# An Improved Mixed AC/DC Power Flow Algorithm in Hybrid AC/DC Grids with MT-HVDC Systems
## 4 Results and Discussions
### Case 7: AC/DC Power Flow for the Large-Scale Hybrid AC/DC Grids with MT-HVDC Systems  
In order to validate and show the performance of the mixed AC/DC PF algorithm for the large-scale hybrid AC/DC grids with the integration of MT-HVDC system, the modified IEEE 39-bus test system with two four-bus MT-HVDC systems (with different colors) is simulated in MATLAB software, as shown in Figure 2. The data of the MT-HVDC systems are provided in Tables 16-17. As it can be observed from Figure 2, the IEEE 39-bus test system is divided into three areas, in which area 1 comprises of three coherent generators (G8, G9, and G10), area 2 comprises of three coherent generators (G1, G2, and G3), and area 3 comprises of four coherent generators (G4, G5, G6, and G7). The main corridors to interconnect those three areas are given as follows:  
* Area 1 to Area 2: Lines from bus 1 to bus 39, and from bus 3 to bus 4
* Area 1 to Area 3: Lines from bus 3 to bus 18, and from bus 27 to bus 17
* Area 2 to Area 3: Line from bus 14 to bus 15  
The parameters of the converter stations for the PF calculations are as follows:  
* Converter Station #1: \(P-Q\) control mode, \(P_{g}=-60\) MW and \(Q_{g}=-20\) MVAR
* Converter Station #2: \(V_{DC}-V\) control mode, \(V_{DC}=1\) p.u. and \(V=1\) p.u. * Converter Station #3: \(P-Q\) control mode, \(P_{g}=40\) MW and \(Q_{g}=40\) MVAR
* Converter Station #4: \(P-Q\) control mode, \(P_{g}=40\) MW and \(Q_{g}=40\) MVAR
* Converter Station #5: \(V_{DC}-V\) control mode, \(V_{DC}=1\) p.u. and \(V=1\) p.u. * Converter Station #6: \(P-Q\) control mode, \(P_{g}=40\) MW and \(Q_{g}=30\) MVAR
* Converter Station #7: \(P-Q\) control mode, \(P_{g}=40\) MW and \(Q_{g}=20\) MVAR
* Converter Station #8: \(P-Q\) control mode, \(P_{g}=40\) MW and \(Q_{g}=40\) MVAR  
From the operation and planning perspectives, the outage of the mentioned lines can cause entirely disconnection of the two areas from each other and accordingly, prevention of power exchange between two areas, operating in islanded mode, and instability of the AC grids. Therefore, there is a need for strengthening the power transmission lines among the mentioned areas. To do so, two four-bus MT-HVDC systems are considered to interconnect the mentioned areas together. Areas 1 and 3 are interconnected with four converter stations (CS1, CS2, CS3, and CS4) and areas 2 and 3 are interconnected with four converter stations (CS5, CS6, CS7, and CS8). Hence, in case of AC lines outage, the power can be transferred via DC links. Tables 16 and 17 show the results of AC PF on the IEEE 39-bus test system without DC grids (Case 7-1). Tables 16-17 show the obtained results of the mixed AC/DC PF calculations when MT-HVDC systems are connected to the IEEE 39-bus test system (Case 7-2). In a general view, due to the fact that by interconnecting the MT-HVDC systems to the grid, more power is required, the total generated  
active and reactive power by the generators should increase and decrease, respectively. There is no connection between the MT-HVDC systems and any of the generators. Therefore, only the voltage magnitude and angles are changed. This should be considered that each converter has its own power losses. Therefore, compared to the AC PF, the total power losses on the AC lines in the mixed AC/DC PF is increased by 0.11 MW. There are some slight changes in the total active power generated by the generator #31. However, the generated reactive power by all the generators is changed. The changes of the PF on the AC lines 1-39, 3-4, 3-18, 4-14, 14-15, 15-16, and 17-27 are significant since they are directly connected to the MT-HVDC systems. To check the changes of the PF on the other lines, the connected lines to the mentioned lines are checked and it is observed that there are some slight changes of the PF on the lines 4-5 and 13-14. Based on the obtained results, the slack converters are capable of transferring power on the DC lines based on the total demand.