# Coordinated Control Strategy of CU-MTDC under Abnormal Conditions Considering Power Supply Security
## 3 Proposed Coordinated Control Strategy of CU-MTDC under Abnormal Conditions
### Calculation of the APC Converter Controller Parameters  
Take the CU-MTDC, which is shown in Figure 1 as an example; the detailed calculation procedure of the APC converter controller parameters is described. Meanwhile, the master converter outage is used as an application scenario to guarantee the security operation of the DC system under the most serious abnormal condition. The DC gird equation can be written as:  
\[\mathrm{P}=[\mathrm{U}][\mathrm{Y}]\mathrm{U} \tag{14}\]  
where \([\mathrm{U}]_{n-1\times n-1}=diag[U_{dc2},U_{dc3},U_{dc4},\dots\ U_{dcn-1}]\) is a diagonal matrix comprised of DC bus voltage.  
As shown in Figures 4 and 5, when the VSC\({}_{i1}\) and VSC\({}_{i2}\) are set to control DC voltage, two parameters \(U_{dc1}\) and \(U_{dc1}\) are very important for control objective implementation. The detailed calculation procedure is described as follows:  
1. The calculation of \(U_{dc1}\). \(U_{dc1}\) is the starting voltage of the droop control and should be determined by the minimum DC voltage of the APC converter under normal conditions. In this paper, \(U_{dc1}\) should be calculated when the power of the wind farm is zero and APC converters output maximum power.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Criterion** & **VSC\({}_{i1}\)** & **VSC\({}_{i2}\)** & **VSC\({}_{i3}\)** \\ \hline \(\Delta P_{dc}<\Delta P_{dc1 max}\) & Droop & Constant power & Constant power \\ \(\Delta P_{dclimax}<\Delta P_{dc}<\Delta P_{dc2 max}\) & Constant power & Droop & Constant power \\ \(\Delta P_{dclimax}<\Delta P_{dc}<\Delta P_{dc13 max}\) & Constant power & Constant power & Droop \\ \(\Delta P_{dclimax}<\Delta P_{dc}<\Delta P_{dc13 max}\) & Droop & Constant power & Droop \\ \(\Delta P_{dclimax}+\Delta P_{dc13 max}<\Delta P_{dc}<\Delta P_{dc2 max}+\Delta P _{dc13 max}\) & Constant power & Droop \\ \(\Delta P_{dc12 max}+\Delta P_{dc13 max}<\Delta P_{dc}\) & Droop & Droop & Droop \\ \hline \hline \end{tabular}
\end{table}
Table 1: Coordinated distribution strategy when the number of the active power control (APC) converter is three.  
Under shared control mode, the \(U_{dcL}\) of VSC\({}_{i1}\) and VSC\({}_{i2}\) can be obtained by DC power flow calculation, and a DC voltage security margin should be reserved, which is:  
\[U_{dcL}=U_{dcL}^{*}-U_{dcx} \tag{15}\]  
where \(U_{dcL}^{*}\) is the DC voltage got from the power flow calculation, \(U_{dcx}\) is the DC voltage security margin.  
Under priority control mode, such as VSC\({}_{i1}\) priority mode, the \(U_{dcL}\) of VSC\({}_{i1}\) can be determined according to (15). The \(U_{dcL}\) of VSC\({}_{i2}\) should be confirmed along with \(U_{dcL}\) of VSC\({}_{i1}\).  
1. The calculation of \(U_{dcL}\). \(U_{dcL}\) is the cut-out DC voltage of the droop control. Under shared control mode, \(U_{dcL}\) of the two converters, which are set to control DC voltage, determines the DC unbalanced power distribution directly.  
Substitute (10) and (12) into (9), the characteristics of the APC converter can be expressed as:  
\[\left\{\begin{array}{l}U_{dc1}=\frac{(U_{dcL1}-U_{dcL1})}{(P_{ ref1}-P_{MAX1})}(f_{p}(P_{Li,jgeq})-P_{ref1})+U_{dcL1}\\ U_{dcL2}=\frac{(U_{dcL2}-U_{dcL2})}{(P_{ref2}-P_{MAX2})}(f_{p}(P_{Lg,k,lgeq})- P_{ref2})+U_{dcL2}\end{array}\right. \tag{16}\]  
According to (12), (13), (14) and (16), the controller parameters can be calculated.  
Based on the above-mentioned, under VSC\({}_{i1}\) priority mode, the selection of \(U_{dcL1}\) should consider the control margin, which is reserved for VSC\({}_{i2}\). To ensure control security, the control margin should refer to the practical requirements and not be set too small. In this paper, 3% of the rated DC voltage should be set as the security margin for DC voltage control of VSC\({}_{i2}\).  
The flowchart of complete operation mode confirmation and controller parameters calculation can be shown in Figure 6.