## 1 Introduction  
Over the recent years, the unified power flow controller (UPFC) has been widely recognized as one of the most advanced flexible alternate current systems (FACTS) devices with versatile functionalities of regulating the power systems. Among all the functions, the regulation of the power flows in the transmission system has usually been the most primary and general function of UPFC in applications. More and more concerns are being attracted regarding the modelling and control of the power flow regulations by UPFC [1; 2; 3; 4; 5]. Amounts of researches on the equivalent power flow modelling of UPFC have been conducted in [6; 7; 8; 9; 10; 11; 12; 13]. In [6], the real and reactive power references were tracked based on UPFC's discrete sliding mode technique. Experts in [7; 8] established the mathematical models of UPFC considering operation constraints or operational characteristics. The steady-state and dynamic power flow models of UPFCwere specifically built in [9; 10]. In [11], several operation modes of UPFC were researched individually to estimate the power system state. In [12; 13] a current based model and dc-based model of UPFC were also proposed, in order to improve the load flows of the system. Moreover, the authors in [14] researched an optimal power flow model of UPFC based on preventive security constraints to increase the economic efficiency and static security of the power system. However, in the above studies, the output of the series converters in UPFC are mostly equivalent to voltage sources with alterable magnitudes and phase angles, and they are only integrated into the mathematical models of the UPFC embedded system to realize special requirements of power flows, but the detailed regulation principles of the power flow changing rates or gradients dependent on the magnitudes and phase angles of the voltage sources are usually ignored. There are also a lot of studies carried out regarding the power flow control and applications in [15; 16; 17; 18; 19; 20; 21]. The optimal power flow control methods of UPFC aiming to improve the transfer capability of the system are studied in [15; 16]. A hybrid electromagnetic model of UPFC with more flexibility was proposed in [17]. In [18], a new real time Lyapunov based controller in UPFC was investigated to improve the power quality. In [19; 20; 21], several power flow control strategies and approaches of UPFC were designed for damping the power flow oscillations and enhancing the power system stability. However, most of these power flow control methods or applications of UPFC concentrate on realizing the presupposed power flow regulation targets or purposes more precisely and smoothly through improving the power flow regulation capabilities or performances by UPFC. The detailed power flow regulation processes and efficiencies dependent on the characteristic variables such as the magnitudes and phase angles of the OSIV of UPFC have never been researched and remain to be evaluated specifically. The power flows in the system might fluctuate intensely within certain short periods during the regulation processes by UPFC, especially when the power flow references are being regulated by larger ranges or scales. On this occasion, potential perturbations or shocks may inevitably be exerted on the system by the impulsive power flows, such as surge current, unbalanced electromotive forces, power angle swings, booming thermal energy at certain points, and so on. In these cases, the stabilities of the power angle, the frequency or the voltage of the system are more likely to fluctuate or deteriorate by some extent. It is thus essential to research and outline the specific changing rates of the power flows or PFG during the regulation processes of UPFC. Moreover, the PFG at different positions from the sending end to receiving end of the power system have become different after the insertions of UPFC.