UPFC Ideal Transformer Model

This paper presents a unified power flow controller (UPFC) model, which consists of an ideal transformer with a complex turns ratio and a variable shunt admittance. In this model, the UPFC control variables do not depend explicitly on UPFC input and output currents and voltages. Accordingly, this model does not require adding extra busses for UPFC input and output. This model is easily combined with transmission line models using ABCD two-port representations, which can then be converted to Y-parameter representations. The complex turns ratio and the variable admittance can be mapped to actual UPFC control variables, such as UPFC injected series and shunt voltages and currents or other equivalent representations. I. I NTRODUCTION The unified power flow controller (UPFC) is one of the most promising devices in the FACTS family [1], [2], [3], [4]. It has the capability to control voltage magnitude and phase angle, and can also independently provide (positive or negative) reactive power injections. Therefore the UPFC can provide voltage support, control of real power flow, and other functions. The UPFC injection model [3] and the uncoupled model [5] have been proposed for steady-state power flow analysis. These models can be easily incorporated into steadystate loadflow or optimal power flow problems. However, in these models four UPFC control variables depend on the UPFC input and output currents and voltages and both models require adding two additional busses to the loadflow or OPF (optimal power flow) problem formulation as well as a constraint on real power conservation, thereby reducing the degrees of freedom to three. Therefore, these models do not seem to be suitable for efficient steady-state power flow analysis with multiple UPFCs. Since electricity prices at the UPFC input and output busses, which are the dual variables (or prices) associated with real power injections, are uninformative when no power is bought or sold at these busses, and so their addition to the problem only serves to increase the size of the problem. This paper presents a mathematical model of a steady-state UPFC, which consists of an ideal transformer with a complex turns ratio and a variable shunt admittance. In this model, UPFC control variables do not depend on UPFC input and output voltages and currents, and the UPFC power flow equations are self-contained. An ABCD two-port representation is used to combine transmission lines cascaded with a UPFC. This paper also introduces basic UPFC operating principles [4], the UPFC injection model [3], and the uncoupled model [5] to provide the background for the development of the UPFC ideal transformer model. II. OPERATING PRINCIPLES A UPFC consists of a shunt transformer and a series transformer, power electronic switching devices and a DC link, as shown in figure 1 [4]. Inverter 1 is functionally a static VAR compensator assuming that inverter 2 is not connected. It injects reactive power in the form of current at the shunt transformer, and the current phasor ~ IT is perpendicular to the input voltage~ VI . Inverter 2 alone represents the so-called advanced controllable series compensator (ACSC) assuming that inverter 1 is not connected. It injects reactive power by adding voltage at the series transformer. The injected voltage ~ VT is perpendicular to the receiving end current ~ Io. Now if we connect inverter 1 to inverter 2 through the DC link, inverter 1 can provide real power to inverter 2. Therefore the UPFC can independently control real and reactive power injections through the series transformer, but the real power injected at the series transformer is provided by the shunt transformer through the DC link. Inverter 1 must provide the real power used by inverter 2 via the DC link, but can also independently inject reactive power (positive or negative) through the shunt transformer. In summary, note that the UPFC conserves real power but can still generate (or sink) reactive power at either transformer or both. III. E XISTING UPFC MODELS The UPFC injection [3] and uncoupled [5] models can both be easily incorporated in loadflow and optimal power flow, but both models require adding two additional busses for UPFC Fig. 1. General UPFC scheme [4] Fig. 2. A series-connected VSI as a voltage source and a reactance input and output voltages and currents, and, in these models, UPFC behavior is dependent not only on the UPFC control variables but explicitly on the input and output voltages and currents. The real power balance equation must be included as a constraint, so, although these models seem to be suitable for general purpose UPFC studies in a large power system, there is still room for improvement. These two additional busses for each UPFC only serve to make the problem larger. A. Injection Model We will first review modeling the UPFC as a seriesconnected voltage source inverter (VSI) [3]. Then, inverter 1 is incorporated into the model of the series connected VSI for a complete UPFC model [3]. Suppose a series connected voltage source is located between busses I andO in a power system. The series voltage source inverter can be modelled with an ideal injection voltageVT in series with a reactance XS . Figure 2 shows a representation of a series connected VSI. The injected voltage~ VT consists of in-phase component Vp and quadrature component Vq with respect to the UPFC input voltage~ VI . Then, it can be written by ~ VT = (Vp + jVq) eI , (1) whereθI is the UPFC input voltage phase angle. The injection model [3] is obtained by transforming the voltage source VT in series withXS to an equivalent current source in parallel with the admittance corresponding to XS . The current source can be obtained by ~ IS = −jbS ~ VT = bS (Vq − jVp) eI , (2)