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

autotransformer with an electrical connection between the primary and secondary windings, called a Shunt–Series configuration. In both types of transformers, the line voltage is applied to the primary windings. In the two‐winding transformer, the full line voltage is induced in the secondary windings, whereas, in the autotransformer, only a fraction of the line voltage is induced in the secondary windings that are connected to the primary windings to produce the full line voltage. In both cases, the magnitude of the line voltage is regulated. The secondary voltage is varied with the use of LTCs. An LTC can step up/down the voltage without interruption of the load current. Both primary and secondary windings in the two‐winding transformer carry the full transmitted power. Both primary and secondary windings in the autotransformer carry only a fraction of the full transmitted power. Therefore, if the galvanic isolation is not needed, the rating of the transformer can be significantly reduced with a Shunt–Series configuration as compared to a Shunt–Shunt configuration. Regardless of which configuration is used, the voltages at the input (primary) and output (secondary) terminals of both a two‐winding transformer and an autotransformer are identical as discussed in Chapter 4, Section 4.1.

The primary reason for voltage regulation is due to the exchange of reactive power at the Point of Connection (POC) to the utility. However, a transformer neither generates nor absorbs reactive power. If a transformer delivers reactive power at one side (primary or secondary), it absorbs the same amount of reactive power on the other side (secondary or primary). Therefore, in the process of increasing voltage on the secondary side, it reduces voltage on the primary side. The opposite is true as well when, in the process of decreasing voltage on the secondary side, it increases voltage on the primary side. Figure 1-12 shows that a compensating voltage of ±15% of the natural primary voltage (V_sn) of 0.988 pu results in a secondary voltage (V_s′) in the range of 0.872 to 1.095 pu. In the process, the primary voltage (V_s) varies in the range of 1.022 to 0.945 pu. Therefore, a desired 15% change in voltage at the secondary terminal may result in a net 10.7% increase due to the reduction of voltage at the primary terminal and a net 11.6% decrease due to the increase of voltage at the primary terminal as discussed in Chapter 4, Section 4.1.

The indirect way to regulate the magnitude of the line voltage is to connect a reactor or a capacitor in shunt with the line. A shunt‐connected reactor absorbs reactive power from the line and lowers the line voltage, whereas a shunt‐connected capacitor raises the line voltage with its generated reactive power as discussed in Chapter 2. With a series‐connected switch, such as back‐to‐back thyristors (triac), whose duty cycle can be varied, the shunt reactor can be made to operate as a variable reactor, which is called a Thyristor‐Controlled Reactor (TCR). A Thyristor‐Switched Capacitor (TSC) connects fixed capacitors in a step‐like manner in shunt with the line through triacs. Therefore, a combination of the variable reactor and a parallel capacitor acts as a variable compensating reactor or capacitor, which is called SVC.

Figure 1-12 Ranges of voltages (V_s and V_s′) at the primary and secondary sides of a Voltage‐Regulating Transformer.

      Voltage regulation can also be achieved by the field control of a synchronous motor (Synchronous Condenser or SynCon) that generates or absorbs var as in the cases of a shunt‐connected capacitor or a shunt‐connected reactor. Voltage regulation can also be achieved when the back emf of the SynCon is replaced with a power electronics‐based Voltage‐Sourced Converter (VSC), which is called STATCOM as discussed in Chapter 2, Section 2.3.1.2. More discussion on this topic is given in “Introduction to FACTS Controllers: Theory, Modeling, and Applications,” by Sen and Sen, IEEE Press and John Wiley & Sons, 2009, Chapter 8, Section 8.1.

      The power flow in a transmission line has traditionally been regulated with the use of a PAR. The line voltage is applied to the primary windings and the induced secondary voltage, called a compensating voltage that is varied with the use of LTCs is connected in series with the line. This compensating voltage is in quadrature with the phase‐to‐neutral voltage and as a result, the phase angle of the line voltage is regulated as discussed in Chapters 2 and 4. The PAR is configured in two forms – PAR asymmetric (asym) and symmetric (sym). In the process of varying the phase angle of the line voltage, a PAR (asym) also increases the magnitude of the line voltage. In a PAR (sym), while the phase angle is varied, the magnitude of the line voltage stays unchanged. When a high power flow enhancement is desired, the application of a PAR (sym) becomes limited, because of the need for a large amount of reactive power flow through the line. This large amount of reactive power flow creates significant additional losses, because of a large line current. Also, a larger‐than‐necessary rating of the PAR results when a large increase in active power flow is desired as discussed in Chapter 2, Section 2.5.2. Also as discussed in Chapter 2, Section 2.2.2.6, a PAR emulates an impedance in series with the line; however, this emulated impedance is not an independently controlled resistance and reactance; therefore, a PAR cannot control the active and reactive power flows in the line independently, whereas an IR offers an independent control of active and reactive power flows in the line as desired.

If the variable capacitor/reactor is connected in series with the line, the effective line reactance between the two ends of the line is regulated by the additional variable capacitor/reactor, which is called TCSC. The functionality of a TCSC can be realized with a series‐compensating voltage as in the case of a SSSC. The SSSC maintains the compensating voltage almost in quadrature with the prevailing line current. A leading voltage emulates a reactor; a lagging voltage emulates a capacitor. A TCSC or SSSC modifies the magnitude and phase angle of the line voltage, which are the combined functionalities of a VR and a PAR as shown in Figure 2‐28. Since, the series reactance compensation technique does not change the effective line resistance, it cannot control the active and reactive power flows in the line independently as shown in Figure 1‐30.

      In a lightly loaded line, the reactive power absorbed by the series reactance of the line may be much less in comparison to the reactive power generated by the line‐to‐ground, shunt capacitance of the line. The resulting voltage increase in the line may reach or exceed the allowable limits for other loads that are connected to the grid. In a heavily loaded transmission line, the reactive power needed by the series reactance of the line may be much more in comparison to the reactive power generated by the shunt capacitance of the line. The resulting voltage along the line may decrease to a point that is below an acceptable limit when the full performance of the load is not possible. If the voltage along the transmission line is increased to be regulated at its nominal value by using a VR, the active power flow increases over the natural flow as discussed in Chapter 2, Section 2.6.1 (Shunt‐Compensating Reactance). If the phase angle between the voltages at the two ends of the transmission line is increased by using a PAR, the active power flow also increases. The unintended consequence of increasing active power flow by voltage regulation or phase angle regulation is that the reactive power flow in the line is also affected. When the line reactance is regulated, both the active and reactive power flows in the transmission line are varied simultaneously.

      If the reactive power along the line is reduced, the freed‐up capacity of the line can be used to increase the revenue‐generating active power flow. As a result, the connected‐generators will be required to supply less reactive