## 3 Upper-Level Multiple Resources Coordinated Optimization Modeling and Solving  
### Resources Modeling  
For the receiving-end power grid with multi-infeed HVDC, after one HVDC line blocking occurs, the remaining HVDC lines can increase the power supply through DC modulation to reduce the active power imbalance of the receiving-end power grid. The overload capacity of a HVDC line is inversely proportional to the duration, and DC modulation also requires a power supply at the sending-end grid to increase their power generation output. So only the long-time overload capacity is considered in this work. The response process characteristic of HVDC emergency power support is shown in Figure 3, and it can be expressed as  
\[P_{\text{dc},i}(t)=P_{\text{dc},i}^{0}+\min(K_{\text{dc},i}(t-t_{\text{f}}-t_ {\text{st}}^{\text{dc}}),k_{\text{dc},i}P_{\text{dc},i}^{0}) \tag{1}\]  
where \(P_{\text{dc},0}\) is the initial operating power of the HVDC line. \(K_{\text{dc},i}\) is the power increase rate. \(t_{\text{f}}\) is the time when the disturbance occurs; \(t_{\text{st}}^{\text{dc}}\) is the time duration from disturbance occurrence to the starting point of the HVDC power increase, that is, the whole group action time of HVDC line. \(k_{\text{dc},i}\) is the maximum increment of the HVDC line power. ELS can rapidly reduce load power by directly cutting off the outlet or the substation. Therefore, the response process characteristic of ELS can be described by a step function, as shown in Figure 4. The load power of the bus where the ELS station is located can be expressed as  
\[P_{\text{tl},i}(t)=\left\{ \begin{array}{ll}P_{\text{tl},i}^{0},&t\leq t_{ \text{f}}+t_{\text{st}}^{\text{tl}}+t_{\text{br}}^{\text{tl}}\\ P_{\text{tl},i}^{0}-P_{\text{tl},i},&t>t_{\text{f}}+t_{\text{st}}^{\text{tl}}+ t_{\text{br}}^{\text{tl}}\end{array} \right. \tag{2}\]  
Figure 3: Illustration of the HVDC emergency power support. where \(P_{\rm tl,0}\) is the initial load power of the bus, \(P_{\rm tl}\) is the shedding power, \(t_{\rm 1,tl}\) is the time duration from disturbance occurrence to the starting point of circuit breaker action, that is, the whole group action time of ELS, and \(t_{\rm br}^{\rm tl}\) is the circuit breaker tripping duration. Compared with ELS, the control instructions go through more intermediate levels from the grid dispatching center to the DER devices, and the communication delay of the DER device using 4G/5G instead of optical fiber is longer than that of the HVDC and ELS station. On the other hand, for ON/OFF-type DER devices, the load-switch tripping time is larger than that of the high-voltage circuit breaker, and for converter type devices, there is a transition time from charging to discharging state switching. Therefore, the response speed of VEP is slower than that of ELS. If the number of DER devices in VPP is large, the response of VPP has an obvious transition process due to the difference in communication delay and response speed between DER devices. Taking a VPP containing switching-type and converter-type devices as an example, the response process of the VPP is shown in Figure 5. DER\({}_{1}\) and DER\({}_{2}\) are ON/OFF-type devices, DER\({}_{3}\) and DER\({}_{4}\) are converters with reverse discharge ability. \(t_{2,i}\) is the response time of the DER device; \(t_{3,1}\) and \(t_{3,2}\) correspond to the tripping completion time of DER\({}_{1}\) and DER\({}_{2}\) load switches, respectively. \(t_{3,3}\) and \(t_{3,4}\) correspond to the state switching completion time of DER\({}_{3}\) and DER\({}_{4}\) converters, respectively. For the response process of VPP, \(t_{\rm st,1}^{\rm vpp}\) is the time duration from disturbance occurrence to the instruction issued by the VPP control center. After \(t_{\rm de}^{\rm vpp}\), the fastest DER device completes the response, which is the starting time of the VPP response process.