Power Flow Control Solutions for a Modern Grid Using SMART Power Flow Controllers. Kalyan K. Sen

(V_s′) as shown in Figure 1-27. The relationship is given by the following equation:

(2‐79)

      where

      (2‐61)

Equation (2‐79) represents the locus of a circle, centered at with a radius of a′.

      For a Shunt–Series Compensator, the relationship between active and reactive power flows (P_r and Q_r) at the receiving end is shown by the small circle in Figure 1-27 and is given by the following equation:

(2‐136)

      where P_rn and Q_rn are the natural active and reactive power flows at the receiving end of the line and

(2‐132)

Equation (2‐136) represents the locus of a circle, centered at [P_rn, Q_rn], with a radius of a_r that is given in Equation (2‐132).

An ideal PFC controls the values of the power flow control parameters (line voltage magnitude, its phase angle, and line reactance) to regulate the magnitude and the phase angle of the line voltage simultaneously by adding a series‐compensating voltage to the original voltage with the use of a Shunt–Series Compensator as shown in Figure 1-28. The compensating voltage is variable in magnitude and phase angle with respect to the line voltage. The series‐connected VSC is rated for a fraction of the line voltage, but carries the full line current. The shunt‐connected VSC is rated for the full line voltage, but carries only a fraction of the line current. Therefore, each VSC carries only a fraction of the full transmitted power. In an actual installation, both shunt‐ and series‐connected VSCs are designed to be of the same voltage and current ratings, which reduces the inventory of spare parts. Therefore, their different interface voltages with the line are accomplished with selection of proper turns‐ratios of the respective coupling transformers. For example, in the world’ first UPFC at the AEP Inez substation, the two VSCs were designed identically to be rated at ±160 MVA and 37 kV phase‐to‐phase voltage. However, the shunt VSC was connected to a 138 kV‐line through a coupling transformer and the series VSC was designed to inject 13.33 kV (~16% of the phase voltage) in series with the line through a coupling transformer.

Figure 1-28 Independent active and reactive power flow controller with local reactive power compensation using a Shunt–Series Compensator‐based UPFC.

      The Shunt–Series Compensator connects a compensating voltage in series with the line at any relative phase angle in the range of 0^° ≤ β ≤ 360^° with respect to the line voltage at the POC. Figure 1-27 shows that a series‐compensating voltage of 0.2 pu modifies the power angle by 11.54^°, which may be near the allowable limit. The most important and unique feature of the Shunt–Series configuration is that for a given amount of transmission line power, the series‐connected VSC has a large leverage between its own rating and the controlled transmission line power. The series‐compensating voltage needs to be rated for only a fractional amount of transmitted power, whereas the shunt‐connected VSC in the Shunt–Shunt configuration has no such leverage and it needs to be rated for the full amount of transmitted power. Because of this uniqueness, the Shunt–Series configuration is a preferred topology for a PFC. However, in some special cases for point‐to‐point transfer of power between two isolated networks with POC voltages (V_s and V_s′) as shown in Figure 1-26 or interconnection of two transmission lines with different voltages or phase angles (or frequencies), Shunt–Shunt configuration may be the preferred solution. One such system, called the North American Electric Reliability Corporation (NERC) Interconnections, consists of Eastern Interconnection, Western Interconnection, and Electric Reliability Council of Texas (ERCOT) Interconnection, which are three separate systems of 60 Hz frequency that are asynchronous to each other. Another such system exists in Japan, connecting a 50 Hz frequency system in the North and the East with a 60 Hz frequency system in the South and the West, that is asynchronous to each other.

The UPFC consists of two VSCs with a common DC link capacitor. The two VSCs are connected to the same transmission line through two coupling transformers: one is connected in shunt and the other is connected in series with the line. The series‐compensating voltage is of variable magnitude and phase angle and it is also at any phase angle with the prevailing line current. Therefore, it exchanges active and reactive powers with the line. The exchanged active power (P_link) flows bidirectionally through the common DC link to and from the same line under compensation. Both shunt‐ and series‐connected VSCs can also provide independent reactive power compensation at their respective AC terminals. The compensating voltage, being at any phase angle with the prevailing line current, emulates a four‐quadrant, series‐compensating impedance (Z_se = R_se − jX_se) that consists of a resistance (R_se = +R or −R) and a reactance (X_se = X_C or − X_L) in series with the line. Therefore, the series‐compensating voltage (V_s′s) acts as an IR. A positive resistance (+R) absorbs active power from the line; a negative resistance (−R) delivers active power to the line. The quadrature component of the compensating voltage with respect to the line current emulates a capacitive reactance if the compensating voltage lags the prevailing line current or an inductive reactance if the compensating voltage leads the prevailing line current. A capacitive reactance (X_C) decreases the effective line reactance between its two ends and, in the process, increases the power flow in the line; an inductive reactance (X_L) increases the effective line reactance between its two ends and decreases the power flow in the line; since the power flow in the line is inversely proportional to the effective line impedance, which is assumed to be inductive.

      As a special case, when the DC link capacitors of the two VSCs are not connected together, each of the shunt‐connected VSC (STATCOM) and the series‐connected VSC (SSSC) provides only a reactive power compensation that is independent of each other. Since there is no exchange of active power between the STATCOM and the SSSC, they act as RRs (X_sh or X_se = X_C or − X_L).

In 1998, Westinghouse installed a ±160 MVA, 138 kV‐rated FACTS Controller, namely UPFC, at the AEP’s Inez substation in Kentucky, USA. This UPFC demonstrated for