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

line current (I) by 90°. This leads to the concept of an emulated reactance, which is defined as

      (1‐3a)

      or

      (1‐3b)

and is shown in Figure 1-7. In this concept, a compensating voltage is created, maintaining the quadrature relationship with the prevailing line current, and is connected in series with the line. Note that is defined to be a capacitive compensation and V_s′s < 0 is defined to be an inductive compensation, respectively.

The concept of an emulated reactance can be further extended to represent an emulated impedance when the compensating voltage is not restricted to be in quadrature, but at any phase angle with respect to the prevailing line current (I). That means the compensating voltage can be made to look like a virtual, four‐quadrant, 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 without any discrete circuit component as shown in Figure 1-8b. This two‐parameter, resistive (R_se) and reactive (X_se), control makes it possible to modify the magnitude and the phase angle of the line voltage simultaneously, which results in an independent control of active and reactive power flows in the line.

Figure 1-7 Power flow in a lossless line with a series‐compensating voltage (V_s′s).

Figure 1-8 (a) Power transmission system with a series‐compensating voltage (V_s′s); (b) four‐quadrant emulated impedance.

      The series‐compensating voltage (V_s′s) is related to (V_dq), such that

      (1‐4)

      and

      (1‐5)

      where V_d = V_d and V_q = jV_q are the respective active or direct and reactive or quadrature components of the compensating voltage with load convention, meaning the line current (I) enters at the higher potential terminal of the voltages (V_d and V_q) as shown in Figure 1-8a.

      The natural or uncompensated power flow through a transmission line in a power system network is, in general, not optimal. Any of the power flow control parameters (line voltage magnitude, its phase angle, and line reactance) can be regulated with the use of the following equipment:

       Voltage‐Regulating Transformer (VRT), shunt or parallel‐connected switched reactor/capacitor, also known as Shunt Reactor (SR)/Shunt Capacitor (SC), Static Var Compensator (SVC), or STATic synchronous COMpensator (STATCOM) for voltage regulation as shown in Figure 1-9

       PAR or Phase‐Shifting Transformer (PST) for phase angle regulation as shown in Figure 1-10

       Thyristor‐Controlled Series Capacitor (TCSC) or Static Synchronous Series Compensator (SSSC) for series reactance regulation as shown in Figure 1-11.

The dynamic performance of a VRT is limited by the speed of operation of the mechanical Load Tap Changers (LTCs), which respond in seconds; this level of response time is acceptable in most utility applications. However, if a faster response is desired, the mechanical LTCs can be upgraded with power electronics‐based LTCs, called Thyristor‐Controlled (TC) LTCs as discussed in Chapter 2. More on LTCs can be found in the book, titled “On‐Load Tap‐Changers For Power Transformers: Operation, Principles, Applications and Selection,” by A. Krämer, Maschinenfabrik Reinhausen, 2000. The power electronics‐based solutions can be divided into two categories, based on the type of semiconductor switches: naturally commutated switch, such as a thyristor and forced‐commutated switch, such as Insulated Gate Bipolar Transistor (IGBT). Each of these solutions is based on engineering trade‐offs.

Figure 1-9 Transmission line Voltage Regulators: (a) Two‐winding Transformer, (b) Autotransformer, (c) Switched Reactor, (d) Switched Capacitor, (e) TSC + TCR = SVC, and (f) STATCOM.

Figure 1-10 Transmission line voltage Phase Angle Regulators: (a) asymmetric and (b) symmetric.

Figure 1-11 Transmission line Reactance Regulators: (a) Thyristor‐Controlled Series Capacitor (TCSC) and (b) Static Synchronous Series Compensator (SSSC).

      When discussing dynamic and transient events, mechanical LTCs react in ≈ 3–5 s (3,000–5,000 ms); TC LTCs react in < 1 s (1,000 ms) and IGBT‐based converters react in < 0.010 s (10 ms). These different technologies are referred to as slow, medium speed, and fast, respectively. Note that as the response time of a particular solution increases from slow using mechanical LTCs to medium speed using TC LTCs to fast using IGBTs, there is a corresponding increase in the solution’s life‐cycle costs (installation, operation, and maintenance), complexity, and impracticability of relocation. Other important features to consider are reliability, efficiency, component non‐obsolescence, and interoperability.

      For more than a century, the transmission line voltage magnitude has been regulated with transformers and tap changers. They are referred to, in this book, as the VRT in the form of a two‐winding transformer with galvanically isolated