5 CASE STUDIES
5.2 Point-to-point VSC-HVDC-upgraded power systems
5.2.2 New England 39-bus network, 1 embedded VSC-HVDC link
100
101 Figure 5.21 New England test system with embedded VSC-HVDC link
During steady-state conditions, the rectifier s tation delivers 153.291 MVAr to the network so as to uphold its target voltage magnitude with a modulation index of 0.8484, whereas the inverter station operates with a modulation index of 0.8412, injecting 27.3 MVAr to the grid. In the c ase of the power flowing through the HVDC system, the active power entering the rectifier station stands at 100.869 MW and the active power leaving the inverter station takes a value of 99.667 MW. It is clear that the difference between these two powers is the total power loss incurred by the HVDC system, including the power loss in the DC cable. Taking as a reference the nominal apparent power of each converter, the total power losses stand at 0.4% of which 0.29% corresponds to the rectifier station and 0.104% to the inverter station whilst the power loss produced by Joule’s effect in the DC cable stands at 0.006%, recalling that its magnitude is dependent on the length of the DC transmission line. Table 5.7 shows the main VSC-HVDC results as given by the steady-state power-flow solution with which the dynamic simulation is started.
Table 5.7 VSC-HVDC results given by the power-flow solution
Co nverter Pgk,Pgm (MW)
Qg k ,Qg m (MVAr)
Edc (p.u.) ma
(deg)
Beq (p.u.)
OLTCs tap
lo s s
P (MW) Rectifier -100.869 153.291 1.0002 0.8484 -3.7380 1.2433 1.0252 0.8697
Inverter 99.667 27.300 1.0000 0.8412 7.9373 -0.0062 1.0044 0.3124
102
Using the information of Table 5.7, it is a starighforward matter to proceed with the calculation of the initial values for the control variables taking part in the dynamics of the VSC-HVDC link, as shown in Table 5.8; these values of the state variables are employed to initialise the dynamic simulation where the modified test network is assumed to undergo the same disturbance as that of the original network, that is, the transmission lines connecting nodes 25-2, 2-3 and 3-4 are tripped at t=0.1 s.
Table 5.8 Initial values of the STATCOM variables for the dynamic simulation
Ed cI (p.u) Id c Ia ux (p.u) Ra ux (rad) d ma R dmaI
1.000 0.4999 0.0232 0.0 0.0
Figure 5.22 shows the voltage magnitudes at several nodes following the change in the topology of the power network. During the transient period, the target voltage set point is achieved very quickly by the action of the AC-bus voltage controllers that regulate the modulation indices of the converters, as shown in Figure 5.23. The prompt action of both controllers leads to a rapid reactive power injection at both converters’ AC terminal, as seen in Figure 5.24, resulting in a very effective damping of the voltage oscillations, enabling a smooth voltage recovery throughout the grid.
Figure 5.22 Voltage performance at different nodes of the network
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.98 1 1.02 1.04 1.06
Time [s]
Voltage [p.u]
V4
V5 V14 V15
V16 V17 V18 V26
V27
103 Figure 5.23 Dynamic behaviour of the modulation indices
Figure 5.24 Reactive power generated by the VSCs of the HVDC link
The disturbance occurs in the AC system breaks the power balance in the DC link and the volt-age sags that take place at both converters’ AC terminal reduce the power being transferred through the DC link. Accordingly, the current of the rectifier Id c R drops abruptly from 0.4999 p.u. to 0.4849 p.u., as illustrated by the blue line in Figure 5.25. A momentary mismatch between both converters DC currents is then produced because the DC current cannot be instantly re-established due to the time constants involved in the current controller of the inverter station; as a result, DC voltage oscillations take place, as shown in Figure 5.26. Nevertheless, once this control-ler takes action in response to the DC voltage variations, the current Id c I starts following the DC current of the rectifier Id c R to compensate for the voltage drop, as shown in Figure 5.25. This ena-bles a speedy recovery of the DC link voltages. It should be remarked that given that the cable resistance is relatively small in this case, so is the voltage drop along the DC transmission line.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.84 0.845 0.85 0.855 0.86 0.865
Time [s]
Modulation indices
m
aR
m
aI
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.5 1 1.5 2
Time [s]
Reactive power [p.u]
Qg k
Qg m
104
Notice the differences that exist between the performance of the v oltages Ed cR,Ed cI and the v olt-ages EdcRx,EdcIx; the voltage oscillations of EdcRx and EdcIxare smoother due to the damping effect of the DC inductors.
Figure 5.25 DC current behaviour of the rectifier and inverter
Figure 5.26 DC voltage behaviour of the VSC-HVDC system
The s imulation results for the active powers and the DC power transfer through the HVDC link, following the disconnection of the transmission lines, are illustrated in Figure 5.27. The blue line represents the active power entering to the high-voltage side of the OLTC transformer coupled to the rectifier station whereas the green line is the active power leaving the high-voltage side of the OLTC transformer c oupled to the inverter station. The difference between both powers represents the total power losses incurred by the VSC-HVDC link, including those incurred by the DC link. The DC power transfer Pd c R is also shown in the same graph. Since the voltage and current controls have been proven to operate quite efficiently, as illustrated in Figure 5.25 and Figure 5.26, then a fast power recovery is achieved in spite of the relatively severe disturbance occurred in the power network. Given that the power flowing from the rectifier towards the inverter station has been
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.485 0.49 0.495 0.5 0.505
Time [s]
DC current [p.u]
-IdcR
I
dcI
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.997 0.998 0.999 1 1.001 1.002
Time [s]
DC voltage [p.u]
E
dcR
E
dcR x
E
dcI
E
dcIx
105 brought back to its initial target power transfer of Ps c h= 1.0 p.u., the deviation of the power angle
R experiences a marginal increase, as can be seen in Figure 5.28. This is to agree with the new steady-state conditions where different currents and, therefore, active power losses are incurred.
Figure 5.28 also s hows the performance of the phase-shifting angles for the rectifier and inverter converters. As expected, such angles follow the same pattern as those obtained for the voltage angles of the network at the nodes where the VSC-HVDC system is connected.
Figure 5.27 AC active powers and DC power behaviour of the HVDC link
Figure 5.28 Dynamic performance of the various angles involved in the HVDC link