1415 10 0.1125 0.1617 0.1415 11 0.1439 0.1617 0.1415 12 0.2266 0.1617 0.1415 13 0.2000 0.1617 0.1415 14 0.2514 0.1617 0.1415 15 0.2601 0.1617 0.1415 16 0.2944 0.1617 0.1415 Label:
Low sensibility level: Z < Z and Z < Z Medium sensibility level: Z > Z High sensibility level: Z > Z
~
~
~
Source: the author.
Figure 6.15 – Load and line variation.
1
11 10
12 16
15
13 2
14 39
4 6 5
8
7 L R Eg
PCC Z Z Z
1 0.0682 0.1637 0.1418 2 0.0796 0.1637 0.1418
3 0.0950 0.1637 0.1418 4 0.1030 0.1637 0.1418 5 0.1262 0.1637 0.1418 6 0.1344 0.1637 0.1418 7 0.1593 0.1637 0.1418 8 0.2043 0.1637 0.1418 9 0.1044 0.1637 0.1418 10 0.1114 0.1637 0.1418 11 0.1492 0.1637 0.1418 12 0.2223 0.1637 0.1418 13 0.2160 0.1637 0.1418 14 0.2617 0.1637 0.1418 15 0.2736 0.1637 0.1418 16 0.3101 0.1637 0.1418 Label:
Low sensibility level: Z < Z and Z < Z Medium sensibility level: Z > Z High sensibility level: Z > Z
~
~
~
Source: the author.
48
7 CONCLUSIONS
This work presents a methodology to verify the effects of DG in an electrical system using current sources. Sensitivity indexes have been proposed based on simulation results.
It turns out that connecting the DG to a PCC affects PCCs in the same branch, and connecting multiple DGs not only regulates the voltage levels in the PCC that was inserted, but can also cause overvoltage in the other PCCs. In addition, the equivalent impedance of a PCC influences its sensitivity and the current required for voltage regulation. Three cases of line and load impedance variation were analyzed, and the PCCs of greater sensitivity did not change with these variations, although some PCCs in the circuit did change the sensitivity according to the proposed changes. An analysis was also made of the variation of the DG power factor, from 1.0 to 0.92 and 0.85 lagging and leading, showing that the sensitivity of the PCCs changes with this variation, and also changes according to the location where the DG is inserted.
With the presented indexes it is possible to analyze which points of installation of a DG cause more impact on the voltage levels of an electrical network, without the need for simulations. The impedance sensitivity index facilitates the analysis because the only necessary variable is the impedance of the network points, which is easy to obtain. The voltage sensitivity index contributes to the analysis of the voltage variation of electrical systems and the sensitivity index by power factor helps determining which points are most susceptible to voltage variation, according to the active and reactive power levels injected in the network by the DG. The proposed indexes can also be used as part of optimization algorithms for allocation and impact measurement of DG.
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