The improved adaptive droop control of VSC-MTDC have been implemented by PSACD/EMTDC, and the configuration and control system of VSC-MTDC is shown in
Figure 3. Four-terminal HVDC system is a bipolar scheme with a nominal 300 kV DC voltage. The wind farm is modeled as one aggregated PMSG driven by a single equivalent wind turbine. Parameters of DC cables and communicating transformers are displayed in
Table 1 and
Table 2 respectively. The total rated capacity of MTDC grid is about 2180 MVA, and rated ac voltage is 175 kV,
= 2.5,
= 900 MW.
5.1. Wind Speed Variation
The performance of a VSC station integrated with wind farms is investigated in the case of variable wind speed, and the simulation results are shown in
Figure 10. The gust wind speed of wind farm 1 and 2 are introduced at 1.8 s and 3.0 s with the fluctuation, slowing down from 12 to 10 m/s and ramping up from 10 to 12 m/s for wind farm 1, ramping up from 12 to 14 m/s and slowing down from 14 to 12 m/s for wind farm 2 in
Figure 10a. To collect the stochastic wind power, the ac side needs to supply constant ac voltage for the wind farm network and absorb fluctuant power automatically.
Figure 10.
Simulation result with variation wind speed. (a) Wind speed; (b) AC voltage for different wind farm; (c) Active power on wind farm side.
Figure 10.
Simulation result with variation wind speed. (a) Wind speed; (b) AC voltage for different wind farm; (c) Active power on wind farm side.
With the increased or decreased wind speed at 1.8 s and 3.0 s, it can be seen from
Figure 10b that active power generated by wind farm rose or fell near to a constant value, thus the control strategy of wind turbine can follow the wind speed fluctuation effectively. In addition, it can be seen from
Figure 10c that the ac voltage on the wind farm side was held at 13.8 kV throughout the wind speed fluctuation as the control strategy designed. Corresponding to the power variation of the VSC rectifier side due to the wind speed change, then slack converter (VSC inverter side) would take effect to balance power flow in VSC-MTDC system.
5.2. Normal Operation of VSC-MTDC
In this section, the performance of the fixed droop control and improved adaptive droop control are compared under normal operation condition. For fixed droop, droop coefficient of station #4 is equal to 0.03418, the one at station #3 is 0.01519 according to their converter ratings. In terms of improved droop control, station #4 is a benchmark converter station whose droop coefficient is constant. The one at station #3 is 0.1424 under the condition of optimal power sharing, which is much larger than the one of reference [
19]. Therefore, station #3 would share much more power transmission to reduce the copper loss of VSC-MTDC grid, and
= 2.5 was used for the improved adaptive droop control. Five different operational scenarios for inverter side converter station #3 and #4 are investigated, which mainly includes P
3ref/P
4ref = 6, 3, 1, 1/3 and 1/6.
Table 3 and
Table 4 show results of copper loss of VSC-MTDC without or with local load respectively.
Based on the above discussion, if there are two DC lines in inverter side of VSC-MTDC, the condition obtained for minimum copper loss is that P
3ref/P
4ref = R
4/R
3 = 3.001. From
Table 3 and
Table 4, the minimum copper loss is about 16.7382 MW (without local load) and 16.6435 MW (with local load) respectively when P
3ref/P
4ref = 3.0. In addition, if the capacity ratio of P
3ref/P
4ref is much greater or smaller than the optimal ratio value 3.0, all the reduced copper loss are larger than the ones of optimal ratio.
Table 3.
Copper loss of VSC-HVDC (without local load).
Table 3.
Copper loss of VSC-HVDC (without local load).
Capacity Ratio | Droop Control | Proposed Method |
---|
P3ref/P4ref = 6 | 17.0368 MW [12] | 16.8933 MW |
P3ref/P4ref = 3 | 16.8793 MW [18] | 16.7382 MW |
P3ref/P4ref = 1 | 17.3963 MW [12] | 17.1495 MW |
P3ref/P4ref = 1/3 | 18.1844 MW [12] | 17.8648 MW |
P3ref/P4ref = 1/6 | 19.0705 MW [12] | 18.7209 MW |
Table 4.
Copper loss of VSC-HVDC (with local load).
Table 4.
Copper loss of VSC-HVDC (with local load).
