# Analysis of Six Active Power Control Strategies of Interconnected Grids with VSC-HVDC
## 2 Identify PGs (Participating Generators) with the GVIF Index  
As shown in Figure 1, areas 1 and 2 are interconnected by a VSC-HVDC link. The initial DC power direction is from area 1 to area 2, so the converter is used to provide auxiliary service for area 2. This grid structure may be in the form of an interconnection link between countries or between regions [18]. If multiple generators are connected in parallel to each area, it is difficult to detect which generator contributes to incremental power according to the converter power change. The TSOs must determine which generators respond to the converter control, and this process is needed to distinguish the participating generators (PGs) group.  
A traditional synchronous generator consists of a governor and a prime mover to support frequency regulation. The simplified first-order differential equation of the dynamic generator model is shown in Equations (1) and (2), where \(P_{v}\) is the valve position of the governor; \(P_{ref}\) is the power reference of governor; \(R\) is the droop value; \(P_{m}\) is the prime mover output power; and \(T_{G}\) and \(T_{P}\) are the time constants of the governor and prime mover, respectively [22].  
\[\frac{d\Delta P_{v}}{dt}=-\frac{\Delta P_{v}}{T_{G}}+\frac{\Delta P_{ref}}{T_{ G}}-\frac{1}{T_{G}R}\Delta f. \tag{1}\]  
\[\frac{d\Delta P_{m}}{dt}=-\frac{\Delta P_{m}}{T_{P}}+\frac{\Delta P_{v}}{T_{ P}}. \tag{2}\]  
Figure 1: Two interconnected grids with a voltage-source converter (VSC)-based high-voltage DC (HVDC).  
Based on Equations (1) and (2), the generators react to grid frequency change as \(\Delta f\). If all generators have the same frequency droop value, an individual generator increases in the same MW power in a liner decrease in speed corresponding to the percent droop selected and no-load frequency. However, in the real grid operation, the frequency measurement result as \(\Delta f\) is slightly different at each region at the same time; thus, the \(\Delta P_{v}\) and \(\Delta P_{m}\) were made unlike the expected values. During the dynamic state, the generator output power is mainly determined by the droop value as \(R\), but it is also related to the distance to the point at which the frequency change occurs. As a result, the approximate incremental output of each generator with the droop slope can be estimated, but it is difficult to derive the exact incremental power from each generator. In order to consider both the governor droop value and the electrical distance between the generators and the converter, the new grouping index, referred to as the Generators-VSC Interaction Factor (GVIF) to select the PGs is implemented as follows.  
\[GVIF_{i,j}=\frac{\Delta P_{i}}{\Delta P_{j}}. \tag{3}\]  
where bus \(i\) is the generator bus connected in area 1. Bus \(j\) is the VSC-HVDC bus, and as we know, the multi-infeed HVDC system has several bus positions as \(j\geq 2\). The GVIF is the dynamic active power change of bus \(j\) over the active power change of bus \(i\). When the active power change \(\Delta P_{j}\) is 1%, the active power change ratio of bus \(i\) is the GVIF. If the generators have the same frequency-power droop value, the electrical distance is the main factor impacting the GVIF since the frequency measurement results are slightly different at each region. Thus, using the GVIF, the frequency measurement result errors could be corrected on each generator output. In the steady-state condition, since the frequency change point is always the converter bus as bus \(j\), the generators with a high GVIF index could be considered to be closer to the converter or to have a high droop value. The generator which has a zero value of GVIF does not participate in the incremental power generation. In this paper, we define the generators with GVIF \(>\) 0 as PGs, and the angle stabilities of all PGs are evaluated by the general transient stability index as angle spread in Section 5.