Let real and reactive power generated at bus- i be denoted by PGi and QGi respectively. Also let us denote the real and reactive power consumed at the i th th bus by PLi and QLi respectively. Then the net real power injected in bus- i is
 | (4.8) |
Let the injected power calculated by the load flow program be Pi, calc . Then the mismatch between the actual injected and calculated values is given by
 | (4.9) |
In a similar way the mismatch between the reactive power injected and calculated values is given by
 | (4.10) |
The purpose of the load flow is to minimize the above two mismatches. . However since the magnitudes of all the voltages and their angles are not known a priori, an iterative procedure must be used to estimate the bus voltages and their angles in order to calculate the mismatches. It is expected that mismatches ΔPi and ΔQi reduce with each iteration and the load flow is said to have converged when the mismatches of all the buses become less than a very small number.
For the load flow studies we shall consider the system of Fig. 4.1, which has 2 generator and 3 load buses. We define bus-1 as the slack bus while taking bus-5 as the P-V bus. Buses 2, 3 and 4 are P-Q buses. The line impedances and the line charging admittances are given in Table 4.1. Based on this data the Y bus matrix is given in Table 4.2. This matrix is formed using the same procedure as given in Section 3.1.3. It is to be noted here that the sources and their internal impedances are not considered while forming the Ybus matrix for load flow studies which deal only with the bus voltages.
Fig. 4.1 The simple power system used for load flow studies.
Table 4.1 Line impedance and line charging data of the system of Fig. 4.1.
Line (bus to bus) | Impedance | Line charging ( Y /2) |
1-2 | 0.02 + j 0.10 | j 0.030 |
1-5 | 0.05 + j 0.25 | j 0.020 |
2-3 | 0.04 + j 0.20 | j 0.025 |
2-5 | 0.05 + j 0.25 | j 0.020 |
3-4 | 0.05 + j 0.25 | j 0.020 |
3-5 | 0.08 + j 0.40 | j 0.010 |
4-5 | 0.10 + j 0.50 | j 0.075 |
Table 4.2 Ybus matrix of the system of Fig. 4.1.
1 | 2 | 3 | 4 | 5 | |
1 | 2.6923 - j 13.4115 | - 1.9231 + j 9.6154 | 0 | 0 | - 0.7692 + j 3.8462 |
2 | - 1.9231 + j 9.6154 | 3.6538 - j 18.1942 | - 0.9615 + j 4.8077 | 0 | - 0.7692 + j 3.8462 |
3 | 0 | - 0.9615 + j 4.8077 | 2.2115 - j 11.0027 | - 0.7692 + j 3.8462 | - 0.4808 + j 2.4038 |
4 | 0 | 0 | - 0.7692 + j 3.8462 | 1.1538 - j 5.6742 | - 0.3846 + j 1.9231 |
5 | - 0.7692 + j 3.8462 | - 0.7692 + j 3.8462 | - 0.4808 + j 2.4038 | - 0.3846 + j 1.9231 | 2.4038 - j 11.8942 |
The bus voltage magnitudes, their angles, the power generated and consumed at each bus are given in Table 4.3. In this table some of the voltages and their angles are given in boldface letters. This indicates that these are initial data used for starting the load flow program. The power and reactive power generated at the slack bus and the reactive power generated at the P-V bus are unknown. Therefore each of these quantities are indicated by a dash ( - ). Since we do not need these quantities for our load flow calculations, their initial estimates are not required. Also note from Fig. 4.1 that the slack bus does not contain any load while the P-V bus 5 has a local load and this is indicated in the load column.
Table 4.3 Bus voltages, power generated and load - initial data.
Bus no. | Bus voltage | Power generated | Load | |||
Magnitude (pu) | Angle (deg) | P (MW) | Q (MVAr) | P (MW) | P (MVAr) | |
1 | 1.05 | 0 | - | - | 0 | 0 |
2 | 1 | 0 | 0 | 0 | 96 | 62 |
3 | 1 | 0 | 0 | 0 | 35 | 14 |
4 | 1 | 0 | 0 | 0 | 16 | 8 |
5 | 1.02 | 0 | 48 | - | 24 | 11 |
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