# Power Flow Modeling in Power System With Multiple FACTS Controller

DOI: 10.4018/978-1-5225-6971-8.ch006

## Abstract

Flexible AC transmission systems (FACTS) devices are integrated into power system networks to control power flow, increase transmission line capability to its thermal limit, and improve the security of transmission systems. Power flow is an important mathematical calculation for planning, operation, and control of power systems network. The focus of the chapter is to explore how to modify Newton-Raphson power flow method to include various FACTS devices such as static VAR compensator (SVC), static synchronous compensator (STATCOM), static synchronous series compensator (SSSC), thyristor-controlled series capacitor (TCSC), thyristor-controlled phase shifter (TCPS), unified power flow controller (UPFC) controllers. This chapter briefly describes the power flow equations of the aforesaid FACTS-based power system network, and how the conventional power flow calculation is systematically extended to include these controllers is also been discussed.
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## Modeling Of Power System With Multiple Facts Controller

### Power System With Static VAR Compensator (SVC)

The SVC is the most widely used employed FACTS controller. It is a shunt-connected static VAR generator or absorber whose output is adjusted to exchange capacitive or inductive current so as to maintain or control specific parameters of the electrical power system (typically bus voltage).

The SVC in general, may be a Thyristor Controlled Reactor (TCR) or Thyristor Switched Capacitor (TSC) or a combination of both. Some other configuration of SVC is Fixed Capacitor-TCR(FC-TCR) or TCR-Mechanically Switched Capacitor(TCR-MSC). The high voltage side system bus voltage is measured and filtered and compared with the reference voltage. The error voltage is processed through a gain-time constant regulator to provide the desired Susceptance requirement for the SVC. From the operational point of view, the SVC adjusts its value automatically in response to changes in the operating conditions of the network. By suitable control of its equivalent susceptance, it is possible to regulate the voltage magnitude at the SVC point of connection, thus enhancing significantly the performance of the power system.

Figure 1.

Schematic diagram of SVC device

The equivalent susceptance, which neglects harmonic current, can be expressed as

(1) where,

,
(2)

Let the complex power injected at . s

Taking conjugate of

= For inductor
(For inductor)

The reactive power drawn by the SVC, which is also the reactive power injected at bus S, is given by

(For capacitor)

The constraint on the reactive power at bus k is

Let us consider an IEEE-7 Bus system, where Bus 1 is swing bus (v,. own), bus 2, 5 are . gerator buses (P,V known), bus 3,4,6,7 are Load buses (P,Q known). Buses 3, 4 are Voltage control buses where the two SVC are connected.

The system matrix becomes

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