Control Method for Inhibiting Chain Reaction of Commutation Failure

Due to the coupling effect between the DC/AC system as well as between different LCC-HVDC, the first commutation failure can cause a series of chain reactions, including successive commutation failure, overvoltage of the rectifier station, and subsequent commutation failure. The existing control methods for suppressing overvoltage or commutation failure cannot simultaneously meet the needs of the sending and receiving end grid of MIDC. It may expand the impact and scope of a single fault. Therefore, a commutation failure chain reaction suppression method is proposed based on the characterization of chain reaction boundary conditions. The effectiveness is verified by using the CIGRE standard test model.


Introduction
Multiple LCC-HVDCs are fed into the same area to form a MIDC system, increasing transmission capacity and improving operational flexibility.However, LCC-HVDC brings a series of challenges to power systems, especially the commutation failure (CF) [1] .The first CF may trigger subsequent CF (sub-CF) if not properly controlled.Multiple CFs may trigger LCC-HVDC blocking, causing power interruption in DC transmission.During the CF recovery process, overvoltage results from the rectifier station's reduced reactive power consumption due to a drop in DC [2] .Overvoltage may cause the renewable energy units at the sending end to tripping.Besides, due to the coupling of MIDC inverter stations, the output changes of the inverter station with CF may affect adjacent LCC-HVDC, and may also cause adjacent LCC-HVDC successive CF (suc-CF).The CF chain reaction at the sending and receiving end of MIDC expands the impact of a single fault, affecting the safety and stability of power systems.
Some studies have improved the immune ability of CF by configuring reactive power compensation devices [3] .However, this method increases costs and complicates the coordination and control between devices.Therefore, researchers improved the firing angle control [4] .However, the effectiveness of this method in suppressing CF is limited.On the other side, the existing study solves overvoltage by adding reactive power devices [5] , but the method has high costs and complex coordination.Wang et al. propose improving VDCOL to suppress overvoltage [6] .However, the electric quantities of rectifier and inverter stations interact with each other.The influence of control on the other side is ignored in existing research and may intensify the chain reaction.
A control method to inhibit the CF chain reaction is presented.A current control method is put forward on the grounds of the mechanism and boundary conditions of the CF chain.

Mechanism of CF chain reaction
When the receiving end grid experiences an AC fault, the voltage of the inverter falls, leading to the first CF.The control system responds to facilitate the recovery of the first CF.Accordingly, the DC system has gone through three stages:  Stage I is the rise stage of DC.At time t 0 , the i-th LCC-HVDC's first CF results in a sharp rise in DC.During Stage I, the rectifier station's reactive power consumption is enlarged due to a rise in DC.The black line in Figure 1(a) illustrates how the growing reactive power exchange between the inverter stations generates a continual decrease in the j-th LCC-HVDC's voltage.In turn, it causes a drop in extinction angle (EA) of j-th LCC-HVDC and results in subsequent CF at t 1 .
In Stage II, DC is reduced as controllers respond.Therefore, reactive power consumption is reduced.Considering the slow response speed of reactive power compensation equipment compared to the LCC-HVDC control system, excessive reactive power has occurred at the sending end, causing overvoltage, as shown in Figure 1(c).In Stage Ⅲ, the converter stations return to normal operation.However, when the fault is not removed promptly or the control response is insufficient, the subsequent CF may occur.
In MIDC, CF evolves into a special chain reaction process with successive CF, overvoltage, and subsequent CF.The chain reaction of CF generates multiple power shocks and threatens the transient voltage stability.

DC current to avoid subsequent CF
Based on CEAC, the firing advance angle change is written as: where the subscript "i" represents the i-th LCC-HVDC; ref  is the initial value of EA; pi K and si T are parameters of the PI controller for CEAC.
According to (1)(1), it can be inferred that: where γ k is the decreasing slope of extinction angle under CEAC.By integrating equation( 2), the firing advance angle can be derived: where 1 C is an integral constant depending on the normal operation state.By combining the control equation of VDCOL and (3)(3), DC voltage is: where where U Li is the AC voltage of the inverter; T i is the transformer ratio; N i is the number of inverters; X ri is the commutation reactance; the subscript "N" represents the rated value; k i , U dh and I dh are parameters for VDCOL; k i is the regulation slope of DC.
To prevent CF, the extinction angle needs to be maintained above the critical value  th .According to (4)(4), the DC current range to avoid subsequent CF is as follows: where I di, sc is the critical DC to avoid subsequent CF; a i  U dNi U dh , b i  I dNi I dh .

