# Power Flow Calculation Methods for Power Systems with Novel Structure UPFC
## 1 Introduction  
Flexible AC transmission systems (FACTS) are a collection of power electronic-based controllers [1, 2], including the static var compensator (SVC), static synchronous compensator (STATCOM), static synchronous series compensator (SSSC), unified power flow controller (UPFC), etc. FACTS provide an effective means to enhance the controllability and stability of power systems, and a solution to improve the utilization of power equipment [3]. As the latest generation of FACTS devices, unified power flow controllers (UPFC) have comprehensive control capability [4]. While improving transmission capacity and stability of power grids, UPFC also has unique advantages such as accurate and flexible power flow control, centralized layout and little impact on short-circuit current [5]. Therefore, it has a good application prospect in modern power systems. In recent years, UPFCs have been widely adopted in China. Three UPFC projects have been put into operation in the last five years. These projects have made some improvements in the device structure [6, 7, 8, 9]. As shown in Figure 1, different from the early projects, the latest projects present the following characteristics in terms of the UPFC device structure: (1) As most of the 110 kV and above power grids in China adopt double-circuit lines, the UPFC series side may contain two converters that control the power flows of the double-circuit lines separately, in order to improve the overall transmission capacity; (2) In view of the low demand for reactive power in urban high-voltage grids, the UPFC shunt-side bus can be changed from the original bus to a lower voltage bus to save occupation and investment. These novel UPFC structures have been practically applied because of their technical and economic advantages, and also provide important references for further applications ofUPFC. The analysis, development and comparison of power flow calculation methods for these novel structures are of great significance to the design and operation of related projects. A large amount of research has been conducted on the power flow calculation method for the power system with UPFC, and various UPFC models have been proposed. In terms of algorithms, the unified iteration method and alternating iteration method are the two most important algorithms. The unified iteration method iteratively calculates the UPFC state variables (such as the magnitude and phase angle of the converter output voltage) together with the system state variables; the alternating iterative method decouples the UPFC from the external system, and then it solves the state variables of the UPFC and the external system separately. In terms of UPFC models, various UPFC models have been proposed, such as the decoupled model, the comprehensive model, the load injection model, the \(\pi\) load injection model, etc. [10]. The decoupled model is adopted in [11; 12; 13; 14]. In [11], for the typical control strategy that the UPFC controls the line active and reactive power and the AC bus voltage, an additional UPFC bus is added to the system. Then, the two buses connected with the UPFC are regarded as PV bus and PQ bus, respectively. Using this method, the UPFC can be removed from the system, and the power flow calculation can be realized by conventional power flow calculation programs. In [12], the UPFC state variables and the system state variables are calculated by the alternating iterative method. In [13; 14], the equivalent circuit of the UPFC-embedded line is deduced according to the UPFC control targets, and thus the output voltages of the UPFC can be determined directly. Then, the modifications of power mismatch equations and the Jacobian matrix are presented, and a Newton-Raphson algorithm-based calculation method is proposed. In [15], the load injection model is adopted, and the UPFC is equivalent to an impedance and two injected loads at UPFC terminals. In [16], the \(\pi\) load injection model is adopted, and the UPFC is modeled with the \(\pi\) equivalent circuit and injected loads.