# Analysis of Six Active Power Control Strategies of Interconnected Grids with VSC-HVDC
## 4 Analysis of Active Power Control Strategies
### Introduction of Step Control and Ramp-Rate Control Strategies  
As is generally known, the step control sustains its initial power in normal stable operation, then increases power at certain times, when area 2 has a frequency drop or emergency event. By contrast, the ramp-rate control has a preset ramp-rate slope (RRS), as shown in Figure 5. The power changes from one stable state to another stable state with a ramping event, and considering a discrete time representation, the ramp-rate of \(P_{\text{\tiny{PSC}}}\) at the \(k\)th instant can be determined using the following expression:  
\[RRS=\frac{dP_{\text{\tiny{PSC}}}}{dt}(k)=\frac{\left[P_{\text{\tiny{PSC}}}(k)- P_{\text{\tiny{PSC}}}(k-1)\right]}{t(k)-t(k-1)}. \tag{10}\]  
Figure 4: Two major active power control schemes: (**a**) step control (**b**) ramp-rate control with different ramp-rate slopes (RRSs).  
Figure 3: D-axis current control structure of the VSC; PI: Proportional and Integral.  
The RRS can vary depending upon \(|\Delta P_{\mathit{vsc}}(k)|\), which is the absolute value of the deviation between \(P_{\mathit{vsc}}(k-1)\) and the active power reference as \(P_{\mathit{vsc}}^{\mathit{ref}}\). If the \(|\Delta P_{\mathit{vsc}}(k)|\) is large, a high RRS is applied so as to ensure a fast response. On the other hand, if the power order as \(P_{\mathit{vsc}}^{\mathit{ref}}\) is small, a low RRS is applied to follow the final \(P_{\mathit{vsc}}^{\mathit{ref}}\) value. Such a droo characteristic is given in Equation (11) with Figure 5.  
\[RRS(k)=\left\{\begin{array}{c}RRS_{\mathit{min}},\;if\;\;|\Delta P_{\mathit{ vsc}}(k)|<\Delta P_{\mathit{min}}\\ RRS_{\mathit{min}}+\frac{DB_{\mathit{RRS}}}{DB_{\Delta P}}\times\left[|\Delta P _{\mathit{vsc}}(k)|-\Delta P_{\mathit{min}}|\right],\\ if\;\Delta P_{\mathit{min}}\leq|\Delta P_{\mathit{vsc}}(k)|\leq\Delta P_{ \mathit{max}}\\ RRS_{\mathit{max}},\;if\;|\Delta P_{\mathit{vsc}}(k)|>\Delta P_{\mathit{max}} \end{array}\right.. \tag{11}\]  
The RRS(k) is a droo-based desired ramp-rate; \(RRS_{\mathit{max}}\) and \(RRS_{\mathit{min}}\) are the max and min ramp-rate slopes of \(\Delta P_{\mathit{vsc}}\), respectively; \(DB_{\mathit{RRS}}\) is the difference between and \(RRS_{\mathit{max}}\) and \(RRS_{\mathit{min}}\); \(\Delta P_{\mathit{min}}\) and \(\Delta P_{\mathit{max}}\) are the lower and upper bands of dynamic change of active power variation; and \(DB_{\Delta P}\) is the difference between and \(\Delta P_{\mathit{min}}\) and \(\Delta P_{\mathit{max}}\). As mentioned previously, if the converter receives a high \(P_{\mathit{vsc}}^{\mathit{ref}}\) order by the TSO, the active power sharply increases with a ramp rate of \(RRS_{\mathit{max}}\), and a large active power is transferred from area 1 to area 2. Based on References [16; 17], it was confirmed that converter power control is helpful when the power system has a contingency event; therefore, this control strategy largely contributes to the frequency stability of area 2. However, we can also expect that the angle stability of area 1 could be further worsened. On the other hand, if the converter reaches \(RRS_{\mathit{min}}\) when the \(|\Delta P_{\mathit{vsc}}(k)|\) is smaller than \(\Delta P_{\mathit{min}}\), a small amount of active power is delivered to area 2, and the angle stability of the PGs in area 1 will be more improved than that in the \(RRS_{\mathit{max}}\) case.