DC current to avoid overvoltage
The consumed reactive power of the converter station is: where P d  U d I d is the active power of the converter station.The change in reactive power meets: where the subscript " R " represents the rectifier side; Q dR,i is the reactive power consumption; Q cR,i is the reactive power supplied by filters; Q ACR,i is the reactive power from the AC grid to the converter station.AC voltage of the rectifier is expressed as: where S cr is the short-circuit capacity of the AC grid.
According to ( 6), (7), and (8), to avoid overvoltage at the rectifier station causing high-voltage disconnection of the renewable energy group, the DC should meet the following requirements: where U pcc, max is the threshold for HVRT of renewable energy units; R d is the resistance of the DC transmission line.
By solving (9), the critical DC I di, ov to avoid overvoltage can be obtained.The DC current range preventing disconnection of renewable energy group caused by high-voltage is:

DC current to avoid successive CF
The reactive power of the inverter meets the following relationship: where Q exj is reactive power between LCC-HVDCs; the subscript "I" represents the inverter station.AC voltage of the j-th LCC-HVDC of inverter meets: where the subscript "j" represents the j-th LCC-HVDC; the subscript "f" represents the electrical quantity after the fault; LNi U and LNj U are the rated AC voltage values; ij MIIF is the multi-feed interaction factor.Under the influence of coupling between inverter stations, the change in AC voltage of the j-th LCC-HVDC inverter station is: The AC voltage can be denoted by: where U Lj , U dj ,  j , and  j are AC voltage, DC voltage, extinction angle, and firing advance angle before fault, respectively.By combining ( 6) and (11-14), it can be obtained that the safe range of DC current to prevent successive CF:   Under method 2, the 2nd LCC-HVDC suffers the successive CF.Under method 1, there is no successive CF, and the AC voltage is maintained below 1.1 p.u. as shown in Figure 2(c).As shown in Figure 2, method 1 successfully avoids successive CF and effectively inhibits overvoltage and subsequent CF.

Conclusion
In response to the impact of CF on AC/DC systems and different HVDC transmission systems, this paper delves into the generation mechanism of rectifier station overvoltage, subsequent CF, and successive CF after the CF.On the foundation of analyzing boundary conditions, a control method to

Figure 1 .
Figure 1.CF chain reaction.StageI is the rise stage of DC.At time t 0 , the i-th LCC-HVDC's first CF results in a sharp rise in DC.During Stage I, the rectifier station's reactive power consumption is enlarged due to a rise in DC.The black line in Figure1(a) illustrates how the growing reactive power exchange between the inverter stations generates a continual decrease in the j-th LCC-HVDC's voltage.In turn, it causes a drop in extinction angle (EA) of j-th LCC-HVDC and results in subsequent CF at t 1 .In Stage II, DC is reduced as controllers respond.Therefore, reactive power consumption is reduced.Considering the slow response speed of reactive power compensation equipment compared to the LCC-HVDC control system, excessive reactive power has occurred at the sending end, causing overvoltage, as shown in Figure1(c).In Stage Ⅲ, the converter stations return to normal operation.However, when the fault is not removed promptly or the control response is insufficient, the subsequent CF may occur.In MIDC, CF evolves into a special chain reaction process with successive CF, overvoltage, and subsequent CF.The chain reaction of CF generates multiple power shocks and threatens the transient voltage stability.

4 .
Current command value to suppress chain reactionWhen AC fault is detectable, the added control is activated.I di, sc and I d, cj are calculated by (5) and (15).I di, ov is calculated by (9).When I di, sc and I d, cj are higher than I di, ov , the command value of DC is set to I di, ov .When I di, sc and I d, cj are lower than I di, ov , the command value of DC is set to min [I di, sc , I d, cj ].5.Case studies A dual-feed HVDC is constructed in PSCAD.Method 1 represents the proposed control.Method 2 represents the traditional control of the CIGRE test model.(a) Method 1 (b) Method 2 (c) AC voltage of the rectifier

Figure 2 .
Figure 2. Electrical quantities under different control methods.The AC fault happens in the 1st LCC-HVDC converter bus at 1 second.The EA of two LCC-HVDC under different control is displayed in Figure 2 (a) and (b).The first CF occurs in 1st LCC-HVDC.Under method 2, the 2nd LCC-HVDC suffers the successive CF.Under method 1, there is no successive CF, and the AC voltage is maintained below 1.1 p.u. as shown in Figure2(c).As shown in Figure2, method 1 successfully avoids successive CF and effectively inhibits overvoltage and subsequent CF.