Regional power grids are often connected by multiple DC lines to improve transfer capability and stability. Typical structure of multi-channel interconnected system can be found in China as shown in Figure 1. The centre grid is

Huazhong power grid, connecting northwest power grid through Hazheng/ Lingbao HVDC lines to the west, connecting Huadong power grid through Genan/Longzheng/Linfeng/Yi hua HVDC lines to the east and connecting Huabei power grid synchronously through Changnan line to the north. Besides, another three HVDC lines (Fufeng/Binjin/Jinsu) connect southwest power grid to Huadong power grid, forming a typical hybrid AC/DC power grid configuration.

The power transmission capacity between Huazhong and Huadong power grid will decrease if a block fault happened in Longzheng HVDC line. A huge amount of power electricity will be blocked in Huazhong power grid, resulting in serious power flow transferring and severe power fluctuation on Changnan transmission line. The generator angle of Huazhong power grid gradually goes ahead, islanding devicescut off the Changnan synchronous line when the connected two areas cannot remain synchronous. Figure 2 and Figure 3 shows the fluctuation of Changnan transmission line and regional generator relative angle, from which we can observe that the relative angle goes different after the fault. Changnan line opens at 2.6 second. Even though the islanding strategy can prevent the blackout, extra load and generators need to be tripped, and thus causes enormous economic losses.

N-1 security criteria shows that power system can stand certain amount of disturbance such as the single line outage. According to N-1 security criteria, if one

of the interconnected channels is cut off after a fault, the whole interconnected system can remain synchronized if the capacity of transmission power is above a certain minimum value. This minimum value can be defined as the critical transmission power (P_i,min) for stability , and can be calculated through off-line simulation as follows.

To find the P_i,min of line i and reduce the transmission power of HVDC line i gradually as a disturbance, until the connected two system cannot keep synchronized. The critical remaining transmission power is P_i,min shown in Figure 4.

Suppose line I trips for the sake of a fault. If the other paralleling HVDC lines are able to transmit more power instantly than P_i,min in total as an emergency control, then the system can remain synchronized.

Therefore, we can get the power capacity of emergency control by Equation (1).

where P_i,c indicates the capacity of emergency control. To improve the effect of emergency control, the capacity is often a little bit more than P_i,min, which means the value of should be 1.2 - 1.3.

1) When to start

If the blocking faults happen on transmission lines, not only the generation angle will become different but also its operating point will deviate from the original one. Therefore, the emergency control should take effect as quickly as possible after the fault, otherwise, it will lose its effect.

To demonstrate the viewpoint above, the case of bipolar blocking fault in Longzheng HVDC is given. Linfeng HVDC line increases transmission power at different time point as emergency control. In Figures 5-7, it is shown that the later emergency control starts, the larger the relative angle, the lower bus voltage and the more severe power fluctuation will be. Emergency control will fail if it is started later than 2 seconds after the fault.

However, take the signal transmission time into consideration, the emergency control strategy is often demonstrated 0.3 second delay after the fault [2].

2) When to stop

To diminish the bad influence when regional relative angle swings back from the peak point, the regional relative angle should be monitored by the PMU devices on both terminals of Changnan transmission line, and a signal should be sent to stop the emergency control when the relative angle reach the peak point (shown in Figure 8) at the first time.

To define the priority control order parameter, two aspects should be considered: HVDC available transmission power and the electrical distance.

1) HVDC available transmission power

HVDC available transmission power (ATP) indicates the overload capacity of non-fault DC lines. A normal HVDC line can sustain 1.5 times rated power overload for 3 to 10 seconds and 1.1 times up to 2 hours [10]. Making full use of the overload capacity can increase interconnecting transmission power after block faults happens.

2) The shortest electrical distance

The electrical distance indicates the electrical contact among different nodes in a power system [11]. However, it is hard to calculate the electrical distance accurately between two nodes if the system structure is complex. When two nodes are connected through a tie line, the electrical connection is strong and thus the electrical distance is little and vice versa. Therefore, the shortest electrical distance (SED) can be utilized to make a comparison of the electrical contact between two nodes easily [12].

The SED problem can be deemed to find the shortest path of a certain network, where the impedance is the weight of lines. Then, SED of two nodes can be calculated by Equation (2) based on the Dijkstra algorithm.

where and stand for a set of bus nodes and transmission lines separately. w(e_i) indicates the weight of e_i as impedance of transmission line.

3) Prioritycontrol parameter (PCP)

When the block faults occurs on DC transmission line, the non-fault DC line with less SED and larger ATP should be assigned with the top priority. Less SEDindicates that non-fault DC line is near to the faulted line, which can limit power flow transferring to the minimum degree. While the DC line with “larger ATP” will be likely to transfer more power, contributing the system to reach P_i,min and remain synchronized. Then a prioritycontrol parameter (PCP) for synthesizing SED and ATP together is proposed based on entropy weight method, this procedure is shown as follows.

Firstly, normalize ATP and SED parameters to the same unit as

Therefore, the ratio of the two parameters above of line i can be derived as.

Thus the entropy of ATP and SED are available below

The weight w_j can be calculated as.

Finally, the factor PCP can be obtained as.

If the loss of inter-area transmission power is so huge that a single HVDC line cannot meet the requirement, the multi-channel emergency control strategy should be applied and coordinate all non-fault paralleling HVDC lines in a proper way. However, the total overload capacity of all the non-fault paralleling HVDC lines should be above P_i,c to make sure the emergency strategy is feasible.

Since the power increase of non-fault HVDC line is costly, the principle of the emergency control is to make full use of the overload capacity of each HVDC line and minimize the number of total controlled lines. Hence, those HVDC ranked at the highestpriority should operate at 1.5 times overload and the one ranked at second assumes the rest of transmission power requirement. The flow chart for the coordination is shown in Figure 9.

A block on Fulong HVDC unipolar occurs at 1 s. Emergency control strategy

takes effect instead of traditional controlstrategy. Transmission line structure of Sichuan province is shown as Figure 11.

In this case, non-fault HVDC links are: non-fault unipolar of Fulong HVDC, Binjin HVDC and Jinping HVDC line. After calculating the SED and ATP of each link above, the priority control order can be made depending on PCP. Detailed results can be seen from Table 1.

It can be seen that the highest priority of controlling HVDC is Binjin HVDC. The P_i,min of Fufeng HVDC can be get to 1400 MW through simulation. Then P_i,c should be 1950 MW (where the value of is 1.3). Therefore, the emergency control strategy should be: Binjin HVDC line increase 1950 MW power, starting at 1.3 second and ending at 4.63 second.

Figure 12 shows the comparison among non-strategy, traditional cutting strategy and emergency power controlling strategy, from which we can see that both of the latter two strategies can preserve the system synchronous operation and avoid islanding. Additionally, the emergency controlling strategy avoid loads shedding and generator tripping, which reduces the economic and energy cost.

Simulation works on the Three Gorges multi-channel cooperating strategy is done with a block on Longzheng HVDC bipolar occurring at 1 seconds. The transmission structure and parameters are given in Figure 13 and Table 2, from which we can see the priority controlling order is Linfeng, Yihua and Genan HVDC line.

The P_i,min of Longzheng HVDC line is 1400 MW, then P_i,c should be 1820 MW (where is 1.3). Since the requirement on P_i,c is larger than the available overload of any single HVDC line, the multi-channel cooperating strategy should be established. Specifically, Linfeng and Yihua HVDC improve 1500 MW and 320 MW respectively at the same time, starting at 1.3 second and stopping at 4.12 second. From Figure 14 we can see that the multi-channel cooperating strategy prevents the system from islanding.