Capacity Ratio | Droop Control [
12] | Proposed Method |
---|
P3ref/P4ref = 6 | 17.0156 MW [12] | 16.8672 MW |
P3ref/P4ref = 3 | 16.7841 MW [18] | 16.6435 MW |
P3ref/P4ref = 1 | 17.3718 MW [12] | 17.1211 MW |
P3ref/P4ref = 1/3 | 18.1528 MW [12] | 17.8232 MW |
P3ref/P4ref = 1/6 | 19.0115 MW [12] | 18.6413 MW |
The capacity ratio of P
3ref/P
4ref is inverse proportion to optimal ratio value of the resistance of DC line 3 and 4, and improved adaptive droop control is used for VSC-MTDC without local load and the dynamic responses of four-terminal HVDC are shown in
Figure 11. It can be seen from
Figure 11a,b that converter station can follow the power reference value quickly, among which stations #1 and #2 export about 300 MW. In addition, due to the obvious DC voltage loss caused by large resistance of DC line, voltage of rectifier side (stations #1 and #2) is about 306 kV and voltage of inverter side (stations #3 and #4) is about 300 kV that is hold by the introduced common DC voltage
Udc_slack. If DC line resistance of VSC-MTDC system increases, the voltage loss would be greater.
Figure 11.
Dynamic response of normal operation (a) Active power (b) DC side voltage.
Figure 11.
Dynamic response of normal operation (a) Active power (b) DC side voltage.
5.3. Converter Outage of VSC-MTDC
In this section, the performance of the fixed droop and improved adaptive droop scheme is compared in the case of a converter outage. Unequal loading conditions are considered to demonstrate the benefit of the improved adaptive droop. If a DC fault of converter appears, the differential protection will be actuated. When a certain current level is reached, IGBTs would be blocked. As DC breakers have not been used, it is necessary to block converter stations and to use AC circuit breakers to clear the fault. In this case, both rectifier and inverter converter outages are simulated which represent two different operational scenarios.
(1) Inverter Outage: In the first case, stations #3 and #4 imports 465 MW and 155 MW, respectively. Stations #1 and #2 export around 620 MW into the DC grid. The outage of station #4 is considered. The results of copper loss of VSC-MTDC without/with local load are shown in
Table 5. It can be seen from
Table 5, the amounts of copper loss without/with local load reduced from 16.7124 MW and 16.6357 MW to 16.5131 MW and 16.4265 MW as the optimal power sharing of VSC-HVDC grid (P3ref/P4ref = 3), which are more effective for improved droop control than the ones of reference [
19]. The reason is that station #3 can adjust droop coefficient dynamic according to available headroom of converter capacity, and ensure the appropriate
P-U curve, so that reduce copper loss of four-terminal HVDC system.
Table 5.
Copper loss as outage of VSC4.
Table 5.
Copper loss as outage of VSC4.
Type | Capacity Ratio | Droop Control [19] | Proposed Method |
---|
Without local load | P3ref/P4ref = 3 | 16.7124 MW | 16.5131 MW |
With local load | P3ref/P4ref = 3 | 16.6357 MW | 16.4265 MW |
The dynamic response of four-terminal HVDC system following inverter outage is shown in
Figure 12.
Figure 12a shows that in absence of station #4, slack converter station #3 operating in voltage-power droop control mode increases its power to compensate the power imbalance of the inverter. From
Figure 12b, the power sharing of station #3 by improved adaptive droop is larger than that of fixed droop. The reduction of the copper loss is because improved droop control ensures a higher droop value than fixed droop. Variation of DC voltage at converter station #3 is shown in
Figure 12c, which is larger than common bus voltage 300 kV with very little overshoot in its transient response for fixed droop control. Therefore, the improved adaptive droop scheme can steady the DC voltage dynamics. In addition,
Figure 12d indicates that control strategy of station #3 and #4 can follow the dynamic response effectively. Then HVDC system could reach the post-outage steady-state operating point at 2.4 s. The results in this case are related to system parameters, such as the line resistances. Because the copper loss of HVDC system is square to the line resistances, if line resistances of VSC-HVDC system are much larger, much copper loss would be reduced, and then simulations will be more evident.
Figure 12.
Dynamic responses of inverter outage (a) Voltage droop control of station #3; (b) Active power of station #3; (c) DC side voltage of station #3; (d) Active power of all stations.
