Table of Contents

## Introduction

**Static Phase Shifting Transformer** or **Phase-shifting transformers (PST)** have been in use since the 1930s for control of power flows in transmission lines in a steady state. The primary objective is to control loop flows and ensure the power flow in the contracted path. They are not meant to increase power transfer in a line and hence not intended to be used in long lines. By applying power electronic controllers, the operation of PSTs can be made fast which enables dynamic regulation of power flow and improvement of system stability and dynamic security. These are called **Static Phase Shifting Transformers (SPST)** or **Thyristor Controlled Phase Angle Regulator (TCPAR)** as thyristor devices have been primarily suggested to achieve the objective. However, with the advent of **Voltage Source Converter (VSC)** based FACTS controllers, it is also possible to apply a UPFC-type device for SPST.

## Basic Principle of a PST

Consider an ideal phase shifting transformer shown in Fig. This also shows Thevenin’s equivalents connected at the two ports of PST. The turns ratio of the transformer is a complex quantity of magnitude unity (a = e^{jφ}) where φφ is the phase angle shift (positive or negative).

From Fig., we have

V_{2} = aV_{1}, I_{1} = a^{∗} I_{2} = e^{−jφ} I_{2}

Note that Eq. results from the fact that there are no power (both active and reactive) losses in an ideal transformer. That is

V_{1}I^{∗}_{1} = V_{2}I^{∗}_{2}

Since,

I_{2} = V_{2} − E_{2} / Z_{2}

we get from Eq.,

I_{1} = a^{∗} (aV_{1} − E_{2}) / Z_{2} = V1 − a^{∗} E_{2} / Z_{2}

Eq. represents the equivalent circuit shown in Fig.

If the losses are neglected in the circuit, i.e.,

Z_{1} = jx_{1}, Z_{2}2 = jx_{2}

we can derive the power flow in the circuit as

P = E_{1}E_{2} sin(δ + φ) / (x_{1} + x_{2})

Note that φ can be adjusted in the range φ_{min} < φ < φ_{max}

Typically the limits on φ are symmetric about zero, i.e. φmin = −φmax. The limitations are directly related to the PST rating.

## Configurations of Static Phase Shifting Transformer (SPST)

A detailed review of various configurations is presented in reference, we will consider here only 3 configurations given below

- Point-on-wave controlled phase angle regulator
- Discrete step-controlled phase angle regulator
- Using a voltage source converter (VSC)

The first two configurations can be obtained using a single-phase bridge circuit with four bi-directional thyristor switches. There are other configurations proposed that we will not take up as, in general, continuous control of the phase angle (φ) is not desirable as it generates harmonics that are difficult to filter. (Note that zero sequence triplen harmonics are not eliminated).

## Improvement of Transient Stability Using SPST

This will be illustrated using a Single Machine connected to an Infinite Bus (SMIB) system and from an equal area criterion. Consider the SMIB system shown in Fig.(a). Here, the generator transformer is configured to work also as an SPST. Assuming a 3-phase fault occurs at the sending end of one of the transmission lines which is cleared by tripping the faulted line section. The power angle curves for (i) pre-fault and (ii) post-fault cases are shown in Fig. for the case without SPST. If the area A_{2} < A_{1}, then the system will be unstable. Since the electrical power output (Pe) changes to

Pe = EgEb / X. sin(δ ± φ)

in the presence of the SPST; the power angle curves for this case are shown in fig. Here, it is assumed that,

(a) The SPST is activated when (i) the electrical power output is maximum and dP_{e} / dt changes from positive to negative

(b) The control algorithm is given by

dφ / dt = dδ / dt

## Application of Static Phase Shifting Transformer (SPST)

Although work on static phase shift transformers has been reported for more than 25 years, it has yet to be applied to transmission line applications. The introduction of any technology depends essentially on the cost-benefit analysis. A major drawback of SPST is the cost of the two transformers (Excitation and Boost) and the power semiconductor switches. In contrast, a TCSC has no limitations and has found wide acceptance commercially (depending on the control requirements). Although some applications of SPST were considered for enhancing the transfer capability of AC ties (interconnecting two systems) they have not been implemented.

An interesting new technology introduced recently is the **Variable Frequency Transformer (VFT)** developed by General Electric (U.S.A) to transfer power between two asynchronous networks. The first installation of this new technology is located at Langlois substation, interconnecting the New York (USA) and the Hydro-Quebec (Canada) system.

The technology is based on a rotary transformer (continuously variable phase-shifting transformer) with three-phase windings on both rotor and stator. A drive system adjusts the VFT rotor to control the phase shift between the networks through the action of a fast power controller. The first installation at Langlois controls power transfer up to 100 MW in both directions. The development of VFT shows that a 360◦ PST is feasible with a rotary device based on old technology. However, the control and drive systems for VFT are based on modern technology. It is to be noted that by regulating torque applied to the rotor, through a motor drive system, the power transfer through the VFT is controlled. The rotor will rotate continuously if the two grids operate at different frequencies.

## Frequently Asked Questions (FAQs)

#### Why 30-degree phase shift in the transformer?

In a Delta connection, the line and phase voltages are the same and in phase with each other. However, in a Star connection, the line and phase voltages are different, with the line voltage having a 30-degree phase shift relative to the phase voltage.

#### What is a static phase shifter?

The purpose of a static phase shifter is to create a voltage phase shift between the ends of a transmission line. This phase shift is controlled by adding a voltage component at a right angle (quadrature) to the voltage at one end of the line.

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