# Analysis of Six Active Power Control Strategies of Interconnected Grids with VSC-HVDC
## 1 Introduction  
Presently, renewable energy resources are considered a best practice in the response to global warming, and these power resources are concentrated in remote areas in order to effectively generate power. However, several instability issues arising from uneven large power generation requires TSOs (transmission system operators) to complement the grid structure [1]. Moreover, based on References [2; 3; 4], grid interconnection is emerging as an effective alternative for solving stability problems. For example, Nordic power systems in which several grids are interconnected by AC or DC links have increasingly accepted renewable energy resources, and have updated their hourly power exchange clauses [5]. This additional effort has led to the mitigation of several instability issues caused by uneven power generation, and many research works have also reported that renewable energy resources have become more accepted in many other countries [6]. In order to interconnect two different power systems, there are two options for TSOs: AC or DC lines. Nowadays, grid interconnection using an AC transmission line has a problem that increases the system complexity from the operation point of view, and may adversely decrease the system reliability. In fact, large blackouts have clearly confirmed that the close coupling of the neighboringsystems might also include the risk of uncontrolled cascading effects in large and heavily loaded systems [7]. Furthermore, the AC system is vulnerable to sub-sea transmission connections and long interconnection; thus, the DC system, which has the advantage of high controllability, has been widely deployed for grid interconnection projects [8]. Considering the grid strength as the SCR (short circuit ratio) at each point, it is well known that the LCC (line commutated converter)-based high-voltage DC (HVDC) is restricted in that the converter cannot work properly if the connected AC system is weak [9]. Conservatively, in the case of AC systems with an SCR lower than 1.5, synchronous condensers have to be installed so as to increase the SCR of the AC system. In addition, the reactive power should be compensated depending upon the power sent, which reduces the simplicity of controllability in LCCs. The voltage-source converter (VSC)-HVDC has similar stability issues; however, it offers significant advantages such as high controllability, reliability, and small size. Benefiting from the significant technical advances in insulated gate bipolar transistors (IGBT), the VSC has become a competitive alternative to the LCC, so the VSC-HVDC is more commonly deployed nowadays. In the VSC system, two main stability issues have generally been presented in detail to date:  
(1) Operation region of the VSC-HVDC  
The reactive power of the VSC-HVDC can be limited according to the AC grid voltage and the equivalent impedance. In addition, the DC voltage control and PLL (Phase-Locked Loop) can restrict the power angle to approximately 51\({}^{\circ}\) for a stable operation without the support of the dynamic reactive power [10]. In order to obtain an improved power transfer capability from the VSC-HVDC, the X/R ratio (the ratio of the system reactance to the system resistance) and the impedance angle must be considered. Therefore, the SCR index representing the grid strength is an important factor from the perspective of the capability region. (2) Dynamic performance of the VSC-HVDC  
In previous studies on the relationship between the PLL and the VSC-HVDC, many authors have mentioned that a converter with large PLL gains that is connected to a weak AC grid (2 < SCR) is prone to instabilities when subjected to a disturbance [11]. This is because the PLL that is used for the angle-reference generation can easily generate an unstable eigenvalue with high proportional gains. The AC voltage phase is highly sensitive to the \(d\) and \(q\) current injections of the converter in a weak grid. Detailed results have been described in a few references [12; 13].