# Coordinated Control Strategy of CU-MTDC under Abnormal Conditions Considering Power Supply Security
## 3 Proposed Coordinated Control Strategy of CU-MTDC under Abnormal Conditions
### Unbalanced Power Coordinated Distribution Strategy Considering Power Supply Security  
When the system DC voltage is out of control, the proposed unbalanced power coordinated distribution strategy will start immediately. The detailed implementation procedure can be divided into three steps, as follows:  
Step 1: Calculate the unbalanced power of the DC system Assuming M converters operate under rectifier mode, and then the DC unbalanced power can be calculated:  
\[\Delta P_{dc}=\sum_{m=1}^{M}\Delta P_{m} \tag{4}\]  
where \(\Delta P_{dc}\) and \(\Delta P_{m}\) are the DC unbalanced power and active power variation of rectifier converter \(m\), respectively. Step 2: Calculate the maximum regulation capacity of every APC converter  
According to the power flow calculation method, the maximum allowable value of the APC converter active power can be written as:  
\[P_{MAXn}=P_{refmax} \tag{5}\]  
where \(P_{refmax}\) is the maximum active power reference value of the APC converter \(n\) when the active power of interconnected critical line will not exceed the limit value. The maximum regulation capacity of converter \(n\) can be expressed as:  
\[\Delta P_{dcmax}=P_{MAXn}-P_{refn} \tag{6}\]  
Step 3: Compare \(\Delta P_{dc}\) with \(\Delta P_{dcmax}\) and confirm operation mode  
After comparing \(\Delta P_{dc}\) with \(\Delta P_{dcmax}\), the operation modes of the APC converters are confirmed based on the proposed two scenarios. Because two converters participating in the DC unbalanced power regulation is the most basic and common operation mode in the system, this mode is studied first in this paper. To facilitate analysis, VSC\({}_{il}\) and VSC\({}_{i2}\) of CU-MTDC, which are shown in Figure 1, are set to control DC voltage after the DC unbalanced power exceeds the system regulation capacity of the master converter and auxiliary converter. 1. Priority control mode: As shown in Figure 1, the control mode can be further divided into VSC\({}_{i1}\) priority mode and VSC\({}_{i2}\) priority mode. Because the two modes have a similar calculation procedure, only the VSC\({}_{i1}\) priority mode is introduced in detail and is shown in Figure 4.  
Assuming \(\Delta P_{dc1 max}>\Delta P_{dc2 max}\), the judgment process is introduced as follows:  
Under this condition, VSC\({}_{i1}\) turns into droop control, and VSC\({}_{i2}\) keeps the initial operation mode. If (\(\Delta P_{dc2 max}<\Delta P_{dc}<\Delta P_{dc1 max}\)), the DC unbalanced power will be absorbed by VSC\({}_{i1}\), which is:  
\[\left\{ \begin{array}{c}P_{i2}=P_{ref2}\\ P_{i1}=1/k_{i1}*(U_{dc1}-U_{dc11})+P_{ref1}\end{array} \right. \tag{7}\]  
Figure 4: Control characteristics of voltage source converter (VSC)\({}_{il}\) priority mode. (**a**). \(U_{dc\cdot p}\) characteristics of VSC\({}_{i1}\). (**b**). \(U_{dc\cdot p}\) characteristics of VSC\({}_{i2}\). where \(k_{i1}\) is the droop coefficient of VSC\({}_{i1}\):  
\[k_{i1}=\frac{U_{dcLi1}-U_{dcLi1}}{P_{ref1}-P_{MAXi1}} \tag{8}\]  
It should be noticed that a backup droop control is applied in VSC\({}_{i2}\). The main responsibility of this design is to avoid DC voltage out of control in case of some accidents occur, such as information loss or wind power fluctuation. In addition, the shadow area is represented as the range of droop coefficient and can be confirmed with the requirement of the control effect. Moreover, the control margin, which is reserved for VSC\({}_{i2}\), should also be considered. If (\(\Delta P_{dc}<\Delta P_{dcLi2 max}\)), VSC\({}_{i2}\) will operate on a similar mode, and the distribution result can refer to the analysis above. (2) Shared control mode: As shown in Figure 5, under this condition, VSC\({}_{i1}\) and VSC\({}_{i2}\) jointly realize the unbalanced power distribution. If (\(\Delta P_{dcLimax}<\Delta P_{dc}<\Delta P_{dcLimax}+\Delta P_{dcLi2 max}\)), the DC unbalanced power will be distributed as follows:  
\[\left\{ \begin{array}{l}P_{i2}=1/k_{i2}*(U_{dcLi2}-U_{dcLi2})+P_{ref2}\\ P_{i1}=1/k_{i1}*(U_{dcLi1}-U_{dcLi1})+P_{ref1}\end{array} \right.