Figure 12.
Dynamic responses of inverter outage (a) Voltage droop control of station #3; (b) Active power of station #3; (c) DC side voltage of station #3; (d) Active power of all stations.
(2) Rectifier Outage: In order to validate the effectiveness of proposed method, the outage of station #2 is considered, only 300MW is imported into MTDC grid. The results of copper loss of VSC-MTDC without/with local load are shown in
Table 6. As we can see, if P
3ref/P
4ref = 3.0, improved adaptive droop control can reduce copper loss effectively. The minimum copper loss without/with local load are 4.2794 MW and 4.2481 MW respectively, which are smaller than those using methods in reference [
12]. The reduced amounts of copper loss are 0.2748 MW and 0.251 MW respectively in this case.
Table 6.
Copper loss of station #2.
Table 6.
Copper loss of station #2.
Type | Capacity Ratio | Droop Control [12] | Proposed Method |
---|
Without local load | P3ref/P4ref = 3 | 4.5542 MW | 4.2794 MW |
With local load | P3ref/P4ref = 3 | 4.4991 MW | 4.2481 MW |
The outage of station #2 appears at 2.3 s, and dynamic response of VSC-MTDC system with fixed droop and improved adaptive droop following the contingency are shown in
Figure 13. It is to be noted from
Figure 13a that control strategy of station #1 and #2 can follow the power dynamics. In addition, it can be seen from
Figure 13b,c that the AC voltage of station #1 can stable operate at 13.8 kV, and it has no effect on DC voltage of VSC inverter side (station #3 and 4) under condition following station #2 outage.
Figure 13.
Dynamic response of rectifier outage (a) Active power of station # 1 and 2; (b) DC side voltage of station # 3 and 4; (c) AC side voltage of station # 1.
Figure 13.
Dynamic response of rectifier outage (a) Active power of station # 1 and 2; (b) DC side voltage of station # 3 and 4; (c) AC side voltage of station # 1.
5.4. Converter Short Circuit of VSC-MTDC
In this section, the performance of the fixed droop and improved adaptive droop control is compared. If a short-circuit fault is detected in AC side close to points of common coupling (PCC), the PCC voltage will be reduced, which in turn affects voltages and currents of ac transmission grid close to PCC. To prevent destructive overcurrent, then distance protection would be actuated at this time. In this case, a three-phase short-circuit fault is introduced at 2.3 s on station #4 with a duration of 300 ms. If the short-circuit fault is detected, the AC side voltage of station #4 decreased from 13.8 kV to 7.0 kV. Dynamic responses of MTDC grid with fixed droop following the contingency are shown in
Figure 14. During the disturbance, as shown in
Figure 14a,b, DC voltage of station #4 decreased to 298 kV from 300 kV as using the improved droop control while the ones decreased to 293 kV from 300 kV as using fixed droop control method. Therefore, overshoot amount of improved droop control is less than the ones of fixed droop control. Since AC voltage of wind farm was controlled at constant value, its power output about 600 MW injected into VSC-MTDC network remained unchanged. In addition, improved droop control can hold DC voltage of station #3 at 300 kV while fixed droop control cannot realize this objective. The reason is that common DC voltage and available headroom of converter are considered as designing the control strategy of HVDC grid, and the proposed method could improve the stable operation of converter. From
Figure 14d,e, it can be seen that the control strategy of station #3 and #4 can follow the active/reactive power dynamic response, and there is small variation for power when improved droop control is employed.
Therefore, the improved droop control method can reduce the copper loss of system effectively, and improved stable operational performances under the condition of inverter outage, rectifier outage and a short-circuit fault of converter, and decrease dc voltage fluctuation and dc power oscillation caused by AC side fault of VSC-HVDC system. Therefore, the improved droop control scheme leads to desirable system performance.
Figure 14.
Dynamic response of short-circuit fault. (a) DC voltage of station # 4; (b) DC voltage of station # 3;(c) AC side voltage of station # 4; (d) Active power of VSC-MTDC; (e) Reactive power of VSC-MTDC.
Figure 14.
Dynamic response of short-circuit fault. (a) DC voltage of station # 4; (b) DC voltage of station # 3;(c) AC side voltage of station # 4; (d) Active power of VSC-MTDC; (e) Reactive power of VSC-MTDC.